Hydrodynamic Behavior and Interacting Particle Systems

1. Front Matter

   Pages i-xi

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2. Stochastic Modelling of a Dilute Fluid-Particle Suspension

   • Russel E. Caflisch

   Pages 1-12

3. Experiments on Suspensions of Interacting Particles in Fluids

   • P. M. Chaikin, W. D. Dozier, H. M. Lindsay

   Pages 13-24

4. Stochastic Models of Parallel Systems for Global Optimization

   • D. A. Dawson

   Pages 25-44

5. Remarks on the point interaction approximation

   • R. Figari, G. Papanicolaou, J. Rubinstein

   Pages 45-55

6. Renormalization Group Treatment of the Hydrodynamics of Polymer Chains in the Rigid Body Approximation

   • Karl F. Freed, Shi-Qing Wang, Jack F. Douglas

   Pages 57-74

7. On the Hydrodynamic Limit of a Scalar Ginzburg-Landau Lattice Model: The Resolvent Approach

   • J. Fritz

   Pages 75-97

8. Convergence of the Random Vortex Method

   • Jonathan Goodman

   Pages 99-106

9. Supercritical Branching Random Fields. Asymptotics of a Process Involving the Past

   • Luis G. Gorostiza

   Pages 107-112

10. A Simple Mathematical Model of a Slurry

    • David E. Loper, Paul H. Roberts

    Pages 113-116

11. Limit Points of Empirical Distributions of Vorticies with Small Viscosity

    • Hirofumi Osada

    Pages 117-126

12. Mathematical Study of Spectra in Random Media

    • Shin Ozawa

    Pages 127-136

13. Hydrodynamic Screening in Random Media

    • Jacob Rubinstein

    Pages 137-149

14. Interacting Brownian Particles: A Study of Dyson’s Model

    • Herbert Spohn

    Pages 151-179

15. A Propagation of Chaos Result for Burgers’ Equation

    • A. S. Sznitman

    Pages 181-188

16. Limit Distributions for One-Dimensional Diffusion Processes in Self-Similar Random Environments

    • H. Tanaka

    Pages 189-210

This IMA Volume in Mathematics and its Applications HYDRODYNAMIC BEHAVIOR AND INTERACTING PARTICLE SYSTEMS is in part the proceedings of a workshop which was an integral part of the 1985-86 IMA program on STOCHASTIC DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS. We are grateful to the Scientific Committee: Daniel Stroock (Chairman) Wendell Fleming Theodore Harris Pierre-Louis Lions Steven Orey George Papanicolaou for planning and implementing an exciting and stimulating year-long program. We especially thank the Program Organizer, George Papanicolaou for orga­ nizing a workshop which brought together scientists and mathematicians in a variety of areas for a fruitful exchange of ideas. George R. Sell Hans Weinberger PREFACE A workshop on the hydrodynamic behavior of interacting particle systems was held at the Institute for Mathematics and its Applications at the University of Minnesota during the week of March 17, 1986. Fifteen papers presented at the workshop are collected in this volume. They contain research in several different directions that are currently being pursued. The paper of Chaikin, Dozier and Lindsay is concerned with experimental results on suspensions in regimes where modern mathematical methods could be useful. The paper of Fritz gives an introduction to these methods as does the paper of Spohn. Analytical methods currently used by in the physics and chemistry literature are presented in the paper of Freed, Wang and Douglas. The paper of Caflisch deals with time dependent effects in sedimentation.

• Renormalization group
• applied mathematics
• chaos
• diffusion
• diffusion process
• interacting particle system
• stochastic equation

• Courant Institute for Mathematical Sciences, New York University, New York, USA

  George Papanicolaou

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