623 research outputs found
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 , be two time-independent Hamiltonians with one
degree of freedom and , be the one-parametric groups of
shifts along the orbits of Hamiltonian systems generated by , . In
some problems of population genetics there appear the transformations of the
plane having the form under some
conditions on , . We study in this paper asymptotical properties of
trajectories of .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
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