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Recently, diffusion models have been used to solve various inverse problems in an unsupervised manner with appropriate modifications to the sampling process. However, the current solvers, which recursively apply a reverse diffusion step…
Context. The numerical modeling of the generation and transfer of polarized radiation is a key task in solar and stellar physics research and has led to a relevant class of discrete problems that can be reframed as linear systems. In order…
The development of radiation hydrodynamical methods that are able to follow gas dynamics and radiative transfer self-consistently is key to the solution of many problems in numerical astrophysics. Such fluid flows are highly complex, rarely…
We discuss the electromagnetic scattering and radiation problems of multilayered spheres, reviewing the history of the Lorentz-Mie theory and the numerical stability issues encountered in handling multilayered spheres. By combining…
Radiative energy transfer between closely spaced bodies is known to be significantly larger than that predicted by classical radiative transfer because of tunneling due to evanescent waves. Theoretical analysis of near--field radiative…
In the dynamic diffusion limit of radiation hydrodynamics, advection dominates diffusion; the latter primarily affects small scales and has negligible impact on the large scale flow. The radiation can thus be accurately regarded as an ideal…
Given a set of heterogeneous source datasets with their classifiers, how can we quickly find the most useful source dataset for a specific target task? We address the problem of measuring transferability between source and target datasets,…
A new lower bound on the average reconstruction error variance of multidimensional sampling and reconstruction is presented. It applies to sampling on arbitrary lattices in arbitrary dimensions, assuming a stochastic process with constant,…
This paper is concerned with the electromagnetic inverse scattering problem that aims to determine the location and shape of anisotropic scatterers from far field data (at a fixed frequency). We study the orthogonality sampling method which…
We discuss the radiative transfer theory for translucent clouds illuminated by an extended background source. First we derive a rigorous solution based on the assumption that multiple scattering produce an isotropic flux. Then we derive a…
In this paper, we study the diffusion approximation for slow-fast stochastic differential equations with state-dependent switching, where the slow component $X^{\varepsilon}$ is the solution of a stochastic differential equation with…
Aspects of of plane wave electromagnetic scattering by a radially inhomogeneous sphere is discussed. The vector problem is reduced to two scalar radial `Schr\"odinger-like' equations, and a connection with time-independent potential…
In this paper, an efficient iterative method is proposed for solving multiple scattering problem in locally inhomogeneous media. The key idea is to enclose the inhomogeneity of the media by well separated artificial boundaries and then…
The problem of radio wave reflection from an optically thick plane monotonous layer of magnetized plasma is considered at present work. The plasma electron density irregularities are described by spatial spectrum of an arbitrary form. The…
Problems with localized nonhomogeneous material properties present well-known challenges for numerical simulations. In particular, such problems may feature large differences in length scales, causing difficulties with meshing and…
This paper investigates the optimization of beamforming design in a system with integrated sensing and communication (ISAC), where the base station (BS) sends signals for simultaneous multiuser communication and radar sensing. We aim at…
The description of the inhomogeneity of the cosmic ray spectrum in the region of 10 TV, which is observed in experimental data, in terms of isotropic diffusion from a single close source is considered. It is shown that such a description is…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
This paper is concerned with the inverse electromagnetic scattering problem for anisotropic media. We use the interior resonant modes to develop an inverse scattering scheme for imaging the scatterer. The whole procedure consists of three…
We present a new finite volume scheme for anisotropic heterogeneous diffusion problems on unstructured irregular grids, which simultaneously gives an approximation of the solution and of its gradient. In the case of simplicial meshes, the…