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Ph.D., University of Arizona 1988
Professor Aceves' research focuses on the mathematical modeling of
phenomena in nonlinear optics. By using techniques from perturbation
theory and asymptotics together with numerical simulations, this
research studies the pulse dynamics in nonlinear optical media. Most
recent work includes light localization in optical fiber arrays,
trapping of light in waveguide gratings and ultraviolet light filament
formation in the atmosphere.
Besides working with his current PhD students, other collaborations
include scientists at the Air Force Research Laboratory, the Department
of Physics and Astronomy at the University of New Mexico and with the
Electromagnetism and Photonics group at the Universita di Brescia in
Italy. Recent work has appeared in Physica D, Studies in Applied Mathematics, Physical Review A, and Optics Communications. For
the past five years, he has been an affiliate of the Mathematical
Modeling and Analysis group (T7) of the Theoretical Division at the Los
Alamos National Laboratory.
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Ph.D., Northwestern, 1999
Professor Ajaev's research involves applications of asymptotic and
perturbation as well as numerical methods for partial differential
equations to various problems in fluid mechanics and crystal growth. Of
particular interest are simulations of moving interfaces in systems with
phase transitions by means of finite-difference and boundary-integral
He collaborates with scientists at the University of Aix-Marseille,
France, the Technical University of Darmstadt, Germany, and the Institute of
Thermophysics in Novosibirsk, Russia. His
published work has appeared in Annual Review of Fluid Mechanics,
Journal of Fluid Mechanics, Physics of Fluids, Physical Review E,
Journal of Computational Physics, Numerical Heat Transfer, Proceedings
of the Royal Society A, Journal of Crystal Growth, and Journal of Colloid and Interface Science.
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Ph.D., New York University, 2006
Professor Barreiro's research is in mathematical modeling, analysis
and simulation of neural networks. She is particularly interested in how
network architecture and dynamics combine to produce correlated
activity (or synchrony) in neural "microcircuits", and in the resulting
consequences for computation. Such microcircuits form the building
blocks of biological neural circuits, and thus the operation of the
nervous system. The ultimate goal of this work is to give insight into
the fundamental architecture of how the brain works, and it has the
potential to address models of diseases that manifest as excessive
synchrony, such as Parkinson's disease. Some of the tools she uses for
this work are dynamical systems, probability and stochastic processes,
information theory, perturbation methods and numerical simulations. She
also works on models of neural integrators, which allow the brain to
store evidence and memories, on numerical methods for neural population
dynamics, and on analytical and computational modeling in geophysical
Professor Barreiro collaborates with both mathematicians and
experimental neuroscientists at the University of Washington and other
institutions. Her work has appeared in journals such as Physical Review E, Journal of Computational Neuroscience, andthe Proceedings of the Royal Society of London A.
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Associate Professor and Graduate Advisor
Ph.D., Northwestern, 1993
Professor Carr's research focuses on the dynamics of physical systems
modeled by nonlinear ordinary and partial differential euqations. He
uses local and global bifurcation theory, asymptotic analysis, and
numerical simulation and continuation to study the system's behavior and
parameter sensitivities. Of particular interest is the synchronization
characteristics of coupled oscillators. Areas of application include
laser instabilities, coupled electronic circuits and mathematical
He collaborates with scientists at the U.S. Naval Research Laboratory
and the Free University of Brussels, Belgium. His research has appeared
in Physical Review A, Physical Review E, Physical Letters A, Chaos, Physica D, and SIAM Journal of Applied Mathematics.
Ph.D., Michigan State University, 2008
Professor Geng's research focuses on modeling problems in structural and systems biology using differential equations and integral equations, and solving these problems numerically with fast algorithms and high performance computing. Particularly, Professor Geng is interested in numerically solving interface problems described by PDEs and integral equations. These problems appear when adjacent layers with different physical, chemical and biological properties are present. As far as the numerical algorithms are concerned, Professor Geng is interested in 1) matched interface and boundary (MIB) methods (high order, finite difference mesh-based algorithms used in solving elliptic PDEs with discontinuities and singularities); and 2) boundary integral methods combined with treecode (a fast algorithm for evaluating interactions of N-body problems) to achieve high accuracy and efficiency. Recently Professor Geng has been working on the extension of these numerical algorithms to electrodynamics and fluid mechanics for the structural biology study at the molecular level.
