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Spontaneous pattern formation in driven nonlinear lattices

Vanossi1, Rasmussen, Bishop

  • 1Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 and Dipartimento di Fisica, Universita di Bologna, Viale Berti Pichat 6/2, I-40127, Bologna, Italy and INFM e Dipartimento di Fisi.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|December 2, 2000
PubMed
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Researchers observed spontaneous spatial pattern formation in nonlinear lattices. These patterns arise from intrinsic localized modes in damped, ac-driven cubic Klein-Gordon systems.

Area of Science:

  • Nonlinear dynamics
  • Condensed matter physics
  • Pattern formation

Background:

  • Nonlinear lattices exhibit complex behaviors under external driving.
  • Intrinsic localized modes (ILMs) are fundamental to energy localization in such systems.
  • Understanding pattern formation mechanisms is crucial for controlling nonlinear phenomena.

Purpose of the Study:

  • To demonstrate and analyze the spontaneous formation of spatial patterns.
  • To investigate the role of modulation instability in pattern genesis.
  • To explore these phenomena in a damped, ac-driven cubic Klein-Gordon lattice.

Main Methods:

  • Numerical simulations of the cubic Klein-Gordon lattice model.
  • Analysis of modulation instability in the system.

Related Experiment Videos

  • Characterization of the emergent spatial patterns.

    • Main Results:

    • Spontaneous formation of spatial patterns was observed.
    • Patterns were identified as arrays of intrinsic localized modes.
    • Modulation instability was confirmed as the driving mechanism for pattern formation.

    Conclusions:

    • The study successfully demonstrates spontaneous pattern formation in nonlinear lattices.
    • Intrinsic localized modes are key components of these observed patterns.
    • Modulation instability provides a theoretical framework for understanding this phenomenon.