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Quantitative prediction of thermodynamic properties in solution is essential for translating atomistic simulations into reliable chemical insight. As an exemplar system, the behaviour of CaCO$_3$ in water has been widely studied to…
Treating water as a linearly responding dielectric continuum on molecular length scales allows very simple estimates of solvation structure and thermodynamics for charged and polar solutes. While this approach can successfully account for…
Within the theory of interacting continua, we develop a model for a heat conducting mixture of two interacting fluids described in terms of the densities and the velocities for each fluid and the temperature field for the mixture as a…
Physics based emulators offer a fast and reliable replacement for an exact solution of the scattering problem in nuclear physics. Previous work developed a reduced-basis emulator for single-channel elastic scattering using an optical…
We investigate a two-scale system featuring an upscaled parabolic dispersion-reaction equation intimately linked to a family of elliptic cell problems. The system is strongly coupled through a dispersion tensor, which depends on the…
This paper presents a mathematically exact self-similar solution to the joint nonsteady problems of vapour diffusion towards a droplet growing in a vapour-gas medium and of removal of heat released by a droplet into a vapour-gas medium…
We investigate a coupled hyperbolic-parabolic system modeling thermoelastic diffusion (resp. thermo-poroelasticity) in plates, consisting of a fourth-order hyperbolic partial differential equation for plate deflection and two second-order…
The many-body Coulomb repulsive energy of strictly correlated electrons provides direct information of the exact Hohenberg-Kohn exchange-correlation functional in the strong interaction limit. Until now the treatment of strictly correlated…
In theory, diffusion curves promise complex color gradations for infinite-resolution vector graphics. In practice, existing realizations suffer from poor scaling, discretization artifacts, or insufficient support for rich boundary…
A method to calculate particle fluxes applicable in most of the spectroscopy techniques is described. Flux intensities of backscattered or absorbed electrons and emitted photons are calculated using a method of convergence to solve the…
Realistic nucleon-nucleon interaction induce correlations to the nuclear many-body system which lead to a fragmentation of the single-particle strength over a wide range of energies and momenta. We address the question of how this…
We develop a numerical code to calculate the neutrino transfer with multi-energy and multi-angle in three dimensions (3D) for the study of core-collapse supernovae. The numerical code solves the Boltzmann equations for neutrino…
We numerically determine the entropy for heat-conducting states, which is connected to the so-called excess heat considered as a basic quantity for steady-state thermodynamics in nonequilibrium. We adopt an efficient method to estimate the…
We previously developed an algorithm, called resolution exchange, which improves canonical sampling of atomic resolution models by swapping conformations between high- and low-resolution simulations[1]. Here, we demonstrate a generally…
Mathematical modeling at the level of the full cardiovascular system requires the numerical approximation of solutions to a one-dimensional nonlinear hyperbolic system describing flow in a single vessel. This model is often simulated by…
In this paper, we consider a numerical method to solve scattering problems with multi-periodic layers with different periodicities. The main tool applied in this paper is the Bloch transform. With this method, the problem is written into an…
Context: The solution of the nonlocal thermodynamical equilibrium (non-LTE) radiative transfer equation usually relies on stationary iterative methods, which may falsely converge in some cases. Furthermore, these methods are often unable to…
In this paper, we propose a new adaptation of the D-iteration algorithm to numerically solve the differential equations. This problem can be reinterpreted in 2D or 3D (or higher dimensions) as a limit of a diffusion process where the…
The solitary wave naturally arises in many areas of mathematical physics, including in nonlinear optics, plasma physics, quantum field theory, and fluid mechanics. In the past few years, for an advanced nuclear energy system, a particular…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…