相关论文: The Steady State Distribution of the Master Equati…
We introduce the concept of stationary metastable states (SMS's) in the presence of another more stable state. The stationary nature allows us to study SMS's by using a restricted partition function formalism as advocated by Penrose and…
The quantum master equation obtained by generalizing the geometric formulation of nonequilibrium thermodynamics to dissipative quantum systems is seriously nonlinear. We argue that nonlinearity occurs naturally in the step from reversible…
A novel geometric formalism for statistical estimation is applied here to the canonical distribution of classical statistical mechanics. In this scheme thermodynamic states, or equivalently, statistical mechanical states, can be…
Reaction diffusion systems with Turing instability and mass conservation are studied. In such systems, abrupt decays of stripes follow quasi-stationary states in sequence. At steady state, the distance between stripes is much longer than…
A longstanding goal of nonequilibrium statistical mechanics has been to extend the conceptual power of the Boltzmann distribution to driven systems. We report some new progress towards this goal. Instead of writing the nonequilibrium…
In this paper, global-in-time existence and blow up results are shown for a reaction-diffusion equation appearing in the theory of aggregation phenomena (including chemotaxis). Properties of the corresponding steady-state problem are also…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the corresponding stochastic reaction-diffusion equation is…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…
The (asymptotic) behaviour of the second moment of solutions to stochastic differential equations is treated in mean-square stability analysis. This property is discussed for approximations of infinite-dimensional stochastic differential…
The generalized master equation with two times, introduced in earlier, applies to the problem of diffusion in an time-dependent (in general inhomogeneous) external field. We consider the case of the quasi Fokker-Planck approximation, when…
We study the electron magnetohydrodynamics (MHD) in two dimensional geometry, which has a rich family of steady states. In an anisotropic resistivity context, we show global in time existence of small smooth solution near a shear type…
The stability properties and perturbation-induced dynamics of the full set of stationary states of the nonlinear Schroedinger equation are investigated numerically in two physical contexts: periodic solutions on a ring and confinement by a…
We report a general class of steady and transient states of granular gases. We find that the kinetic theory of inelastic gases admits stationary solutions with a power-law velocity distribution, f(v) ~ v^(-sigma). The exponent sigma is…
The existence and uniqueness of the stationary distribution of the numerical solution generated by the stochastic theta method is studied. When the parameter theta takes different values, the requirements on the drift and diffusion…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
The steady state of the Fokker-Planck equation corresponding to a density dependent one-step process is approximated by a suitable normal distribution. Starting from the master equations of the process, written in terms of the time…
A growing body of theoretical and empirical evidence shows that the global steady-state distributions of many equilibrium and nonequilibrium systems approximately satisfy an analogue of the Boltzmann distribution, with a local dynamical…
The propagation of a fast particle in a low-density gas at thermal equilibrium is studied in the context of quantum mechanics. A quantum master equation in the Redfield form governing the reduced density matrix of the particle is derived…
We discuss the existence and nonexistence of solutions to the steady-state Gierer-Meinhardt system $$ \begin{cases} \displaystyle -\Delta u=\frac{u^p}{v^q}+\lambda \rho(x) \,, u>0 &\quad\mbox{ in }\mathbb{R}^N\setminus K,\\[0.1in]…