TY - BOOK
TI - Computer Algebra Handbook
AU - Grabmeier, J.
AU - Weispfenning, V.
A3 - Grabmeier, J.
A3 - Kaltofen, E.
A3 - Weispfenning, V.
DA - 2003///
PY - 2003///
PB - Springer Verlag
ER -
TY - JOUR
TI - Enhanced growth of tumors in SPARC null mice is associated with changes the ECM
AU - Brekken, R. A.
AU - Puolakkainen, P.
AU - Graves, D. C.
AU - Workman, G.
AU - Lubkin, S. R.
AU - Sage, E. H.
T2 - Journal of Clinical Investigation
AB - SPARC, a 32-kDa glycoprotein, participates in the regulation of morphogenesis and cellular differentiation through its modulation of cell-matrix interactions. Major functions defined for SPARC in vitro are de-adhesion and antiproliferation. In vivo, SPARC is restricted in its expression to remodeling tissues, including pathologies such as cancer. However, the function of endogenous SPARC in tumor growth and progression is not known. Here, we report that implanted tumors grew more rapidly in mice lacking SPARC. We observed that tumors grown in SPARC null mice showed alterations in the production and organization of ECM components and a decrease in the infiltration of macrophages. However, there was no change in the levels of angiogenic growth factors in comparison to tumors grown in wild-type mice, although there was a statistically significant difference in total vascular area. Whereas SPARC did inhibit the growth of tumor cells in vitro, it did not have a demonstrable effect on the proliferation or apoptosis of tumor cells in vivo. These data indicate that host-derived SPARC is important for the appropriate organization of the ECM in response to implanted tumors and highlight the importance of the ECM in regulating tumor growth.
DA - 2003///
PY - 2003///
DO - 10.1172/jci16804
VL - 111
IS - 4
SP - 487-495
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000181050200011&KeyUID=WOS:000181050200011
ER -
TY - JOUR
TI - Generalized Snell's Law for Weighted Minimal Surface in Heterogeneous Media
AU - Li, Zhilin
AU - Lin, Xiaobiao
AU - Torres, Monica
AU - Zhao, Hongkai
T2 - Methods and Applications of Analysis
AB - The weighted minimal surface problem in heterogeneous media is studied in this paper. The solution to the weighted minimal surface problem is continuous but the derivatives have a jump across the interface where the medium property is discontinuous. The jump condition of the derivatives derived in this paper generalized the Snell's law in geometric optics to weighted minimal surfaces of co-dimension one in any dimensional space. A numerical method based on the gradient flow and the maximum principal preserving immersed interface method is developed to solve this nonlinear elliptic interface problem with jump conditions. Numerical computations are presented to verify both the analysis and the numerical algorithm. 1. Introduction. The minimal surface problem, that is, the problem of finding the surface of the least area among all surfaces having fixed boundary data, has been extensively studied. A recent workshop on minimal surfaces presented the latest re- search on minimal surface applications in chemistry and biology (5). Many phenomena that occur in nature relate to this problem which has been a motivation for devel- oping new mathematical theories and techniques to solve the problem analytically and numerically. Minimal surfaces were shown to be important in various chemical micro-structures and their corresponding phase transitions (5). Computer graphics and image analysis use minimal surfaces frequently for boundary detection, and to construct surfaces that are visually appealing (2), (15). Soap films and other mem- branes passing through a fixed boundary provide mechanical examples of minimal surfaces (14). A related concept is the idea of capillary surfaces, which result from surface tension in liquids. These surfaces are closely related to minimal surfaces (6). For a precise mathematical description of the minimal surface problem we refer, for example, to the classical treatises (7) and (16). The minimal surface problem can be described in two different ways, using the parametric or the non-parametric formulation. In the non-parametric setting the candidate surfaces are graphs of functions, while in the parametric setting the surfaces are treated as boundaries of sets (7). The former is usually seen in more physically- based treatments of the problem, whereas the later provides an excellent framework for the mathematical analysis of minimal surfaces. When the medium is homogeneous, the energy density at each point is constant, and therefore the surface energy is equivalent to the surface area. This is the standard minimal surface problem. In this paper, we consider the weighted minimal surface problem in a heterogeneous medium in which the energy density is piecewise smooth. For example this is the case for capillary interfaces in porous media or composite materials. In particular we derive a jump condition for the weighted minimal surface at the interface between two different media. The jump condition can be regarded as a generalized Snell's law which describes the refraction of minimal surfaces instead of light rays in geometric optics.
DA - 2003///
PY - 2003///
DO - 10.4310/maa.2003.v10.n2.a3
VL - 10
IS - 2
SP - 199-214
LA - en
OP -
SN - 1073-2772 1945-0001
UR - http://dx.doi.org/10.4310/maa.2003.v10.n2.a3
DB - Crossref
ER -
TY - JOUR
TI - A Fast Finite Differenc Method For Solving Navier-Stokes Equations on Irregular Domains
AU - Li, Zhilin
AU - Wang, Cheng
T2 - Communications in Mathematical Sciences
AB - A fast finite difference method is proposed to solve the incompressible
Navier-Stokes equations defined on a general domain. The method is based
on the voricity stream-function formulation and a fast Poisson solver defined
on a general domain using the immersed interface method. The key to the new
method is the fast Poisson solver for general domains and the interpolation
scheme for the boundary condition of the stream function. Numerical examples
thats show second order accuracy of the computed solution are also provided.
DA - 2003///
PY - 2003///
DO - 10.4310/cms.2003.v1.n1.a11
VL - 1
IS - 1
SP - 180-196
LA - en
OP -
SN - 1539-6746 1945-0796
UR - http://dx.doi.org/10.4310/cms.2003.v1.n1.a11
DB - Crossref
ER -
TY - CONF
TI - State Estimation and Tracking Control of Nonlinear Dynamical Systems
AU - Banks, H.T.
AU - Beeler, S.C.
AU - Tran, H.T.
T2 - 8th International Conference on Control of Diagnostics of Processes and Systems
A2 - Desch, W.
A2 - Kappel, F.
A2 - Kunisch, K.
T3 - ISNM International Series of Numerical Mathematics
AB - In this paper state estimation and feedback tracking control methods for nonlinear systems are presented. The methods, which are based on the “state-dependent Riccati equation”, allow the construction of nonlinear estimators and nonlinear feedback tracking controls for a wide class of systems. Our emphasis will be on development of computational methods that are easily implementable as well as efficient. Simulation results of the performance of the nonlinear estimator and tracking control are included. In addition, comparisons with the linear estimator and linear tracking control found through the linearized system are also made.
C2 - 2003/7//
C3 - Control and Estimation of Distributed Parameter Systems
CY - Graz, Austria
DA - 2003/7//
PY - 2001/7//
DO - 10.1007/978-3-0348-8001-5_1
VL - 143
SP - 1–24
PB - Basel/Springer
ER -
TY - CHAP
TI - FoxBox and other blackbox systems
AU - Kaltofen, E.
T2 - Computer Algebra Handbook
A2 - Grabmeier, J.
A2 - Kaltofen, E.
A2 - Weispfenning, V.
PY - 2003///
SP - 383–385
PB - Springer Verlag
ER -
TY - CHAP
TI - Hybrid methods
AU - Corless, M.
AU - Kaltofen, E.
AU - Watt, S. M.
T2 - Computer Algebra Handbook
A2 - Grabmeier, J.
A2 - Kaltofen, E.
A2 - Weispfenning, V.
PY - 2003///
SP - 112–125
PB - Springer Verlag
ER -
TY - CHAP
TI - Linear systems
AU - Kaltofen, E.
AU - Saunders, B. D.
T2 - Computer algebra handbook: foundations, applications, systems
A2 - Grabmeier, J.
A2 - Kaltofen, E.
A2 - Weispfenning, V.
PY - 2003///
SP - 36–38
PB - Springer Verlag
ER -
TY - CHAP
TI - Absolute factorization of polynomials
AU - Kaltofen, E.
T2 - Computer Algebra Handbook
A2 - Grabmeier, J.
A2 - Kaltofen, E.
A2 - Weispfenning, V.
PY - 2003///
SP - 26
PB - Springer Verlag
ER -
TY - CHAP
TI - Computer algebra - impact on research
AU - Kaltofen, E.
AU - Weispfenning, V.
T2 - Computer Algebra Handbook
A2 - Grabmeier, J.
A2 - Kaltofen, E.
A2 - Weispfenning, V.
PY - 2003///
SP - 4–6
PB - Springer Verlag
ER -
TY - CONF
TI - Early decision making when using proper auxiliary signals
AU - Campbell, S.L.
AU - Drake, K.
AU - Nikoukhah, R.
T2 - IEEE Conference on Decision and Control
AB - Recently an approach for multi-model identification and failure detection in the presence of bounded energy noise over finite time intervals has been introduced. This approach involved offline computation of an auxiliary signal and online application of a hyperplane test. This approach has several advantages but as presented, observation over the full time interval was required before a decision could be made. In this paper it is shown how to modify this approach to permit early decision making with the hyperplane test.
C2 - 2003/8/27/
C3 - Proceedings of the 41st IEEE Conference on Decision and Control, 2002.
DA - 2003/8/27/
DO - 10.1109/cdc.2002.1184790
PB - IEEE
SN - 0780375165
UR - http://dx.doi.org/10.1109/cdc.2002.1184790
DB - Crossref
ER -
TY - CONF
TI - Polynomial factorization
AU - Kaltofen, Erich
T2 - the 2003 international symposium
AB - The problem of factoring a polynomial in a single or several variables over a finite field, the rational numbers or the complex numbers is one of the success stories in the discipline of symbolic computation. In the early 1960s implementors investigated the constructive methods known from classical algebra books, but--with the exception of Gauss's distinct degree factorization algorithm--found the algorithms quite inefficient in practice [16]. The contributions in algorithmic techniques that have been made over the next 40 years are truly a hallmark of symbolic computation research.
C2 - 2003///
C3 - Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03
DA - 2003///
DO - 10.1145/860854.860857
PB - ACM Press
SN - 1581136412
UR - http://dx.doi.org/10.1145/860854.860857
DB - Crossref
ER -
TY - CONF
TI - On approximate irreducibility of polynomials in several variables
AU - Kaltofen, Erich
AU - May, John
T2 - the 2003 international symposium
AB - We study the problem of bounding a polynomial away from polynomials which are absolutely irreducible. Such separation bounds are useful for testing whether a numerical polynomial is absolutely irreducible, given a certain tolerance on its coefficients. Using an absolute irreducibility criterion due to Ruppert, we are able to find useful separation bounds, in several norms, for bivariate polynomials. We also use Ruppert's criterion to derive new, more effective Noether forms for polynomials of arbitrarily many variables. These forms lead to small separation bounds for polynomials of arbitrarily many variables.
C2 - 2003///
C3 - Proceedings of the 2003 international symposium on Symbolic and algebraic computation - ISSAC '03
DA - 2003///
DO - 10.1145/860854.860893
PB - ACM Press
SN - 1581136412
UR - http://dx.doi.org/10.1145/860854.860893
DB - Crossref
ER -
TY - BOOK
TI - Algebraic combinatorics and quantum groups
DA - 2003///
PY - 2003///
ER -
TY - CONF
TI - Auxiliary signal design for failure detection in uncertain sampled-data systems
AU - Nikoukhah, R.
AU - Campbell, S. L.
T2 - 2003 European Control Conference (ECC)
AB - In this paper the normal and the failed behaviors of a sampleddata system are modeled using two distinct uncertain models. A proper auxiliary signal is an input signal for which the behaviors of the two systems do not intersect making guaranteed failure detection possible. Algorithms for the design of optimal proper auxiliary signals are developed.
C2 - 2003/9//
C3 - 2003 European Control Conference (ECC)
DA - 2003/9//
DO - 10.23919/ecc.2003.7085087
PB - IEEE
SN - 9783952417379
UR - http://dx.doi.org/10.23919/ecc.2003.7085087
DB - Crossref
ER -
TY - CHAP
TI - A well-posedness Result for a Shear Wave Propagation Model
AU - Banks, H. T.
AU - Tran, H.
AU - Wynne, S.
T2 - Control and Estimation of Distributed Parameter Systems
AB - We consider a nonlinear model for propagation of shear waves in viscoelastic tissue. Existence and uniqueness results for solutions are established.
PY - 2003///
DO - 10.1007/978-3-0348-8001-5_2
SP - 25-40
OP -
PB - Birkhäuser Basel
SN - 9783034893992 9783034880015
UR - http://dx.doi.org/10.1007/978-3-0348-8001-5_2
DB - Crossref
ER -
TY - CONF
TI - Beam optics analysis - a 3D finite element charged particle code with adaptive meshing
AU - Bui, T.
AU - Vogler, B.
AU - Ives, L.
AU - Shephard, M.
AU - Klaas, O.
AU - Remacle, J.-F.
AU - Kapraun, D.
AU - Tran, H.
T2 - Third IEEE International Vacuum Electronics Conference
AB - Development of the next generation of RF devices is in progress with research on sheet beam and multiple beam devices on-going at several institutions. Analysis of inherently three dimensional devices requires a new set of analytical tools to model the electromagnetic fields and the behavior of electron and ion beams. Existing codes, such as HFSS and MAFIA, are widely used to model the electromagnetic fields in these devices, but there is a need for simple, accurate, and efficient codes to model the behavior of charged particles in 3D geometries and fields. Calabazas Creek Research, Inc. (CCR) is funded by the U.S. Department of Energy to develop a finite element, charged particle, analysis code suitable for the next generation of RF devices. The principle feature of the new program is adaptive meshing, which removes the burden for mesh generation from the user and assigns responsibility to field solver and particle pusher routines.
C2 - 2003/6/25/
C3 - Third IEEE International Vacuum Electronics Conference (IEEE Cat. No.02EX524)
DA - 2003/6/25/
DO - 10.1109/ivelec.2002.999314
PB - IEEE
SN - 0780372565
UR - http://dx.doi.org/10.1109/ivelec.2002.999314
DB - Crossref
ER -
TY - CONF
TI - SCATTER - a new computer code for modeling reflected electrons from surfaces
AU - Kapraun, D.
AU - Tran, H.
AU - Ives, R.L.
AU - Vogler, W.
AU - Bui, T.
T2 - Third IEEE International Vacuum Electronics Conference
AB - Calabazas Creek Research, Inc. is funded by the U.S. Department of Energy to develop an advanced charged particle code using adaptive meshing. One of the tasks in that program is to model secondary and reflected electrons in collectors. The Center for Research in Scientific Computing (CRSC) received a subcontract to develop a 3D Monte Carlo technique for modeling these electrons. Taking into account the energy and direction of an incident electron, as well as the atomic number, atomic mass and density of the solid, the program calculates a statistically reasonable path for the electron through the solid via Monte Carlo techniques. When applied to large numbers of electrons, the algorithm provides statistically accurate results. The success of the effort resulted in a stand-alone code that could be use to investigate the effect of various materials and coatings to reduce the emission and there by achieve higher depressed collector efficiencies.
C2 - 2003/6/25/
C3 - Third IEEE International Vacuum Electronics Conference (IEEE Cat. No.02EX524)
DA - 2003/6/25/
DO - 10.1109/ivelec.2002.999300
PB - IEEE
SN - 0780372565
UR - http://dx.doi.org/10.1109/ivelec.2002.999300
DB - Crossref
ER -
TY - CONF
TI - On the structure of some phase retrieval algorithms
AU - Bauschke, H.H.
AU - Combettes, P.L.
AU - Luke, D.R.
