Related papers: A fast simple algorithm for computing the potentia…
The length and time scales of atomistic simulations are limited by the computational cost of the methods used to predict material properties. In recent years there has been great progress in the use of machine learning algorithms to develop…
A numerical method using implicit surface representations is proposed to solve the linearized Poisson-Boltzmann equations that arise in mathematical models for the electrostatics of molecules in solvent. The proposed method used an implicit…
All-atom dynamics simulations are an indispensable quantitative tool in physics, chemistry, and materials science, but large systems and long simulation times remain challenging due to the trade-off between computational efficiency and…
We present a fast and accurate method to calculate the electrostatic energy and forces of interacting particles with the boundary conditions appropriate to surfaces, i.e periodic in the two directions parallel to the surface and free in the…
Utilizing the integral expression of Coulomb's Law to determine the electric potential from a continuous charge distribution is a canonical exercise in Electricity and Magnetism (E&M). In this study, we use both think-aloud interviews and…
We demonstrate an electric field-resolved approach for probing ultrafast dynamics of photoinjected charges in solids. Direct access to the electric field of few-cycle pulses enables us to measure a broadband response of a medium with…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
We present an algorithm for evaluating a linear ``intersection transform'' of a function defined on the lattice of subsets of an $n$-element set. In particular, the algorithm constructs an arithmetic circuit for evaluating the transform in…
The problem of electron scattering on the one-dimensional complexes is considered. We propose a novel theoretical approach to solution of the transport problem for a quantum graph. In the frame of the developed approach the solution of the…
We find a succinct expression for computing the sequence $x_t = a_t x_{t-1} + b_t$ in parallel with two prefix sums, given $t = (1, 2, \dots, n)$, $a_t \in \mathbb{R}^n$, $b_t \in \mathbb{R}^n$, and initial value $x_0 \in \mathbb{R}$. On…
We propose new algorithms for the computation of the first N terms of a vector (resp. a basis) of power series solutions of a linear system of differential equations at an ordinary point, using a number of arithmetic operations which is…
Dimensional analysis, superposition principle, and continuity of electric potential are used to study electric potential of a uniformly charged square sheet at its plane. It is shown that knowing the electric potential on the diagonal and…
Artificial electrostatic potentials can be present in supercells constructed for atomistic simulations of surfaces and interfaces in ionic crystals. Treating the ions as point charges, we systematically derive an electrostatic formalism for…
We introduce a class of interatomic potential models that can be automatically generated from data consisting of the energies and forces experienced by atoms, derived from quantum mechanical calculations. The resulting model does not have a…
A closed form of the electrostatic potential of a homogeneously charged cube is derived by integration. The exact result is compared with multipole expansions for the exterior and interior of the cube. The electrostatic potential of a…
A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than…
The most critical limitation to the wide-scale use of classical molecular dynamics for alloy design is the availability of suitable interatomic potentials. In this work, we demonstrate a simple procedure to generate a library of accurate…
We revisit Christol's theorem on algebraic power series in positive characteristic and propose yet another proof for it. This new proof combines several ingredients and advantages of existing proofs, which make it very well-suited for…
The evaluation of Coulomb forces is a difficult task. The summations that are involved converge only conditionally and care has to be taken in selecting the appropriate procedure to define the limits. The Ewald method is a standard method…
We introduce ELECTRAFI, a fast, end-to-end differentiable model for predicting periodic charge densities in crystalline materials. ELECTRAFI constructs anisotropic Gaussians in real space and exploits their closed-form Fourier transforms to…