Related papers: A simple criterion for identifying slow-fast relax…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
A critical review of experimental studies of the so-called 'slow light' arising due to anomalously high steepness of the refractive index dispersion under conditions of electromagnetically induced transparency or coherent population…
A common problem to all applications of linear finite dynamical systems is analyzing the dynamics without enumerating every possible state transition. Of particular interest is the long term dynamical behaviour. In this paper, we study the…
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or…
Optical tweezers setup is often used to probe the motion of individual tracer particle, which promotes the study of relaxation dynamics of a generic process confined in a harmonic potential. We uncover the dependence of ensemble- and…
The relaxion mechanism is a novel solution to the hierarchy problem. In this first statistical analysis of the relaxion mechanism, we quantify the relative plausibility of a QCD and a non-QCD relaxion model versus the Standard Model with…
We present Monte Carlo simulations in a modification of the north-or-east-or-front model recently investigated by Berthier and Garrahan [J. Phys. Chem. B 109, 3578 (2005)]. In this coarse-grained model for relaxation in supercooled liquids,…
Simple dynamical systems -- with a small number of degrees of freedom -- can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small…
In this paper, we determine a condition of applicability of a very simple formalism for the calculation of a fast process taking place in a non-equilibrium medium, in which the particle distribution functions are frozen in time. Indeed, a…
A method is provided for approximating random slow manifolds of a class of slow-fast stochastic dynamical systems. Thus approximate, low dimensional, reduced slow systems are obtained analytically in the case of sufficiently large time…
An autonomous system of ordinary differential equations describing nonlinear oscillations on the plane is considered. The influence of time-dependent perturbations decaying at infinity in time is investigated. It is assumed that the…
We investigate the static and dynamic properties of a celebrated model of social segregation, providing a complete explanation of the mechanisms leading to segregation both in one- and two-dimensional systems. Standard statistical physics…
In this paper we present necessary and sufficient conditions for the existence of a unique solution to the relaxed commutant lifting problem. The obtained conditions are more complicated than those for the classical commutant lifting…
Relaxation processes of dislocation systems are studied by two-dimensional dynamical simulations. In order to capture generic features, three physically different scenarios were studied and power-law decays found for various physical…
Minimalist theories of complex systems are broadly of two kinds: mean-field and axiomatic. So far all theories of complex properties absent from simple systems and intrinsic to glasses are axiomatic. Stretched Exponential Relaxation (SER)…
Although there have been many studies of statistical mechanical models of magnetic friction, most of these have focused on the behavior in the steady state. In this study, we prepare a system composed of a chain and a lattice of Ising spins…
Scaling transformations involving a small parameter ({\em degenerate scalings}) are frequently used for ordinary differential equations that model (bio-) chemical reaction networks. They are motivated by quasi-steady state (QSS) of certain…
We study sufficient conditions for stability and recurrence in a class of singularly perturbed stochastic hybrid dynamical systems. The systems considered combine multi-time-scale deterministic continuous-time dynamics, modeled by…
The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…
Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural…