Exact solutions to the time-dependent Landau-Ginzburg model of phase transitions

Tuszyński, Jack A.; Paul, R.; Chatterjee, R.

doi:10.1103/physrevb.29.380

Cited by 16 publications

(2 citation statements)

References 5 publications

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“…(IV.5) and (IV. 7) shows that both the linear and the nonlinear problems are attenuated in the same manner by the friction coefficient.…”

Section: Solution Of the Evolution Equation For Spiral Wavesmentioning

confidence: 95%

“…Experimentally, the work of Rowlands et al [5] in connection with the phenomenon of rouleaux formation in erythrocytes is a direct observation of the existence of long range forces in biological systems. A theoretical model dealing with this problem was presented by Paul et al [6] and Tuszynski et al [7]. The nature of the forces involved is of an electromagnetic nature with the photons acting as the particles mediating the interaction between the red blood cells.…”

Section: Introductionmentioning

confidence: 98%

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A coherent wave model for pattern generation during the aggregation of slime mould amoeba

Paul

Olson

1988

J Biol Phys

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ABSTRACT." In this paper we examine the finite difference equation describing the acrasin concentration as used by Parnas and Segel [11] in a computer simulation of the aggregation of slime mould amoeba. We consider the corresponding differential equation in two spatial dimensions rather than the single dimension used in [11]. We solve this equation along a spiral curve to within a quadrature and for low concentrations (in keeping with the simulation conditions) we extract an analytical form for the traveling wave. For a "quantized" relationship between the period of this wave and the refractory period of the amoeba we show the creation of an aggregation process along the spiral curve.We introduce a thermodynamic analysis from which we show that the production of the above acrasin wave is a typical symmetry breaking phenomenon dependent upon the amount of nutrients (bacteria) in the medium. This phase transition displays a critical exponent of 1/2 dependent upon the deviation of the bacterial concentration from its critical value. We are able to show that the broken symmetry state possesses lower free energy than a homogenous state. We also show, from a linear stability analysis, that this state is not destroyed by cnvironmental perturbations.By utilizing the free energy expression in a time dependcnt Landau-Ginzburg type model we make contact with othcr well known physical phenomena such as rouleaux formation and superconductivity. This approach immediately opens up the possibility of examining the problem from a more gcneral perspective.

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“…(IV.5) and (IV. 7) shows that both the linear and the nonlinear problems are attenuated in the same manner by the friction coefficient.…”

Section: Solution Of the Evolution Equation For Spiral Wavesmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 98%

A coherent wave model for pattern generation during the aggregation of slime mould amoeba

Paul

Olson

1988

J Biol Phys

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Comments on the davydov hamiltonian for quasi‐one‐dimensional molecular chains

Tuszyński

1986

Int J of Quantum Chemistry

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The almost lossless transfer of energy and electronic charge along quasi-one-dimensional molecular substances such as peptide chains (H-N-C=O),found an explanation in a model proposed by Davydov. The Davydov model is based on the dipole-dipole interactions between neighboring peptide groups and on the fact that the internal C=O vibrations are coupled to the elastic deformations of the chain. The Davydov Hamiltonian is written in the position-space representation and, on making a continuum transformation, leads to a nonlinear Schrodinger equation whose solutions are sol8ons. A Davydov soliton is a coupled pair of an exciton and a lattice deformation. In this paper, the Davydov Hamiltonian is transformed to the reciprocal lattice and its equivalent, second-quantized Hamiltonian is investigated. Some important obsemations are made about the coupling constants, their dispersion relations, and the equation of motion for the ladder operators. Our procedure is free of semiclassical approximations but, instead, assumes the onset of Bose condensation. The resultant nonlinear Schrodinger equation is similar to that of Davydov, but a more complete set of solutions is found.

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Solitons, Bose-Einstein condensation, and superfluidity in helium II

Chela-Flores

Ghassib

1987

Int J Theor Phys

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Exact solutions to the time-dependent Landau-Ginzburg model of phase transitions

Cited by 16 publications

References 5 publications

A coherent wave model for pattern generation during the aggregation of slime mould amoeba

A coherent wave model for pattern generation during the aggregation of slime mould amoeba

Comments on the davydov hamiltonian for quasi‐one‐dimensional molecular chains

Solitons, Bose-Einstein condensation, and superfluidity in helium II

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