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First Law: Particles in Two-dimensional Equilibrium01:18

First Law: Particles in Two-dimensional Equilibrium

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
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Phase Transitions02:31

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Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
11:51

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Published on: February 22, 2018

Phase instability and coarsening in two dimensions.

Chaouqi Misbah1, Paolo Politi

  • 1Laboratoire de Spectrométrie Physique, UMR, 140 Avenue de la Physique, Université Joseph Fourier Grenoble and CNRS, 38402 Saint Martin d'Heres, France. chaouqi.misbah@ujf-grenoble.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2009
PubMed
Summary
This summary is machine-generated.

In nonequilibrium systems, pattern formation dynamics are clarified. Coarsening in two dimensions depends on the phase diffusion coefficient

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Area of Science:

  • Physics
  • Complex Systems
  • Nonlinear Dynamics

Background:

  • Nonequilibrium systems exhibit instabilities and pattern formation.
  • Two primary dynamics are length scale selection and coarsening.
  • Understanding the conditions favoring each dynamic, especially in higher dimensions, is challenging.

Purpose of the Study:

  • To investigate the conditions governing coarsening versus length scale selection in two-dimensional nonequilibrium systems.
  • To elucidate the role of phase diffusion in determining these dynamics.

Main Methods:

  • Utilizing the concept of the phase diffusion equation in two dimensions.
  • Analyzing the dependence of the phase diffusion coefficient on system parameters (lambda).
  • Applying analytical methods to prototypical nonlinear equations.

Main Results:

  • Coarsening dynamics are directly linked to the lambda dependence of the phase diffusion coefficient, D11(lambda).
  • The behavior of D11(lambda) is influenced by lattice symmetry and conservation laws.
  • Analytical examples on nonlinear equations demonstrate these findings.

Conclusions:

  • The phase diffusion equation provides a framework to understand coarsening in 2D systems.
  • Lattice symmetry and conservation laws are critical factors controlling coarsening dynamics.
  • This work offers insights into fundamental pattern formation processes in nonequilibrium physics.