TY - CONF
TI - Algorithms for sparse and black box matrices over finite fields
AU - Kaltofen, E.
T2 - International Conference on Finite Fields and Applications
C2 - 2001/5/23/
CY - Oaxaca, Mexico
DA - 2001/5/23/
ER -
TY - RPRT
TI - Industrial Mathematics Modeling Workshop for Graduate Students Series
DA - 2001///
PY - 2001///
M3 - CRSC Technical Reports
ER -
TY - CHAP
TI - Numerical Method for Simulation of Bubbles Flowing Through Another Fluid
AU - Li, Zhilin
T2 - Advances in Scientific Computing
A2 - Mu, M.
A2 - Shi, Z.
A2 - Xue, W.
A2 - Zou, J.
PY - 2001///
SP - 74–81
PB - Science Pr
SN - 9787030094452
ER -
TY - BOOK
TI - Book Review: Generalized Difference Methods for Differential Equations
AU - Li, Zhilin
AU - Chen, Z
AU - Li, R
AU - Wu, W
DA - 2001///
PY - 2001///
VL - 43
SE - 203–205,
ER -
TY - CONF
TI - Convexité et signal
AU - Combettes, P.L.
T2 - Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01
C2 - 2001/5/28/
C3 - Actes du Congrès de Mathématiques Appliquées et Industrielles SMAI'01
CY - Pompadour, France
DA - 2001/5/28/
PY - 2001/5/28/
SP - 6–16
ER -
TY - JOUR
TI - An energy-based approach for modeling the batch culture of Lactococcus lactis in vegetable broth
AU - Dougherty, D. P.
AU - Lubkin, S.
AU - Breidt, F.
T2 - Abstracts of the General Meeting of the American Society for Microbiology
DA - 2001///
PY - 2001///
VL - 101
SP - 434-435
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=BCI&KeyUT=BCI:BCI200200212002&KeyUID=BCI:BCI200200212002
ER -
TY - BOOK
TI - Lectures on Tensor Categories and Modular Functors
AU - Bakalov, Bojko
AU - Kirillov, Alexander, Jr.
T2 - University Lecture Series
AB - Introduction Braided tensor categories Ribbon categories Modular tensor categories 3-dimensional topological quantum field theory Modular functor Moduli spaces and complex modular functor Wess-Zumino-Witten model Bibliography Index Index of notation.
DA - 2001///
PY - 2001///
DO - 10.1090/ulect/021
M1 - 21
PB - American Mathematical Society
SN - 9780821826867 9781470421687
UR - http://dx.doi.org/10.1090/ulect/021
ER -
TY - JOUR
TI - Realistic Distributions of Infectious Periods in Epidemic Models: Changing Patterns of Persistence and Dynamics
AU - Lloyd, Alun L.
T2 - Theoretical Population Biology
AB - Most mathematical models used to study the epidemiology of childhood viral diseases, such as measles, describe the period of infectiousness by an exponential distribution. The effects of including more realistic descriptions of the infectious period within SIR (susceptible/infectious/recovered) models are studied. Less dispersed distributions are seen to have two important epidemiological consequences. First, less stable behaviour is seen within the model: incidence patterns become more complex. Second, disease persistence is diminished: in models with a finite population, the minimum population size needed to allow disease persistence increases. The assumption made concerning the infectious period distribution is of a kind routinely made in the formulation of mathematical models in population biology. Since it has a major effect on the central issues of population persistence and dynamics, the results of this study have broad implications for mathematical modellers of a wide range of biological systems.
DA - 2001///
PY - 2001///
DO - http://dx.doi.org/10.1006/tpbi.2001.1525
VL - 60
IS - 1
SP - 59–71
ER -
TY - JOUR
TI - Infection dynamics on scale-free networks
AU - May, Robert
AU - Lloyd, Alun
T2 - Physical Review E
AB - We discuss properties of infection processes on scale-free networks, relating them to the node-connectivity distribution that characterizes the network. Considering the epidemiologically important case of a disease that confers permanent immunity upon recovery, we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual's degree of connectivity within the population. As in an earlier study [R. Pastor-Satorras and A. Vesipignani, Phys. Rev. Lett. 86, 3200 (2001); Phys. Rev. E. 63, 006117 (2001)] for an infection that did not confer immunity upon recovery, the epidemic process--in contrast with many traditional epidemiological models--does not exhibit threshold behavior, and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale-free network. Finally, we discuss effects that arise from finite population sizes, showing that networks of finite size do exhibit threshold effects: infections cannot spread for arbitrarily low transmission probabilities.
DA - 2001///
PY - 2001///
DO - http://dx.doi.org/10.1103/physreve.64.066112
VL - 64
IS - 6
ER -
TY - CHAP
TI - Chemical Vapor Deposition Processes: Reduced-order Modeling
AU - Tran, H.
AU - Lee, C.H.
T2 - Encyclopedia of Materials: Science and Technology
A2 - Jürgen Buschow, K.H.
A2 - Flemings, Merton C.
A2 - Kramer, Edward J.
A2 - Veyssière, Patrick
A2 - Cahn, Robert W.
A2 - Ilschner, Bernhard
A2 - Mahajan, Subhash
PY - 2001///
DO - 10.1016/B0-08-043152-6/00221-7
ET - 2nd
SP - 1183–1187
PB - Elsevier Science Ltd
ER -
TY - JOUR
TI - Ore Principal Subresultant Coefficients in Solutions
AU - Hong, Hoon
T2 - Applicable Algebra in Engineering, Communication and Computing
DA - 2001/2/1/
PY - 2001/2/1/
DO - 10.1007/s002000000041
VL - 11
IS - 3
SP - 227-237
UR - http://dx.doi.org/10.1007/s002000000041
KW - ore polynomials
KW - resultants
KW - subresultants
KW - elimination theory
ER -
TY - CONF
TI - Feedback control of thin film growth in an HPCVD reactor via reduced order models
AU - Banks, H.T.
AU - Beeler, S.C.
AU - Kepler, G.M.
AU - Tran, H.T.
T2 - 40th Conference on Decision and Control
AB - This paper describes the development of a reduced order model-based feedback control methodology for the regulation of the growth of thin films in a high-pressure chemical vapor deposition (HPCVD) reactor. This is achieved in the context of gas dynamics coupled with a nonlinear reduced order model of the surface reactions involved in the source vapor decomposition and film growth on the substrate. Also modeled is the realtime observation technique used to obtain a partial measurement of the deposition process. The control problems are optimal tracking problems of the film thickness that employ state-dependent Riccati gains with nonlinear observations and the resulting dual state dependent Riccati equations for the compensator gains.
C2 - 2001/7/10/
C3 - Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228)
DA - 2001/7/10/
DO - 10.1109/cdc.2001.981123
PB - IEEE
SN - 0780370619
UR - http://dx.doi.org/10.1109/cdc.2001.981123
ER -
TY - JOUR
TI - q-discriminants and vertex operators
AU - Ismail, M.E.H.
AU - Jing, N.
T2 - Advances in Applied Mathematics
AB - Discriminants and their discrete and q -analogs are usually studied in the q -analysis theory. In this paper we propose a unified realization of discriminants using vertex operators coming from infinite dimensional Lie algebras and their quantum deformations as well as Yangian deformations. In this picture all of them appear as matrix coefficients of certain products of vertex operators according to respective cases.
DA - 2001///
PY - 2001///
DO - 10.1006/aama.2001.0745
VL - 27
IS - 2-3
SP - 482-492
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0035413459&partnerID=MN8TOARS
KW - discriminants
KW - orthogonal polynomials
KW - zeros
KW - vertex operators
KW - q-deformations
ER -
TY - JOUR
TI - Epidemiology: How Viruses Spread Among Computers and People
AU - Lloyd, A.L.
AU - May, R.M.
T2 - Science
AB - The spread of diseases in human and other populations can be described in terms of networks, where individuals are represented by nodes and modes of contact by edges. Similar models can be applied to the spread of viruses on the Internet. In their Perspective,
Lloyd and May
discuss the similarities and differences between the dynamics of computer viruses and infections of human and other populations.
DA - 2001/5/18/
PY - 2001/5/18/
DO - 10.1126/SCIENCE.1061076
VL - 292
IS - 5520
SP - 1316-1317
SN - 0036-8075 1095-9203
UR - http://dx.doi.org/10.1126/science.1061076
ER -
TY - CHAP
TI - Reduced Order Based Compensator Control of Thin Film Growth in a CVD Reactor
AU - Banks, H. T.
AU - Tran, H. T.
T2 - Optimal Control of Complex Structures
AB - This paper reports on an interdisciplinary effort, which involves applied mathematicians, material scientists and physicists at North Carolina State University, to integrate new intelligent processing approaches with advanced mathematical modeling, optimization, and control theory to guide the construction and experimental implementation of a series of high pressure (up to 100 atm) organometallic chemical vapor deposition (CVD) reactors. An integral component of this research program is the design of the reactor so that control and sensing are a basic component of the optimal design efforts for the reactor. We report here on the successful use of mathematics in a fundamental role in the development of linear and nonlinear feedback control methods for real-time implementation on the reactor. This is achieved in the required context of gas dynamics coupled with nonlinear surface deposition processes. The problems are optimal tracking problems (for the chemical component fluxes over the substrate) that employ state-dependent Riccati gains with nonlinear observations and the resulting dual state dependent Riccati equations for the compensator gains This control methodology is successfully combined with reduced order model methods based on proper orthogonal decomposition techniques. Computational results to support the efficacy of our approach and methods are also included.
PY - 2001///
DO - 10.1007/978-3-0348-8148-7_1
SP - 1-17
OP -
PB - Birkhäuser Basel
SN - 9783034894562 9783034881487
UR - http://dx.doi.org/10.1007/978-3-0348-8148-7_1
DB - Crossref
ER -
TY - JOUR
TI - Essential smoothness, essential strict convexity, and Legendre functions in Banach spaces
AU - Bauschke, Heinz H.
AU - Borwein, Jonathan M.
AU - Combettes, Patrick L.
T2 - Communications in Contemporary Mathematics
AB - The classical notions of essential smoothness, essential strict convexity, and Legendreness for convex functions are extended from Euclidean to Banach spaces. A pertinent duality theory is developed and several useful characterizations are given. The proofs rely on new results on the more subtle behavior of subdifferentials and directional derivatives at boundary points of the domain. In weak Asplund spaces, a new formula allows the recovery of the subdifferential from nearby gradients. Finally, it is shown that every Legendre function on a reflexive Banach space is zone consistent, a fundamental property in the analysis of optimization algorithms based on Bregman distances. Numerous illustrating examples are provided.
DA - 2001/11//
PY - 2001/11//
DO - 10.1142/s0219199701000524
VL - 3
IS - 4
SP - 615-647
SN - 0219-1997 1793-6683
UR - http://dx.doi.org/10.1142/s0219199701000524
KW - Bregman distance
KW - Bregman projection
KW - coercive
KW - cofinite function
KW - convex function of Legendre type
KW - essentially smooth
KW - essentially strictly convex
KW - Legendre function
KW - Schur property
KW - Schur space
KW - subdifferential
KW - supercoercive
KW - weak Asplund space
KW - zone consistent
ER -
TY - CHAP
TI - Fejér-monotonicity in convex optimization
AU - Combettes, P.L.
T2 - Encyclopedia of Optimization
A2 - Floudas, C.A.
A2 - Pardalos, P.M.
PY - 2001///
VL - 2
SP - 106–114
PB - Springer-Verlag
ER -
TY - CHAP
TI - A Cartesian Perfectly Matched Layer for the
̆ppercaseHelmholtz Equation
AU - Tsynkov, S. V.
AU - Turkel, E.
T2 - Absorbing Boundaries and Layers, Domain Decomposition Methods.
̆ppercaseApplications to Large Scale Computations
A2 - Tourrette, Loı̈c
A2 - Halpern, Lorance
PY - 2001///
SP - 279-309
PB - Nova Science Publishers, Inc.
UR - https://stsynkov.math.ncsu.edu/publications/a24e7.pdf
ER -
TY - JOUR
TI - Algorithms for Noisy Problems in Gas Transmission Pipeline Optimization
AU - Carter, R.
AU - Gablonsky, J.M.
AU - Patrick, A.
AU - Kelley, C.T.
AU - Eslinger, O.J.
T2 - Optimization and Engineering
DA - 2001///
PY - 2001///
VL - 2
SP - 139–157
ER -
TY - JOUR
TI - An Aggregation-based Domain Decomposition Preconditioner for Groundwater Flow
AU - Jenkins, E W
AU - Kelley, C T
AU - Miller, C T
AU - Kees, C E
T2 - SIAM J. Sci. Comp.
DA - 2001///
PY - 2001///
VL - 23
SP - 430-441
ER -
TY - RPRT
TI - Optimal Design for Problems Involving Flow and Transport Phenomena in Saturated Subsurface Systems
AU - Mayer, A S
AU - Kelley, C T
AU - Miller, C T
A3 - North Carolina State University, Center for Research in Scientific Computation
DA - 2001/12//
PY - 2001/12//
M1 - CRSC-TR01-33
PB - North Carolina State University, Center for Research in Scientific Computation
SN - CRSC-TR01-33
ER -
TY - CONF
TI - Nonlinear Equations: Contraction-Mapping Principle
AU - Kelley, C T
A2 - Floudas, C A
A2 - Pardalos, P M
C2 - 2001///
C3 - Encyclopedia of Optimization
CY - Dordrecht
DA - 2001///
SP - two pages
PB - Kluwer
ER -
TY - JOUR
TI - On the numerical robustness of the parallel projection method in signal synthesis
AU - Combettes, P.L.
T2 - IEEE Signal Processing Letters
AB - The parallel projection method (PPM) uses successive averages of projections onto constraint sets to construct a signal that least violates these constraints in an average squared-distance sense. In this paper, we study the robustness of PPM to errors in the computation of the projections. It is shown that the convergence properties of PPM remain valid under a simple summability condition on the relaxed averages of the errors.
DA - 2001/2//
PY - 2001/2//
DO - 10.1109/97.895371
VL - 8
IS - 2
SP - 45-47
J2 - IEEE Signal Process. Lett.
OP -
SN - 1070-9908 1558-2361
UR - http://dx.doi.org/10.1109/97.895371
DB - Crossref
KW - convex constraint
KW - numerical errors
KW - parallel computing
KW - projection
KW - signal recovery
KW - signal synthesis
ER -
TY - JOUR
TI - A Weak-to-Strong Convergence Principle for Fejér-Monotone Methods in Hilbert Spaces
AU - Bauschke, Heinz H.
AU - Combettes, Patrick L.
T2 - Mathematics of Operations Research
AB - We consider a wide class of iterative methods arising in numerical mathematics and optimization that are known to converge only weakly. Exploiting an idea originally proposed by Haugazeau, we present a simple modification of these methods that makes them strongly convergent without additional assumptions. Several applications are discussed.
DA - 2001/5//
PY - 2001/5//
DO - 10.1287/moor.26.2.248.10558
VL - 26
IS - 2
SP - 248-264
J2 - Mathematics of OR
LA - en
OP -
SN - 0364-765X 1526-5471
UR - http://dx.doi.org/10.1287/moor.26.2.248.10558
DB - Crossref
KW - convex feasibility
KW - Fejer-monotonicity
KW - firmly nonexpansive mapping
KW - fixed point
KW - Haugazeau
KW - maximal monotone operator
KW - projection
KW - proximal point algorithm
KW - resolvent
KW - subgradient algorithm
ER -
TY - CHAP
TI - Quasi-Fejérian Analysis of Some Optimization Algorithms
AU - Combettes, Patrick L.
