TY - CHAP
TI - Quadratic Inverse Eigenvalue Problem and Its Applications to Model Updating — An Overview
AU - Chu, Moody T.
T2 - Mathematics in Industry
PY - 2008///
DO - 10.1007/978-3-540-78841-6_15
SP - 323-340
PB - Springer Berlin Heidelberg
SN - 9783540788409 9783540788416
UR - http://dx.doi.org/10.1007/978-3-540-78841-6_15
ER -
TY - CHAP
TI - Quadratic inverse eigenvalue problem and its applications to model updating - an overview
T2 - Model Order Reduction: Theory, Research Aspects and Applications
AB - The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the disc
PY - 2008///
DO - 10.1007/978-3-540-78841-6
UR - https://link.springer.com/book/10.1007/978-3-540-78841-6
ER -
TY - CONF
TI - Data mining and applied linear algebra
AU - Chu, M.
AB - In this era of hyper-technological innovation, massive amounts of data are being generated at almost every level of applications in almost every area of disciplines. Extracting interesting knowledge from raw data, or data mining in a broader sense, has become an indispensable task. Nevertheless, data collected from complex phenomena represent often the integrated result of several interrelated variables, whereas these variables are less precisely defined. The basic principle of data mining is to distinguish which variable is related to which and how the variables are related. In many situations, the digitized information is gathered and stored as a data matrix. It is often the case, or so assumed, that the exogenous variables depend on the endogenous variables in a linear relationship. Retrieving "useful" information therefore can often be characterized as finding "suitable" matrix factorization. This paper offers a synopsis from this prospect on how linear algebra techniques can help to carry out the task of data mining. Examples from factor analysis, cluster analysis, latent semantic indexing and link analysis are used to demonstrate how matrix factorization helps to uncover hidden connection and do things fast. Low rank matrix approximation plays a fundamental role in cleaning the data and compressing the data. Other types of constraints, such as nonnegativity, will also be briefly discussed.
C2 - 2008///
C3 - Proceedings - International Conference on Informatics Education and Research for Knowledge-Circulating Society, ICKS 2008
DA - 2008///
DO - 10.1109/ICKS.2008.39
SP - 20-25
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-50149102774&partnerID=MN8TOARS
ER -
TY - CONF
TI - Completions of Implicitly Defined Vector fields and their applications
AU - Okay, I.
AU - Campbell, S.L.
AU - Kunkel, Peter
T2 - International Symposium on Mathematical Theory of Networks and Systems (MTNS 08)
C2 - 2008///
C3 - Proceedings of the International Symposium on Mathematical Theory of Networks and Systems (MTNS 08)
CY - Virginia Tech, Blacksburg, Virginia, USA
DA - 2008///
PY - 2008/7/28/
ER -
TY - JOUR
TI - BRAID FAMILY REPRESENTATIVES
AU - JABLAN, SLAVIK
AU - SAZDANOVIĆ, RADMILA
T2 - Journal of Knot Theory and Its Ramifications
AB - Imposing different conditions on minimality of reduced braid words and new criteria on their representatives, we define braid family representatives and establish one-to-one correspondence with families of knots and links given in Conway notation.
DA - 2008/7//
PY - 2008/7//
DO - 10.1142/s0218216508006427
VL - 17
IS - 07
SP - 817-833
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-49449083565&partnerID=MN8TOARS
KW - Conway notation
KW - minimum braid
KW - reduced braid word
KW - braid family representative
ER -
TY - CONF
TI - Implementation of Computer Optimization for Design of Electron Guns
AU - David, J.
AU - Ives, R.L.
AU - Tran, H.
AU - Bui, T.
AU - Read, M.
AU - Attarian, A.
AU - Posth, M.
T2 - 9th IEEE International Vacuum Electronics Conference
C2 - 2008///
C3 - 'Proceedings of the 9th IEEE International Vacuum Electronics Conference
CY - Monterey, CA
DA - 2008///
PY - 2008/4/22/
PB - IEEE
ER -
TY - BOOK
TI - Special Issues: Short-term Cardiovascular–Respiratory Control Mechanisms
A3 - Batzel, J.J.
A3 - Novak, V,
A3 - Kappel, F.
A3 - Olufsen, Mette S.
A3 - Tran, H.
DA - 2008/3//
PY - 2008/3//
VL - 9
SE - 1–71
ER -
TY - JOUR
TI - On the first group of the chromatic cohomology of graphs
AU - Pabiniak, Milena D.
AU - Przytycki, Józef H.
AU - Sazdanović, Radmila
T2 - Geometriae Dedicata
AB - The Hochschild homology of the algebra of truncated polynomials $${{\mathcal {A}_m=\mathbb {Z}[x]/(x^m)}}$$ is closely related to the Khovanov-type homology as shown by the second author. In the present paper we utilize this in the study of the first graph cohomology group of an arbitrary graph G with v vertices. The complete description of this group is given for m = 2, 3. For the algebra $${\mathcal {A}_2}$$ we relate the chromatic graph cohomology with the Khovanov homology of adequate links. We describe the chromatic cohomology over the algebra $${\mathcal {A}_3}$$ using the homology of a cell complex built on the graph G. In particular we prove that $${{H_{\mathcal {A}_{3}}^{1,2v-3}(G)}}$$ can be isomorphic to any finite abelian group. Moreover, we give a characterization of graphs which have torsion in cohomology $${{H_{\mathcal {A}_{3}}^{1,2v-3}(G)}}$$ and construct graphs which have the same (di)chromatic polynomial but different $${{H_{\mathcal {A}_{3}}^{1,2v-3}(G)}}$$ .
DA - 2008/11/12/
PY - 2008/11/12/
DO - 10.1007/S10711-008-9307-4
VL - 140
IS - 1
SP - 19-48
J2 - Geom Dedicata
LA - en
OP -
SN - 0046-5755 1572-9168
UR - http://dx.doi.org/10.1007/S10711-008-9307-4
DB - Crossref
KW - Chromatic graph cohomology
KW - Khovanov homology
KW - Hochschild homology
KW - Torsion
KW - Codichromatic graphs
ER -
TY - JOUR
TI - Linear algebra algorithms as dynamical systems
AU - Chu, Moody T.
T2 - Acta Numerica
AB - Any logical procedure that is used to reason or to infer either deductively or inductively, so as to draw conclusions or make decisions, can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state develops into another state by following a certain specific rule. Such an action is generally formalized as a dynamical system. In mathematics, especially for existence questions, a realization process often appears in the form of an iterative procedure or a differential equation. For years researchers have taken great effort to describe, analyse, and modify realization processes for various applications. The thrust in this exposition is to exploit the notion of dynamical systems as a special realization process for problems arising from the field of linear algebra. Several differential equations whose solutions evolve in submanifolds of matrices are cast in fairly general frameworks, of which special cases have been found to afford unified and fundamental insights into the structure and behaviour of existing discrete methods and, now and then, suggest new and improved numerical methods. In some cases, there are remarkable connections between smooth flows and discrete numerical algorithms. In other cases, the flow approach seems advantageous in tackling very difficult open problems. Various aspects of the recent development and application in this direction are discussed in this paper.
DA - 2008/4/25/
PY - 2008/4/25/
DO - 10.1017/S0962492906340019
VL - 17
SP - 1-86
J2 - Acta Numerica
LA - en
OP -
SN - 0962-4929 1474-0508
UR - http://dx.doi.org/10.1017/S0962492906340019
DB - Crossref
ER -
TY - JOUR
TI - Connectivity in semialgebraic sets (abstract only)
AU - Quinn, Robert
AU - Hong, Hoon
T2 - ACM Commun. Comput. Algebra
AB - A semialgebraic set is a subset of real space defined by polynomial equations and inequalities. A semialgebraic set is a union of finitely many maximally connected components. In this talk, we consider the problem of deciding whether two given points in a semialgebraic set are connected, that is, whether the two points lie in the same connected component. In particular, we consider the semialgebraic set defined by f not equal 0 where f is a given bivariate polynomial. The motivation comes from the observation that many important/non-trivial problems in science and engineering can be often reduced to that of connectivity. Due to its importance, there has been intense research effort on the problem. We will describe a method based on gradient fields and provide a sketch of the proof of correctness based on the Morse complex. The method seems to be more efficient than the previous methods in practice.
DA - 2008///
PY - 2008///
DO - 10.1145/1394042.1394094
VL - 42
IS - 1-2
SP - 86
UR - https://doi.org/10.1145/1394042.1394094
ER -
TY - THES
TI - Existence, Uniqueness, and Blow-up of Solutions to Wave Equations with Supercritical Boundary/interior Sources and Damping
DA - 2008///
PY - 2008///
ER -
TY - JOUR
TI - Corrigendum to “Are Buchberger’s criteria necessary for the chain condition?” [J. Symbolic Comput. 42 (2007) 717–732]
AU - Hong, Hoon
AU - Perry, John
T2 - Journal of Symbolic Computation
DA - 2008/3//
PY - 2008/3//
DO - 10.1016/j.jsc.2007.10.002
VL - 43
IS - 3
SP - 233
J2 - Journal of Symbolic Computation
LA - en
OP -
SN - 0747-7171
UR - http://dx.doi.org/10.1016/j.jsc.2007.10.002
DB - Crossref
ER -
TY - JOUR
TI - Mathematical Modelling of the Systemic Circulation: investigating pressure and flow throughout the microcirculation
AU - Vaughan, G.A.
AU - Olufsen, M.S.
AU - Hill, N.A.
AU - Sainsbury, C.A.
T2 - Artery Research
DA - 2008/8//
PY - 2008/8//
DO - 10.1016/j.artres.2008.08.391
VL - 2
IS - 3
SP - 112
J2 - Artery Research
LA - en
OP -
SN - 1872-9312
UR - http://dx.doi.org/10.1016/j.artres.2008.08.391
DB - Crossref
ER -
TY - JOUR
TI - A high order compact MAC finite difference scheme for the Stokes equations: Augmented variable approach
AU - Ito, Kazufumi
AU - Qiao, Zhonghua
T2 - Journal of Computational Physics
AB - This paper deals with the steady Stokes flow on a rectangular domain. A high order compact MAC finite difference scheme based on the staggered grid is developed for solving Stokes equations with a Dirichlet boundary condition on the velocity. A novel high order boundary treatment is developed via introducing a suitable augmented variable. The accuracy of the proposed method is demonstrated in test problems. Creeping flow solutions for driven cavity problem are obtained numerically and compared with published results.
DA - 2008/9//
PY - 2008/9//
DO - 10.1016/j.jcp.2008.05.021
VL - 227
IS - 17
SP - 8177-8190
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2008.05.021
DB - Crossref
KW - Stokes equations
KW - compact fourth order MAC finite difference scheme
KW - staggered grid
ER -
TY - JOUR
TI - Modelling HIV immune response and validation with clinical data
AU - Banks, H. T.
AU - Davidian, M.
AU - Hu, Shuhua
AU - Kepler, Grace M.
AU - Rosenberg, E. S.
T2 - Journal of Biological Dynamics
AB - A system of ordinary differential equations is formulated to describe the pathogenesis of HIV infection, wherein certain features that have been shown to be important by recent experimental research are incorporated in the model. These include the role of CD4+ memory cells that serve as a major reservoir of latently infected cells, a critical role for T-helper cells in the generation of CD8 memory cells capable of efficient recall response, and stimulation by antigens other than HIV. A stability analysis illustrates the capability of this model in admitting multiple locally asymptotically stable (locally a.s.) off-treatment equilibria.We show that this more biologically detailed model can exhibit the phenomenon of transient viremia experienced by some patients on therapy with viral load levels suppressed below the detection limit. We also show that the loss of CD4+ T-cell help in the generation of CD8+ memory cells leads to larger peak values for the viral load during transient viremia. Censored clinical data is used to obtain parameter estimates. We demonstrate that using a reduced set of 16 free parameters, obtained by fixing some parameters at their population averages, the model provides reasonable fits to the patient data and, moreover, that it exhibits good predictive capability. We further show that parameter values obtained for most clinical patients do not admit multiple locally a.s off-treatment equilibria. This suggests that treatment to move from a high viral load equilibrium state to an equilibrium state with a lower (or zero) viral load is not possible for these patients.
DA - 2008/10//
PY - 2008/10//
DO - 10.1080/17513750701813184
VL - 2
IS - 4
SP - 357-385
J2 - Journal of Biological Dynamics
LA - en
OP -
SN - 1751-3758 1751-3766
UR - http://dx.doi.org/10.1080/17513750701813184
DB - Crossref
ER -
TY - JOUR
TI - Problems and techniques
AU - Ipsen, I.C.F.
T2 - SIAM Review
DA - 2008///
PY - 2008///
VL - 50
IS - 3
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-50949105062&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
DA - 2008/1//
PY - 2008/1//
DO - 10.1137/siread000050000001000035000001
VL - 50
IS - 1
SP - 35-35
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-56349149490&partnerID=MN8TOARS
ER -
TY - CONF
TI - Implementation of computer optimization for design of electron guns
AU - Ives, R. Lawrence
AU - Bui, Thuc
AU - Attarian, Adam
AU - Davis, Steven
AU - Gadson, Sean
AU - Tallis, William
AU - Tran, Hien
AU - Read, Michael
AU - Posth, Mattie
T2 - 2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves (IRMMW-THz 2008)
AB - Computer optimization can dramatically reduce the time and cost to design electron beam devices. It also allows design of complex, 3D devices that would be impractical with manual design. Recent implementation of a magnetic solver into a 3D finite element electron beam trajectory code is allowing optimized design of the electrostatic, optical and magnetic configuration of 3D device. The process and examples will be presented.
C2 - 2008/9//
C3 - 2008 33rd International Conference on Infrared, Millimeter and Terahertz Waves
DA - 2008/9//
DO - 10.1109/icimw.2008.4665480
PB - IEEE
SN - 9781424421190
UR - http://dx.doi.org/10.1109/icimw.2008.4665480
DB - Crossref
ER -
TY - CONF
TI - Computer optimized design of electron guns
AU - Ives, R. Lawrence
AU - Bui, Thuc
AU - Read, Michael
AU - David, John
AU - Attarian, Adam
AU - Tran, Hien
T2 - 2008 IEEE International Vacuum Electronics Conference (IVEC)
AB - Calabazas Creek Research, Inc. (CCR) and North Carolina State University are developing optimization techniques for advanced, 3D, electron guns. Our approach uses advanced solid modeling CAD programs capable of controlling geometrical parameters with design tables manipulated by an optimization control program. Geometrical and parametric changes are simulated using a 3D, finite element, adaptive meshing charged particle program. Results of the beam analysis are analyzed and an optimization routine modifies the parameters to obtain user-defined performance goals. These techniques are applied to a number of gun geometries, and the results are described.
C2 - 2008/5//
C3 - 2008 IEEE International Vacuum Electronics Conference
DA - 2008/5//
DO - 10.1109/ivelec.2008.4556399
PB - IEEE
SN - 9781424417155
UR - http://dx.doi.org/10.1109/ivelec.2008.4556399
DB - Crossref
ER -
TY - CONF
TI - Active fault detection in nonlinear systems using auxiliary signals
AU - Andjelkovic, Ivan
AU - Sweetingham, Kelly
AU - Campbell, Stephen L.
T2 - 2008 American Control Conference (ACC '08)
AB - In recent years active approaches for fault detection using test signals have been developed. This paper reports on progress in extending one of these approaches from linear systems to nonlinear systems. Theoretical results are presented on the use of linearizations which is based on sufficiently small nonlinearities. An optimization based approach is also presented for large nonlinearities. Examples are given.
C2 - 2008/6//
C3 - 2008 American Control Conference
DA - 2008/6//
DO - 10.1109/acc.2008.4586809
PB - IEEE
SN - 9781424420780
UR - http://dx.doi.org/10.1109/acc.2008.4586809
DB - Crossref
ER -
TY - PAT
TI - Masking Changes for Seamless Roaming in Heterogenous Networking
C2 - 2008/6/19/
DA - 2008/6/19/
PY - 2008/6/19/
UR - https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2008073492
ER -
TY - PAT
TI - Expiditing Seamless Roaming in Heterogenous Networking
C2 - 2008/6/19/
DA - 2008/6/19/
PY - 2008/6/19/
UR - https://patentscope.wipo.int/search/en/detail.jsf?docId=WO2008073438
ER -
TY - JOUR
TI - A Dykstra-like algorithm for two monotone operators
AU - Bauschke, H.H.