T2 - ICIP 2002 International Conference on Image Processing
AB - The state of the art for solving the phase retrieval problem in two dimensions relies heavily on the algorithms proposed by Gerchbercy, Saxton, and Fienup. Despite the widespread use of these algorithms, current mathematical theory cannot explain their remarkable success. It is already known that the Gerchberg-Saxton algorithm is a nonconvex version of method of alternating projections. In this paper, we show that two other prominent phase retrieval methods also have well known counterparts in the world of convex optimization algorithms: Fienup's basic input-output algorithm corresponds to Dykstra's algorithm, and Fienup's hybrid input-output algorithm can be viewed as an instance of the Douglas-Rachford algorithm. This work provides a theoretical framework to better understand and, potentially, improve existing phase recovery algorithms.
C2 - 2003/6/25/
C3 - Proceedings. International Conference on Image Processing
CY - Rochester, New York
DA - 2003/6/25/
PY - 2002/9/22/
DO - 10.1109/icip.2002.1040082
PB - IEEE
SN - 0780376226
UR - http://dx.doi.org/10.1109/icip.2002.1040082
ER -
TY - CONF
TI - Image deconvolution with total variation bounds
AU - Combettes, P.L.
AU - Pesquet, J.-C.
T2 - Seventh International Symposium on Signal Processing and Its Applications
AB - Total variation has been used exclusively as an objective in the formulation of image deconvolution problems. In this paper, we propose an alternative framework in which total variation is used as a constraint. In contrast with the standard approach, this framework requires an a priori bound on the total variation of the original image, while no a priori information on the noise is necessary. Furthermore, it places no limitation on the incorporation of additional constraints in the recovery process and can be solved efficiently via powerful block-iterative methods.
C2 - 2003///
C3 - Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings.
CY - Paris, France
DA - 2003///
PY - 2003/7/4/
DO - 10.1109/isspa.2003.1224735
PB - IEEE
SN - 0780379462
UR - http://dx.doi.org/10.1109/isspa.2003.1224735
ER -
TY - RPRT
TI - Artificial Boundary Conditions for the Numerical Simulation of
Unsteady Electromagnetic Waves
AU - Tsynkov, S. V.
A3 - Center for Research in Scientific Computation, North Carolina State University
DA - 2003///
PY - 2003///
M1 - CRSC–TR03–19
PB - Center for Research in Scientific Computation, North Carolina State University
SN - CRSC–TR03–19
UR - https://stsynkov.math.ncsu.edu/publications/a34p.ncsu.pdf
ER -
TY - CHAP
TI - Lacunae-Based Artificial Boundary Conditions for the Numerical Simulation
of Unsteady Waves Governed by Vector Models
AU - Tsynkov, S. V.
T2 - Mathematical
and Numerical Aspects of Wave Propagation --- WAVES 2003,
The Sixth International Conference, Jyväskylä, Finland, June 30 -- July 4, 2003.
Proceedings
A2 - Cohen, G. C.
A2 - Heikkola, E.
A2 - Joly, P.
A2 - Neittaanmäki, P.
PY - 2003///
SP - 103-108
PB - Springer
UR - https://stsynkov.math.ncsu.edu/publications/waves2003p.pdf
ER -
TY - CONF
TI - Numerical Tools for the Study of Instabilities within the Positive-Differential-Resistance Regions of Tunnelling Devices
AU - Lasater, M S
AU - Kelley, C T
AU - Zhao, P
AU - Woolard, D L
T2 - North Carolina State University, Center for Research in Scientific Computation
C2 - 2003///
C3 - Proceedings of 2003 3nd IEEE Conference on Nanotechnology, San Francisco, CA, August 12--14, 2003
DA - 2003///
SP - 390-393
M1 - CRSC-TR03-23
PB - IEEE
ER -
TY - BOOK
TI - Solving Nonlinear Equations with Newton's Method
AU - Kelley, C T
DA - 2003///
PY - 2003///
PB - SIAM
ER -
TY - JOUR
TI - Globally Convergent Algorithms for Nonsmooth Nonlinear Equations in Computational Fluid Dynamics
AU - Coffey, T S
AU - McMullan, R J
AU - Kelley, C T
AU - McRae, D S
T2 - J. Comp. Appl. Math.
DA - 2003///
PY - 2003///
VL - 152
SP - 69-81
ER -
TY - CONF
TI - Implicit filtering and nonlinear least squares problems
AU - Kelley, C T
A2 - Sachs, E W
A2 - Tichatschke, R
C2 - 2003///
C3 - System Modeling and Optimization XX
CY - Dordrecht
DA - 2003///
SP - 71-90
PB - Kluwer Academic Publishers
ER -
TY - RPRT
TI - Implicit filtering and nonlinear least squares problems
AU - Kelley, C T
A3 - Kluwer Academic Publishers
DA - 2003/7//
PY - 2003/7//
SP - 71-90
M1 - CRSC-TR01-17
PB - Kluwer Academic Publishers
SN - CRSC-TR01-17
ER -
TY - JOUR
TI - Electronic Supplement to ``{O}ptimal Design for Problems Involving Flow and Transport Phenomena in Saturated Subsurface Systems''
AU - Mayer, A S
AU - Kelley, C T
AU - Miller, C T
DA - 2003///
PY - 2003///
ER -
TY - JOUR
TI - Iterating Bregman Retractions
AU - Bauschke, Heinz H.
AU - Combettes, Patrick L.
T2 - SIAM Journal on Optimization
AB - The notion of a Bregman retraction of a closed convex set in Euclidean space is introduced. Bregman retractions include backward Bregman projections and forward Bregman projections, as well as their convex combinations, and are thus quite flexible. The main result on iterating Bregman retractionsunifies several convergence results on projection methods for solving convex feasibility problems. It is also used to construct new sequential and parallel algorithms.
DA - 2003/1//
PY - 2003/1//
DO - 10.1137/s1052623402410557
VL - 13
IS - 4
SP - 1159-1173
J2 - SIAM J. Optim.
LA - en
OP -
SN - 1052-6234 1095-7189
UR - http://dx.doi.org/10.1137/s1052623402410557
DB - Crossref
KW - backward Bregman projection
KW - Bregman distance
KW - Bregman function
KW - Bregman projection
KW - Bregman retraction
KW - convex feasibility problem
KW - forward Bregman projection
KW - Legendre function
KW - paracontraction
KW - projection algorithm
ER -
TY - JOUR
TI - Hybrid projection–reflection method for phase retrieval
AU - Bauschke, Heinz H.
AU - Combettes, Patrick L.
AU - Luke, D. Russell
T2 - Journal of the Optical Society of America A
AB - The phase-retrieval problem, fundamental in applied physics and engineering, addresses the question of how to determine the phase of a complex-valued function from modulus data and additional a priori information. Recently we identified two important methods for phase retrieval, namely, Fienup's basic input-output and hybrid input-output (HIO) algorithms, with classical convex projection methods and suggested that further connections between convex optimization and phase retrieval should be explored. Following up on this work, we introduce a new projection-based method, termed the hybrid projection-reflection (HPR) algorithm, for solving phase-retrieval problems featuring nonnegativity constraints in the object domain. Motivated by properties of the HPR algorithm for convex constraints, we recommend an error measure studied by Fienup more than 20 years ago. This error measure, which has received little attention in the literature, lends itself to an easily implementable stopping criterion. In numerical experiments we found the HPR algorithm to be a competitive alternative to the HIO algorithm and the stopping criterion to be reliable and robust.
DA - 2003/6/1/
PY - 2003/6/1/
DO - 10.1364/josaa.20.001025
VL - 20
IS - 6
SP - 1025
J2 - J. Opt. Soc. Am. A
LA - en
OP -
SN - 1084-7529 1520-8532
UR - http://dx.doi.org/10.1364/josaa.20.001025
DB - Crossref
ER -
TY - JOUR
TI - Bregman Monotone Optimization Algorithms
AU - Bauschke, Heinz H.
AU - Borwein, Jonathan M.
AU - Combettes, Patrick L.
T2 - SIAM Journal on Control and Optimization
AB - A broad class of optimization algorithms based on Bregman distances in Banach spaces is unified around the notion of Bregman monotonicity. A systematic investigation of this notion leads to a simplified analysis of numerous algorithms and to the development of a new class of parallel block-iterative surrogate Bregman projection schemes. Another key contribution is the introduction of a class of operators that is shown to be intrinsically tied to the notion of Bregman monotonicity and to include the operators commonly found in Bregman optimization methods. Special emphasis is placed on the viability of the algorithms and the importance of Legendre functions in this regard. Various applications are discussed.
DA - 2003/1//
PY - 2003/1//
DO - 10.1137/s0363012902407120
VL - 42
IS - 2
SP - 596-636
J2 - SIAM J. Control Optim.
LA - en
OP -
SN - 0363-0129 1095-7138
UR - http://dx.doi.org/10.1137/s0363012902407120
DB - Crossref
KW - Banach space
KW - block-iterative method
KW - Bregman distance
KW - Bregman monotone
KW - Bregman projection
KW - B-class operator
KW - convex feasibility problem
KW - essentially smooth function
KW - essentially strict convex function
KW - Fejer monotone
KW - Legendre function
KW - monotone operator
KW - proximal mapping
KW - proximal point algorithm
KW - resolvent
KW - subgradient projection
ER -
TY - JOUR
TI - A block-iterative surrogate constraint splitting method for quadratic signal recovery
AU - Combettes, P.L.
T2 - IEEE Transactions on Signal Processing
AB - A block-iterative parallel decomposition method is proposed to solve general quadratic signal recovery problems under convex constraints. The proposed method proceeds by local linearizations of blocks of constraints, and it is therefore not sensitive to their analytical complexity. In addition, it naturally lends itself to implementation on parallel computing architectures due to its flexible block-iterative structure. Comparisons with existing methods are carried out, and the case of inconsistent constraints is also discussed. Numerical results are presented.
DA - 2003/7//
PY - 2003/7//
DO - 10.1109/tsp.2003.812846
VL - 51
IS - 7
SP - 1771-1782
J2 - IEEE Trans. Signal Process.
LA - en
OP -
SN - 1053-587X
UR - http://dx.doi.org/10.1109/tsp.2003.812846
DB - Crossref
KW - block-iterative optimization
KW - convex analysis
KW - deconvolution
KW - quadratic programming
KW - signal recovery
KW - subgradient projection
ER -
TY - JOUR
TI - Construction of best Bregman approximations in reflexive Banach spaces
AU - Bauschke, Heinz H.
AU - Combettes, Patrick L.
T2 - Proceedings of the American Mathematical Society
AB - An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.
DA - 2003/12/1/
PY - 2003/12/1/
DO - 10.1090/s0002-9939-03-07050-3
VL - 131
IS - 12
SP - 3757-3766
J2 - Proc. Amer. Math. Soc.
LA - en
OP -
SN - 0002-9939 1088-6826
UR - http://dx.doi.org/10.1090/s0002-9939-03-07050-3
DB - Crossref
KW - best approximation
KW - Bregman distance
KW - decomposition
KW - Haugazeau
ER -
TY - JOUR
TI - Invariant Euler-Lagrange equations and the invariant variational bicomplex
AU - Kogan, I.A.
AU - Olver, P.
T2 - Acta Applicandae Mathematicae
DA - 2003///
PY - 2003///
DO - 10.1023/A:1022993616247
VL - 76
IS - 2
SP - 137–193
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0037393424&partnerID=MN8TOARS
KW - calculus of variations
KW - Lie group
KW - moving frame
KW - differential invariant
KW - Euler-Lagrange equation
KW - variational bicomplex
ER -
TY - JOUR
TI -
AU - Bakalov, Bojko
AU - Kac, Victor
T2 - International Mathematics Research Notices
AB - A field algebra is a noncommutative generalization of a vertex algebra. In this paper, we develop foundations of the theory of field algebras.
DA - 2003///
PY - 2003///
DO - 10.1155/s1073792803204232
VL - 2003
IS - 3
SP - 123
J2 - Internat. Math. Res. Notices
OP -
SN - 1073-7928
UR - http://dx.doi.org/10.1155/s1073792803204232
DB - Crossref
ER -
TY - JOUR
TI - Two Algorithms for a Moving Frame Construction
AU - Kogan, Irina A.
T2 - Canadian Journal of Mathematics
AB - Abstract The method of moving frames, introduced by Elie Cartan, is a powerful tool for the solution of various equivalence problems. The practical implementation of Cartan's method, however, remains challenging, despite its later significant development and generalization. This paper presents two new variations on the Fels and Olver algorithm, which under some conditions on the group action, simplify a moving frame construction. In addition, the first algorithm leads to a better understanding of invariant differential forms on the jet bundles, while the second expresses the differential invariants for the entire group in terms of the differential invariants of its subgroup.
DA - 2003/4/1/
PY - 2003/4/1/
DO - 10.4153/cjm-2003-013-2
VL - 55
IS - 2
SP - 266-291
J2 - Can. j. math.
LA - en
OP -
SN - 0008-414X 1496-4279
UR - http://dx.doi.org/10.4153/cjm-2003-013-2
DB - Crossref
ER -
TY - JOUR
TI - Auxiliary signal design for robust active failure detection: the general cost case
AU - Nikoukhah, R.
AU - Campbell, S.L.
T2 - Proc. Safeprocess 2003
DA - 2003///
PY - 2003///
SP - 259–264
ER -
TY - JOUR
TI - Lexicographic Shellability for Balanced Complexes
AU - Hersh, Patricia
T2 - Journal of Algebraic Combinatorics
AB - We introduce a notion of lexicographic shellability for pure, balanced boolean cell complexes, modelled after the CL-shellability criterion of Björner and Wachs (Adv. in Math. 43 (1982), 87–100) for posets and its generalization by Kozlov (Ann. of Comp. 1(1) (1997), 67–90) called CC-shellability. We give a lexicographic shelling for the quotient of the order complex of a Boolean algebra of rank 2n by the action of the wreath product S 2 ≀ S n of symmetric groups, and we provide a partitioning for the quotient complex Δ(Π n )/S n. Stanley asked for a description of the symmetric group representation β S on the homology of the rank-selected partition lattice Πn S in Stanley (J. Combin. Theory Ser. A 32(2) (1982), 132–161), and in particular he asked when the multiplicity b S(n) of the trivial representation in β S is 0. One consequence of the partitioning for Δ(Π n )/S n is a (fairly complicated) combinatorial interpretation for b S(n); another is a simple proof of Hanlon's result (European J. Combin. 4(2) (1983), 137–141) that b 1,⋯,i(n) = 0. Using a result of Garsia and Stanton from (Adv. in Math. 51(2) (1984), 107–201), we deduce from our shelling for Δ(B 2n )/S 2 ≀ S n that the ring of invariants k[x 1,⋯,x 2 n ] S2 ≀ Sn is Cohen-Macaulay over any field k.
DA - 2003/5//
PY - 2003/5//
DO - 10.1023/a:1025044720847
VL - 17
IS - 3
SP - 225-254
SN - 0925-9899
UR - http://dx.doi.org/10.1023/a:1025044720847
KW - shellability
KW - Boolean cell complex
KW - simplicial poset
KW - partition lattice
KW - wreath product
ER -
TY - JOUR
TI - The order dimension of the poset of regions in a hyperplane arrangement
AU - Reading, Nathan
T2 - Journal of Combinatorial Theory, Series A
AB - We show that the order dimension of the weak order on a Coxeter group of type A, B or D is equal to the rank of the Coxeter group, and give bounds on the order dimensions for the other finite types. This result arises from a unified approach which, in particular, leads to a simpler treatment of the previously known cases, types A and B. The result for weak orders follows from an upper bound on the dimension of the poset of regions of an arbitrary hyperplane arrangement. In some cases, including the weak orders, the upper bound is the chromatic number of a certain graph. For the weak orders, this graph has the positive roots as its vertex set, and the edges are related to the pairwise inner products of the roots.
