Finsler geometrization of classic theory for fields on the interphase boundary including monomolecular 2D-system

TL;DR

This paper applies Finsler geometry to model electro-capillary phenomena at the interphase boundary, linking geometric curvature to physical effects in monolayer phase transitions.

Contribution

It introduces a Finsler geometric framework to describe electro-capillary effects and structure formation in monolayer phase transitions, connecting geometric objects to physical parameters.

Findings

Ricci and Berwald scalar curvatures relate to electro-capillary effects

Cartan tensor and nonlinear connection characterize phase transition structures

Geometric objects depend on compression speed and charge characteristics

Abstract

We prove that the Ricci scalar curvature and the Berwald scalar curvature of a two-dimensional Finsler space, considered over a vector field on the 3-dimensional flat space, are naturally related to 2-dimensional electro-capillary phenomena effects observed for a compressed monolayer. The Cartan tensor and the nonlinear Barthel connection of the Finsler model are determined, and the geometric objects which depend on compression speed and on the characteristics of the electrically charged double layer are used in order to reveal several classes of structure formation within the phase transition of the first order.