Coming volcanic eruptions will seem random and totally out of the blue to mortal observers despite literally aeons of warning through regular seismic motions of the erath´s plates - but how to relate the explosive violence, the rain of molten debris shooting through thousands of feet per second to the inches per century tectonic creep which predede and caused it? The middle terms are missing and only primitive augury fills the gap. "Lempieres Dictionary" by Lawrence Norfolk

# Singular Perturbation on the Web

The following list of links contains links to homepages of people and groups interested in the development and/or in the application of singular perturbation methods. The list is based on search results of the search engine Alta Vista in July 97. The description of the research interests are all copied from the homepage or the site where the homepage can be found.

This list is under development. If you know of any relevant links which are not on the list or find outdated links, please let me know. To give the list some structure the links are sorted by the following categories.

Please do not take the categories to seriously.
 Tip: If you are looking for specific information use the Find-function of your browser. In Netscape Navigator this function can be found in the Edit-Menue.

# Singular perturbation theory

Applied Dynamics Group, Division of Applied Mathematics, Brown University.
 Christopher Jones: Hompage including publication list. Research Interests: ...dynamics of optical systems, resonance phenomena in celestial mechanics and pattern formation. [...] dynamical systems methods in the study of nonlinear wave motion. He has developed techniques for determining the stability of traveling and standing waves with applications in nerve impulse and optical beam propagation. [...] stable (multiple) pulse propagation in optical fibers with phase-sensitive amplifiers. [...] transport and mixing in mesoscale ocean structures. [...] geometric methods, particularly invariant manifolds in phase space [..and] singularly perturbed systems. Jonathan E. Rubin: Homepage including publication list. Research Interests: Geometric singular perturbation theory Stability of solutions to parabolic systems of partial differential equations Pattern formation and bifurcation mechanisms in systems of pde Applications of dynamical systems to nonlinear fiber optics, neural oscillators, cellular processes, and particle flows in fluids. Applied Dynamics Group Publications: Includes full text preprints.

Center of Applied Mathematics and Statistics, Department of Mathematics at New Jersey Institute of Technology
 Amitabha Bose: email-address. Research Interests: dynamical systems, mathematical biology, stability of travelling waves, geometric singular perturbation theory.

The Dynamical Systems Group At Boston University .
 Tasso Kaper: Homepage including publication list. Research Interests: Dynamical systems and ordinary differential equations, singular perturbation theory, applied mathematics, resonances in Hamiltonian systems, applications of dynamical systems to fluid mixing, oceanography, bubble dynamics, and problems from mechanical engineering. Nancy Kopell: Homepage under construction. Research Interests: Mathematical modeling in neurophysiology, oscillating systems, geometric analysis of dynamical systems with several time scales.

Optique Non-Linéaire Théoretique, Université Libre de Bruxelles

• Dynamical Systems Group, Limburgs Universitair Centrum, Diepenbeek, Belgium
• Freddy Dumortier: Contact information. Research Inrterests: bifurcations of families of (mainly planar) vector fields, limit periodic sets and Hilbert's 16th problem, singularly perturbed problems...
• Bert Smits: Homepage including publication list. Research interrests: transit time analysis in boundary value problems for ODE's and study of cyclicity of singularly perturbed planar quadratic systems

• Department of Mathematics,North Carolina State University
• Stephen Schecter: Hompage including publication list and preprints. Research interests:Shock Waves and Riemann Problems for Systems of Conservation Laws,Homoclinic and Heteroclinic Bifurcation, Averaging, Singular Perturbations, Polynomial Vector Fields, Mathematical Economics

• Laboratoire de Mathématiques. Université de Haute Alsace, Mulhouse, France
• Tewfik Sari: Homepage including preprints. Research interests: Actuellement je m'intéresse aux aspects asymptotiques et géométriques dans la théorie des équations différentielles et des systèmes dynamiques, et à leurs applications, principalement en biologie, ainsi qu'aux fondements des mathématiques (Analyse Non Standard), et à la géométrie différentielle.

• Departement de mathematiques, Universite de la Rochelle, France.

• Departement de mathematiques, Université de Nice-Sophia Antipolis , Nice, Fance.
• Francine and Marc Diener: email-address.

• Department of mathematics, Universiteit Utrecht.