DA - 2003/11//
PY - 2003/11//
DO - 10.1016/j.jcta.2003.08.002
VL - 104
IS - 2
SP - 265-285
J2 - Journal of Combinatorial Theory, Series A
LA - en
OP -
SN - 0097-3165
UR - http://dx.doi.org/10.1016/j.jcta.2003.08.002
DB - Crossref
ER -
TY - JOUR
TI - Lattice and order properties of the poset of regions in a hyperplane arrangement
AU - Reading, Nathan
T2 - Algebra Universalis
AB - We show that the poset of regions (with respect to a canonical base region) of a supersolvable hyperplane arrangement is a congruence normal lattice. Specifically, the poset of regions of a supersolvable arrangement of rank k is obtained via a sequence of doublings from the poset of regions of a supersolvable arrangement of rank k - 1. An explicit description of the doublings leads to a proof that the order dimension of the poset of regions (again with respect to a canonical base region) of a supersolvable hyperplane arrangement is equal to the rank of the arrangement. In particular, the order dimension of the weak order on a finite Coxeter group of type A or B is equal to the number of generators. The result for type A (the permutation lattice) was proven previously by Flath [11]. We show that the poset of regions of a simplicial arrangement is a semi-distributive lattice, using the previously known result [2] that it is a lattice. A lattice is congruence uniform (or “bounded” in the sense of McKenzie [18]) if and only if it is semi-distributive and congruence normal [7]. Caspard, Le Conte de Poly-Barbut and Morvan [4] showed that the weak order on a finite Coxeter group is congruence uniform. Inspired by the methods of [4], we characterize congruence normality of a lattice in terms of edge-labelings. This leads to a simple criterion to determine whether or not a given simplicial arrangement has a congruence uniform lattice of regions. In the case when the criterion is satisfied, we explicitly characterize the congruence lattice of the lattice of regions.
DA - 2003/12/1/
PY - 2003/12/1/
DO - 10.1007/s00012-003-1834-0
VL - 50
IS - 2
SP - 179-205
J2 - Algebra Universalis
OP -
SN - 0002-5240 1420-8911
UR - http://dx.doi.org/10.1007/s00012-003-1834-0
DB - Crossref
KW - bounded lattice
KW - Cayley lattice
KW - congruence normal
KW - congruence uniform
KW - Coxeter group
KW - critical pair
KW - doubling
KW - hyperplane arrangement
KW - order dimension
KW - order quotient
KW - permutation lattice
KW - poset of regions
KW - semi-distributive lattice
KW - simplicial
KW - subcritical pair
KW - supersolvable
KW - weak order
ER -
TY - JOUR
TI - Multiplicity of the trivial representation in rank-selected homology of the partition lattice
AU - Hanlon, Phil
AU - Hersh, Patricia
T2 - Journal of Algebra
AB - We study the multiplicity bS(n) of the trivial representation in the symmetric group representations βS on the (top) homology of the rank-selected partition lattice ΠnS. We break the possible rank sets S into three cases: (1) 1∉S, (2) S=1,…,i for i⩾1, and (3) S=1,…,i,j1,…,jl for i,l⩾1, j1>i+1. It was previously shown by Hanlon that bS(n)=0 for S=1,…,i. We use a partitioning for Δ(Πn)/Sn due to Hersh to confirm a conjecture of Sundaram [S. Sundaram, The homology representations of the symmetric group on Cohen–Macaulay subposets of the partition lattice, Adv. Math. 104 (1994) 225–296] that bS(n)>0 for 1∉S. On the other hand, we use the spectral sequence of a filtered complex to show bS(n)=0 for S=1,…,i,j1,…,jl unless a certain type of chain of support S exists. The partitioning for Δ(Πn)/Sn allows us then to show that a large class of rank sets S=1,…,i,j1,…,jl for which such a chain exists do satisfy bS(n)>0. We also generalize the partitioning for Δ(Πn)/Sn to Δ(Πn)/Sλ; when λ=(n−1,1), this partitioning leads to a proof of a conjecture of Sundaram about (S1×Sn−1)-representations on the homology of the partition lattice.
DA - 2003/8//
PY - 2003/8//
DO - 10.1016/s0021-8693(03)00372-7
VL - 266
IS - 2
SP - 521-538
J2 - Journal of Algebra
LA - en
OP -
SN - 0021-8693
UR - http://dx.doi.org/10.1016/s0021-8693(03)00372-7
DB - Crossref
ER -
TY - JOUR
TI - A partitioning and related properties for the quotient complex Δ(Blm)/Sl≀Sm
AU - Hersh, Patricia
T2 - Journal of Pure and Applied Algebra
AB - We study the quotient complex Δ(Blm)/Sl≀Sm as a means of deducing facts about the ring k[x1,…,xlm]Sl≀Sm. It is shown in Hersh (preprint, 2000) that Δ(Blm)/Sl≀Sm is shellable when l=2, implying Cohen–Macaulayness of k[x1,…,x2m]S2≀Sm for any field k. We now confirm for all pairs (l,m) with l>2 and m>1 that Δ(Blm)/Sl≀Sm is not Cohen–Macaulay over Z/2Z, but it is Cohen–Macaulay over fields of characteristic p>m (independent of l). This yields corresponding characteristic-dependent results for k[x1,…,xlm]Sl≀Sm. We also prove that Δ(Blm)/Sl≀Sm and the links of many of its faces are collapsible, and we give a partitioning for Δ(Blm)/Sl≀Sm.
DA - 2003/3//
PY - 2003/3//
DO - 10.1016/s0022-4049(02)00192-5
VL - 178
IS - 3
SP - 255-272
J2 - Journal of Pure and Applied Algebra
LA - en
OP -
SN - 0022-4049
UR - http://dx.doi.org/10.1016/s0022-4049(02)00192-5
DB - Crossref
ER -
TY - JOUR
TI - Chain decomposition and the flag f-vector
AU - Hersh, Patricia
T2 - Journal of Combinatorial Theory, Series A
AB - Ehrenborg introduced a quasi-symmetric function encoding, denoted F P , for the flag f -vector of any finite, graded poset P with 0 ̂ and 1 ̂ . Stanley observed that F P is a symmetric function whenever P is locally rank-symmetric and asked for conditions under which F P is Schur-positive. We provide formulas for F P for three classes of locally rank-symmetric posets: graded monoid posets, generalized posets of shuffles and noncrossing partition lattices for classical reflection groups. Our flag f -vector expressions for generalized shuffle posets and noncrossing partition lattices exhibit Schur-positivity, while graded monoid posets do not always have Schur-positive flag f -vector. Each of our flag f -vector expressions results from a poset chain decomposition. For the noncrossing partition lattices and shuffle posets, these also yield symmetric chain decompositions (by restriction to 1-chains), shellability and supersolvability results and combinatorial formulae including characteristic polynomial and zeta polynomial. Our (more complicated) flag f -vector expression for graded monoid posets involves Gröbner bases and a weighted notion of Möbius function for the poset of partitions of a multiset and related multiset intersection posets.
DA - 2003/7//
PY - 2003/7//
DO - 10.1016/s0097-3165(03)00066-9
VL - 103
IS - 1
SP - 27-52
J2 - Journal of Combinatorial Theory, Series A
LA - en
OP -
SN - 0097-3165
UR - http://dx.doi.org/10.1016/s0097-3165(03)00066-9
DB - Crossref
ER -
TY - JOUR
TI - Markov Bases of Binary Graph Models
AU - Sullivant, Seth
AU - Develin, Mike
T2 - Annals of Combinatorics
AB - This paper is concerned with the topological invariant of a graph given by the maximum degree of a Markov basis element for the corresponding graph model for binary contingency tables. We describe a degree four Markov basis for the model when the underlying graph is a cycle and generalize this result to the complete bipartite graph K 2,n . We also give a combinatorial classification of degree two and three Markov basis moves as well as a Buchberger-free algorithm to compute moves of arbitrary given degree. Finally, we compute the algebraic degree of the model when the underlying graph is a forest.
DA - 2003/12/1/
PY - 2003/12/1/
DO - 10.1007/s00026-003-0196-9
VL - 7
IS - 4
SP - 441-466
J2 - Annals of Combinatorics
OP -
SN - 0218-0006 0219-3094
UR - http://dx.doi.org/10.1007/s00026-003-0196-9
DB - Crossref
ER -
TY - BOOK
TI - Golf the fundamentals
AU - Frank Ormond, Charles E. Patch
DA - 2003///
PY - 2003///
PB - Durham, NC: Carolina Academic Press
ER -
TY - BOOK
TI - Computer algebra handbook foundations, applications, systems
DA - 2003///
PY - 2003///
DO - 10.1007/978-3-540-72122-2_20
PB - Berlin ;|aNew York: Springer
ER -
TY - RPRT
TI - Evaluating the Effectiveness of the Leave No Trace Program in the City of Durango, Colorado
AU - Leung, Y.-F
AU - Attarian, A.
A3 - Boulder, CO: The Leave No Trace, Inc.
DA - 2003///
PY - 2003///
VL - Final Report
PB - Boulder, CO: The Leave No Trace, Inc.
ER -
TY - CHAP
TI - Affine, quasi-affine and co-affine wavelets
AU - Gressman, P.
AU - Labate, D.
AU - Weiss, G.
AU - Wilson, E.
T2 - Beyond wavelets
AB - Abstract “Classical” wavelets are obtained by the action of a particular countable subset of operators associated with the affine group on a function ψ ∈ L 2 (ℝ). More precisely, this set is the collection { D 2j T k : j,k ∈ ℤ}, where T k is the translation by the integer k and D 2j is the (unitary) dilation by 2 j . We thus obtain the discrete wavelet system. Ron and Shen [ 4 ] have shown that by interchanging and renormalizing “half” of the operators in this set one obtains an important collection of systems that can be considered “equivalent” to this affine system. In this paper we show that, in a precise sense, the choice of Ron and Shen is optimal.
PY - 2003///
DO - 10.1016/s1570-579x(03)80036-8
SP - 215-224
PB - San Diego, CA: Academic Press
SN - 0127432736
ER -
TY - JOUR
TI - Thin film traveling waves and the Navier slip condition
AU - Buckingham, R.
AU - Shearer, Michael
AU - Bertozzi, A.
T2 - SIAM Journal on Applied Mathematics
AB - We consider the lubrication model for a thin film driven by competing gravitational forces and thermal gradients on an inclined plane. We are interested in the general traveling wave problem when the Navier slip boundary condition is used. We contrast (1) gravity dominated flow, (2) Marangoni dominated flow, and (3) flow in which the two driving effects balance. For a "singular slip" model we show that when Marangoni forces are present the resulting traveling wave ODE reduces locally near the contact line to a case not considered previously in the literature. We compute an asymptotic expansion of the solution near the contact line and compare with numerical simulations of the full problem. Using numerical simulations and phase space analysis involving Poincaré sections, we show that for all three problems there is a finite range of admissible contact angles for which traveling wave solutions exist. Even in the well-studied case (1), this is a new observation that has ramifications for the use of constitutive laws at the contact line in the case of singular slip. For case (3) multiple traveling wave solutions are observed with the same contact angle.
DA - 2003///
PY - 2003///
DO - 10.1137/s0036139902401409
VL - 63
IS - 2
SP - 722–744
ER -
TY - BOOK
TI - Research Directions in Distributed Parameter Systems
AU - Smith, Ralph
AU - Demetriou, M.
A3 - Smith, Ralph C.
A3 - Demetriou, Michael A.
AB - Research Directions in Distributed Parameter Systems is composed of eleven chapters, written by experts in their respective fields, on topics ranging from control of the Navier-Stokes equations to nondestructive evaluation - all of which are modeled by distributed parameters systems. Written by the plenary speakers for the Conference on Future Directions in Distributed Parameter Systems (October 2000), the volume addresses the state of the art, open questions, and important research directions in applications modeled by partial differential equations and delay systems, with the ultimate goal of passing along these perspectives to researchers in the field.
CN - QA402.3 .R48 2003
DA - 2003/1//
PY - 2003/1//
DO - 10.1137/1.9780898717525
OP -
PB - Society for Industrial and Applied Mathematics
SN - 9780898715484 9780898717525
UR - http://dx.doi.org/10.1137/1.9780898717525
DB - Crossref
ER -
TY - JOUR
TI - Time-reversed refocusing of surface water waves
AU - Fouque, JP
AU - Nachbin, A
T2 - MULTISCALE MODELING & SIMULATION
AB - A time-reversal mirror is, roughly speaking, a device which is capable of receiving a signal in time, keeping it in memory, and sending it back into the medium in the reversed direction of time. A brief mathematical review of the time-reversal (in reflection) theory is presented in the context of the linear shallow water equations. In particular, an explicit expression is given for the refocused pulse in the simplest time-reversal case. The explicit expression for the power spectral density of the reflection process is used to construct the highpass filter, which controls the refocusing process. Time-reversal numerical experiments in the (effectively) linear regime are used to validate the nonlinear shallow water code. The numerically refocused pulse is compared with the theoretical predicted shape. Further numerical experiments illustrate the robustness of the theory, in particular the time-reversal refocusing with smaller cutoff windows, the self-averaging property, and finally refocusing when the nonlinear term is small but not negligible.
DA - 2003///
PY - 2003///
DO - 10.1137/S1540345902412110
VL - 1
IS - 4
SP - 609-629
SN - 1540-3467
KW - water waves
KW - inhomogeneous media
KW - asymptotic theory
ER -
TY - JOUR
TI - Multiscale stochastic volatility asymptotics
AU - Fouque, JP
AU - Papanicolaou, G
AU - Sircar, R
AU - Solna, K
T2 - MULTISCALE MODELING & SIMULATION
AB - In this paper we propose to use a combination of regular and singular perturbations to analyze parabolic PDEs that arise in the context of pricing options when the volatility is a stochastic process that varies on several characteristic time scales. The classical Black--Scholes formula gives the price of call options when the underlying is a geometric Brownian motion with a constant volatility. The underlying might be the price of a stock or an index, say, and a constant volatility corresponds to a fixed standard deviation for the random fluctuations in the returns of the underlying. Modern market phenomena make it important to analyze the situation when this volatility is not fixed but rather is heterogeneous and varies with time. In previous work (see, for instance, [J. P. Fouque, G. Papanicolaou, and K. R. Sircar, Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge, UK, 2000]), we considered the situation when the volatility is fast mean reverting. Using a singular perturbation expansion we derived an approximation for option prices. We also provided a calibration method using observed option prices as represented by the so-called term structure of implied volatility. Our analysis of market data, however, shows the need for introducing also a slowly varying factor in the model for the stochastic volatility. The combination of regular and singular perturbations approach that we set forth in this paper deals with this case. The resulting approximation is still independent of the particular details of the volatility model and gives more flexibility in the parametrization of the implied volatility surface. In particular, the introduction of the slow factor gives a much better fit for options with longer maturities. We use option data to illustrate our results and show how exotic option prices also can be approximated using our multiscale perturbation approach.
DA - 2003///
PY - 2003///
DO - 10.1137/030600291
VL - 2
IS - 1
SP - 22-42
SN - 1540-3459
KW - stochastic volatility
KW - time scales
KW - singular regular perturbations
KW - option pricing
KW - implied volatility
ER -
TY - JOUR
TI - A forward-trajectory global semi-Lagrangian transport scheme
AU - Nair, RD
AU - Scroggs, JS
AU - Semazzi, FHM
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - A forward-trajectory semi-Lagrangian scheme for advection on the surface of the sphere is proposed. The advection scheme utilizes the forward (downstream) trajectory originating at Eulerian grid points and cascade interpolation, a sequence of 1D interpolations, to transfer data from the downstream Lagrangian points to the Eulerian points. A new and more accurate algorithm determines pole values. The resulting forward-trajectory semi-Lagrangian scheme can easily incorporate high-order trajectory integration methods. This avoids the standard iterative process in a typical backward-trajectory scheme. Two third-order accurate schemes and a second-order accurate scheme are presented. A mass-conservative version of the forward-trajectory semi-Lagrangian scheme is also derived within the cascade interpolation framework. Mass from a Lagrangian cell is transferred to the corresponding Eulerian cell with two 1D remappings through an intermediate cell system. Mass in the polar region is redistributed by way of an efficient local approximation. The resulting scheme is globally conservative, but restricted to meridional Courant number, Cθ⩽1.
