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Dissipative system
About: Dissipative system is a research topic. Over the lifetime, 21838 publications have been published within this topic receiving 440255 citations.
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01 Dec 2010
TL;DR: In this article, a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field is presented. But the focus is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion and the dynamical and statistical properties of the dynamics when it is chaotic.
Abstract: This book treats nonlinear dynamics in both Hamiltonian and dissipative systems. The emphasis is on the mechanics for generating chaotic motion, methods of calculating the transitions from regular to chaotic motion, and the dynamical and statistical properties of the dynamics when it is chaotic. The book is intended as a self consistent treatment of the subject at the graduate level and as a reference for scientists already working in the field. It emphasizes both methods of calculation and results. It is accessible to physicists and engineers without training in modern mathematics. The new edition brings the subject matter in a rapidly expanding field up to date, and has greatly expanded the treatment of dissipative dynamics to include most important subjects. It can be used as a graduate text for a two semester course covering both Hamiltonian and dissipative dynamics.
996 citations
TL;DR: In this article, the authors extended the theory of acoustic propagation in porous media to include anisotropy, viscoelasticity, and solid dissipation, and a more refined analysis of the relative motion of the fluid in the pores is also developed by introducing the concept of viscodynamic operational tensor.
Abstract: The theory of acoustic propagation in porous media is extended to include anisotropy,viscoelasticity, and solid dissipation. A more refined analysis of the relative motion of the fluid in the pores is also developed by introducing the concept of viscodynamic operational tensor. The nature of this operator is analyzed by applying variational and Lagrangian methods. Viscoelasticity and solid dissipation are introduced by applying the correspondence principle as derived from thermodynamics in earlier work by the author. Various dissipative models are discussed and the corresponding operators and relaxation spectra are derived. The physical chemistry of the multiphase porous medium including surface effects lies within the scope of the thermodynamic theory. The nature of thermoelastic dissipation and electrokinetic effects in relation to the thermodynamic theory is also brought out.
978 citations
TL;DR: The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra as discussed by the authors, which has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc.
Abstract: The concept of parity-time symmetric systems is rooted in non-Hermitian quantum mechanics where complex potentials obeying this symmetry could exhibit real spectra. The concept has applications in many fields of physics, e.g., in optics, metamaterials, acoustics, Bose-Einstein condensation, electronic circuitry, etc. The inclusion of nonlinearity has led to a number of new phenomena for which no counterparts exist in traditional dissipative systems. Several examples of nonlinear parity-time symmetric systems in different physical disciplines are presented and their implications discussed.
938 citations
TL;DR: A linear hyperbolic system is constructed with a stiff lower order term that approximates the original system with a small dissipative correction and can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally.
Abstract: We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers temporally. Numerical results for 1-D and 2-D problems are presented. The second-order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations. ©1995 John Wiley & Sons, Inc.
928 citations
TL;DR: Under suitable conditions, diffraction gives rise to an instability which leads to the emergence of a stationary spatial dissipative structure in the transverse profile of the transmitted beam.
Abstract: We consider a nonlinear, passive optical system contained in an appropriate cavity, and driven by a coherent, plane-wave, stationary beam. Under suitable conditions, diffraction gives rise to an instability which leads to the emergence of a stationary spatial dissipative structure in the transverse profile of the transmitted beam.
927 citations