• Centro Studi di Teoria dei Sistemi, Politecnico di Milano, Italy

• Department of Mathematics, Wageningen Agricultural University.
• Johan Grasman. Homepage.

• Inst. of Applied Mathematics, Comenius University, Bratislava.
• Pavol Brunovsky: email-address. Research interests: evelopment of a method for the study of bifurcations of singularly perturbed boundary value problems.
• Publications

• Weierstrass Institute for Applied Analysis and Stochastics, Berlin, Germany
• Dynamical Systems and Control Theory Group: Homepage. Research: Our research is mainly concerned with the behavior of nonlinear dynamical systems including aspects from control theory. We develop general approaches for a qualitative analysis and the control of the longtime behavior of dynamical systems by exploiting special structures as symmetries and small perturbations at the highest derivatives. Furthermore, we construct algorithms for the numerical analysis of control systems, of homoclinic orbits and their bifurcations, and for large scale systems. The methods are applied to simulations and control of processes in chemical engineering, optoelectronics/nonlinear optics and problems in geophysics.
• Klaus Schneider: Homepage.
• Björn Sandstede: Homepage.
• Workshop on Singularly Perturbed Systems and Applications

• The Center for Applied Mathematics Cornell University
• John Guckenheimer: Homepage including publication list and preprints. Research interests: ...Much of my theoretical work has involved study of the iterations of a single, real-valued function. Though at first glance these models seem too simple to reflect the dynamics observed in the real world, detailed analysis of their properties has revealed many features subsequently observed in diverse experimental realms. I have also investigated the influence of symmetry on generic features of dynamical systems. In addition to extending the theory, I am interested in its application to many fields of science and engineering. I have worked with applications in biology, chemistry, engineering, and physics. My current work focuses on applications to the neurosciences and to problems of control. ..
• Towards a Global Theory of singularly perturbed systems manuscript by John Guckenheimer.
• Alexander I. Khibnik: Contact Information

• DFG-Schwerpunktprogramm Dynamik.
 preprints im DFG-Schwerpunktprogramm Dynamik: preprints by M. Stiefenhofer

Department of Mathematical Sciences, Rensselaer Polytechnic Institute.
 Gregor Kovacic: Homepage including publication list and preprints. Research Interests: Theory of nonlinear dynamical systems for ordinary and partial differential equations, and its applications to problems in physics and engineering; in particular, in laser and nonlinear fiber optics, classical mechanics, and fluid mechanics. Laura K. Gross: Homepage including publication list. Research Interests:nonlinear dynamics, partial differential equations, ordinary differential equations, numerical analysis, applications to optics, and applications to combustion.

Institute for Mathematics and its Applications. University of Minnesota.
 IMA Workshop: Multiple-Time-Scales Dynamical Systems - October 27 - 31, 1997. program description, abstracts of talks.

Department of Mathematics, University of Athens Panepistimioupolis.
 Nicholas Alikakos : Homepage including list of publications. Research Interests:Differential Equations, Dynamical Systems, Applied Mathematics, Non-Linear Analysis.

Department of Applied Mathematics, University of Washington.
 Jirair Kevorkian: Homepage including publication list. Research interests: ...slowly-varying oscillatory nonlinear systems. The mathematical models for a wide variety of problems--including free-electron lasers, biological cells, wave-guides, planetary orbits, etc.--are in the form of oscillatory systems of nonlinear differential equations with slowly varying parameters. The aim of this research is to calculate analytical results that accurately describe the often anomalous resonant behavior as well as the long time evolution of the system. This work is primarily motivated by the applications to be studied, and involves the extension of existing techniques in singular perturbations and the development of new ones. Robert E. O'Malley, Jr.: Homepage including publication list. Research Interests: ....the relationship between singular perturbation theory and various regularization methods for differential-algebraic systems, geometric approaches to understanding the limiting solutions to singularly perturbed boundary value problems, the motion of shock layers and other interfaces, the interplay between asymptotic and numerical methods, and tough problems of asymptotic matching......

Department of Mathematics, University of Arizona
 Robert S. Maier: Homepage including Publication list. Research Interests: Applied probability, Singular perturbation theory and related asymptotic methods, Theoretical computer science .

