TY - CONF
TI - From Concept to Real-time Implementation: POD Based Reduced Order Control of a Cantilever Beam
AU - Tran, H.
AU - Lewis, B.M.
T2 - 16th International Symposium on Mathematical Theory of Networks and Systems(MTNS 2004)
A2 - De Moor, B.
A2 - Motmans, Bart
A2 - Willems, J.
A2 - Van Dooren, Paul
A2 - Blondel, Vincent
C2 - 2004///
C3 - Proceedings of the 16th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2004)
CY - Catholic University of Leuven (K.U.Leuven-Belgium)
DA - 2004///
PY - 2004/7/5/
ER -
TY - JOUR
TI - Well-posedness for a nonsmooth acoustic system
AU - Banks, H.T
AU - Raye, J.K
T2 - Applied Mathematics Letters
AB - We consider an acoustic wave system with discontinuous coefficients and nonsmooth inputs. Existence, uniqueness, and continuous dependence on input data of weak solutions are established.
DA - 2004/3//
PY - 2004/3//
DO - 10.1016/S0893-9659(04)90069-9
VL - 17
IS - 3
SP - 317-322
J2 - Applied Mathematics Letters
LA - en
OP -
SN - 0893-9659
UR - http://dx.doi.org/10.1016/S0893-9659(04)90069-9
DB - Crossref
KW - well-posedness
KW - wave equations
KW - acoustics
ER -
TY - JOUR
TI - Modeling Cerebral Blood Flow Control During Posture Change from Sitting to Standing
AU - Olufsen, Mette
AU - Tran, Hien
AU - Ottesen, Johnny
T2 - Cardiovascular Engineering
AB - Hypertension, decreased cerebral blood flow, and diminished cerebral blood flow velocity regulation, are among the first signs indicating the presence of cerebral vascular disease. In this paper, we will present a mathematical model that can predict blood flow and pressure during posture change from sitting to standing. The mathematical model uses a compartmental approach to describe pulsatile blood flow velocity and pressure in a number of compartments representing the systemic circulation. Our model includes compartments representing the trunk and upper extremities, the lower extremities, the brain, and the heart. We use physiologically based control mechanisms to describe the regulation of cerebral blood flow velocity and arterial pressure in response to orthostatic hypotension resulting from postural change. To justify the fidelity of our mathematical model and control mechanisms development, we will show validation results of our model against experimental data from a young subject.
DA - 2004/3//
PY - 2004/3//
DO - 10.1023/b:care.0000025122.46013.1a
VL - 4
IS - 1
SP - 47-58
J2 - Cardiovascular Engineering
LA - en
OP -
SN - 1567-8822
UR - http://dx.doi.org/10.1023/b:care.0000025122.46013.1a
DB - Crossref
ER -
TY - JOUR
TI - On wavelet-based numerical homogenization
AU - Chertock, Alina
AU - Levy, Doron
T2 - Multiscale Model. Simul.
AB - Recently, a wavelet-based method was introduced for the systematic derivation of subgrid scale models in the numerical solution of partial differential equations. Starting from a discretization of the multiscale differential operator, the discrete operator is represented in a wavelet space and projected onto a coarser subspace. The coarse (homogenized) operator is then replaced by a sparse approximation to increase the efficiency of the resulting algorithm. In this work we show how to improve the efficiency of this numerical homogenization method by choosing a different compact representation of the homogenized operator. In two dimensions our approach for obtaining a sparse representation is significantly simpler than the alternative sparse representations. $L^{\infty}$ error estimates are derived for a sample elliptic problem. An additional improvement we propose is a natural fine-scales correction that can be implemented in the final homogenization step. This modification of the scheme improves the resolution of the approximation without any significant increase in the computational cost. We apply our method to a variety of test problems including one- and two-dimensional elliptic models as well as wave propagation problems in materials with subgrid inhomogeneities.
DA - 2004///
PY - 2004///
DO - 10.1137/030600783
VL - 3
IS - 1
SP - 65-88
UR - https://doi-org.prox.lib.ncsu.edu/10.1137/030600783
KW - numerical homogenization
KW - wavelets
KW - Helmholtz equation
ER -
TY - JOUR
TI - On the application of lacunae-based methods to Maxwell's equations
AU - Tsynkov, S.V.