T2 - Studies in Computational Mathematics
AB - A quasi-Fejér sequence is a sequence which satisfies the standard Fejér monotonicityproperty to within an additional error term. This notion is studied in detail in a Hilbert space setting and shown to provide a powerful framework to analyze the convergence of a wide range of optimization algorithms in a systematic fashion. A number of convergence theorems covering and extending existing results are thus established. Special emphasis is placed on the design and the analysis of parallel algorithms.
PY - 2001///
DO - 10.1016/s1570-579x(01)80010-0
SP - 115-152
OP -
PB - Elsevier
SN - 9780444505958
UR - http://dx.doi.org/10.1016/s1570-579x(01)80010-0
DB - Crossref
ER -
TY - JOUR
TI - A lumped parameter model for cerebral blood flow regulation
AU - Olufsen, M.S.
AU - Lipsitz, L.A.
AU - Nadim, A.
T2 - Advances in Bioengineering
DA - 2001///
PY - 2001///
VL - 51
SP - 277–278
ER -
TY - CHAP
TI - A Cartesian Perfectly Matched Layer for the Helmholtz Equation
AU - Tsynkov, S.V.
AU - Turkel, E.
T2 - Absorbing Boundaries and Layers, Domain Decomposition Methods. Applications to Large Scale Computations
A2 - Tourrette, Loı̈c
A2 - Halpern, Lorance
PY - 2001///
SP - 279–309
PB - Nova Science Publishers
ER -
TY -
ER -
TY -
ER -
TY - JOUR
TI - The dependence of viral parameter estimates on the assumed viral life cycle: limitations of studies of viral load data
AU - Lloyd, A. L.
T2 - Proceedings of the Royal Society of London. Series B: Biological Sciences
AB - Estimation of viral parameters, such as the basic reproductive number (R0) and infected cell life span, is central to the quantitative study of the within-host dynamics of viral diseases such as human immunodeficiency virus, hepatitis B or hepatitis C. As these parameters can rarely be determined directly, they are usually estimated indirectly by fitting mathematical models to viral load data. This paper investigates how parameter estimates obtained by such procedures depend on the assumptions made concerning the viral life cycle. It finds that estimates of the basic reproductive number obtained using viral load data collected during the initial stages of infection can depend quite sensitively on these assumptions. The use of models which neglect the intracellular delay before virion production can lead to severe underestimates of R0 and, hence, to overly optimistic predictions of how efficacious treatment must be in order to prevent or eradicate the disease. These results are also of importance for attempts at estimating R0 from similar epidemiological data as there is a correspondence between within-host and between-host models. Estimates of the life span of infected cells obtained from viral load data collected during drug treatment studies also depend on the assumptions made in modelling the virus life cycle. The use of more realistic descriptions of the life cycle is seen to increase estimates of infected cell life span, in addition to providing a new explanation for the shoulder phase seen during drug treatment. This study highlights the limitations of what can be learnt by fitting mathematical models to infectious disease data without detailed independent knowledge of the life cycle of the infectious agent.
DA - 2001/4/22/
PY - 2001/4/22/
DO - 10.1098/rspb.2000.1572
VL - 268
IS - 1469
SP - 847-854
J2 - Proceedings of the Royal Society of London. Series B: Biological Sciences
LA - en
OP -
SN - 1471-2954
UR - http://dx.doi.org/10.1098/rspb.2000.1572
DB - Crossref
KW - virus dynamics
KW - parameter estimation
KW - basic reproductive number
KW - cell life span
KW - non-exponential distribution
ER -
TY - JOUR
TI - Destabilization of epidemic models with the inclusion of realistic distributions of infectious periods
AU - Lloyd, A. L.
T2 - Proceedings of the Royal Society of London. Series B: Biological Sciences
AB - Most mathematical models used to understand the dynamical patterns seen in the incidence of childhood viral diseases, such as measles, employ a simple, but epidemiologically unrealistic, description of the infection and recovery process. The inclusion of more realistic descriptions of the recovery process is shown to cause a significant destabilization of the model. When there is seasonal variation in discase transmission this destabilization leads to the appearance of complex dynamical patterns with much lower levels of seasonality than previously predicted. More generally this study illustrates how detailed dynamical properties of a model may depend in an important way on the assumptions made in the formulation of the model.
DA - 2001/5/7/
PY - 2001/5/7/
DO - 10.1098/rspb.2001.1599
VL - 268
IS - 1470
SP - 985-993
J2 - Proceedings of the Royal Society of London. Series B: Biological Sciences
LA - en
OP -
SN - 1471-2954
UR - http://dx.doi.org/10.1098/rspb.2001.1599
DB - Crossref
KW - epidemic model
KW - infectious period distribution
KW - seasonally forced dynamics
ER -
TY - JOUR
TI - Realistic Distributions of Infectious Periods in Epidemic Models: Changing Patterns of Persistence and Dynamics
AU - Lloyd, Alun L.
T2 - Theoretical Population Biology
AB - Most mathematical models used to study the epidemiology of childhood viral diseases, such as measles, describe the period of infectiousness by an exponential distribution. The effects of including more realistic descriptions of the infectious period within SIR (susceptible/infectious/recovered) models are studied. Less dispersed distributions are seen to have two important epidemiological consequences. First, less stable behaviour is seen within the model: incidence patterns become more complex. Second, disease persistence is diminished: in models with a finite population, the minimum population size needed to allow disease persistence increases. The assumption made concerning the infectious period distribution is of a kind routinely made in the formulation of mathematical models in population biology. Since it has a major effect on the central issues of population persistence and dynamics, the results of this study have broad implications for mathematical modellers of a wide range of biological systems.
DA - 2001/8//
PY - 2001/8//
DO - 10.1006/tpbi.2001.1525
VL - 60
IS - 1
SP - 59-71
J2 - Theoretical Population Biology
LA - en
OP -
SN - 0040-5809
UR - http://dx.doi.org/10.1006/tpbi.2001.1525
DB - Crossref
ER -
TY - JOUR
TI - Infection dynamics on scale-free networks
AU - May, Robert M.
AU - Lloyd, Alun L.
T2 - Physical Review E
AB - We discuss properties of infection processes on scale-free networks, relating them to the node-connectivity distribution that characterizes the network. Considering the epidemiologically important case of a disease that confers permanent immunity upon recovery, we derive analytic expressions for the final size of an epidemic in an infinite closed population and for the dependence of infection probability on an individual's degree of connectivity within the population. As in an earlier study [R. Pastor-Satorras and A. Vesipignani, Phys. Rev. Lett. 86, 3200 (2001); Phys. Rev. E. 63, 006117 (2001)] for an infection that did not confer immunity upon recovery, the epidemic process--in contrast with many traditional epidemiological models--does not exhibit threshold behavior, and we demonstrate that this is a consequence of the extreme heterogeneity in the connectivity distribution of a scale-free network. Finally, we discuss effects that arise from finite population sizes, showing that networks of finite size do exhibit threshold effects: infections cannot spread for arbitrarily low transmission probabilities.
DA - 2001/11/19/
PY - 2001/11/19/
DO - 10.1103/physreve.64.066112
VL - 64
IS - 6
SP - 066112
J2 - Phys. Rev. E
LA - en
OP -
SN - 1063-651X 1095-3787
UR - http://dx.doi.org/10.1103/physreve.64.066112
DB - Crossref
ER -
TY - JOUR
TI - Stability Radius and Optimal Scaling of Discrete-Time Periodic Systems
AU - Genin, Y.
AU - Ipsen, I.
AU - Ştefan, R.
AU - Van Dooren, P.
T2 - IFAC Proceedings Volumes
AB - Robust stability properties of periodic discrete time systems are investigated. Analytic expressions are derived for the stability radius in the scalar case.
DA - 2001/8//
PY - 2001/8//
DO - 10.1016/s1474-6670(17)34081-8
VL - 34
IS - 12
SP - 179-182
J2 - IFAC Proceedings Volumes
LA - en
OP -
SN - 1474-6670
UR - http://dx.doi.org/10.1016/s1474-6670(17)34081-8
DB - Crossref
ER -
TY - CHAP
TI - A One-Dimensional Fluid Dynamic Model of the Systemic Arteries
AU - Olufsen, Mette S.
T2 - Computational Modeling in Biological Fluid Dynamics
PY - 2001///
DO - 10.1007/978-1-4613-0151-6_9
SP - 167-187
OP -
PB - Springer New York
SN - 9781461265399 9781461301516
UR - http://dx.doi.org/10.1007/978-1-4613-0151-6_9
DB - Crossref
ER -
TY - JOUR
TI - Theory of Finite Pseudoalgebras
AU - Bakalov, Bojko
AU - D'Andrea, Alessandro
AU - Kac, Victor G
T2 - Advances in Mathematics
AB - Conformal algebras, recently introduced by Kac, encode an axiomatic description of the singular part of the operator product expansion in conformal field theory. The objective of this paper is to develop the theory of ``multi-dimensional'' analogues of conformal algebras. They are defined as Lie algebras in a certain ``pseudotensor'' category instead of the category of vector spaces. A pseudotensor category (as introduced by Lambek, and by Beilinson and Drinfeld) is a category equipped with ``polylinear maps'' and a way to compose them. This allows for the definition of Lie algebras, representations, cohomology, etc. An instance of such a category can be constructed starting from any cocommutative (or more generally, quasitriangular) Hopf algebra $H$. The Lie algebras in this category are called Lie $H$-pseudoalgebras.
The main result of this paper is the classification of all simple and all semisimple Lie $H$-pseudoalgebras which are finitely generated as $H$-modules. We also start developing the representation theory of Lie pseudoalgebras; in particular, we prove analogues of the Lie, Engel, and Cartan-Jacobson Theorems. We show that the cohomology theory of Lie pseudoalgebras describes extensions and deformations and is closely related to Gelfand-Fuchs cohomology. Lie pseudoalgebras are closely related to solutions of the classical Yang-Baxter equation, to differential Lie algebras (introduced by Ritt), and to Hamiltonian formalism in the theory of nonlinear evolution equations. As an application of our results, we derive a classification of simple and semisimple linear Poisson brackets in any finite number of indeterminates.
DA - 2001/9//
PY - 2001/9//
DO - 10.1006/aima.2001.1993
VL - 162
IS - 1
SP - 1-140
J2 - Advances in Mathematics
LA - en
OP -
SN - 0001-8708
UR - http://dx.doi.org/10.1006/aima.2001.1993
DB - Crossref
ER -
TY - JOUR
TI - Particle Methods for Dispersive Equations
AU - Chertock, Alina
AU - Levy, Doron
T2 - Journal of Computational Physics
AB - We introduce a new dispersion-velocity particle method for approximating solutions of linear and nonlinear dispersive equations. This is the first time in which particle methods are being used for solving such equations. Our method is based on an extension of the diffusion-velocity method of Degond and Mustieles (SIAM J. Sci. Stat. Comput.11(2), 293 (1990)) to the dispersive framework. The main analytical result we provide is the short time existence and uniqueness of a solution to the resulting dispersion-velocity transport equation. We numerically test our new method for a variety of linear and nonlinear problems. In particular we are interested in nonlinear equations which generate structures that have nonsmooth fronts. Our simulations show that this particle method is capable of capturing the nonlinear regime of a compacton–compacton type interaction.
DA - 2001/8//
PY - 2001/8//
DO - 10.1006/jcph.2001.6803
VL - 171
IS - 2
SP - 708-730
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1006/jcph.2001.6803
DB - Crossref
KW - particle methods
KW - dispersive equations
KW - diffusion-velocity
KW - dispersion-velocity
KW - compacton equations
ER -
TY - JOUR
TI - SIAG/LA and ILAS mark twenty years of progress at joint applied linear algebra meeting
AU - Ipsen, I.C.F.
AU - Mehrmann, V.
T2 - SIAM News
DA - 2001/1//
PY - 2001/1//
VL - 34
IS - 1
ER -
TY - JOUR
TI - High-Order Two-Way Artificial Boundary Conditions for Nonlinear Wave Propagation with Backscattering
AU - Fibich, Gadi
AU - Tsynkov, Semyon
T2 - Journal of Computational Physics
AB - When solvinglinear scattering problems, one typically first solves for the impinging wave in the absence of obstacles. Then, using the linear superposition principle, the original problem is reduced to one which involves only the scattered wave (which is driven by the values of the impinging field at the surface of the obstacles). When the original domain is unbounded, special artificial boundary conditions (ABCs) have to be set at the outer (artificial) boundary of the finite computational domain in order to guarantee the reflectionless propagation of waves through this external artificial boundary. The situation becomes conceptually different when the propagation equation is nonlinear. In this case the impinging and scattered waves can no longer be separated, and the problem has to be solved in its entirety. In particular, the boundary on which the incoming field values are prescribed should transmit the given incoming waves in one direction and simultaneously be transparent to all the outgoing waves that travel in the opposite direction. We call such boundary conditions two-way ABCs. In the paper, we construct the two-way ABCs for the nonlinear Helmholtz equation, which models a continuous-wave laser beam propagation in a medium with a Kerr nonlinear index of refraction. In this case, the forward propagation of the beam is accompanied by backscattering, i.e., generation of waves in the opposite direction to that of the incoming signal. Our two-way ABCs generate no reflection of the backscattered waves and at the same time impose the correct values of the incoming wave. The ABCs are obtained in the framework of a fourth-order accurate discretization to the Helmholtz operator inside the computational domain. The fourth-order convergence of our methodology is corroborated experimentally by solving linear model problems. We also present solutions in the nonlinear case using the two-way ABC which, unlike the traditional Dirichlet boundary condition approach, allows for direct calculation of the magnitude of backscattering.
DA - 2001/8//
PY - 2001/8//
DO - 10.1006/jcph.2001.6800
VL - 171
IS - 2
SP - 632-677
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1006/jcph.2001.6800
DB - Crossref
KW - artificial boundary conditions (ABCs)
KW - two-way ABCs
KW - radiation
KW - Helmholtz equation
KW - nonlinearity
KW - nonparaxiality
KW - fourth-order schemes
KW - self-focusing
KW - backscattering
ER -
TY - JOUR
TI - Active Shielding and Control of Noise
AU - Loncaric, J.
AU - Ryaben'kii, V. S.
AU - Tsynkov, S. V.