Department of Mathematics, Cleveland State University.
 Sally Shao : Homepage including list of publications. Research interests: Differential Equations, Asymptotic Analysis, Singular Perturbation Theory and Applications, Asymptotic-Numerical Methods for ODEs and PDEs, Mathematical Fluid Dynamics, Supersionic Flow with Shock Structure, Applied Analysis.

Department of Mathematics and Statistics, Utah State University.
 Xiaofeng Ren : Homepage including publication list and preprints, Research interests: Spike layer solutions of nonlinear elliptic equations, Transition layer solutions of nonlinear elliptic equations, Nonlocal models for phase transformation problems, Higher order local models approximating nonlocal model.

Department of Mathematics and Computer, Science State University of New York at New Paltz
 Chirakkal V. Easwaran: Homepage including publication list. Research interests: Asymptotics of partial differential equations, Non-Newtonian fluid mechanics, petroleum engineering.

Department of Mathematics ,University of Oklahoma.
 Walter Kelley, Email-address, Research Interests: Nonlinear Differential Equations, Singular Perturbation Problems.

Institute of Applied Mathematics, University of British Columbia.
 Michèle Susanne Titcombe: Homepage including preprints. Research intersts: ...applying asymptotic analysis, perturbation methods and a dash of numerics to solving certain two-dimensional singular perturbation problems. Applied Analysis, (Perturbation methods, asymptotic analysis) Fluid Dynamics, Numerical Analysis. Michael Jeffrey Ward: Hompage including preprints. Research Interests: Applied Analysis, Singular Perturbations, Mathematical Modeling and Scientific Computation.

Department of Ordinary Differential Equations: Steklov Mathematical Institute of the Russian Academy of Science.

Departement of Mathematics, Fac. Sci, Saitama University.
 Shigeaki Koike: Homepage including publication list. Research Interests: viscosity solution theory and its applications, Semicontinuous solutions, Differential games with state constraints, Degenerate or singular coefficients, Boundary value problems....

## Numerical aspects of singular perturbations

Martin Stynes: Hompage including publication list and preprints. Research Interests: ...design and analysis of numerical methods for singularly perturbed differential equations. This includes convection-diffusion problems, linearised Navier-Stokes equations...Location: Numerical Analysis, Department of Mathematics, University College, Cork, Ireland.

Jerry F. Magnan: Homepage. Research Intereststs: Bifurcation, singular perturbation, Navier-Stokes and reaction-diffusion equations; thermal, double-diffusive, and rotating Benard convection; gaseous discharges and nonlinear stability in lasers and gaseous discharge plasmas; dynamical systems and chaos; symbolic computation methods; numerical analysis and simulation; numerical solution of elliptic and parabolic equations; numerical linear algebra; vector and parallel algorithms for SIMD and MIMD computers; cellular automata and neural network processing; numerical optimization; inverse problems. Location:Department of Mathematics, Florida State University.

Pieter de Groen : Homepage including publication list. Research interests: Numerical Analysis, Differential equations & Singular Perturbations. Location: Department of Mathematics, Vrije Universiteit Brussel .

Paul A. Farrell: Homepage including publication list and preprints. Research Interests: parallel numerical computation and algorithms, application of numerical methods to singularly perturbed differential equations, semi-conductor devices, Navier-Stokes equations, and liquid crystal problems, scientific visualization, data communications and networking, automatic code generation for parallel architectures, application of expert systems in numerical computing, and mathematical text processing Location: Department of Mathematics &Computer Science,Kent State University.

## Singular perturbations in chemical kinetics and combustion

Morten Brøns : Homepage inluding publication list. Research Interests: Dynamical systems applied to fluid mechanics: Topology of streamlines, vortex dynamics, lumped-parameter models of turbomachinery, reduction methods for partial differential equations. Non-linear dynamics in biology and chemistry: Bifurcations in autocatalytic systems, glycolytic oscillations, pattern formation in reaction-diffusion systems. Singular perturbations of ODE's, canard phenomenae. Industrial Mathematics. Location: Department of Mathematics, Technical University of Denmark.

Combustion Group: at the Institute of Chemical Engineering and High Temperature Chemical Processes, Greece. Research: Combustion research at ICE/HT is a very active area that emphasizes on calculation methods for laminar and turbulent flames and heat transfer in industrial furnaces. The Combustion Group is a world leader in the novel method of Computational Singular Pertrubation (CSP), which is a mathematical method to systematically and automatically reduce large mechanisms of elementary reactions describing the combustion of hydrocarbon fuels.....

