相关论文: Nonlocal diffusion currents at the nanoscale

This is part II of our study on the free boundary problems with nonlocal and local diffusions. In part I, we obtained the existence, uniqueness, regularity and estimates of global solution. In part II here, we show a spreading-vanishing…

We are interested in the threshold phenomena for propagation in nonlocal diffusion equations with some compactly supported initial data. In the so-called bistable and ignition cases, we provide the first quantitative estimates for such…

An investigation of the effect of surface diffusion in random deposition model is made by analytical methods and reasoning. For any given site, the extent to which a particle can diffuse is decided by the morphology in the immediate…

We study the effect of correlations between impurity potentials in different layers on the Coulomb drag in a double-layer electron system. It is found that for strongly correlated potentials the drag in the diffusive regime is considerably…

We analyze the propagation properties of the numerical versions of one and two-dimensional wave equations, semi-discretized in space by finite difference schemes. We focus on high-frequency solutions whose propagation can be described, both…

We study the curl-div-system with variable coefficients and a nonlocal homogenisation problem associated with it. Using, in part refining, techniques from nonlocal $H$-convergence for closed Hilbert complexes, we define the appropriate…

We study the role of global system topology in governing deep thermalization, the relaxation of a local subsystem towards a maximally-entropic, uniform distribution of post-measurement states, upon observing the complementary subsystem in a…

We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a non-universal space-time correlation which depends explicitly on the short-distance properties of disorder, source size,…

Long, cylindrical metal nanowires have recently been observed to form and be stable for seconds at a time at room temperature. Their stability and structural dynamics is well described by a continuum model, the nanoscale free-electron…

Via nonlocality distillation, a number of copies of a given nonlocal correlation can be turned into a new correlation displaying a higher degree of nonlocality. Apart from its clear relevance in situations where nonlocality is a resource,…

We prove existence and uniqueness of a reaction-diffusion equation whose diffusivity is a non-linear functional of the boundary temperature. We do this by studying systems of one-dimensional reflecting diffusions whose noise is a function…

Richardson's theory of turbulent particle pair diffusion [Richardson, L. F. Proc. Roy. Soc. Lond. A 100, 709--737, 1926], based upon observational data, is equivalent to a locality hypothesis in which the turbulent pair diffusivity $(K)$…

Consider a particle diffusing in a confined volume which is divided into two equal regions. In one region the diffusion coefficient is twice the value of the diffusion coefficient in the other region. Will the particle spend equal…

We systematically study linear and nonlinear wave propagation in a chain composed of piecewise-linear bistable springs. Such bistable systems are ideal testbeds for supporting nonlinear wave dynamical features including transition and…

In recent work, we have proposed a theory for the derivation of an exact nonlinear dispersion relation for elastic wave propagation which here we consider for a thin rod (linearly nondispersive) and a thick rod (linearly dispersive). The…

Reactio-nonlocal diffusion equations model nonlocal transport and anomalous diffusion by replacing the Laplacian with a fractional power, capturing diffusion mechanisms beyond Brownian motion. We primarily study the semilinear problem \[…

Acceleration-induced nonlocality is discussed and a simple field theory of nonlocal electrodynamics is developed. The theory involves a pair of real parameters that are to be determined from observation. The implications of this theory for…

We study a system of particles which jump on the sites of the interval $[1,L]$ of $\mathbb Z$. The density at the boundaries is kept fixed to simulate the action of mass reservoirs. The evolution depends on two parameters $\lambda'\ge 0$…

Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…

Using an attractive Hubbard model we examine spatial variations of superconducting order parameter and local charge on a two dimensional lattice. For various band filling we show the effect of destruction of the order parameter around a…