T2 - SIAM Journal on Applied Mathematics
AB - We present a mathematical framework for the active control of time-harmonic acoustic disturbances. Unlike many existing methodologies, our approach provides for the exact volumetric cancellation of unwanted noise in a given predetermined region of space while leaving unaltered those components of the total acoustic field that are deemed friendly. Our key finding is that for eliminating the unwanted component of the acoustic field in a given area, one needs to know relatively little; in particular, neither the locations nor structure nor strength of the exterior noise sources need to be known. Likewise, there is no need to know the volumetric properties of the supporting medium across which the acoustic signals propagate, except, perhaps, in the narrow area of space near the boundary (perimeter) of the domain to be shielded. The controls are built based solely on the measurements performed on the perimeter of the region to be shielded; moreover, the controls themselves (i.e., additional sources) are also concentrated only near this perimeter. Perhaps as important, the measured quantities can refer to the total acoustic field rather than only to its unwanted component, and the methodology can automatically distinguish between the two. In the paper, we construct a general solution to the aforementioned noise control problem. The apparatus used for deriving the general solution is closely connected to the concepts of generalized potentials and boundary projections of Calderon's type. For a given total wave field, the application of Calderon's projections allows us to definitively split its incoming and outgoing components with respect to a particular domain of interest, which may have arbitrary shape. Then the controls are designed so that they suppress the incoming component for the domain to be shielded or alternatively, the outgoing component for the domain, which is complementary to the one to be shielded. To demonstrate that the new noise control technique is appropriate, we thoroughly work out a two-dimensional model example that allows full analytical consideration. To conclude, we very briefly discuss the numerical (finite-difference) framework for active noise control that has, in fact, already been worked out, as well as some forthcoming extensions of the current work: optimization of the solution according to different criteria that would fit different practical requirements, applicability of the new technique to quasi-stationary problems, and active shielding in the case of the broad-band spectra of disturbances. In the future, the aforementioned finite-difference framework for active noise control is going to be used for analyzing complex configurations that originate from practical designs.
DA - 2001/1//
PY - 2001/1//
DO - 10.1137/s0036139900367589
VL - 62
IS - 2
SP - 563-596
J2 - SIAM J. Appl. Math.
LA - en
OP -
SN - 0036-1399 1095-712X
UR - http://dx.doi.org/10.1137/s0036139900367589
DB - Crossref
KW - active shielding
KW - noise control
KW - time-harmonic acoustic fields
KW - the Helmholtz equation
KW - generalized Calderon's potentials
KW - exact volumetric cancellation
KW - general solution
KW - incoming and outgoing waves
KW - near surface control sources
KW - spatial anisotropies
KW - material discontinuities
KW - optimization
KW - Bessel functions
ER -
TY - JOUR
TI - Time-frequency analysis of pseudodifferential operators
AU - Labate, D
T2 - MONATSHEFTE FUR MATHEMATIK
DA - 2001///
PY - 2001///
DO - 10.1007/s006050170028
VL - 133
IS - 2
SP - 143-156
SN - 0026-9255
KW - Kohn-Niremberg correspondence
KW - modulation spaces
KW - pseudodifferential operators
KW - time-frequency analysis
KW - trace-class operators
KW - twisted product
KW - Weyl correspondence
ER -
TY - JOUR
TI - Pseudodifferential operators on modulation spaces
AU - Labate, D
T2 - JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
AB - We establish a connection between certain classes of pseudodifferential operators and Hille–Tamarkin operators. As an application, we find the conditions that guarantee compactness and summability of the eigenvalues of pseudodifferential operators acting on the modulation spaces Mp, p.
DA - 2001/10/1/
PY - 2001/10/1/
DO - 10.1006/jmaa.2001.7566
VL - 262
IS - 1
SP - 242-255
SN - 1096-0813
ER -
TY - JOUR
TI - Quenching problem of a functional parabolic equation
AU - Pao, C. V.
T2 - Journal of High Energy Physics
DA - 2001///
PY - 2001///
VL - 8
IS - 1
SP - 89-98
ER -
TY - BOOK
TI - Stability and time-optimal control of hereditary systems: With application to the economic dynamics of the US (2nd ed.)
AU - Chukwu, E. N.
CN - QA402.3 .C5567 2001
DA - 2001///
PY - 2001///
DO - 10.1142/4745
PB - River Edge, NJ: World Scientific
SN - 9810246749
ER -
TY - JOUR
TI - Numerical analysis of interfacial two-dimensional Stokes flow with discontinuous viscosity and variable surface tension
AU - Li, ZL
AU - Lubkin, , SR
T2 - INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS
AB - A fluid model of the incompressible Stokes equations in two space dimensions is used to simulate the motion of a droplet boundary separating two fluids with unequal viscosity and variable surface tension. Our theoretical analysis leads to decoupled jump conditions that are used in constructing the numerical algorithm
DA - 2001/11/15/
PY - 2001/11/15/
DO - 10.1002/fld.185
VL - 37
IS - 5
SP - 525-540
SN - 0271-2091
UR - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=ORCID&SrcApp=OrcidOrg&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=WOS:000171932200002&KeyUID=WOS:000171932200002
KW - discontinuous and non-smooth solution
KW - immersed interface method
KW - interface
KW - jump condition
KW - Stokes equation
KW - variable surface tension
ER -
TY - JOUR
TI - Level-set function approach to an inverse interface problem
AU - Ito, K
AU - Kunisch, K
AU - Li, ZL
T2 - INVERSE PROBLEMS
AB - A model problem in electrical impedance tomography for the identification of unknown shapes from data in a narrow strip along the boundary of the domain is investigated. The representation of the shape of the boundary and its evolution during an iterative reconstruction process is achieved by the level set method. The shape derivatives of this problem involve the normal derivative of the potential along the unknown boundary. Hence an accurate resolution of its derivatives along the unknown interface is essential. It is obtained by the immersed interface method.
DA - 2001/10//
PY - 2001/10//
DO - 10.1088/0266-5611/17/5/301
VL - 17
IS - 5
SP - 1225-1242
SN - 1361-6420
ER -
TY - JOUR
TI - Existence of solutions to the Hamilton-Jacobi-Bellman equation under quadratic growth conditions
AU - Ito, K
T2 - JOURNAL OF DIFFERENTIAL EQUATIONS
AB - In this paper we show the existence of solutions with quadratic growth to Hamilton–Jacobi–Bellman equations. We assume that the Hamiltonian has the quadratic growth both in x and p . We obtain the explicit Lipschitz bound of solutions in the weighted sup-norm. Also, we discuss the vanishing viscosity limit of solutions and show the existence of viscosity solutions to the resulting Hamilton–Jacobi equation.
DA - 2001/10/10/
PY - 2001/10/10/
DO - 10.1006/jdeq.2000.3980
VL - 176
IS - 1
SP - 1-28
SN - 0022-0396
ER -
TY - JOUR
TI - The orthogonally constrained regression revisited
AU - Chu, MT
AU - Trendafilov, NT
T2 - JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
AB - The Penrose regression problem, including the orthonormal Procrustes problem and rotation problem to a partially specified target, is an important class of data matching problems arising frequently in multivariate analysis, yet its optimality conditions have never been clearly understood. This work offers a way to calculate the projected gradient and the projected Hessian explicitly. One consequence of this calculation is the complete characterization of the first order and the second order necessary and sufficient optimality conditions for this problem. Another application is the natural formulation of a continuous steepest descent ow that can serve as a globally convergent numerical method. Applications to the orthonormal Procrustes problem and Penrose regression problem with partially specified target are demonstrated in this article. Finally, some numerical results are reported and commented.
DA - 2001/12//
PY - 2001/12//
DO - 10.1198/106186001317243430
VL - 10
IS - 4
SP - 746-771
SN - 1061-8600
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0035565472&partnerID=MN8TOARS
KW - continuous-time approach
KW - Penrose regression
KW - procrustes rotation
KW - rotation to partially specified target
KW - projected gradient
KW - projected Hessian
KW - optimality conditions
ER -
TY - JOUR
TI - Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation
AU - Ryaben'kii, V.S.
AU - Tsynkov, S.V.
AU - Turchaninov, V.I.
T2 - Journal of Computational Physics
AB - We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.
DA - 2001/12//
PY - 2001/12//
DO - 10.1006/jcph.2001.6936
VL - 174
IS - 2
SP - 712-758
J2 - Journal of Computational Physics
LA - en
OP -
SN - 0021-9991
UR - http://dx.doi.org/10.1006/jcph.2001.6936
DB - Crossref
KW - artificial boundary conditions
KW - wave propagation
KW - lacunae
KW - nondeteriorating method
ER -
TY - CONF
TI - Rapid multi-model identification in systems with delay
AU - Campbell, S.L.
AU - Drake, K.
AU - Nikoukhah, R.
AU - Delebecque, F.
A2 - K. Gu, C. T. Abdallah
A2 - Niculescu, S.-I.
C2 - 2001///
C3 - Time delay systems 2001 (TDS 2001): A proceedings volume from the 3rd IFAC Workshop, Sante Fe, New Mexico, USA, 8-10 December 2001
CN - TJ212.2 .I328 2001
DA - 2001///
SP - 296-301
PB - Oxford: Pergamon
ER -
TY - JOUR
TI - Ore subresultant coefficients in solutions
AU - Hong, H
T2 - APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING
DA - 2001/10//
PY - 2001/10//
DO - 10.1007/s002000100082
VL - 12
IS - 5
SP - 421-428
SN - 1432-0622
UR - http://dx.doi.org/10.1007/s002000100082
KW - ore polynomials
KW - resultants
KW - subresultants
ER -
TY - JOUR
TI - On the combined performance of nonlocal artificial boundary conditions with the new generation of advanced multigrid flow solvers
AU - Roberts, T. W.
AU - Sidilkover, D.
AU - Tsynkov, Semyon
T2 - Computers & Fluids
AB - We develop theoretically and implement numerically a unified flow solution methodology that combines the advantages relevant to two independent groups of methods in computational fluid dynamics that have recently proven successful: The new factorizable schemes for the equations of hydrodynamics that facilitate the construction of optimally convergent multigrid algorithms, and highly accurate global far-field artificial boundary conditions (ABCs). The primary result that we have obtained is the following. Global ABCs do not hamper the optimal (i.e., unimprovable) multigrid convergence rate pertinent to the solver. At the same time, contrary to the standard local ABCs, the solution accuracy provided by the global ABCs deteriorates very slightly or does not deteriorate at all when the computational domain shrinks, which clearly translates into substantial savings of computer resources.
DA - 2001///
PY - 2001///
DO - 10.1016/s0045-7930(01)00045-7
VL - 31
IS - 3
SP - 269–308
ER -
TY - JOUR
TI - Formation of parthenocarpic fruit, undeveloped flowers and aborted flowers in tomato under moderately elevated temperatures
AU - Sato, S
AU - Peet, MM
AU - Gardner, RG
T2 - SCIENTIA HORTICULTURAE
AB - Incidence of parthenocarpic fruit, undeveloped flowers and flower abortion in tomato plants (Lycopersicon esculentum Mill.) were compared under optimal temperature (OT, 28/22°C day/night) and chronic, mild high temperature conditions (HT, 32/26°C). Seeded fruits were found only under OT conditions, where 37±9% of all flowers developed into seeded fruit. However, flower aborted was also higher under OT, with an additional 24±7% of flowers aborted under optimal temperature conditions, compared to only 4±1% of flowers aborted under HT conditions. Under HT, most flowers (53±8%) developed into parthenocarpic fruit, and the remainder (43±7%) stayed on the plant as undeveloped flowers. A slow transition of undeveloped flowers to parthenocarpic fruit was also observed under HT. Factors determining whether flowers abort, develop parthenocarpically, remain on the plant without developing further, or develop into seeded fruit were discussed in relation to carbohydrate availability and the presence of seeded fruit on the vine.
DA - 2001/11/16/
PY - 2001/11/16/
DO - 10.1016/S0304-4238(00)00262-4
VL - 90
IS - 3-4
SP - 243-254
SN - 0304-4238
KW - Lycopersicon esculentum. Mill.
KW - moderately elevated temperatures
KW - heat stress
KW - flower development
KW - parthenocarpy
KW - flower abortion
KW - seedlessness
ER -
TY - JOUR
TI - Epithelial branching
AU - Nakanishi, Y.
AU - Hieda, Y.
AU - Cardoso, W. V.
AU - Lubkin, Sharon
AU - Daniel, C. W.
T2 - Encyclopedia of life sciences
DA - 2001///
PY - 2001///
DO - 10.1038/npg.els.0001145
IS - 2001
ER -
TY - JOUR
TI - Biomathematics
AU - Lubkin, S. R.
T2 - Encyclopedia of mathematics education
CN - QA11 .E665 2001
DA - 2001///
PY - 2001///
SP - 77-78
ER -
TY - CONF
TI - Auxiliary signal design for failure detection in uncertain systems
AU - Nikoukhah, R.
AU - Campbell, S.L.
AU - Delebecque, F.
T2 - 9th IEEE Mediterranean Conference on Control and Automation
A2 - P. P. Groumpos, N. T. Koussoulas
A2 - Polycarpou, M.
C2 - 2001///
C3 - Proceedings of the 9th IEEE Mediterranean Conference on Control and Automation
CN - TJ212.2 .I325 2000
CY - Dubrovnik, Croatia
DA - 2001///
PY - 2001/6/27/
PB - Piscataway, N.J.: IEEE
ER -
TY - JOUR
TI - A nonconvex scalar conservation law with trilinear flux
AU - Hayes, BT
AU - Shearer, M
T2 - QUARTERLY OF APPLIED MATHEMATICS
AB - The focus of this paper is on traveling wave solutions of the equation \[ u t + f ( u ) x = ϵ u x x + ϵ 2 γ u x x x {u_t} + f{\left ( u \right )_x} = \epsilon {u_{xx}} + {\epsilon ^2}\gamma {u_{xxx}} \] , in which the flux function f f is trilinear and nonconvex. In particular, it is shown that for combinations of parameters in certain ranges, there are traveling waves that converge as ϵ → 0 \epsilon \to 0 to undercompressive shocks, in which the characteristics pass through the shock. The analysis is based on explicit solutions of the piecewise linear ordinary differential equation satisfied by traveling waves. The analytical results are illustrated by numerical solutions of the Riemann initial value problem, and are compared with corresponding explicit results for the case of a cubic flux function.
DA - 2001/12//
PY - 2001/12//
DO - 10.1090/qam/1866551
VL - 59
IS - 4
SP - 615-635
SN - 0033-569X
ER -
TY - JOUR
TI - Unified solutions to classical flow problems based on the BGK model
AU - Barichello, LB
AU - Camargo, M
AU - Rodrigues, P
AU - Siewert, CE
T2 - ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
DA - 2001/5//
PY - 2001/5//
DO - 10.1007/pl00001559
VL - 52
IS - 3
SP - 517-534
SN - 0044-2275
KW - discrete ordinates
KW - rarefied gas dynamics
ER -
TY - JOUR
TI - Nonlinear exothermic contributions to radio-frequency bonding of adhesives
AU - Banks, HT
AU - Choi, MG
AU - Durso, , SR
AU - Ito, K
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
DA - 2001/9//
PY - 2001/9//
DO - 10.1016/S0362-546X(00)00110-3
VL - 2
IS - 3
SP - 357-386
SN - 1468-1218
KW - radio-frequency electromagnetic bonding
KW - nonlinear thermal processes
KW - operator splitting
KW - existence and uniqueness
ER -
TY - JOUR
TI - Multiple extinctions in a discrete competitive system
AU - Chan, DM
AU - Franke, JE
T2 - NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
DA - 2001/3//
PY - 2001/3//
DO - 10.1016/S0362-546X(99)00282-5
VL - 2
IS - 1
SP - 75-91
SN - 1468-1218
KW - extinction
KW - Lyapunov function
KW - omega-limit set
KW - weakly dominate
KW - competition
ER -
TY - JOUR
TI - Existence of stationary solutions to an energy drift-diffusion model for semiconductor devices
AU - Fang, WF
AU - Ito, K
T2 - MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
AB - We analyze a mathematical model for semiconductors derived from the hydrodynamic model under the massless assumption. This model augments the classical drift-diffusion model by including temperature as a dependent variable. We establish the existence of stationary solutions near the equilibrium state.
