Related papers: Accumulation time of diffusion in a 2D singularly …
We investigate Lagrangian relative dispersion in direct numerical simulation of two-dimensional inverse cascade turbulence. The analysis is performed by using both standard fixed time statistics and an exit time approach. Our results are in…
We study the time-dependent properties of double quantum dots coupled to two reservoirs using the nonequilibrium Green function method. For an arbitrary time-dependent bias, we derive an expression for the time-dependent electron density of…
I present a first-principles theory of diffusion-limited aggregation in two dimensions. A renormalized mean-field approximation gives the form of the unstable manifold for branch competition, following the method of Halsey and Leibig [Phys.…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We consider the penetration length $l$ of random walkers diffusing in a medium of perfect or imperfect absorbers of number density $\rho$. We solve this problem on a lattice and in the continuum in all dimensions $D$, by means of a…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
We consider nonequilibrium critical dynamics of the two-dimensional Ising model for which the initial state is prepared by switching on random fields with zero mean and variance $H$. In the initial state there is no magnetic order but the…
Our aim is to study the backward problem, i.e. recover the initial data from the terminal observation, of the subdiffusion with time dependent coefficients. First of all, by using the smoothing property of solution operators and a…
In this paper, we study the asymptotic estimate of solution for a mixed-order time-fractional diffusion equation in a bounded domain subject to the homogeneous Dirichlet boundary condition. Firstly, the unique existence and regularity…
We investigate the asymptotic behavior of probability measures associated with stochastic dynamical systems featuring either globally contracting or $B_{r}$-contracting drift terms. While classical results often assume constant diffusion…
Using pointwise semigroup techniques, we establish sharp rates of decay in space and time of a perturbed reaction diffusion front to its time-asymptotic limit. This recovers results of Sattinger, Henry and others of time-exponential…
On certain self-similar substrates the time behavior of a random walk is modulated by logarithmic periodic oscillations on all time scales. We show that if disorder is introduced in a way that self-similarity holds only in average, the…
We analyze a space-time hybridizable discontinuous Galerkin method to solve the time-dependent advection-diffusion equation on deforming domains. We prove stability of the discretization in the advection-dominated regime by using weighted…
We study the inverse problem of recovering a spatially dependent variable order in a time-fractional diffusion model from the boundary flux measurement generated by a single boundary excitation. It arises in the identification of…
At a composition far above the percolation threshold, the resistance of a composite sample increases with time due to Joule heating as a constant current of sufficiently large value is passed through the sample. If the current is less than…
Discrete diffusion models with absorbing processes have shown promise in language modeling. The key quantities to be estimated are the ratios between the marginal probabilities of two transitive states at all timesteps, called the concrete…
In studying the time evolution of isolated many-body quantum systems, a key focus is determining whether the system undergoes relaxation and reaches a steady state at a given point in time. Traditional approaches often rely on specific…
We introduce a discrete-time random walk model on a one-dimensional lattice with a nonconstant sojourn time and prove that the discrete density converges to a solution of a continuum diffusion equation. Our random walk model is not…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
In this work, a two-dimensional time-fractional subdiffusion model is developed to investigate the underlying transport phenomena evolving in a binary medium comprised of two sub-domains occupied by homogeneous material. We utilise an…