Professor Geng collaborates with mathematicians, computer scientists, and biologists at the Michigan State University, University of Michigan, University of Alabama, Pacific Northwest National Laboratory, and other institutions. His work has appeared in journals such as Journal of Computational Physics, Journal of Computational Chemistry, Computer Physics Communications, and Journal of Chemical Physics.
Ph.D., University of Manchester, 1970
Professor Gladwell works in a variety of numerical analysis and
scientific computation research areas - including ordinary differential
equation initial and boundary value problems, mathematical software, and
parallel computing - with an emphasis on developing tools to assist
scientists and engineers with large-scale computing problems. His
research has involved scientific computation for sintering and grooving
of materials, diffusion-convection equations, waves generated by a
semi-infinite plate, and chromosome synapsis in grasses.
Recently, he has worked on use of symbolic software for aiding the
numerical solution of singularly perturbed boundary value ordinary
differential equations, parallel codes for almost block diagonal
systems, variable step Runge-Kutta-Nystrom algorithms for special
second-order systems, integration of Hamiltonian systems,
parallelization of numerical integration, and wavelet collocation for
boundary value problems. He has been working with faculty members at the
University of Manchester, Emory University and the Colorado School of
Mines, with members of the Numerical Algorithms Group, and with former
SMU graduate students at the Johns Hopkins University, Texas
Instruments, Oakland University, the University of New Hampshire, the
Polish Academy of Sciences, University of Texas at Dallas, Texas Women's
University and Collin County Community College.
Professor Gladwell was a faculty member at the University of
Manchester, UK, before joining SMU in 1987. He has consulted with Texas
Instruments and with NAG, is Editor-in-Chief of the ACM Transactions on
Mathematical Software, and an Associate Editor of the IMA Journal on
Numerical Analysis and of Scalable Computing: Practice and Experience,
and is the editor and author of seven research monographs and special
journal issues. His recent research has appeared in journals such as ACM
Transactions on Mathematical Software, Applied Numerical Methods, SIAM
Review, Parallel Computing, Journal of Computational and Applied
Mathematics, Computational Materials Science, International Journal of
Numerical Methods in Engineering, Numerical Linear Algebra and its
Applications, Philosophical Magazine (Series A), and Computers and
Mathematics with Applications, Journal of Crystal Growth, and SIAM Review.
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Ph.D., Massachusetts Institute of Technology, 1971
Professor Haberman is the author of textbooks on ordinary and partial
differential equations in science and engineering and on mathematical
modeling in mechanical vibrations, population dynamics, and traffic
flow. His research has involved various areas of physical applied
mathematics: Hydrodynamic stability, solitons for nonlinear dispersive
waves, slowly varying bifurcations in nonlinear ordinary differential
equations, and transitions such as caustics and shocks in partial
differential equations. He has investigated the change in action
(adiabatic invariant) resulting from the slow passage of a separatrix
and has extended this work to the slow passage of a separatrix for
bifurcations of Hamiltonian systems. His work usually involves singular
perturbation techniques: the methods of matched asymptotic expansions
(boundary layers) and multiple scales (averaging).
Recently, he has used dynamical systems and singular perturbation
methods to study chaotic collisions of nonlinear solitary wave in
various different problems in fiber optics. He has analyzed the trapping
of light due to interaction of a nonlinear pulse with an optical
defect. He has introduced a universal separatrix map that explains the
fractal structure in solitary wave interactions for dispersive nonlinear
partial differential equations. He has been working with faculty
members at the New Jersey Institute of Technology and the University of
His research has appeared in the last few years in journals such asSIAM
Journals of Applied Mathematics and Applied Dynamical Systems, Physical
Review Letters, Physica D, Chaos, and the Journal of Nonlinear
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Ph.D., California Institute of Technology, 1983
Prof. Hagstrom's research is focused on computational methods for
simulating time-domain wave propagation phenomena. Current projects
- The development and analysis of radiation boundary conditions and fast
propagation algorithms for scattering problems utilizing novel plane
wave representations of the wave field,
- Adaptive, high-order Hermite discretization methods on structured, composite or embedded grids,
- High-order/high-resolution discontinuous Galerkin discretizations on
unstructured grids utilizing polynomial and nonpolynomial bases,
- Efficient time-stepping for equations with stiff components and on adapted grids.
