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The bounded rationality plays a vital role in the collective behavior of the evacuation process. Also investigating human behavior in such an extreme situation is a continuing concern within social psychology. In this paper, we construct a…
The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed…
We investigate toy dynamical models of energy-level repulsion in quantum eigenvalue sequences. We focus on parametric (with respect to a running coupling or "complexity" parameter) stochastic processes that are capable of relaxing towards a…
The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The…
We study the critical behavior of the nonequilibrium dynamics and of the steady states emerging from the competition between coherent and dissipative dynamics close to quantum phase transitions. The latter is induced by the coupling of the…
This paper focuses on the connections between four stochastic and deterministic models for the motion of straight screw dislocations. Starting from a description of screw dislocation motion as interacting random walks on a lattice, we prove…
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…
A class of stochastic individual-based models, written in terms of coupled velocity jump processes, is presented and analysed. This modelling approach incorporates recent experimental findings on behaviour of locusts. It exhibits nontrivial…
The aim of this review is to provide a concise overview of some of the generic approaches that have been developed to deal with the statistical description of large systems of interacting dissipative 'units'. The latter notion includes,…
We consider a dc-driven damped sine-Gordon model with a small nonlinear spatial-disorder term, onto which a sinusoidal modulation is superimposed. It describes, e.g., a weakly disordered system with a regular grain structure. We demonstrate…
A two-lane exclusion process is studied where particles move in the two lanes in opposite directions and are able to change lanes. The focus is on the steady state behavior in situations where a positive current is constrained to an…
Two generically different but universal dynamical quantum many-body behaviors are discovered by probing the stability of trapped fragmented bosonic systems with strong repulsive finite/long range inter-particle interactions. We use…
In the work of Colliander et al. (2010), a minimal lattice model was constructed describing the transfer of energy to high frequencies in the defocusing nonlinear Schr\"odinger equation. In the present work, we present a systematic study of…
We investigate fluid transport in random velocity fields with unsteady drift. First, we propose to quantify fluid transport between flow regimes of different characteristic motion, by escape probability and mean residence time. We then…
We study the dissipative dynamics of a class of interacting ``gamma-matrix'' spin models coupled to a Markovian environment. For spins on an arbitrary graph, we construct a Lindbladian that maps to a non-Hermitian model of free Majorana…
The exit problem for small perturbations of a dynamical system in a domain is considered. It is assumed that the unperturbed dynamical system and the domain satisfy the Levinson conditions. We assume that the random perturbation affects the…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
This work focuses on a class of regime-switching jump diffusion processes with a countably infinite state space for the discrete component. Such processes can be used to model complex hybrid systems in which both structural changes, small…
Invariant manifolds play an important role in organizing global dynamical behaviors. For example, it is found that in multi-well conservative systems where the potential energy wells are connected by index-1 saddles, the motion between…
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearest neighbor exchanges that conserve each of the three species. For the case in which the…