Related papers: Exact solution for the non-equilibrium attractor i…
We reformulate the Boltzmann equation in the relaxation time approximation undergoing Bjorken flow in terms of a novel partial differential equation for the generating function of the moments of the distribution function. This is used to…
We establish the existence of a far-from-equilibrium attractor in weakly-coupled gauge theory undergoing one-dimensional Bjorken expansion. We demonstrate that the resulting far-from-equilibrium evolution is insensitive to certain features…
Understanding how hydrodynamics emerges rapidly in the medium produced by relativistic heavy-ion collisions remains a key theoretical challenge. While the attractor solution -- manifesting as a non-thermal fixed point during the early…
We present exact solutions of the (0+1)-dimensional kinetic equation for a massive gas in the relaxation time approximation. At first, we analyse the case of classical statistics and argue that the traditional second-order hydrodynamics…
In this paper, C1-conforming element methods are analyzed for the stream function formulation of a single layer non-stationary quasi-geostrophic equation in the ocean circulation model. In its first part, some new regularity results are…
In this paper, we study the asymptotic behavior of the solutions of a nonautonomous differential inclusion modeling a reaction-diffusion equation with a discontinuous nonlinearity. We obtain first several properties concerning the…
We consider an ordinary differential equation with a unique hyperbolic attractor at the origin, to which we add a small random perturbation. It is known that under general conditions, the solution of this stochastic differential equation…
We consider non-equilibrium evolution of non-Gaussian fluctuations within relativistic hydrodynamics relevant for the QCD critical point search in heavy-ion collision experiments. We rely on the hierarchy of relaxation time scales, which…
In this paper, we investigate the continuity of the attractors in time-dependent phase spaces. (i) We establish two abstract criteria on the upper semicontinuity and the residual continuity of the pullback $\mathscr D$-attractor with…
We study the one-dimensional boost-invariant Boltzmann equation in the relaxation-time approximation using special moments of the distribution function for a system with a finite particle mass. The infinite hierarchy of moments can be…
We exactly solve the one-dimensional boost-invariant Boltzmann equation in the relaxation time approximation for arbitrary shear viscosity. The results are compared with the predictions of viscous and anisotropic hydrodynamics. Studying…
We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the…
A numerical method for approximating weak solutions of an aggregation equation with degenerate diffusion is introduced. The numerical method consists of a stabilized finite element method together with a mass lumping technique and an extra…
A parametric family of reaction-diffusion equations with nonlocal viscosity is considered. Existence of solutions and actually of pullback attractors is known from previous works. In this paper we obtain a robustness result of the…
In this paper, we shall investigate the existence and upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with a strong damping in the time-dependent space $X_t$. After deriving the existence and…
The hydrodynamic attractor is a concept that describes universal equilibration behavior in which systems lose microscopic details before hydrodynamics becomes applicable. We propose a setup to observe hydrodynamic attractors in ultracold…
We consider dynamical behavior of non-autonomous wave-type evolutionary equations with nonlinear damping, critical nonlinearity, and time-dependent external forcing which is translation bounded but not translation compact (i.e., external…
We develop an iterative, numerically exact approach for the treatment of nonequilibrium quantum transport and dissipation problems that avoids the real-time sign problem associated with standard Monte Carlo techniques. The method requires a…
We consider a hydrodynamic system that models the Smectic-A liquid crystal flow. The model consists of the Navier-Stokes equation for the fluid velocity coupled with a fourth-order equation for the layer variable $\vp$, endowed with…
We study the non-equilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a…