AU - Combettes, P.L.
T2 - Pacific Journal of Optimization
DA - 2008/9//
PY - 2008/9//
VL - 4
IS - 3
SP - 383–391
ER -
TY - JOUR
TI - Projected Pseudo-Transient Continuation
AU - Kelley, C T
AU - Liao, L-Z.
AU - Qi, L
AU - Chu, M T
AU - Reese, J P
AU - Winton, C
T2 - SIAM J. Numer. Anal.
DA - 2008///
PY - 2008///
VL - 46
IS - 6
SP - 3071-3083
ER -
TY - JOUR
TI - A Comparison of Derivative-Free Optimization Methods for Groundwater Supply and Hydraulic Capture Problems
AU - Fowler, K R
AU - Reese, J P
AU - Kees, C E
AU - Dennis, J E
AU - Kelley, C T
AU - Miller, C T
AU - Audet, Charles
AU - Booker, A J
AU - Couture, Gilles
AU - Darwin, Robert W
AU - Farthing, M W
AU - Finkel, D E
AU - Gablonsky, J M
AU - Gray, G
AU - Kolda, T G
T2 - Advances in Water Resources
DA - 2008///
PY - 2008///
DO - 10.1016/j.advwatres.2008.10.010
VL - 31
SP - 743-757
ER -
TY - JOUR
TI - Estimation and identification of parameters in a lumped cerebrovascular model
AU - Pope, S R
AU - Ellwein, L M
AU - Zapata, C I
AU - Novak, V
AU - Kelley, C T
AU - Olufsen, M S
T2 - Math. Biosci. Eng.
DA - 2008///
PY - 2008///
VL - 6
SP - 93-115
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The two papers in this issue are about short recurrences for computing bases of Krylov subspaces, and numerical methods for computing the Laplace transform and its inverse. Systems of linear equations $Ax=b$, where the matrix A is large and sparse (i.e., only a few elements of A are nonzero), are often solved by so-called Krylov subspace methods. Such methods restrict operations involving A to matrix vector products. In the simplest case the iterates $x^{(k)}$ are computed from vectors in the Krylov space $\mathcal{K}_k=span\{b, Ab,\ldots, A^{k-1}b\}$. For instance, when A is Hermitian positive-definite (or real symmetric positive-definite) the conjugate gradient method computes $x^{(k)}$ as a linear combination of $x^{(k-1)}$ and a “direction vector” $p_k$. The direction vectors form an A-orthogonal basis for the Krylov space $\mathcal{K}_k$, that is, $p_i^*Ap_j=0$ for $i\neq j$ (the superscript $*$ denotes the conjugate transpose). As a consequence, a direction vector $p_k$ can be computed from $Ap_{k-1}$, $p_{k-1}$ and $p_{k-2}$. This is called a 3-term recurrence. However, if A is a general matrix, then it is well known that the direction vectors cannot be computed with 3-term recurrences—even if one relaxes the orthogonality to B-orthogonality, where B is any Hermitian positive-definite matrix. The question is, if 3-term recurrences are not possible, then how short can the recurrences possibly be? In their paper “On Optimal Short Recurrences for Generating Orthogonal Krylov Subspace Bases,” J. Liesen and Z. Strakoš derive necessary and sufficient conditions for a nonsingular matrix A to admit $(s+2)$-term recurrences for $s\geq 1$. They also give a comprehensive overview of work on short recurrences for Krylov subspace methods. This is a clear and carefully written paper, and the authors go to great lengths to illuminate the subtle issues involved. In the second paper, “The Bad Truth about Laplace's Transform,” Charles Epstein and John Schotland are concerned with the difficulties of inverting the Laplace transform. This may be necessary, for instance, when solving inverse scattering problems from optical tomography and image reconstruction. The Laplace transform of a real function $f(x)$ is defined as the integral $\mathcal{L}\>f(x)=\int_0^{\infty}{e^{-xy}f(y)dy}.$ Inverting $\mathcal{L}$ to recover $f(x)$ is an ill-posed problem. Ill-posed problems are extremely hard to solve numerically because they may not have a solution, the solution may not be unique, or the solution may not depend continuously on the data. The authors use harmonic analysis to derive fast algorithms for approximating the Laplace transform and its inverse (when the function values are sampled on geometrically uniformly spaced data), and to derive regularized inverses.
DA - 2008/1//
PY - 2008/1//
DO - 10.1137/siread000050000003000483000001
VL - 50
IS - 3
SP - 483-483
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-56349149490&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The paper featured in this issue is “Logically Rectangular Grids and Finite Volume Methods for PDEs in Circular and Spherical Domains” by Donna Calhoun, Christiane Helzel, and Randy LeVeque. The topic is the numerical solution of partial differential equations (PDEs) whose domains are circles, balls, spheres, and related geometries. The main idea is to solve the PDE on a “logically rectangular” grid. This means, for instance, if the physical space is a circle, then the computational space is a square. The authors focus on hyperbolic PDEs, including Euler, acoustics, and shallow water equations, and also give an example for solving reaction-diffusion equations. This paper is a pleasure to read. One finds lucid explanations of what can go wrong with different types of grids for circular and spherical domains, such as grid cells of widely differing sizes and extreme shapes. In contrast, the algorithms in this paper map a single rectangular block into a spherical shape; and the resulting cell sizes differ by a factor of at most two. The different mappings from computational space to physical space are presented as short, intuitive MATLAB algorithms. Many crisp pictures illustrate the uniform appearance and effectiveness of the grids. Even those who are not PDE experts will appreciate the simplicity, elegance, and generality of the logically rectangular grids when they are combined with a discretization of the PDE by finite volume methods.
DA - 2008/1//
PY - 2008/1//
DO - 10.1137/siread000050000004000721000001
VL - 50
IS - 4
SP - 721-721
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-50949105062&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Problems and Techniques
AU - Ipsen, Ilse
T2 - SIAM Review
AB - The three papers in this issue are concerned with asymptotic expansions of integrals, calculus of variations, and singular perturbation techniques. 1. Among integral transforms, the Fourier transform is arguably the best known, but there are many others, including Laplace, Stieltjes, Mellin, Hankel, and Poisson transforms. They can all be represented as $I(x)\equiv\int_0^{\infty}{f(t)h(xt)dt}$. If x is an asymptotic parameter, which means that x is close to zero or very large, then one may be able to approximate $I(x)$ by an asymptotic expansion. In his paper “Asymptotic Expansions of Mellin Convolution Integrals,” José López presents a general and simple method to generate asymptotic expansions for $I(x)$ that encompasses many existing methods as special cases. 2. Analysis of “slope stability” is an important aspect of geology and soil mechanics: How likely is a sloped terrain (an embankment, a dam) to succumb to erosion and turn into a landslide? And how should the slope profile be modified to prevent further sliding? Analysis of slope stability is one of the applications envisioned by Enrique Castillo, Antonio Conejo, and Ernesto Aranda in their paper “Sensitivity Analysis in Calculus of Variations. Some Applications.” They propose to perform slope stability by means of a sensitivity analysis in the calculus of variations. In the context of slope stability, for instance, one might want to determine how sensitive the slope safety factor is to changes in the slope profile or to changes in soil strength. The mathematical problem comes down to this: How sensitive to changes in parameters are the following quantities: objective function values, primal solutions, and dual solutions? The authors show how to express the sensitivities in terms of partial derivatives, and how to compute them numerically by solving a boundary value problem. 3. In their paper “High-Frequency Oscillations of a Sphere in a Viscous Fluid near a Rigid Plane,” Richard Chadwick and Zhijie Liao model the operation of atomic force microscopes. An atomic force microscope (AFM) is a high resolution scanning device for imaging at nanoscales. Unlike conventional microscopes, which use light, an AFM scans a specimen by “feeling” the surface with a mechanical probe, which in this case consists of a sphere attached to a cantilever. When the specimens are delicate biological samples, such as tissues of the inner ear, they are scanned in a fluid, and the AFM is employed in “tapping mode.” In tapping mode, the sphere is forced to oscillate up and down. When it approaches the specimen, its oscillations are changed by hydrodynamic forces. This provides information about properties of the specimen. To understand the hydrodynamic interactions taking place between sphere and wall, one can model the situation as a fluid that contains a sphere oscillating close to a rigid wall. The problem becomes singular when the sphere approaches the wall. The authors revive singular perturbation techniques developed in the 1960s to derive asymptotic expansions for the forces acting on the sphere.
DA - 2008/1//
PY - 2008/1//
DO - 10.1137/siread000050000002000273000001
VL - 50
IS - 2
SP - 273-273
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-44949224981&partnerID=MN8TOARS
ER -
TY - CONF
TI - Expressing a fraction of two determinants as a determinant
AU - Kaltofen, Erich
AU - Koiran, Pascal
T2 - the twenty-first international symposium
AB - Suppose the polynomials f and g in K[x1,...,xr] over the field K are determinants of non-singular m x m and n x n matrices, respectively, whose entries are in K ∪ x1,...,xr. Furthermore, suppose h = f/g is a polynomial in K[x1,..., xr]. We construct an s x s matrix C whose entries are in K ∪ x1,...,xr, such that h = det(C) and s = γ (m+n)6, where γ = O(1) if K is an infinite field or if for the finite field K = F{q} with q elements we have m = O(q), and where γ = (logq m)1+o(1) if q = o(m). Our construction utilizes the notion of skew circuits by Toda and WSK circuits by Malod and Portier. Our problem was motivated by resultant formulas derived from Chow forms.
C2 - 2008///
C3 - Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08
DA - 2008///
DO - 10.1145/1390768.1390790
PB - ACM Press
SN - 9781595939043
UR - http://dx.doi.org/10.1145/1390768.1390790
DB - Crossref
ER -
TY - CONF
TI - Exact certification of global optimality of approximate factorizations via rationalizing sums-of-squares with floating point scalars
AU - Kaltofen, Erich
AU - Li, Bin
AU - Yang, Zhengfeng
AU - Zhi, Lihong
T2 - the twenty-first international symposium
AB - We generalize the technique by Peyrl and Parillo [Proc. SNC 2007] to computing lower bound certificates for several well-known factorization problems in hybrid symbolic-numeric computation. The idea is to transform a numerical sum-of-squares (SOS) representation of a positive polynomial into an exact rational identity. Our algorithms successfully certify accurate rational lower bounds near the irrational global optima for benchmark approximate polynomial greatest common divisors and multivariate polynomial irreducibility radii from the literature, and factor coefficient bounds in the setting of a model problem by Rump (up to n = 14, factor degree = 13.
C2 - 2008///
C3 - Proceedings of the twenty-first international symposium on Symbolic and algebraic computation - ISSAC '08
DA - 2008///
DO - 10.1145/1390768.1390792
PB - ACM Press
SN - 9781595939043
UR - http://dx.doi.org/10.1145/1390768.1390792
DB - Crossref
ER -
TY - JOUR
TI - Differential-algebraic equations
AU - Campbell, Stephen
AU - Linh, Vu
AU - Petzold, Linda
T2 - Scholarpedia
DA - 2008///
PY - 2008///
DO - 10.4249/scholarpedia.2849
VL - 3
IS - 8
SP - 2849
J2 - Scholarpedia
LA - en
OP -
SN - 1941-6016
UR - http://dx.doi.org/10.4249/scholarpedia.2849
DB - Crossref
ER -
TY - JOUR
TI - Proximal Thresholding Algorithm for Minimization over Orthonormal Bases
AU - Combettes, Patrick L.
AU - Pesquet, Jean-Christophe
T2 - SIAM Journal on Optimization
AB - The notion of soft thresholding plays a central role in problems from various areas of applied mathematics, in which the ideal solution is known to possess a sparse decomposition in some orthonormal basis. Using convex-analytical tools, we extend this notion to that of proximal thresholding and investigate its properties, providing, in particular, several characterizations of such thresholders. We then propose a versatile convex variational formulation for optimization over orthonormal bases that covers a wide range of problems, and we establish the strong convergence of a proximal thresholding algorithm to solve it. Numerical applications to signal recovery are demonstrated.
DA - 2008/1//
PY - 2008/1//
DO - 10.1137/060669498
VL - 18
IS - 4
SP - 1351-1376
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/060669498
DB - Crossref
KW - convex programming
KW - deconvolution
KW - denoising
KW - forward-backward splitting algorithm
KW - Hilbert space
KW - orthonormal basis
KW - proximal algorithm
KW - proximal thresholding
KW - proximity operator
KW - signal recovery
KW - soft thresholding
KW - strong convergence
ER -
TY - CHAP
TI - A Convex Programming Algorithm for Noisy Discrete Tomography
AU - Capricelli, T.D.
AU - Combettes, P.L.
T2 - Advances in Discrete Tomography and Its Applications
AB - A convex programming approach to discrete tomographic image reconstruction in noisy environments is proposed. Conventional constraints are mixed with noise-based constraints on the sinogram and a binariness-promoting total variation constraint. The noise-based constraints are modeled as confidence regions that are constructed under a Poisson noise assumption. A convex objective is then minimized over the resulting feasibility set via a parallel block-iterative method. Applications to binary tomographic reconstruction are demonstrated.
PY - 2008/1/18/
DO - 10.1007/978-0-8176-4543-4_10
SP - 207-226
OP -
PB - Birkhäuser Boston
SN - 9780817636142 9780817645434
UR - http://dx.doi.org/10.1007/978-0-8176-4543-4_10
DB - Crossref
ER -
TY - JOUR
TI - Visco-penalization of the sum of two monotone operators
AU - Combettes, Patrick L.
AU - Hirstoaga, Sever A.
T2 - Nonlinear Analysis: Theory, Methods & Applications
AB - A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a particular strictly monotone variational inequality. As an off-spring of this result, we obtain an approximating curve for finding a particular zero of the sum of several maximal monotone operators. Applications to convex optimization are discussed.
DA - 2008/7//
PY - 2008/7//
DO - 10.1016/j.na.2007.06.003
VL - 69
IS - 2
SP - 579-591
J2 - Nonlinear Analysis: Theory, Methods & Applications
LA - en
OP -
SN - 0362-546X
UR - http://dx.doi.org/10.1016/j.na.2007.06.003
DB - Crossref
KW - approximating curve
KW - monotone operator
KW - penalization
KW - variational inequality
KW - viscosity
KW - Yosida approximation
ER -
TY - JOUR
TI - A proximal decomposition method for solving convex variational inverse problems
AU - Combettes, Patrick L
AU - Pesquet, Jean-Christophe
T2 - Inverse Problems
AB - A broad range of inverse problems can be abstracted into the problem of minimizing the sum of several convex functions in a Hilbert space. We propose a proximal decomposition algorithm for solving this problem with an arbitrary number of nonsmooth functions and establish its weak convergence. The algorithm fully decomposes the problem in that it involves each function individually via its own proximity operator. A significant improvement over the methods currently in use in the area of inverse problems is that it is not limited to two nonsmooth functions. Numerical applications to signal and image processing problems are demonstrated.
DA - 2008/11/7/
PY - 2008/11/7/
DO - 10.1088/0266-5611/24/6/065014
VL - 24
IS - 6
SP - 065014
J2 - Inverse Problems
OP -
SN - 0266-5611 1361-6420
UR - http://dx.doi.org/10.1088/0266-5611/24/6/065014
DB - Crossref
ER -
TY - JOUR
TI - Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping
AU - Bociu, Lorena
AU - Lasiecka, Irena
T2 - Applicationes Mathematicae
AB - We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove t
DA - 2008///
PY - 2008///
DO - 10.4064/am35-3-3
VL - 35
IS - 3
SP - 281-304
J2 - Appl. Math. (Warsaw)
LA - en
OP -
SN - 1233-7234 1730-6280
UR - http://dx.doi.org/10.4064/am35-3-3
DB - Crossref
ER -
TY - JOUR
TI - Uniqueness of weak solutions for the semilinear wave equations with supercritical boundary/interior sources and damping
AU - Lasiecka, Irena
AU - Bociu, Lorena
T2 - Discrete and Continuous Dynamical Systems
AB - We consider finite energy solutions of a wave equation with supercritical nonlinear sources and nonlinear damping. A distinct feature of the model under consideration is the presence of nonlinear sources on the boundary driven by Neumann boundary conditions. Since Lopatinski condition fails to hold (unless the $\text{dim} (\Omega) = 1$), the analysis of the nonlinearities supported on the boundary, within the framework of weak solutions, is a rather subtle issue and involves the strong interaction between the source and the damping. Thus, it is not surprising that existence theory for this class of problems has been established only recently. However, the uniqueness of weak solutions was declared an open problem. The main result in this work is * uniqueness* of weak solutions. This result is proved for the same (even larger) class of data for which existence theory holds. In addition, we prove that weak solutions are continuously depending on initial data and that the flow corresponding to weak and global solutions is a dynamical system on the finite energy space.
