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A method for practical realization of the inverse scattering transform method for the Korteweg-de Vries equation is proposed. It is based on analytical representations for Jost solutions and for integral kernels of transformation operators…
The paper introduces a new characterisation of strictly positive definiteness for kernels on the 2-sphere without assuming the kernel to be radially (isotropic) or axially symmetric. The results use the series expansion of the kernel in…
The coplete analysis of the model-independent leading radiative corrections to cross-section and polarization observables in semi-inclusive deep-inelastic electron-nucleus scattering with detection of a proton and scattered electron in…
Mie theory is one of the main tools describing scattering of propagating electromagnetic waves by spherical particles. Evanescent optical fields are also scattered by particles and exert radiation forces which can be used for optical…
Traditional interpolation techniques for particle tracking include binning and convolutional formulas that use pre-determined (i.e., closed-form, parameteric) kernels. In many instances, the particles are introduced as point sources in time…
Dealing with land cover classification of the new image sources has also turned to be a complex problem requiring large amount of memory and processing time. In order to cope with these problems, statistical learning has greatly helped in…
Compton scattering of polarized radiation in a strong magnetic field is considered. The recipe for calculation of the scattering matrix elements, the differential and total cross sections based on quantum electrodynamic (QED) second order…
Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power…
A method of approximating the inverse Radon transform on the plane by integrating against a smooth kernel is investigated. For piecewise smooth integrable functions, convergence theorems are proven and Gibbs phenomena are ruled out.…
Some general remarks about integral transform approaches to response functions are made. Their advantage for calculating cross sections at energies in the continuum is stressed. In particular we discuss the class of kernels that allow…
Frequency domain Mie solutions to scattering from spheres have been used for a long time. However, deriving their transient analogue is a challenge as it involves an inverse Fourier transform of the spherical Hankel functions (and their…
Many estimation problems in astrophysics are highly complex, with high-dimensional, non-standard data objects (e.g., images, spectra, entire distributions, etc.) that are not amenable to formal statistical analysis. To utilize such data and…
The theory of radiative transfer provides the link between the physical conditions in an astrophysical object and the observable radiation which it emits. Thus accurately modelling radiative transfer is often a necessary part of testing…
We extend our framework for 3D radiative transfer calculations with a non-local operator splitting methods along (full) characteristics to spherical and cylindrical coordinate systems. These coordinate systems are better suited to a number…
A fast method for the computation of layer potentials that arise in acoustic scattering is introduced. The principal idea is to split the singular kernel into a smooth and a local part. The potential due to the smooth part is computed…
The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the…
We introduce a non-exponential radiative framework that takes into account the local spatial correlation of scattering particles in a medium. Most previous works in graphics have ignored this, assuming uncorrelated media with a uniform,…
The scattering of scalar waves by a set of scatterers is considered. It is proven that the scattered field can be represented as an integral supported by any smooth surface enclosing the scatterers. This is a generalization of the series…
We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media.
A method for the nonperturbative calculation of scattering amplitudes and cross sections is discussed in the context of light-cone quantization. The Lanczos-based recursion method of Haydock is suggested for the computation of matrix…