DA - 2001/7//
PY - 2001/7//
DO - 10.1142/S0218202501001124
VL - 11
IS - 5
SP - 827-840
SN - 0218-2025
ER -
TY - JOUR
TI - BRST resolution for the principally graded Wakimoto module of (sl)over-cap(2)
AU - Hara, Y
AU - Jing, NH
AU - Misra, K
T2 - LETTERS IN MATHEMATICAL PHYSICS
DA - 2001/12//
PY - 2001/12//
DO - 10.1023/A:1014559525117
VL - 58
IS - 3
SP - 181-188
SN - 0377-9017
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0041814659&partnerID=MN8TOARS
KW - affine Lie algebra
KW - Wakimoto module
ER -
TY - JOUR
TI - n-symplectic algebra of observables in covariant Lagrangian field theory
AU - Norris, LK
T2 - JOURNAL OF MATHEMATICAL PHYSICS
AB - n -symplectic geometry on the adapted frame bundle λ:LπE→E of an n=(m+k)-dimensional fiber bundle π:E→M is used to set up an algebra of observables for covariant Lagrangian field theories. Using the principle bundle ρ:LπE→J1π we lift a Lagrangian L:J1π→R to a Lagrangian L≔ρ*(L):LπE→R, and then use L to define a “modified n-symplectic potential” θ̂L on LπE, the Cartan–Hamilton–Poincaré (CHP) Rn-valued 1-form. If the lifted Lagrangian is nonzero, then (LπE,dθ̂L) is an n-symplectic manifold. To characterize the observables we define a lifted Legendre transformation φL from LπE into LE. The image QL≔φL(LπE) is a submanifold of LE, and (QL,d(θ̂|QL)) is shown to be an n-symplectic manifold. We prove the theorem that θ̂L=φL*(θ|QL), and pull back the reduced canonical n-symplectic geometry on QL to LπE to define the algebras of observables on the n-symplectic manifold (LπE,dθ̂L). To find the reduced n-symplectic algebra on QL we set up the equations of n-symplectic reduction, and apply the general theory to the model of a k-tuple of massless scalar fields on Minkowski space–time. The formalism set forth in this paper lays the ground work for a geometric quantization theory of fields.
DA - 2001/10//
PY - 2001/10//
DO - 10.1063/1.1396835
VL - 42
IS - 10
SP - 4827-4845
SN - 1089-7658
ER -
TY - JOUR
TI - Surface reaction kinetics of Ga1-xInxP growth during pulsed chemical beam epitaxy
AU - Dietz, N
AU - Beeler, SC
AU - Schmidt, JW
AU - Tran, HT
T2 - APPLIED SURFACE SCIENCE
AB - The understanding of thin film growth processes and their control requires the development of surface-sensitive real-time optical characterization techniques that are able to provide insight into the surface reaction kinetics during an organometallic deposition process. These insights will allow us to move the control point closer to the point where the growth occurs, which in a chemical beam epitaxy (CBE) process is a surface reaction layer (SRL), built up of physisorbed and chemisorbed precursor fragments between the ambient and film interface. This contribution presents results on parameter estimations of rate constants and optical response factors in a reduced order surface kinetics (ROSK) model, which has been developed to describe the decomposition and growth kinetics of the involved organometallic precursors and their incorporation in the film deposition. As a real-time characterization technique, we applied p-polarized reflectance spectroscopy (PRS) during low temperature growth of epitaxial Ga1−xInxP heterostructures on Si(0 0 1) substrates by pulsed chemical beam epitaxy (PCBE). The high surface sensitivity of PRS allows us to follow alterations in composition and thickness of the SRL as they are encountered during periodic precursor supply. The linkage of the PRS response to the ROSK model provides the base for the parameter estimation, giving insights into the organometallic precursor decomposition and growth kinetics.
DA - 2001/7/2/
PY - 2001/7/2/
DO - 10.1016/S0169-4332(01)00302-6
VL - 178
IS - 1-4
SP - 63-74
SN - 1873-5584
KW - real-time optical growth monitoring
KW - III-V epitaxy
KW - surface reaction kinetics
KW - parameter estimation
KW - growth modeling
KW - p-polarized reflectance
ER -
TY - JOUR
TI - Reciprocity in character theory of finite semigroups
AU - Putcha, MS
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
AB - This paper concerns the complex characters of finite semigroups. We begin by reducing the general problem to the study of local monoids M = G ∪ J ∪{0}, where G is the unit group and J is a regular J -class. Let H be a maximal subgroup of J . For a C H -module U with character θ , let Ũ be the associated C M -module and let θ ̃ be the character of the C G -module Ũ . For a C G -module V with character ψ , we construct a natural C H -module V ∼ with character ψ ∼ . We prove the reciprocity theorem: 〈 θ ̃ ,ψ〉 G =〈θ, ψ ∼ 〉 H . As a consequence we find a characterization of the J -cuspidal characters of G . We go on to interpret our results for groups, introducing the concept of double parabolic induction.
DA - 2001/10/8/
PY - 2001/10/8/
DO - 10.1016/S0022-4049(00)00162-6
VL - 163
IS - 3
SP - 339-351
SN - 0022-4049
ER -
TY - JOUR
TI - Numerical methods for time-periodic solutions of nonlinear parabolic boundary value problems
AU - Pao, CV
T2 - SIAM JOURNAL ON NUMERICAL ANALYSIS
AB - This paper is devoted to a numerical analysis of periodic solutions of a finite difference system which is a discrete version of a class of nonlinear reaction-diffusion-convection equations under nonlinear boundary conditions. Three monotone iterative schemes for the finite difference system are presented, and it is shown by the method of upper and lower solutions that the sequence of iterations from each of these iterative schemes converges monotonically to either a maximal periodic solution or a minimal periodic solution depending on whether the initial iteration is an upper solution or a lower solution. A comparison theorem for the various monotone sequences is given. It is also shown that the maximal and minimal periodic solutions of the finite difference system converge to the corresponding maximal and minimal periodic solutions of the reaction-diffusion-convection equation as the mesh size decreases to zero. Some error estimates between the theoretical and the computed iterations for each of the three iterative schemes are obtained, and a discussion on the numerical stability of these schemes is given. Also given are some numerical results of a logistic reaction diffusion problem.
DA - 2001/7/8/
PY - 2001/7/8/
DO - 10.1137/S0036142999361396
VL - 39
IS - 2
SP - 647-667
SN - 0036-1429
KW - time-periodic solution
KW - reaction-diffusion-convection equation
KW - monotone iterations
KW - finite difference equations
KW - convergence
KW - error estimates
ER -
TY - JOUR
TI - Kramers' problem for a variable collision frequency model
AU - Siewert, CE
T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS
AB - The often-studied problem known as Kramers' problem, in the general area of rarefied-gas dynamics, is investigated in terms of a linearized, variable collision frequency model of the Boltzmann equation. A convenient change of variables is used to reduce the general case considered to a canonical form that is well suited for analysis by analytical and/or numerical methods. While the general formulation developed is valid for an unspecified collision frequency, a recently developed version of the discrete-ordinates method is used to compute the viscous-slip coefficient and the velocity defect in the Knudsen layer for three specific cases: the classical BGK model, the Williams model (the collision frequency is proportional to the magnitude of the velocity) and the rigid-sphere model.
DA - 2001/4//
PY - 2001/4//
DO - 10.1017/s0956792501004491
VL - 12
SP - 179-191
SN - 0956-7925
ER -
TY - JOUR
TI - Finite difference solutions of reaction diffusion equations with continuous time delays
AU - Pao, CV
T2 - COMPUTERS & MATHEMATICS WITH APPLICATIONS
AB - This paper is an extension of the monotone iterative methods for finite difference equations with discrete time delays to a class of nonlinear finite difference system with continuous time delays. The system under consideration is a finite difference approximation of a class of reaction diffusion equations with continuous time delays in the nonlinear reaction under either Dirichlet or Neumann-Robin boundary conditions. Various monotone iterative schemes, which depend on the property of the nonlinear reaction mechanism, are developed for the computation of numerical solutions. It is shown by the method of upper and lower solutions that the two sequences obtained from each iterative scheme converge monotonically from above and below, respectively, to a unique solution of the finite difference system. Applications are given to two model problems known as the diffusive logistic equation and the Fisher's diffusion equation in population genetics.
DA - 2001///
PY - 2001///
DO - 10.1016/S0898-1221(01)00165-1
VL - 42
IS - 3-5
SP - 399-412
SN - 1873-7668
KW - finite difference system
KW - reaction diffusion equation
KW - monotone iterative schemes
KW - method of upper and lower solutions
KW - continuous time delay
KW - existence and uniqueness
ER -
TY - JOUR
TI - Effective methods in algebraic geometry
AU - Singer, MF
T2 - JOURNAL OF PURE AND APPLIED ALGEBRA
DA - 2001/10/24/
PY - 2001/10/24/
DO - 10.1016/S0022-4049(00)00141-9
VL - 164
IS - 1-2
SP - 1-2
SN - 0022-4049
ER -
TY - BOOK
TI - Differential models and neutral systems for controlling the wealth of nations
AU - Chukwu, E. N.
AB - Continuous delay models - motivation, economic dynamic model main results economic interpretation and fundamental economic principles economic hereditary models of Canada soft landing of key economic indicators with private and government controls under scarcity economic systems with delay in control the nonlinear theory of controllability of volterra neutral integrodifferential dynamics economic models of USA, Canada, UK, Germany and India model programmes and graphs optimal control of volterra integral neutral equations and of linear neutral equations nonlinear neutral systems controllable nonlinear neutral systems function space control of nonlinear interconnected economic systems of neutral type nonlinear mathematical controllability theory of the growth of wealth of nations oscillation construction of econometric meter and reform of global economic systems structure.
CN - HB141 .C538 2001
DA - 2001///
PY - 2001///
DO - 10.1142/9789812791863
PB - Singapore; River Edge, N.J.: World Scientific
SN - 9810243812
ER -
TY - JOUR
TI - A locally-biased form of the DIRECT algorithm
AU - Gablonsky, JM
AU - Kelley, CT
T2 - JOURNAL OF GLOBAL OPTIMIZATION
DA - 2001/9//
PY - 2001/9//
DO - 10.1023/A:1017930332101
VL - 21
IS - 1
SP - 27-37
SN - 0925-5001
KW - DIRECT
KW - locally-biased formulation
KW - local clustering
ER -
TY - CHAP
TI - A Level Set-Boundary Element Method for Simulation of Dynamic Powder Consolidation of Metals
AU - Li, Zhilin
AU - Cai, Wei
T2 - Lecture Notes in Computer Science
A2 - L. Vulkov, J. Wasniewski
A2 - Yalamov, P.
CN - QA297 .N8415 2001
PY - 2001///
DO - 10.1007/3-540-45262-1_62
VL - 1988
SP - 527-534
OP -
PB - Springer Berlin Heidelberg
SN - 9783540418146 9783540452621
UR - http://dx.doi.org/10.1007/3-540-45262-1_62
DB - Crossref
ER -
TY - JOUR
TI - Dynamic simulation of the temporal response of microstructure formation in magnetorheological fluids
AU - Ly, HV
AU - Ito, K
AU - Banks, HT
AU - Jolly, MR
AU - Reitich, F
T2 - INTERNATIONAL JOURNAL OF MODERN PHYSICS B
AB - Efficient numerical simulations of microstructure development in magnetorheological (MR) fluids are conducted. The simulations, which are based upon a fast multipole algorithm, treat the magnetic inclusions as two-dimensional continuum magnetic entities. The development of microstructure is quantified by computing and recording the time evolution of the effective permeability of the composite fluid. Such a principle has been previously exploited for the experimental measurements of microstructure development [Jolly, Bender and Mathers, ERMR'97, Yonezawa, Japan 1997]. As was observed experimentally, numerical simulations reveal the evolution of microstructure to be multimodal in nature. Unlike the experiments, the numerical simulations afford us the ability to observe the physical mechanisms associated with various modes.
DA - 2001/3/20/
PY - 2001/3/20/
DO - 10.1142/s0217979201005416
VL - 15
IS - 6-7
SP - 894-903
SN - 0217-9792
ER -
TY - JOUR
TI - The fundamental relations between geometric programming duality, parametric programming duality, and ordinary Lagrangian duality
AU - Peterson, EL
T2 - ANNALS OF OPERATIONS RESEARCH
DA - 2001///
PY - 2001///
DO - 10.1023/A:1013353515966
VL - 105
SP - 109-153
SN - 0254-5330
KW - geometric programming
KW - ordinary programming
KW - parametric programming
KW - Lagrange multipliers
KW - post-optimality analysis
KW - conjugate transformation
KW - Legendre transformation
KW - dual cones
KW - orthogonal complementary subspaces
KW - duality theory
KW - orthogonal projection
KW - optimization
KW - convex optimization
KW - recession directions
KW - separable optimization
KW - sub-optimization
ER -
TY - JOUR
TI - Reduced basis method for optimal control of unsteady viscous flows
AU - Ito, K
AU - Ravindran, SS
T2 - INTERNATIONAL JOURNAL OF COMPUTATIONAL FLUID DYNAMICS
AB - Abstract In this article we discuss the reduced basis method (RBM) for optimal control of unsteady viscous flows. RBM is a reduction method in which one can achieve the versatility of the finite element method or another for that matter and gain significant reduction in the number of degrees of freedom. The essential idea in this method is to define a reduced order subspace spanned by few basis elements and then obtain the solution via a Galerkin projection. We present several ways to define this subspace. Feasibility of the approach is demonstrated on two boundary control problems in cavity and wall bounded channel flows. Control action is effected through boundary surface movement on part of the solid wall. Application of RBM to the control problems leads to finite dimensional optimal control problems which are solved using Newton's method. Through computational experiments we demonstrate the feasibility and applicability of the reduced basis method for control of unsteady viscous flows.
DA - 2001///
PY - 2001///
DO - 10.1080/10618560108970021
VL - 15
IS - 2
SP - 97-113
SN - 1061-8562
KW - reduced order models
KW - optimal control
KW - unsteady viscous flows
ER -
TY - JOUR
TI - Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions
AU - Pao, CV
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - The purpose of this paper is to present some iterative methods for numerical solutions of a class of nonlinear reaction–diffusion equations with nonlocal boundary conditions. Using the finite-difference method and the method of upper and lower solutions we present some monotone iterative schemes for both the time-dependent and the steady-state finite-difference systems. Each monotone iterative scheme gives a computational algorithm for numerical solutions and an existence-comparison theorem for the corresponding finite-difference system. The existence-comparison theorems are used to investigate the asymptotic behavior of the discrete time-dependent solution in relation to the discrete maximal and minimal solutions of the steady-state problem. Numerical results are given to a model problem where the solution of the continuous problem is explicitly known and its values at the mesh points are used to compare with the numerical solutions obtained by the monotone iterative schemes.
