Related papers: Time-Dependent Duhamel Renormalization method with…
Combining the time-dependent variational principle (TDVP) algorithm with the parallelization scheme introduced by Stoudenmire and White for the density matrix renormalization group (DMRG), we present the first parallel matrix product state…
When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…
This work concerns the analysis of the discontinuous Galerkin spectral element method (DGSEM) with implicit time stepping for the numerical approximation of nonlinear scalar conservation laws in multiple space dimensions. We consider either…
The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints. As a result, there has been a recent effort to design finite volume time domain (FVTD) and discontinuous Galerkin…
Diffusion Magnetic Resonance Imaging (dMRI) is an imaging technique with exquisite sensitivity to the microstructural properties of heterogeneous media. The conventionally adopted acquisition schemes involving single pulsed field gradients…
The Density Matrix Renormalization Group (DMRG) method with periodic boundary conditions is introduced for two dimensional classical spin models. It is shown that this method is more suitable for derivation of the properties of infinite 2D…
In many applications and physical phenomena, bivariate signals are polarized, i.e. they trace an elliptical trajectory over time when viewed in the 2D planes of their two components. The smooth evolution of this elliptical trajectory,…
In this contribution, a wave equation with a time-dependent variable-order fractional damping term and a nonlinear source is considered. Avoiding the circumstances of expressing the nonlinear variable-order fractional wave equations via…
In this paper, a new reinforcement learning (RL) method known as the method of temporal differential is introduced. Compared to the traditional temporal-difference learning method, it plays a crucial role in developing novel RL techniques…
A new alternate method for evaluating linear response theory is formally developed, and results are presented. This method involves the time-evolution of the system using TDHF and is constructed directly on top of a static Hartree-Fock…
In recent work, Li et al.\ (Comm.\ Math.\ Sci., 7:81-107, 2009) developed a diffuse-domain method (DDM) for solving partial differential equations in complex, dynamic geometries with Dirichlet, Neumann, and Robin boundary conditions. The…
We develop methods to learn the correlation potential for a time-dependent Kohn-Sham (TDKS) system in one spatial dimension. We start from a low-dimensional two-electron system for which we can numerically solve the time-dependent…
Ideal systems of equations such as Euler and MHD may develop singular structures like shocks, vortex/current sheets. Among these, vortical singularities arise due to vortex stretching which can lead to unbounded growth of enstrophy.…
This paper investigates the problem of reconstructing a random source from statistical phaseless data for the two-dimensional Helmholtz equation. The major challenge of this problem is non-uniqueness, which we overcome through a reference…
Applications of the similarity renormalization group (SRG) approach [F. Wegner, Ann. Phys. 506, 77 (1994), S. D. G{\l}azek and K. G. Wilson, Phys. Rev. D 49, 4214 (1994)] to the formulation of useful many-body theories of electron…
We propose and analyse numerical schemes for a system of quasilinear, degenerate evolution equations modelling biofilm growth as well as other processes such as flow through porous media and the spreading of wildfires. The first equation in…
The numerical integration of phase-field equations is a delicate task which needs to recover at the discrete level intrinsic properties of the solution such as energy dissipation and maximum principle. Although the theory of energy…
We introduce a new regularization of the Redfield equation based on a replacement of the Kossakowski matrix with its closest positive semidefinite neighbor. Unlike most of the existing approaches, this procedure is capable of retaining the…
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…
This paper addresses the inverse source problem for a mixed-type fractional wave-diffusion-wave equation posed in a cylindrical domain. The governing equation involves a time-dependent variable-order fractional derivative, which enables the…