R. Kotowski

Variational approach to the thermo-electrodynamics of liquid crystals

A variational principle for liquid crystals subject to the thermal and electromagnetic interactions is proposed in order to obtain the complete system of field equations. The ideas suggested by Natanson and Sedov are applied. Problems concerning the description of dissipative processes are discussed. The polynomial form of the nonequilibrium constitutive equations of nematic liquid crystals in the Lagrange description is considered.

A Nonequilibrium Evolution Criterion for Electromagnetic Bodies

Abstract In this paper the micropolar medium exposed to the action of mechanical, thermal and electromagnetic fields is considered. The generalization of the global evolution criterion of nonequilibrium thermodynamics of micropolar media in the case of nonvanishing electromagnetic fields is derived. Interaction with the environment is modeled by the black-body radiation. Application of the criterion to liquid crystals in equilibrium state is given and the complete set of fundamental equations is derived.

Variational principle for dissipative processes in continuum physics

Abstract The authors present the variational formulation of the theory describing the dissipative processes in electromagnetic bodies. Electromagnetic elastic solids, electromagnetic micropolar elastic solids, electromagnetic fluids and electromagnetic micropolar fluids and liquid crystals are considered.

Nonlinear diffusion and Nelson-Brown movement

The nonlinear diffusion process, which can be described as the Nelson-Brown motion, is considered. The obtained equation becomes the classical linear diffusion equation for small relaxation times, and for long relaxation times it is transferred into the Schrödinger-like equation. The possible nonequilibrium stationary states are discussed.

On the Brillouin delta function of cubic and hexagonal lattices

In many problems of solid state physics one faces the task of integrating functions over polyhedra. This is necessary, for example, for the form factor in the theory of scattering, the Wannier function in band theory, and the Brillouin delta function in pseudocontinuum theory of crystal lattices. The integrands of these quantities are of similar form; the last two require integration over Brillouin zones. In the paper the properties of the Brillouin delta function are shortly rewieved. This function allows, in pseudocontinuum theory, the establishment of a unique relationship between functions of discrete and continuous arguments.A method of simplifying the integration of functions over polyhedra is proposed. The method is based on dividing a polyhedron into simplexes and calculating the integral in new barycentric coordinates. This method is applyied to the calculation of Brillouin delta functions for body centred and face centred cubic crystals. Explicit formulae for hexagonal and orthorhombic lattices are also given and discussed.

Cooperative optimization in cellular automata - based multiagent systems with spatio-temporally generalized prisoner's dilemma model

A multiagent system operating in the two-dimensional cellular automata (CA) space is considered. Each cell of CA is treated as an agent taking part in Spatio-temporally Generalized Prisoners Dilemma (STGPD) game. Each agent currently uses one of the following strategies: always defect (all D), always cooperate (all C) or k-D denoting a wiling to cooperate until a number of defecting neighbors is less or equal to k. Periodically agents update their current actions in order to maximize their own profit. We are interested in the phenomena of possibly emerging global cooperation of CA-based agents of STGPD model. Our study is motivated by a potential application of presented model for organization of mobile ad hoc networks. We study the model under different starting settings of the model parameters and observe conditions of emerging a global cooperation between agents. We discover a number of perspective regions of the game with different types and patterns of cooperation.

Peierls stress in a simple model of a screw dislocation

Abstract A simple model of a screw dislocation with first neighbours interactions is presented. The interaction energy of atoms is a piece-wisely parabolic function of distortions. The equilibrium configurations of weak bonds as a function of the model parameter γ and the quasi-static motion of the dislocation are examined. Sessile and glissile configurations of weak bonds and symmetric and asymmetric equilibrium positions of the dislocation are found. The dependence of the Peierls stress on the model parameter γ is discussed.