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Derivation and Analysis of Nonlinear Evolution Equations for Multiscale Physics

We are addressing the solution and analysis of multiscale systems in an integrated, multidisciplinary way, by pursuing the development of the following, two basic capabilities:

1. Methods for the derivation of new partial differential equations from first principles that accurately capture the effects of small scales when the system is modeled numerically on a coarse scale.

2. Analytical methods for analyzing the behavior of complex multiscale systems as revealed through large-scale computation and validation via comparison with real data.

To focus our efforts in a concrete way towards developing these capabilities, our Los Alamos program is presently organized around four major topical areas: turbulence modeling, nonlinear optical processes, pattern formation in reaction-diffusion systems, and hydrodynamical mixing processes.

One main research objective is to produce effective new ways to solve multiscale problems in nonlinear fluid dynamics, such as turbulent flows and global ocean circulation. This is accomplished by developing new methods for averaging over random, or rapidly varying, phases in nonlinear systems at multiple scales, and using these methods to derive new equations for analyzing the mean behavior of fluctuation processes coupled self-consistently to nonlinear fluid dynamics.

Recent Research Highlights

People

Michael Chertkov chertkov@ cut.this.part. lanl.gov Los Alamos National Laboratory
Aric Hagberg hagberg@ cut.this.part. lanl.gov Los Alamos National Laboratory
Bradley J. Plohr plohr@ cut.this.part. lanl.gov Los Alamos National Laboratory