Related papers: On exact solutions and numerics for cold, shallow,…
The exact evolution in time and space of a distribution of the temperature (or density of diffusing matter) in an isotropic homogeneous medium is determined where the initial distribution is described by a piecewise polynomial. In two…
The thermal response function given to a unit-step dissipation accurately characterizes the thermal system. Instead of the thermal response function the so-called structure function describing three-dimensional as the equivalent model of…
A model glass with fast and slow processes is studied. The statics is simple and the facilitated slow dynamics is exactly solvable. The main features of a fragile glass take place: Kauzmann transition, Vogel-Fulcher law, Adam-Gibbs relation…
The existing polar continuum theory contains unresolved indeterminacies in the spherical part of the couple-stress tensor. This severely restricts its applicability in the study of micro and nano-scale solid and fluid mechanics and, perhaps…
We assess precision thermometry for an arbitrary single quantum system. For a $d$-dimensional harmonic system we show that the gap sets a single temperature that can be optimally estimated. Furthermore, we establish a simple linear…
This paper introduces improved numerical techniques for addressing numerical boundary and interface coupling conditions in the context of diffusion equations in cellular biophysics or heat conduction problems in fluid-structure…
Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical…
In a series of two articles, we propose a comprehensive mathematical framework for Coupled-Cluster-type methods. In this second part, we analyze the nonlinear equations of the single-reference Coupled-Cluster method using topological degree…
We complete the Solomon-Wilson-Alexiades's mushy zone model (Letters Heat Mass Transfer, 9 (1982), 319-324) for the one-phase Lam\'e-Clapeyron-Stefan problem. We obtain explicit solutions when a convective or heat flux boundary condition is…
We introduce a numerical workflow to model and simulate transient close-contact melting processes based on the space-time finite element method. That is, we aim at computing the velocity at which a forced heat source melts through a…
The application of the consolidation equation is based on Taylor's approximate solution alone. The existence of the exact solution emerged from the analysis of the logical structure of d'Alambert's, Fourier' and Laplace's differential…
Surface-subsurface flow models for hydrological applications solve a coupled multiphysics problem. This usually consists of some form of the Richards and shallow water equations. A typical setup couples these two nonlinear partial…
The thesis focuses on the prediction of solvation thermodynamics using integral equation theories. Our main goal is to improve the approach using a rational correction. We achieve it by extending recently introduced pressure correction, and…
This report addresses the boundary value problem for a second-order linear singularly perturbed FIDE. Traditional methods for solving these equations often face stability issues when dealing with small perturbation parameters. We propose an…
The kinetic equations describing irreversible aggregation and the scaling approach developed to describe them in the limit of large times and large sizes are tersely reviewed. Next, a system is considered in which aggregates can only react…
To follow up on the unexpectedly-good performance of several coupled-cluster models with approximate inclusion of 3-body clusters [J. Chem. Phys. 151, 064102 (2019)] we performed a more complete assessment of the 3CC method [J. Chem. Phys.…
This paper presents a physics-based analytical model for the MOS transistor operating continuously from room temperature down to liquid-helium temperature (4.2 K) from depletion to strong inversion and in the linear and saturation regimes.…
This study uses continuum thermodynamics of pure thermoelastic fluids to examine their phase transformation. To examine phase transformation kinetics, a special emphasis is placed on the jump condition for the axiom of entropy inequality,…
We design and analyse a semi-implicit finite volume scheme for the two-dimensional rotating shallow water (RSW) equations that is energy stable, well-balanced (capable of preserving discrete geostrophic steady states), consistent, and…
We present and analyze in a unified setting two schemes for the numerical discretization of a Darcy-Forchheimer fluid flow model coupled with an advection-diffusion equation modeling the temperature distribution in the fluid. The first…