Related papers: Carr-Nadtochiy's Weak Reflection Principle for Mar…
We present a conception of the slow diffusion processes in the Euclidean spaces $\Bbb R^m, \; m\ge 1$, based on the theory of random flights with small constant speed that are driven by a homogeneous Poisson process of small rate. The slow…
In this paper, we investigate the construction of a diffusion process whose time-marginal densities are constrained to belong to a given set at all time. The construction is obtained from a penalization approximation to the constraint set,…
Resonant Andreev reflection through superconductor-carbon-nanotube devices was investigated theoretically with a focus on the superconducting proximity effect. Consistent with a recent experiment, we find that for high transparency devices…
In this work we investigate an inverse coefficient problem for the one-dimensional subdiffusion model, which involves a Caputo fractional derivative in time. The inverse problem is to determine two coefficients and multiple parameters (the…
Analytic and passivity properties of reflection and transmission coefficients of thin-film multilayered stacks are investigated. Using a rigorous formalism based on the inverse Helmholtz operator, properties associated to causality…
We examine the applicability of the weak wave turbulence theory in explaining experimental scaling results obtained for the diffusion and relative diffusion of particles moving on turbulent surface waves. For capillary waves our theoretical…
We solve the large deviations of the Kardar-Parisi-Zhang (KPZ) equation in one dimension at short time by introducing an approach which combines field theoretical, probabilistic and integrable techniques. We expand the program of the weak…
Bulk matter produced in heavy ion collisions has multiple conserved quantum numbers like baryon number, strangeness and electric charge. The diffusion process of these charges can be described by a diffusion matrix describing the…
Monte Carlo (MC) simulations of transport in random porous networks indicate that for high variances of the log-normal permeability distribution, the transport of a passive tracer is non-Fickian. Here we model this non-Fickian dispersion in…
We comment on a recent paper by Li and Wang [Phys. Rev. Lett. 91, 044301 (2003)], and argue that their results violate the non-existence of a characteristic time scale in subdiffusive systems.
A key optical parameter characterizing the existence of negative refraction in a thin layer of a composite material is the effective refractive index of an equivalent, homogenized layer with the same physical thickness as the initial…
This paper explicitly computes the transition densities of a spectrally negative stable process with index greater than one, reflected at its infimum. First we derive the forward equation using the theory of sun-dual semigroups. The…
This paper investigates an incompressible chemotaxis-Navier-Stokes system with slow $p$-Laplacian diffusion \begin{eqnarray} \left\{\begin{array}{lll} n_t+u\cdot\nabla n=\nabla\cdot(|\nabla n|^{p-2}\nabla n)-\nabla\cdot(n\chi(c)\nabla c),&…
There has been interest in the spin transport properties of the Aubry-Andre-Harper model at high temperatures under weak integrability breaking, in particular for small interactions or small fields. We present old unpublished and new…
Exploiting a Lagrangian strategy we present a numerical study for both perturbative and nonperturbative regions of the Kraichnan advection model. The major result is the numerical assessment of the first-order $1/d$-expansion by M.…
Given a domain G, a reflection vector field d(.) on the boundary of G, and drift and dispersion coefficients b(.) and \sigma(.), let L be the usual second-order elliptic operator associated with b(.) and \sigma(.). Under suitable…
We present a multichannel quantum-defect theory for slow atomic collisions that takes advantages of the analytic solutions for the long-range potential, and both the energy and the angular-momentum insensitivities of the short-range…
The diffusion of uni-directional magnetic fields by two dimensional turbulent flows in a weakly ionized gas is studied. The fields here are orthogonal to the plane of fluid motion. This simple model arises in the context of the decay of the…
These comments aim to correct some apparent weaknesses in the theory of field electron emission given in a recent paper about nanoscale vacuum channel transistors, and to improve the presentation of this theory. In particular, it is argued…
A Comment on the Letter by Victor Gurarie and Alexander E. Lobkovsky, Phys. Rev. Lett. 88, 178301 (2002). The authors of the Letter offer a Reply.