DA - 2001/11/1/
PY - 2001/11/1/
DO - 10.1016/S0377-0427(00)00614-2
VL - 136
IS - 1-2
SP - 227-243
SN - 0377-0427
KW - finite-difference equation
KW - reaction-diffusion
KW - nonlocal boundary condition
KW - numerical solution
KW - monotone iterations
ER -
TY - JOUR
TI - Numerical methods for nonlinear integro-parabolic equations of Fredholm type
AU - Pao, CV
T2 - COMPUTERS & MATHEMATICS WITH APPLICATIONS
AB - This paper is concerned with iterative methods for numerical solutions of a class of nonlocal reaction-diffusion-convection equations under either linear or nonlinear boundary conditions. The discrete approximation of the problem is based on the finite-difference method, and the computation of the finite-difference solution is by the method of upper and lower solutions. Three types of quasi-monotone reaction functions are considered and for each type, a monotone iterative scheme is obtained. Each of these iterative schemes yields two sequences which converge monotonically from above and below, respectively, to a unique solution of the finite-difference system. This monotone convergence leads to an existence-uniqueness theorem as well as a computational algorithm for the computation of the solution. An error estimate between the computed approximations and the true finite-difference solution is obtained for each iterative scheme. These error estimates are given in terms of the strength of the reaction function and the effect of diffusion-convection, and are independent of the true solution. Applications are given to three model problems to illustrate some basic techniques for the construction of upper and lower solutions and the implementation of the computational algorithm.
DA - 2001/4//
PY - 2001/4//
DO - 10.1016/S0898-1221(00)00325-4
VL - 41
IS - 7-8
SP - 857-877
SN - 0898-1221
KW - integro-parabolic equation
KW - finite-difference solution
KW - reaction-diffusion convection
KW - monotone iteration
KW - error estimate
KW - upper and lower solutions
ER -
TY - JOUR
TI - Graduate education in computational science and engineering
AU - Petzold, L. R.
AU - Ascher, U.
AU - Banks, H. T.
AU - Crowley, J.
AU - Gander, W.
AU - Greengard, L.
AU - Heath, M.
AU - Lumsdaine, A.
AU - Moler, C.
AU - Oden, T.
AU - Schnabel, R.
AU - Stewart, K.
AU - Trefethen, A.
T2 - SIAM Review
DA - 2001///
PY - 2001///
VL - 43
IS - 1
SP - 163-177
ER -
TY - JOUR
TI - An electrochemistry model with nonlinear diffusion: steady-state solutions
AU - Fang, WF
AU - Ito, K
T2 - IMA JOURNAL OF APPLIED MATHEMATICS
AB - We formulate and study the steady-state solutions for an electrochemistry model with nonlinear diffusion. We establish the existence and uniqueness of solutions, prove the global convergence of a successive iteration scheme, and use examples to illustrate the formation of vacuum regions, which is not possible in a linear diffusion model.
DA - 2001/4//
PY - 2001/4//
DO - 10.1093/imamat/66.2.195
VL - 66
IS - 2
SP - 195-213
SN - 0272-4960
KW - electrochemistry
KW - integro-differential equations
KW - nonlinear diffusion
ER -
TY - JOUR
TI - Virasoro algebra and wreath product convolution
AU - Frenkel, IB
AU - Wang, WQ
T2 - JOURNAL OF ALGEBRA
AB - We present a group theoretic construction of the Virasoro algebra in the framework of wreath products. This can be regarded as a counterpart of a geometric construction of Lehn in the theory of Hubert schemes of points on a surface.
DA - 2001/8/15/
PY - 2001/8/15/
DO - 10.1006/jabr.2001.8860
VL - 242
IS - 2
SP - 656-671
SN - 1090-266X
ER -
TY - JOUR
TI - Stability of compressive and undercompressive thin film travelling waves
AU - Bertozzi, AL
AU - Munch, A
AU - Shearer, M
AU - Zumbrun, K
T2 - EUROPEAN JOURNAL OF APPLIED MATHEMATICS
AB - Recent studies of liquid films driven by competing forces due to surface tension gradients and gravity reveal that undercompressive travelling waves play an important role in the dynamics when the competing forces are comparable. In this paper, we provide a theoretical framework for assessing the spectral stability of compressive and undercompressive travelling waves in thin film models. Associated with the linear stability problem is an Evans function which vanishes precisely at eigenvalues of the linearized operator. The structure of an index related to the Evans function explains computational results for stability of compressive waves. A new formula for the index in the undercompressive case yields results consistent with stability. In considering stability of undercompressive waves to transverse perturbations, there is an apparent inconsistency between long-wave asymptotics of the largest eigenvalue and its actual behaviour. We show that this paradox is due to the unusual structure of the eigenfunctions and we construct a revised long-wave asymptotics. We conclude with numerical computations of the largest eigenvalue, comparisons with the asymptotic results, and several open problems associated with our findings.
DA - 2001/6//
PY - 2001/6//
DO - 10.1017/s0956792501004466
VL - 12
IS - 2001 June
SP - 253-291
SN - 0956-7925
ER -
TY - JOUR
TI - Physiologically based pharmacokinetic modeling of benzene metabolism in mice through extrapolation from in vitro to in vivo
AU - Cole, CE
AU - Tran, HT
AU - Schlosser, PM
T2 - JOURNAL OF TOXICOLOGY AND ENVIRONMENTAL HEALTH-PART A
AB - Benzene (C6H6) is a highly flammable, colorless liquid. Ubiquitous exposures result from its presence in gasoline vapors, cigarette smoke, and industrial processes. Benzene increases the incidence of leukemia in humans when they are exposed to high doses for extended periods; however, leukemia risks in humans at low exposures are uncertain. The exposure-dose-response relationship of benzene in humans is expected to be nonlinear because benzene undergoes a series of metabolic transformations, detoxifying and activating, in the liver, resulting in multiple metabolites that exert toxic effects on the bone marrow. We developed a physiologically based pharmacokinetic model for the uptake and elimination of benzene in mice to relate the concentration of inhaled and orally administered benzene to the tissue doses of benzene and its key metabolites, benzene oxide, phe nol, and hydroquinone. As many parameter values as possible were taken from the literature; in particular, metabolic parameters obtained from in vitro studies with mouse liver were used since comparable parameters are also available for humans. Parameters estimated by fitting the model to published data were first-order rate constants for pathways lacking in vitro data and the concentrations of microsomal and cytosolic protein, which effectively alter overall enzyme activity. The model was constrained by using the in vitro metabolic parameters (maximum velocities, first-order rate constants, and saturation parameters), and data from multiple laboratories and experiments were used. Despite these constraints and sources of variability, the model simulations matched the data reasonably well in most cases, showing that in vitro metabolic constants can be successfully extrapolated to predict in vivo data for benzene metabolism and dosimetry. Therefore in vitro metabolic constants for humans can subsequently be extrapolated to predict the dosimetry of benzene and its metabolites in humans. This will allow us to better estimate the risks of adverse effects from low-level benzene exposures.
DA - 2001/3//
PY - 2001/3//
DO - 10.1080/00984100150501178
VL - 62
IS - 6
SP - 439-465
SN - 1528-7394
ER -
TY - JOUR
TI - On multi-color partitions and the generalized Rogers-Ramanujan identities
AU - Jing, NH
AU - Misra, KC
AU - Savage, CD
T2 - COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
AB - Basil Gordon, in the sixties, and George Andrews, in the seventies, generalized the Rogers–Ramanujan identities to higher moduli. These identities arise in many areas of mathematics and mathematical physics. One of these areas is representation theory of infinite dimensional Lie algebras, where various known interpretations of these identities have led to interesting applications. Motivated by their connections with Lie algebra representation theory, we give a new interpretation of a sum related to generalized Rogers–Ramanujan identities in terms of multi-color partitions.
DA - 2001/11//
PY - 2001/11//
DO - 10.1142/S0219199701000482
VL - 3
IS - 4
SP - 533-548
SN - 0219-1997
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-27144449078&partnerID=MN8TOARS
ER -
TY - JOUR
TI - A note on preconditioning nonsymmetric matrices
AU - Ipsen, ICF
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - Previous article A Note on Preconditioning Nonsymmetric MatricesIlse C. F. IpsenIlse C. F. Ipsenhttps://doi.org/10.1137/S1064827500377435PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractThe preconditioners for indefinite matrices of KKT form in [M. F. Murphy, G. H. Golub, and A. J. Wathen, SIAM J. Sci. Comput., 21 (2000), pp. 1969--1972] are extended to general nonsymmetric matrices.[1] Philip Gill, , Walter Murray, , Dulce Poncele{\'o}n and , Michael Saunders, Preconditioners for indefinite systems arising in optimization, SIAM J. Matrix Anal. Appl., 13 (1992), 292–311 92j:65088 LinkISIGoogle Scholar[2] Malcolm Murphy, , Gene Golub and , Andrew Wathen, A note on preconditioning for indefinite linear systems, SIAM J. Sci. Comput., 21 (2000), 1969–1972 10.1137/S1064827599355153 2001a:65055 LinkISIGoogle ScholarKeywordspreconditionerminimal polynomial Previous article FiguresRelatedReferencesCited byDetails Algebraic spectral analysis of the DSSR preconditionerComputers & Mathematics with Applications, Vol. 125 Cross Ref Lopsided shift-splitting preconditioner for saddle point problems with three-by-three structure25 July 2022 | Computational and Applied Mathematics, Vol. 41, No. 6 Cross Ref Parameter-Robust Preconditioning for Oseen Iteration Applied to Stationary and Instationary Navier--Stokes ControlSantolo Leveque and John W. 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Pearson and Martin Stoll10 September 2013 | SIAM Journal on Scientific Computing, Vol. 35, No. 5AbstractPDF (1653 KB)Composable Linear Solvers for Multiphysics Cross Ref A note on the group inverse of some 2 × 2 block matrices over skew fieldsApplied Mathematics and Computation, Vol. 217, No. 24 Cross Ref A Relaxed Dimensional Factorization preconditioner for the incompressible Navier–Stokes equationsJournal of Computational Physics, Vol. 230, No. 16 Cross Ref Schur Complement Preconditioners for Surface Integral-Equation Formulations of Dielectric Problems Solved with the Multilevel Fast Multipole AlgorithmTahİr Malas and Levent Gürel4 October 2011 | SIAM Journal on Scientific Computing, Vol. 33, No. 5AbstractPDF (1339 KB)Preconditioners for regularized saddle point matricesJournal of Numerical Mathematics, Vol. 19, No. 2 Cross Ref Solution of linear systems from an optimal control problem arising in wind simulation26 November 2010 | Numerical Linear Algebra with Applications, Vol. 17, No. 6 Cross Ref Some results on the group inverse of the block matrix with a sub-block of linear combination or product combination of matrices over skew fieldsLinear and Multilinear Algebra, Vol. 58, No. 8 Cross Ref The spectral properties of the preconditioned matrix for nonsymmetric saddle point problemsJournal of Computational and Applied Mathematics, Vol. 235, No. 1 Cross Ref Substructure preconditioners for a class of structured linear systems of equationsMathematical and Computer Modelling, Vol. 52, No. 9-10 Cross Ref Preconditioning of matrices partitioned in 2 × 2 block form: eigenvalue estimates and Schwarz DD for mixed FEM8 June 2010 | Numerical Linear Algebra with Applications, Vol. 17, No. 5 Cross Ref A note for preconditioning nonsymmetric matrices14 March 2010 | Applied Mathematics-A Journal of Chinese Universities, Vol. 25, No. 1 Cross Ref Block triangular Schur complement preconditioners for saddle point problems and application to the Oseen equationsApplied Numerical Mathematics, Vol. 60, No. 3 Cross Ref Preconditioning techniques for a mixed Stokes/Darcy model in porous media applicationsJournal of Computational and Applied Mathematics, Vol. 233, No. 2 Cross Ref Analysis of photonic-crystal problems with MLFMA and approximate Schur preconditioners Cross Ref Generalized block triangular preconditioner for symmetric saddle point problems27 March 2009 | Computing, Vol. 84, No. 3-4 Cross Ref Optimization of the parameterized Uzawa preconditioners for saddle point matricesJournal of Computational and Applied Mathematics, Vol. 226, No. 1 Cross Ref Constraint Preconditioners for Symmetric Indefinite MatricesZhong-Zhi Bai, Michael K. Ng, and Zeng-Qi Wang22 April 2009 | SIAM Journal on Matrix Analysis and Applications, Vol. 31, No. 2AbstractPDF (286 KB)Constraint Schur complement preconditioners for nonsymmetric saddle point problemsApplied Numerical Mathematics, Vol. 59, No. 1 Cross Ref Group inverse for a class block matrices over skew fieldsApplied Mathematics and Computation, Vol. 204, No. 1 Cross Ref Positive stable block triangular preconditioners for symmetric saddle point problemsApplied Numerical Mathematics, Vol. 57, No. 8 Cross Ref Preconditioning and iterative solution of symmetric indefinite linear systems arising from interior point methods for linear programming6 March 2007 | Computational Optimization and Applications, Vol. 36, No. 2-3 Cross Ref Eigenvalue estimates for preconditioned saddle point matrices1 January 2006 | Numerical Linear Algebra with Applications, Vol. 13, No. 4 Cross Ref A note on block diagonal and constraint preconditioners for non-symmetric indefinite linear systemsInternational Journal of Computer Mathematics, Vol. 83, No. 4 Cross Ref Preconditioners for Generalized Saddle-Point ProblemsChris Siefert and Eric de Sturler25 July 2006 | SIAM Journal on Numerical Analysis, Vol. 44, No. 3AbstractPDF (244 KB)A robust preconditioner for fluid–structure interaction problemsComputer Methods in Applied Mechanics and Engineering, Vol. 194, No. 39-41 Cross Ref Numerical simulations of glacial rebound using preconditioned iterative solution methodsApplications of Mathematics, Vol. 50, No. 3 Cross Ref Representations of the Drazin inverse for a class of block matricesLinear Algebra and its Applications, Vol. 400 Cross Ref On Inexact Preconditioners for Nonsymmetric MatricesZhong-Zhi Bai and Michael K. Ng25 July 2006 | SIAM Journal on Scientific Computing, Vol. 26, No. 5AbstractPDF (165 KB)Further note on constraint preconditioning for nonsymmetric indefinite matricesApplied Mathematics and Computation, Vol. 152, No. 1 Cross Ref Schur complement preconditioning for elliptic systems of partial differential equations1 January 2003 | Numerical Linear Algebra with Applications, Vol. 10, No. 5-6 Cross Ref A Preconditioner for the Steady-State Navier--Stokes EquationsDavid Kay, Daniel Loghin, and Andrew Wathen25 July 2006 | SIAM Journal on Scientific Computing, Vol. 24, No. 1AbstractPDF (610 KB) Volume 23, Issue 3| 2001SIAM Journal on Scientific Computing History Published online:25 July 2006 InformationCopyright © 2001 Society for Industrial and Applied MathematicsKeywordspreconditionerminimal polynomialMSC codes65F1015A23PDF Download Article & Publication DataArticle DOI:10.1137/S1064827500377435Article page range:pp. 1050-1051ISSN (print):1064-8275ISSN (online):1095-7197Publisher:Society for Industrial and Applied Mathematics
DA - 2001/10/1/
PY - 2001/10/1/
DO - 10.1137/S1064827500377435
VL - 23
IS - 3
SP - 1050-1051
SN - 1064-8275
KW - preconditioner
KW - minimal polynomial
ER -
TY - JOUR
TI - The polynomial behavior of weight multiplicities for the affine Kac-Moody algebras A(r)((1))
AU - Benkart, G
AU - Kang, SJ
AU - Lee, H
AU - Misra, KC
AU - Shin, DU
T2 - COMPOSITIO MATHEMATICA
AB - We prove that the multiplicity of an arbitrary dominant weight for an irreducible highest weight representation of the affine Kac–Moody algebra A(1)r is a polynomial in the rank r. In the process we show that the degree of this polynomial is less than or equal to the depth of the weight with respect to the highest weight. These results allow weight multiplicity information for small ranks to be transferred to arbitrary ranks.
