Reversibility and Non-reversibility in Stochastic Chemical Kinetics

Mathematical problems with mean field and local type interaction related to stochastic chemical kinetics,are considered. Our main concern various definitions of reversibility, their corollaries (Boltzmann type equations, fluctuations, Onsager relations, etc.) and emergence of irreversibility

Dynamics of Tectonic Plates

We suggest a model that describes a mutual dynamic of tectonic plates. The dynamic is a sort of stick-slip one which is modeled by a Markov random process. The process defines a microlevel of the dynamic. A macrolevel is obtained by a scaling limit which leads to a system of integro-differential equations which determines a kind of mean field systems. Conditions when Gutenberg-Richter empirical law are presented on the mean field level. These conditions are rather universal and do not depend on features of resistant forces.Comment: 3 figure

On products of skew rotations

Let $H_1(p,q)$, $H_2(p,q)$ be two time-independent Hamiltonians with one degree of freedom and $\{S_1^t\}$, $\{S_2^t\}$ be the one-parametric groups of shifts along the orbits of Hamiltonian systems generated by $H_1$, $H_2$. In some problems of population genetics there appear the transformations of the plane having the form $T^{(h_1,h_2)}=S^{h_2}_2\cdot S_1^{h_1}$ under some conditions on $H_1$, $H_2$. We study in this paper asymptotical properties of trajectories of $T^{(h_1,h_2)}$.Comment: 13 pages, 10 figure

Unimodular metagravity vs. General Relativity with a scalar field

The unimodular metagravity, with the graviscalar as a dark matter, is compared with General Relativity (GR) in the presence of a scalar field. The effect of the graviscalar on the static spherically symmetric metric is studied. An exact limit solution representing a new cosmic object, the (harmonic) graviscalar black hole, is given. The relation with the black hole in the environment of a scalar field in GR is discussed.Comment: 7 pages. Report presented at the RAS Conference "Physics of Fundamental Interactions", Protvino, December 22-25, 200

Markov Process of Muscle Motors

We study a Markov random process describing a muscle molecular motor behavior. Every motor is either bound up with a thin filament or unbound. In the bound state the motor creates a force proportional to its displacement from the neutral position. In both states the motor spend an exponential time depending on the state. The thin filament moves at its velocity proportional to average of all displacements of all motors. We assume that the time which a motor stays at the bound state does not depend on its displacement. Then one can find an exact solution of a non-linear equation appearing in the limit of infinite number of the motors.Comment: 10 page