Related papers: A partial differential equation for pseudocontact …
Current research presents an innovative model of half-space plasmon excitations for electron gas of arbitrary degeneracy in an ambient jellium-like positive background . The linearized Schr\"{o}dinger-Poisson system is used to derive…
Almost all materials are anisotropic. In this paper, interface relations of anisotropic elliptic partial differential equations involving discontinuities across interfaces are derived in two and three dimensions. Compared with isotropic…
We introduce a closed-form expansion for the transition density of elliptic and hypo-elliptic multivariate Stochastic Differential Equations (SDEs), over a period $\Delta\in (0,1)$, in terms of powers of $\Delta^{j/2}$, $j\ge 0$. Our…
A recently published correlated electron pseudopotentials (CEPPs) method has been adapted for application to the 3d-transition metals, and to include relativistic effects. New CEPPs are reported for the atoms Sc$-$Fe, constructed from…
Partial differential equations with distributional sources---in particular, involving (derivatives of) delta distributions---have become increasingly ubiquitous in numerous areas of physics and applied mathematics. It is often of…
The scalar-pseudoscalar interaction constant of PbF in its ground state electronic configuration is calculated using the Z-vector method in the relativistic coupled-cluster framework. The precise calculated value is very important to set…
Electronic structures are fully determined by the exchange-correlation (XC) potential. In this work, we develop a new method to construct reliable XC potentials by properly mixing the exact exchange and the local density approximation…
We propose elliptical graphical models based on conditional uncorrelatedness as a general- ization of Gaussian graphical models by letting the population distribution be elliptical instead of normal, allowing the fitting of data with…
We calculate the transmission coefficient for electrons passing through the helically shaped potential barrier, which can be, for example, produced by DNA molecules.
Single component pseudo-potential lattice Boltzmann model has been widely applied in multiphase simulation due to its simplicity and stability. In many research, it has been claimed that this model can be stable for density ratios larger…
Electromagnetic interactions of protons and alpha particles are modeled in a form that is suitable for Monte Carlo simulation of the transport of charged particles. The differential cross section (DCS) for elastic collisions with neutral…
Starting from a model of an elastic medium, partial differential equations with the form of the coupled Einstein-Dirac-Maxwell equations are derived. The form of these equations describes particles with mass and spin coupled to…
We combine the Dyson-Schwinger/Bethe-Salpeter equations framework with modern numerical reconstruction methods to derive the three-dimensional and transverse two-dimensional charge distribution of an array of ground-state pseudoscalar and…
Assume that we observe a large number of curves, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective…
Term "asymmetrical pseudoelasticity" refers to the theory, in which a symmetrical stress tensor and a symmetrical strain tensor are connected by means of an asymmetrical material tensor. An 6-dimensional asymmetrical matrix of elasticity…
Various device-based experiments have indicated that electron transfer in certain chiral molecules may be spin-dependent, a phenomenon known as the Chiral Induced Spin Selectivity (CISS) effect. However, due to the complexity of these…
In this article we propose and investigate a hierarchy of mathematical models based on partial differential equations (PDE) and ordinary differential equations (ODE) for the simulation of the biophysical phenomena occurring in the…
We study the computation of equilibrium points of electrostatic potentials: locations in space where the electrostatic force arising from a collection of charged particles vanishes. This is a novel scenario of optimization in which…
In multi-phase fluid flow, fluid-structure interaction, and other applications, partial differential equations (PDEs) often arise with discontinuous coefficients and singular sources (e.g., Dirac delta functions). These complexities arise…
A multiscale numerical method is proposed for the solution of semi-linear elliptic stochastic partial differential equations with localized uncertainties and non-linearities, the uncertainties being modeled by a set of random parameters. It…