Applications include electromagnetic and acoustic scattering, the
generation of sound by unsteady and turbulent flows, gas-phase
combustion, and the multiscale coupling of kinetic models, such as the
Boltzmann equation, with continuum models such as the
This research has been supported by the National Science Foundation,
the Air Force Office of Scientific Research, the Army Research Office,
and NASA. Recent publications have appeared in the SIAM Journals on Numerical Analysis, Applied Mathematics,and Scientific
Computing, the Journal of Computational Physics, Communications in
Applied Mathematics and Computational Science, the Journal of
Computational Mathematics, and Communications in Partial Differential
Ph.D., University of Colorado at Boulder, 1996
Professor Lee’s research focuses on the mathematical modeling, numerical algorithmic development, and scientific computing of large-scale industrial and laboratory applications. His current research interests include efficient methods for the Boltzmann transport equation (neutron/photon transport), Maxwell equations (fusion), equations of elasticity (structural designs), general coupled systems of elliptic partial differential equations (uncertainty quantification), and large systems of algebraic-differential equations (electric power grid networks). Central to his research is the development of schemes that give optimal computational efficiency on serial and large-scale parallel
computer platforms. Thus, an essential component of his research is computational linear algebra, particularly scalable multigrid and multilevel methods.
His current collaborations include mathematicians and physicists at the Lawrence Livermore, Pacific Northwest, and Argonne National Laboratories. His research has appeared in SIAM J. Scientific Computing, SIAM J. Numerical Analysis, Numerical Linear Algebra with Applications, Mathematics of Computation, and Electronic Transactions of Numerical Analysis. For the past 15 years, he has been affiliated with several Department of Energy national laboratories.
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Associate Professor, Emeritus
Ph.D., Technical University of Denmark, 1983
Professor Melander's current research focuses on fundamental issues
in vortex dynamics and statistical fluid mechanics. His topics include
vortex/boundary interactions in 2-D, morphology of vortex interactions
in 2- and 3-D, identification of underlying mechanisms, topological
description of 3-D viscous flows in terms of global bifurcation analysis
of the vorticity field (i.e., vortex line history), construction and
analysis of shell models of turbulence, statistical behavior of
ensembles of shell model solutions, and the transition to turbulence in
Professor Melander's research is problem-driven and thus employs
tools from classical and applied mathematics, numerical analysis, and
scientific computation. Concepts from dynamical systems play a central
role. His publications have appeared in the Journal of Fluid Mechanics, Physics of Fluids, Physical Review Letters, Fluid Dynamics Research, Physica D, and Physical Review E.
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Ph.D., Rensselaer Polytechnic Institute, 1988
The primary focus of Professor Moore's research has been on
developing adapative finite element methods for solving
reaction-diffusion systems in one, two, and three space dimensions.
Reaction-diffusion systems appear in a variety of applications. These
include models in cardiac electrophysiology such as Fitzhugh-Nagumo,
Ebihara-Johnston and Luo-Rudy I, combustion, catalytic surface
reactions, and pattern formation. Adaptive methods have proved effective
in solving such systems increasing the reliability, robustness and
efficiency of standard methods.
Professor Moore was a faculty member of Tulane University for eleven
years before arriving at SMU. His published work has appeared in SIAM
Journal on Numerical Anaylsis, SIAM Journal of Scientific Computation,
Journal of Computational Physics, BIT, Physica D, Applied Numerical
Mathematics, Mathematical Biosciences and the Journal of Cardiovascual Electrophysiology.
Scott Norris, Ph.D.
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Professor Norris's research focuses on multi-scale continuum descriptions of problems at small scales in materials science, with an emphasis on thin films dominated by interfacial phenomena. This involves a variety of mathematical techniques, including continuum modeling, asymptotic and perturbation methods, linear and nonlinear stability analysis, various kinds of numerical simulation, and the extraction of meaningful statistics from large data sets. Recent specific topics of interest include the coarsening of faceted crystal films, spontaneous nanoscale pattern formation on ion-irradiated semiconductors, and the growth of nanostructured solids by means of phase separation during deposition.
Professor Norris collaborates with scientists at Harvard University, the University of Helsinki (Finland), the University of Glasgow (Scotland), the Helmholtz Center of Dresden-Rossendorf (Germany), the Ecole Polytechnique (France), and the University of Kentucky. His publications have appeared in Nature Communications, Physical Review Letters, Physical Review B and E, Journal of Applied Physics, Journal of Computational Physics, Acta Materialia, Journal of Crystal Growth, and Nuclear Instruments and Methods in Physics Research B.
