Related papers: Analytic solution of Balitsky-Kovchegov equation w…
We present a comprehensive a priori error analysis of a practical energy based atomistic/continuum coupling method (Shapeev, arXiv:1010.0512) in two dimensions, for finite-range pair-potential interactions, in the presence of vacancy…
Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled…
With the relativistic Coulomb wave function boundary condition, the energies, widths and wave functions of the single proton resonant orbitals for $^{17}$Ne are studied by the analytical continuation of the coupling constant (ACCC) approach…
We informally review a few PDEs for which the Monge-Kantorovich distance between pairs of solutions, possibly with some judicious cost function, decays: heat equation, Fokker-Planck equation, heat equation with varying coefficients,…
We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE…
The spinless Salpeter equation is the combination of relativistic kinematics with some static interaction potential. The nonlocal nature of the Hamiltonian resulting from this approximation renders difficult to obtain rigorous analytic…
This article is concerned with numerical methods to approximate effective coefficients in stochastic homogenization of discrete linear elliptic equations, and their numerical analysis --- which has been made possible by recent contributions…
The osmotic coefficient of solutions of rod-like polyelectrolytes is considered by comparing current theoretical treatments and simulations to recent experimental data. The discussion is restricted to the case of monovalent counterions and…
Using the Kadanoff-Baym non-equilibrium Green's function formalism, we derive the self-consistent Hartree-Fock-Bogoliubov (HFB) collisionless kinetic equations and the associated equation of motion for the condensate wavefunction for a…
We present recent developments on the role of the running coupling constant at the intersection of perturbative and nonperturbative QCD. A number of experiments show a smooth transition from small to large scales given by the four-momentum…
Although the convergent close-coupling (CCC) method has achieved unprecedented success in obtaining accurate theoretical cross sections for electron-atom scattering, it generally fails to yield converged energy distributions for ionization.…
The Strang splitting method has been widely used to solve nonlinear reaction-diffusion equations, with most theoretical convergence analysis assuming periodic boundary conditions. However, such analysis presents additional challenges for…
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…
A unified framework to derive discrete time-marching schemes for coupling of immersed solid and elastic objects to the lattice Boltzmann method is presented. Based on operator splitting for the discrete Boltzmann equation, second-order…
This paper applies meshless method of lines, which uses radial basis functions (RBFs) as a spatial collocation scheme to solve the Coupled Drinfeld's-Sokolov-Wilson System. Runge-Kutta method is used for time integration of the system of…
We present a lattice calculation of the renormalized running coupling constant in symmetric (MOM) and asymmetric ($\widetilde{\rm MOM}$) momentum substraction schemes including $u$, $d$, $s$ and $c$ quarks in the sea. An Operator Product…
The processes of simultaneous coagulation and Ostwald ripening of particles in the concluding stage of phase transformation are considered. We solve the integro-differential system of Smoluchowski-type kinetic and mass balance equations…
The continuum-scale electrokinetic porous-media flow and excess charge redistribution equations are uncoupled using eigenvalue decomposition. The uncoupling results in a pair of independent diffusion equations for "intermediate" potentials…
We have studied the spin-polarized three-dimensional homogeneous electron gas using the diffusion quantum Monte Carlo method, with trial wave functions including backflow and three-body correlations in the Jastrow factor, and we have used…
In this technical note a general procedure is described to construct internally consistent splitting methods for the numerical solution of differential equations, starting from matching pairs of explicit and diagonally implicit Runge-Kutta…