arXiv subjects

A. Samoletov

Publications and source records attributed to A. Samoletov.

5 recordsLinked to original sources

arXiv2023

A statistical interpretation of biologically inspired growth models

Biological entities are inherently dynamic. As such, various ecological disciplines use mathematical models to describe temporal evolution. Typically, growth curves are modelled as sigmoids, with the evolution modelled by ordinary differential equations. Among the various sigmoid models, the logistic and Gompertz equations are well established and widely used in fitting growth data in the fields of biology and ecology. This paper suggests a statistical interpretation of the logistic equation within the general framework. This interpretation is based on modelling the population environment relationship, the mathematical theory of which we discuss in detail. By applying this theory, we obtain stochastic evolutionary equations, for which the logistic equation is a limiting case. The prospect of modifying logistic population growth is discussed. We support our statistical interpretation of population growth dynamics with test numerical simulations. We show that the Gompertz equation and other related models can be treated in a similar way.

math.DS↗

arXiv2019

Temperature expressions and ergodicity of the Nosé-Hoover deterministic schemes

Thermostats are dynamic equations used to model thermodynamic variables in molecular dynamics. The applicability of thermostats is based on the ergodic hypothesis. The most commonly used thermostats are designed according to the Nosé-Hoover scheme, although it is known that it often violates ergodicity. Here, following a method from our recent study \citep{SamoletovVasiev2017}, we have extended the classic Nosé-Hoover scheme with an additional temperature control tool. However, as with the NH scheme, a single thermostat variable is used. In the present study we analyze the statistical properties of the modified equations of motion with an emphasis on ergodicity. Simultaneous thermostatting of all phase variables with minimal extra computational costs is an advantage of the specific theoretical scheme presented here.

physics.comp-ph↗

arXiv2017

Dynamic principle for ensemble control tools

Dynamical equations describing physical systems at statistical equilibrium are commonly extended by mathematical tools called "thermostats". These tools are designed for sampling ensembles of statistical mechanics. We propose a dynamic principle for derivation of stochastic and deterministic thermostats. It is based on fundamental physical assumptions such that the canonical measure is invariant for the thermostat dynamics. This is a clear advantage over a range of recently proposed and widely discussed in the literature mathematical thermostat schemes. Following justification of the proposed principle we show its generality and usefulness for modeling a wide range of natural systems.

physics.data-an↗

arXiv2004

Global Spatiotemporal Order and Induced Stochastic Resonance due to a Locally Applied Signal

We study the phenomenon of spatiotemporal stochastic resonance (STSR) in a chain of diffusively coupled bistable oscillators. In particular, we examine the situation in which the \textit{global} STSR response is controlled by a \textit{locally applied signal} and reveal a wave front propagation. In order to deepen the understanding of the system dynamics, we introduce, on the time scale of STSR, the study of the effective statistical renormalization of a generic lattice system. Using this technique we provide a new criterion for STSR, and predict and observe numerically a bifurcation-like behaviour that reflects the difference between the most probable value of the local quasi-equilibrium density and its mean value. Our results, tested with a chain of nonlinear oscillators, appear to possess some universal qualities and may stimulate a deeper search for more generic phenomena

physics.bio-ph↗

arXiv2003

A Remark on the Kramers Problem

We present new point of view on the old problem, the Kramers problem. The passage from the Fokker-Planck equation to the Smoluchowski equation, including corrections to the Smoluchowski current, is treated through an asymptotic expansion of the solution of the stochastic dynamical equations. The case of an extremely weak force of friction is also discussed

physics.class-ph↗