DA - 2008/9//
PY - 2008/9//
DO - 10.3934/dcds.2008.22.835
VL - 22
IS - 4
SP - 835-860
J2 - DCDS-A
LA - en
OP -
SN - 1078-0947
UR - http://dx.doi.org/10.3934/dcds.2008.22.835
DB - Crossref
ER -
TY - JOUR
TI - Local absorbing boundary conditions for elliptical shaped boundaries
AU - Medvinsky, M.
AU - Turkel, E.
AU - Hetmaniuk, U.
T2 - Journal of Computational Physics
AB - We compare several local absorbing boundary conditions for solving the Helmholtz equation, by a finite difference or finite element method, exterior to a general scatterer. These boundary conditions are imposed on an artificial elliptical or prolate spheroid outer surface. In order to compare the computational solution with an analytical solution, we consider, as an example, scattering about an ellipse. We solve the Helmholtz equation with both finite differences and finite elements. We also introduce a new boundary condition for an ellipse based on a modal expansion.
DA - 2008/9//
PY - 2008/9//
DO - 10.1016/j.jcp.2008.05.010
VL - 227
IS - 18
SP - 8254-8267
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2008.05.010
DB - Crossref
KW - Helmholtz equation
KW - absorbing boundary conditions
KW - Mathieu functions
ER -
TY - JOUR
TI - Optimal control of stochastic functional differential equations with a bounded memory
AU - Chang, Mou-Hsiung (Harry)
AU - Pang, Tao
AU - Pemy, Moustapha
T2 - Stochastics
AB - This paper treats a finite time horizon optimal control problem in which the controlled state dynamics are governed by a general system of stochastic functional differential equations with a bounded memory. An infinite dimensional Hamilton–Jacobi–Bellman (HJB) equation is derived using a Bellman-type dynamic programming principle. It is shown that the value function is the unique viscosity solution of the HJB equation.
DA - 2008/2//
PY - 2008/2//
DO - 10.1080/17442500701605494
VL - 80
IS - 1
SP - 69-96
J2 - Stochastics
LA - en
OP -
SN - 1744-2508 1744-2516
UR - http://dx.doi.org/10.1080/17442500701605494
DB - Crossref
KW - Stochastic control
KW - Stochastic functional differential equations
KW - Viscosity solutions
KW - Hamilton-Jacobi-Bellman equation
ER -
TY - JOUR
TI - The Dynamic Mechanical Environment of the Chondrocyte: A Biphasic Finite Element Model of Cell-Matrix Interactions Under Cyclic Compressive Loading
AU - Kim, Eunjung
AU - Guilak, Farshid
AU - Haider, Mansoor A.
T2 - Journal of Biomechanical Engineering
AB - Cyclic mechanical loading of articular cartilage results in a complex biomechanical environment at the scale of the chondrocytes that strongly affects cellular metabolic activity. Under dynamic loading conditions, the quantitative relationships between macroscopic loading characteristics and solid and fluid mechanical variables in the local cellular environment are not well understood. In this study, an axisymmetric multiscale model of linear biphasic cell-matrix interactions in articular cartilage was developed to investigate the cellular microenvironment in an explant subjected to cyclic confined compressive loading. The model was based on the displacement-velocity-pressure (u-v-p) mixed-penalty weighted residual formulation of linear biphasic theory that was implemented in the COMSOL MULTIPHYSICS software package. The microscale cartilage environment was represented as a three-zone biphasic region consisting of a spherical chondrocyte with encapsulating pericellular matrix (PCM) that was embedded in a cylindrical extracellular matrix (ECM) subjected to cyclic confined compressive loading boundary conditions. Biphasic material properties for the chondrocyte and the PCM were chosen based on previous in vitro micropipette aspiration studies of cells or chondrons isolated from normal or osteoarthritic cartilage. Simulations performed at four loading frequencies in the range 0.01–1.0 Hz supported the hypothesized dual role of the PCM as both a protective layer for the cell and a mechanical transducer of strain. Time varying biphasic variables at the cellular scale were strongly dependent on relative magnitudes of the loading period, and the characteristic gel diffusion times for the ECM, the PCM, and the chondrocyte. The multiscale simulations also indicated that axial strain was significantly amplified in the range 0.01–1.0 Hz, with a decrease in amplification factor and frequency insensitivity at the higher frequencies. Simulations of matrix degradation due to osteoarthritis indicated that strain amplification factors were more significantly altered when loss of matrix stiffness was exclusive to the PCM. The findings of this study demonstrate the complex dependence of dynamic mechanics in the local cellular environment of cartilage on macroscopic loading features and material properties of the ECM and the chondron.
DA - 2008///
PY - 2008///
DO - 10.1115/1.2978991
VL - 130
IS - 6
SP - 061009
J2 - J. Biomech. Eng.
LA - en
OP -
SN - 0148-0731
UR - http://dx.doi.org/10.1115/1.2978991
DB - Crossref
KW - biomechanics
KW - cellular biophysics
KW - compressibility
KW - finite element analysis
ER -
TY - JOUR
TI - Monitored steady-state excitation and recovery (MSSR) radiation force imaging using viscoelastic models
AU - Mauldin, F.W.
AU - Haider, M.A.
AU - Loboa, E.G.
AU - Behler, R.H.
AU - Euliss, L.E.
AU - Pfeiler, T.W.
AU - Gallippi, C.M.
T2 - IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control
AB - Acoustic radiation force imaging methods distinguish tissue structure and composition by monitoring tissue responses to applied radiation force excitations. Although these responses are a complex, multidimensional function of the geometric and viscoelastic nature of tissue, simplified discrete biomechanical models offer meaningful insight to the physical phenomena that govern induced tissue motion. Applying Voigt and standard linear viscoelastic tissue models, we present a new radiation force technique - monitored steady-state excitation and recovery (MSSER) imaging - that tracks both steady-state displacement during prolonged force application and transient response following force cessation to estimate tissue mechanical properties such as elasticity and viscosity. In concert with shear wave elasticity imaging (SWEI) estimates for Young's modulus, MSSER methods are useful for estimating tissue mechanical properties independent of the applied force magnitude. We test our methods in gelatin phantoms and excised pig muscle, with confirmation through mechanical property measurement. Our results measured 10.6 kPa, 14.7 kPa, and 17.1 kPa (gelatin) and 122.4 kPa (pig muscle) with less than 10% error. This work demonstrates the feasibility of MSSER imaging and merits further efforts to incorporate relevant mechanical tissue models into the development of novel radiation force imaging techniques.
DA - 2008/7//
PY - 2008/7//
DO - 10.1109/tuffc.2008.836
VL - 55
IS - 7
SP - 1597-1610
J2 - IEEE Trans. Ultrason., Ferroelect., Freq. Contr.
OP -
SN - 0885-3010
UR - http://dx.doi.org/10.1109/tuffc.2008.836
DB - Crossref
ER -
TY - CHAP
TI - Propagation of Diffusing Pollutant by a Hybrid Eulerian–Lagrangian Method
AU - Chertock, Alina
AU - Kashdan, E.
AU - Kurganov, A.
AU - BenzoniGavage, S
AU - Serre, D
T2 - Hyperbolic Problems: Theory, Numerics, Applications
PY - 2008///
DO - 10.1007/978-3-540-75712-2_33
SP - 371-379
OP -
PB - Springer Berlin Heidelberg
SN - 9783540757115 9783540757122
UR - http://dx.doi.org/10.1007/978-3-540-75712-2_33
DB - Crossref
ER -
TY - JOUR
TI - Constructing models of vertex algebras in higher dimensions
AU - Bakalov, B.
AU - Nikolov, N.M.
T2 - Bulgarian Journal of Physics
DA - 2008///
PY - 2008///
VL - 35
IS - s1
SP - 36–42
ER -
TY - JOUR
TI - Combinatorial symbolic powers
AU - Sullivant, Seth
T2 - Journal of Algebra
AB - Symbolic powers are studied in the combinatorial context of monomial ideals. When the ideals are generated by quadratic squarefree monomials, the generators of the symbolic powers are obstructions to vertex covering in the associated graph and its blowups. As a result, perfect graphs play an important role in the theory, dual to the role played by perfect graphs in the theory of secants of monomial ideals. We use Gröbner degenerations as a tool to reduce questions about symbolic powers of arbitrary ideals to the monomial case. Among the applications are a new, unified approach to the Gröbner bases of symbolic powers of determinantal and Pfaffian ideals.
DA - 2008/1//
PY - 2008/1//
DO - 10.1016/j.jalgebra.2007.09.024
VL - 319
IS - 1
SP - 115-142
J2 - Journal of Algebra
LA - en
OP -
SN - 0021-8693
UR - http://dx.doi.org/10.1016/j.jalgebra.2007.09.024
DB - Crossref
KW - symbolic power
KW - Grobner basis
KW - perfect graph
KW - edge ideal
KW - determinantal ideal
ER -
TY - JOUR
TI - Toric geometry of cuts and splits
AU - Sturmfels, Bernd
AU - Sullivant, Seth
T2 - The Michigan Mathematical Journal
AB - Associated to any graph is a toric ideal whose generators record relations among the cuts of the graph. We study these ideals and the geometry of the corresponding toric varieties. Our theorems and conjectures relate the combinatorial structure of the graph and the corresponding cut polytope to algebraic properties of the ideal. Cut ideals generalize toric ideals arising in phylogenetics and the study of contingency tables.
DA - 2008/8//
PY - 2008/8//
DO - 10.1307/mmj/1220879432
VL - 57
IS - 0
SP - 689-709
J2 - Michigan Math. J.
LA - en
OP -
SN - 0026-2285
UR - http://dx.doi.org/10.1307/mmj/1220879432
DB - Crossref
ER -
TY - JOUR
TI - Algebraic geometry of Gaussian Bayesian networks
AU - Sullivant, Seth
T2 - Advances in Applied Mathematics
AB - Conditional independence models in the Gaussian case are algebraic varieties in the cone of positive definite covariance matrices. We study these varieties in the case of Bayesian networks, with a view towards generalizing the recursive factorization theorem to situations with hidden variables. In the case when the underlying graph is a tree, we show that the vanishing ideal of the model is generated by the conditional independence statements implied by graph. We also show that the ideal of any Bayesian network is homogeneous with respect to a multigrading induced by a collection of upstream random variables. This has a number of important consequences for hidden variable models. Finally, we relate the ideals of Bayesian networks to a number of classical constructions in algebraic geometry including toric degenerations of the Grassmannian, matrix Schubert varieties, and secant varieties.
DA - 2008/5//
PY - 2008/5//
DO - 10.1016/j.aam.2007.04.004
VL - 40
IS - 4
SP - 482-513
J2 - Advances in Applied Mathematics
LA - en
OP -
SN - 0196-8858
UR - http://dx.doi.org/10.1016/j.aam.2007.04.004
DB - Crossref
KW - Bayesian network
KW - graphical model
KW - algebraic statistics
KW - multivariate Gaussian
KW - Grobbner basis
ER -
TY - CHAP
TI - Numerical Solution of the Nonlinear Helmholtz Equation
AU - Fibich, G
AU - Tsynkov, S
T2 - Effective Computational Methods for Wave Propagation
PY - 2008/2/25/
DO - 10.1201/9781420010879.ch2
VL - 5
SP - 37-62
OP -
PB - Chapman and Hall/CRC
SN - 9781584885689 9781420010879
UR - http://dx.doi.org/10.1201/9781420010879.ch2
DB - Crossref
ER -
TY - JOUR
TI - ORDINAL RANKING FOR GOOGLE'S PAGERANK
AU - Wills, Rebecca S.
AU - Ipsen, Ilse C. F.
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - We present computationally efficient criteria that can guarantee correct ordinal ranking of Google's PageRank scores when they are computed with the power method (ordinal ranking of a list consists of assigning an ordinal number to each item in the list). We discuss the tightness of the ranking criteria, and illustrate their effectiveness for top k and bucket ranking. We present a careful implementation of the power method, combined with a roundoff error analysis that is valid for matrix dimensions $n<10^{14}$. To first order, the roundoff error depends neither on n nor on the iteration count, but only on the maximal number of inlinks and the dangling nodes. The applicability of our ranking criterion is limited by the roundoff error from a single matrix vector multiply. Numerical experiments suggest that our criteria can effectively rank the top PageRank scores. We also discuss how to implement ranking for extremely large practical problems, by curbing roundoff error, reducing the matrix dimension, and using faster converging methods.
DA - 2008///
PY - 2008///
DO - 10.1137/070698129
VL - 30
IS - 4
SP - 1677-1696
SN - 1095-7162
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-70449368930&partnerID=MN8TOARS
KW - ranking distance
KW - power method
KW - stochastic matrix
KW - PageRank
KW - Google matrix
KW - ordinal rank
KW - roundoff error
ER -
TY - JOUR
TI - Semi-smooth Newton methods for the Signorini problem
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - APPLICATIONS OF MATHEMATICS
AB - Semi-smooth Newton methods are analyzed for the Signorini problem. A proper regularization is introduced which guarantees that the semi-smooth Newton method is superlinearly convergent for each regularized problem. Utilizing a shift motivated by an augmented Lagrangian framework, to the regularization term, the solution to each regularized problem is feasible. Convergence of the regularized problems is shown and a report on numerical experiments is given.
DA - 2008/10//
PY - 2008/10//
DO - 10.1007/s10492-008-0036-7
VL - 53
IS - 5
SP - 455-468
SN - 0862-7940
KW - Signorini problem
KW - variational inequality
KW - semi-smooth Newton method
KW - primal-dual active set strategy
ER -
TY - JOUR
TI - QUANTIFYING UNCERTAINTY IN THE ESTIMATION OF PROBABILITY DISTRIBUTIONS
AU - Banks, H. T.
AU - Davis, Jimena L.
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - We consider ordinary least squares parameter estimation problems where the unknown parameters to be estimated are probability distributions. A computational framework for quantification of uncertainty (e.g., standard errors) associated with the estimated parameters is given and sample numerical findings are presented.
DA - 2008/10//
PY - 2008/10//
DO - 10.3934/mbe.2008.5.647
VL - 5
IS - 4
SP - 647-667
SN - 1551-0018
KW - approximation
KW - asymptotic standard error theory
KW - confidence bands
KW - parameter estimation
KW - probability distributions
KW - size-structured populations
ER -
TY - JOUR
TI - Trustworthy Web services provisioning for differentiated customer services
AU - Xiong, Kaiqi
AU - Perros, Harry
T2 - TELECOMMUNICATION SYSTEMS
DA - 2008/12//
PY - 2008/12//
DO - 10.1007/s11235-008-9126-9
VL - 39
IS - 3-4
SP - 171-185
SN - 1572-9451
KW - Web services
KW - Security
KW - Trustworthiness
KW - Percentile response time
KW - Service availability
ER -
TY - JOUR
TI - REDUCED-ORDER OPTIMAL CONTROL BASED ON APPROXIMATE INERTIAL MANIFOLDS FOR NONLINEAR DYNAMICAL SYSTEMS
AU - Ito, Kazufumi
AU - Kunisch, Karl
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - A reduced-order method for optimal control problems in infinite dimensions based on approximate inertial manifolds is developed. Convergence of the cost, optimal controls, and optimal states of the finite dimensional, reduced-order, optimal control problems to the original optimal control problem is analyzed. Special attention is given to the particular case when the dynamics are described by the Navier–Stokes equations in dimension two.
DA - 2008///
PY - 2008///
DO - 10.1137/060666421
VL - 46
IS - 6
SP - 2867-2891
SN - 1095-7170
KW - reduced-order methods
KW - approximate inertial manifold
KW - nonlinear Galerkin
KW - decomposition of state space
KW - infinite dimensional system
ER -
TY - JOUR
TI - PROJECTED PSEUDOTRANSIENT CONTINUATION
AU - Kelley, C. T.
AU - Liao, Li-Zhi
AU - Qi, Liqun
AU - Chu, Moody T.