DA - 2003/9/1/
PY - 2003/9/1/
DO - 10.1016/S0021-9991(03)00274-2
VL - 190
IS - 1
SP - 275-294
SN - 1090-2716
KW - semi-Lagrangian advection
KW - spherical geometry
KW - forward trajectory
KW - cascade interpolation
KW - mass conservation
KW - Runge-Kutta method
ER -
TY - JOUR
TI - On inverse quadratic eigenvalue problems with partially prescribed eigenstructure
AU - Chu, MT
AU - Kuo, YC
AU - Lin, WW
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - The inverse eigenvalue problem of constructing real and symmetric square matrices M, C, and K of size $n \times n$ for the quadratic pencil $Q(\lambda) = \lambda^2 M + \lambda C + K$ so that $Q(\lambda)$ has a prescribed subset of eigenvalues and eigenvectors is considered. This paper consists of two parts addressing two related but different problems. The first part deals with the inverse problem where M and K are required to be positive definite and semidefinite, respectively. It is shown via construction that the inverse problem is solvable for any k, given complex conjugately closed pairs of distinct eigenvalues and linearly independent eigenvectors, provided $k \leq n$. The construction also allows additional optimization conditions to be built into the solution so as to better refine the approximate pencil. The eigenstructure of the resulting $Q(\lambda)$ is completely analyzed. The second part deals with the inverse problem where M is a fixed positive definite matrix (and hence may be assumed to be the identity matrix $I_n$). It is shown via construction that the monic quadratic pencil $Q(\lambda)=\lambda^2 I_n + \lambda C + K$, with $n + 1$ arbitrarily assigned complex conjugately closed pairs of distinct eigenvalues and column eigenvectors which span the space $\mathbb{C}^n$, always exists. Sufficient conditions under which this quadratic inverse eigenvalue problem is uniquely solvable are specified.
DA - 2003///
PY - 2003///
DO - 10.1137/S0895479803404484
VL - 25
IS - 4
SP - 995-1020
SN - 1095-7162
KW - quadratic eigenvalue problem
KW - inverse eigenvalue problem
KW - partially prescribed spectrum
KW - partial eigenstructure assignment
ER -
TY - JOUR
TI - Mixed finite element methods and higher order temporal approximations for variably saturated groundwater flow
AU - Farthing, MW
AU - Kees, CE
AU - Miller, CT
T2 - ADVANCES IN WATER RESOURCES
AB - Richards’ equation (RE) is commonly used to model flow in variably saturated porous media. However, its solution continues to be difficult for many conditions of practical interest. Among the various time discretizations applied to RE, the method of lines (MOL) has been used successfully to introduce robust, accurate, and efficient temporal approximations. At the same time, a mixed-hybrid finite element method combined with an adaptive, higher order time discretization has shown benefits over traditional, lower order temporal approximations for modeling single-phase groundwater flow in heterogeneous porous media. Here, we extend earlier work for single-phase flow and consider two mixed finite element methods that have been used previously to solve RE using lower order time discretizations with either fixed time steps or empirically based adaption. We formulate the two spatial discretizations within a MOL context for the pressure head form of RE as well as a fully mass-conservative version. We conduct several numerical experiments for both spatial discretizations with each formulation, and we compare the higher order, adaptive time discretization to a first-order approximation with formal error control and adaptive time step selection. Based on the numerical results, we evaluate the performance of the methods for robustness and efficiency.
DA - 2003/4//
PY - 2003/4//
DO - 10.1016/S0309-1708(02)00187-2
VL - 26
IS - 4
SP - 373-394
SN - 1872-9657
ER -
TY - JOUR
TI - Identification of contact regions in semiconductor transistors by level-set methods
AU - Fang, WF
AU - Ito, K
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - In this paper we present the formulation of level-set methods for the inverse problem of identifying an interface in the coefficient of an elliptic equation from a boundary measurement. This problem arises from the modeling of the identification of contact regions by boundary measurements for semiconductor transistors. We propose the Gauss–Newton direction as the interface velocity, and implement the scheme for a parameterized class of interfaces.
DA - 2003/10/15/
PY - 2003/10/15/
DO - 10.1016/S0377-0427(03)00543-0
VL - 159
IS - 2
SP - 399-410
SN - 0377-0427
KW - inverse problem
KW - level-set methods
KW - semiconductor
ER -
TY - JOUR
TI - Goodness through optimal dynamics of the wealth of nations
AU - Chukwu, EN
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - In this paper, we survey the mathematical theory of competitive an co-operative systems that monitor national interactions and economic systems. The dynamics are described by ordinary differential equations, functional differential equations and coupled partial differential equations. Conditions are given which guarantee finite time extinction, finite time unbounded growth, and persistence. These conditions are already available in the literature (Proceedings of the First World Congress of Nonlinear Analysis, 1992 Vol I–IV 359–368 Gruyler, Berlin; Appl. Anal. 57 (1995) 3–4, pp. 309–323; Math. Biosci. 118 (1993) 197; In: T.G. Hallam, S.A. Levin (Eds.), Mathematical Ecology, Biomathematics, Vol. 17, Biomathematics, Springer, Berlin, Heidelberg, 1986; Convex Structures and Economic Theory, Academic Press, New York, 1968; SIAM J. Math. Anal. 18 (1987) 642; Introduction to Differential Equation, Prentice-Hall, Englewood Cliffs, NJ, 1987; SIAM J. Appl. Math. 36 (1979) 421; Proc. Nat. Acad. Sci. USA 68 (1971) 980; SIAM J. Math. Anal. 24 (1993) 1331; The Passionate God, Paulist Press, New York, 1981; Nonlinear Parabolic and Elliptic Equation, Plenum Press, New York, 1992; Economic Theory and Social Justice, MacMillan, London, UK, 1999; Extinction in finite time of solutions to nonlinear absorption–diffusion equations, personal communication). The theory is applied to national wealth that is carefully defined. It is shown that the wealth of co-operating nations can grow unbounded and competing ones become extinct. Using the principle of “trickle down of wealth” and incorporating a strategy of internally generated wealth due to improved health and education, we derive the dynamics of wealth.
DA - 2003/12//
PY - 2003/12//
DO - 10.1016/S1468-1218(02)00055-X
VL - 4
IS - 5
SP - 653-666
SN - 1468-1218
KW - wealth functions
KW - competitive and cooperative systems
KW - inflow of wealth
KW - internally generated wealth
ER -
TY - JOUR
TI - Block monotone iterations for numerical solutions of fourth-order nonlinear elliptic boundary value problems
AU - Pao, CV
AU - Lu, X
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - This paper is concerned with monotone iterative methods for numerical solutions of a class of nonlinear fourth-order elliptic boundary value problems in a two-dimensional domain. The boundary value problem is discretized by the finite difference method, and two iterative processes, called block Jacobi and block Gauss-Seidel monotone iterations, are presented for the computation of solutions of the finite difference system using either an upper solution or a lower solution as the initial iteration. It is shown that the sequence of iterations converges monotonically to a maximal solution or a minimal solution if the nonlinear function is quasi-monotone nondecreasing. A sufficient condition is given to ensure that the maximal and minimal solutions coincide and their common value is the unique solution of the finite difference system. Similar results are obtained for quasi-monotone nonincreasing functions. An analytical comparison relation between the block Jacobi and block Gauss--Seidel monotone iterations is obtained. It is also shown that the finite difference solution converges to the continuous solution as the mesh size tends to zero. Numerical results by the block monotone iterative schemes are given for two model problems and are compared with the known analytical solutions for accuracy. Also compared are the rates of convergence of the two types of block monotone iterations as well as similar types of pointwise monotone iterations.
DA - 2003///
PY - 2003///
DO - 10.1137/S1064827502409912
VL - 25
IS - 1
SP - 164-185
SN - 1095-7197
KW - fourth-order elliptic equations
KW - finite difference systems
KW - block monotone iterations
KW - numerical solutions
KW - convergence
KW - upper and lower solutions
ER -
TY - JOUR
TI - Backscattering and Nonparaxiality Arrest Collapse of Damped Nonlinear Waves
AU - Ilan, B.
AU - Fibich, G.
AU - Tsynkov, S.
T2 - SIAM Journal on Applied Mathematics
AB - The critical nonlinear Schrödinger equation (NLS) models the propagation of intense laser light in Kerr media. This equation is derived from the more comprehensive nonlinear Helmholtz equation (NLH) by employing the paraxial approximation and neglecting the backscattered waves. It is known that if the input power of the laser beam (i.e., L2 norm of the initial solution) is sufficiently high, then the NLS model predicts that the beam will self-focus to a point (i.e., collapse) at a finite propagation distance. Mathematically, this behavior corresponds to the formation of a singularity in the solution of the NLS. A key question which has been open for many years is whether the solution to the NLH, i.e., the "parent" equation, may nonetheless exist and remain regular everywhere, particularly for those initial conditions (input powers) that lead to blowup in the NLS. In the current study we address this question by introducing linear damping into both models and subsequently comparing the numerical solutions of the damped NLH (boundary-value problem) with the corresponding solutions of the damped NLS (initial-value problem) for the case of one transverse dimension. Linear damping is introduced in much the same way as is done when analyzing the classical constant-coefficient Helmholtz equation using the limiting absorption principle. Numerically, we have found that it provides a very efficient tool for controlling the solutions of both the NLH and NLS. In particular, we have been able to identify initial conditions for which the NLS solution does become singular, while the NLH solution still remains regular everywhere. We believe that our finding of a larger domain of existence for the NLH than for the NLS is accounted for by precisely those mechanisms that have been neglected when deriving the NLS from the NLH, i.e., nonparaxiality and backscattering.
DA - 2003/1//
PY - 2003/1//
DO - 10.1137/S0036139902411855
VL - 63
IS - 5
SP - 1718-1736
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/S0036139902411855
DB - Crossref
KW - Kerr medium
KW - nonlinear wave propagation
KW - self-focusing
KW - singularity formation
KW - linear damping
KW - limiting absorption
KW - two-way ABCs
ER -
TY - JOUR
TI - Artificial boundary conditions for the numerical simulation of unsteady acoustic waves
AU - Tsynkov, S.V.
T2 - Journal of Computational Physics
AB - We construct non-local artificial boundary conditions (ABCs) for the numerical simulation of genuinely time-dependent acoustic waves that propagate from a compact source in an unbounded unobstructed space. The key property used for obtaining the ABCs is the presence of lacunae, i.e., sharp aft fronts of the waves, in wave-type solutions in odd-dimension spaces. This property can be considered a manifestation of the Huygens’ principle. The ABCs are obtained directly for the discrete formulation of the problem. They truncate the original unbounded domain and guarantee the complete transparency of the new outer boundary for all the outgoing waves. A central feature of the proposed ABCs is that the extent of their temporal non-locality is fixed and limited, and it does not come at the expense of simplifying the original model. It is rather a natural consequence of the existence of lacunae, which is a fundamental property of the corresponding solutions. The proposed ABCs can be built for any consistent and stable finite-difference scheme. Their accuracy can always be made as high as that of the interior approximation, and it will not deteriorate even when integrating over long time intervals. Besides, the ABCs are most flexible from the standpoint of geometry and can handle irregular boundaries on regular grids with no fitting/adaptation needed and no accuracy loss induced. Finally, they allow for a wide range of model settings. In particular, not only one can analyze the simplest advective acoustics case with the uniform background flow, but also the case when the waves’ source (or scatterer) is engaged in an accelerated motion.
DA - 2003/8//
PY - 2003/8//
DO - 10.1016/S0021-9991(03)00249-3
VL - 189
IS - 2
SP - 626-650
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/S0021-9991(03)00249-3
DB - Crossref
KW - time-dependent sound waves
KW - unbounded domains
KW - lacunae
KW - non-deteriorating method
KW - long-term computation
KW - limited temporal non-locality
ER -
TY - JOUR
TI - A Free Energy Model for Hysteresis in Ferroelectric Materials
AU - Smith, Ralph C.
AU - Seelecke, Stefan
AU - Ounaies, Zoubeida
AU - Smith, Joshua
T2 - Journal of Intelligent Material Systems and Structures
AB - This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques. In the first step of the model development, Helmholtz and Gibbs free energy relations are constructed at the lattice or domain level to quantify the relation between the field and polarization in homogeneous, single crystal compounds which exhibit uniform effective fields. The effects of material nonhomogeneities, polycrystallinity, and variable effective fields are subsequently incorporated through the assumption that certain physical parameters, including the local coercive and effective fields, are randomly distributed and hence manifestations of stochastic density functions associated with the material. Stochastic homogenization in this manner provides low-order macroscopic models with effective parameters that can be correlated with physical properties of the data. This facilitates the identification of parameters for model construction, model updating to accommodate changing operating conditions, and control design utilizing model-based inverse compensators. Attributes of the model, including the guaranteed closure of biased minor loops in quasistatic drive regimes, are illustrated through examples.
DA - 2003/11//
PY - 2003/11//
DO - 10.1177/1045389X03038841
VL - 14
IS - 11
SP - 719-739
J2 - Journal of Intelligent Material Systems and Structures
LA - en
OP -
SN - 1045-389X 1530-8138
UR - http://dx.doi.org/10.1177/1045389x03038841
DB - Crossref
KW - hysteresis model
KW - ferroelectric materials
KW - piezoceramic compounds
ER -
TY - JOUR
TI - A domain wall model for hysteresis in ferroelastic materials
AU - Massad, J. E.
AU - Smith, Ralph
T2 - Journal of Intelligent Material Systems and Structures
DA - 2003///
PY - 2003///
DO - 10.1177/104538903035235
VL - 14
IS - 7
SP - 455–471
ER -
TY - JOUR
TI - The immersed interface method for elasticity problems with interfaces
AU - Yang, X. Z.
AU - Li, B.
AU - Li, Z. L.
T2 - Dynamics of Continuous, Discrete & Impulsive Systems. Series A, Mathematical Analysis
DA - 2003///
PY - 2003///
VL - 10
IS - 5
SP - 783-808
ER -
TY - JOUR
TI - Secondary circulation in granular flow through nonaxisymmetric hoppers
AU - Gremaud, PA
AU - Matthews, JV
AU - Schaeffer, DG
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - Jenike's radial solution, widely used in the design of materials-handling equipment, is a similarity solution of steady-state continuum equations for the flow under gravity of granular material through an infinite, right-circular cone. In this paper we study how the geometry of the hopper influences this solution. Using perturbation theory, we compute a first-order correction to the (steady-state) velocity resulting from a small change in hopper geometry, either distortion of the cross section or tilting away from vertical. Unlike for the Jenike solution, all three components of the correction velocity are nonzero; i.e., there is secondary circulation in the perturbed flow.
DA - 2003///
PY - 2003///
DO - 10.1137/S0036139903415124
VL - 64
IS - 2
SP - 583-600
SN - 1095-712X
KW - granular
KW - similarity solution
KW - perturbation theory
ER -
TY - JOUR
TI - Optimization of Acoustic Source Strength in the Problems of Active Noise Control
AU - Loncaric, J.
AU - Tsynkov, S. V.
