Solitons as dissipative structures

Velarde, Manuel G.

doi:10.1002/qua.10879

Cited by 12 publications

(8 citation statements)

References 44 publications

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“…More recently, Heeger and coworkers have used (topological) solitons to explain the electric conductivity of polymers [80] though in this case solitons come from the degeneracy of the ground state and not from an originally underlying lattice anharmonicity in trans-polyacetylene the case most studied by those authors. Finally, let us mention that Del Rio et al [81] have shown that in driven-dissipative lattices solitonic traveling periodic waves [82] can act as dynamical ratchets (as in Brownian ratchets and molecular motors) and hence can transport matter or charge due to the asymmetry of the wave peaks and not of the underlying potential.…”

Section: Appendix: Solitons As Matter or Charge Carriersmentioning

confidence: 99%

Thermal solitons and solectrons in nonlinear conducting chains

Chetverikov

Ébeling

Velarde

2009

Int J of Quantum Chemistry

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We present a model for nonlinear excitations in bio(macro)-molecules stable at room temperature and offering a possible mechanism for electron transfer over long distances (e.g., 100 Å and beyond). It is based on the excitation of generally supersonic solitons in a heated one-dimensional lattice with Morse interactions in a temperature range from low to physiological level. We study the influence of these supersonic excitations on electrons moving in the lattice. The lattice units (considered as "atoms") are treated by classical Langevin equations. The densities of the core electrons are in a first estimate represented by Gaussian densities, thus permitting to visualize lattice compressions as enhanced density regions. The evolution of excess, added free electrons is modeled in the tight-binding approximation using first Schrödinger equation and, subsequently, the assumption of local canonical equilibrium corresponding to an adiabatic approximation. The relaxation to thermal equilibrium is studied in a perturbative approach by means of the Pauli master equation.

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Section: Appendix: Solitons As Matter or Charge Carriersmentioning

confidence: 99%

Thermal solitons and solectrons in nonlinear conducting chains

Chetverikov

Ébeling

Velarde

2009

Int J of Quantum Chemistry

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“…[1], where a transition from Ohmic to non-Ohmic conductions is predicted, the carrier is a dissipative soliton that dynamically binds the electron. The concept of dissipative soliton has been shown of utility in fluid dynamics, in active lattices, nonlinear optics and lasers [9][10][11][12][13]. Although the proposed soliton-mediated transport seems to offer universal features yet the theory above referred suffers from various limitations.…”

Section: Introductionmentioning

confidence: 99%

Anharmonic Excitations, Time Correlations and Electric Conductivity

Chetverikov

Ébeling

Röpke

et al. 2007

Contrib. Plasma Phys.

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We study the influence of anharmonic mechanical excitations of a classical ionic lattice on its electric properties. First, to illustrate salient features, we investigate a simple model, an one-dimensional (1D) system consisting of ten semiclassical electrons embedded in a lattice or a ring with ten ions interacting with exponentially repulsive interactions. The lattice is embedded in a thermal bath. The behavior of the velocity autocorrelation function and the dynamic structure factor of the system are analyzed. We show that in this model the nonlinear excitations lead to long lasting time correlations and, correspondingly, to an increase of the conductivity in a narrow temperature region, where the excitations are supersonic soliton-like. In the second part we consider the quantum statistics of general ion-electron systems with arbitrary dimension and express -following linear response transport theory -the quantum-mechanical conductivity by means of equilibrium time correlation functions. Within the relaxation time approach an expression for the effective collision frequency is derived in Born approximation, which takes into account quantum effects and dynamic effects of the ion motion through the dynamic structure factor of the lattice and the quantum dynamics of the electrons. An evaluation of the influenec of solitons predicts for 1D-lattices a conductivity increase in the temperature region where most thermal solitons are excited, similar as shown in the classical Drude-Lorentz-Kubo framework.

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“…face [57]; a nonlocal Kuramoto-Sivashinsky (KS) equation describing nanostructuring by ion beam sputtering [14] and a wide spectrum of fluid flow problems, such as combined shear-flow and thermocapillary instabilities in two-layer systems [60] and core annular flows [38]; the nonlocal nonlinear Schrödinger equation [27]; and the nonlocal Klein-Gordon equation to describe Josephson junctions in thin films [20].…”

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confidence: 99%

Coherent Structures in Nonlocal Dispersive Active-Dissipative Systems

Lin¹,

Pradas

Kalliadasis

et al. 2015

SIAM J. Appl. Math.

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Abstract. We analyze coherent structures in nonlocal dispersive active-dissipative nonlinear systems, using as a prototype the Kuramoto-Sivashinsky (KS) equation with an additional nonlocal term that contains stabilizing/destabilizing and dispersive parts. As for the local generalized Kuramoto-Sivashinsky (gKS) equation (see, e.g., [T. Kawahara and S. Toh, Phys. Fluids, 31 (1988), pp. 2103-2111]), we show that sufficiently strong dispersion regularizes the chaotic dynamics of the KS equation, and the solutions evolve into arrays of interacting pulses that can form bound states. We analyze the asymptotic characteristics of such pulses and show that their tails tend to zero algebraically but not exponentially, as for the local gKS equation. Since the Shilnikov-type approach is not applicable for analyzing bound states in nonlocal equations, we develop a weak-interaction theory and show that the standard first-neighbor approximation is no longer applicable. It is then essential to take into account long-range interactions due to the algebraic decay of the tails of the pulses. In addition, we find that the number of possible bound states for fixed parameter values is always finite, and we determine when there is long-range attractive or repulsive force between the pulses. Finally, we explain the regularizing effect of dispersion by showing that, as dispersion is increased, the pulses generally undergo a transition from absolute to convective instability. We also find that for some nonlocal operators, increasing the strength of the stabilizing/destabilizing term can have a regularizing/deregularizing effect on the dynamics.

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Solitons as dissipative structures

Cited by 12 publications

References 44 publications

Thermal solitons and solectrons in nonlinear conducting chains

Thermal solitons and solectrons in nonlinear conducting chains

Anharmonic Excitations, Time Correlations and Electric Conductivity

Coherent Structures in Nonlocal Dispersive Active-Dissipative Systems

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