AU - Reese, J. P.
AU - Winton, C.
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - We propose and analyze a pseudotransient continuation algorithm for dynamics on subsets of $R^N$. Examples include certain flows on manifolds and the dynamic formulation of bound-constrained optimization problems. The method gets its global convergence properties from the dynamics and inherits its local convergence properties from any fast locally convergent iteration.
DA - 2008///
PY - 2008///
DO - 10.1137/07069866X
VL - 46
IS - 6
SP - 3071-3083
SN - 1095-7170
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-55349118529&partnerID=MN8TOARS
KW - pseudotransient continuation
KW - constrained dynamics
KW - gradient flow
KW - bound-constrained optimization
KW - quasi-Newton method
ER -
TY - JOUR
TI - Infinite-dimensional super Lie groups
AU - Cook, James
AU - Fulp, Ronald
T2 - DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS
AB - A super Lie group is a group whose operations are G ∞ mappings in the sense of Rogers. Thus the underlying supermanifold possesses an atlas whose transition functions are G ∞ functions. Moreover the images of our charts are open subsets of a graded infinite-dimensional Banach space since our space of supernumbers is a Banach Grassmann algebra with a countably infinite set of generators. In this context, we prove that if h is a closed, split sub-super Lie algebra of the super Lie algebra of a super Lie group G , then h is the super Lie algebra of a sub-super Lie group of G . Additionally, we show that if g is a Banach super Lie algebra satisfying certain natural conditions, then there is a super Lie group G such that the super Lie algebra g is in fact the super Lie algebra of G . We also show that if H is a closed sub-super Lie group of a super Lie group G , then G → G / H is a principal fiber bundle. We emphasize that some of these theorems are known when one works in the super-analytic category and also when the space of supernumbers is finitely generated in which case, one can use finite-dimensional techniques. The issues dealt with here are that our supermanifolds are modeled on graded Banach spaces and that all mappings must be morphisms in the G ∞ category.
DA - 2008/10//
PY - 2008/10//
DO - 10.1016/j.difgeo.2008.04.009
VL - 26
IS - 5
SP - 463-482
SN - 0926-2245
KW - Super Lie group
KW - Supermanifold
KW - Banach Lie group
KW - Grassmann algebra
KW - Banach manifold
ER -
TY - JOUR
TI - INTERFACE TRACKING METHOD FOR COMPRESSIBLE MULTIFLUIDS
AU - Chertock, Alina
AU - Karni, Smadar
AU - Kurganov, Alexander
T2 - ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
AB - This paper is concerned with numerical methods for compressible multicomponent fluids. The fluid components are assumed immiscible, and are separated by material interfaces, each endowed with its own equation of state (EOS). Cell averages of computational cells that are occupied by several fluid components require a EOS, which may not always be physically meaningful, and often leads to spurious oscillations. We present a new interface tracking algorithm, which avoids using mixed-cell information by solving the Riemann problem between its single-fluid neighboring cells. The resulting algorithm is oscillation-free for isolated material interfaces, conservative, and tends to produce almost perfect jumps across material fronts. The computational framework is general and may be used in conjunction with one's favorite finite-volume method. The robustness of the method is illustrated on shock-interface interaction in one space dimension, oscillating bubbles with radial symmetry and shock-bubble interaction in two space dimensions.
DA - 2008///
PY - 2008///
DO - 10.1051/m2an:2008036
VL - 42
IS - 6
SP - 991-1019
SN - 1290-3841
UR - https://doi-org.prox.lib.ncsu.edu/10.1051/m2an:2008036
KW - Compressible Euler equations
KW - multicomponent fluids
KW - material interfaces
KW - finite-volume schemes
ER -
TY - JOUR
TI - BLOOD FLOW IN THE CIRCLE OF WILLIS: MODELING AND CALIBRATION
AU - Devault, Kristen
AU - Gremaud, Pierre A.
AU - Novak, Vera
AU - Olufsen, Mette S.
AU - Vernieres, Guillaume
AU - Zhao, Peng
T2 - MULTISCALE MODELING & SIMULATION
AB - A numerical model based on one-dimensional balance laws and ad hoc zero-dimensional boundary conditions is tested against experimental data. The study concentrates on the circle of Willis, a vital subnetwork of the cerebral vasculature. The main goal is to obtain efficient and reliable numerical tools with predictive capabilities. The flow is assumed to obey the Navier-Stokes equations, while the mechanical reactions of the arterial walls follow a viscoelastic model. Like many previous studies, a dimension reduction is performed through averaging. Unlike most previous work, the resulting model is both calibrated and validated against in vivo data, more precisely transcranial Doppler data of cerebral blood velocity. The network considered has three inflow vessels and six outflow vessels. Inflow conditions come from the data, while outflow conditions are modeled. Parameters in the outflow conditions are calibrated using a subset of the data through ensemble Kalman filtering techniques. The rest of the data is used for validation. The results demonstrate the viability of the proposed approach.
DA - 2008///
PY - 2008///
DO - 10.1137/07070231X
VL - 7
IS - 2
SP - 888-909
SN - 1540-3467
KW - blood flow
KW - viscoelastic arteries
KW - fluid-structure interaction
KW - Kalman filtering
ER -
TY - JOUR
TI - An immersed interface method for solving incompressible viscous flows with piecewise constant viscosity across a moving elastic membrane
AU - Tan, Zhijun
AU - Le, D. V.
AU - Li, Zhilin
AU - Lim, K. M.
AU - Khoo, B. C.
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - This paper presents an implementation of the second-order accurate immersed interface method to simulate the motion of the flexible elastic membrane immersed in two viscous incompressible fluids with different viscosities, which further develops the work reported in Tan et al. [Z.-J. Tan, D.V. Le, K.M. Lim, B.C. Khoo, An Immersed Interface Method for the Incompressible Navier–Stokes Equations with Discontinuous Viscosity Across the Interface, submitted for publication] focussing mainly on the fixed interface problems. In this work, we introduce the velocity components at the membrane as two augmented unknown interface variables to decouple the originally coupled jump conditions for the velocity and pressure. Three forms of augmented equation are derived to determine the augmented variables to satisfy the continuous condition of the velocity. The velocity at the membrane, which determine the motion of the membrane, is then solved by the GMRES iterative method. The forces calculated from the configuration of the flexible elastic membrane and the augmented variables are interpolated using cubic splines and applied to the fluid through the jump conditions. The position of the flexible elastic membrane is updated implicitly using a quasi-Newton method (BFGS) within each time step. The Navier–Stokes equations are solved on a staggered Cartesian grid using a second order accurate projection method with the incorporation of spatial and temporal jump conditions. In addition, we also show that the inclusion of the temporal jump contributions has non-negligible effect on the simulation results when the grids are crossed by the membrane. Using the above method, we assess the effect of different viscosities on the flow solution and membrane motion.
DA - 2008/12/1/
PY - 2008/12/1/
DO - 10.1016/j.jcp.2008.08.013
VL - 227
IS - 23
SP - 9955-9983
SN - 1090-2716
KW - Incompressible viscous flows
KW - Piecewise constant viscosity
KW - Singular force
KW - Immersed interface method
KW - Projection method
KW - Front tracking method
ER -
TY - JOUR
TI - A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models
AU - Chertock, Alina
AU - Kurganov, Alexander
T2 - NUMERISCHE MATHEMATIK
DA - 2008/12//
PY - 2008/12//
DO - 10.1007/s00211-008-0188-0
VL - 111
IS - 2
SP - 169-205
SN - 0945-3245
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s00211-008-0188-0
ER -
TY - JOUR
TI - A Killer-Rescue system for self-limiting gene drive of anti-pathogen constructs
AU - Gould, Fred
AU - Huang, Yunxin
AU - Legros, Mathieu
AU - Lloyd, Alun L.
T2 - PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES
AB - A number of genetic mechanisms have been suggested for driving anti-pathogen genes into natural populations. Each of these mechanisms requires complex genetic engineering, and most are theoretically expected to permanently spread throughout the target species' geographical range. In the near term, risk issues and technical limits of molecular methods could delay the development and use of these mechanisms. We propose a gene-drive mechanism that can be self-limiting over time and space, and is simpler to build. This mechanism involves one gene that codes for toxicity (killer) and a second that confers immunity to the toxic effects (rescue). We use population-genetic models to explore cases with one or two independent insertions of the killer gene and one insertion of the rescue gene. We vary the dominance and penetrance of gene action, as well as the magnitude of fitness costs. Even with the fitness costs of 10 per cent for each gene, the proportion of mosquitoes expected to transmit the pathogen decreases below 5 per cent for over 40 generations after one 2 : 1 release (engineered : wild) or after four 1 : 2 releases. Both the killer and rescue genes will be lost from the population over time, if the rescue construct has any associated fitness cost. Molecular approaches for constructing strains are discussed.
DA - 2008/12/22/
PY - 2008/12/22/
DO - 10.1098/rspb.2008.0846
VL - 275
IS - 1653
SP - 2823-2829
SN - 0962-8452
UR - https://publons.com/publon/8709314/
KW - gene drive
KW - selfish genes
KW - Aedes
KW - Anopheles
KW - dengue
KW - malaria
ER -
TY - JOUR
TI - Simulations of the nonlinear Helmholtz equation: arrest of beam collapse, nonparaxial solitons and counter-propagating beams
AU - Baruch, G.
AU - Fibich, G.
AU - Tsynkov, Semyon
T2 - Optics Express
AB - We solve the (2+1)D nonlinear Helmholtz equation (NLH) for input beams that collapse in the simpler NLS model. Thereby, we provide the first ever numerical evidence that nonparaxiality and backscattering can arrest the collapse. We also solve the (1+1)D NLH and show that solitons with radius of only half the wavelength can propagate over forty diffraction lengths with no distortions. In both cases we calculate the backscattered field, which has not been done previously. Finally, we compute the dynamics of counter-propagating solitons using the NLH model, which is more comprehensive than the previously used coupled NLS model.
DA - 2008/8/14/
PY - 2008/8/14/
DO - 10.1364/OE.16.013323
VL - 16
IS - 17
SP - 13323
J2 - Opt. Express
LA - en
OP -
SN - 1094-4087
UR - http://dx.doi.org/10.1364/OE.16.013323
DB - Crossref
ER -
TY - JOUR
TI - Sequence and genetic map of Meloidogyne hapla: A compact nematode genome for plant parasitism
AU - Opperman, Charles H.
AU - Bird, David M.
AU - Williamson, Valerie M.
AU - Rokhsar, Dan S.
AU - Burke, Mark
AU - Cohn, Jonathan
AU - Cromer, John
AU - Diener, Steve
AU - Gajan, Jim
AU - Graham, Steve
AU - Houfek, T. D.
AU - Liu, Qingli
AU - Mitros, Therese
AU - Schaff, Jennifer
AU - Schaffer, Reenah
AU - Scholl, Elizabeth
AU - Sosinski, Bryon R.
AU - Thomas, Varghese P.
AU - Windham, Eric
T2 - PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
AB - We have established Meloidogyne hapla as a tractable model plant-parasitic nematode amenable to forward and reverse genetics, and we present a complete genome sequence. At 54 Mbp, M. hapla represents not only the smallest nematode genome yet completed, but also the smallest metazoan, and defines a platform to elucidate mechanisms of parasitism by what is the largest uncontrolled group of plant pathogens worldwide. The M. hapla genome encodes significantly fewer genes than does the free-living nematode Caenorhabditis elegans (most notably through a reduction of odorant receptors and other gene families), yet it has acquired horizontally from other kingdoms numerous genes suspected to be involved in adaptations to parasitism. In some cases, amplification and tandem duplication have occurred with genes suspected of being acquired horizontally and involved in parasitism of plants. Although M. hapla and C. elegans diverged >500 million years ago, many developmental and biochemical pathways, including those for dauer formation and RNAi, are conserved. Although overall genome organization is not conserved, there are areas of microsynteny that may suggest a primary biological function in nematodes for those genes in these areas. This sequence and map represent a wealth of biological information on both the nature of nematode parasitism of plants and its evolution.
DA - 2008/9/30/
PY - 2008/9/30/
DO - 10.1073/pnas.0805946105
VL - 105
IS - 39
SP - 14802-14807
SN - 1091-6490
KW - compaction
KW - dauer
KW - development
KW - horizontal gene transfer
KW - gene
ER -
TY - JOUR
TI - PERTURBATION BOUNDS FOR DETERMINANTS AND CHARACTERISTIC POLYNOMIALS
AU - Ipsen, Ilse C. F.
AU - Rehman, Rizwana
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - We derive absolute perturbation bounds for the coefficients of the characteristic polynomial of a $n\times n$ complex matrix. The bounds consist of elementary symmetric functions of singular values, and suggest that coefficients of normal matrices are better conditioned with regard to absolute perturbations than those of general matrices. When the matrix is Hermitian positive-definite, the bounds can be expressed in terms of the coefficients themselves. We also improve absolute and relative perturbation bounds for determinants. The basis for all bounds is an expansion of the determinant of a perturbed diagonal matrix.
DA - 2008///
PY - 2008///
DO - 10.1137/070704770
VL - 30
IS - 2
SP - 762-776
SN - 0895-4798
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-67649206986&partnerID=MN8TOARS
KW - elementary symmetric functions
KW - singular values
KW - eigenvalues
KW - condition number determinant
ER -
TY - JOUR
TI - LDU FACTORIZATION OF NONSINGULAR TOTALLY NONPOSITIVE MATRICES
AU - Canto, Rafael
AU - Koev, Plamen
AU - Ricarte, Beatriz
AU - Urbano, Ana M.
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - An $n \times n$ real matrix A is said to be (totally negative) totally nonpositive if every minor is (negative) nonpositive. In this paper, we study the properties of a totally nonpositive matrix and characterize the case of a nonsingular totally nonpositive matrix A, with $a_{11}< 0$ in terms of its $LDU$ factorization ($L(U)$) is a unit lower- (upper-) triangular matrix, respectively, and D is a diagonal matrix). This characterization allows us to significantly reduce the number of minors to be checked in order to decide the total nonpositivity of a nonsingular matrix with a negative (1,1) entry.
DA - 2008///
PY - 2008///
DO - 10.1137/060662897
VL - 30
IS - 2
SP - 777-782
SN - 1095-7162
KW - nonsingular matrix
KW - totally nonpositive matrix
KW - LDU factorization
ER -
TY - JOUR
TI - A molecular based model for polymer viscoelasticity: Intra- and inter-molecular variability
AU - Banks, H. T.
AU - Hood, J. B.
AU - Medhin, N. G.
T2 - APPLIED MATHEMATICAL MODELLING
AB - We develop dynamic equations for rubber viscoelasticity based on a stick-slip continuum molecular-based model. The model developed is a continuum tube reptation model in which a chemically cross-linked (CC) system of molecules act as constraint box per unit volume for a physically constrained (PC) system of molecules. The CC-system carries along the PC-system during instantaneous step deformations. The subsequent relaxation of the PC-system is determined by the configuration of the CC-system, its own configuration and confirmation, and external force fields. Conversely, the deformation of the PC-system acts as an internal variable affecting the deformations of the constraining CC-system. We model the relationship between these processes to derive a model of viscoelasticity in rubber deformation. In developing a relaxation process for the PC-system, we start from the fact that the PC-system is composed of long molecular chains. The dynamics of these molecular chains are developed by modelling them as chains of beads connected by springs, which represent inter-molecular potentials. Various segments of the molecular chains relax at different rates. In addition, variability in relaxation times across molecular chains is permitted.
DA - 2008/12//
PY - 2008/12//
DO - 10.1016/j.apm.2007.09.018
VL - 32
IS - 12
SP - 2753-2767
SN - 1872-8480
KW - molecular chain bead models
KW - polymer viscoelasticity
KW - variable and distributed relaxation times
ER -
TY - JOUR
TI - Separability of multi-partite quantum states
AU - Huang, Xiaofen
AU - Jing, Naihuan
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - We give a direct tensor decomposition for any density matrix into Hermitian operators. Based upon the decomposition we study when the mixed states are separable and generalize the separability indicators to multi-partite states and show that a density operator is separable if and only if the separable indicator is non-negative. We then derive two bounds for the separable indicator in terms of the spectrum of the factor operators in the tensor summands.