T2 - SIAM Journal on Applied Mathematics
AB - We consider a problem of eliminating the unwanted time-harmonic noise on a predetermined region of interest. The desired objective is achieved by active means, i.e., by introducing additional sources of sound called control sources, which generate the appropriate annihilating acoustic signal (antisound). A general solution for the control sources has been obtained previously in both continuous and discrete formulation of the problem. In the current paper, we focus on optimizing the overall absolute acoustic source strength of the control sources. Mathematically, this amounts to the minimization of multivariable complex-valued functions in the sense of L1 with conical constraints, which are only "marginally" convex. The corresponding numerical optimization problem appears very challenging even for the most sophisticated state-of-the-art methodologies, and even when the dimension of the grid is small and the waves are long. Our central result is that the global L1 -optimal solution can, in fact, be obtained without solving the numerical optimization problem. This solution is given by a special layer of monopole sources on the perimeter of the protected region. We provide a rigorous proof of global L1 minimality for both continuous and discrete optimization problems in the one-dimensional case. We also provide numerical evidence that corroborates our result in the two-dimensional case, when the protected domain is a cylinder. Even though we cannot fully justify it, we believe that the same result holds in the general case, i.e., for multidimensional settings and domains of arbitrary shape. We formulate this notion as a conjecture at the end of the paper.
DA - 2003/1//
PY - 2003/1//
DO - 10.1137/S0036139902404220
VL - 63
IS - 4
SP - 1141-1183
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/S0036139902404220
DB - Crossref
KW - noise cancellation
KW - control sources
KW - minimization of amplitude
KW - volume velocity
KW - surface monopoles
ER -
TY - BOOK
TI - Bioterrorism: Mathematical modeling applications in homeland security
AU - Banks, H. T.
AU - Castillo-Chavez, C.
CN - UG447.8 .B585 2003
DA - 2003///
PY - 2003///
PB - Philadelphia, PA: Society for Industrial and Applied Mathematics
SN - 0898715490
ER -
TY - JOUR
TI - Semi-smooth Newton methods for variational inequalities of the first kind
AU - Ito, K
AU - Kunisch, K
T2 - ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
AB - Semi–smooth Newton methods are analyzed for a class of variational inequalities in infinite dimensions. It is shown that they are equivalent to certain active set strategies. Global and local super-linear convergence are proved. To overcome the phenomenon of finite speed of propagation of discretized problems a penalty version is used as the basis for a continuation procedure to speed up convergence. The choice of the penalty parameter can be made on the basis of an L∞ estimate for the penalized solutions. Unilateral as well as bilateral problems are considered.
DA - 2003///
PY - 2003///
DO - 10.1051/m2an:2003021
VL - 37
IS - 1
SP - 41-62
SN - 1290-3841
KW - semi-smooth Newton methods
KW - contact problems
KW - variational inequalities
KW - bilateral constraints
KW - superlinear convergence
ER -
TY - JOUR
TI - Oxidation heat pulses in two-phase expansive flow in porous media
AU - Marchesin, D
AU - Schecter, S
T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
DA - 2003/1//
PY - 2003/1//
DO - 10.1007/pl00012634
VL - 54
IS - 1
SP - 48-83
SN - 0044-2275
KW - combustion
KW - porous media
KW - multiphase flow
KW - conservation laws
ER -
TY - JOUR
TI - Incorporation of variability into the modeling of viral delays in HIV infection dynamics
AU - Banks, HT
AU - Bortz, DM
AU - Holte, SE
T2 - MATHEMATICAL BIOSCIENCES
AB - We consider classes of functional differential equation models which arise in attempts to describe temporal delays in HIV pathogenesis. In particular, we develop methods for incorporating arbitrary variability (i.e., general probability distributions) for these delays into systems that cannot readily be reduced to a finite number of coupled ordinary differential equations (as is done in the method of stages). We discuss modeling from first principles, introduce several classes of non-linear models (including discrete and distributed delays) and present a discussion of theoretical and computational approaches. We then use the resulting methodology to carry out simulations and perform parameter estimation calculations, fitting the models to a set of experimental data. Results obtained confirm the statistical significance of the presence of delays and the importance of including delays in validating mathematical models with experimental data. We also show that the models are quite sensitive to the mean of the distribution which describes the delay in viral production, whereas the variance of this distribution has relatively little impact.
DA - 2003/5//
PY - 2003/5//
DO - 10.1016/S0025-5564(02)00218-3
VL - 183
IS - 1
SP - 63-91
SN - 1879-3134
KW - HIV pathogenesis
KW - eclipse phase
KW - variability
KW - non-linear delay equations
ER -
TY - JOUR
TI - Global asymptotic stability of Lotka-Volterra 3-species reaction-diffusion systems with time delays
AU - Pao, CV
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - This paper is concerned with three 3-species time-delayed Lotka–Volterra reaction–diffusion systems and their corresponding ordinary differential systems without diffusion. The time delays may be discrete or continuous, and the boundary conditions for the reaction–diffusion systems are of Neumann type. The goal of the paper is to obtain some simple and easily verifiable conditions for the existence and global asymptotic stability of a positive steady-state solution for each of the three model problems. These conditions involve only the reaction rate constants and are independent of the diffusion effect and time delays. The result of global asymptotic stability implies that each of the three model systems coexists, is permanent, and the trivial and all semitrivial solutions are unstable. Our approach to the problem is based on the method of upper and lower solutions for a more general reaction–diffusion system which gives a common framework for the 3-species model problems. Some global stability results for the 2-species competition and prey–predator reaction–diffusion systems are included in the discussion.
DA - 2003/5/1/
PY - 2003/5/1/
DO - 10.1016/S0022-247X(03)00033-7
VL - 281
IS - 1
SP - 186-204
SN - 0022-247X
ER -
TY - JOUR
TI - Truncated Newton methods for optimization with inaccurate functions and gradients
AU - Kelley, CT
AU - Sachs, EW
T2 - JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
AB - We consider unconstrained minimization problems that have functions and gradients given by black box codes with error control. We discuss several modifications of the Steihaug truncated Newton method that can improve performance for such problems. We illustrate the ideas with two examples.
DA - 2003/1//
PY - 2003/1//
DO - 10.1023/A:1022110219090
VL - 116
IS - 1
SP - 83-98
SN - 0022-3239
KW - trust region methods
KW - inexact Newton methods
KW - optimal control
ER -
TY - JOUR
TI - Pricing Asian options with stochastic volatility
AU - Fouque, JP
AU - Han, CH
T2 - QUANTITATIVE FINANCE
AB - Abstract In this paper, we generalize the recently developed dimension reduction technique of Vecer for pricing arithmetic average Asian options. The assumption of constant volatility in Vecer's method will be relaxed to the case that volatility is randomly fluctuating and is driven by a mean-reverting (or ergodic) process. We then use the fast mean-reverting stochastic volatility asymptotic analysis introduced by Fouque, Papanicolaou and Sircar to derive an approximation to the option price which takes into account the skew of the implied volatility surface. This approximation is obtained by solving a pair of one-dimensional partial differential equations.
DA - 2003/10//
PY - 2003/10//
DO - 10.1088/1469-7688/3/5/301
VL - 3
IS - 5
SP - 353-362
SN - 1469-7696
ER -
TY - JOUR
TI - Numerical approximation of blow-up of radially symmetric solutions of the nonlinear Schrodinger equation
AU - Akrivis, GD
AU - Dougalis, VA
AU - Karakashian, OA
AU - McKinney, WR
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - We consider the initial-value problem for the radially symmetric nonlinear Schrödin\-ger equation with cubic nonlinearity (NLS) in d=2 and 3 space dimensions. To approximate smooth solutions of this problem, we construct and analyze a numerical method based on a standard Galerkin finite element spatial discretization with piecewise linear, continuous functions and on an implicit Crank--Nicolson type time-stepping procedure. We then equip this scheme with an adaptive spatial and temporal mesh refinement mechanism that enables the numerical technique to approximate well singular solutions of the NLS equation that blow up at the origin as the temporal variable t tends from below to a finite value $t^\star$. For the blow-up of the amplitude of the solution we recover numerically the well-known rate $(t^\star - t)^{-1/2}$ for d=3. For d=2 our numerical evidence supports the validity of the $\log \log$ law $[\ln\ln \frac {1}{t^\star -t} /(t^\star-t)]^{1/2}$ for t extremely close to $t^\star.$ The scheme also approximates well the details of the blow-up of the phase of the solution at the origin as $t\to t^\star.$
DA - 2003///
PY - 2003///
DO - 10.1137/S1064827597332041
VL - 25
IS - 1
SP - 186-212
SN - 1095-7197
KW - nonlinear Schrodinger equation
KW - point blow-up
KW - finite element methods
KW - adaptive mesh refinement
ER -
TY - JOUR
TI - New formulations for interface problems in polar coordinates
AU - Li, ZL
AU - Wang, WC
AU - Chern, IL
AU - Lai, MC
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - In this paper, numerical methods are proposed for some interface problems in polar or Cartesian coordinates. The new methods are based on a formulation that transforms the interface problem with a nonsmooth or discontinuous solution into a problem with a smooth solution. The new formulation leads to a simple second order finite difference scheme for the partial differential equation and a new interpolation scheme for the normal derivative of the solution. In conjunction with the fast immersed interface method, a fast solver has been developed for the interface problems with a piecewise constant but a discontinuous coefficient using the new formulation in a polar coordinate system.
DA - 2003///
PY - 2003///
DO - 10.1137/S106482750139618X
VL - 25
IS - 1
SP - 224-245
SN - 1095-7197
KW - interface problems
KW - singular source
KW - delta function
KW - level set function
KW - discontinuous coefficients
KW - polar coordinates
KW - immersed interface method
KW - smooth extension
KW - fast Poisson solver
ER -
TY - JOUR
TI - Early termination in sparse interpolation algorithms
AU - Kaltofen, E
AU - Lee, ES
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - A probabilistic strategy, early termination, enables different interpolation algorithms to adapt to the degree or the number of terms in the target polynomial when neither is supplied in the input. In addition to dense algorithms, we implement this strategy in sparse interpolation algorithms. Based on early termination, racing algorithms execute simultaneously dense and sparse algorithms. The racing algorithms can be embedded as the univariate interpolation substep within Zippel’s multivariate method. In addition, we experimentally verify some heuristics of early termination, which make use of thresholds and post-verification.
DA - 2003///
PY - 2003///
DO - 10.1016/S0747-7171(03)00088-9
VL - 36
IS - 3-4
SP - 365-400
SN - 0747-7171
KW - early termination
KW - sparse polynomial
KW - black box polynomial
KW - interpolation
KW - sparse interpolation
KW - randomized algorithm
ER -
TY - JOUR
TI - Algorithms for computing sparsest shifts of polynomials in power, Chebyshev, and Pochhammer bases
AU - Giesbrecht, M
AU - Kaltofen, E
AU - Lee, WS
T2 - JOURNAL OF SYMBOLIC COMPUTATION
AB - We give a new class of algorithms for computing sparsest shifts of a given polynomial. Our algorithms are based on the early termination version of sparse interpolation algorithms: for a symbolic set of interpolation points, a sparsest shift must be a root of the first possible zero discrepancy that can be used as the early termination test. Through reformulating as multivariate shifts in a designated set, our algorithms can compute the sparsest shifts that simultaneously minimize the terms of a given set of polynomials. Our algorithms can also be applied to the Pochhammer and Chebyshev bases for the polynomials, and potentially to other bases as well. For a given univariate polynomial, we give a lower bound for the optimal sparsity. The efficiency of our algorithms can be further improved by imposing such a bound and pruning the highest degree terms.
DA - 2003///
PY - 2003///
DO - 10.1016/S0747-7171(03)00087-7
VL - 36
IS - 3-4
SP - 401-424
SN - 0747-7171
KW - sparse shifts
KW - early termination
KW - sparse polynomial
KW - sparse interpolation
KW - Chebyshev basis
KW - Pochhammer basis
ER -
TY - JOUR
TI - Versatile two-level Schwarz preconditioners for multiphase flow
AU - Kees, CE
AU - Miller, CT
AU - Jenkins, EW
AU - Kelley, CT
T2 - COMPUTATIONAL GEOSCIENCES
DA - 2003///
PY - 2003///
DO - 10.1023/A:1023514922877
VL - 7
IS - 2
SP - 91-114
SN - 1420-0597
KW - aggregation
KW - domain decomposition
KW - multilevel Schwarz
KW - multiphase flow
ER -
TY - JOUR
TI - Stability of shear bands in an elastoplastic model for granular flow: The role of discreteness
AU - Shearer, M
AU - Schaeffer, DG
AU - Witelski, TP
T2 - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
AB - Continuum models for granular flow generally give rise to systems of nonlinear partial differential equations that are linearly ill-posed. In this paper we introduce discreteness into an elastoplasticity model for granular flow by approximating spatial derivatives with finite differences. The resulting ordinary differential equations have bounded solutions for all time, a consequence of both discreteness and nonlinearity. We study how the large-time behavior of solutions in this model depends on an elastic shear modulus ℰ. For large and moderate values of ℰ, the model has stable steady-state solutions with uniform shearing except for one shear band; almost all solutions tend to one of these as t→∞. However, when ℰ becomes sufficiently small, the single-shear-band solutions lose stability through a Hopf bifurcation. The value of ℰ at the bifurcation point is proportional to the ratio of the mesh size to the macroscopic length scale. These conclusions are established analytically through a careful estimation of the eigenvalues. In numerical simulations we find that: (i) after stability is lost, time-periodic solutions appear, containing both elastic and plastic waves, and (ii) the bifurcation diagram representing these solutions exhibits bi-stability.
DA - 2003/11//
PY - 2003/11//
DO - 10.1142/S0218202503003069
VL - 13
IS - 11
SP - 1629-1671
SN - 0218-2025
KW - shear band
KW - stability
KW - granular
KW - discrete model
ER -
TY - JOUR
TI - Inclusion regions for matrix eigenvalues
AU - Beattie, C
AU - Ipsen, ICF
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - We review Lehmann’s inclusion bounds and provide extensions to general (non-normal) matrices. Each inclusion region has a diameter related to the singular values of a restriction of the matrix to a subspace and dependent on either an eigenvector condition number or the departure of the matrix from normality. The inclusion regions are optimal for normal matrices. Similar considerations lead to inclusion bounds based on relative distances expressed analogously in terms of appropriately defined generalized singular values.
DA - 2003/1/1/
PY - 2003/1/1/
DO - 10.1016/S0024-3795(02)00279-3
VL - 358
IS - 1-3
SP - 281-291
SN - 0024-3795
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84867969159&partnerID=MN8TOARS
KW - eigenvalue bounds
KW - singular values
KW - inclusion regions
ER -
TY - JOUR
TI - Global attractor of a coupled finite difference reaction diffusion system with delays
AU - Pao, CV
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - In the study of asymptotic behavior of solutions for reaction diffusion systems, an important concern is to determine whether and when the system has a global attractor which attracts all positive time-dependent solutions. The aim of this paper is to investigate the global attraction problem for a finite difference system which is a discrete approximation of a coupled system of two reaction diffusion equations with time delays. Sufficient conditions are obtained to ensure the existence and global attraction of a positive solution of the corresponding steady-state system. Applications are given to three types of Lotka–Volterra reaction diffusion models, where time-delays may appear in the opposing species.
DA - 2003/12/1/
PY - 2003/12/1/
DO - 10.1016/j.jmaa.2003.08.011
VL - 288
IS - 1
SP - 251-273
SN - 1096-0813
ER -
TY - JOUR
TI - Finite difference reaction-diffusion systems with coupled boundary conditions and time delays (vol 272, pg 407, 2002)
AU - Pao, C. V.
T2 - Journal of Mathematical Analysis and Applications
DA - 2003///
PY - 2003///
VL - 288
IS - 2
SP - 870
ER -
TY - JOUR
TI - Accelerated monotone iterations for numerical solutions of nonlinear elliptic boundary value problems
AU - Pao, C. V.
T2 - Computers & Mathematics With Applications
DA - 2003///
PY - 2003///
DO - 10.1016/S0898-1221(03)00381-X
VL - 46
IS - 37905
SP - 1535-1544
ER -
TY - JOUR
TI - A note on unifying absolute and relative perturbation bounds
AU - Ipsen, ICF
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Perturbation bounds for invariant subspaces and eigenvalues of complex matrices are presented that lead to absolute as well as a large class of relative bounds. In particular it is shown that absolute bounds (such as those by Davis and Kahan, Bauer and Fike, and Hoffman and Wielandt) and some relative bounds are special cases of `universal' bounds. As a consequence, we obtain a new relative bound for subspaces of normal matrices, which contains a deviation of the matrix from (positive-) definiteness. We also investigate how row scaling affects eigenvalues and their sensitivity to perturbations, and we illustrate how the departure from normality can affect the condition number (with respect to inversion) of the scaled eigenvectors.
