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Related Experiment Videos

Recent results on multiplicative noise.

W Genovese1, M A Muñoz

  • 1INFM, Sezione di Roma and Dipartimento di Fisica, Università di Roma La Sapienza, Piazzale Aldo Moro 2, I-00185 Roma, Italy.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
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Multiplicative noise (MN) equations exhibit distinct coupling phases, similar to the Kardar-Parisi-Zhang (KPZ) equation. Noise-induced ordering transitions in MN equations are representation-dependent and occur at zero spatial coupling.

Area of Science:

  • Statistical Physics
  • Nonlinear Dynamics
  • Computational Physics

Background:

  • Langevin equations with multiplicative noise (MN) are crucial for modeling complex systems.
  • Understanding the phase transitions and critical behavior of MN equations is an active research area.
  • Connections between MN and Kardar-Parisi-Zhang (KPZ) equations suggest shared universal properties.

Purpose of the Study:

  • To investigate the phase structure and critical exponents of MN equations.
  • To explore the role of noise-induced ordering transitions in MN equations.
  • To establish the relationship between MN and KPZ equations through numerical and analytical methods.

Main Methods:

  • Three-dimensional numerical simulations of MN equations.
  • Dimensional and mean-field analysis for computing critical exponents.

Related Experiment Videos

  • Comparison of Stratonovich and Ito representations for noise-induced phenomena.

    • Main Results:

    • MN equations exhibit both weak and strong coupling phases, analogous to the KPZ equation.
    • Critical exponents for MN equations were computed using dimensional and mean-field analyses.
    • Noise-induced ordering transitions were observed exclusively in the Stratonovich representation.

    Conclusions:

    • The study supports a proposed relationship between multiplicative noise (MN) and Kardar-Parisi-Zhang (KPZ) equations.
    • A first-order-like phase transition at zero spatial coupling identifies the MN equation as a minimal model for noise-induced ordering.
    • The representation of noise (Stratonovich vs. Ito) critically influences the occurrence of noise-induced ordering transitions.