Related papers: Deterministic Equations of Motion and Phase Orderi…
In this paper we consider the one-dimensional dynamical evolution of a particle traveling at constant speed and performing, at a given rate, random reversals of the velocity direction. The particle is subject to stochastic resetting,…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
The ordering dynamics of the Higgs field is studied, using techniques inspired by the study of phase ordering in condensed matter physics, as a first step to understanding the evolution of cosmic structure through the formation of…
A general prescription for the treatment of constrained quantum motion is outlined. We consider in particular constraints defined by algebraic submanifolds of the quantum state space. The resulting formalism is applied to obtain solutions…
Natural orbital theory is a computationally useful approach to the few and many-body quantum problem. While natural orbitals are known and applied since many years in electronic structure applications, their potential for time-dependent…
We consider initial value problems of nonlinear dynamical systems, which include physical parameters. A quantity of interest depending on the solution is observed. A discretisation yields the trajectories of the quantity of interest in many…
A discrete model of traffic on a multilane road is considered. The traffic is presented as particles movement with a deterministic component and a stochastic one. Formulas for the traffic characteristics have been found. The model can…
It is shown that physical mechanics for pointlike bodies can be effectively modeled in terms of the action of transformation groups that act as symmetries of the solutions of systems of differential equations that describe the integrability…
We revisit the equilibrium one-dimensional $\phi^4$ model from the dynamical systems point of view. We find an infinite number of periodic orbits which are computationally stable. At the same time some of the orbits are found to exhibit…
Based on the Hamiltonian equation of motion of the $\phi^4$ theory with quenched disorder, we investigate the depinning phase transition of the domain-wall motion in two-dimensional magnets. With the short-time dynamic approach, we…
The diffusion in two dimensions of non-interacting active particles that follow an arbitrary motility pattern is considered for analysis. Accordingly, the transport equation is generalized to take into account an arbitrary distribution of…
Collective motion is an ubiquitous phenomenon in nature, inspiring engineers, physicists and mathematicians to develop mathematical models and bio-inspired designs. Collective motion at small to medium group sizes ($\sim$10-1000…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
We introduce and study a deterministic lattice model describing the motion of an infinite system of oppositely charged particles under the action of a constant electric field. As an application this model represents a traffic flow of cars…
The classical dynamics of a particle that is driven by a rapidly oscillating potential (with frequency $\omega$) is studied. The motion is separated into a slow part and a fast part that oscillates around the slow part. The motion of the…
We investigate the stationary states of one-dimensional driven diffusive systems, coupled to boundary reservoirs with fixed particle densities. We argue that the generic phase diagram is governed by an extremal principle for the macroscopic…
We explore the dynamics of active elements performing persistent random motion with fluctuating active speed and in the presence of translational noise in a $d$-dimensional harmonic trap, modeling active speed generation through an…
We study the problem of phase separation in systems with a positive definite order parameter, and in particular, in systems with absorbing states. Owing to the presence of a single minimum in the free energy driving the relaxation kinetics,…
We study numerically the coarsening dynamics of the Ising model on a regular lattice with random bonds and on deterministic fractal substrates. We propose a unifying interpretation of the phase-ordering processes based on two classes of…
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in…