Johannes Kaiser: Homepage including masters thesis (german). Research Interests: Numerical Treatment of Chemical Rate Networks for the Modelling of Oxygenrich Stellar Envelopes , computational singular perturbation. Location: Institut für Astronomie und Astrophysik Technische Universität Berlin.

Gaetano Continillo: Homepage of the Theoretical and Computational research group including Interenet-posters. Research Interests: e.g: Bifurcation Analysis and Dinamical Simulation of Gasless Combustion. Location: Laboratory of Modelling and Simulation of the Dynamics of Reactive Systems, Istituto di Ricerche sulla Combustione.

George Gogos: Homepage including publication list. Research interests: Thermal/fluid sciences; fundamental processes associated with vaporizing/combusting sprays with applications in liquid-fueled rocket engines, gas turbines, diesel engines and industrial furnaces; jet vapor deposition; tribology heat transfer; bioheat transfer and rotational molding. Location: Department of Mechanical Engineering, University of Nebraska - Lincoln.

## Singular perturbations in mathematical biology

David Terman: Homepage including recent publiction list and preprints. Current Research Interests: oscillatory properties of networks of neurons,[...}, neuronal models for oscillations in the hippocampus and models for spindling and delta sleep rhythms, [...] neural network model for image segmentation, [...] developing techniques for wave propagation in reaction diffusion systems, [..] traveling waves in [..] models for nerve impulses, laminar flames, reactions on the surfaces of catalysts, and wave propagation in various neuronal systems.

Frank C. Hoppensteadt: Hompage including publication list. Research Interests: perturbations and dynamical systems, population biology, brain science. Location: Center for System Science and Engineering Research, Arizona State University.

Jun-cheng Wei: Homepage including publication list. Research Interests: Nonlinear Partial Differential Equations/Applied Analysis Mathematical Biology/Singular Perturbation Problems. Location: Department of Mathematics, Chinese University of Hong Kong.

Wenzhang Huang: Homepage including publication list, Research interests: differential equations (including ordinary, partial, and functional differential equations),dynamical systems, bifurcation, singular perturbation, population dynamics, mathematical biology. Location: Department of Mathematical Sciences, University of Alabama in Huntsville.

Amitabha Bose: email-address. Research Interests: dynamical systems, mathematical biology, stability of travelling waves, geometric singular perturbation theory. Location: Center of Applied Mathematics and Statistics, Department of Mathematics at New Jersey Institute of Technology .

Shagi-Di Shih: Homepage including publication list. Research Interests: Singular perturbation problems, Partial differential equations, and Asymptotic-induced numerical methods,Periodic solution of Lotka-Volterra system,Singular integral equations of Volterra type, Slowly moving shock wave. Location: Department of Mathematics, University of Wyoming.

Time and Space Scales in Ecological Systems: P. Auger, Project at Biometrie-Genetique et Biologie des Populations, Universite Claude Bernard-Lyon 1.

Gerda de Vries: Homepage including publication list with abstracts. Research Interests:modelling electrical activity, calcium handling, and stimulus-secretion coupling in insulin-secreting pancreatic $\beta$-cells. Location: Mathematical Research Branch (MRB) of the National Institute of Diabetes, Digestive and Kidney Diseases (NIDDK) of the National Institutes of Health (NIH).

Vadim Biktashev : Homepage including publication list and preprints. Research Interests: e.g.movement of excitation wave breaks. Location: Computational Biology Group, University of Leeds.

Betty(Biyue) Liu: Homepage including publication list. Research Interests: Mathematical modeling of blood flow in collapsible arteries, Computational fluid dynamics, Numerical solutions of nonlinear compressible Navier Stokes equations. Location: Department of Mathematics, University of Rhode Island.

Mark Pernarowski: Homepage including publication list and pictures. Research Interests: Applied Mathematics, Mathematical Biology, Asymptotics, Dynamical Systems, Scientific Computing . Location: Department of Mathematical Sciences, Montana State University.

## Singular perturbations in fluid dynamics

John Hunter: Hompage including publication list, Research Interests: Nonlinear partial differential equations, wave propagation, singular perturbation methods, fluid mechanics, Location: Institute of Theoretical Dynamics, University of California.