T2 - Journal of Computational Physics
AB - A straightforward application of the previously designed lacunae-based numerical methods to unsteady electro-magnetic problems would encounter certain difficulties, as it may violate the continuity of the charges and currents, which is a necessary solvability condition for the Maxwell equations. In the paper, we prove existence of the special auxiliary charges and currents that satisfy the continuity equations identically. We also show that using such charges and currents as a part of the numerical procedure provides a clear and unobstructed venue toward implementation of the lacunae-based methods in electromagnetics.
DA - 2004/9//
PY - 2004/9//
DO - 10.1016/j.jcp.2004.02.003
VL - 199
IS - 1
SP - 126-149
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1016/j.jcp.2004.02.003
DB - Crossref
KW - electromagnetic waves
KW - continuity equation
KW - solenoidal currents
KW - partition of unity
KW - unsteady propagation
KW - unbounded domains
KW - truncation
KW - finite computational domain
KW - sharp aft fronts
KW - Huygens' principle
KW - non-deteriorating method
KW - long-term numerical integration
ER -
TY - CONF
TI - Parallel Solution of the {Wigner-Poisson} Equations for {RTDs}
AU - Lasater, M S
AU - Kelley, C T
AU - Salinger, A
AU - Woolard, D L
AU - Zhao, P
A2 - Qingping, Quo
C2 - 2004///
C3 - 2004 International Symposium on Distributed Computing and Applications to Business, Engineering and Science
CY - Wuhan, China
DA - 2004///
SP - 672-676
PB - Hubei Science and Technology Press
ER -
TY - CONF
TI - Simulation of Nondifferentiable Models for Groundwater Flow and Transport
AU - Kelley, C T
AU - Fowler, K R
AU - Kees, C E
A2 - Miller, C T
A2 - Farthing, M. W.
A2 - Gray, W G
A2 - Pinter, G F
C2 - 2004///
C3 - Proceedings of Computational Methods in Water Resources XV
CY - Amsterdam
DA - 2004///
SP - 939-952
PB - Elsevier
ER -
TY - JOUR
TI - Implicit Filtering Revisited
AU - Conn, A R
AU - Kelley, C T
AU - Scheinberg, K
AU - Vicente, L N
DA - 2004///
PY - 2004///
ER -
TY - CONF
TI - Enhancement of Numerical Computations of the {W}igner-{P}oisson Equations for Application to the Simulation of {TH}z-Frequency {RTD} Oscillators
AU - Lasater, M S
AU - Kelley, C T
AU - Salinger, A
AU - Woolard, D L
AU - Zhao, P
T2 - North Carolina State University, Center for Research in Scientific Computation
A2 - Jensen, J O
A2 - Theriault, J-M
C2 - 2004///
C3 - Proceedings of SPIE: Chemical and Biological Standoff Detection II Volume 5584, paper number 07
DA - 2004///
SP - 42-51
ER -
TY - CONF
TI - A Hydraulic Capture Application for Optimal Remeidation Design
AU - Fowler, K R
AU - Kelley, C T
AU - Kees, C E
AU - Miller, C T
A2 - Miller, C T
A2 - Farthing, M. W.
A2 - Gray, W G
A2 - Pinter, G F
C2 - 2004///
C3 - Proceedings of Computational Methods in Water Resources XV
CY - Amsterdam
DA - 2004///
SP - 1149-1158
PB - Elsevier
ER -
TY - JOUR
TI - A Fast Algorithm for the {Ornstein-Zernike} Equations
AU - Kelley, C T
AU - Pettitt, B Montgomery
T2 - J. Comp. Phys.
DA - 2004///
PY - 2004///
VL - 197
SP - 491-591
ER -
TY - JOUR
TI - Modeling and optimal regulation of erythropoiesis subject to benzene intoxication
AU - Banks, HT
AU - Cole, CE
AU - Schlosser, PM
AU - Tran, HT
T2 - MATHEMATICAL BIOSCIENCES AND ENGINEERING
AB - Benzene (C6H6) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, andindustrial processes. Benzene increases the incidence of leukemia in humanswhen they are exposed to high doses for extended periods; however, leukemiarisks in humans subjected to low exposures are uncertain. The exposure-dose-response relationship of benzene in humans is expected to be nonlinear becausebenzene undergoes a series of metabolic transformations, detoxifying and activating, resulting in various metabolites that exert toxic e ffects on the bonemarrow. Since benzene is a known human leukemogen, the toxicity of benzene in thebone marrow is of most importance. And because blood cells are producedin the bone marrow, we investigated the eff ects of benzene on hematopoiesis(blood cell production and development). An age-structured model was usedto examine the process of erythropoiesis, the development of red blood cells.This investigation proved the existence and uniqueness of the solution of thesystem of coupled partial and ordinary di fferential equations. In addition, weformulated an optimal control problem for the control of erythropoiesis andperformed numerical simulations to compare the performance of the optimalfeedback law and another feedback function based on the Hill function.
