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Many modern semiempirical molecular orbital models are built on the neglect of diatomic differential overlap (NDDO) approximation. An in-depth understanding of this approximation is therefore indispensable to rationalize the success of…
We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the…
We present linear response theories in the continuum capable of describing continuum spectra and dynamical correlations of finite systems with no spatial symmetry. Our formulation is essentially the same as the continuum random-phase…
The quasidiffusion (QD) method, also known as the Variable Eddington Factor (VEF) method in the astrophysical community, is an established iterative method for accelerating source iterations in SN calculations. A great advantage of the QD…
An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are…
In this paper we study the stability of explicit finite difference discretizations of linear advection-diffusion equations (ADE) with arbitrary order of accuracy in the context of method of lines. The analysis first focuses on the stability…
To establish the electron energy distribution function (EEDF), the second derivative of a Langmuir probe current-voltage (I-V) characteristic is numerically integrated using the Tikhonov singular value decomposition regularized method. A…
From a mathematical perspective, radiation hydrodynamics can be thought of as a system of hyperbolic balance laws with dual multiscale behavior (multiscale behavior associated with the hyperbolic wave speeds as well as multiscale behavior…
We present a comprehensive analytical study of radiative transfer using the method of moments and include the effects of non-isotropic scattering in the coherent limit. Within this unified formalism, we derive the governing equations and…
In a frame of quasi-crystal approximation the dispersion equations are obtained for the wave vector of a coherent electromagnetic wave propagating in a media which contains a random set of parallel dielectric cylinders with possible…
In a relativistic context, the main purpose of Extended Irreversible Thermodynamics (EIT) is to generalize the principles of non-equilibrium thermodynamics to the domain of fluid dynamics. In particular, the theory aims at modelling any…
In this article we study the numerical approximation of a variable coefficient fractional diffusion equation. Using a change of variable, the variable coefficient fractional diffusion equation is transformed into a constant coefficient…
Analytical expressions for radial distribution function (RDF) are of critical importance for various applications, such as development of the perturbation theories for equilibrium properties. Theoretically, RDF expressions for…
Anomaly-diffusing energy balance models (AD-EBM) are routinely employed to analyze and emulate the warming response of both observed and simulated Earth systems. We demonstrate a deficiency in common multi-layer as well as…
Recent high resolution Compton scattering experiments clearly reveal that there are fundamental limitations to the conventional local density approximation (LDA) based description of the ground state electron momentum density (EMD) in…
We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an adaptive grid. We show that this…
We study the symmetric facilitated exclusion process (FEP) on the finite one-dimensional lattice $\lbrace 1,\dots ,N-1\rbrace$ when put in contact with boundary reservoirs, whose action is subject to an additional kinetic constraint in…
We consider stability of regimes of hydromagnetic thermal convection in a rotating horizontal layer with free electrically conducting boundaries, to perturbations involving large spatial and temporal scales. Equations governing the…
In this work we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the…
Two-stream radiative transfer is a workhorse in the Earth, planetary and exoplanetary sciences due to its simplicity and ease of implementation. However, a longstanding limitation of the two-stream approximation is its inaccuracy in the…