DA - 2003/1/1/
PY - 2003/1/1/
DO - 10.1016/S0024-3795(01)00571-7
VL - 358
IS - 1-3
SP - 239-253
SN - 1873-1856
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-84867926408&partnerID=MN8TOARS
KW - invariant subspace
KW - eigenvalue
KW - absolute bound
KW - relative bound
KW - subspace angle
KW - departure from normality
ER -
TY - JOUR
TI - Semi-smooth Newton methods for state-constrained optimal control problems
AU - Ito, K
AU - Kunisch, K
T2 - SYSTEMS & CONTROL LETTERS
AB - A regularized optimality system for state-constrained optimal control problems is introduced and semi-smooth Newton methods for its solution are analyzed. Convergence of the regularized problems is proved. Numerical tests confirm the theoretical results and demonstrate the efficiency of the proposed methodology.
DA - 2003/10/22/
PY - 2003/10/22/
DO - 10.1016/s0167-6911(03)00156-7
VL - 50
IS - 3
SP - 221-228
SN - 1872-7956
KW - semi-smooth Newton methods
KW - state-constrained optimal control
KW - superlinear convergence
KW - augmented Lagrangians
ER -
TY - JOUR
TI - On robust matrix completion with prescribed eigenvalues
AU - Chu, MT
AU - Diele, F
AU - Sgura, I
T2 - FUTURE GENERATION COMPUTER SYSTEMS
AB - Matrix completion with prescribed eigenvalues is a special kind of inverse eigenvalue problems. Thus far, only a handful of specific cases concerning its existence and construction have been studied in the literature. The general problem where the prescribed entries are at arbitrary locations with arbitrary cardinalities proves to be challenging both theoretically and computationally. This paper investigates some continuation techniques by recasting the completion problem as an optimization of the distance between the isospectral matrices with the prescribed eigenvalues and the affine matrices with the prescribed entries. The approach not only offers an avenue to solving the completion problem in its most general setting but also makes it possible to seek a robust solution that is least sensitive to perturbation.
DA - 2003/10//
PY - 2003/10//
DO - 10.1016/s0167-739x(03)00040-2
VL - 19
IS - 7
SP - 1139-1153
SN - 0167-739X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0042692965&partnerID=MN8TOARS
KW - matrix completion
KW - inverse eigenvalue problem
KW - robust solution
KW - isospectral matrices
KW - continuation method
KW - steepest descent gradient flow
ER -
TY - JOUR
TI - New Cartesian grid methods for interface problems using the finite element formulation
AU - Li, ZL
AU - Lin, T
AU - Wu, XH
T2 - NUMERISCHE MATHEMATIK
AB - New finite element methods based on Cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients. The triangulations in these methods do not need to fit the interfaces. The basis functions in these methods are constructed to satisfy the interface jump conditions either exactly or approximately. Both non-conforming and conforming finite element spaces are considered. Corresponding interpolation functions are proved to be second order accurate in the maximum norm. The conforming finite element method has been shown to be convergent. With Cartesian triangulations, these new methods can be used as finite difference methods. Numerical examples are provided to support the methods and the theoretical analysis.
DA - 2003/11//
PY - 2003/11//
DO - 10.1007/s00211-003-0473-x
VL - 96
IS - 1
SP - 61-98
SN - 0029-599X
ER -
TY - JOUR
TI - Invariant measures of nonholonomic flows with internal degrees of freedom
AU - Zenkov, DV
AU - Bloch, AM
T2 - NONLINEARITY
AB - In this paper we study measure preserving flows associated with nonholonomic systems with internal degrees of freedom. Our approach reveals geometric reasons for the existence of measures in the form of an integral invariant with smooth density that depends on the internal configuration of the system.
DA - 2003/9//
PY - 2003/9//
DO - 10.1088/0951-7715/16/5/313
VL - 16
IS - 5
SP - 1793-1807
SN - 1361-6544
ER -
TY - JOUR
TI - Heat transfer and evaporation/condensation problems based on the linearized Boltzmann equation
AU - Siewert, CE
T2 - EUROPEAN JOURNAL OF MECHANICS B-FLUIDS
AB - A polynomial expansion procedure and an analytical discrete-ordinates method are used to solve four basic problems, all based on the linearized Boltzmann equation for rigid-sphere interactions, that describe heat transfer and/or evaporation–condensation between two parallel surfaces or for the case of a semi-infinite half space. Relevant to the case of two surfaces, the basic problem of heat transfer driven by a temperature difference at two confining walls described by a general Maxwell gas–surface interaction law (a mixture of specular and diffuse reflection) is solved for the case where different accommodation coefficients can be used for each of the two bounding surfaces. In addition, the classical problem of “reverse temperature gradient” in the theory of evaporation and condensation is also solved for the case of two parallel liquid–vapor interfaces kept at different temperatures. In regard to half-space applications, an evaporation/condensation problem based on a presumed known interface condition and a heat-conduction problem (with no net flow) driven by energy flow from a bounding surface with know properties are each solved with what is considered a high degree of accuracy.
DA - 2003///
PY - 2003///
DO - 10.1016/S0997-7546(03)00053-0
VL - 22
IS - 4
SP - 391-408
SN - 1873-7390
KW - Boltzmann equation
KW - rarefied gas dynamics
KW - heat transfer
KW - evaporation-condensation
ER -
TY - JOUR
TI - Error estimates for random boundary value problems with applications to a hanging cable problem
AU - Ladde, G. S.
AU - Medhin, N. G.
AU - Sambandham, M.
T2 - Mathematical and Computer Modelling
DA - 2003///
PY - 2003///
DO - 10.1016/S0895-7177(03)00315-7
VL - 38
IS - 10
SP - 1037-1050
ER -
TY - JOUR
TI - Viscous-slip, thermal-slip, and temperature-jump coefficients as defined by the linearized Boltzmann equation and the Cercignani-Lampis boundary condition
AU - Siewert, CE
T2 - PHYSICS OF FLUIDS
AB - A polynomial expansion procedure and an analytical discrete-ordinates method are used to evaluate the viscous-slip coefficient, the thermal-slip coefficient, and the temperature-jump coefficient as defined by a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions and the Cercignani–Lampis boundary condition.
DA - 2003/6//
PY - 2003/6//
DO - 10.1063/1.1567284
VL - 15
IS - 6
SP - 1696-1701
SN - 1070-6631
ER -
TY - CHAP
TI - Optimization in the Context of Active Control of Sound
AU - Lončarić, Josip
AU - Tsynkov, Semyon
T2 - Computational Science and Its Applications — ICCSA 2003
AB - A problem of eliminating the unwanted time-harmonic noise on a predetermined region of interest is solved by active means, i.e., by introducing the additional sources of sound, called controls, that generate the appropriate annihilating signal (anti-sound). The general solution for controls has been obtained previously for both the continuous and discrete formulation of the problem. Next, the control sources are optimized using different criteria. Minimization of the overall absolute acoustic source strength is equivalent to minimization of multi-variable complex functions in the sense of L 1 with conical constraints. The global L 1 optimum appears to be a special layer of monopoles on the perimeter of the protected region. The use of quadratic cost functions, e.g., the L 2 norm of the controls, leads to a versatile numerical procedure. It allows one to analyze sophisticated geometries in the case of a constrained minimization. Finally, minimization of power consumed by an active control system always involves interaction between the sources of sound and the surrounding acoustic field, which was not the case for either L 1 or L 2. One can, in fact, build a control system that would require no power input for operation and may even produce a net power gain while providing the exact noise cancellation. This, of course, comes at the expense of having the original sources of noise produce even more energy.
CN - QA75.5 .I12 2003 v.1-3
PY - 2003///
DO - 10.1007/3-540-44843-8_87
VL - 2668
SP - 801-810
OP -
PB - Springer Berlin Heidelberg
SN - 9783540401612 9783540448433
UR - http://dx.doi.org/10.1007/3-540-44843-8_87
DB - Crossref
ER -
TY - JOUR
TI - Off-axis neutrino scattering in gamma-ray burst central engines
AU - Miller, WA
AU - George, ND
AU - Kheyfets, A
AU - McGhee, JM
T2 - ASTROPHYSICAL JOURNAL
AB - The search for an understanding of an energy source great enough to explain the gamma-ray burst (GRB) phenomena has attracted much attention from the astrophysical community since its discovery. In this paper we extend the work of K. Asano and T. Fukuyama, and J. D. Salmonson and J. R. Wilson, and analyze the off-axis contributions to the energy-momentum deposition rate (MDR) from the neutrino anti-neutrino collisions above a rotating black hole/thin accretion disk system. Our calculations are performed by imaging the accretion disk at a specified observer using the full geodesic equations, and calculating the cumulative MDR from the scattering of all pairs of neutrinos and anti-neutrinos arriving at the observer. Our results shed light on the beaming efficiency of GRB models of this kind. Although we confirm Asano and Fukuyama's conjecture as to the constancy of the beaming for small angles away from the axis; nevertheless, we find the dominant contribution to the MDR comes from near the surface of the disk with a tilt of approximately \pi/4 in the direction of the disk's rotation. We find that the MDR at large radii is directed outward in a conic section centered around the symmetry axis and is larger, by a factor of 10 to 20, than the on-axis values. By including this off-axis disk source, we find a linear dependence of the MDR on the black hole angular momentum (a). In addition, we find that scattering is directed back onto the black hole in regions just above the horizon of the black hole. This gravitational ``in scatter'' may provide an observable high energy signature of the central engine, or at least another channel for accretion.
DA - 2003/2/1/
PY - 2003/2/1/
DO - 10.1086/345471
VL - 583
IS - 2
SP - 833-841
SN - 1538-4357
KW - black hole physics
KW - gamma rays : bursts
KW - gravitation
KW - neutrinos
ER -
TY - JOUR
TI - Modeling of HPA and HPA linearization through a predistorter: Global Broadcasting Service applications
AU - Nguyen, TM
AU - Yoh, J
AU - Lee, CH
AU - Tran, HT
AU - Johnson, DM
T2 - IEEE TRANSACTIONS ON BROADCASTING
AB - This paper presents a technique to linearize the high power amplifier (HPA) through a predistorter (PD). The characteristics of the PD circuit are derived based on the extension of Saleh's model for HPA and a simple linear-log model. Numerical results are shown for Global Broadcasting Service (GBS) applications.
DA - 2003/6//
PY - 2003/6//
DO - 10.1109/TBC.2003.813650
VL - 49
IS - 2
SP - 132-141
SN - 0018-9316
KW - Global Broadcasting Service
KW - high power amplifier
KW - predistorter
ER -
TY - JOUR
TI - Formation of discontinuities in flux-saturated degenerate parabolic equations
AU - Chertock, A
AU - Kurganov, A
AU - Rosenau, P
T2 - NONLINEARITY
AB - We endow the nonlinear degenerate parabolic equation used to describe propagation of thermal waves in plasma or in a porous medium, with a mechanism for flux saturation intended to correct the nonphysical gradient-flux relations at high gradients. We study both analytically and numerically the resulting equation: ut = [unQ(g(u)x)]x, n>0, where Q is a bounded increasing function. This model reveals that for n>1 the motion of the front is controlled by the saturation mechanism and instead of the typical infinite gradients resulting from the linear flux-gradients relations, Q∼ux, we obtain a sharp, shock-like front, typically associated with nonlinear hyperbolic phenomena. We prove that if the initial support is compact, independently of the smoothness of the initial datum inside the support, a sharp front discontinuity forms in a finite time, and until then the front does not expand.
DA - 2003/11//
PY - 2003/11//
DO - 10.1088/0951-7715/16/6/301
VL - 16
IS - 6
SP - 1875-1898
SN - 0951-7715
UR - https://doi-org.prox.lib.ncsu.edu/10.1088/0951-7715/16/6/301
ER -
TY - JOUR
TI - Efficient steady-state solution techniques for variably saturated groundwater flow
AU - Farthing, MW
AU - Kees, CE
AU - Coffey, TS
AU - Kelley, CT
AU - Miller, CT
T2 - ADVANCES IN WATER RESOURCES
AB - We consider the simulation of steady-state variably saturated groundwater flow using Richards’ equation (RE). The difficulties associated with solving RE numerically are well known. Most discretization approaches for RE lead to nonlinear systems that are large and difficult to solve. The solution of nonlinear systems for steady-state problems can be particularly challenging, since a good initial guess for the steady-state solution is often hard to obtain, and the resulting linear systems may be poorly scaled. Common approaches like Picard iteration or variations of Newton’s method have their advantages but perform poorly with standard globalization techniques under certain conditions. Pseudo-transient continuation has been used in computational fluid dynamics for some time to obtain steady-state solutions for problems in which Newton’s method with standard line-search strategies fails. Here, we examine the use of pseudo-transient continuation as well as Newton’s method combined with standard globalization techniques for steady-state problems in heterogeneous domains. We investigate the methods’ performance with direct and preconditioned Krylov iterative linear solvers. We then make recommendations for robust and efficient approaches to obtain steady-state solutions for RE under a range of conditions.
DA - 2003/8//
PY - 2003/8//
DO - 10.1016/S0309-1708(03)00076-9
VL - 26
IS - 8
SP - 833-849
SN - 0309-1708
KW - Richards' equation
KW - steady-state
KW - pseudo-transient continuation
ER -
TY - JOUR
TI - Alterations in the mechanical properties of the human chondrocyte pericellular matrix with osteoarthritis
AU - Alexopoulos, LG
AU - Haider, MA
AU - Vail, TP
AU - Guilak, F
T2 - JOURNAL OF BIOMECHANICAL ENGINEERING-TRANSACTIONS OF THE ASME
AB - In articular cartilage, chondrocytes are surrounded by a pericellular matrix (PCM), which together with the chondrocyte have been termed the "chondron." While the precise function of the PCM is not know there has been considerable speculation that it plays a role in regulating the biomechanical environment of the chondrocyte. In this study, we measured the Young's modulus of the PCM from normal and osteoarthritic cartilage using the micropipette aspiration technique, coupled with a newly developed axisymmetric elastic layered half-space model of the experimental configuration. Viable, intact chondrons were extracted from human articular cartilage using a new microaspiration-based isolation technique. In normal cartilage, the Young's modulus of the PCM was similar in chondrons isolated from the surface zone (68.9 +/- 18.9 kPa) as compared to the middle and deep layers (62.0 +/- 30.5 kPa). However, the mean Young's modulus of the PCM (pooled for the two zones) was significantly decreased in osteoarthritic cartilage (66.5 +/- 23.3 kPa versus 41.3 +/- 21.1 kPa, p < 0.001). In combination with previous theoretical models of cell-matrix interactions in cartilage, these findings suggest that the PCM has an important influence on the stress-strain environment of the chondrocyte that potentially varies with depth from the cartilage surface. Furthermore, the significant loss of PCM stiffness that was observed in osteoarthritic cartilage may affect the magnitude and distribution of biomechanical signals perceived by the chondrocytes.
DA - 2003/6//
PY - 2003/6//
DO - 10.1115/1.1579047
VL - 125
IS - 3
SP - 323-333
SN - 0148-0731
ER -
TY - JOUR
TI - Air quality research: perspective from climate change modelling research
AU - Semazzi, F
T2 - ENVIRONMENT INTERNATIONAL
AB - A major component of climate change is a manifestation of changes in air quality. This paper explores the question of air quality from the climate change modelling perspective. It reviews recent research advances on the cause-effect relationships between atmospheric air composition and climate change, primarily based on the Intergovernmental Panel on Climate Change (IPCC) assessment of climate change over the past decade. There is a growing degree of confidence that the warming world over the past century was caused by human-related changes in the composition of air. Reliability of projections of future climate change is highly dependent on future emission scenarios that have been identified that in turn depend on a multitude of complicated interacting social-economic factors. Anticipated improvements in the performance of climate models is a major source of optimism for better climate projections in the future, but the real benefits of its contribution will be closely coupled with other sources of uncertainty, and in particular emission projections.
