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When lifting the assumption of spatially-independent scattering centers in classical linear transport theory, collision rate is no longer proportional to angular flux / radiance because the macroscopic cross-section $\Sigma_t(s)$ depends on…
A quantum interatomic scattering is implemented in the direct simulation Monte Carlo (DSMC) method applied to transport phenomena in rarefied gases. In contrast to the traditional DSMC method based on the classical scattering, the proposed…
We consider flux-corrected finite element discretizations of 3D convection-dominated transport problems and assess the computational efficiency of algorithms based on such approximations. The methods under investigation include…
Many porous media are mixtures of inert and reactive materials, manifesting spatio-chemical heterogeneity. We study the evolution of scalar transport in a chemically heterogeneous material that mimics a green roof soil substrate,…
This research is aimed at achieving an efficient digital infrastructure for evaluating risks and damages caused by tsunami flooding. It is mainly focused on the suitable modeling of debris dynamics for a simple (but accurate enough)…
This is Part II of the paper series on data-compatible T-matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series contains theory and here we present simulations for inverse scattering of…
In this work, we extend the solid harmonics derivation, which was used by Ackroyd et al to derive the steady-state SP$_N$ equations, to transient problems. The derivation expands the angular flux in ordinary surface harmonics but uses…
We consider the problem of existence of entropy weak solutions to scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect both to the space variable x and the unknown quantity u. The problem…
In this paper, we present an open-source, automated, and multi-faceted computational-statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport. A parallel implementation of the well-known…
A variety of problems in acoustic and electromagnetic scattering require the evaluation of impedance or layered media Green's functions. Given a point source located in an unbounded half-space or an infinitely extended layer, Sommerfeld and…
Single-molecule junctions - nanoscale systems where a molecule is connected to metallic electrodes - offer a unique platform for studying charge, spin and energy transport in non-equilibrium many-body quantum systems, with few parallels in…
Two benchmark problems for quantitative assessment of anisotropic curvature driving force in phase field method were developed and introduced. Both benchmarks contained an anisotropically shrinking grain in homogeneous matrix. The first…
We evaluate the Gutzwiller trace formula for the level density of classically chaotic systems by considering the level density in a bounded energy range and truncating its Fourier integral. This results in a limiting procedure which…
Dispersion of a passive scalar from concentrated sources in fully developed turbulent channel flow is studied with the probability density function (PDF) method. The joint PDF of velocity, turbulent frequency and scalar concentration is…
The non-equilibrium Green's function method combined with density functional theory (NEGF-DFT) provides a rigorous framework for simulating nanoscale electronic transport, but its computational cost scales steeply with system size. Recent…
The optimal mass transport problem gives a geometric framework for optimal allocation, and has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Even though it can be…
Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within…
In this thesis, Riemann problems and Godunov methods are developed for higher order traffic flow models. A rigorous analysis of the first order traffic flow model of inhomogeneous road is presented. A two-level simulation framework of…
Neural operators, which learn mappings between the function spaces, have been applied to solve boundary value problems in various ways, including learning mappings from the space of the forcing terms to the space of the solutions with the…
In recent years, research and development in nanoscale science and technology have grown significantly, with electrical transport playing a key role. A natural challenge for its description is to shed light on anomalous behaviours observed…