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

Neagu, M.; Krylova, N. G.; Grushevskaya, H. V.
March 2013
Journal of Mathematical Physics;Mar2013, Vol. 54 Issue 3, p031508
Academic Journal
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 J1([0,∞),R2) 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 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 geometrical Yang-Mills energy is introduced and some computer graphic simulations are exposed.


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