DA - 2008/10/3/
PY - 2008/10/3/
DO - 10.1088/1751-8113/41/39/395302
VL - 41
IS - 39
SP -
SN - 1751-8121
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-54749142880&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Disease-induced mortality in density-dependent discrete-time S-I-S epidemic models
AU - Franke, John E.
AU - Yakubu, Abdul-Aziz
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
DA - 2008/12//
PY - 2008/12//
DO - 10.1007/s00285-008-0188-9
VL - 57
IS - 6
SP - 755-790
SN - 1432-1416
KW - basin of attraction
KW - disease-induced mortality
KW - multiple attractors
ER -
TY - JOUR
TI - A stick-slip/Rouse hybrid model for viscoelasticity in polymers
AU - Banks, H. T.
AU - Hood, J. B.
AU - Medhin, N. G.
AU - Samuels, J. S., Jr.
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - A Rouse model for polymer chains is incorporated into the linear continuous stick-slip molecular-based tube reptation ideas of Doi–Edwards and Johnson–Stacer. This treats the physically constrained (PC) molecular stretches as internal strain variables for the overall PC/chemically cross-linked (CC) system. It yields an explicit system of stress–strain equations for the system permitting simple calculations of complex stress–strain relations. The model that is developed here treats PC molecule as entrapped within a constraining tube, which is comprised of both CC and PC molecules. The model is compared with experimental data sets from the literature.
DA - 2008/12//
PY - 2008/12//
DO - 10.1016/j.nonrwa.2007.06.015
VL - 9
IS - 5
SP - 2128-2149
SN - 1468-1218
KW - viscoelasticity
KW - stick-slip-Rouse model
KW - parameter estimation
ER -
TY - JOUR
TI - A domain decomposition solver for acoustic scattering by elastic objects in layered media
AU - Ito, Kazufumi
AU - Qiao, Zhonghua
AU - Toivanen, Jari
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - A finite element solution procedure is presented for accurately computing time-harmonic acoustic scattering by elastic targets buried in sediment. An improved finite element discretization based on trilinear basis functions leading to fourth-order phase accuracy is described. For sufficiently accurate discretizations 100 million to 1 billion unknowns are required. The resulting systems of linear equations are solved iteratively using the GMRES method with a domain decomposition preconditioner employing a fast direct solver. Due to the construction of the discretization and preconditioner, iterations can be reduced onto a sparse subspace associated with the interfaces. Numerical experiments demonstrate capability to evaluate the scattered field with hundreds of wavelengths.
DA - 2008/10/1/
PY - 2008/10/1/
DO - 10.1016/j.jcp.2008.06.015
VL - 227
IS - 19
SP - 8685-8698
SN - 1090-2716
KW - fast Helmholtz solver
KW - scattering from elastic targets
KW - domain decomposition preconditioner
ER -
TY - JOUR
TI - Modified Optimal Prediction and its Application to a Particle-Method Problem
AU - Chertock, Alina
AU - Gottlieb, David
AU - Solomonoff, Alex
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2008/11//
PY - 2008/11//
DO - 10.1007/s10915-008-9242-4
VL - 37
IS - 2
SP - 189-201
SN - 1573-7691
UR - https://doi-org.prox.lib.ncsu.edu/10.1007/s10915-008-9242-4
KW - Optimal prediction
KW - Particle methods
KW - Multiscale computations
ER -
TY - JOUR
TI - High Speed Model Implementation and Inversion Techniques for Ferroelectric and Ferromagnetic Transducers
AU - Braun, T. R.
AU - Smith, R. C.
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - Ferroelectric and ferromagnetic materials are employed as both actuators and sensors in a wide variety of applications including fluid pumps, nanopositioning stages, sonar transducers, vibration control, ultrasonic sources, and high-speed milling. They are attractive because the resulting transducers are solid-state and often very compact. However, the coupling of field to mechanical deformation, which makes these materials effective transducers, also introduces hysteresis and time-dependent behavior that must be accommodated in device designs and models before the full potential of compounds can be realized. In this article, we present highly efficient modeling techniques to characterize hysteresis and constitutive nonlinearities in ferroelectric and ferromagnetic compounds and model inversion techniques which permit subsequent linear control designs.
DA - 2008/11//
PY - 2008/11//
DO - 10.1177/1045389X07085638
VL - 19
IS - 11
SP - 1295-1310
SN - 1530-8138
KW - actuator
KW - ferroelectric
KW - magnetostrictive
KW - piezoelectric
KW - Terfenol
ER -
TY - JOUR
TI - A SIMPLE EULERIAN FINITE-VOLUME METHOD FOR COMPRESSIBLE FLUIDS IN DOMAINS WITH MOVING BOUNDARIES
AU - Chertock, Alina
AU - Kurganov, Alexander
T2 - COMMUNICATIONS IN MATHEMATICAL SCIENCES
AB - We introduce a simple new Eulerian method for treatment of moving boundaries in compressible fluid computations. Our approach is based on the extension of the interface tracking method recently introduced in the context of multifluids. The fluid domain is placed in a rectangular computational domain of a fixed size, which is divided into Cartesian cells. At every discrete time level, there are three types of cells: internal, boundary, and external ones. The numerical solution is evolved in internal cells only. The numerical fluxes at the cells near the boundary are computed using the technique from [A. Chertock, S. Karni and A. Kurganov, M2AN Math. Model. Numer. Anal., to appear] combined with a solid wall ghost-cell extrapolation and an interpolation in the phase space. The proposed computational framework is general and may be used in conjunction with one’s favorite finite-volume method. The robustness of the new approach is illustrated on a number of one- and two-dimensional numerical examples.
DA - 2008/9//
PY - 2008/9//
DO - 10.4310/CMS.2008.v6.n3.a1
VL - 6
IS - 3
SP - 531-556
SN - 1539-6746
UR - http://projecteuclid.org.prox.lib.ncsu.edu/euclid.cms/1222716944
KW - Compressible Enter equations
KW - ghost-cell extrapolation
KW - moving boundaries
KW - semi-discrete finite-volume schemes
ER -
TY - JOUR
TI - Effects of differences in nasal anatomy on airflow distribution: A comparison of four individuals at rest
AU - Segal, Rebecca A.
AU - Kepler, Grace M.
AU - Kimbell, Julia S.
T2 - ANNALS OF BIOMEDICAL ENGINEERING
DA - 2008/11//
PY - 2008/11//
DO - 10.1007/s10439-008-9556-2
VL - 36
IS - 11
SP - 1870-1882
SN - 1573-9686
KW - Computational fluid dynamics
KW - Nasal airflow simulation
KW - Flow experiments
KW - Flow visualization
KW - Human
KW - Inspiratory airflow
ER -
TY - JOUR
TI - The penetration function and its application to microscale problems
AU - Babuska, Ivo
AU - Lipton, Robert
AU - Stuebner, Michael
T2 - BIT NUMERICAL MATHEMATICS
DA - 2008/6//
PY - 2008/6//
DO - 10.1007/s10543-008-0182-z
VL - 48
IS - 2
SP - 167-187
SN - 1572-9125
KW - penetration function
KW - approximation theory
KW - homogenization
KW - Saint Venant principle
ER -
TY - JOUR
TI - Numerical solutions of a three-competition Lotka-Volterra system
AU - Pao, C. V.
AU - Wang, Yuan-Ming
T2 - APPLIED MATHEMATICS AND COMPUTATION
AB - This paper is concerned with finite difference solutions of a Lotka–Volterra reaction–diffusion system with three-competing species. The reaction–diffusion system is discretized by the finite difference method, and the investigation is devoted to the finite difference system for the time-dependent solution and its asymptotic behavior in relation to the corresponding steady-state problem. Three monotone iterative schemes for the computation of the time-dependent solution are presented, and the sequences of iterations are shown to converge monotonically to a unique positive solution. Also discussed is the asymptotic behavior of the time-dependent solution in relation to various steady-state solutions. A simple condition on the competing rate constants is obtained, which ensures that for every nontrivial nonnegative initial function the corresponding time-dependent solution converges either to a unique positive steady-state solution or to one of the semitrivial steady-state solutions. The above results lead to the coexistence and permanence of the competing system as well as computational algorithms for numerical solutions. Some numerical results from these computational algorithms are given. All the conclusions for the reaction–diffusion equations are directly applicable to the finite difference solution of the corresponding ordinary differential system.
DA - 2008/10/1/
PY - 2008/10/1/
DO - 10.1016/j.amc.2008.06.057
VL - 204
IS - 1
SP - 423-440
SN - 1873-5649
KW - Lotka-Volterra competition
KW - reaction-diffusion system
KW - finite difference system
KW - monotone iterative method
KW - upper and lower solutions
KW - asymptotic behavior
ER -
TY - JOUR
TI - Mechanics of mesenchymal contribution to clefting force in branching morphogenesis
AU - Wan, Xiaohai
AU - Li, Zhilin
AU - Lubkin, Sharon R.
T2 - BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
DA - 2008/10//
PY - 2008/10//
DO - 10.1007/s10237-007-0105-y
VL - 7
IS - 5
SP - 417-426
SN - 1617-7959
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000258612200008&KeyUID=WOS:000258612200008
ER -
TY - JOUR
TI - Couette flow of a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
AB - A concise and accurate solution to the problem of plane Couette flow for a binary mixture of rigid-sphere gases described by the linearized Boltzmann equation and general (specular-diffuse) Maxwell boundary conditions for each of the two species of gas particles is developed. An analytical version of the discrete-ordinates method is used to establish the velocity, heat-flow, and shear-stress profiles for both types of particles, as well as the particle-flow and heat-flow rates associated with each of the two species. Accurate numerical results are given for the case of a mixture of helium and argon confined between molybdenum and tantalum plates.
DA - 2008///
PY - 2008///
DO - 10.1016/j.euromechflu.2008.01.004
VL - 27
IS - 6
SP - 823-836
SN - 0997-7546
KW - Rarefied gas dynamics
KW - Couette flow
KW - Linearized Boltzmann equation
KW - Binary mixtures
KW - Rigid spheres
ER -
TY - CONF
TI - A high order finite difference scheme for the Stokes equations
AU - Ito, K.
AU - Qiao, Z.
C2 - 2008///
C3 - Moving interface problems and applications in fluid dynamics
DA - 2008///
DO - 10.1090/conm/466/09115
VL - 466
SP - 35-51
ER -
TY - CONF
TI - A finite element method for interface problems with locally modified triangulations
AU - Xie, H.
AU - Ito, K.
AU - Li, Zhilin
AU - Toivanen, J.
C2 - 2008///
C3 - Moving interface problems and applications in fluid dynamics
DA - 2008///
DO - 10.1090/conm/466/09122
VL - 466
SP - 179–190
ER -
TY - JOUR
TI - A continuous {N}ewton-type method for unconstrained optimization
AU - Zhang, L-H.
AU - Kelley, C T
AU - Liao, L.-Z.
T2 - Pacific Journal of Optimization
DA - 2008///
PY - 2008///
VL - 4
IS - 2
SP - 259-277
ER -
TY - JOUR
TI - Differential Galois theory of linear difference equations
AU - Hardouin, Charlotte
AU - Singer, Michael F.
T2 - MATHEMATISCHE ANNALEN
AB - We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hölder’s theorem that the Gamma function satisfies no polynomial differential equation and are able to give general results that imply, for example, that no differential relationship holds among solutions of certain classes of q-hypergeometric equations.
DA - 2008/10//
PY - 2008/10//
DO - 10.1007/s00208-008-0238-z
VL - 342
IS - 2
SP - 333-377
SN - 1432-1807
ER -
TY - JOUR
TI - Sensitivity to noise variance in a social network dynamics model
AU - Banks, H. T.
AU - Karr, A. F.
AU - Nguyen, H. K.
AU - Samuels, J. R., Jr.
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - Abstract : The dynamics of social networks are modeled with a system of continuous Stochastic Ordinary Differential Equations (SODE). With the proper amount of noise input, the SODE model captures dynamic features that are lacking in the corresponding deterministic ODE model. Therefore, sensitivity to noise levels is investigated by considering four different regimes: essentially deterministic, noise-enriched, noise-enlarged, and noise-dominated. Each regime is defined based on the behavior of solutions of the SODE, and the geometry of the regimes is categorized with stochastic simulations.
DA - 2008///
PY - 2008///
DO - 10.1090/S0033-569X-08-01124-0
VL - 66
IS - 2
SP - 233-247
SN - 1552-4485
ER -
TY - JOUR
TI - Sensitivity analysis and model assessment: Mathematical models for arterial blood flow and blood pressure
AU - Ellwein, Laura M.
AU - Tran, Hien T.
AU - Zapata, Cheryl
AU - Novak, Vera
AU - Olufsen, Mette S.
T2 - CARDIOVASCULAR ENGINEERING
DA - 2008/6//
PY - 2008/6//
DO - 10.1007/s10558-007-9047-3
VL - 8
IS - 2
SP - 94-108
SN - 1573-6806
KW - cardiovascular modeling
KW - sensitivity analysis
KW - model reduction
KW - parameter estimation
ER -
TY - JOUR
TI - Modeling heart rate regulation - Part II: Parameter identification and analysis
AU - Fowler, K. R.
AU - Gray, G. A.
AU - Olufsen, M. S.
T2 - CARDIOVASCULAR ENGINEERING
DA - 2008/6//
PY - 2008/6//
DO - 10.1007/s10558-007-9048-2
VL - 8
IS - 2
SP - 109-119
SN - 1573-6806
KW - derivative-free optimization
KW - model based prediction of heart rate
KW - sensitivity analysis
ER -
TY - JOUR
TI - Modeling heart rate regulation - Part I: Sit-to-stand versus head-up tilt
AU - Olufsen, Mette S.
AU - Alston, April V.
AU - Tran, Hien T.
AU - Ottesen, Johnny T.
AU - Novak, Vera
T2 - CARDIOVASCULAR ENGINEERING
AB - In this study we describe a model predicting heart rate regulation during postural change from sitting to standing and during head-up tilt in five healthy elderly adults. The model uses blood pressure as an input to predict baroreflex firing-rate, which in turn is used to predict efferent parasympathetic and sympathetic outflows. The model also includes the combined effects of vestibular and central command stimulation of muscle sympathetic nerve activity, which is increased at the onset of postural change. Concentrations of acetylcholine and noradrenaline, predicted as functions of sympathetic and parasympathetic outflow, are then used to estimate the heart rate response. Dynamics of the heart rate and the baroreflex firing rate are modeled using a system of coupled ordinary delay differential equations with 17 parameters. We have derived sensitivity equations and ranked sensitivities of all parameters with respect to all state variables in our model. Using this model we show that during head-up tilt, the baseline firing-rate is larger than during sit-to-stand and that the combined effect of vestibular and central command stimulation of muscle sympathetic nerve activity is less pronounced during head-up tilt than during sit-to-stand.
DA - 2008/6//
PY - 2008/6//
DO - 10.1007/s10558-007-9050-8
VL - 8
IS - 2
SP - 73-87
SN - 1573-6806
KW - mathematical modeling
KW - heart rate regulation
KW - sensitivity analysis
ER -
TY - JOUR
TI - Introduction to the special issues: Short-term cardiovascular-respiratory control mechanisms
AU - Batzel, Jerry J.
AU - Novak, Vera
AU - Kappel, Franz
AU - Olufsen, Mette S.
AU - Tran, Hien T.
T2 - CARDIOVASCULAR ENGINEERING
AB - This and the following issue of Cardiovascular Engineering are special issues reflecting research discussed during an interdisciplinary focused workshop entitled Short-term Cardiovascular–Respiratory Control Mechanisms. The workshop was organized by Mette Olufsen and Hien Tran at the Department of Mathematics at North Carolina State University, Jerry Batzel and Franz Kappel at the Institute for Mathematics and Scientific Computing, University of Graz, and Vera Novak at the Department of Gerontology at Harvard Medical School, and hosted by the American Institute of Mathematics (AIM), Palo Alto, California, October 9–13, 2006. The workshop was co-sponsored by AIM and the National Science Foundation.
DA - 2008/3//
PY - 2008/3//
DO - 10.1007/s10558-007-9053-5
VL - 8
IS - 1
SP - 1-4
SN - 1567-8822
ER -
TY - JOUR
TI - Chains in the noncrossing partition lattice
AU - Reading, Nathan
T2 - SIAM JOURNAL ON DISCRETE MATHEMATICS
AB - We establish recursions counting various classes of chains in the noncrossing partition lattice of a finite Coxeter group. The recursions specialize a general relation which is proven uniformly (i.e., without appealing to the classification of finite Coxeter groups) using basic facts about noncrossing partitions. We solve these recursions for each finite Coxeter group in the classification. Among other results, we obtain a simpler proof of a known uniform formula for the number of maximal chains of noncrossing partitions and a new uniform formula for the number of edges in the noncrossing partition lattice. All of our results extend to the $m$-divisible noncrossing partition lattice.
