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A. A. Zamyatin

Publications and source records attributed to A. A. Zamyatin.

11 recordsLinked to original sources
arXiv2023

Introduction to Micro Life of Graphs. I

Multiparticle systems on complicated metric graphs might have many applications in physics, biology and social life. But the corresponding science still does not exist. Here we start it with simplest examples where there is quadratic interaction between neighboring particles and deterministic external forces. In this introduction we consider stable configurations and stable flows on one and two edge graphs. Moreover, distribution of mean (as in virial theorem) kinetic and potential energies along the graph is considered.

math-ph↗
arXiv2023

Regular Dynamics and Collisions Inside Classical Closed String

We consider classical closed string with $N$ particles inside. Taking collisions into account, we consider dynamics of this $N$-particle system under the influence of constant external force. We get Euler equations and explicit formula for the pressure.

math-ph↗
arXiv2015

One-dimensional Coulomb multi-particle systems

We consider the system of particles with equal charges and nearest neighbour Coulomb interaction on the interval. We study local properties of this system, in particular the distribution of distances between neighbouring charges. For zero temperature case there is sufficiently complete picture and we give a short review. For Gibbs distribution the situation is more difficult and we present two related results.

math-ph↗
arXiv2013

Explicit asymptotic velocity of the boundary between particles and antiparticles

On the real line initially there are infinite number of particles on the positive half-line., each having one of $K$ negative velocities $v_{1}^{(+)},...,v_{K}^{(+)}$. Similarly, there are infinite number of antiparticles on the negative half-line, each having one of $L$ positive velocities $v_{1}^{(-)},...,v_{L}^{(-)}$. Each particle moves with constant speed, initially prescribed to it. When particle and antiparticle collide, they both disappear. It is the only interaction in the system. We find explicitly the large time asymptotics of $β(t)$ - the coordinate of the last collision before $t$ between particle and antiparticle.

math.PR↗
arXiv2013

Mathematics for some classes of networks

Network (as a general notion) is not a mathematical object - there is no even any definition. However, there is a lot of good rigorous mathematics for well-defined classes of networks. In sections 1-3 we give a short overview of classes of networks which interested the authors for some time. In section 4 we consider in detail a new class of networks, related to markets with many agents.

math-ph↗
arXiv2011

Accumulation on the boundary for one-dimensional stochastic particle system

We consider infinite particle system on the positive half-line moving independently of each other. When a particle hits the boundary it immediately disappears, and the boundary moves to the right on some fixed quantity (particle size). We study the speed of the boundary movement (growth). Possible applications - dynamics of the traffic jam growth, growth of thrombus, epitaxy. Nontrivial mathematics is related to the correlation between particle dynamics and boundary growth.

math.PR↗
arXiv2011

Homeostasis in Chemical Reaction Pathways

We consider stochastic models of chemical reaction networks with time dependent input rates and several types of molecules. We prove that, in despite of strong time dependence of input rates, there is a kind of homeostasis phenomenon: far away from input nodes the mean numbers of molecules of each type become approximately constant (do not depend on time).

math-ph↗
arXiv2011

Introduction to stochastic models of transportation flows. Part I

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having visual simplicity and simple (but rigorous) formulation, the main objects being cars not abstract flows. The papers consists of three parts. First part considers mainly linear flows on short time scale - dynamics of the flow due to changing driver behavior. Second part studies linear flow on longer time scales - individual car trajectory from entry to exit from the road. Part three considers collective car movement in complex transport networks.

math.PR↗