Related papers: A 3D radiative transfer framework: IV. spherical &…
We provide a comprehensive survey of splitting and composition methods for the numerical integration of ordinary differential equations (ODEs). Splitting methods constitute an appropriate choice when the vector field associated with the ODE…
We present new methods for radiative transfer on hierarchial grids. We develop a new method for calculating the scattered flux that employs the grid structure to speed up the computation. We describe a novel subiteration algorithm that can…
In this paper, we develop a class of samplers for the diffusion model using the operator-splitting technique. The linear drift term and the nonlinear score-driven drift of the probability flow ordinary differential equation are split and…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
In the limit where partons become collinear to each other, scattering amplitudes factorize into a product of universal, process-independent building blocks and scattering amplitudes involving fewer partons. We compute these universal…
The discussion regarding the numerical integration of the polarized radiative transfer equation is still open and the comparison between the different numerical schemes proposed by different authors in the past is not fully clear. Aiming at…
This paper presents an efficient parallel radiative transfer-based inverse-problem solver for time-domain optical tomography. The radiative transfer equation provides a physically accurate model for the transport of photons in biological…
An ordinary differential operator of the fourth order with coefficients converging at infinity sufficiently rapidly to constant limits is considered. Scattering theory for this operator is developed in terms of special solutions of the…
The increasing complexity of neural networks and the energy consumption associated with training and inference create a need for alternative neuromorphic approaches, e.g. using optics. Current proposals and implementations rely on physical…
In this paper, we consider the problem of mechanical wave scattering from a spatially finite system into an infinite surrounding environment. The goal is to illuminate why the scattering spectrum undergoes peaks and dips (resonances) at…
The two-body Coulomb scattering problem is solved using the standard complex scaling method. The explicit enforcement of the scattering boundary condition is avoided. Splitting of the scattering wave function based on the Coulomb modified…
Recently, 3D Gaussian Splatting (3DGS) has enabled photorealistic view synthesis at high inference speeds. However, its splatting-based rendering model makes several approximations to the rendering equation, reducing physical accuracy. We…
In this paper we present a novel multiscale splitting approach to solve multiscale Schroedinger equation, which have large different time-scales. The energy potential is based on highly oscillating functions, which are magnitudes faster…
This paper describes a numerical formulation for calculating wave propagation with high precision in a three-dimensional system. Yee's discretization scheme is used to formulate a frequency domain method that is compatible with the…
We present algorithms for solving spatially nonlocal diffusion models on the unit sphere with spectral accuracy in space. Our algorithms are based on the diagonalizability of nonlocal diffusion operators in the basis of spherical harmonics,…
We present describe a new computer code that solves the radiative transfer problem on multi-resolution grids. If the cloud model is from an MHD simulation on a regular cartesian grid, criteria based for example on local density or velocity…
A numerical scheme is proposed for the solution of the three-dimensional radiative transfer equation with variable optical depth. We show that time-dependent ray tracing is an attractive choice for simulations of astrophysical ionization…
The solidification and macro-segregation problem involving unsteady multi-physics and multi-phase fields is typically a complex process with mass, momentum, heat, and species transfers among solid, mushy, and liquid phase regions. The…
A new set of discrete ordinates is proposed for one-dimensional radiative transfer in spheres with central symmetry. The set is structured with un-normalized circular functions. This resulted in a conservative and closed set of discrete…
The multi-component nonlinear Schrodinger equation related to C.I=Sp(2p)/U(p) and D.III=SO(2p)/U(p)-type symmetric spaces with non-vanishing boundary conditions is solvable with the inverse scattering method (ISM). As Lax operator L we use…