Numerical simulation of sine-Gordon soliton dynamics in the presence of perturbations

Currie, J. F.; Trullinger, S. E.; Bishop, A. R.; Krumhansl, J. A.

doi:10.1103/physrevb.15.5567

Cited by 210 publications

(86 citation statements)

References 22 publications

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“…Discreteness effects have been considered before in the context of kink dynamics [5]. Trullinger and Sasaki have already obtained the lowest-order discreteness corrections to the Schrödinger equation that emerges from the transfer integral approach [6].…”

Section: Introductionmentioning

confidence: 99%

Controlling one-dimensional Langevin dynamics on the lattice

1999

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Stochastic evolutions of classical field theories have recently become popular in the study of problems such as determination of the rates of topological transitions and the statistical mechanics of nonlinear coherent structures. To obtain high precision results from numerical calculations, a careful accounting of spacetime discreteness effects is essential, as well as the development of schemes to systematically improve convergence to the continuum. With a kink-bearing φ 4 field theory as the application arena, we present such an analysis for a 1+1-dimensional Langevin system. Analytical predictions and results from high resolution numerical solutions are found to be in excellent agreement.

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Section: Introductionmentioning

confidence: 99%

Controlling one-dimensional Langevin dynamics on the lattice

1999

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“…x-r p(x) = o o f(r,s) dr ds [8] [3] in which AS, is the entropy and AfHS the enthalpy of formation of an open segment, R is the gas constant, and T is absolute temperature (13). Because, by hypothesis, each segment contains (L/i) open base pairs and the mean of the excursion is x = f1 -p(x)ldx.…”

mentioning

confidence: 99%

Nature of the open state in long polynucleotide double helices: possibility of soliton excitations.

Englander¹,

Kallenbach²,

Heeger³

et al. 1980

Proc. Natl. Acad. Sci. U.S.A.

453

184

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The existence of transiently open states in DNA and synthetic polynucleotide double helices as been demonstrated by hydrogen exchange measurements; base pairs reversibly separate and reclose, exposing nucleotide protons to exchange with solvent protons. Recently it has been possible to define the equilibrium kinetic, and activation parameters of the major open state tdat determines base pair hydrogen exchange. However, there is no direct information at the moment about the conformation of the open form. Here we consider the possibility that the low energy and slow opening and closing rates observed reflect a deformation involving several adjacent base pairs. Assuming a mobile open unit capable of diffusing along the double helix, we find that available data are consistent with structures of 10 or so adjacent open pairs. It is further suggested that these structures correspond to thermally induced so on excitations of the double helix, which retain coherence by sharing the energy of a twist deformation among several base tairs. Solitons

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“…In the thermodynamic regime, one-dimensional (1D) lattice systems with degenerated vacuum, reveal the coexistence of localized and extended excitations, kinks and phonons, respectively, that is accompanied by characteristic hump developed in a specific heat [1,2]. Three--dimensional (3D) version of such a system exhibits phase transition of second order.…”

Section: Motivationmentioning

confidence: 99%

“…mass of single atom in the chain; x l is dimensionless coordinate at l-th site of the chain (N -sites with a periodic boundary conditions),ẋ l denotes (dimensionless) time derivative, and k is dimensionless coupling constant. Thermodynamics of system (1) may be found by means of the transfer integral method, in continuum, classical limit [2][3][4]. Namely, the thermodynamic properties are related to the pseudo-Schrödinger eigenvalue problem…”

Section: Sequence Of Phase Conversions -1d Systemsmentioning

confidence: 99%

Asymmetry Driven Phase Transformations

et al. 2010

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Motivated by the properties of one-dimensional lattice systems with asymmetric on-site potential, one can formulate a hypothesis of an asymmetry driven phase transformation. Characteristic feature of one-dimensional systems exhibiting asymmetry driven phase transformation is a sequence of the two phase conversions. In particular class of such systems with a triple-well potential, phase conversions of one-dimensional systems would evolve into a sequence of two phase transitions in three-dimensional models. We propose here a model of three-dimensional system exhibiting a sequence of two first order asymmetry driven phase transitions.PACS numbers: 05.70.−a, 64.60.−i, 63.70.+h MotivationIn the thermodynamic regime, one-dimensional (1D) lattice systems with degenerated vacuum, reveal the coexistence of localized and extended excitations, kinks and phonons, respectively, that is accompanied by characteristic hump developed in a specific heat [1,2]. Three--dimensional (3D) version of such a system exhibits phase transition of second order. In fact, it is one of the simplest manifestations of spontaneously broken (discrete) symmetry.It has been recently observed [3,4] that one--dimensional, multistable systems, with non-degenerated vacuum would exhibit interesting behavior. Specific heat of systems with local asymmetric, double-well or triple--well potential, may reveal quite rich, two-peak structure, possibly corresponding to two phase conversions. One can ask whether such a property of one-dimensional systems, would indicate a sequence of the phase transitions in corresponding three-dimensional systems.The aim of this paper is to give a comprehensive analysis of unconventional behaviour of specific heat of a class of one-dimensional lattice systems with triple-well potential. It is argued that large, shape-type asymmetry of these systems is manifested by "energy level crossing", associated with two-peak structure of specific heat. In this case it reflects a sequence of two phase conversions. These phase conversions would turn into phase transitions in three-dimensional version of the model. We propose here a model of a three-dimensional lattice system exhibiting a sequence of two phase transitions -they may be referred to as asymmetry driven phase transitions. The

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Numerical simulation of sine-Gordon soliton dynamics in the presence of perturbations

Cited by 210 publications

References 22 publications

Controlling one-dimensional Langevin dynamics on the lattice

Controlling one-dimensional Langevin dynamics on the lattice

Nature of the open state in long polynucleotide double helices: possibility of soliton excitations.

Asymmetry Driven Phase Transformations

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