Effective Behavior of Composite and Nonlinear Media

Abstract

Systems with composite or nonlinear structure are of great importance to current science and technology. Under this grant, we have investigated several such system: nonlinear optical media, fluids with vortex motion, rarified gases and composite elastic or electrostatic materials. Our research goals have been to derive mathematical theories or models for these systems, to develop numerical algorithms and compute solutions for the resulting equations, and to mathematically analyze the equations. For example, for systems with microscopic variation, such as a composite elastic material or a rarified gas, we derived theories that describe the systems on a macroscopic scale. For nonlinear systems with singularities, such as nonlinear optics or vortex dynamics, we find simple descriptions of the development of the singularities and performed numerical solutions with singularities to verify the simpler theories.

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Document Details

Document Type
Technical Report
Publication Date
Jul 09, 1988
Accession Number
ADA217038

Entities

People

  • Russel E. Caflisch

Organizations

  • New York University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boltzmann Equation
  • Brownian Motion
  • Composite Materials
  • Computational Science
  • Diffusion Coefficient
  • Elastic Materials
  • Equations
  • Fluids
  • Gases
  • Materials
  • Nonlinear Optics
  • Nonlinear Systems
  • Optics
  • Phase Transformations

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Structural Dynamics.
  • Wave Propagation and Nonlinear Chaotic Dynamics.