Journal ArticleDOI
Chaotic Localized States near the Onset of Electroconvection.
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TLDR
It is reported on chaotic localized traveling-wave states (pulses) near the onset of electroconvection in a nematic liquid crystal that coexist with the conduction state, are long lived, appear and die at irregular locations and times, have unique small widths, and vary irregularly in length.Abstract:
We report on chaotic localized traveling-wave states (pulses) near the onset of electroconvection in a nematic liquid crystal. They coexist with the conduction state, are long lived, appear and die at irregular locations and times, have unique small widths, and vary irregularly in length. In this system there are only four linearly unstable modes. Thus it should be possible to reproduce the dynamics of the pulses by four coupled complex Ginzburg-Landau equations once their coefficients are derived from the equations of motion (the weak-electrolyte model).read more
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Journal ArticleDOI
Pattern Formation in Nonequilibrium Physics
TL;DR: Our understanding of the physics of pattern formation has led us to speculate about a more general science of complexity, and to pose deep questions about our ability to predict and control natural phenomena.
Book ChapterDOI
Dissipative Solitons in the Complex Ginzburg-Landau and Swift Hohenberg Equations
Nail Akhmediev,Adrian Ankiewicz +1 more
TL;DR: In this paper, the meaning of dissipative solitons and their applications in various scientific fields are explained and placed in a framework for the investigation of phenomena involving stable structures in nonlinear systems far from equilibrium.
Journal ArticleDOI
To snake or not to snake in the planar Swift-Hohenberg equation
TL;DR: The bifurcation structure of stationary localized patterns of the two-dimensional Swift–Hohenberg equation on an infinitely long cylinder and on the plane is investigated and fully localized roll structures are studied, which are often referred to as worms.
Journal ArticleDOI
Patterns, fronts and structures in a Liquid-Crystal-Light-Valve with optical feedback
TL;DR: In this paper, the basic mechanisms of optical pattern formation are reviewed, with particular reference to a system based on a Liquid-Crystal-Light-Valve with optical feedback, and the linear stability analysis for pattern formation is given with the most relevant analytical results, whereas the nonlinear behavior of pattern dynamics are described and discussed with reference to the experimental findings.
Journal ArticleDOI
Localized patterns for the quintic complex Swift—Hohenberg equation
TL;DR: In this paper, a variety of localized patterns arise in a model equation: the quintic Swift-Hohenberg equation with complex coefficients, and various sizes of localized standing wave patterns are possible when the imaginary part of the complex coefficient is small.