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A Riemannian stochastic representation of model uncertainties in molecular dynamics is proposed. The approach relies on a reduced-order model, the projection basis of which is randomized on a subset of the Stiefel manifold characterized by…
The development of a neutrino moment based radiative-transfer code to simulate binary neutron-star mergers can easily become an obstacle path because of the numerous ways in which the solution of the equations may fail. We describe the…
Estimating the state of an environment from high-dimensional, multimodal, and noisy observations is a fundamental challenge in reinforcement learning (RL). Traditional approaches rely on probabilistic models to account for the uncertainty,…
We propose a new semi-Lagrangian Vlasov-Poisson solver. It employs elements of metric to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $Q(P)$ of any test particle…
Distortions in the electron distribution function driven by intense temperature gradients critically influence the generation and evolution of heat flux and magnetic fields in plasmas under the condition of inertial confinement fusion.…
Fully describing light propagation in a rotating, anisotropic medium with thermal nonlinearity requires modeling the interplay between nonlinear refraction, birefringence, and the nonlinear group index. Incorporating these factors into a…
We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…
Modeling the propagation of radiative heat-waves in optically thick material using a diffusive approximation is a well-known problem. In optically thin material, classic methods, such as classic diffusion or classic $P_1$, yield the wrong…
Medical ultrasound imaging is the most widespread real-time non-invasive imaging system and its formulation comprises signal transmission, signal reception, and image formation. Ultrasound signal transmission modelling has been formalized…
We present a 3D finite element solver for the nonlinear Poisson-Nernst-Planck (PNP) equations for electrodiffusion, coupled to the Stokes system of fluid dynamics. The model serves as a building block for the simulation of macromolecule…
This paper presents a novel method for evaluating second-order consistent hydrodynamic loads, which employs nonlinear wave and body kinematics. The pseudo-spectral formulation of nonlinear potential flow wave solvers is exploited,…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
The steady-state simplified $P_N$ approximation to the radiative transport equation has been successfully applied to many problems involving radiation. Recently, time-dependent simplified $P_N$ equations have been derived by an asymptotic…
We explore an asymmetric two-fermion Hubbard dimer to test the accuracy of the adiabatic approximation of time-dependent density functional theory in modelling time-resolved charge transfer. We show that the model shares essential features…
We propose a projection based multi-moment matching method for model order reduction of quadratic-bilinear systems. The goal is to construct a reduced system that ensures higher-order moment matching for the multivariate transfer functions…
The Wigner distribution function and its spatial-angular moments (intensity-moments) are known as efficient instruments for characterization of complex quasimonochromatic light beams and their transformations. In this paper, the…
We survey a number of moment hierarchies and test their performances in computing one-dimensional shock structures. It is found that for high Mach numbers, the moment hierarchies are either computationally expensive or hard to converge,…
This paper describes the formulation and experimental testing of a novel method for the estimation and approximation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold $Q$…
This work presents a new finite volume framework for solid dynamics based on a momentum-deformation formulation. Building on the C-TOUCH methodology [1], a novel Roe-type Riemann solver is developed to enhance the stability and accuracy of…
Many physical systems are described by probability distributions that evolve in both time and space. Modeling these systems is often challenging to due large state space and analytically intractable or computationally expensive dynamics. To…