Jet theoretical Yang-Mills energy in the geometric dynamics of 2D-monolayer

TL;DR

This paper develops a geometric framework on jet spaces to model the dynamics of 2D monolayers in LB-films, introducing a Yang-Mills energy concept with physical interpretations related to phase transitions.

Contribution

It introduces a novel geometric approach using jet space Lagrangian geometry to describe monolayer structuration and phase transitions, including a Yang-Mills energy formulation.

Findings

Derived particle trajectories under electrocapillarity forces.

Proposed a geometric model for phase transitions in LB-monolayers.

Introduced a Yang-Mills energy concept with physical insights.

Abstract

Langmuir-Blodgett films (LB-films) consist from few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe structurization into LB-monolayers. Consequently, we develop on the 1-jet space J^1([0,\infty),R^2) the single-time Lagrange geometry (in the sense of distinguished (d-) connection, d-torsions and an abstract anisotropic electromagnetic-like d-field) for the Lagrangian governing the 2D-motion of a particle of monolayer. One assumed that an expansion near singular points for the constructed geometrical Lagrangian theory describe phase transitions to LB-monolayer. Trajectories of particles in a field of the electrocapillarity forces of monolayer have been calculated in a resonant approximation utilizing some Jacobi equations. A jet geometrical Yang-Mills energy is introduced and some physical interpretations are given.