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Professor and Department Chair
Ph.D., California Institute of Technology, 1983
Professor Reinelt's research involves mathematical modeling of
applied physical problems and the development of solution techniques for
these problems. Past problems he has examined include the motion of
long bubbles in capillary tubes, fluid draining from a tube under the
effect of gravity, and the shapes of bubbles and fingers as a fluid
penetrates into a more viscous fluid.
His current research interests include foam flow, and the stability
and variations of thin film thickness in coating flows. His foam
research involves the development of theories that relate foam structure
and the physical properties of the constituent phases and interfaces to
macroscopic rheology. In the coating flow problem, he is investigating
the instabilities that occur when a thin liquid film is deposited on a
moving roller or cylinder. This problem is of particular interest to the
printing and photographic industries, and other problems have
applications in petroleum and geothermal energy production and
manufacture of coatings and polymeric foams.
He recently has done research at the Laboratoire de Dynamique des
Fluides Complexes at the Universite Louis Pasteur in Strasbourg, France,
and has collaborated with colleagues in applied mathematics and fluid
and thermal science at Sandia National Laboratories.
Some of his publications have appeared in the Journal of Fluid Mechanics, Physics of Fluids, Journal of Colloid and Interface Science, and International Journal of Multiphase Flow.
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Ph.D., Rice University, 2003
Professor Reynolds' research focuses on numerical methods of
relevance to large scale scientific computing applications involving the
nonlinear interaction of multiple physical processes, typically modeled
using systems of partial differential equations (PDE). Such work aims
to allow mathematical insight and innovation to impact the physical,
biological and engineering sciences through the incorporation of
increased realism into mathematical modeling systems, the development of
increasingly robust and accurate numerical methods for solving these
mathematical models, and the invention of computational algorithms to
implement these numerical methods on increasingly large-scale
Specifically, Professor Reynolds investigates three fundamental
applied mathematics issues: accurate modeling of physical systems
involving disparate time and space scales, the development and use of
highly-accurate and efficient time evolution algorithms for stiff
multi-rate problems, and the investigation of discretization and
solution methods that retain constraint-preserving properties of PDE
models. To this end, Professor Reynolds relies on his expertise in large
scale parallel computation as well as a broad range of numerical
analysis techniques, including space-time discretization approaches for
PDE systems and iterative solution approaches for nonlinear and linear
systems of equations.
Professor Reynolds collaborates with scientists at the University of
California San Diego, Columbia University, SUNY Stony Brook, Lawrence
Livermore National Laboratory, Princeton Plasma Physics Laboratory, the
University of Neuchatel (Switzerland), and others. His published work
has appeared in SIAM Journal of Scientific Computing, Journal of
Computational Physics, Computational Methods in Applied Mechanics and
Engineering, Continuum Mechanics and Thermodynamics, Systems and Control
Letters, Future Generation Computer Systems, Lecture Notes in Computer
Science, ACM Transactions on Mathematical Software, Journal of Physics:
Conference Series, Proceedings of SPIE, andProceedings of ENUMATH.
Ph.D., TU Darmstadt, Germany, 1998
Professor Rumpf's research covers topics in applied mathematics and
in theoretical physics with an emphasis on statistical methods and on
nonlinear dynamics. Focus of his scientific work has been the dynamics
of spatially extended systems with applications in solid state physics,
fluid mechanics, nonlinear optics, plasma physics and nanosystems. His
special interest is the spontaneous formation of regular coherent
structures from a turbulent or thermally disordered background.
Professor Rumpf collaborates with scientists from TU Chemnitz
(Germany), Rensselaer Polytechnic Institute and the University of
Arizona. His recent research has appeared in Physical Review Letters, Physical Review E, Europhysics Letters, Annual Reviews of Fluid Mechanics and Physica D, and he has edited a monograph on nonlinear dynamics of nanosystems.
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Ph.D., California Institute of Technology, 1964
Professor Shampine began working in numerical analysis just as it was
emerging as a discipline and later helped start the subdiscipline of
mathematical software. He joined SMU after a distinguished career at
Sandia National Laboratories, where he was supervisor of the Numerical
Mathematics Division. He is the author of several items of mathematical
software used around the world and is a past president of the
Association of Computer Machinery's (ACM's) Special Interest Group on
Numerical Mathematics (SIGNUM). He has held numerous editorial positions
and is an associate editor of the SIAM Journal on Numerical Analysis.
