84 research outputs found
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
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
Large Deviations in Some Queueing Systems
Logarithmic asymptotics of probabilities of large delays are derived for the “last come—first served” system and system with priorities. Trajectories that determine the mean dynamics of arrival flow under the condition of large delay are described
Percolation properties of non-ideal gas
We estimate locations of the regions of the percolation and of the
non-percolation in the plane : the Poisson rate -- the inverse
temperature, for interacted particle systems in finite dimension Euclidean
spaces. Our results about the percolation and about the non-percolation are
obtained under different assumptions. The intersection of two groups of the
assumptions reduces the results to two dimension Euclidean space, , and
to a potential function of the interactions having a hard core.
The technics for the percolation proof is based on a contour method which is
applied to a discretization of the Euclidean space. The technics for the
non-percolation proof is based on the coupling of the Gibbs field with a
branching process.Comment: 28 pages, 3 figure
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