Sunday Chikwendu: Homepage, Research Interests: Partial Differential Equations, Fluid Dynamics, Singular Perturbation Methods, Location: Department of Mathematics and Computer Science , State University of New York New Paltz

David Halpern: Hompage including publication list with abstracts, Research interests: fluid mechanics, Location: Department of Mathematics, University of Alabama.

Tao Tang: Homepage including publication list and students thesis. Research interests: Hyperbolic conservation laws; Computational Fluid Dynamics, Numerical solutions for Differential and Integral Equations. Location: Applied Mathematics , Department of Mathematics and Statistics , Simon Fraser University , Burnaby, Vancouver .

Richard Bodonyi: Homepage including publication list. Research Interests: Hydrodynamics Stability Theory, Three-Dimensional Separated Flows, Singular Perturbation Methods, Computational Methods. Location: Department of Aerospace Engineering, Ohio State University.

Michael R. Foster: Homepage including publication list. Research Interests: Geophysical Fluid Dynamics, Vortex Stability, Singular Perturbation Methods, Crystal Growth. Location: Department of Aerospace Engineering, Ohio State University.

Morten Brøns : Homepage inluding publication list. Research Interests: Dynamical systems applied to fluid mechanics: Topology of streamlines, vortex dynamics, lumped-parameter models of turbomachinery, reduction methods for partial differential equations. Non-linear dynamics in biology and chemistry: Bifurcations in autocatalytic systems, glycolytic oscillations, pattern formation in reaction-diffusion systems. Singular perturbations of ODE's, canard phenomenae. Industrial Mathematics. Location: Department of Mathematics, Technical University of Denmark.

Betty(Biyue) Liu: Homepage including publication list. Research Interests: Mathematical modeling of blood flow in collapsible arteries, Computational fluid dynamics, Numerical solutions of nonlinear compressible Navier Stokes equations. Location: Department of Mathematics, University of Rhode Island.

Tony Watts: Homepage including list of publications. Research Interests: Fluid dynamics, singular perturbation methods, and applied mathematics generally. Operations research. Numerical solution of differential equations . Location: Department of Mathematics, University of Queensland.

Xuesong WU: email-address. Research interest: Theoretical fluid mechanics and applied mathematics including: hydrodynamic instability and transition, boundary layer theory, flow separation, aeroacoustics, nonlinear waves, nonlinear dynamics, coherent structures in turbulent flows and turbulence modelling, and also singular perturbation methods, numerical methods, analytical continuation technique, nonlinear differential equations. Location: Department of Mathematics, Imperial College, Queen's Gate.

Section of Engineering Mechanics: of Department of Applied Mathematics and Physics, Kyoto University. Research interests: .....2. Nonlinear Waves in Fluids Some of the behavior of water waves or internal waves ( waves in density-stratified fluid ) cannot be explained by the linear theory. This behavior has been examined using a variety of theories on nonlinear waves. The most famous one among them is the theory of solitons, solitary waves which do not lose their identity through their collision with each other. In our Section, generation of nonlinear waves due to the external forcing such as the oscillation of the container or the movement of a submerged object, pattern formation in the generated waves, resonant interaction among waves, and three-dimensional nonlinear waves are studied, using the soliton theory, the theory of nonlinear dynamical systems, and singular perturbation theory. ......

## Singular perturbations in condensed matter physics

R.C. Desai : Homepage including publication list. Research Interests: Statistical mechanics, non-linear field theories, instabilities in hydrodynamics and elasticity theory, generalized Boltzmann equation. Non-linear stochastic partial differential equations, infinite order singular perturbation theory, coupled map lattice models, bifurcations and chaos, cellular automation models. Location: Condensed Matter Physics, Department of Physics, University of Toronto.

Oliver Schönborn: Homepage including publication list with abstracts. Research Interests: Phase-ordering dynamics on curved surfaces. Location: Department of Physics, University of Toronto.

R. V. Craster: Homepage including publication list with abstracts, Research Interests: Fracture mechanics, Linear and nonlinear free boundary problems. Location: Department of Theoretical Mechanics,at the University of Nottingham.

