相关论文: Local equilibrium and retardation revisited

Takens' Embedding Theorem asserts that when the states of a hidden dynamical system are confined to a low-dimensional attractor, complete information about the states can be preserved in the observed time-series output through the delay…

In this paper, we study averaging principles for a class of time-inhomogeneous stochastic differential equations (SDEs) with slow and fast time-scales, where the drift term in the fast component is time-dependent and only partially…

The Eulerian variational formulation is presented to obtain governing equations of the electromagnetic turbulent gyrokinetic system. A local momentum balance in the system is derived from the invariance of the Lagrangian of the system under…

The aim of this paper is to introduce a finite element formulation within Arbitrary Lagrangian Eulerian framework with vanishing discrete {\it Space Conservation Law} (SCL) for differential equations on time dependent domains. The novelty…

We consider mixing problems in the form of transient convection--diffusion equations with a velocity vector field with multiscale character and rough data. We assume that the velocity field has two scales, a coarse scale with slow spatial…

In this paper, we present a thorough von Neumann stability analysis of explicit and implicit Arbitrary-Lagrangian-Eulerian (ALE) ADER discontinuous Galerkin (DG) methods on classical and degenerate spacetime geometries for hyperbolic…

The Fractional Langevin Equation (FLE) describes a non-Markovian Generalized Brownian Motion with long time persistence (superdiffusion), or anti-persistence (subdiffusion) of both velocity-velocity correlations, and position increments. It…

Discrete Element Methods (DEM), i.e.~the simulation of many rigid particles, suffer from very stiff differential equations plus multiscale challenges in space and time. The particles move smoothly through space until they interact almost…

The dispersion of solute in porous media shows a non-linear increase in the transition from diffusion to advection dominated dispersion as the flow velocity is raised. In the past, the behavior in this intermediate regime has been explained…

Semi-discrete Galerkin formulations of transient wave equations, either with conforming or discontinuous Galerkin finite element discretizations, typically lead to large systems of ordinary differential equations. When explicit time…

Using a Lagrangian framework, we discuss different conceptualizations of the blockscale dispersion tensor. We distinguish effective and ensemble blockscale dispersion, which measure the impact of subscale velocity fluctuations on solute…

Defect transport is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant…

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…

An approach that extends equilibrium thermodynamics principles to out-of-equilibrium systems is based on the local equilibrium hypothesis. However, the validity of the a priori assumption of local equilibrium has been questioned due to the…

We consider the problem of inferring latent stochastic differential equations (SDEs) with a time and memory cost that scales independently with the amount of data, the total length of the time series, and the stiffness of the approximate…

We study the global and the local transport and diffusion in the case of the standard map, by calculating the diffusion exponent $\mu$. In the global case we find that the mean diffusion exponent for the whole phase space is either $\mu=1$,…

Spatiotemporal forecasting in physical systems, such as large-scale traffic networks, requires modeling a dual dynamic: continuous macroscopic rhythms and discrete, unpredictable microscopic shocks. While Neural Ordinary Differential…

The coupling between advection and diffusion in position space can often lead to enhanced mass transport compared to diffusion without flow. An important framework used to characterize the long-time diffusive transport in position space is…

Accurately predicting spatio-temporal network traffic is essential for dynamically managing computing resources in modern communication systems and minimizing energy consumption. Although spatio-temporal traffic prediction has received…

Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference…