arXiv subjects

S. S. Borysov

Publications and source records attributed to S. S. Borysov.

4 recordsLinked to original sources

arXiv2011

Analytical and numerical studies of creation probabilities of hierarchical trees

We consider the creation conditions of diverse hierarchical trees both analytically and numerically. A connection between the probabilities to create hierarchical levels and the probability to associate these levels into a united structure is studied. We argue that a consistent probabilistic picture requires the use of deformed algebra. Our consideration is based on the study of the main types of hierarchical trees, among which both regular and degenerate ones are studied analytically, while the creation probabilities of Fibonacci, scale-free and arbitrary trees are determined numerically.

cond-mat.stat-mech↗

arXiv2010

Statistical field theories deformed within different calculi

Within framework of basic-deformed and finite-difference calculi, as well as deformation procedures proposed by Tsallis, Abe, and Kaniadakis to be generalized by Naudts, we develop field-theoretical schemes of statistically distributed fields. We construct a set of generating functionals and find their connection with corresponding correlators for basic-deformed, finite-difference, and Kaniadakis calculi. Moreover, we introduce pair of additive functionals, whose expansions into deformed series yield both Green functions and their irreducible proper vertices. We find as well formal equations, governing by the generating functionals of systems which possess a symmetry with respect to a field variation and are subjected to an arbitrary constrain. Finally, we generalize field-theoretical schemes inherent in concrete calculi in the Naudts spirit.

cond-mat.stat-mech↗

arXiv2010

Suppression of oscillations by Levy noise

We find analytical solution of pair of stochastic equations with arbitrary forces and multiplicative Lévy noises in a steady-state nonequilibrium case. This solution shows that Lévy flights suppress always a quasi-periodical motion related to the limit cycle. We prove that difference between stochastic systems driven by Lévy and Gaussian noises is that the Lévy variation $ΔL\sim(Δt)^{1/α}$ with the exponent $α<2$ is much less than the Gaussian one $ΔW\sim(Δt)^{1/2}$ in the $Δt\to 0$ limit. Moreover, this difference is shown to remove the problem of the calculus choice because related addition to the physical force is of order $(Δt)^{2/α}\llΔt$.

cond-mat.stat-mech↗

arXiv2009

Noise induced oscillations in non-equilibrium steady state systems

We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle at certain relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest variations displays a principle variable, which is coupled with two different degrees of freedom or more.

cond-mat.stat-mech↗