相关论文: Ray Effect Mitigation for the Discrete Ordinates M…
Resonant (elastic) soft x-ray scattering (RSXS) offers a unique element, site, and valence specific probe to study spatial modulations of charge, spin, and orbital degrees of freedom in solids on the nanoscopic length scale. It cannot only…
We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…
Resonant solutions of the quantum Schr\"odinger equation occur at complex energies where the S-matrix becomes singular. Knowledge of such resonances is important in the study of the underlying physical system. Often the Schr\"odinger…
Recently, split ring-resonators (SRR's) have been realized experimentally in the near infrared (NIR) and optical regime. In this contribution we numerically investigate light propagation through an array of metallic SRR's in the NIR and…
Reduced-order modeling is an efficient approach for solving parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space and an online step…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Resonant X-ray scattering (RXS) is a spectroscopy where both the power of site selective diffraction and the power of local absorption spectroscopy regarding atomic species are combined. By virtue of the dependence on the core level state…
The transfer equation in spherical geometry with central symmetry, which is a partial differential equation in two variables r and m, is reduced to a one-dimensional transfer equation in r parametric in m. This is done by dropping the…
Aims. The main goal of this paper is to present an accurate and efficient numerical strategy for solving the radiative transfer problem for polarised radiation in strong resonance lines forming out of local thermodynamic equilibrium, taking…
Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order…
We show that a rectangular collocation method, equivalent to evaluating all matrix elements with a quadrature-like scheme and using more points than basis functions, is an effective approach for solving the electronic Schr\"odinger equation…
Applications such as unbalanced and fully shuffled regression can be approached by optimizing regularized optimal transport (OT) distances, such as the entropic OT and Sinkhorn distances. A common approach for this optimization is to use a…
The nonclassical transport equation models particle transport processes in which the particle flux does not decrease as an exponential function of the particle's free-path. Recently, a spectral approach was developed to generate…
Numerical integration of ODEs by standard numerical methods reduces a continuous time problems to discrete time problems. Discrete time problems have intrinsic properties that are absent in continuous time problems. As a result, numerical…
In highly diffusion regimes when the mean free path $\varepsilon$ tends to zero, the radiative transfer equation has an asymptotic behavior which is governed by a diffusion equation and the corresponding boundary condition. Generally, a…
When circularly polarized light is scattered from a rotating target, a rotational Doppler shift (RDS) emerges from an exchange of angular momentum between the spinning object and the electromagnetic field. Here, we used coherently spinning…
Stochastic Gradient (SG) is the defacto iterative technique to solve stochastic optimization (SO) problems with a smooth (non-convex) objective $f$ and a stochastic first-order oracle. SG's attractiveness is due in part to its simplicity of…
We consider the numerical approximation of the radiative transfer equation using discontinuous angular and continuous spatial approximations for the even parts of the solution. The even-parity equations are solved using a diffusion…
The integro-differential formulation of the RTE and its solution by iterations on the source has been extended here to handle anisotropic scattering. The iterative part of the method is O(N ln N ), thanks to an efficient use of H-matrices.…
Applications such as uncertainty quantification and optical tomography, require solving the radiative transfer equation (RTE) many times for various parameters. Efficient solvers for RTE are highly desired. Source Iteration with Synthetic…