Related papers: Interacting Particle Systems in Time-Dependent Geo…
In this paper, time-dependent dynamical systems given by sequences of maps are studied. For systems built from expanding C^2-maps on a compact Riemannian manifold M with uniform bounds on expansion factors and derivatives, we provide…
We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form…
The principles of behavior of the system with discrete interactions are applied to description of motion of the relativistic particle. Applying the concept of non-local behavior both to position in space and to time, the apparently…
Small particles transported by a fluid medium do not necessarily have to follow the flow. We show that for a wide class of time-periodic incompressible flows inertial particles have a tendency to spontaneously align in one-dimensional…
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
Scale invariance is a central organizing principle in physics, underlying phenomena that range from critical behaviour in statistical mechanics to transport and chaos in nonlinear dynamical systems. Here we present a unified and physically…
Driven non-equilibrium lattice models have wide-ranging applications in contexts such as mass transport, traffic flow, and transport in biological systems. In this work, we investigate the steady-state properties of a one-dimensional…
We study systems of interacting Brownian particles in one dimension constructed as the diffusion scaling limits of Fisher's vicious walk models. We define two types of nonintersecting Brownian motions, in which we impose no condition (resp.…
Motivated by a general principle governing regulation mechanisms in biological cells, we investigate a general interaction scheme between different populations of particles and specific particles, referred to as agents. Assuming that each…
Dynamics of information flow in adaptively interacting stochastic processes is studied. We give an extended form of game dynamics for Markovian processes and study its behavior to observe information flow through the system. Examples of the…
The particle-scale dynamics of granular materials have commonly been characterized by the self-diffusion coefficient $D$. However, this measure discards the collective and topological information known to be an important characteristic of…
While topology is a property of a quantum state itself, most existing methods for characterizing the topology of interacting phases of matter require direct knowledge of the underlying Hamiltonian. We offer an alternative by utilizing the…
In evolving complex systems such as air traffic and social organizations, collective effects emerge from their many components' dynamic interactions. While the dynamic interactions can be represented by temporal networks with nodes and…
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and…
In a living system composed of interacting components such as molecules, cells, and tissues, each component often adaptively changes its internal states in response to interactions with its surrounding components. For example, individual…
We present a collision model for particle-particle and particle-wall interactions in interface-resolved simulations of particle-laden flows. Three types of inter-particle interactions are taken into account: (1) long- and (2) short-range…
We present a framework for the scale-invariance characterization of stochastic processes in reconstructed finite-dimensional phase spaces. This framework analyses the structural and dynamical properties of the phase space and is based on a…
We discuss the symmetry properties of the reparametrization invariant model of an interacting relativistic particle where the electromagnetic field is taken as the constant background field. The direct coupling between the relativistic…
Many complex systems are characterized by intriguing spatio-temporal structures. Their mathematical description relies on the analysis of appropriate correlation functions. Functional integral techniques provide a unifying formalism that…
We consider a reduction procedure in Wiener-type path integral for a finite-dimensional mechanical system with a symmetry representing the motion of two interacting scalar particles on a manifold that is the product of the total space of…