DA - 2008///
PY - 2008///
DO - 10.1137/07069777X
VL - 22
IS - 3
SP - 875-886
SN - 1095-7146
UR - https://doi.org/10.1137/07069777X
KW - absolute order
KW - Catalan number
KW - chain enumeration
KW - Coxeter element
KW - Coxeter group
KW - generalized cluster complex
KW - noncrossing partition
KW - parking function
ER -
TY - JOUR
TI - BCWEEVIL: A simulation model of the joint population dynamics between spruce weevil and Sitka spruce, over the lifetime of a plantation
AU - Bishir, John
AU - Yanchuk, Alvin D.
AU - Russell, John H.
AU - Polsson, Ken R.
T2 - ECOLOGICAL COMPLEXITY
AB - Abstract The spruce terminal weevil Pissodes strobi (Peck) is a major pest in western spruces, attacking trees of all ages beyond the juvenile stage, killing the leader and causing tree distortion. This paper describes a computer simulation model of the joint population dynamics within this tree/pest system, over the lifetime of a plantation, and is combined with the Province of British Columbia's Tree and Stand Simulator (TASS) to drive individual tree growth and stand establishment and development. The model differs from current models of this system, and of other similar systems, in two important ways: (1) it simulates the entire life of a stand, from planting until harvest, and (2) it is based on the underlying biological processes that govern behavior of individual weevils on and in each tree. Each model simulation begins by planting a stand using tree materials from seed or clonal hedge orchards, choosing trees either individually and independently or in groups represented as clones or families. Stand growth and mortality are advanced through a juvenile period, after which weevils appear in the stand. From this time until harvest, the model simulates daily changes in the weevil populations on each tree, tracking mortality, oviposition, and juvenile maturation and emergence, as well as weevil movement from tree to tree. Once a year, the code projects tree mortality and growth, taking into account within-stand competition and damage to leaders caused by weevil attacks. At harvest, the model computes an estimate of the merchantable timber produced by the stand. As illustrations of model output, we present (1) simulated average numbers of adult and juvenile weevils in stands generated using materials from seed orchards, both throughout a single season and also through the years from stand planting until harvest; and (2) the differential effect of weevil damage on two tree genotypes, one resistant and one susceptible, in a stand composed of adjacent clonal blocks. The results of model simulations are in agreement with some of the population dynamics statistics observed in plantations, suggesting that the model reflects biological realism and can be used as a research or management tool.
DA - 2008/9//
PY - 2008/9//
DO - 10.1016/j.ecocom.2008.05.001
VL - 5
IS - 3
SP - 260-271
SN - 1476-9840
KW - simulation model
KW - population dynamics
KW - Sitka spruce
KW - spruce and white pine weevil
KW - Pissodes strobi
ER -
TY - JOUR
TI - A respiratory system model: Parameter estimation and sensitivity analysis
AU - Fink, Martin
AU - Batzel, Jerry J.
AU - Tran, Hien
T2 - CARDIOVASCULAR ENGINEERING
DA - 2008/6//
PY - 2008/6//
DO - 10.1007/s10558-007-9051-7
VL - 8
IS - 2
SP - 120-134
SN - 1567-8822
KW - respiratory system
KW - mathematical models
KW - sensitivity analysis
KW - parameter identification
ER -
TY - JOUR
TI - Sparse directional image representations using the discrete shearlet transform
AU - Easley, Glenn
AU - Labate, Demetrio
AU - Lim, Wang-Q
T2 - APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS
AB - In spite of their remarkable success in signal processing applications, it is now widely acknowledged that traditional wavelets are not very effective in dealing multidimensional signals containing distributed discontinuities such as edges. To overcome this limitation, one has to use basis elements with much higher directional sensitivity and of various shapes, to be able to capture the intrinsic geometrical features of multidimensional phenomena. This paper introduces a new discrete multiscale directional representation called the discrete shearlet transform. This approach, which is based on the shearlet transform, combines the power of multiscale methods with a unique ability to capture the geometry of multidimensional data and is optimally efficient in representing images containing edges. We describe two different methods of implementing the shearlet transform. The numerical experiments presented in this paper demonstrate that the discrete shearlet transform is very competitive in denoising applications both in terms of performance and computational efficiency.
DA - 2008/7//
PY - 2008/7//
DO - 10.1016/j.acha.2007.09.003
VL - 25
IS - 1
SP - 25-46
SN - 1096-603X
KW - curvelets
KW - denoising
KW - image processing
KW - shearlets
KW - sparse representation
KW - wavelets
ER -
TY - JOUR
TI - Bidiagonal decompositions of oscillating systems of vectors
AU - Dopico, Froilan M.
AU - Koev, Plamen
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - We establish necessary and sufficient conditions, in the language of bidiagonal decompositions, for a matrix V to be an eigenvector matrix of a totally positive matrix. Namely, this is the case if and only if V and V - T are lowerly totally positive. These conditions translate into easy positivity requirements on the parameters in the bidiagonal decompositions of V and V - T . Using these decompositions we give elementary proofs of the oscillating properties of V . In particular, the fact that the j th column of V has j - 1 changes of sign. Our new results include the fact that the Q matrix in a QR decomposition of a totally positive matrix belongs to the above class (and thus has the same oscillating properties).
DA - 2008/6/1/
PY - 2008/6/1/
DO - 10.1016/j.laa.2007.12.002
VL - 428
IS - 11-12
SP - 2536-2548
SN - 0024-3795
KW - totally positive matrix
KW - eigenvectors
KW - variation diminishing property
ER -
TY - JOUR
TI - A bidirectionally coupled magnetoelastic model and its validation using a Galfenol unimorph sensor
AU - Mudivarthi, C.
AU - Datta, S.
AU - Atulasimha, J.
AU - Flatau, A. B.
T2 - Smart Materials & Structures
DA - 2008///
PY - 2008///
VL - 17
IS - 3
ER -
TY - JOUR
TI - Variational approach to shape derivatives
AU - Ito, Kazufumi
AU - Kunisch, Karl
AU - Peichl, Gunther H.
T2 - ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS
AB - A general framework for calculating shape derivatives for optimization problems with partial differential equations as constraints is presented. The proposed technique allows to obtain the shape derivative of the cost without the necessity to involve the shape derivative of the state variable. In fact, the state variable is only required to be Lipschitz continuous with respect to the geometry perturbations. Applications to inverse interface problems, and shape optimization for elliptic systems and the Navier-Stokes equations are given.
DA - 2008///
PY - 2008///
DO - 10.1051/cocv:2008002
VL - 14
IS - 3
SP - 517-539
SN - 1292-8119
KW - shape derivative
ER -
TY - JOUR
TI - Lacunae based stabilization of PMLs
AU - Qasimov, H.
AU - Tsynkov, S.
T2 - Journal of Computational Physics
AB - Perfectly matched layers (PMLs) are used for the numerical solution of wave propagation problems on unbounded regions. They surround the finite computational domain (obtained by truncation) and are designed to attenuate and completely absorb all the outgoing waves while producing no reflections from the interface between the domain and the layer. PMLs have demonstrated excellent performance for many applications. However, they have also been found prone to instabilities that manifest themselves when the simulation time is long. Hereafter, we propose a modification that stabilizes any PML applied to a hyperbolic partial differential equation/system that satisfies the Huygens’ principle (such as the 3D d’Alembert equation or Maxwell’s equations in vacuum). The modification makes use of the presence of lacunae in the corresponding solutions and allows us to establish a temporally uniform error bound for arbitrarily long-time intervals. At the same time, it does not change the original PML equations. Hence, the matching properties of the layer, as well as any other properties deemed important, are fully preserved. We also emphasize that besides the aforementioned PML instabilities per se, the methodology can be used to cure any other undesirable long-term computational phenomenon, such as the accuracy loss of low order absorbing boundary conditions.
DA - 2008/7//
PY - 2008/7//
DO - 10.1016/j.jcp.2008.04.018
VL - 227
IS - 15
SP - 7322-7345
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2008.04.018
DB - Crossref
KW - perfectly matched layer (PML)
KW - long-time stability
KW - weak well-posedness
KW - wave propagation
KW - hyperbolicity
KW - the Huygens' principle
KW - Lacunae
KW - Maxwell's equations
KW - artificial boundary conditions (ABCs)
KW - numerical solution
ER -
TY - JOUR
TI - Finite difference approximations for stochastic control systems with delay
AU - Chang, Mou-Hsiung
AU - Pang, Tao
AU - Pemy, Moustapha
T2 - STOCHASTIC ANALYSIS AND APPLICATIONS
AB - Abstract This article considers the computation issues of the infinite dimensional HJB equation arising from the finite horizon optimal control problem of a general system of stochastic functional differential equations with a bounded memory treated in [2 Chang , M.H. , Pang , T. , and Pemy , M. accepted. Optimal control of functional stochastic differential equations with a bounded memory. Stochastics 80 ( 1 ): 69 – 96 . [Google Scholar]]. The finite difference scheme, using the result in [1 Barles , G. , and Souganidis , P.E. 1991 . Convergence of approximative schemes for fully nonlinear second order equations . J. Asymptotic Analysis 4 : 557 – 579 . [Google Scholar]], is obtained to approximate the viscosity solution of the infinite dimensional HJB equation. The convergence of the scheme is proved using the Banach fixed point theorem. The computational algorithm also is provided based on the scheme obtained.
DA - 2008///
PY - 2008///
DO - 10.1080/07362990802006980
VL - 26
IS - 3
SP - 451-470
SN - 0736-2994
KW - finite difference approximation
KW - stochastic control
KW - stochastic functional differential equations
KW - viscosity solutions
ER -
TY - JOUR
TI - Dynamic models for insect mortality due to exposure to insecticides
AU - Banks, H. T.
AU - Banks, John E.
AU - Joyner, Sarah Lynn
AU - Stark, John D.
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - Ordinary differential equation models for insecticide induced sublethal damage and delayed death in insect populations are considered. It is shown that such models with time-varying mortality rates provide excellent fits to experimental data for populations subjected to numerous levels of insecticide exposure. The effects on fecundity rates are also examined.
DA - 2008/7//
PY - 2008/7//
DO - 10.1016/j.mcm.2007.10.005
VL - 48
IS - 1-2
SP - 316-332
SN - 1872-9479
KW - differential equation models
KW - insect populations
KW - insecticide exposure
KW - time-varying mortality rates
ER -
TY - JOUR
TI - Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems
AU - Fowler, K. R.
AU - Reese, J. P.
AU - Kees, C. E.
AU - Dennis, J. E., Jr.
AU - Kelley, C. T.
AU - Miller, C. T.
AU - Audet, C.
AU - Booker, A. J.
AU - Couture, G.
AU - Darwin, R. W.
AU - Farthing, M. W.
AU - Finkel, D. E.
AU - Gablonsky, J. M.
AU - Gray, G.
AU - Kolda, T. G.
T2 - ADVANCES IN WATER RESOURCES
AB - Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research.
DA - 2008/5//
PY - 2008/5//
DO - 10.1016/j.advwatres.2008.01.010
VL - 31
IS - 5
SP - 743-757
SN - 1872-9657
KW - sampling methods
KW - genetic algorithm
KW - local minima
KW - nondifferentiable objective function
ER -
TY - JOUR
TI - An explicit jump immersed interface method for two-phase Navier-Stokes equations with interfaces
AU - Rutka, Vita
AU - Li, Zhilin
T2 - COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
AB - Abstract In this paper, we propose an explicit jump immersed interface method (EJIIM) for the incompressible Navier–Stokes equations with a discontinuous viscosity and singular forces along one or several interfaces in the solution domain. The EJIIM is used to get a second-order finite difference discretization at the grid points near or on the interface even if the jump conditions for the two-phase flow are complicated. The new method is based on a projection method with modifications only at grid points near or on the interface. From the derivation of the new method, we expect fully second-order accuracy for the velocity and nearly second-order accuracy for the pressure in the maximum norm including those grid points near or on the interface. This has been confirmed in our numerical experiments. Furthermore, the computed solutions are sharp across the interface. The work here is a necessary first step in developing second-order accurate algorithm for two-phase Navier–Stokes equations with a moving interface.
DA - 2008///
PY - 2008///
DO - 10.1016/j.cma.2007.12.016
VL - 197
IS - 25-28
SP - 2317-2328
SN - 1879-2138
KW - Navier-Stokes equations
KW - interface
KW - discontinuous viscosity
KW - immersed interface method
KW - explicit jump immersed interface method
KW - projection method
ER -
TY - JOUR
TI - Algorithms for computations in local symmetric spaces
AU - Daniel, Jennifer R.
AU - Helminck, Aloysius G.
T2 - COMMUNICATIONS IN ALGEBRA
AB - In the last two decades much of the algebraic/combinatorial structure of Lie groups, Lie algebras, and their representations has been implemented in several excellent computer algebra packages, including LiE, GAP4, Chevie, Magma, and Maple. The structure of reductive symmetric spaces or more generally symmetric k-varieties is very similar to that of the underlying Lie group, with a few additional complications. A computer algebra package enabling one to do computations related to these symmetric spaces would be an important tool for researchers in many areas of mathematics, including representation theory, Harish Chandra modules, singularity theory, differential and algebraic geometry, mathematical physics, character sheaves, Lie theory, etc. In this article we lay the groundwork for computing the fine structure of symmetric spaces over the real numbers and other base fields, give a complete set of algorithms for computing the fine structure of symmetric varieties and use this to compute nice bases for the local symmetric varieties.
DA - 2008/5//
PY - 2008/5//
DO - 10.1080/00927870801940434
VL - 36
IS - 5
SP - 1758-1788
SN - 1532-4125
KW - Lie algebras of linear algebraic groups
KW - symmetric spaces
ER -
TY - JOUR
TI - Adjoint estimation using direct transcription multipliers: compressed trapezoidal method
AU - Engelsone, Anna
AU - Campbell, Stephen L.
T2 - OPTIMIZATION AND ENGINEERING
DA - 2008/9//
PY - 2008/9//
DO - 10.1007/s11081-008-9038-2
VL - 9
IS - 3
SP - 291-305
SN - 1573-2924
KW - direct transcription
KW - adjoint estimation
KW - trapezoid method
KW - optimal control
ER -
TY - JOUR
TI - A bound for the Rosenfeld-Grobner algorithm
AU - Golubitsky, Oleg
AU - Kondratieva, Marina
AU - Maza, Marc Moreno
AU - Ovchinnikov, Alexey
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal generated by a set of ordinary differential polynomials in n indeterminates. For a set of ordinary differential polynomials F, let M(F) be the sum of maximal orders of differential indeterminates occurring in F. We propose a modification of the Rosenfeld-Groebner algorithm, in which for every intermediate polynomial system F, the bound M(F) is less than or equal to (n-1)!M(G), where G is the initial set of generators of the radical ideal. In particular, the resulting regular systems satisfy the bound. Since regular ideals can be decomposed into characterizable components algebraically, the bound also holds for the orders of derivatives occurring in a characteristic decomposition of a radical differential ideal. We also give an algorithm for converting a characteristic decomposition of a radical differential ideal from one ranking into another. This algorithm performs all differentiations in the beginning and then uses a purely algebraic decomposition algorithm.
DA - 2008/8//
PY - 2008/8//
DO - 10.1016/j.jsc.2007.12.002
VL - 43
IS - 8
SP - 582-610
SN - 0747-7171
KW - differential algebra
KW - characteristic sets
KW - radical differential ideals
KW - decomposition into regular components
ER -
TY - JOUR
TI - Representation of Fourier integral operators using shearlets
AU - Guo, Kanghui
AU - Labate, Demetrio
T2 - JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
DA - 2008///
PY - 2008///
DO - 10.1007/s00041-008-9018-0
VL - 14
IS - 3
SP - 327-371
SN - 1531-5851
KW - curvelets
KW - Fourier integral operators
KW - pseudo differential operators
KW - shearlets
KW - sparsity
KW - wavelets
ER -
TY - JOUR
TI - On the detection of small parameter variations in linear uncertain systems
AU - Nikoukhah, Ramine
AU - Campbell, Steve L.