Much of his research has been directed toward more effective
numerical solution of ordinary differential equations (ODEs). He is
developing methods and software appropriate for graphical user
interfaces. This work is being used for computer experiments in courses
on ODEs and for scientific computation in the MATLAB environment.
He is the author of four books: Nonlinear Two-Point Boundary Value
Problems; Numerical Computing: An Introduction; Numerical Solution of
Ordinary Differential Equations: The initial Value Problem; and Numerical Solution of Ordinary Differential Equations. His recent research has appeared in journals such asComputers
and Mathematics with Applications, SIAM Journal of Numerical Analysis,
SIAM Journal of Scientific and Statistical Computation, Journal of
Computational and Applied Mathematics, Applied Numerical Mathematics, and Mathematics of Computation.
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Ph.D., Virginia Tech University, 2005
Professor Stigler's research focuses on the development of a
mathematical framework for the reverse engineering of gene networks,
using computational algebra as a primary source of tools. The main tool
is that of Groebner bases of polynomial ideals. The models used in this
work are time- and state-discrete finite dynamical systems, described by
polynomial functions over a finite field. She and collaborators have
developed an algorithm for reverse engineering gene networks from
experimental time series data, including concentrations of mRNAs,
proteins, and/or metabolite. She has applied this method to an oxidative
stress response network in yeast and developmental networks in C.
elegans and the fruit fly.
She has been actively involved with the DREAM (Dialogue for Reverse
Engineering Assessments and Methods) Initiative and SACNAS (Society for
Advancement of Chicanos and Native Americans in Science). One of her
main collaborations is with the Applied Discrete Mathematics Group at
the Virginia Bioinformatics Institute. Her work has been listed as one
of the top 25 Hottest Articles in Journal of Theoretical Biology.
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Ph.D., Colorado State University, 1995
Professor Tausch's research focuses on the numerical analysis of
integral and partial differential equations. He has developed efficient
numerical algorithms to solve problems that arise in Electromagnetics,
Optics and Fluid Mechanics. He currently uses integral equation methods
to solve high-dimensional parabolic equations that arise, for instance,
in free surface or shape identification problems.
He has collaborated with engineers to simulate the behavior of
integrated circuits, micro-mechanical devices and photonic waveguides.
His software has been used in industry to help the design of
semiconductor lasers with optical gratings.
His work has appeared in Mathematics as well as Engineering publications, such as, SIAM
Journal of Scientific Computing, Mathematics of Computation, Computing,
Journal of Numerical Mathematics, Journal of Computational Physics,
Computational Mechanics, Journal of the Optical Society of America A,
IEEE Transactions on Microwave Theory and Technology, IEEE Transactions
on Computer-Aided Design and Inverse Problems.
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Ph.D., Cornell University, 2002
Professor Xu's research interests center on the development of
computational techniques for problems in fluid mechanics and
aerodynamics, including biological flows with tissues or membranes,
supersonic and hypersonic turbulence with shockwaves, flow control by
passive means, and fluid dynamics of nature's flyers and swimmers. The
present development focuses on the immersed interface method, which
models solids in a fluid with singular forces and solves the fluid flow
subject to the singular forces by incorporating jump conditions into
numerical schemes. The method is currently used to study the wing pitch
reversal and fore-hind wing interaction in dragonfly flight.
Prior to joining the faculty at SMU, Professor Xu worked for GE
Energy on steam turbine aerodynamics. He also worked at Cornell
University and Princeton University as a post-doctoral research
associate. His published work has appeared in Journal of Computational Physics, SIAM Journal on Scientific Computing, Physics of Fluids, and Journal of Fluid Mechanics.
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Ph.D., Rice University, 2002
Professor Zhou's research focuses on numerical linear algebra,
scientific computing, and their broad range of applications; especially
applications in material sciences and electrical engineering. He has
developed algorithms that greatly improve the efficiency in solving
large-scale eigenvalue problems arisen in density functional theory
His current research includes extending the polynomial filtered
subspace methods for generalized eigenvalue problems;
improving/developing more efficient mixing-schemes for self-consistent
field calculations; and extending the subspace techniques that have been
successful for time-independent DFT to time-dependent DFT calculations.
His publications have appeared in Numerical Linear Algebra and Its
Application, Physical Review Letters, Journal of Computational Physics,
System and Control Letters, Journal of Applied Mathematics, and Computer Physics Communications.