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Heterogeneous versus discrete mapping problem.

P G Kevrekidis1, I G Kevrekidis

  • 1Theoretical Division and Center for Nonlinear Studies, MS B258, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA. pgk@cnls.lanl.gov

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 12, 2001
PubMed
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We developed a novel method to map discrete problems, like those from partial differential equations, to heterogeneous systems. This approach reveals comparable dynamics and coherent structures in different scientific models.

Area of Science:

  • Computational physics
  • Mathematical modeling
  • Dynamical systems theory

Background:

  • Partial differential equations (PDEs) are fundamental in describing physical phenomena.
  • Discretization methods are essential for numerically solving PDEs.
  • Understanding the relationship between discrete and continuous systems is crucial.

Purpose of the Study:

  • To introduce a method for mapping spatially discrete problems to heterogeneous systems.
  • To analyze the dynamical features and coherent structures of these mapped systems.
  • To explore the generalizability of the mapping method.

Main Methods:

  • Developing a mapping technique from discrete to heterogeneous systems.
  • Applying the method to a (1+1)-dimensional phi(4) model.

Related Experiment Videos

  • Conducting numerical simulations to validate theoretical predictions.

    • Main Results:

    • Successfully mapped discrete problems to heterogeneous systems with comparable dynamics.
    • Identified and confirmed the presence of coherent structures in the mapped systems.
    • Demonstrated the effectiveness of the method on the phi(4) model.

    Conclusions:

    • The proposed method provides a valuable tool for analyzing discrete systems through heterogeneous models.
    • The findings highlight qualitative analogies between discrete and heterogeneous system dynamics.
    • The method offers potential for broader applications in physics and applied mathematics.