Langmuir-Blodgett (LB)-films consist of few LB-monolayers which are high structured nanomaterials that are very promising materials for applications. We use a geometrical approach to describe a structurization into LB-monolayers. Consequently, we develop on the 1-jet space 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 geometricalLagrangian theory describes 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 a Jacobi equation. A jet geometricalYang-Mills energy is introduced and some computer graphic simulations are exposed.
Received 10 August 2012Accepted 04 March 2013Published online 22 March 2013
The present work was developed under the auspices of Grant No. 11962012-BRFFR-RA F12RA-002, within the cooperation framework between Romanian Academy and Belarusian Republican Foundation for Fundamental Research.
Article outline: I. INTRODUCTION II. THE CANONICAL NONLINEAR CONNECTION III. THE CARTAN CANONICAL Γ-LINEAR CONNECTION AND ITS D-TORSIONS IV. FROM THE DYNAMICS OF 2D-MONOLAYER TO A JET GEOMETRICALYANG-MILLS ENERGY V. JACOBI EQUATIONS FOR DEVIATION OF GEODESICS FROM AN INSTANTON-LIKE SOLUTION: COMPUTER IMAGING SIMULATIONS AND PHYSICAL INTERPRETATIONS
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