DA - 2004/6//
PY - 2004/6//
DO - 10.3934/mbe.2004.1.15
VL - 1
IS - 1
SP - 15-48
SN - 1547-1063
KW - hematopoiesis
KW - age-structured model
KW - existence and uniqueness
KW - optimal control
ER -
TY - JOUR
TI - Dynamic multidrug therapies for HIV: Optimal and STI control approaches
AU - Adams, B. M.
AU - Banks, H. T.
AU - Kwon, H. D.
AU - Tran, Hien
T2 - Mathematical Biosciences and Engineering
AB - We formulate a dynamic mathematical model that describes the interaction of the immune system with the human immunodeficiency virus (HIV) and that permits drug ''cocktail'' therapies. We derive HIV therapeutic strategies by formulating and analyzing an optimal control problem using two types of dynamic treatments representing reverse transcriptase (RT) inhibitors and protease inhibitors (PIs). Continuous optimal therapies are found by solving the corresponding optimality systems. In addition, using ideas from dynamic programming, we formulate and derive suboptimal structured treatment interruptions (STI) in antiviral therapy that include drug-free periods of immune-mediated control of HIV. Our numerical results support a scenario in which STI therapies can lead to long-term control of HIV by the immune response system after discontinuation of therapy.
DA - 2004///
PY - 2004///
DO - 10.3934/mbe.2004.1.223
VL - 1
IS - 2
SP - 223–241
ER -
TY - JOUR
TI - On the application of lacunae-based methods to Maxwell's equations
AU - Tsynkov, Semyon
T2 - Journal of Computational Physics
DA - 2004///
PY - 2004///
DO - 10.1016/.jcp.2004.02.003
VL - 199
IS - 1
SP - 126–149
ER -
TY - JOUR
TI - Approximate solution of singular integro-differential equations by reduction over Faber-Laurent polynomials
AU - Zolotarevskii, VA
AU - Li, ZL
AU - Caraus, I
T2 - DIFFERENTIAL EQUATIONS
DA - 2004/12//
PY - 2004/12//
DO - 10.1007/s10625-005-0108-3
VL - 40
IS - 12
SP - 1764-1769
SN - 0012-2661
ER -
TY - JOUR
TI - Solution of a well-field design problem with implicit filtering
AU - Fowler, KR
AU - Kelley, CT
AU - Miller, CT
AU - Kees, CE
AU - Darwin, RW
AU - Reese, JP
AU - Farthing, MW
AU - Reed, MSC
T2 - OPTIMIZATION AND ENGINEERING
AB - Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this ap- plication field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.
DA - 2004/6//
PY - 2004/6//
DO - 10.1023/B:OPTE.0000033375.33183.e7
VL - 5
IS - 2
SP - 207-234
SN - 1573-2924
KW - implicit filtering
KW - well field design
KW - groundwater flow and transport
ER -
TY - JOUR
TI - Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model
AU - Banks, HT
AU - Potter, LK
T2 - MATHEMATICAL BIOSCIENCES
AB - Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.
DA - 2004/12//
PY - 2004/12//
DO - 10.1016/j.mbs.2004.11.008
VL - 192
IS - 2
SP - 193-225
SN - 1879-3134
KW - parameter estimation
KW - biological modeling
KW - population variability
KW - model uncertainty
KW - toxicokinetics
KW - trichloroethylene
ER -
TY - JOUR
TI - Existence-uniqueness and monotone approximation for an erythropoiesis age-structured model
AU - Ackleh, AS
AU - Deng, K
AU - Cole, CE
AU - Tran, HT
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - We develop a monotone approximation to the solution of an age-structured model which describes the regulation of erythropoiesis, the process in which red blood cells are developed. The convergence of this approximation to the unique solution of the model is also established.
