An Exact Ewald Summation Method in Theory and Practice

2020 ◽  
Vol 124 (19) ◽  
pp. 3943-3946
Author(s):  
S. Stenberg ◽  
B. Stenqvist
Keyword(s):  
Summation Method ◽  
Theory And Practice ◽  
Ewald Summation

Simulation of a PEO based solid polyelectrolyte, comparison of the CMM and the Ewald summation method

Polymer ◽  
2000 ◽  
Vol 41 (6) ◽  
pp. 2149-2155 ◽  
Author(s):  
J. Ennari ◽  
I. Neelov ◽  
F. Sundholm
Keyword(s):  
Summation Method ◽  
Ewald Summation

scholarly journals Simulations of Coulomb systems with slab geometry using an efficient 3D Ewald summation method

2016 ◽  
Vol 144 (14) ◽  
pp. 144103 ◽  
Author(s):  
Alexandre P. dos Santos ◽  
Matheus Girotto ◽  
Yan Levin
Keyword(s):  
Coulomb Systems ◽  
Summation Method ◽  
Ewald Summation ◽  
Slab Geometry

An Ewald summation method for planar surfaces and interfaces

1992 ◽  
Vol 75 (2) ◽  
pp. 379-395 ◽  
Author(s):  
Joseph Hautman ◽  
Michael L. Klein
Keyword(s):  
Summation Method ◽  
Ewald Summation ◽  
Planar Surfaces ◽  
Surfaces And Interfaces

High Efficiency Algorithm for the Dipolar Interaction Energy of 2D Magnetic Nanoparticle Systems

2011 ◽  
Vol 689 ◽  
pp. 108-113
Author(s):  
Ke Tang ◽  
Hong Jie Yang ◽  
Lin Hong Cao ◽  
Hong Tao Yu ◽  
Jing Song Liu ◽  
...  
Keyword(s):  
Interaction Energy ◽  
High Efficiency ◽  
Dipolar Interaction ◽  
Summation Method ◽  
Ewald Summation ◽  
Range Interaction ◽  
Self Energy ◽  
N Body Problem ◽  
Magnetic Dipolar Interaction ◽  
Large Ensembles

Most of simulations often require the calculation of all pairwise interaction in large ensembles of particles, such as N-body problem of gravitation, electrostatic interaction and magnetic dipolar interaction, etc. The main difficulty in the calculation of long-range interaction is how to accelerate the slow convergence of the occurring sums. In this work, we are interested in the dipolar interaction in the two dimensional (2D) magnetic dipolar nanoparticle systems, which have attracted much attention due to both their important technological applications such as high-density patterned recording media and their rich and often unusual experimental behaviours. We develop a high efficiency algorithm based on the Lekner method to evaluate the magnetic dipolar energy for such systems, where the simulation cell is periodically replicated in the plane. Taking advantage of the symmetry of the systems, the dipolar interaction energy is expressed by rapidly converging series of modified Bessel functions in our algorithm. We found that our algorithm is better than the traditional Ewald summation method in efficiency for the regular arrays. Moreover, two simple formulas are obtained to evaluate the self-energy, which is important in the simulation of the dipolar systems.

A numerical study of the shearing motion of emulsions and foams

1995 ◽  
Vol 286 ◽  
pp. 379-404 ◽  
Author(s):  
Xiaofan Li ◽  
Hua Zhou ◽  
C. Pozrikidis
Keyword(s):  
Rheological Properties ◽  
Volume Fraction ◽  
Numerical Study ◽  
High Volume ◽  
Summation Method ◽  
Boundary Integral ◽  
Simple Shear Flow ◽  
Ewald Summation ◽  
Shearing Flow ◽  
Volume Fractions

A numerical study is presented of the motion of two-dimensional, doubly periodic, dilute and concentrated emulsions of liquid drops with constant surface tension, subject to a simple shear flow. The numerical method is based on a boundary integral formulation that employs a Green's function for doubly periodic Stokes flow, computed using the Ewald summation method. Under the assumption that the viscosity of the drops is equal to that of the ambient fluid, the motion is examined in a broad range of capillary numbers, volume fractions, and initial geometrical configurations. The latter include square and hexagonal lattices of circular and closely packed hexagonal drops with rounded corners. Based on the nature of the asymptotic motion at large times, a phase diagram is constructed separating regions where periodic motion is established, or the emulsion is destabilized due to continued elongation or coalescence of intercepting drops. Comparisons with previous computations for bounded systems illustrate the significance of the walls on the evolution and rheological properties of an emulsion. It is shown that the shearing flow is able to stabilize a concentrated emulsion against the tendency of the drops to become circular and coalesce, thereby allowing for periodic evolution even when the volume fraction of the suspended phase might be close to that for dry foam. This suggests that the imposed shearing flow plays a role similar to that of the disjoining pressure for stationary foam. At high volume fractions, the geometry of the microstructure and flow at the Plateau borders and within the thin films separating adjacent drops are illustrated and discussed with reference to the predictions of the quasi-steady theory of foam. Although the accuracy of certain fundamental assumptions underlying the quasi-steady theory is not confirmed by the numerical results, we find qualitative agreement regarding the basic geometrical features of the evolving microstructure and effective rheological properties of the emulsion.

Theory and Practice in Acute Care of Psychological Trauma

2002 ◽  
Vol 17 (S2) ◽  
pp. S8
Author(s):  
Rob Gordon
Keyword(s):  
Acute Care ◽  
Psychological Trauma ◽  
Theory And Practice
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