DA - 2003/6//
PY - 2003/6//
DO - 10.1016/S0160-4120(02)00184-8
VL - 29
IS - 2-3
SP - 253-261
SN - 0160-4120
KW - air quality
KW - climate change
KW - climate models
ER -
TY - JOUR
TI -
AU - Tsynkov, S. V.
T2 - Journal of Scientific Computing
DA - 2003///
PY - 2003///
DO - 10.1023/A:1021111713715
VL - 18
IS - 2
SP - 155-189
OP -
SN - 0885-7474
UR - http://dx.doi.org/10.1023/A:1021111713715
DB - Crossref
KW - linear differential operator
KW - discontinuous solution
KW - distribution
KW - monopole
KW - dipole
KW - fundamental solution
KW - convolution
KW - boundary integral
KW - single- and double-layer potentials
KW - surface density of the potential
KW - linear difference operator
KW - multi-layer grid boundary
KW - discontinuous grid function
KW - discrete monopole and dipole layers
KW - Calderon's potential
KW - difference potential
ER -
TY - JOUR
TI - Three-dimensional elliptic solvers for interface problems and applications
AU - Deng, SZ
AU - Ito, K
AU - Li, ZL
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - Second-order accurate elliptic solvers using Cartesian grids are presented for three-dimensional interface problems in which the coefficients, the source term, the solution and its normal flux may be discontinuous across an interface. One of our methods is designed for general interface problems with variable but discontinuous coefficient. The scheme preserves the discrete maximum principle using constrained optimization techniques. An algebraic multigrid solver is applied to solve the discrete system. The second method is designed for interface problems with piecewise constant coefficient. The method is based on the fast immersed interface method and a fast 3D Poisson solver. The second method has been modified to solve Helmholtz/Poisson equations on irregular domains. An application of our method to an inverse interface problem of shape identification is also presented. In this application, the level set method is applied to find the unknown surface iteratively.
DA - 2003/1/1/
PY - 2003/1/1/
DO - 10.1016/S0021-9991(02)00028-1
VL - 184
IS - 1
SP - 215-243
SN - 0021-9991
KW - 3D elliptic interface problem
KW - irregular domain
KW - discontinuous coefficient
KW - discrete maximum preserving scheme
KW - quadratic optimization
KW - algebraic multigrid
KW - shape identification
KW - level set method
ER -
TY - JOUR
TI - Real-valued, low rank, circulant approximation
AU - Chu, MT
AU - Plemmons, RJ
T2 - SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS
AB - Partially due to the fact that the empirical data collected by devices with finite bandwidth often neither preserves the specified structure nor induces a certain desired rank, retrieving the nearest structured low rank approximation from a given data matrix becomes an imperative task in many applications. This paper investigates the case of approximating a given target matrix by a real-valued circulant matrix of a specified, fixed, and low rank. A fast Fourier transform (FFT)-based numerical procedure is proposed to speed up the computation. However, since a conjugate-even set of eigenvalues must be maintained to guarantee a real-valued matrix, it is shown by numerical examples that the nearest real-valued, low rank, and circulant approximation is sometimes surprisingly counterintuitive.
DA - 2003///
PY - 2003///
DO - 10.1137/S0895479801383166
VL - 24
IS - 3
SP - 645-659
SN - 0895-4798
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0041663838&partnerID=MN8TOARS
KW - real-valued circulant matrix
KW - lower rank
KW - nearest approximation
KW - conjugate-even
KW - fast Fourier transform
KW - truncated singular value decomposition
ER -
TY - JOUR
TI - Convergence of iterative split-operator approaches for approximating nonlinear reactive transport problems
AU - Kanney, JF
AU - Miller, CT
AU - Kelley, CT
T2 - ADVANCES IN WATER RESOURCES
AB - Numerical solutions to nonlinear reactive solute transport problems (NRTPs) are often computed using split-operator (SO) approaches, which separate the transport and reaction processes. This uncoupling introduces an additional source of numerical error, known as the splitting error. The iterative split-operator (ISO) algorithm removes the splitting error through iteration. Although the ISO algorithm is often used, there has been very little analysis of its convergence behavior. This work uses theoretical analysis and numerical experiments to investigate the convergence rate of the ISO approach for solving NRTPs. We show that under certain assumptions regarding smoothness, the convergence rate of the ISO algorithm applied NRTPs is O(Δt2). We demonstrate that the theoretical convergence rate can be achieved in practice if the numerical solution of the transport and reaction steps are carried out with sufficient accuracy. We also show that accurate estimation of the lagged operator in each step is crucial to obtaining the theoretical convergence rate.
DA - 2003/3//
PY - 2003/3//
DO - 10.1016/S0309-1708(02)00162-8
VL - 26
IS - 3
SP - 247-261
SN - 1872-9657
KW - reactive transport
KW - nonlinear mass transfer
KW - numerical solution
KW - operator splitting
KW - iterative split-operator
KW - convergence rate
ER -
TY - JOUR
TI - Acoustic attenuation employing variable wall admittance
AU - Banks, H. T.
AU - Furati, K. M.
AU - Ito, K.
AU - Luke, N. S.
AU - Smith, C. J.
T2 - Directions in mathematical systems theory and optimization (Lecture notes in control and information sciences; 286)
DA - 2003///
PY - 2003///
IS - 2003
SP - 15-26
ER -
TY - JOUR
TI - New roles for the gamma rhythm: Population tuning and preprocessing for the beta rhythm
AU - Olufsen, MS
AU - Whittington, MA
AU - Camperi, M
AU - Kopell, N
T2 - JOURNAL OF COMPUTATIONAL NEUROSCIENCE
DA - 2003///
PY - 2003///
DO - 10.1023/A:1021124317706
VL - 14
IS - 1
SP - 33-54
SN - 0929-5313
KW - gamma rhythms
KW - beta rhythms
KW - cell assembly formation
KW - plasticity
KW - hippocampus
KW - neocortex
KW - preprocessing
ER -
TY - JOUR
TI - Free energy model for hysteresis in magnetostrictive transducers
AU - Smith, RC
AU - Dapino, MJ
AU - Seelecke, S
T2 - JOURNAL OF APPLIED PHYSICS
AB - This article addresses the development of a free energy model for magnetostrictive transducers operating in hysteretic and nonlinear regimes. Such models are required both for material and system characterization and for model-based control design. The model is constructed in two steps. In the first, Helmholtz and Gibbs free energy relations are constructed for homogeneous materials with constant internal fields. In the second step, the effects of material nonhomogeneities and nonconstant effective fields are incorporated through the construction of appropriate stochastic distributions. Properties of the model are illustrated through comparison and prediction of data collected from a typical Terfenol-D transducer.
DA - 2003/1/1/
PY - 2003/1/1/
DO - 10.1063/1.1524312
VL - 93
IS - 1
SP - 458-466
SN - 1089-7550
ER -
TY - JOUR
TI - Globally convergent algorithms for nonsmooth nonlinear equations in computational fluid dynamics
AU - Coffey, T
AU - McMullan, RJ
AU - Kelley, CT
AU - McRae, DS
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - In this paper we report on a computational study in which a nonsmooth discretization of the Euler equations for flow in a nozzle is solved with splitting method which is in turn globalized with the method of pseudo-transient continuation.
DA - 2003/3/1/
PY - 2003/3/1/
DO - 10.1016/S0377-0427(02)00697-0
VL - 152
IS - 1-2
SP - 69-81
SN - 0377-0427
KW - pseudo-transient continuation
KW - nonlinear equations
KW - steady-state solutions
KW - global convergence
KW - splitting methods
KW - Euler equations
KW - MUSCL approximation
ER -
TY - JOUR
TI - The linearized Boltzmann equation: a concise and accurate solution of the temperature-jump problem
AU - Siewert, CE
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - Polynomial expansion procedures, along with an analytical discrete-ordinates method, are used to solve the temperature-jump problem based on a rigorous version of the linearized Boltzmann equation for rigid-sphere interactions. In particular, the temperature and density perturbations and the temperature-jump coefficient are obtained (essentially) analytically in terms of a modern version of the discrete-ordinates method. The developed algorithms are implemented for general values of the accommodation coefficient to yield numerical results that can be considered a new standard of reference.
DA - 2003/4/1/
PY - 2003/4/1/
DO - 10.1016/S0022-4073(02)00172-3
VL - 77
IS - 4
SP - 417-432
SN - 0022-4073
KW - Boltzmann equation
KW - rarefied gas dynamics
KW - temperature-jump problem
ER -
TY - JOUR
TI - Numerical simulation of aerated powder consolidation
AU - Coffey, KA
AU - Gremaud, PA
T2 - INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
AB - When a fine powder is dumped into a silo, the gas trapped by the particles will slowly escape by diffusing through the material. The corresponding uneven gas pressure distribution creates a body force that is taken into account through Darcy's law. By using spatial averaging, the formulation, even though essentially one-dimensional in space, includes effects due the geometry of the container. An efficient and robust numerical scheme based on a differential algebraic equation formulation is proposed and implemented. Various computational results are presented and discussed to establish the validity of the approach.
DA - 2003/10//
PY - 2003/10//
DO - 10.1016/S0020-7462(02)00063-X
VL - 38
IS - 8
SP - 1185-1194
SN - 0020-7462
ER -
TY - JOUR
TI - Multiple stable periodic solutions in a model for hormonal control of the menstrual cycle
AU - Clark, LH
AU - Schlosser, PM
AU - Selgrade, JF
T2 - BULLETIN OF MATHEMATICAL BIOLOGY
DA - 2003/1//
PY - 2003/1//
DO - 10.1006/bulum.2002.0326
VL - 65
IS - 1
SP - 157-173
SN - 0092-8240
ER -
TY - JOUR
TI - Maxwell-systems with nonlinear polarization
AU - Banks, HT
AU - Pinter, GA
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - We establish well-posedness results for a model describing the propagation of high-intensity electromagnetic waves in a nonlinear medium. The nonlinear material properties are represented by a nonlinear polarization in the form of a convolution. We also include some remarks on potential applications.
DA - 2003/9//
PY - 2003/9//
DO - 10.1016/S1468-1218(02)00074-3
VL - 4
IS - 3
SP - 483-501
SN - 1468-1218
ER -
TY - JOUR
TI - Global asymptotic behavior of a two-dimensional difference equation modelling competition
AU - Clark, D
AU - Kulenovic, MRS
AU - Selgrade, JF
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
AB - We investigate the global asymptotic behavior of solutions of the system of difference equationsxn+1=xna+cyn,yn+1=ynb+dxn,n=0,1,…,where the parameters a and b are in (0,1), c and d are arbitrary positive numbers and the initial conditions x0 and y0 are arbitrary nonnegative numbers. We show that the stable manifold of this system separates the positive quadrant into basins of attraction of two types of asymptotic behavior. In the case where a=b we find an explicit equation for the stable manifold.
DA - 2003/3//
PY - 2003/3//
DO - 10.1016/S0362-546X(02)00294-8
VL - 52
IS - 7
SP - 1765-1776
SN - 0362-546X
KW - asymptotic behavior
KW - monotonicity
KW - stability
KW - stable manifold
ER -
TY - JOUR
TI - Enhanced growth of tumors in SPARC null mice is associated with changes the ECM
AU - Brekken, RA
AU - Puolakkainen, P
AU - Graves, DC
AU - Workman, G
AU - Lubkin, , SR
AU - Sage, EH
T2 - JOURNAL OF CLINICAL INVESTIGATION
AB - SPARC, a 32-kDa glycoprotein, participates in the regulation of morphogenesis and cellular differentiation through its modulation of cell-matrix interactions. Major functions defined for SPARC in vitro are de-adhesion and antiproliferation. In vivo, SPARC is restricted in its expression to remodeling tissues, including pathologies such as cancer. However, the function of endogenous SPARC in tumor growth and progression is not known. Here, we report that implanted tumors grew more rapidly in mice lacking SPARC. We observed that tumors grown in SPARC null mice showed alterations in the production and organization of ECM components and a decrease in the infiltration of macrophages. However, there was no change in the levels of angiogenic growth factors in comparison to tumors grown in wild-type mice, although there was a statistically significant difference in total vascular area. Whereas SPARC did inhibit the growth of tumor cells in vitro, it did not have a demonstrable effect on the proliferation or apoptosis of tumor cells in vivo. These data indicate that host-derived SPARC is important for the appropriate organization of the ECM in response to implanted tumors and highlight the importance of the ECM in regulating tumor growth.
DA - 2003/2//
PY - 2003/2//
DO - 10.1172/JCI200316804
VL - 111
IS - 4
SP - 487-495
SN - 1558-8238
ER -
TY - JOUR
TI - Development of a biologically-based controlled growth and differentiation model for developmental toxicology
AU - Whitaker, SY
AU - Tran, HT
AU - Portier, CJ
T2 - JOURNAL OF MATHEMATICAL BIOLOGY
AB - Amathematical model is developed with a highly controlled birth and death process for precursor cells. This model is both biologically- and statistically-based. The controlled growth and differentiation (CGD) model limits the number of replications allowed in the development of a tissue or organ and thus, more closely reflects the presence of a true stem cell population. Leroux et al. (1996) presented a biologically-based dose-response model for developmental toxicology that was derived from a partial differential equation for the generating function. This formulation limits further expansion into more realistic models of mammalian development. The same formulae for the probability of a defect (a system of ordinary differential equations) can be derived through the Kolmogorov forward equations due to the nature of this Markov process. This modified approach is easily amenable to the expansion of more complicated models of the developmental process such as the one presented here. Comparisons between the Leroux et al. (1996) model and the controlled growth and differentiation (CGD) model as developed in this paper are also discussed.
DA - 2003/1//
PY - 2003/1//
DO - 10.1007/s00285-002-0164-8
VL - 46
IS - 1
SP - 1-16
SN - 0303-6812
KW - teratology
KW - multistate process
KW - cellular kinetics
KW - numerical simulation
ER -
TY - BOOK
TI - Optimal control of the growth of wealth of nations
AU - Chukwu, E. N.
CN - HB135 .C48 2003
DA - 2003///
PY - 2003///
PB - London; New York: Taylor & Francis
SN - 0415269660
ER -
TY - JOUR
TI - Zone determinant expansions for nuclear lattice simulations
AU - Lee, DJ
AU - Ipsen, ICF
T2 - PHYSICAL REVIEW C
AB - We discuss simulations of finite temperature nuclear matter on the lattice. We introduce a new approximation to nucleon matrix determinants that is physically motivated by chiral effective theory. The method involves breaking the lattice into spatial zones and expanding the determinant in powers of the boundary hopping parameter.