DA - 2004/1/15/
PY - 2004/1/15/
DO - 10.1016/j.jmaa.2003.08.037
VL - 289
IS - 2
SP - 530-544
SN - 0022-247X
KW - erythropoiesis
KW - age-structured model
KW - monotone approximation
KW - existence uniqueness
ER -
TY - JOUR
TI - Design of an electron gun using computer optimization
AU - Lewis, BM
AU - Tran, HT
AU - Read, ME
AU - Ives, RL
T2 - IEEE TRANSACTIONS ON PLASMA SCIENCE
AB - This paper considers an optimization technique in which the objective is attained via alterations to the physical geometry of the system. This optimization framework, to be considered in the context of electron guns, is known as optimal shape design. Optimal shape design has been used in a number of applications including wing design, magnetic tape design, and nozzle design, among others. In this investigation, we use the methods of shape optimization to design the cathode of an electron gun. The dynamical equations modeling the electron particle path as well as the generalized shape optimization problem will be presented. Illustrative examples of the technique on gun designs that were previously limited to spherical cathodes will be given.
DA - 2004/6//
PY - 2004/6//
DO - 10.1109/TPS.2004.827572
VL - 32
IS - 3
SP - 1242-1250
SN - 1939-9375
KW - cathode shape optimization
KW - electron gun
KW - optimal shape design
KW - optimization techniques
ER -
TY - JOUR
TI - An immersed finite element space and its approximation capability
AU - Li, Z.
AU - Lin, T.
AU - Lin, Y.
AU - Rogers, R. C.
T2 - Numerical Methods for Partial Differential Equations
AB - This article discusses an immersed finite element (IFE) space introduced for solving a second-order elliptic boundary value problem with discontinuous coefficients (interface problem). The IFE space is nonconforming and its partition can be independent of the interface. The error estimates for the interpolation of a function in the usual Sobolev space indicate that this IFE space has an approximation capability similar to that of the standard conforming linear finite element space based on body-fit partitions. Numerical examples of the related finite element method based on this IFE space are provided. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 338–367, 2004
DA - 2004///
PY - 2004///
DO - 10.1002/num.10092
VL - 20
IS - 3
SP - 338-367
J2 - Numer. Methods Partial Differential Eq.
LA - en
OP -
SN - 0749-159X 1098-2426
UR - http://dx.doi.org/10.1002/num.10092
DB - Crossref
KW - interface problems
KW - immersed interface
KW - finite element
KW - error estimates
ER -
TY - JOUR
TI - On a hybrid finite-volume-particle method
AU - Chertock, A
AU - Kurganov, A
T2 - ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE
AB - We present a hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow. The flow is modeled by the one- and two-dimensional Saint-Venant system of shallow water equations and the pollutant propagation is described by a transport equation. This paper is an extension of our previous work [Chertock, Kurganov and Petrova, J. Sci. Comput. (to appear)], where the one-dimensional finite-volume-particle method has been proposed. The core idea behind the finite-volume-particle method is to use different schemes for the flow and pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. This way the specific advantages of each scheme are utilized at the right place. A special attention is given to the recovery of the point values of the numerical solution from its particle distribution. The reconstruction is obtained using a dual equation for the pollutant concentration. This results in a significantly enhanced resolution of the computed solution and also makes it much easier to extend the finite-volume-particle method to the two-dimensional case.
DA - 2004///
PY - 2004///
DO - 10.1051/m2an:2004051
VL - 38
IS - 6
SP - 1071-1091
SN - 1290-3841
UR - https://doi-org.prox.lib.ncsu.edu/10.1051/m2an:2004051
KW - shallow water equations
KW - transport of passive pollutant
KW - finite-volume schemes
KW - particle method
ER -
TY - JOUR
TI - Nonlinear reptation in molecular based hysteresis models for polymers
AU - Banks, HT
AU - Medhin, NG
AU - Pinter, GA
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - We extend the linear “stick-slip” models of Doi-Edwards and Johnson-Stacer to nonlinear tube reptation models. We then show that such models, when combined with probabilistic formulations allowing distributions of relaxation times, provide a good description of dynamic experiments with highly filled rubber in tensile deformations. A connection to other applications including dielectric polarization and reptation in other viscoelastic materials (e.g., living tissue) is noted.
