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Localization and coherence in nonintegrable systems

PHYSICA D-NONLINEAR PHENOMENA 2003年第1-4期184卷 162-191页

作者： Rumpf, B newell, AC Max Planck Inst Phys Komplexer Syst D-01187 Dresden Germany Univ Arizona Dept Math Tucson AZ 85721 USA

We study the irreversible dynamics of nonlinear, nonintegrable Hamiltonian oscillator chains approaching their statistical asymptotic states. In systems constrained by more than one conserved quantity, the partitioning of the conserved quantities leads naturally to localized and coherent structures. If the phase space is compact, the final equilibrium state is governed by entropy maximization and the coherent structures are stable lumps. In systems where the phase space is not compact, the coherent structures can be collapsed, represented in phase space by a heteroclinic connection of some unstable saddle to infinity. (C) 2003 Elsevier B.V. All rights reserved.

关键词： localized structures statistical physics

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Global description of patterns far from onset: a case study

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PHYSICA D-NONLINEAR PHENOMENA 2003年第1-4期184卷 127-140页

作者： Ercolani, M Indik, R newell, AC Univ Arizona Dept Math Tucson AZ 85721 USA CNRS Observ Cote Azur F-06304 Nice 4 France

The Cross-newell phase diffusion equation tau(k)Theta(T) = -del (.) kB(k), k = delTheta, \k\ = k, and its regularization describe patterns and defects far from onset in large aspect ratio systems with translational and rotational symmetry. In this paper we show how director field solutions of this equation can be used to describe features of global patterns. The ideas are illustrated in the context of a non-trivial case study of high Prandtl number convection in a large aspect ratio, shallow, elliptical container with heated sidewalls, for which we also have the results of simulation and experiment. (C) 2003 Elsevier B.V. All rights reserved.

关键词： patterns defects convection

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Structure functions and breakdown criteria for wave turbulence

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PHYSICA D-NONLINEAR PHENOMENA 2003年第1-4期184卷 98-113页

作者： Biven, LJ Connaughton, C newell, AC Univ Warwick Inst Math Coventry CV4 7AL W Midlands England Univ Arizona Dept Math Tucson AZ 85721 USA

We study the structure functions of wave turbulence at small separations. We show that the criteria for breakdown obtained previously by examining the uniform validity of the asymptotic closure govern how close wave turbulence stays to joint Gaussianity. A new result in the case of small separations in that the system behavior is organized by a special point in the (alpha, beta) plane where alpha and beta are the homogeneity parameters for the linear and nonlinear coupling coefficients. Finally, we explore how modifications of the breakdown criteria are necessary because of the strengths of non-local long-wave-short-wave interactions. (C) 2003 Elsevier B.V. All rights reserved.

关键词： wave turbulence asymptotic closure Gaussianity

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Localization and coherence in nonintegrable systems

Localization and coherence in nonintegrable systems

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conference on complexity and nonlinearity in physical systems held in honor of alan newell

作者： Rumpf, B newell, AC Max Planck Inst Phys Komplexer Syst D-01187 Dresden Germany Univ Arizona Dept Math Tucson AZ 85721 USA

关键词： localized structures statistical physics

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Global description of patterns far from onset: a case study

Global description of patterns far from onset: a case study

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conference on complexity and nonlinearity in physical systems held in honor of alan newell

作者： Ercolani, M Indik, R newell, AC Univ Arizona Dept Math Tucson AZ 85721 USA CNRS Observ Cote Azur F-06304 Nice 4 France

关键词： patterns defects convection

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Dimensional analysis and weak turbulence

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PHYSICA D-NONLINEAR PHENOMENA 2003年第1-4期184卷 86-97页

作者： Connaughton, C Nazarenko, S newell, AC Univ Warwick Math Inst Coventry CV4 7AL W Midlands England Univ Arizona Dept Math Tucson AZ 85721 USA

In the study of weakly turbulent wave systems possessing incomplete self-similarity, it is possible to use dimensional arguments to derive the scaling exponents of the Kolmogorov-Zakharov spectra, provided the order of the resonant wave interactions responsible for nonlinear energy transfer is known. Furthermore, one can easily derive conditions for the breakdown of the weak turbulence approximation. It is found that for incompletely self-similar systems dominated by three wave interactions, the weak turbulence approximation usually cannot break down at small scales. It follows that such systems cannot exhibit small scale intermittency. For systems dominated by four wave interactions, the incomplete self-similarity property implies that the scaling of the interaction coefficient depends only on the physical dimension of the system. These results are used to build a complete picture of the scaling properties of the surface wave problem where both gravity and surface tension play a role. We argue that, for large values of the energy flux, there should be two weakly turbulent scaling regions matched together via a region of strongly nonlinear turbulence. (C) 2003 Elsevier B.V All rights reserved.

关键词： dimensional analysis weak turbulence approximation incomplete self-similarity

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Structure functions and breakdown criteria for wave turbulence

Structure functions and breakdown criteria for wave turbulen...

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conference on complexity and nonlinearity in physical systems held in honor of alan newell

作者： Biven, LJ Connaughton, C newell, AC Univ Warwick Inst Math Coventry CV4 7AL W Midlands England Univ Arizona Dept Math Tucson AZ 85721 USA

关键词： wave turbulence asymptotic closure Gaussianity

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Numerical integration of Maxwell's full-vector equations in nonlinear focusing media

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PHYSICA D-NONLINEAR PHENOMENA 2003年第1-4期184卷 352-375页

作者： Bennett, PM Aceves, A Univ New Mexico Dept Math & Stat Albuquerque NM 87131 USA Comp Sci Corp Vicksburg MS 39180 USA

In this paper, we present results of parallel numerical simulations on Maxwell's equations. The parallel code is used to study the effect of the instantaneous focusing nonlinearity upon dispersionless pulse propagation in bulk dielectric. Indications are given of the development of shocks on the optical carrier wave and upon the pulse envelope. We then use the code to study focusing and collapse of optical pulses at anomalously dispersive frequencies. We examine the effect of varying the focusing of the light by varying the intensity as a way to compensate linear dispersion. We demonstrate blow up of sufficiently intense short pulses at finite propagation distances, and we show numerically that the location of blow up depends nontrivially upon the intensity of the light. (C) 2003 Elsevier B.V. All rights reserved.

关键词： nonlinear optics parallel numerical algorithms ultrashort intense pulses Maxwell's equations anomalous dispersion instantaneous nonlinearity

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Dimensional analysis and weak turbulence

Dimensional analysis and weak turbulence

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conference on complexity and nonlinearity in physical systems held in honor of alan newell

作者： Connaughton, C Nazarenko, S newell, AC Univ Warwick Math Inst Coventry CV4 7AL W Midlands England Univ Arizona Dept Math Tucson AZ 85721 USA