Related papers: Reflecting Diffusion Process on Time-Inhomogeneous…
This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due…
We consider the boundary crossing problem for time-homogeneous diffusions and general curvilinear boundaries. Bounds are derived for the approximation error of the one-sided (upper) boundary crossing probability when replacing the original…
We show that the delay time distribution for wave reflection from a one-dimensional random potential is related directly to that of the reflection coefficient, derived with an arbitrarily small but uniform imaginary part added to the random…
This paper considers a time-fractional diffusion-wave equation with a high-contrast heterogeneous diffusion coefficient. A numerical solution to this problem can present great computational challenges due to its multiscale nature.…
Reflectance bounds the frequency spectrum of illumination in the object appearance. In this paper, we introduce the first stochastic inverse rendering method, which recovers the attenuated frequency spectrum of an illumination jointly with…
This paper derives physically meaningful boundary conditions for fractional diffusion equations, using a mass balance approach. Numerical solutions are presented, and theoretical properties are reviewed, including well-posedness and steady…
We obtain explicit expressions for one unknown thermal coefficient (among the conductivity, mass density, specific heat and latent heat of fusion) of a semi-infinite material through the one-phase fractional Lam\'e-Clapeyron-Stefan problem…
We discuss how the reflective scattering would affect elastic scattering in the region of small and moderate values of $-t$, in particular, we demonstrate that diffractive pattern in the angular distribution will be kept in a modified form.
The diffraction of electromagnetic plane waves by a rectangular grating formed by discrete steps in the interface of a homogeneous, isotropic, linear, negative phase--velocity (negative index) material with free space is studied using the…
In the recent literature, the g-subdiffusion equation involving Caputo fractional derivatives with respect to another function has been studied in relation to anomalous diffusions with a continuous transition between different subdiffusive…
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material…
A probabilistic framework for studying single-particle diffusion in partially absorbing media has recently been developed in terms of an encounter-based approach. The latter computes the joint probability density (generalized propagator)…
Continuous-time long-term event prediction plays an important role in many application scenarios. Most existing works rely on autoregressive frameworks to predict event sequences, which suffer from error accumulation, thus compromising…
Simple finite differencing of the anisotropic diffusion equation, where diffusion is only along a given direction, does not ensure that the numerically calculated heat fluxes are in the correct direction. This can lead to negative…
We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression…
Transparent surfaces, such as glass, create complex reflections that obscure images and challenge downstream computer vision applications. We introduce Flash-Split, a robust framework for separating transmitted and reflected light using a…
As a generalization to the heat semigroup on the Heisenberg group, the diffusion semigroup generated by the subelliptic operator $L:=\ff 1 2 \sum_{i=1}^m X_i^2$ on $\R^{m+d}:= \R^m\times\R^d$ is investigated, where $$X_i(x,y)= \sum_{k=1}^m…
We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which,…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
In a preceding paper, Mukhopadhyay and I studied the diffusive motion of a tagged molecule in a heterogeneous glass-forming liquid at temperatures just above a glass transition. Among other features of this system, we postulated a relation…