DA - 2001/3//
PY - 2001/3//
DO - 10.1023/A:1017584131106
VL - 126
IS - 1
SP - 91-111
SN - 0010-437X
KW - affine Kac-Moody algebra
KW - highest weight representations
KW - weight multiplicities
ER -
TY - JOUR
TI - Realization of level one representations of $U\sb q(\hat{\mathfrak {g}})$ at a root of unity
AU - Chari, V.
AU - Jing, Naihuan
T2 - Duke Mathematical Journal
AB - Using vertex operators, we construct explicitly Lusztig's ℤ[q,q−4]-lattice for the level one irreducible representations of quantum affine algebras of ADE type. We then realize the level one irreducible modules at roots of unity and show that the character is given by the Weyl-Kac character formula.
DA - 2001///
PY - 2001///
DO - 10.1215/s0012-7094-01-10816-8
VL - 108
IS - 1
SP - 183-197
UR - http://www.scopus.com/inward/record.url?eid=2-s2.0-0013121572&partnerID=MN8TOARS
ER -
TY - JOUR
TI - Numerical methods for fourth-order nonlinear elliptic boundary value problems
AU - Pao, CV
T2 - NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
AB - The aim of this article is to present several computational algorithms for numerical solutions of a nonlinear finite difference system that represents a finite difference approximation of a class of fourth-order elliptic boundary value problems. The numerical algorithms are based on the method of upper and lower solutions and its associated monotone iterations. Three linear monotone iterative schemes are given, and each iterative scheme yields two sequences, which converge monotonically from above and below, respectively, to a maximal solution and a minimal solution of the finite difference system. This monotone convergence property leads to upper and lower bounds of the solution in each iteration as well as an existence-comparison theorem for the finite difference system. Sufficient conditions for the uniqueness of the solution and some techniques for the construction of upper and lower solutions are obtained, and numerical results for a two-point boundary-value problem with known analytical solution are given. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17:347–368, 2001
DA - 2001/7//
PY - 2001/7//
DO - 10.1002/num.1016
VL - 17
IS - 4
SP - 347-368
SN - 1098-2426
KW - fourth-order elliptic equations
KW - two-point boundary problems
KW - finite difference system
KW - monotone iterations
KW - upper and lower solutions
KW - numerical solutions
KW - existence-comparison theorem
ER -
TY - JOUR
TI - Mechanistic model simulations of the East African climate using NCAR regional climate model: Influence of large-scale orography on the Turkana low-level jet
AU - Indeje, M
AU - Semazzi, FHM
AU - Xie, L
AU - Ogallo, LJ
T2 - JOURNAL OF CLIMATE
AB - The National Center for Atmospheric Research regional climate model (RegCM) is employed to study the dynamics of the Turkana low-level jet that lies between the Ethiopian and the East African highlands, and also investigate the mechanisms responsible for the observed dry conditions over the Lake Turkana basin that lies in the wider section of the Turkana channel. The role of the large-scale orography and two other forcing factors namely the large-scale monsoonal flow and the Turkana channel depth are investigated in order to understand the kinematics of the jet. The simulated patterns of the Turkana easterly low-level jet compares well with its observed characteristics. Strong winds are indicated in the channel throughout the study period of October to December, with the wind speed decreasing in the middle and wider region of the channel. A split in the jet core is also shown in the middle of the channel. The level of maximum winds (∼11 m s−1) occurs in the layers 930-hPa and 650-hPa levels. The dynamics of the Turkana channel is explained in terms of the orographic channeling effects associated with the Bernoulli theorem as applied to barotropic steady and nonviscous flows. The main results on the forcing mechanisms responsible for the development of the jet can be summarized as follows: (a) orographic forcing is the most important factor, (b) the large-scale monsoon background flow is important in determining the wind speed in the jet cores, (c) the depth of the channel determines the vertical structure and location of the jet cores, and (d) thermal and frictional forcing play equivalent role as that of the large-scale background winds in the formation and maintenance of the jet. Divergence and anticyclonic vorticity partly explains the observed split in the jet cores in the middle of the channel. The dry conditions observed over the Lake Turkana basin are explained in terms of dominant downward vertical velocity, decrease in moisture flux convergence, and increase in temperature flux divergence that inhibit active developments of mesoscale circulations and their interactions with large-scale flow over these areas. The identified regions of strong winds associated with the jet are important to the safety in the aviation industry. These regions may also provide alternative renewable energy resources in the form of wind energy.
DA - 2001///
PY - 2001///
DO - 10.1175/1520-0442(2001)014<2710:MMSOTE>2.0.CO;2
VL - 14
IS - 12
SP - 2710-2724
SN - 1520-0442
ER -
TY - JOUR
TI - Long-time numerical computation of wave-type solutions driven by moving sources
AU - Ryaben'kii, V.S.
AU - Tsynkov, S.V.
AU - Turchaninov, V.I.
T2 - Applied Numerical Mathematics
AB - Abstract We propose a methodology for calculating the solution of an initial-value problem for the three-dimensional wave equation over arbitrarily long time intervals. The solution is driven by moving sources that are compactly supported in space for any particular moment of time; the extent of the support is assumed bounded for all times. By a simple change of variables the aforementioned formulation obviously translates into the problem of propagation of waves across a medium in motion, which has multiple applications in unsteady aerodynamics, advective acoustics, and other areas. The algorithm constructed in the paper can employ any appropriate (i.e., consistent and stable) explicit finite-difference scheme for the wave equation. This scheme is used as a core computational technique and modified so that to allow for a non-deteriorating calculation of the solution for as long as necessary. Provided that the original underlying scheme converges in some sense, i.e., in suitable norms with a particular rate, we prove the grid convergence of the new algorithm in the same sense uniformly in time on arbitrarily long intervals. Thus, the new algorithm obviously does not accumulate error in the course of time; besides, it requires only a fixed non-growing amount of computer resources (memory and processor time) per one time step; these amounts are linear with respect to the grid dimension and thus optimal. The algorithm is inherently three-dimensional; it relies on the presence of lacunae in the solutions of the wave equation in odd-dimension spaces. The methodology presented in the paper is, in fact, a building block for constructing the nonlocal highly accurate unsteady artificial boundary conditions to be used for the numerical simulation of waves propagating with finite speed over unbounded domains.
DA - 2001/7//
PY - 2001/7//
DO - 10.1016/S0168-9274(01)00038-1
VL - 38
IS - 1-2
SP - 187-222
J2 - Applied Numerical Mathematics
LA - en
OP -
SN - 0168-9274
UR - http://dx.doi.org/10.1016/S0168-9274(01)00038-1
DB - Crossref
KW - wave equation
KW - lacunae
KW - finite-difference approximation
KW - explicit numerical integration
KW - arbitrarily long time intervals
KW - non-accumulation of error
KW - temporally uniform grid convergence
KW - fixed expenses per time step
ER -
TY - JOUR
TI - Construction and asymptotic stability of structurally stable internal layer solutions
AU - Lin, XB
T2 - TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - We introduce a geometric/asymptotic method to treat structurally stable internal layer solutions. We consider asymptotic expansions of the internal layer solutions and the critical eigenvalues that determine their stability. Proofs of the existence of exact solutions and eigenvalue-eigenfunctions are outlined. Multi-layered solutions are constructed by a new shooting method through a sequence of pseudo PoincarÃ© mappings that do not require the transversality of the flow to cross sections. The critical eigenvalues are determined by a coupling matrix that generates the SLEP matrix. The transversality of the shooting method is related to the nonzeroness of the critical eigenvalues. An equivalent approach is given to mono-layer solutions. They can be determined by the intersection of a fast jump surface and a slow switching curve, which reduces Fenichelâs transversality condition to the slow manifold. The critical eigenvalue is determined by the angle of the intersection. We present three examples. The first treats the critical eigenvalues of the system studied by Angenent, Mallet-Paret & Peletier. The second shows that a key lemma in the SLEP method may not hold. The third is a perturbed activator-inhibitor system that can have any number of mono-layer solutions. Some of the solutions can only be found with the new shooting method.
DA - 2001///
PY - 2001///
DO - 10.1090/S0002-9947-01-02769-6
VL - 353
IS - 8
SP - 2983-3043
SN - 0002-9947
KW - singular perturbation
KW - matched asymptotic expansion
KW - internal layers
KW - critical eigenvalues
KW - stability
KW - structural stability
ER -
TY - JOUR
TI - A review of quantitative studies of benzene metabolism
AU - Lovern, MR
AU - Cole, CE
AU - Schlosser, PM
T2 - CRITICAL REVIEWS IN TOXICOLOGY
AB - Benzene is a ubiquitous, highly flammable, colorless liquid that is a known hematotoxin, myelotoxin, and human leukemogen. Benzene-induced toxicity in animals is clearly mediated by its metabolism. The mechanisms of acute hemato- and myelotoxicity in humans are almost certainly the same as in animals, and there is compelling evidence that metabolism is requisite for the induction of leukemia in humans. A very large number of experimental investigations of benzene metabolism have been conducted with animals, both in vivo and in vitro. There have also been many investigations of benzene metabolism in humans and with human tissues, Although the blood or tissue concentrations of benzene metabolites in humans resulting from benzene exposure have never been measured. Further, a number of mathematical models of benzene metabolism and dosimetry have been developed. In this article, we consider results from both experimental and mathematical modeling research, with particular emphasis on the last decade, and discuss the factors that are likely to be most influential in the metabolism of benzene.
DA - 2001///
PY - 2001///
DO - 10.1080/20014091111703
VL - 31
IS - 3
SP - 285-311
SN - 1547-6898
ER -
TY - JOUR
TI - The critical problem with high-order anisotropic scattering
AU - Siewert, CE
T2 - ANNALS OF NUCLEAR ENERGY
AB - A synthetic scattering kernel is used with one-speed transport theory to evaluate the effect of high-order anisotropic scattering on the critical half thickness for a multiplying, unreflected, plane-parallel medium.
DA - 2001/5//
PY - 2001/5//
DO - 10.1016/S0306-4549(00)00090-6
VL - 28
IS - 8
SP - 825-829
SN - 0306-4549
ER -
TY - JOUR
TI - Monoids with idempotent cross-sections
AU - Putcha, MS
T2 - INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION
AB - In this paper we consider monoids M with an idempotent cross-section Λ of regular [Formula: see text]-classes such that for all idempotents e, f of M with e≥f, there exists x in the unit group such that x -1 ex, x -1 fx∈Λ. Such monoids arise frequently in connection with group representations. We show that Λ is then necessarily a semilattice and that the idempotent structure of M can for the most part, be determined within the unit group. We identify a particular class of "canonical monoids" inspired by some projective compactifications of algebraic groups. We show that these canonical monoids are 0-semilattice unions of completely 0-simple semigroups.
DA - 2001/8//
PY - 2001/8//
DO - 10.1142/S0218196701000632
VL - 11
IS - 4
SP - 457-466
SN - 0218-1967
ER -
TY - JOUR
TI - Constant crunch coordinates for black hole simulations
AU - Gentle, AP
AU - Holz, DE
AU - Kheyfets, A
AU - Laguna, P
AU - Miller, WA
AU - Shoemaker, DM
T2 - PHYSICAL REVIEW D
AB - We reinvestigate the utility of time-independent constant mean curvature foliations for the numerical simulation of a single spherically-symmetric black hole. Each spacelike hypersurface of such a foliation is endowed with the same constant value of the trace of the extrinsic curvature tensor, $K$. Of the three families of $K$-constant surfaces possible (classified according to their asymptotic behaviors), we single out a sub-family of singularity-avoiding surfaces that may be particularly useful, and provide an analytic expression for the closest approach such surfaces make to the singularity. We then utilize a non-zero shift to yield families of $K$-constant surfaces which (1) avoid the black hole singularity, and thus the need to excise the singularity, (2) are asymptotically null, aiding in gravity wave extraction, (3) cover the physically relevant part of the spacetime, (4) are well behaved (regular) across the horizon, and (5) are static under evolution, and therefore have no ``grid stretching/sucking'' pathologies. Preliminary numerical runs demonstrate that we can stably evolve a single spherically-symmetric static black hole using this foliation. We wish to emphasize that this coordinatization produces $K$-constant surfaces for a single black hole spacetime that are regular, static and stable throughout their evolution.
DA - 2001/3/15/
PY - 2001/3/15/
DO - 10.1103/physrevd.63.064024
VL - 63
IS - 6
SP -
SN - 2470-0029
ER -
TY - JOUR
TI - Piecewise linear model for field-responsive fluids
AU - Lee, CH
AU - Reitich, F
AU - Jolly, MR
AU - Banks, HT
T2 - IEEE TRANSACTIONS ON MAGNETICS
AB - The Frohlich-Kennelly model provides a constitutive law for saturation that is field dependent and has been widely used for studying nonlinear properties for a variety of electric and magnetic applications. Under the Frohlich-Kennelly model, saturation begins to occupy the entire conducting domain even at low-moderate applied fields, in this paper, we first present a new nonlinear constitutive law for field-responsive fluids that depends on the local fields and allows regions where the fields have not reached a critical value to remain unsaturated. We then study numerically the nonlinear saturated model and compare the results to the Frohlich-Kennelly model and experiments performed at the Lord Corporation, Cary, NC.
DA - 2001/1//
PY - 2001/1//
DO - 10.1109/20.914377
VL - 37
IS - 1
SP - 558-560
SN - 1941-0069
KW - field-responsive fluids
KW - Frohlich-Kennelly
KW - nonlinear saturation
KW - piecewise linear models
ER -
TY - JOUR
TI - On the structure of attractors for discrete, periodically forced systems with applications to population models
AU - Selgrade, JF
AU - Roberds, JH
T2 - PHYSICA D
AB - Abstract This work discusses the effects of periodic forcing on attracting cycles and more complicated attractors for autonomous systems of nonlinear difference equations. Results indicate that an attractor for a periodically forced dynamical system may inherit structure from an attractor of the autonomous (unforced) system and also from the periodicity of the forcing. In particular, a method is presented which shows that if the amplitude of the k-periodic forcing is small enough then the attractor for the forced system is the union of k homeomorphic subsets. Examples from population biology and genetics indicate that each subset is also homeomorphic to the attractor of the original autonomous dynamical system.
DA - 2001/10/15/
PY - 2001/10/15/
DO - 10.1016/s0167-2789(01)00324-4
VL - 158
IS - 1-4
SP - 69-82
SN - 0167-2789
KW - periodic forcing
KW - attractors
KW - discrete population models
ER -
TY - JOUR
TI - Generators for the cohomology ring of Hilbert schemes of points on surfaces
AU - Li, W. P.
AU - Qin, Z. B.
AU - Wang, W. Q.
T2 - International Mathematics Research Notices
DA - 2001///
PY - 2001///
IS - 20
SP - 1057-1074
ER -
TY - JOUR
TI - The effective magnetic properties of magnetorheological fluids
AU - Simon, TM
AU - Reitich, F
AU - Jolly, MR
AU - Ito, K
AU - Banks, HT
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - Magnetorheological (MR) fluids represent a class of smart materials whose rheological properties change in response to the application of a magnetic field. These fluids typically consist of small (μm) magnetizable particles dispersed in a nonmagnetic carrier fluid that generally contains additives such as surfactants and antiwear agents [1]. Due to such additives, there is an outer nonmagnetic layer on the particles that keeps them from touching. The goal of this paper is to study the effective magnetic behavior of an MR composite as a function of the interparticle distance. To this end, we present and employ a model for the effective magnetic properties of MR fluids with periodic microstructure that is based on the theory of homogenization. Finally, we discuss an interpolating formula for the effective permeability of MR fluids as an extension of the work of Keller [2] and Doyle [3].