DA - 2003/12//
PY - 2003/12//
DO - 10.1103/physrevc.68.064003
VL - 68
IS - 6
SP -
SN - 1089-490X
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-85035272077&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Time-reversal aperture enhancement
AU - Fouque, JP
AU - Solna, K
T2 - MULTISCALE MODELING & SIMULATION
AB - Time-reversal refocusing for waves propagating in inhomogeneous media have recently been observed and studied experimentally in various contexts (ultrasound, underwater acoustics, ...); see, for instance, [M. Fink, Scientific American, November (1999), pp. 63--97]. Important potential applications have been proposed in various fields, for instance in imaging or communication. However, the full mathematical analysis, meaning both modeling of the physical problem and derivation of the time-reversal effect, is a deep and complex problem. Two cases that have been considered in depth recently correspond to one-dimensional media and the parabolic approximation regime where the backscattering is negligible. In this paper we give a complete analysis of time-reversal of waves emanating from a point source and propagating in a randomly layered medium. The wave transmitted through the random medium is recorded on a small time-reversal mirror and sent back into the medium, time-reversed. Our analysis enables us to contrast the refocusing properties of a homogeneous medium and a random medium. We show that random medium fluctuations actually enhance the spatial refocusing around the initial source position. We consider a regime where the correlation length of the medium is much smaller than the pulse width, which itself is much smaller than the distance of propagation. We derive asymptotic formulas for the refocused pulse which we interpret in terms of an enhanced effective aperture. This interpretation is, in fact, comparable to the superresolution effect obtained in the other extreme regime corresponding to the parabolic approximation. However, as we discuss, the mechanism that generates the superresolution is very different in these two extreme situations.
DA - 2003///
PY - 2003///
DO - 10.1137/S1540345902414443
VL - 1
IS - 2
SP - 239-259
SN - 1540-3467
KW - wave propagation
KW - random media
KW - superresolution
KW - time-reversal
KW - diffusion approximation
ER -
TY - JOUR
TI - Solving a nonlinear problem in magneto-rheological fluids using the immersed interface method
AU - Ito, K
AU - Li, ZL
T2 - JOURNAL OF SCIENTIFIC COMPUTING
DA - 2003/12//
PY - 2003/12//
DO - 10.1023/A:1025356025745
VL - 19
IS - 1-3
SP - 253-266
SN - 0885-7474
KW - non-linear interface problem
KW - magneto-rheological fluid
KW - maximum principal preserving scheme
KW - immersed interface method
KW - level set method
KW - substitution method
ER -
TY - JOUR
TI - Singular perturbations in option pricing
AU - Fouque, JP
AU - Papanicolaou, G
AU - Sircar, R
AU - Solna, K
T2 - SIAM JOURNAL ON APPLIED MATHEMATICS
AB - After the celebrated Black--Scholes formula for pricing call options under constant volatility, the need for more general nonconstant volatility models in financial mathematics motivated numerous works during the 1980s and 1990s. In particular, a lot of attention has been paid to stochastic volatility models in which the volatility is randomly fluctuating driven by an additional Brownian motion. We have shown in [Derivatives in Financial Markets with Stochastic Volatility, Cambridge University Press, Cambridge, UK, 2000; Internat. J. Theoret. Appl. Finance, 13 (2000), pp. 101--142] that, in the presence of a separation of time scales between the main observed process and the volatility driving process, asymptotic methods are very efficient in capturing the effects of random volatility in simple robust corrections to constant volatility formulas. From the point of view of PDEs, this method corresponds to a singular perturbation analysis. The aim of this paper is to deal with the nonsmoothness of the payoff function inherent to option pricing. We present the case of call options for which the payoff function forms an angle at the strike price. This case is important since these are the typical instruments used in the calibration of pricing models. We establish the pointwise accuracy of the corrected Black--Scholes price by using an appropriate payoff regularization which is removed simultaneously as the asymptotics is performed.
DA - 2003///
PY - 2003///
DO - 10.1137/S0036139902401550
VL - 63
IS - 5
SP - 1648-1665
SN - 1095-712X
KW - mathematical finance
KW - option pricing
KW - stochastic volatility
KW - singular perturbations
ER -
TY - JOUR
TI - Semiclean rings
AU - Ye, YQ
T2 - COMMUNICATIONS IN ALGEBRA
AB - Abstract The notion of semiclean elements in a ring is defined. Every clean element is semiclean. A ring R is said to be semiclean if every element in R is semiclean. The group ring Z p G with G a cyclic group of order 3 is proved to be semiclean. The n × n matrix ring M n (R) over a semiclean ring is semiclean. If R is a torsion free semiclean ring in which every element of R can be written as a sum of periodic and ±1, then R is clean. Every element in a semiclean ring R with 2 invertible is a sum of no more than 3 units.
DA - 2003///
PY - 2003///
DO - 10.1081/AGB-120023977
VL - 31
IS - 11
SP - 5609-5625
SN - 0092-7872
KW - clean rings
KW - semiclean rings
KW - group rings
ER -
TY - JOUR
TI - On the solvability of nonlinear discrete boundary value problems
AU - Rodriguez, J
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
AB - In this paper, we establish sufficient conditions for the existence of solutions to nonlinear, second-order, discrete boundary value problems of the form: \mgreek{D} ( \hspace{1pt} p(t-1) \hspace{1pt} x \hspace{1pt} (t-1)) + q \hspace{1pt} (t) \hspace{1pt} x \hspace{1pt} (t) = f(t,x \hspace{1pt} (t)), subject to x(0) = 0 and x \hspace{1pt} (N) = 0. The nonlinearity f:R \times R \rightarrow R is assumed to be continuous, but not necessarily differentiable. We provide conditions for the solvability of the boundary value problem when f is of the “perturbation type” as well as when f is of “slow growth”.
DA - 2003/7//
PY - 2003/7//
DO - 10.1080/1023619031000062934
VL - 9
IS - 9
SP - 863-867
SN - 1023-6198
KW - difference equations
KW - boundary value problems
KW - degree theory
ER -
TY - JOUR
TI - Nonlinear discrete systems with global boundary conditions
AU - Rodriguez, J.
T2 - Journal of Mathematical Analysis and Applications
DA - 2003///
PY - 2003///
DO - 10.1016/S022-247X(03)00536-5
VL - 286
IS - 2
SP - 782-794
ER -
TY - JOUR
TI - Attractors for discrete periodic dynamical systems
AU - Franke, JE
AU - Selgrade, JF
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - A mathematical framework is introduced to study attractors of discrete, nonautonomous dynamical systems which depend periodically on time. A structure theorem for such attractors is established which says that the attractor of a time-periodic dynamical system is the union of attractors of appropriate autonomous maps. If the nonautonomous system is a perturbation of an autonomous map, properties that the nonautonomous attractor inherits from the autonomous attractor are discussed. Examples from population biology are presented.
DA - 2003/10/1/
PY - 2003/10/1/
DO - 10.1016/S0022-247X(03)00417-7
VL - 286
IS - 1
SP - 64-79
SN - 0022-247X
ER -
TY - JOUR
TI - The primal-dual active set strategy as a semismooth Newton method
AU - Hintermuller, M
AU - Ito, K
AU - Kunisch, K
T2 - SIAM JOURNAL ON OPTIMIZATION
AB - This paper addresses complementarity problems motivated by constrained optimal control problems. It is shown that the primal-dual active set strategy, which is known to be extremely efficient for this class of problems, and a specific semismooth Newton method lead to identical algorithms. The notion of slant differentiability is recalled and it is argued that the $\max$-function is slantly differentiable in Lp-spaces when appropriately combined with a two-norm concept. This leads to new local convergence results of the primal-dual active set strategy. Global unconditional convergence results are obtained by means of appropriate merit functions.
DA - 2003///
PY - 2003///
DO - 10.1137/S1052623401383558
VL - 13
IS - 3
SP - 865-888
SN - 1095-7189
KW - complementarity problems
KW - function spaces
KW - semismooth Newton method
ER -
TY - JOUR
TI - The linearized Boltzmann equation: Concise and accurate solutions to basic flow problems
AU - Siewert, CE
T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
DA - 2003/3//
PY - 2003/3//
DO - 10.1007/s000330300005
VL - 54
IS - 2
SP - 273-303
SN - 0044-2275
KW - Boltzmann equation
KW - rarefied gas dynamics
KW - Kramers
KW - thermal creep
KW - Poiseuille
KW - Couette
ER -
TY - JOUR
TI - Structured low rank approximation
AU - Chu, MT
AU - Funderlic, RE
AU - Plemmons, RJ
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - This paper concerns the construction of a structured low rank matrix that is nearest to a given matrix. The notion of structured low rank approximation arises in various applications, ranging from signal enhancement to protein folding to computer algebra, where the empirical data collected in a matrix do not maintain either the specified structure or the desirable rank as is expected in the original system. The task to retrieve useful information while maintaining the underlying physical feasibility often necessitates the search for a good structured lower rank approximation of the data matrix. This paper addresses some of the theoretical and numerical issues involved in the problem. Two procedures for constructing the nearest structured low rank matrix are proposed. The procedures are flexible enough that they can be applied to any lower rank, any linear structure, and any matrix norm in the measurement of nearness. The techniques can also be easily implemented by utilizing available optimization packages. The special case of symmetric Toeplitz structure using the Frobenius matrix norm is used to exemplify the ideas throughout the discussion. The concept, rather than the implementation details, is the main emphasis of the paper.
DA - 2003/6/1/
PY - 2003/6/1/
DO - 10.1016/S0024-3795(02)00505-0
VL - 366
IS - SPEC. ISS.
SP - 157-172
SN - 0024-3795
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0037409774&partnerID=MN8TOARS
KW - structured matrix
KW - low rank approximation
KW - optimization techniques
KW - Toeplitz matrix
ER -
TY - JOUR
TI - Stability of self-similar solutions of the Dafermos regularization of a system of conservation laws
AU - Lin, XB
AU - Schecter, S
T2 - SIAM JOURNAL ON MATHEMATICAL ANALYSIS
AB - In contrast to a viscous regularization of a system of n conservation laws, a Dafermos regularization admits many self-similar solutions of the form \( u=u(\frac{X}{T})\). In particular, it is known in many cases that Riemann solutions of a system of conservation laws have nearby self-similar smooth solutions of an associated Dafermos regularization. We refer to these smooth solutions as {\em Riemann--Dafermos solutions}. In the coordinates $x=\frac{X}{T}$, $t=\ln T$, Riemann--Dafermos solutions become stationary, and their time-asymptotic stability as solutions of the Dafermos regularization can be studied by linearization. We study the stability of Riemann--Dafermos solutions near Riemann solutions consisting of n Lax shock waves. We show, by studying the essential spectrum of the linearized system in a weighted function space, that stability is determined by eigenvalues only. We then use asymptotic methods to study the eigenvalues and eigenfunctions. We find there are fast eigenvalues of order $\frac{1}{\epsilon}$ and slow eigenvalues of order 1. The fast eigenvalues correspond to eigenvalues of the viscous profiles for the individual shock waves in the Riemann solution; these have been studied by other authors using Evans function methods. The slow eigenvalues are related to inviscid stability conditions that have been obtained by various authors for the underlying Riemann solution.
DA - 2003///
PY - 2003///
DO - 10.1137/S0036141002405029
VL - 35
IS - 4
SP - 884-921
SN - 1095-7154
KW - conservation law
KW - Riemann problem
KW - Dafermos regularization
KW - stability
KW - spectrum
KW - singular perturbation
ER -
TY - JOUR
TI - Some comments on modeling the linearized Boltzmann equation
AU - Barichello, LB
AU - Siewert, CE
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - Some exact solutions of the homogeneous and the inhomogeneous linearized Boltzmann equation (LBE) for rigid-sphere collisions are used to define two model equations in the general area of rarefied-gas dynamics. These equations are obtained from a systematic development of two synthetic scattering kernels that yield model equations that have as exact solutions certain known exact solutions of the homogeneous and of the inhomogeneous LBE. The first model established is defined in terms of the collisional invariants and the Chapman–Enskog integral equations for viscosity and for heat conduction. An extended model is defined also in terms of the collisional invariants and the Chapman–Enskog functions for viscosity and heat conduction, but the first and second Burnett functions are also included in the model. The variable collision frequency or generalized BGK model is also obtained as a special case. In addition, the exact mean-free paths defined, for rigid-sphere collisions and the LBE, in terms of viscosity or heat conduction are employed to define approximations of these quantities that are consistent with the use of the variable collision frequency model.
DA - 2003/2/15/
PY - 2003/2/15/
DO - 10.1016/S0022-4073(02)00074-2
VL - 77
IS - 1
SP - 43-59
SN - 0022-4073
KW - Boltzmann equation
KW - rarefied-gas dynamics
KW - synthetic kernels
ER -
TY - JOUR
TI - Pseudotransient continuation and differential-algebraic equations
AU - Coffey, TS
AU - Kelley, CT
AU - Keyes, DE
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - Pseudotransient continuation is a practical technique for globalizing the computation of steady-state solutions of nonlinear differential equations. The technique employs adaptive time-stepping to integrate an initial value problem derived from an underlying ODE or PDE boundary value problem until sufficient accuracy in the desired steady-state root is achieved to switch over to Newton's method and gain a rapid asymptotic convergence. The existing theory for pseudotransient continuation includes a global convergence result for differential equations written in semidiscretized method-of-lines form. However, many problems are better formulated or can only sensibly be formulated as differential-algebraic equations (DAEs). These include systems in which some of the equations represent algebraic constraints, perhaps arising from the spatial discretization of a PDE constraint. Multirate systems, in particular, are often formulated as differential-algebraic systems to suppress fast time scales (acoustics, gravity waves, Alfven waves, near equilibrium chemical oscillations, etc.) that are irrelevant on the dynamical time scales of interest. In this paper we present a global convergence result for pseudotransient continuation applied to DAEs of index 1, and we illustrate it with numerical experiments on model incompressible flow and reacting flow problems, in which a constraint is employed to step over acoustic waves.
DA - 2003///
PY - 2003///
DO - 10.1137/S106482750241044X
VL - 25
IS - 2
SP - 553-569
SN - 1095-7197
KW - pseudotransient continuation
KW - nonlinear equations
KW - steady-state solutions
KW - global convergence
KW - differential-algebraic equations
KW - multirate systems
ER -
TY - JOUR
TI - Eudoxus meets Cayley
AU - Chandler, RE
AU - Meyer, CD
AU - Rose, NJ
T2 - AMERICAN MATHEMATICAL MONTHLY
DA - 2003/12//
PY - 2003/12//
DO - 10.2307/3647962
VL - 110
IS - 10
SP - 912-927
SN - 0002-9890
ER -
TY - JOUR
TI - Equivariant K-theory, generalized symmetric products, and twisted Heisenberg algebra
AU - Wang, WQ
T2 - COMMUNICATIONS IN MATHEMATICAL PHYSICS
AB - For a space X acted by a finite group $\G$, the product space $X^n$ affords a natural action of the wreath product $\Gn$. In this paper we study the K-groups $K_{\tG_n}(X^n)$ of $\Gn$-equivariant Clifford supermodules on $X^n$. We show that $\tFG =\bigoplus_{n\ge 0}K_{\tG_n}(X^n) \otimes \C$ is a Hopf algebra and it is isomorphic to the Fock space of a twisted Heisenberg algebra. Twisted vertex operators make a natural appearance. The algebraic structures on $\tFG$, when $\G$ is trivial and X is a point, specialize to those on a ring of symmetric functions with the Schur Q-functions as a linear basis. As a by-product, we present a novel construction of K-theory operations using the spin representations of the hyperoctahedral groups.
DA - 2003/3//
PY - 2003/3//
DO - 10.1007/s00220-002-0753-9
VL - 234
IS - 1
SP - 101-127
SN - 1432-0916
ER -
TY - JOUR
TI - An overview of the immersed interface method and its applications
AU - Li, Zhilin
T2 - Taiwanese Journal of Mathematics
AB - Interface problems have many applications. Mathematically, interface problems usually lead to differential equations whose input data and solutions are non-smooth or discontinuous across some interfaces. The immersed interface method (IIM) has been developed in recent years particularly designed for interface problems. The IIM is a sharp interface method based on Cartesian grids. The IIM makes use of the jump conditions across the interface so that the finite difference/element discretization can be accurate. In this survey paper, we will introduce the immersed interface method for various problems, discuss its recent advances and related software packages, and some of its applications. We also review some other related methods and references in this survey paper.
DA - 2003///
PY - 2003///
DO - 10.11650/twjm/1500407515
VL - 7
IS - 1
SP - 1–49
ER -