相关论文: Diffusion-reaction approach to electronic relaxati…
A self-contained discussion of integral equations of scattering is presented in the case of centrally-symmetric potentials in one dimension, which will facilitate the understanding of more complex scattering integral equations in two and…
Under certain reality conditions, a general solution to the dispersionless Toda lattice hierarchy describes deformations of simply-connected plane domains with a smooth boundary. The solution depends on an arbitrary (real positive) function…
This paper presents new analytic solutions to the Dirac equation employing a recently introduced method that is based on the formulation of spinorial fields and their driving electromagnetic fields in terms of geometric algebras. A first…
Calcium dynamics is the highly responsible for intracellular electrical (action potential) and chemical (neurotransmitter) signaling in neuron cell. The Mathematical modeling of calcium dynamics in neurons lead to the reaction diffusion…
In our recent publication, we have proposed an analytical method for solving the problem of electronic relaxation in solution, modeled by a particle undergoing diffusive motion under the influence of two arbitrary potentials and the…
This note is to show that the position-space embedding in \cite{ESP2021embedding} in the position and occupation bases can be obtained by considering the dynamics of Dirac delta function $$\delta(\mathbf{x}- \mathbf{z}(t)) =…
To study the effect of slow heat conduction during phase separation, we discuss the relaxation properties of an $O(N)$ symmetric model with Phase field type dynamics, where a non conserved order parameter field couples bilinearly to a…
We study the density-density response function of a collection of charged massive Dirac particles and present analytical expressions for the dynamical polarization function in one, two and three dimensions. The polarization function is then…
Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…
Compartmental models are widely used in mathematical epidemiology to describe dynamics of infection disease. A new SIS-PDE model, recently derived by Chalub and Souza, is based on a diffusion-drift approximation of probability density in a…
We study the elliptic equation with a line Dirac delta function as the source term subject to the Dirichlet boundary condition in a two-dimensional domain. Such a line Dirac measure causes different types of solution singularities in the…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
The Smoluchowski diffusion equation describes diffusion in the presence of external forces. Studying the mechanical response of soft materials to linear forces, such as shear, results in a boundary value problem involving an…
The nuclear spin relaxation time $T_1$ is calculated taking account of the contributions from orbital currents of Dirac electrons. We consider a simple model of non-interacting Dirac electron gas in the three-dimensional bulk system. The…
Decoherence of a localized electron spin in a solid state material (the ``central spin'' problem) at low temperature is believed to be dominated by interactions with nuclear spins in the lattice. This decoherence is partially suppressed…
We calculate the probability distribution function (PDF) of an overdamped Brownian particle moving in a periodic potential energy landscape $U(x)$. The PDF is found by solving the corresponding Smoluchowski diffusion equation. We derive the…
Despite the widespread use of Scanning Transmission Electron Microscopy (STEM) for observing the structure of materials at the atomic scale, a detailed understanding of some relevant electron beam damage mechanisms is limited. Recent…
We propose a new method to construct an isotropic cellular automaton corresponding to a reaction-diffusion equation. The method consists of replacing the diffusion term and the reaction term of the reaction-diffusion equation with a random…
The time evolution of the Wigner distribution function for a single-particle excitation in a Fermi system was studied within the framework of the diffusion approximation of kinetic theory by numerically solving a nonlinear diffusion…
We study solution techniques for an evolution equation involving second order derivative in time and the spectral fractional powers, of order $s \in (0,1)$, of symmetric, coercive, linear, elliptic, second-order operators in bounded domains…