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Solitons in fluctuating hydrodynamics of diffusive processes.

Alexios P Polychronakos1

  • 1Department of Physics, The City College of New York, New York 10031, USA and The Graduate Center, CUNY, New York, New York 10016, USA.

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Large fluctuations in statistical processes generate solitons and nonlinear waves in fluid systems. The Kipnis-Marchioro-Presutti model exhibits complex sound waves, unlike the symmetric exclusion process.

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Area of Science:

  • Statistical Mechanics
  • Fluid Dynamics
  • Nonlinear Physics

Background:

  • One-dimensional statistical processes can exhibit large fluctuations.
  • These fluctuations can lead to emergent phenomena in fluid mechanical systems.
  • Understanding emergent nonlinear behaviors is crucial in statistical physics.

Purpose of the Study:

  • To demonstrate that fluid systems from 1D statistical processes exhibit solitons and nonlinear waves.
  • To derive and analyze these solutions for specific models.
  • To compare the properties of different fluid systems.

Main Methods:

  • Derivation of explicit soliton and nonlinear wave solutions.
  • Analysis of fluid mechanical systems arising from large fluctuations.
  • Examination of the Kipnis-Marchioro-Presutti (KMP) model and the symmetric exclusion process (SEP).

Main Results:

  • Fluid systems from large fluctuations generically exhibit solitons and nonlinear waves.
  • The KMP and SEP fluids are related by a nonlinear transformation but possess distinct properties.
  • The KMP fluid displays a nontrivial sound wave spectrum with birefringence, while the SEP fluid's sound waves are trivial.
  • Sound waves and solitons in the KMP model are linked to instability onset.

Conclusions:

  • Fluid mechanical systems derived from 1D statistical processes inherently support solitons and nonlinear waves.
  • The KMP model presents complex emergent dynamics, including birefringence, due to instabilities.
  • The SEP model offers a simpler contrasting case for nonlinear wave phenomena.