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The possible ways to describe the states of a system of many hard spheres are considered, in particular by means of functions describing correlations of states. It is stated an approach to the description of the evolution based on the…
The gravitational evolution of the genus and other statistics of isodensity contours of the density field is derived analytically in a weakly nonlinear regime using second-order perturbation theory. The effect of final smoothing in…
We study a 1D nonlinear Schr{\"o}dinger equation appearing in the description of a particle inside an atomic nucleus. For various nonlinearities, the ground states are discussed and given in explicit form. Their stability is studied…
We use event driven simulations to analyze glassy dynamics as a function of density and energy dissipation in a two-dimensional bidisperse granular fluid under stationary conditions. Clear signatures of a glass transition are identified,…
In previous papers we have introduced a natural nonequilibrium free energy by considering the functional describing the large fluctuations of stationary nonequilibrium states. While in equilibrium this functional is always convex, in…
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
The process of phase separation of binary systems is described by the Cahn-Hilliard equation. The main objective of this article is to give a classification on the dynamic phase transitions for binary systems using either the classical…
In the background dynamics of a spatially flat FLRW model of the universe, we investigate an interacting dark energy model in the context of Lyra's geometry. Pressure-less dust is considered as dark matter, mass of which varies with time…
Pattern formation often occurs in spatially extended physical, biological and chemical systems due to an instability of the homogeneous steady state. The type of the instability usually prescribes the resulting spatio-temporal patterns and…
A one dimensional stochastic exclusion process with two species of particles, $+$ and $-$, is studied where density of each species can fluctuate but the total particle density is conserved. From the exact stationary state weights we show…
Point-like topological defects are singular configurations that occur in a variety of in and out of equilibrium systems with two-dimensional orientational order. As they are associated with a nonzero circuitation condition, the presence of…
We study the steady state resulting from instabilities in crystals driven through a dissipative medium, for instance, a colloidal crystal which is steadily sedimenting through a viscous fluid. The problem involves two coupled fields, the…
We study the influence of the preparation of an open quantum system on its reduced time evolution. In contrast to the frequently considered case of an initial preparation where the total density matrix factorizes into a product of a system…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
The dynamics of a system composed of inelastic hard spheres or disks that are confined between two parallel vertically vibrating walls is studied (the vertical direction is defined as the direction perpendicular to the walls). The distance…
Planets and stars are able to generate coherent large-scale magnetic fields by helical convective motions in their interiors. This process, known as hydromagnetic dynamo, involves nonlinear interaction between the flow and magnetic field.…
Dynamical systems studies of differential equations often focus on the behavior of solutions near critical points and on invariant manifolds, to elucidate the organization of the associated flow. In addition, effective methods, such as the…
An ultracold gas is considered, loaded into a lattice, each site of which is formed by a double-well potential. Initial conditions, after the loading, correspond to a nonequilibrium state. The nonlinear dynamics of the system, starting with…
The decay of a passive scalar in a three-dimensional chaotic flow is studied using high-resolution numerical simulations. The (volume-preserving) flow considered is a three-dimensional extension of the randomised alternating sine flow…
Measuring, characterizing and modelling the slow dynamics of glassy soft matter is a great challenge, with an impact that ranges from industrial applications to fundamental issues in modern statistical physics, such as the glass transition…