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00244-2
VL - 33
IS - 1-3
SP - 273-284
SN - 0895-7177
KW - magnetorheological fluids
KW - homogenization
KW - effective properties
ER -
TY - JOUR
TI - Remarks on uncertainty assessment and management in modeling and computation
AU - Banks, HT
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - We discuss questions related to uncertainty in scientific computations for mathematical models. A computationally tractable probabilistic framework to treat uncertainty in the estimation of parameters or inverse problems is given. The theory is illustrated by a simple computational example for the estimation of constant parameters in differential equations by treating the parameters as random variables.
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00227-2
VL - 33
IS - 1-3
SP - 39-47
SN - 1872-9479
KW - computational uncertainty
KW - inverse problems
KW - probability distributions
ER -
TY - JOUR
TI - Predictions for a distributed parameter model describing the hepatic processing of 2,3,7,8-TCDD
AU - Banks, HT
AU - Musante, CJ
AU - Raye, JK
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - A distributed parameter model describing spatially-dependent hepatic processing of the chemical compound 2,3,7,8-tetrachlorodibenzo- p -dioxin (TCDD or dioxin) has previously been reported [1]. The mathematical system consists of coupled nonlinear partial and ordinary differential equations with delays. In this paper, we investigate the qualitative behavior of the system over a six-hour time period following a subcutaneous injection. A brief summary of the model is also given.
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00228-4
VL - 33
IS - 1-3
SP - 49-64
SN - 1872-9479
KW - distributed parameter models
KW - pharmacokinetic models
KW - 2,3,7,8-tetrachlorodibenzopdioxin
KW - liver transport models
KW - delay equations
ER -
TY - JOUR
TI - Numerically constructible observers for linear time-varying descriptor systems
AU - Biehn, N
AU - Campbell, SL
AU - Nikoukhah, R
AU - Delebecque, F
T2 - AUTOMATICA
AB - This paper examines the design of observers for linear time-varying descriptor systems. An observer is designed for which the observer estimates are also physically correct in that they satisfy the same constraints as the solutions of the descriptor system. Careful attention is paid to ensuring that all quantities are computable by numerical algorithms. One way to implement this approach is fully developed. A computational example is given.
DA - 2001/3//
PY - 2001/3//
DO - 10.1016/S0005-1098(00)00168-0
VL - 37
IS - 3
SP - 445-452
SN - 0005-1098
KW - descriptor systems
KW - observers
KW - linear systems
KW - time-varying systems
KW - computational methods
ER -
TY - JOUR
TI - Modeling and control of physical processes using proper orthogonal decomposition
AU - Ly, HV
AU - Tran, HT
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - The proper orthogonal decomposition (POD) technique (or the Karhunan Loève procedure) has been used to obtain low-dimensional dynamical models of many applications in engineering and science. In principle, the idea is to start with an ensemble of data, called snapshots , collected from an experiment or a numerical procedure of a physical system. The POD technique is then used to produce a set of basis functions which spans the snapshot collection. When these basis functions are used in a Galerkin procedure, they yield a finite-dimensional dynamical system with the smallest possible degrees of freedom. In this context, it is assumed that the physical system has a mathematical model, which may not be available for many physical and/or industrial applications. In this paper, we consider the steady-state Rayleigh-Bénard convection whose mathematical model is assumed to be unknown, but numerical data are available. The aim of the paper is to show that, using the obtained ensemble of data, POD can be used to model accurately the natural convection. Furthermore, this approach is very efficient in the sense that it uses the smallest possible number of parameters, and thus, is suited for process control. Particularly, we consider two boundary control problems 1. (a) tracking problem, and 2. (b) avoiding hot spot in a certain region of the domain.
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00240-5
VL - 33
IS - 1-3
SP - 223-236
SN - 1872-9479
KW - proper orthogonal decomposition
KW - boundary control
KW - Rayleigh-Benard convection
ER -
TY - JOUR
TI - Inverse compensation for hysteresis in magnetostrictive transducers
AU - Smith, RC
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - This paper addresses the development of inverse compensation techniques for a class of ferromagnetic transducers including magnetostrictive actuators. If unaccommodated, the hysteresis and nonlinear dynamics can produce severe loss of control authority and potential instabilities when the actuators are incorporated in control design. In this work, hysteresis is modeled through the domain wall theory originally proposed by Jiles and Atherton [1]. This model is based on the quantification of the energy required to translate domain walls pinned at inclusions in the material with the magnetization at a given field level specified through the solution of an ordinary differential equation. A complementary differential equation is then employed to compute the inverse which can be used to compensate for hysteresis and nonlinear dynamics in control design. The performance of the inverse compensator and its employment in LQR control design are illustrated through numerical examples.
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00245-4
VL - 33
IS - 1-3
SP - 285-298
SN - 0895-7177
KW - inverse compensation
KW - hysteresis
KW - magnetostrictive materials
ER -
TY - JOUR
TI - International economic models as surveillance for the optimal control of the growth of wealth of nations
AU - Chukwu, E. N.
T2 - Nonlinear Analysis
DA - 2001///
PY - 2001///
DO - 10.1016/s0362-546x(01)00483-7
VL - 47
IS - 6
SP - 3629-3639
ER -
TY - JOUR
TI - Convergence of approximations in feedback control of structures
AU - Banks, HT
AU - Rosario, RCH
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - Convergence of linear quadratic regulator (LQR) problems in structures is discussed. The abstract formulation of the system using a variational framework based on sesquilinear forms is considered. Since convergence theorems require uniform stabilizability of the finite-dimensional approximating system, we present a detailed proof of a fundamental lemma due to Banks and Ito [1] which can be used to easily verify this condition for many applications. Existing results for the well posedness of the infinite-dimensional system and convergence of Galerkin approximations are summarized.
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00229-6
VL - 33
IS - 1-3
SP - 65-78
SN - 0895-7177
KW - feedback control
KW - approximation
KW - LQR
KW - control convergence
ER -
TY - JOUR
TI - An aggregation-based domain decomposition preconditioner for groundwater flow
AU - Jenkins, EW
AU - Kees, CE
AU - Kelley, CT
AU - Miller, CT
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - We consider theoretical and computational issues associated with an aggregation-based domain decomposition preconditioner applied to a Bi-CGSTAB iterative solver used to solve both Laplace's equation and an important nonlinear model from hydrology used to simulate unsaturated flow, Richards' equation. Theoretical results for Laplace's equation provide estimates of the condition number and the rate of convergence for a two-level Schwarz domain decomposition preconditioner. Computational results for Laplace's equation and Richards’ equation show excellent scalability, although no theory is yet available to support the results for the difficult nonlinear problem.
DA - 2001/8/15/
PY - 2001/8/15/
DO - 10.1137/S1064827500372274
VL - 23
IS - 2
SP - 430-441
SN - 1095-7197
KW - domain decomposition
KW - Newton-Krylov-Schwarz methods
KW - Richards' equation
KW - nonlinear equations
KW - aggregation
ER -
TY - JOUR
TI - A remark on jump conditions for the three-dimensional Navier-Stokes equations involving an immersed moving membrane
AU - Lai, MC
AU - Li, ZL
T2 - APPLIED MATHEMATICS LETTERS
AB - Jump conditions for the pressure, the velocity, and their normal derivatives across an immersed moving membrane in an incompressible fluid are derived. The discontinuities are due to the singular forces along the membrane. Instead of using the delta function formulation, those jump conditions can be used to formulate the governing equations in an alternative form. It is also useful for developing more accurate numerical methods such as immersed interface method for the Navier-Stokes equations involving moving interface.
DA - 2001/2//
PY - 2001/2//
DO - 10.1016/S0893-9659(00)00127-0
VL - 14
IS - 2
SP - 149-154
SN - 0893-9659
KW - immersed boundary method
KW - immersed interface method
KW - jump conditions
ER -
TY - JOUR
TI - The origins of geometric programming
AU - Peterson, EL
T2 - ANNALS OF OPERATIONS RESEARCH
DA - 2001///
PY - 2001///
DO - 10.1023/A:1013320729170
VL - 105
SP - 15-19
SN - 0254-5330
ER -
TY - JOUR
TI - Resolution of singularities of null cones
AU - Wang, WQ
T2 - CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES
AB - Abstract We give canonical resolutions of singularities of several cone varieties arising from invariant theory. We establish a connection between our resolutions and resolutions of singularities of closure of conjugacy classes in classical Lie algebras.
DA - 2001/12//
PY - 2001/12//
DO - 10.4153/CMB-2001-049-6
VL - 44
IS - 4
SP - 491-503
SN - 0008-4395
ER -
TY - JOUR
TI - Reduced order feedback synthesis for viscous incompressible flows
AU - Ito, K
AU - Schroeter, JD
T2 - MATHEMATICAL AND COMPUTER MODELLING
AB - We discuss the application of the reduced basis method for the simulation and control of unsteady viscous flows governed by the incompressible Navier-Stokes equations. We describe how to use this method in terms of the construction of a lower-order compensator design. Our approach includes a construction method of the optimal state feedback law for finite-dimensional nonlinear regulator problems. The method is applied to construct a feedback law for the reduced order control model of the Navier-Stokes equations, and then we apply our feedback law to the original control system. Our method is demonstrated on a control problem formulated in a channel flow using a boundary velocity control. We also show how these ideas can be extended to control problems governed by partial differential equations. Numerical results are reported for the open and closed loop controls, and a compensator design is proposed to complete the closed loop dynamics.
DA - 2001///
PY - 2001///
DO - 10.1016/S0895-7177(00)00237-5
VL - 33
IS - 1-3
SP - 173-192
SN - 0895-7177
KW - flow control
KW - compensator design
KW - Navier-Stokes equations
KW - reduced basis method
KW - finite element method
ER -
TY - JOUR
TI - Reaction diffusion systems with time delays in a half-space domain
AU - Pao, CV
T2 - NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
DA - 2001/8//
PY - 2001/8//
DO - 10.1016/S0362-546X(01)00551-X
VL - 47
IS - 7
SP - 4365-4375
SN - 0362-546X
KW - reaction-diffusion equations
KW - time delays
KW - half-space domain
KW - nonlinear boundary conditions
KW - existence-uniqueness
KW - upper and lower solutions
ER -
TY - JOUR
TI - On the computation of steady hopper flows I. Stress determination for Coulomb materials
AU - Gremaud, PA
AU - Matthews, JV
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - The problem of determining the steady state flow of granular materials in silos under the action of gravity is considered. In the case of Mohr–Coulomb materials, the stress equations correspond to a system of hyperbolic conservation laws with source terms and boundary conditions. A higher order discontinuous Galerkin method is proposed and implemented for the numerical resolution of those equations. The efficiency of the approach is illustrated by the computation of the stress fields induced in silos with sharp changes of the wall angle.
DA - 2001/1/1/
PY - 2001/1/1/
DO - 10.1006/jcph.2000.6641
VL - 166
IS - 1
SP - 63-83
SN - 1090-2716
KW - granular flow
KW - plasticity
KW - hyperbolic conservation laws
KW - discontinuous Galerkin
ER -
TY - JOUR
TI - On a powder consolidation problem
AU - Gremaud, P A
AU - Kelley, C T
AU - Royal, T A
AU - Coffey, K A
T2 - SIAM J. Appl. Math.
AB - The problem of the consolidation of an aerated fine powder under gravity is considered. The industrial relevance of the problem is discussed and a mathematical model is introduced. The mathematical structure is that of a coupled system for three unknowns, pressure, stress, and height of the powder in the (axisymmetric) bunker containing it. The system itself consists of a parabolic PDE, an ODE, and an integral equation determining a free boundary corresponding to the height of the powder. Existence and uniqueness of a solution is established. A numerical method based on a formulation of the semidiscretized problem as an index 1 DAE is proposed and implemented. The feasibility of the approach is illustrated by computational results.
DA - 2001///
PY - 2001///
DO - 10.1137/s0036139900368479
VL - 62
IS - 1
SP - 1-20
ER -
TY - JOUR
TI - Numerical analysis and systems theory
AU - Campbell, S. L.
T2 - International Journal of Applied Mathematics and Computer Science
DA - 2001///
PY - 2001///
VL - 11
IS - 5
SP - 1025-1033
ER -
TY - JOUR
TI - Finite dimensional nilpotent Lie algebras with isomorphic maximal subalgebras
AU - Holmes, K
AU - Stitzinger, E
T2 - COMMUNICATIONS IN ALGEBRA
AB - Nilpotent Lie algebras with maximal subalgebras are considered. A bound on the dimension of these algebras as a function of their coclass is obtained. These algebras are then classified up to coclass two. The result is field dependent and several fields are considered.
DA - 2001///
PY - 2001///
DO - 10.1081/AGB-100002404
VL - 29
IS - 6
SP - 2501-2521
SN - 0092-7872
ER -
TY - JOUR
TI - Existence and uniqueness of steady-state solutions for an electrochemistry model
AU - Fang, WF
AU - Ito, K
T2 - PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
AB - We present a simple proof for the existence and uniqueness of steady-state solutions to an electrochemistry model with multiple species.
DA - 2001///
PY - 2001///
DO - 10.1090/S0002-9939-00-05769-5
VL - 129
IS - 4
SP - 1037-1040
SN - 0002-9939
KW - electrochemistry
KW - integro-differential equations
ER -
TY - JOUR
TI - Discrete boundary value problems on infinite intervals
AU - Rodriguez, J
AU - Sweet, D
T2 - JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS
DA - 2001///
PY - 2001///
DO - 10.1080/10236190108808280
VL - 7
IS - 3
SP - 435-443
SN - 1023-6198
KW - boundary value problems
KW - implicit function theorem
ER -
TY - JOUR
TI - Compensator control for chemical vapor deposition film growth using reduced-order design models
AU - Kepler, GM
AU - Tran, HT
AU - Banks, HT
T2 - IEEE TRANSACTIONS ON SEMICONDUCTOR MANUFACTURING
AB - We present a summary of investigations on the use of proper orthogonal decomposition techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapor deposition (HPCVD) reactor. These investigations incorporate multiple species and controls, gas phase reactions, and time dependent tracking signals that are consistent with pulsed vapor reactant inputs. Numerical implementation of the model-based feedback control uses a reduced-order state estimator, based on partial state observations of the fluxes of reactants at the substrate center, which can be achieved with current sensing technology. We demonstrate that the reduced-order state estimator or compensator system is capable of substantial control authority when applied to the full system.
DA - 2001/8//
PY - 2001/8//
DO - 10.1109/66.939820
VL - 14
IS - 3
SP - 231-241
SN - 1558-2345
KW - compensators
KW - CVD
KW - feedback control
KW - reduced order
ER -
TY - JOUR
TI - A discrete model for an ill-posed nonlinear parabolic PDE
AU - Witelski, TP
AU - Schaeffer, DG
AU - Shearer, M
T2 - PHYSICA D-NONLINEAR PHENOMENA
AB - We study a finite-difference discretization of an ill-posed nonlinear parabolic partial differential equation. The PDE is the one-dimensional version of a simplified two-dimensional model for the formation of shear bands via anti-plane shear of a granular medium. For the discretized initial value problem, we derive analytically, and observed numerically, a two-stage evolution leading to a steady-state: (i) an initial growth of grid-scale instabilities, and (ii) coarsening dynamics. Elaborating the second phase, at any fixed time the solution has a piecewise linear profile with a finite number of shear bands. In this coarsening phase, one shear band after another collapses until a steady-state with just one jump discontinuity is achieved. The amplitude of this steady-state shear band is derived analytically, but due to the ill-posedness of the underlying problem, its position exhibits sensitive dependence. Analyzing data from the simulations, we observe that the number of shear bands at time t decays like t−1/3. From this scaling law, we show that the time-scale of the coarsening phase in the evolution of this model for granular media critically depends on the discreteness of the model. Our analysis also has implications to related ill-posed nonlinear PDEs for the one-dimensional Perona–Malik equation in image processing and to models for clustering instabilities in granular materials.
DA - 2001/12/15/
PY - 2001/12/15/
DO - 10.1016/S0167-2789(01)00350-5
VL - 160
IS - 3-4
SP - 189-221
SN - 0167-2789
KW - nonlinear PDE
KW - ill-posed equations
KW - nonlinear diffusion
KW - granular medium
KW - shear bands
ER -
TY - JOUR
TI - A GCM study of climate change induced by deforestation in Africa
AU - Semazzi, FHM
AU - Song, Y
T2 - CLIMATE RESEARCH
AB - CR Climate Research Contact the journal Facebook Twitter RSS Mailing List Subscribe to our mailing list via Mailchimp HomeLatest VolumeAbout the JournalEditorsSpecials CR 17:169-182 (2001) - doi:10.3354/cr017169 A GCM study of climate change induced by deforestation in Africa Fredrick H. M. Semazzi1,2,*, Yi Song1 1Department of Marine, Earth and Atmospheric Sciences and 2Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695, USA *E-mail: fred_semazzi@ncsu.edu ABSTRACT: In this modeling study we investigated the potential climate change which would result from totally clearing the tropical rain forests in Africa. The primary research vehicle in our investigation was the standard version of the National Center for Atmospheric Research (NCAR) CCM3 global climate model (GCM), with a horizontal resolution of triangular spectral truncation T42 (approximately 2.8° x 2.8°). Two separate 10 yr simulations were performed; for each of these the global climatological sea surface temperature field was prescribed. The purpose of the 10 yr simulations was to provide a sufficiently large ensemble whose average minimizes model noise errors. In the control simulation normal vegetation was prescribed. The design of the anomaly experiment was similar to the control run except that the tropical rainforest regions in Africa were replaced by savanna grassland vegetation. The CCM3 GCM successfully simulated the primary features of the seasonal mean climate conditions over Africa. The model results show that replacement of tropical rain forest vegetation with savanna grassland vegetation produces the following climate changes over Africa: (1) Over the deforested region, the model results indicate a significant reduction in area-averaged rainfall throughout the year. The decrease ranges between 2 to 3 mm d-1 during the northern hemispheric summer months, when the region experiences the driest conditions (July to September), and less than 1 mm d-1 during the wettest months (autumn and spring). (2) Over southern Africa deforestation results in substantial rainfall reduction over Mozambique and rainfall increase over Botswana, Zambia, the southern region of the Democratic Republic of the Congo, and parts of South Africa. Changes in the trapped Rossby wave train activity generated by the mid-tropospheric latent heating over the tropical forest region are responsible for the continental-scale teleconnection climate response. (3) Over Eastern and Western Africa the impact of deforestation is primarily characterized by a reduction in rainfall, however the adopted GCM T42 resolution may not have been adequate to resolve the large contrasts in terrain and vegetation types. (4) Over the rest of Africa the response is relatively weak. KEY WORDS: Climate change · Deforestation · Climate of Africa · Climate modelling Full text in pdf format PreviousNextExport citation RSS - Facebook - Tweet - linkedIn Cited by Published in CR Vol. 17, No. 2. Online publication date: August 15, 2001 Print ISSN: 0936-577X; Online ISSN: 1616-1572 Copyright © 2001 Inter-Research.
DA - 2001/8/15/
PY - 2001/8/15/
DO - 10.3354/cr017169
VL - 17
IS - 2
SP - 169-182
SN - 0936-577X
KW - climate change
KW - deforestation
KW - climate of Africa
KW - climate modelling
ER -
TY - JOUR
TI - The temperature-jump problem for a mixture of two gases
AU - Siewert, CE
AU - Valougeorgis, D
T2 - JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER
AB - An analytical variation of the discrete-ordinates method is used to establish a concise and accurate solution to the temperature-jump problem for a binary gas mixture. The analysis is based on Boltzmann equations of the BGK type subject to Maxwell's boundary conditions with arbitrary accommodation coefficients. The results include the complete temperature and density fields for specified mass, density and collision frequency ratios. The numerical results are of benchmark quality, and the required computational time is only a few seconds on a typical PC.
DA - 2001/8/1/
PY - 2001/8/1/
DO - 10.1016/S0022-4073(00)00142-4
VL - 70
IS - 3
SP - 307-319
SN - 1879-1352
KW - rarefied gas dynamics
KW - discrete ordinates
ER -
TY - JOUR
TI - The immersed interface method for the Navier-Stokes equations with singular forces
AU - Li, ZL
AU - Lai, MC
T2 - JOURNAL OF COMPUTATIONAL PHYSICS
AB - Abstract Peskin's Immersed Boundary Method has been widely used for simulating many fluid mechanics and biology problems. One of the essential components of the method is the usage of certain discrete delta functions to deal with singular forces along one or several interfaces in the fluid domain. However, the Immersed Boundary Method is known to be first-order accurate and usually smears out the solutions. In this paper, we propose an immersed interface method for the incompressible Navier–Stokes equations with singular forces along one or several interfaces in the solution domain. The new method is based on a second-order projection method with modifications only at grid points near or on the interface. From the derivation of the new method, we expect fully second-order accuracy for the velocity and nearly second-order accuracy for the pressure in the maximum norm including those grid points near or on the interface. This has been confirmed in our numerical experiments. Furthermore, the computed solutions are sharp across the interface. Nontrivial numerical results are provided and compared with the Immersed Boundary Method. Meanwhile, a new version of the Immersed Boundary Method using the level set representation of the interface is also proposed in this paper.
DA - 2001/8/10/
PY - 2001/8/10/
DO - 10.1006/jcph.2001.6813
VL - 171
IS - 2
SP - 822-842
SN - 1090-2716
KW - Navier-Stokes equations
KW - interface
KW - discontinuous and nonsmooth solution
KW - immersed interface method
KW - immersed boundary method
KW - projection method
KW - level set method
ER -
TY - JOUR
TI - Some additive results on Drazin inverse
AU - Hartwig, RE
AU - Wang, GR
AU - Wei, YM
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - Some additive perturbation results for Drazin inverses are given. In particular, a formula is given for the Drazin inverse of a sum of two matrices, when one of the products of these matrices vanishes. Some special applications of this are also considered.
DA - 2001/1/1/
PY - 2001/1/1/
DO - 10.1016/S0024-3795(00)00257-3
VL - 322
IS - 1-3
SP - 207-217
SN - 1873-1856
KW - Drazin inverse
KW - additive results
KW - perturbation
ER -
TY - JOUR
TI - Robust limits of risk sensitive nonlinear filters
AU - Fleming, WH
AU - McEneaney, WM
T2 - MATHEMATICS OF CONTROL SIGNALS AND SYSTEMS
DA - 2001///
PY - 2001///
DO - 10.1007/PL00009879
VL - 14
IS - 2
SP - 109-142
SN - 0932-4194
KW - nonlinear filtering
KW - risk sensitive
KW - robust filtering
KW - H-alpha filtering
KW - viscosity solutions
KW - Hamilton-Jacobi-Bellman equations
ER -
TY - JOUR
TI - Orbits and invariants associated with a pair of commuting involutions
AU - Helminck, AG
AU - Schwarz, GW
T2 - DUKE MATHEMATICAL JOURNAL
AB - Let σ,θ be commuting involutions of the connected reductive algebraic group G, where σ,θ, and G are defined over a (usually algebraically closed) field k, char k≠2. We have fixed point groups H:≠Gσ and K:≠Gθ and an action (H×K)×G→G, where ((h, k), g)↦hgk−1, h∈H, k∈K, g∈G. Let G//(H×K) denote Spec $\mathscr{O}$(G)H×K (the categorical quotient). Let A be maximal among subtori S of G such that θ(s)=σ(s)=s−1 for all s∈S. There is the associated Weyl group W:=WH×K(A). We show the following. · The inclusion A→G induces an isomorphism A/W$\widetilde{\to}$G//(H×K). In particular, the closed (H×K)-orbits are precisely those which intersect A. · The fibers of G→G//(H×K) are the same as those occurring in certain associated symmetric varieties. In particular, the fibers consist of finitely many orbits. We investigate · the structure of W and its relation to other naturally occurring Weyl groups and to the action of σθ on the A-weight spaces of $\mathfrak {g}$; · the relation of the orbit type stratifications of A/W and G//(H×K). Along the way we simplify some of R. Richardson's proofs for the symmetric case σ=θ, and at the end we quickly recover results of M. Berger, M. Flensted-Jensen, B. Hoogenboom, and T. Matsuki [Ber], [FJ1], [Hoo], [Mat] for the case k=ℝ.
DA - 2001/2/1/
PY - 2001/2/1/
DO - 10.1215/s0012-7094-01-10622-4
VL - 106
IS - 2
SP - 237-279
SN - 0012-7094
ER -
TY - JOUR
TI - Orbifold Hodge numbers of the wreath product orbifolds
AU - Wang, W. Q.
AU - Zhou, J.
T2 - Journal of Geometry and Physics
DA - 2001///
PY - 2001///
VL - 38
IS - 2
SP - 152-169
ER -
TY - JOUR
TI - Modelling and estimating uncertainty in parameter estimation
AU - Banks, HT
AU - Bihari, KL
T2 - INVERSE PROBLEMS
AB - In this paper we discuss questions related to reliability or variability of estimated parameters in deterministic least-squares problems. By viewing the parameters for the inverse problem as realizations for a random variable we are able to use standard results from probability theory to formulate a tractable probabilistic framework to treat this uncertainty. We discuss method stability and approximate problems and are able to show convergence of solutions of the approximate problems to those of the original problem. The efficacy of our approach is demonstrated in numerical examples involving estimation of constant parameters in differential equations.
DA - 2001/2//
PY - 2001/2//
DO - 10.1088/0266-5611/17/1/308
VL - 17
IS - 1
SP - 95-111
SN - 1361-6420
ER -
TY - JOUR
TI - Maximum principle preserving schemes for interface problems with discontinuous coefficients
AU - Li, ZL
AU - Ito, K
T2 - SIAM JOURNAL ON SCIENTIFIC COMPUTING
AB - New finite difference methods using Cartesian grids are developed for elliptic interface problems with variable discontinuous coefficients, singular sources, and nonsmooth or even discontinuous solutions. The new finite difference schemes are constructed to satisfy the sign property of the discrete maximum principle using quadratic optimization techniques. The methods are shown to converge under certain conditions using comparison functions. The coefficient matrix of the resulting linear system of equations is an M-matrix and is coupled with a multigrid solver. Numerical examples are also provided to show the efficiency of the proposed methods.
DA - 2001/6/27/
PY - 2001/6/27/
DO - 10.1137/S1064827500370160
VL - 23
IS - 1
SP - 339-361
SN - 1064-8275
KW - elliptic interface problems
KW - finite difference methods
KW - discontinuous coefficients
KW - singular source term
KW - discrete maximum principle
KW - quadratic optimization
KW - multigrid methods
ER -
TY - JOUR
TI - Lagrangian construction of the (gl(n),gl(m))-duality
AU - Wang, WQ
T2 - COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
AB - We give a geometric realization of the symmetric algebra of the tensor space [Formula: see text] together with the action of the dual pair (gl n , gl m ) in terms of lagrangian cycles in the cotangent bundles of certain varieties. We establish geometrically the equivalence between the (gl n , gl m )-duality and Schur duality. We establish the connection between Springer's construction of (representations of) Weyl groups and Ginzburg's construction of (representations of) Lie algebras of type A.
DA - 2001/5//
PY - 2001/5//
DO - 10.1142/S0219199701000329
VL - 3
IS - 2
SP - 201-214
SN - 0219-1997
ER -
TY - JOUR
TI - Identification of some source densities of the distribution type
AU - Ito, K
AU - Zou, J
T2 - JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
AB - In this paper we investigate the solvability of an ill-posed two-dimensional Fredholm integral equation of the first kind which allows the solutions of distribution type. The problem is first transformed into a well-posed differential–integral equation using output least-squares approach with a regularization of bounded variations. A globally convergent iterative method is proposed and some numerical results are presented. The methodology discussed may be applied for the identification of the boundary shape of the defects of a dielectric material or the interface between different materials.
DA - 2001/7/15/
PY - 2001/7/15/
DO - 10.1016/S0377-0427(00)00332-0
VL - 132
IS - 2
SP - 295-308
SN - 0377-0427
ER -
TY - JOUR
TI - Howe duality for Lie superalgebras
AU - Cheng, SJ
AU - Wang, WQ
T2 - COMPOSITIO MATHEMATICA
AB - We study a dual pair of general linear Lie superalgebras in the sense of R. Howe. We give an explicit multiplicity-free decomposition of a symmetric and skew-symmetric algebra (in the super sense) under the action of the dual pair and present explicit formulas for the highest-weight vectors in each isotypic subspace of the symmetric algebra. We give an explicit multiplicity-free decomposition into irreducible gl(m|n)-modules of the symmetric and skew-symmetric algebras of the symmetric square of the natural representation of gl(m|n). In the former case, we also find explicit formulas for the highest-weight vectors. Our work unifies and generalizes the classical results in symmetric and skew-symmetric models and admits several applications.
DA - 2001///
PY - 2001///
DO - 10.1023/A:1017594504827
VL - 128
IS - 1
SP - 55-94
SN - 0010-437X
KW - Lie superalgebra
KW - Howe duality
KW - highest-weight vectors
ER -
TY - JOUR
TI - Geometric singular perturbation analysis of oxidation heat pulses for two-phase flow in porous media
AU - Schecter, S
AU - Marchesin, D
T2 - BOLETIM DA SOCIEDADE BRASILEIRA DE MATEMATICA
DA - 2001/11//
PY - 2001/11//
DO - 10.1007/bf01233667
VL - 32
IS - 3
SP - 237-270
SN - 0100-3569
KW - combustion
KW - porous medium
KW - multiphase flow
KW - conservation laws
ER -
TY - JOUR
TI - Comparison of perturbation bounds for the stationary distribution of a Markov chain
AU - Cho, GE
AU - Meyer, CD
T2 - LINEAR ALGEBRA AND ITS APPLICATIONS
AB - The purpose of this paper is to review and compare the existing perturbation bounds for the stationary distribution of a finite, irreducible, homogeneous Markov chain.
DA - 2001/9/15/
PY - 2001/9/15/
DO - 10.1016/S0024-3795(01)00320-2
VL - 335
SP - 137-150
SN - 0024-3795
KW - Markov chains
KW - stationary distribution
KW - stochastic matrix
KW - group inversion
KW - sensitivity analysis
KW - perturbation theory
KW - condition numbers
ER -