DA - 2004/12//
PY - 2004/12//
DO - 10.1090/qam/2104273
VL - 62
IS - 4
SP - 767-779
SN - 1552-4485
KW - viscoelastic
KW - hysteresis
KW - polymers
KW - molecular models
KW - relaxation times
KW - probability
KW - distributions
KW - uncertainty
ER -
TY - JOUR
TI - High-frequency pulse propagation in nonlinear dielectric materials
AU - Banks, HT
AU - Pinter, GA
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
AB - Abstract We consider a variational formulation based on Maxwell's equations for the propagation of high-frequency (gigahertz to terahertz) ultrashort input pulses in dielectric materials modeled by a linear Debye medium. We demonstrate computationally the emergence of Brillouin precursors in the material (water) and the fact that the peak of this transient is attenuated at a much slower rate than is the carrier frequency. In the 0.1– 1 THz regime the carrier frequency does not propagate in our calculations. Only the precursors enter the material, and this is in line with experiments reported by Pleshko and Palocz (Phys. Rev. Lett. 22 (1969) 1201). We also implement models that include nonlinearly forced Debye and nonlinear Debye polarization dynamics and demonstrate the importance of nonlinear effects, especially when the amplitude of the input signal is large. This is an important step in understanding high-frequency pulse propagation, and it has potential applications in the assessment of safety standards and in extending current imaging capabilities in both civilian and military uses.
DA - 2004/9//
PY - 2004/9//
DO - 10.1016/j.nonrwa.2003.10.002
VL - 5
IS - 4
SP - 597-612
SN - 1468-1218
KW - Maxwell's equations
KW - nonlinear dielectrics
KW - terahertz pulse propagation
ER -
TY - JOUR
TI - Well-posedness for a nonsmooth acoustic system
AU - Banks, H. T.
AU - Raye, J. K.
T2 - Applied Mathematics Letters
DA - 2004///
PY - 2004///
DO - 10.1016/S0893-9659(04)00013-8
VL - 17
IS - 3
SP - 317-322
ER -
TY - JOUR
TI - Optimization of power in the problems of active control of sound
AU - Lončarić, J.
AU - Tsynkov, S.V.
T2 - Mathematics and Computers in Simulation
AB - We analyze the problem of suppressing the unwanted component of a time-harmonic acoustic field (noise) on a predetermined region of interest. The suppression is rendered by active means, i.e., by introducing the additional acoustic sources called controls that generate the appropriate anti-sound. Previously, we have obtained general solutions for active controls in both continuous and discrete formulation of the problem. We have also obtained optimal solutions that minimize the L1 or L2 norm of the control sources; the physical interpretation of the former being the overall absolute acoustic source strength. In the current paper, we minimize the power required for the operation of the active control system. It turns out that the corresponding analysis necessarily involves interaction between the sources of sound and the surrounding acoustic field, which was not the case for either L1 or L2. Even though it may first seem counterintuitive, one can build a control system (a particular combination of surface monopoles and dipoles) that would require no power input for operation and would even produce a net power gain while providing the exact noise cancellation. This usually comes at the expense of having the original sources of noise produce even more energy.
DA - 2004/5//
PY - 2004/5//
DO - 10.1016/j.matcom.2004.01.005
VL - 65
IS - 4-5
SP - 323-335
J2 - Mathematics and Computers in Simulation
LA - en
OP -
SN - 0378-4754
UR - http://dx.doi.org/10.1016/j.matcom.2004.01.005
DB - Crossref
KW - noise cancellation
KW - active control sources
KW - volumetric and surface controls
KW - general solution
KW - monopoles and dipoles
KW - radiation of waves
KW - complex-valued quantities
KW - load on the sources by the field
KW - net power gain
ER -
TY - JOUR
TI - A fast solver for the Ornstein-Zernike equations
AU - Kelley, CT
AU - Pettitt, BM
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - In this paper, we report on the design and analysis of a multilevel method for the solution of the Ornstein–Zernike Equations and related systems of integro-algebraic equations. Our approach is based on an extension of the Atkinson–Brakhage method, with Newton-GMRES used as the coarse mesh solver. We report on several numerical experiments to illustrate the effectiveness of the method. The problems chosen are related to simple short ranged fluids with continuous potentials. Speedups over traditional methods for a given accuracy are reported. The new multilevel method is roughly six times faster than Newton-GMRES and 40 times faster than Picard.
DA - 2004/7/1/
PY - 2004/7/1/
DO - 10.1016/j.jcp.2003.12.006
VL - 197
IS - 2
SP - 491-501
SN - 1090-2716
ER -