T2 - EUROPEAN JOURNAL OF CONTROL
AB - The problem of detecting small parameter variations in linear uncertain systems, with the possibility of injecting an input signal to enhance detection, is considered. A constructive method for the construction of an optimal input signal for achieving guaranteed detection with specified precision is presented. The method is an extension of the multi-model approach used for the construction of auxiliary signals for failure detection. The application to the problem of incipient fault detection is investigated.
DA - 2008///
PY - 2008///
DO - 10.3166/EJC.14.158-171
VL - 14
IS - 2
SP - 158-171
SN - 1435-5671
KW - parameter identification
KW - incipient fault detection
KW - auxiliary signal design
KW - multi-model formulation
ER -
TY - JOUR
TI - Multipoint boundary value problems for nonlinear ordinary differential equations
AU - Rodriguez, Jesus
AU - Taylor, Padraic
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
AB - Abstract In this paper we provide sufficient conditions for the existence of solutions to multipoint boundary value problems for nonlinear ordinary differential equations. We consider the case where the solution space of the associated linear homogeneous boundary value problem is less than 2. When this solution space is trivial, we establish existence results via the Schauder Fixed Point Theorem. In the resonance case, we use a projection scheme to provide criteria for the solvability of our nonlinear boundary value problem. We accomplish this by analyzing a link between the behavior of the nonlinearity and the solution set of the associated linear homogeneous boundary value problem.
DA - 2008/6/1/
PY - 2008/6/1/
DO - 10.1016/j.na.2007.03.038
VL - 68
IS - 11
SP - 3465-3474
SN - 0362-546X
KW - boundary value problems
KW - Schauder Fixed Point Theorem
KW - Lyapunov-Schmidt
KW - projection
ER -
TY - JOUR
TI - Infinite-dimensional Lie algebras in 4D conformal quantum field theory
AU - Bakalov, Bojko
AU - Nikolov, Nikolay M.
AU - Rehren, Karl-Henning
AU - Todorov, Ivan
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - The concept of global conformal invariance (GCI) opens the way of applying algebraic techniques, developed in the context of 2-dimensional chiral conformal field theory, to a higher (even) dimensional space-time. In particular, a system of GCI scalar fields of conformal dimension two gives rise to a Lie algebra of harmonic bilocal fields, V_m(x,y), where the m span a finite dimensional real matrix algebra M closed under transposition. The associative algebra M is irreducible iff its commutant M' coincides with one of the three real division rings. The Lie algebra of (the modes of) the bilocal fields is in each case an infinite dimensional Lie algebra: a central extension of sp(infty,R) corresponding to the field R of reals, of u(infty,infty) associated to the field C of complex numbers, and of so*(4 infty) related to the algebra H of quaternions. They give rise to quantum field theory models with superselection sectors governed by the (global) gauge groups O(N), U(N), and U(N,H)=Sp(2N), respectively.
DA - 2008/5/16/
PY - 2008/5/16/
DO - 10.1088/1751-8113/41/19/194002
VL - 41
IS - 19
SP -
SN - 1751-8121
ER -
TY - JOUR
TI - Exchange lemmas 2: General Exchange Lemma
AU - Schecter, Stephen
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - Exchange lemmas are used in geometric singular perturbation theory to track flows near normally hyperbolic invariant manifolds. We prove a General Exchange Lemma, and show that it implies versions of existing exchange lemmas for rectifiable slow flows and loss-of-stability turning points.
DA - 2008/7/15/
PY - 2008/7/15/
DO - 10.1016/j.jde.2007.10.021
VL - 245
IS - 2
SP - 411-441
SN - 0022-0396
KW - geometric singular perturbation theory
KW - normally hyperbolic invariant manifold
ER -
TY - JOUR
TI - Exchange lemmas 1: Deng's lemma
AU - Schecter, Stephen
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - Deng's lemma gives estimates on the behavior of solutions of ordinary differential equations in the neighborhood of a partially hyperbolic equilibrium. We prove a generalization in which “partially hyperbolic equilibrium” is replaced by “normally hyperbolic invariant manifold.”
DA - 2008/7/15/
PY - 2008/7/15/
DO - 10.1016/j.jde.2007.08.011
VL - 245
IS - 2
SP - 392-410
SN - 0022-0396
KW - geometric singular perturbation theory
KW - normally hyperbolic invariant manifold
ER -
TY - JOUR
TI - A fast finite difference method for biharmonic equations on irregular domains and its application to an incompressible Stokes flow
AU - Chen, Guo
AU - Li, Zhilin
AU - Lin, Ping
T2 - ADVANCES IN COMPUTATIONAL MATHEMATICS
DA - 2008/8//
PY - 2008/8//
DO - 10.1007/s10444-007-9043-6
VL - 29
IS - 2
SP - 113-133
SN - 1572-9044
KW - biharmonic equation
KW - irregular domain
KW - augmented method
KW - immersed interface method
KW - incompressible stokes flow
ER -
TY - JOUR
TI - A brief review of some approaches to hysteresis in viscoelastic polymers
AU - Banks, H. T.
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
AB - We give a brief review of hysteresis in viscoelastic polymers. The efforts surveyed range from phenomenological to molecular modelling with applications involving recent efforts on elastomers to biotissue.
DA - 2008/8/1/
PY - 2008/8/1/
DO - 10.1016/j.na.2008.02.103
VL - 69
IS - 3
SP - 807-815
SN - 1873-5215
KW - stress-strain laws
KW - hysteresis
KW - viseoelasticity
KW - polymers
KW - internal variables
ER -
TY - JOUR
TI - Tannakian approach to linear differential algebraic groups
AU - Ovchinnikov, Alexey
T2 - TRANSFORMATION GROUPS
AB - Tannaka’s theorem states that a linear algebraic group G is determined by the category of finite-dimensional G-modules and the forgetful functor. We extend this result to linear differential algebraic groups by introducing a category corresponding to their representations and show how this category determines such a group.
DA - 2008/6//
PY - 2008/6//
DO - 10.1007/s00031-008-9010-4
VL - 13
IS - 2
SP - 413-446
SN - 1531-586X
ER -
TY - JOUR
TI - Radiative transfer in a multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination by obliquely incident parallel rays
AU - Garcia, R. D. M.
AU - Siewert, C. E.
AU - Yacout, A. M.
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - Abstract The ADO (analytical discrete ordinates) method, a pre-processing procedure, and the break-point analysis developed for azimuthally symmetric problems in a previous work are generalized and used to solve a radiative-transfer problem defined by a finite, plane–parallel, multi-layer medium subject to Fresnel boundary and interface conditions and uniform illumination in the form of obliquely incident parallel rays. Illumination is modeled by Dirac distributions in each of the two angles (polar and azimuthal) that define the direction of propagation of the incident rays. Accurate numerical results are tabulated for two sets of test problems.
DA - 2008///
PY - 2008///
DO - 10.1016/j.jqsrt.2008.03.012
VL - 109
IS - 12-13
SP - 2151-2170
SN - 0022-4073
ER -
TY - JOUR
TI - Modeling of viscoelastic shear: A nonlinear stick-slip formulation
AU - Banks, H. T.
AU - Medhin, N. G.
AU - Pinter, G. A.
T2 - Dynamic Systems and Applications
DA - 2008///
PY - 2008///
VL - 17
IS - 2
SP - 383-405
ER -
TY - JOUR
TI - The modeling of magnetomechanical sensors in laminated structures
AU - Datta, S.
AU - Atulasimha, J.
AU - Mudivarthi, C.
AU - Flatau, A. B.
T2 - Smart Materials & Structures
DA - 2008///
PY - 2008///
VL - 17
IS - 2
ER -
TY - JOUR
TI - Solutions of the optimized closure integral equation theory: Heteronuclear polyatomic fluids
AU - Marucho, M.
AU - Kelley, C. T.
AU - Pettitt, B. Montgomery
T2 - JOURNAL OF CHEMICAL THEORY AND COMPUTATION
AB - Recently, we developed a thermodynamically optimized integral equation method which has been successfully tested on both simple and homonuclear diatomic Lennard-Jones fluids [J. Chem. Phys. 2007, 126, 124107]. The systematic evaluation of correlation functions required by the optimization of the chemical potential has shown a clear need for more efficient algorithms to solve these integral equations. In the present paper we introduce a high-performance algorithm which is found to be faster and more efficient than the direct Picard iteration. Here we have utilized this to solve the aforementioned optimized theory for molecules more complex than those considered previously. We analyzed representative models for heteronuclear diatomic and triatomic polar molecular fluids. We include results for several modified SPC-like models for water, obtaining site-site correlation functions in good agreement with simulation data.
DA - 2008/3//
PY - 2008/3//
DO - 10.1021/ct700202h
VL - 4
IS - 3
SP - 385-396
SN - 1549-9626
ER -
TY - JOUR
TI - Root multiplicities of the indefinite Kac-Moody algebras of symplectic type
AU - Klima, Vicky W.
AU - Misra, Kaillash C.
T2 - COMMUNICATIONS IN ALGEBRA
AB - We study the root multiplicities of the indefinite Kac–Moody algebras by viewing them as weight multiplicities of certain integrable -modules. Then using Kang's root multiplicity formula and the path crystal for integrable -modules we calculate the multiplicities of a family of roots for . In particular, we show that for any positive integer k the multiplicity of − 2α−1 − kδ as a root of is a polynomial in n of degree at most k. Furthermore, we observe that Frenkel's conjectured root multiplicity bound does not hold for roots of .
DA - 2008/2//
PY - 2008/2//
DO - 10.1080/00927870701724367
VL - 36
IS - 2
SP - 764-782
SN - 0092-7872
KW - crystal bases
KW - Kac-Moody algebras
KW - root multiplicities
ER -
TY - JOUR
TI - Particular solutions of the linearized Boltzmann equation for a binary mixture of rigid spheres
AU - Garcia, R. D. M.
AU - Siewert, C. E.
T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
DA - 2008/3//
PY - 2008/3//
DO - 10.1007/s00033-007-6106-y
VL - 59
IS - 2
SP - 281-292
SN - 1420-9039
KW - rarefied gas dynamics
KW - binary mixtures
KW - rigid spheres
KW - particular solutions
KW - linearized Boltzmann equation
KW - Chapman-Enskog and Burnett functions
ER -
TY - JOUR
TI - Low-dimensional polytope approximation and its applications to nonnegative matrix factorization
AU - Chu, Moody T.
AU - Lin, Matthew M.
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this study, nonnegative matrix factorization is recast as the problem of approximating a polytope on the probability simplex by another polytope with fewer facets. Working on the probability simplex has the advantage that data are limited to a compact set with a known boundary, making it easier to trace the approximation procedure. In particular, the supporting hyperplane that separates a point from a disjoint polytope, a fact asserted by the Hahn–Banach theorem, can be calculated in finitely many steps. This approach leads to a convenient way of computing the proximity map which, in contrast to most existing algorithms where only an approximate map is used, finds the unique and global minimum per iteration. This paper sets up a theoretical framework, outlines a numerical algorithm, and suggests an effective implementation. Testing results strongly evidence that this approach obtains a better low rank nonnegative matrix approximation in fewer steps than conventional methods.
DA - 2008///
PY - 2008///
DO - 10.1137/070680436
VL - 30
IS - 3
SP - 1131-1155
SN - 1064-8275
KW - nonnegative matrix factorization
KW - polytope approximation
KW - probability simplex
KW - supporting hyperplane
KW - Hahn-Banach theorem
ER -
TY - JOUR
TI - Genomic analysis of closely related astroviruses
AU - Strain, Errol
AU - Kelley, Laura A.
AU - Schultz-Cherry, Stacey
AU - Muse, Spencer V.
AU - Koci, Matthew D.
T2 - JOURNAL OF VIROLOGY
AB - ABSTRACT To understand astrovirus biology, it is essential to understand factors associated with its evolution. The current study reports the genomic sequences of nine novel turkey astrovirus (TAstV) type 2-like clinical isolates. This represents, to our knowledge, the largest genomic-length data set available for any one astrovirus type. The comparison of these TAstV sequences suggests that the TAstV species contains multiple subtypes and that recombination events have occurred across the astrovirus genome. In addition, the analysis of the capsid gene demonstrated evidence for both site-specific positive selection and purifying selection.
DA - 2008/5//
PY - 2008/5//
DO - 10.1128/JVI.01993-07
VL - 82
IS - 10
SP - 5099-5103
SN - 0022-538X
ER -
TY - JOUR
TI - Approximate factorization of multivariate polynomials using singular value decomposition
AU - Kaltofen, Erich
AU - May, John P.
AU - Yang, Zhengfeng
AU - Zhi, Lihong
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We describe the design, implementation and experimental evaluation of new algorithms for computing the approximate factorization of multivariate polynomials with complex coefficients that contain numerical noise. Our algorithms are based on a generalization of the differential forms introduced by W. Ruppert and S. Gao to many variables, and use singular value decomposition or structured total least squares approximation and Gauss–Newton optimization to numerically compute the approximate multivariate factors. We demonstrate on a large set of benchmark polynomials that our algorithms efficiently yield approximate factorizations within the coefficient noise even when the relative error in the input is substantial (10−3).
DA - 2008/5//
PY - 2008/5//
DO - 10.1016/j.jsc.2007.11.005
VL - 43
IS - 5
SP - 359-376
SN - 0747-7171
KW - multivariate polynomial factorization
KW - approximate factorization
KW - singular value decomposition
KW - numerical algebra
KW - Gauss-Newton optimization
ER -
TY - JOUR
TI - Nilpotent variety of a reductive monoid
AU - Putcha, Mohan S.
T2 - JOURNAL OF ALGEBRAIC COMBINATORICS
AB - In this paper we study the variety M nil of nilpotent elements of a reductive monoid M. In general this variety has a completely different structure than the variety G uni of unipotent elements of the unit group G of M. When M has a unique non-trivial minimal or maximal G×G-orbit, we find a precise description of the irreducible components of M nil via the combinatorics of the Renner monoid of M and the Weyl group of G. In particular for a semisimple monoid M, we find necessary and sufficient conditions for the variety M nil to be irreducible.
DA - 2008/5//
PY - 2008/5//
DO - 10.1007/s10801-007-0087-y
VL - 27
IS - 3
SP - 275-292
SN - 0925-9899
KW - reductive monoid
KW - nilpotent variety
KW - unipotent variety
KW - Renner monoid
KW - Weyl group
ER -
TY - JOUR
TI - Modelling of propagating shear waves in biotissue employing an internal variable approach to dissipation
AU - Banks, H. T.
AU - Luke, N. S.
T2 - Communications in Computational Physics
DA - 2008///
PY - 2008///
VL - 3
IS - 3
SP - 603-640
ER -
TY - JOUR
TI - Finite difference approximation for stochastic optimal stopping problems with delays
AU - Chang, M. H.
AU - Pang, T.
AU - Pemy, M.
T2 - Journal of Industrial and Management Optimization
AB - This paper considers the computational issue of the optimal stoppingproblem for the stochastic functional differential equation treatedin [6] The finite difference method developed by Barlesand Souganidis [3] is used to obtain a numerical approximationfor the viscosity solution of the infinite dimensionalHamilton-Jacobi-Bellman variational inequality (HJBVI) associatedwith the optimal stopping problem. The convergence results are thenestablished.
DA - 2008///
PY - 2008///
DO - 10.3934/jimo.2008.4.227
VL - 4
IS - 2
SP - 227-246
ER -
TY - JOUR
TI - Estimation of invasive pneumococcal disease dynamics parameters and the impact of conjugate vaccination in Australia
AU - Sutton, K. L.
AU - Banks, H. T.
AU - Castillo-Chavez, C.
T2 - Mathematical Biosciences and Engineering
AB - Pneumococcal diseases, or infections from the etiological agent Streptococcus pneumoniae, have long been a major cause of morbidity and mortality worldwide. Recent advances in the development of vaccines for these infections have raised questions concerning their widespread and/or long-term use. In this work, we use surveillance data collected by the Australian National Notifiable Diseases Surveillance system to estimate parameters in a mathematical model of pneumococcal infection dynamics in a population with partial vaccination. The parameters obtained are of particular interest as they are not typically available in reported literature or measurable. The calibrated model is then used to assess the impact of the recent federally funded program that provides pneumococcal vaccines to large risk groups. The results presented here suggest the state of these infections may be changing in response to the programs, and warrants close quantitative monitoring.
