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Ewald summation, named after Paul Peter Ewald, is a method for computing long-range interactions (e.g. electrostatic interactions) in periodic systems...

called the Madelung constant that can be efficiently computed using an Ewald sum. When a reasonable form is assumed for the additional repulsive energy...

[15826 citations] T. Darden, D. York, J. Pedersen, Particle mesh Ewald – An N log(N) method for Ewald sums in large systems, 98(12), 10089–10092 (1993) [11591 citations]...

water. The TIP5P-E model is a reparameterization of TIP5P for use with Ewald sums. Note, however, that the BNS and ST2 models do not use Coulomb's law directly...

(luminance). The theory was first proposed in 1892 by the German physiologist Ewald Hering. When staring at a bright color for a while (e.g. red), then looking...

direct sum for particles that are close, and through the particle mesh method for particles that are separated by some distance. "Fourier-based Ewald Summation...

In optics, the Ewald–Oseen extinction theorem, sometimes referred to as just the extinction theorem, is a theorem that underlies the common understanding...

behind Ewald summation. The Poisson summation formula is also useful to bound the errors obtained when an integral is approximated by a (Riemann) sum. Consider...

constants, the empty lattice propagators, must be carried out by the Ewald's sums for each energy and k-point, and (2) the KKR functions have a pole structure...

sufficiently many variables over a finite field have solutions. It was proved by Ewald Warning (1935) and a slightly weaker form of the theorem, known as Chevalley's...

in 1912 in a conversation between Paul Peter Ewald and Max von Laue in the English Garden in Munich. Ewald had proposed a resonator model of crystals for...

Bela Ewald Althans (born 23 March 1966) is a German former neo-Nazi. Once the leading organiser in Germany's neo-Nazi underground, Althans left the movement...

Applied Mathematics. ISBN 0-89871-579-2. Geir Hasle; Knut-Andreas Lie; Ewald Quak, eds. (2007). Geometric Modelling, Numerical Simulation, and Optimization::...

example, the Evjen method) or integral transforms, which are used in the Ewald method. A fast converging formula for the Madelung constant of NaCl is 12...

∑ m v true 2 + ∑ m δ v 2 {\displaystyle E=\sum m\mathbf {v} ^{2}=\sum m\mathbf {v} _{\text{true}}^{2}+\sum m\,\delta \mathbf {v} ^{2}} (The cross term...

{\displaystyle \mathbf {q} } (see Ewald sphere). The amplitude and phase of this scattered wave will be the vector sum of the scattered waves from all the...

infinity. PBCs can be used in conjunction with Ewald summation methods (e.g., the particle mesh Ewald method) to calculate electrostatic forces in the...

mathematical formulation of the theory was made by Paul Peter Ewald. Korringa and Ewald acknowledged the influence on their work of the 1903 doctoral...

\varphi )=\sum _{\ell =0}^{\infty }\,\sum _{m=-\ell }^{\ell }C_{\ell }^{m}(r)\,Y_{\ell }^{m}(\theta ,\varphi )=\sum _{j=1}^{\infty }\,\sum _{\ell =0}^{\infty...

Weber and Gauss's son-in-law Heinrich Ewald. All of them were dismissed, and three of them were expelled, but Ewald and Weber could stay in Göttingen. Gauss...