CNLS Workshop: Stochastic Evolutionary Equations      

Stochastic evolution equations provide the mathematical framework for a large and increasingly important class of physical phenomena. These include, among other topics, turbulent flow, global climate modeling, flow and transport in random media, dynamics of phase transitions, and the optimal design and performance of accelerators. As a result, a thorough understanding of the physical basis underlying the stochastic approach and the development of efficient and accurate numerical schemes for stochastic partial differential equations is of vital importance to many LANL programs.

In general, stochastic equations arise in situations where there is incomplete knowledge resulting from unresolved scales, random media, and/or a coupling to an external or internal environment. Due to their complex nature (typically nonlinear, broad range of scales, etc.) analytic solutions to these equations are very rare, and in the vast majority of cases, the equations must be approximated and solved numerically. Too often though, a clear understanding of the phenomena at hand is prevented because errors arising from the computational model cannot be disentangled from inadequacies of the underlying physical model.

Since the number of important open questions in this subject is overwhelming, we decided to restrict the scope of this workshop to a subset of issues that have particular relevance to current Laboratory programs. These include spatially heterogeneous material properties and the related issue of higher-order spatial approximations; the fusion of discrete and continuum models (e.g., Monte Carlo methods with diffusion approximations); the introduction of intermittency and the role of large deviations.

The workshop was designed to facilitate discussion, for this reason the number of talks was held to three per day.

O. Amir (Arizona)

G.E. Barr (Sandia) Naive Application of Monte CarloTechniques to Nonlinear Differential Equations

R.N. Bhattacharya (Indiana) A Class of Multiscale Phenomena

G.L. Eyink (Arizona) Variational Estimation for Nonlinear Stochastic Dynamics

A.L. Garcia (San Jose St.) Computational Stochastic Models in Kinetic Theory

M. Ghil (UCLA) Sequential Estimation for Nonlinear Stochastic Equations in the Atmosphere and Oceans, or, What You Always Wanted to Know About Data Assimilation

J.G. Glimm (SUNY) Turbulent Mixing

H. Levine (UCSD) Multiplicative Noise Effects on Front Propagation

G.D. Lythe (LANL) Stochastic PDEs: Kink Dynamics and More

C. Molina-Paris (LANL)

C.M. Newman (Courant) Stochastic Dynamics (of Spin Models) and Low-Temperature Domain Structure

D.P. Sornette (IGPP/UCLA) Multiplicative Noise and Extreme Fluctuations

D. Tartakovsky (LANL)

E.C. Waymire (Oregon St.) Estimation of Multiscaling Exponents

Frank Alexander (CIC-19), Salman Habib (T-8), Len Margolin (XHM), and Larry Winter (CIC-19).

Salman Habib / LANL / habib@lanl.gov / revised September 99