DA - 2008///
PY - 2008///
DO - 10.3934/mbe.2008.5.175
VL - 5
IS - 1
SP - 175-204
ER -
TY - JOUR
TI - Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer
AU - Chang, Y. H.
AU - Jau, G. C.
AU - Pao, C. V.
T2 - Nonlinear Analysis. Real World Applications
AB - Abstract In this paper we investigate the blowup property and global existence of a solution for a coupled system of first-order partial differential equation and ordinary differential equation which arises from a catalytic converter in automobile engineering. It is shown, in terms of a single physical parameter σ , that a unique bounded global solution exists if σ σ and the solution blows up in finite time if σ > σ ¯ , where σ σ ¯ . Various estimates for σ ¯ and its associate blow-up time T * are explicitly given. The value of T * can be used to estimate the ignition time and ignition length of the ignition system which is an important concern in automobile engineering.
DA - 2008///
PY - 2008///
DO - 10.1016/j.nonrwa.2007.01.002
VL - 9
IS - 3
SP - 822-829
ER -
TY - JOUR
TI - Are Buchberger's criteria necessary for the chain condition? (vol 42, pg 717, 2007)
AU - Hong, H.
AU - Perry, J.
T2 - Journal of Symbolic Computation
DA - 2008///
PY - 2008///
VL - 43
IS - 3
SP - 233-233
ER -
TY - JOUR
TI - Time-varying vital rates in ecotoxicology: Selective pesticides and aphid population dynamics
AU - Banks, J. E.
AU - Dick, L. K.
AU - Banks, H. T.
AU - Stark, J. D.
T2 - ECOLOGICAL MODELLING
AB - Population dynamics models are useful predictive tools in applied ecology, and especially toxicological risk assessment. Many models that are useful for capturing deterministic constant-parameter dynamics are inadequate for dealing with temporally variable life history parameter values typical of many anthropogenic disturbances, including those associated with toxicological insults. Using aphid-insecticide population data as an example, here we show that constant-parameter versions of commonly used population dynamics models (a matrix model and a simple differential equation model) do not adequately capture the population dynamics of aphids subjected to a selective pesticide. However, a simple modification of the differential equation model with time-varying mortality rates provides a highly accurate fit to aphid population data. Our results suggest that variable coefficient differential equation models with time-dependent parameters provide an accurate and simple means of assessing the effects of disturbances on populations in cases where the effects of disturbance vary significantly through time. We suggest that this approach has potential for a wide range of ecological applications.
DA - 2008/1/10/
PY - 2008/1/10/
DO - 10.1016/j.ecolmodel.2007.07.022
VL - 210
IS - 1-2
SP - 155-160
SN - 0304-3800
KW - ecotoxicology
KW - partial differential equation
KW - Sinko-Streifer
KW - sublethal effects
KW - inverse problem
KW - parameter estimates
KW - Aphididae
KW - risk assessment
ER -
TY - JOUR
TI - Quantum algebras associated with Bell states
AU - Zhang, Yong
AU - Jing, Naihuan
AU - Ge, Mo-Lin
T2 - JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
AB - The antisymmetric solution of the braided Yang--Baxter equation called the Bell matrix becomes interesting in quantum information theory because it can generate all Bell states from product states. In this paper, we study the quantum algebra through the FRT construction of the Bell matrix. In its four dimensional representations via the coproduct of its two dimensional representations, we find algebraic structures including a composition series and a direct sum of its two dimensional representations to characterize this quantum algebra. We also present the quantum algebra using the FRT construction of Yang--Baxterization of the Bell matrix.
DA - 2008/2/8/
PY - 2008/2/8/
DO - 10.1088/1751-8113/41/5/055310
VL - 41
IS - 5
SP -
SN - 1751-8121
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-43049099685&partnerID=MN8TOARS
ER -
TY - JOUR
TI - On the use of Fresnel boundary and interface conditions in radiative-transfer calculations for multilayered media
AU - Garcia, R. D. M.
AU - Siewert, C. E.
AU - Yacout, A. M.
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - The ADO (analytical discrete ordinates) method is used to establish a concise and accurate solution for a multi-layer radiative-transfer problem with Fresnel boundary and interface conditions. A finite plane-parallel medium composed of a number (K) of sub-strata with different material properties is considered to be illuminated by isotropically incident radiation. While a general result is obtained, emphasis in the numerical work is given to computing accurately the currents and the intensities that exit each of the two exterior surfaces. Monochromatic forms (with anisotropic scattering) of the radiative-transfer equation are used, and numerical results are given for several specific cases. The complications introduced by the Fresnel boundary and interface conditions are well resolved, so that the numerical results obtained are thought to define a very high standard.
DA - 2008/3//
PY - 2008/3//
DO - 10.1016/j.jqsrt.2007.09.013
VL - 109
IS - 5
SP - 752-769
SN - 0022-4073
KW - radiative transfer
KW - discrete ordinates
KW - Fresnel conditions
KW - multilayers
ER -
TY - JOUR
TI - Nonlinear optimal control techniques for vibration attenuation using magnetostrictive actuators
AU - Oates, William S.
AU - Smith, Ralph C.
T2 - JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES
AB - This article addresses the development of a nonlinear control design for attenuating structural vibrations using magnetostrictive transducers operating in nonlinear and highly hysteretic operating regimes. We consider as a prototype a thin plate subjected to exogenous pressure waves and controlled via Terfenol-D transducers at the plate edges; however, the methodology is sufficiently general to encompass a wide range of structures and magnetic transducer designs. Hysteresis inherent to the transducer materials is quantified using a homogenized energy framework and the resulting nonlinear constitutive relations are used to construct a PDE representation and corresponding finite dimensional model of the structural system. We employ optimal control theory to construct nonlinear open loop control inputs which accommodate the hysteresis inherent to the transducers but are not robust with regard to unmodeled dynamics or disturbances. Robustness is incorporated by employing perturbation techniques to provide linear feedback laws acting on measured disturbances. As illustrated via numerical examples, the resulting hybrid control design provides excellent control authority and robustness for transducers operating in hysteretic and nonlinear regimes.
DA - 2008/2//
PY - 2008/2//
DO - 10.1177/1045389X06074159
VL - 19
IS - 2
SP - 193-209
SN - 1530-8138
KW - nonlinear optimal control
KW - perturbation control
KW - hysteresis
KW - nonlinear magnetic transducers
ER -
TY - JOUR
TI - Immersed-interface finite-element methods for elliptic interface problems with nonhomogeneous jump conditions
AU - Gong, Yan
AU - Li, Bo
AU - Li, Zhilin
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - In this work, a class of new finite-element methods, called immersed-interface finite-element methods, is developed to solve elliptic interface problems with nonhomogeneous jump conditions. Simple non-body-fitted meshes are used. A single function that satisfies the same nonhomogeneous jump conditions is constructed using a level-set representation of the interface. With such a function, the discontinuities across the interface in the solution and flux are removed, and an equivalent elliptic interface problem with homogeneous jump conditions is formulated. Special finite-element basis functions are constructed for nodal points near the interface to satisfy the homogeneous jump conditions. Error analysis and numerical tests are presented to demonstrate that such methods have an optimal convergence rate. These methods are designed as an efficient component of the finite-element level-set methodology for fast simulation of interface dynamics that does not require remeshing.
DA - 2008///
PY - 2008///
DO - 10.1137/060666482
VL - 46
IS - 1
SP - 472-495
SN - 1095-7170
KW - elliptic interface problems
KW - nonhomogeneous jump conditions
KW - immersed-interface finite-element method
KW - level-set functions
KW - error estimates
ER -
TY - JOUR
TI - Spillover phenomenon in quadratic model updating
AU - Chu, Moody T.
AU - Datta, Biswa
AU - Lin, Wen-Wei
AU - Xu, Shufang
T2 - AIAA JOURNAL
AB - Model updating concerns the modification of an existing but inaccurate model with measured data. For models characterized by quadratic pencils, the measured data usually involve incomplete knowledge of natural frequencies, mode shapes, or other spectral information. In conducting the updating, it is often desirable to match only the part of observed data without tampering with the other part of unmeasured or unknown eigenstructure inherent in the original model. Such an updating, if possible, is said to have no spillover. This paper studies the spillover phenomenon in the updating of quadratic pencils. In particular, it is shown that an updating with no spillover is always possible for undamped quadratic pencils, whereas spillover for damped quadratic pencils is generally unpreventable.
DA - 2008/2//
PY - 2008/2//
DO - 10.2514/1.31320
VL - 46
IS - 2
SP - 420-428
SN - 1533-385X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-43649088765&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Stable solutions of a scalar conservation law for particle-size segregation in dense granular avalanches
AU - Shearer, M.
AU - Gray, J. M. N. T.
AU - Thornton, A. R.
T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS
AB - Dense, dry granular avalanches are very efficient at sorting the larger particles towards the free surface of the flow, and finer grains towards the base, through the combined processes of kinetic sieving and squeeze expulsion. This generates an inversely graded particle-size distribution, which is fundamental to a variety of pattern formation mechanisms, as well as subtle size-mobility feedback effects, leading to the formation of coarse-grained lateral levees that create channels in geophysical flows, enhancing their run-out. In this paper we investigate some of the properties of a recent model [Gray, J. M. N. T. & Thornton, A. R. (2005) A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc . 461, 1447–1473]; [Thornton, A. R., Gray, J. M. N. T. & Hogg, A. J. (2006) A three-phase mixture theory for particle size segregation in shallow granular free-surface flows. J. Fluid. Mech . 550, 1–25] for the segregation of particles of two sizes but the same density in a shear flow typical of shallow avalanches. The model is a scalar conservation law in space and time, for the volume fraction of smaller particles, with non-constant coefficients depending on depth within the avalanche. It is proved that for steady flow from an inlet, complete segregation occurs beyond a certain finite distance down the slope, no matter what the mixture at the inlet. In time-dependent flow, dynamic shock waves can develop; they are interfaces separating different mixes of particles. Shock waves are shown to be stable if and only if there is a greater concentration of large particles above the interface than below. Constructions with shocks and rarefaction waves are demonstrated on a pair of physically relevant initial boundary value problems, in which a region of all small particles is penetrated from the inlet by either a uniform mixture of particles or by a layer of small particles over a layer of large particles. In both cases, and under a linear shear flow, solutions are constructed for all time and shown to have similar structure for all choices of parameters.
DA - 2008/2//
PY - 2008/2//
DO - 10.1017/S0956792507007280
VL - 19
SP - 61-86
SN - 1469-4425
ER -
TY - JOUR
TI - Sensory irritation response in rats: Modeling, analysis and validation
AU - Yokley, Karen A.
AU - Tran, Hien
AU - Schlosser, Paul M.
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
DA - 2008/2//
PY - 2008/2//
DO - 10.1007/s11538-007-9268-z
VL - 70
IS - 2
SP - 555-588
SN - 0092-8240
KW - sensory response
KW - PBPK
KW - formaldehyde
ER -
TY - JOUR
TI - Branched organs: Mechanics of morphogenesis by multiple mechanisms
AU - Lubkin, Sharon R.
T2 - MULTISCALE MODELING OF DEVELOPMENTAL SYSTEMS
AB - Branching morphogenesis is ubiquitous and important in creating bulk transport systems. Branched ducts can be generated by several different mechanisms including growth, cell rearrangements, contractility, adhesion changes, and other mechanisms. We have developed several models of the mechanics of cleft formation, which we review. We discuss the implications of several candidate mechanisms and review what has been found in models and in experiments.
DA - 2008///
PY - 2008///
DO - 10.1016/s0070-2153(07)81008-8
VL - 81
SP - 249-+
SN - 0070-2153
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000252263000008&KeyUID=WOS:000252263000008
ER -
TY - JOUR
TI - Total decoupling of general quadratic pencils, Part II: Structure preserving isospectral flows
AU - Chu, Moody T.
AU - Del Buono, Nicoletta
T2 - JOURNAL OF SOUND AND VIBRATION
AB - Abstract Quadratic pencils, λ 2 M + λ C + K , where M, C, and K are n × n real matrices with or without some additional properties such as symmetry, connectivity, bandedness, or positive definiteness, arise in many important applications. Recently an existence theory has been established, showing that almost all n-degree-of-freedom second-order systems can be reduced to n totally independent single-degree-of-freedom second-order subsystems by real-valued isospectral transformations. In contrast to the common knowledge that generally no three matrices can be diagonalized simultaneously by equivalence transformations, these isospectral transformations endeavor to maintain a special linearization form called the Lancaster structure and do break down M, C and K into diagonal matrices simultaneously. However, these transformations depend on the matrices in a rather complicated way and, hence, are difficult to construct directly. In this paper, a second part of a continuing study, a closed-loop control system that preserves both the Lancaster structure and the isospectrality is proposed as a means to achieve the diagonal reduction. Consequently, these transformations are acquired.
DA - 2008/1/8/
PY - 2008/1/8/
DO - 10.1016/j.jsv.2007.05.052
VL - 309
IS - 1-2
SP - 112-128
SN - 1095-8568
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-35448978753&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Total decoupling of general quadratic pencils, Part I: Theory
AU - Chu, Moody T.
AU - Del Buono, Nicoletta
T2 - JOURNAL OF SOUND AND VIBRATION
AB - The notion of quadratic pencils, λ2M+λC+K, where M, C, and K are n×n real matrices with or without some additional properties such as symmetry or positive definiteness, plays critical roles in many important applications. It has been long desirable, yet with very limited success, to reduce a complicated high-degree-of-freedom system to some simpler low-degree-of-freedom subsystems. Recently, Garvey, Friswell and Prells proposed a promising approach by which, under some mild assumptions, a general quadratic pencils can be converted by real-valued isospectral transformations into a totally decoupled system. This approach, if numerically feasible, would reduce the original n-degree-of-freedom second-order system to n totally independent single-degree-of-freedom second-order subsystems. Such a claim would be a striking breakthrough in the common knowledge that generally no three matrices M, C, and K can be diagonalized simultaneously. This paper intends to serve three purposes: to clarify some of the ambiguities in the original proposition, to simplify some of the computational details and, most importantly, to complete the theory of existence by matrix polynomial factorization tactics.
DA - 2008/1/8/
PY - 2008/1/8/
DO - 10.1016/j.jsv.2007.05.058
VL - 309
IS - 1-2
SP - 96-111
SN - 0022-460X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-35448964347&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Solving over-determined systems by the subresultant method (with an appendix by Marc Chardin)
AU - Szanto, Agnes
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - A general subresultant method is introduced to compute elements of a given ideal with few terms and bounded coefficients. This subresultant method is applied to solve over-determined polynomial systems by either finding a triangular representation of the solution set or by reducing the problem to eigenvalue computation. One of the ingredients of the subresultant method is the computation of a matrix that satisfies certain requirements, called the subresultant properties. Our general framework allows us to use matrices of significantly smaller size than previous methods. We prove that certain previously known matrix constructions, in particular, Macaulay’s, Chardin’s and Jouanolou’s resultant and subresultant matrices possess the subresultant properties. However, these results rely on some assumptions about the regularity of the over-determined system to be solved. The appendix, written by Marc Chardin, contains relevant results on the regularity of n homogeneous forms in n variables.
DA - 2008/1//
PY - 2008/1//
DO - 10.1016/j.jsc.2007.09.001
VL - 43
IS - 1
SP - 46-74
SN - 0747-7171
KW - multivariate subresultant
KW - over-determined polynomial system
KW - solution of polynomial system
ER -
TY - JOUR
TI - Computer optimized design of electron guns
AU - David, John
AU - Ives, R. Lawrence
AU - Tran, Hien T.
AU - Bui, Thuc
AU - Read, Michael E.
T2 - IEEE TRANSACTIONS ON PLASMA SCIENCE
AB - This paper considers the problem of designing electron guns using computer optimization techniques. Several different design parameters are manipulated while considering multiple design criteria, including beam and gun properties. The optimization routines are described. Examples of guns designed using these techniques are presented. Future research is also described.
DA - 2008/2//
PY - 2008/2//
DO - 10.1109/TPS.2007.913884
VL - 36
IS - 1
SP - 156-168
SN - 1939-9375
KW - beam optics analysis
KW - computer optimization
KW - electron gun
KW - implicit filtering
KW - klystron
KW - Nelder-Mead
KW - optimization
KW - simulation
KW - traveling wave tube
ER -