Dr. R. Illner

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Reinhard Illner, Ph.D. (Bonn), Professor.

Research Interests: Kinetic Theories, Nonequilibrium Statistical Mechanics, Neural Networks Theory, Applied Mathematics.

Full CV pdf format

Students

Geoffrey McGregor, M.Sc. (2011), Traffic models.
Ashlin Richardson, M.Sc. (since 2008), Traffic modeling.
Reinel Sospedra, Ph.D. (April 2010), The Cauchy Problem for the 3D relativistic Vlasov-Maxwell system and its Darwin Approximation.
Michele de la Chevrotiere, M.Sc. 2008, On a Jump Markovian Model for a Gene Regulatory Network.
Shahin Ghomeshi, M.Sc. 1998, Existence and Uniqueness of Solutions to the Steady Boltzmann Equation.
Sean Bohun, Ph.D. 1998, Existence, Uniqueness and Asymptotic Behaviour of the Wigner-Poisson System with an External Coulomb Field.
Robert Clifford Bruce Steacy, M.Sc. 1996, Comparison of a Best and a Near-Best Basis Approach to Wavelet Analysis of Electrocardiograms.
David Feldman, M.Sc. 1994, Multi-Dimensional Extensions of Wavelet Analysis.
Roderick Edwards, Ph.D. 1994, Neural Networks and Neural Fields: Discrete and Continuous Space Neural Models.
Patrick Montgomery, M.Sc. 1993, Results Concernig Uniqueness of Solutions to the Steady State Boltzmann Equation.
Daniel Henschell, M.Sc. 1993, Local Existence and Uniqueness Results for Discrete Velocity Models for the Boltzmann Equation.

Books and some (older) selected Publications

R. Illner, C.S. Bohun, S. McCollum, Th. v. Roode, Mathematical Modelling: A Case Studies Approach, AMS Student Mathematical Library vol. 27, 2005. Click here for more details or to buy.
C. Cercignani, R. Illner, and M. Pulvirenti, The Mathematical Theory of Dilute Gases, Springer-Verlag, Monograph, 1994.
C. Cercignani and R. Illner, Global Weak Solutions of the Boltzmann Equation in a Slab with Diffusive Boundary Conditions, Archive Rat. Mech. Anal., 1996.
C. Bose, P. Grzegorczyk, and R. Illner, Asymptotic Behaviour of One-Dimensional Discrete Velocity Models in a Slab, Arch. Rat. Mech. Anal. 127(4), 337-360, 1996.
R. Edwards, R. Illner, G. Leeming, A Class of Self-Generating Neural Networks, preprint, 1995.

Recent Papers (preprints- most have appeared, see CV for references)

R. Illner, Michele de la Chevrotiere (2012). On random Dynamical Systems and their Levels of Description. pdf format
D. Koch, R. Illner, and J. Ma (2012). Edge Removal in Random Contact Networks and the Basic Reproduction Number (draft). pdf format
R. Illner, G. McGregor (2012). On a Functional-Differential Equation Arising from a Traffic-Flow Model. pdf format
D. Godlovitch, R. Illner, and A. Monaghan (2011). Smoluchowski Coagulation Models of Sea Ice Thickness Distribution Dynamics (J. Geophysical Research). pdf format
R. Sospedra Alfonso, M. Agueh, R. Illner (2011). Global Classical Solutions of the Relativistic Vlasov-Darwin System with Small Cauchy Data: The Generalized Variables Approach. pdf format
M. Agueh, R. Illner, A. Richardson (2011). Analysis and Simulation of a Refined Flocking and Swarming Model of Cucker-Smale Type. pdf format
M. Herty, R. Illner, (2009). Analytical and Numerical Investigations of Refined Macroscopic Traffic Flow Models. pdf format
M. Herty, R. Illner (2007). On Stop-and-Go waves in Dense Traffic. pdf format
R. Illner (2007). Modeling with Dynamical Systems and Kinetic Equations. pdf format postscript format
M. Herty, R. Illner, A. Klar, and V. Panferov (2006). Qualitative Properties of Solutions to Systems of Fokker-Planck equations for Multilane Traffic Flow (to appear in Transport Theory and Statistical Physics). pdf format postscript format
M. Junk, R. Illner (2005). A new Derivation of Jeffery's Equation, long preprint version (paper to appear in J. Math. Fluid Mech.) pdf format
R. Gibson, R.Illner (2005). Stop-and-Go Waves in Traffic Flow via Microscopic Simulation, pdf format
R. Illner, H. Lange, and H. Teismann (2005). Limitations on the Control of Schroedinger Equations, to appear in ESAIM pdf format
R. Edwards, R. Gibson, R. Illner, V. Paetkau (2005). Coupled Stochastic Ordinary Differential Equations and Circadian Rhythms, pdf format published version:
V. Paetkau, R. Edwards and R. Illner (2006). A model for generating circadian rhythm by coupling ultradian oscillators, Theoretical Biology and Medical Modelling 2006, electronic format
H. Andreasson, S. Calogero, and R. Illner, On Blowup for Gain-Term-Only classical and relativistic Boltzmann equations (2004). pdf format postscript format
J. Dolbeault and R. Illner, Entropy Methods for Kinetic Models of Traffic Flow (2003). pdf format postscript format
R. Illner, A. Klar and Th. Materne (2003). On Vlasov-Fokker-Planck Type Kinetic Models for Multilane Traffic Flow, pdf format
R. Illner, A. Klar and Th. Materne (2003). Vlasov-Fokker-Planck Models for Multilane Traffic Flow, postscript format dvi format
R. Illner, C. Stoica, A. Klar and R. Wegener, Kinetic Equilibria in Traffic Flow Models, postscript format pdf format
C. Cercignani, R. Illner, and C. Stoica, On Diffusive Equilibria in Generalized Kinetic Theory postscript format pdf format
R. Illner, Stellar Dynamics and Plasma Physics with Corrected Potentials: Vlasov, Manev, Boltzmann, Smoluchowski postscript format pdf format
C. Cercignani, R. Illner, Discrete Velocity Models with General Boundary Conditions in a Slab, postscript format pdf format
R. Illner, Marvin Shinbrot: 1928-1987 pdf format

Research

A Class of Self-Generating Neural Networks by R. Edwards, R. Illner, and G. Leeming

721-7456