Martin Grant : Homepage including publication list. ...problems at the boundary between condensed-matter physics and materials science, such as crystal growth, epitaxy, reaction fronts, spinodal decomposition, and nucleation. ...Location: Physics Department, McGill University.

Anil K. Bajaj: Homepage. Research Interests: Nonlinear behavior of structural systems, Linear stability and dynamics of systems and structures, Systems with low and high frequency modes, applications of singular perturbation techniques. Location: School of Mechanical Engineering, Purdue University.

Chin­Tsau HSU : Homepage including publication list. Research interests: Heat and mass transfer in porous media; sediment transport, microelectronic cooling, air­sea interaction, remote sensing and coastal engineering. Location: Department of Mechanical Engineering, Hong Kong University of Science and Technology.

## Singular perturbations in control theory

Simultaneous Force-Position Control for Grasping Using Flexible Link Manipulators : Conference paper by Sudipto Sur and Richard M. Murray , Division of Engineering and Applied Science, California Intitute of Technology.

D. Subbaram Naidu: Homepage including publication list. Research Interests: Electrical Engineering,Control Systems Engineering,Power Systems Engineering, Guidance and Control of Aerospace Systems, Aeroassisted Orbital Transfer, Mars Mission: Orbital Transfer, Intelligent Control Systems, Geometric Control Theory, Linear System Theory, Optimal Control Theory and Applications, Large Scale Systems, Singular Perturbations and Time Scales (SPaTS), SPaTS in Control Theory and Applications, Robust Control Systems, Modern Control Strategies for Nuclear Reactors. Location: Measurement and Control Engineering Research Center, Idaho State University.

Joe H. Chow: Homepage including publication list. Research Interests: Large-scale modeling, multivariable control systems., Intelligent Control, Robotics and Automation Engineering Education and Interactive Learning. Location: Electrical & Computer Systems Engineering, Rensselaer Polytechnic Institute.

Giovanni Muscato : Homepage including publication list. Research Interests: Model Reduction, Robust Control, Fuzzy Logic and Neural Networks in Control Applications, Robotics. Location: System and Control Group, University of Catania.

Zoran Gajic: Homepage including publication list and preprints. Research Interests: Singular perturbation methods in control system analysis. Linear stochastic estimation and control. Numerical methods and computer aided control system design. Deterministic and stochastic differential games. Optimal output feedback control problem. Bilinear systems - stabilization and optimization. Algebraic Riccati equation. Decentralized control. Location: Department of Electrical and Computer Engineering, Rutgers, The State University of New Jersey.

Douglas B. Price: Homepage including publication list. Research Interests: e.g. Singular Perturbations and Time Scales (SPaTS) in Digital Flight Control Systems. Location: Guidance & Control Branch, NASA Lengley Research Center.

S. Vittal Rao: Homepage including publication list. Research Interests: Control of Adaptive Structures, Integrated Control of Aircraft-Propulsion Systems, Stabilization and Control of Space Structures, Robust Control of Smart Structures, Reduced Order Modeling Techniques, H° Optimal Control. Location: Department of Electrical Engineering, University of Missouri-Rolla .

Control and Power Systems: 1993/ Research Report of Department of Electrical and Electronic Engineering. University of Melbourne .

Flight Dynamics and Control Lab : page describing current research projecte, includes references. Location: University of California, Irvine .

Mikhail Skliar: Homepage including publications. Research interests: Process Control; Optimal, H-infinity and Robust Control, State and Parameter Identification; Monitoring, Fault Detection and Diagnosis; Kalman Filtering; Distributed Parameter Systems; Singularly Perturbed Systems; Noninvertible and Singular Systems; Stochastic Systems; Mathematical Modeling and Numerical Methods; System Analysis and System Engineering; Optimal Sensors and Actuators Location; Environmental Process Engineering and Pollution Prevention; Neural Networks. Location: University of Colorado at Boulder.

Neng Eva Wu: Homepage including publication list. Research interests: Model reduction and robust control of distributed parameter systems Integrated control/diagnostics in fault tolerant control systems Analytical redundancy management for reconfigurable control systems Emitter location technology Decentralized filtering Sampled data control systems Fuzzy set theoretic based reconfigurable control Control of singularly perturbed systems Seismic signal processing. Location: Department of Electrical Engineering State University of New York at Binghamton