Jet theoretical Yang-Mills energy in the geometric dynamics of two-dimensional monolayer

Neagu, Mircea; Крылова, Н. Г.; Grushevskaya, H. V.

doi:10.1063/1.4795715

Cited by 5 publications

(4 citation statements)

References 7 publications

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“…In this section we begin with a brief introduction to a monolayer space [1], [5] and then describe the nonholonomic mechanical system related to it . To obtain the 2Dmotionn equation of a particle of monolayer , we define a first We start with the usual physical time defined by the Euclidian manifold ( )) and we also consider the plane manifold having the polar coordinates (r, ) , where and , and construct the 1-jet vector bundle , locally endowed with the coordinates .…”

Section: Nonholonomic Mechanical Systems In a Monolayer Spacementioning

confidence: 99%

Mechanical behaviour of motion for the two-dimensional monolayer system‎

Azizpour

‎Moazzami

2016

Mathematical Researches

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In this paper we study the dynamics of the 2D-motion of a particle of monolayer. A geometric approach to nonholonomic constrained mechanical systems is applied to a problem from the two dimensional geometric dynamics of the Langmuir-Blodgett monolayer. We consider a constraint submanifold of the 1-jet space (), corresponding to the given constraint condition in a monolayer space and construct the corresponding constrained mechanical system on the constraint submanifold. Then the equation of motion defined on the constraint submanifold is presented.

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Section: Nonholonomic Mechanical Systems In a Monolayer Spacementioning

confidence: 99%

Mechanical behaviour of motion for the two-dimensional monolayer system‎

Azizpour

‎Moazzami

2016

Mathematical Researches

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“…By using (II.9), we will construct the geometrodynamic approach with the electrocapillary forces regarded as information constraints to describe the first-order 2d-phase transition in the compressed Langmuir monolayer. The electrocapillary part of free energy (II.4) is determined by the following Lagrange function [42]:…”

Section: Manifoldmentioning

confidence: 99%

“…A system of differential equations for the variation (δr, δϕ) (which describe Jacobi fields) of the geodesics satisfying the system (IV.2) has the following form [42]:…”

Section: Manifoldmentioning

confidence: 99%

See 1 more Smart Citation

Multiple-relaxation-time Finsler-Lagrange dynamics in a compressed Langmuir monolayer

Balan,

Grushevskaya,

Krylova

et al. 2015

Preprint

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In this paper an information geometric approach has been proposed to describe the two-dimensional (2d) phase transition of the first order in a monomolecular layer (monolayer) of amphiphilic molecules deposited on air/water interface. The structurization of the monolayer was simulated as an entropy evolution of a statistical set of microscopic states with a large number of relaxation times. The electrocapillary forces are considered as information constraints on the statistical manifold. The solution curves of Euler-Lagrange equations and the Jacobi field equations point out contracting pencils of geodesic trajectories on the statistical manifold, which may change into spreading ones, and converse. It was shown that the information geometrodynamics of the first-order phase transition in the Langmuir monolayer finds an appropriate realization within the Finsler-Lagrange framework.

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An anisotropic geometrical approach for non-relativistic extended dynamics

2013

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In this paper we present the distinguished (d-) Riemannian geometry (in the sense of nonlinear connection, Cartan canonical linear connection, together with its d-torsions and d-curvatures) for a possible Lagrangian inspired by optics in non-uniform media. The corresponding equations of motion are also exposed, and some particular solutions are given. For instance, we obtain as geodesic trajectories some circular helices (depending on an angular velocity ω), certain circles situated in some planes (ones are parallel with xOy, and other ones are orthogonal on xOy), or some straight lines which are parallel with the axis Oz. All these geometrical geodesics are very specific because they are completely determined by the non-constant index of refraction n(x). (2010): 53C60, 53C80, 83C10. Mathematics Subject Classification

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Jet theoretical Yang-Mills energy in the geometric dynamics of two-dimensional monolayer

Cited by 5 publications

References 7 publications

Mechanical behaviour of motion for the two-dimensional monolayer system‎

Mechanical behaviour of motion for the two-dimensional monolayer system‎

Multiple-relaxation-time Finsler-Lagrange dynamics in a compressed Langmuir monolayer

An anisotropic geometrical approach for non-relativistic extended dynamics

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