FDTD Analysis of Periodic Structures at Arbitrary Incidence Angles: A Simple and Efficient Implementation of the Periodic Boundary Conditions

2006 ◽  
Author(s):  
Fan Yang ◽  
Ji Chen ◽  
Rui Qiang ◽  
A. Elsherbeni
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Structures ◽  
Periodic Boundary Conditions ◽  
Efficient Implementation

Application of Periodic Boundary Conditions in Studying Stent Expansion

2013 ◽  
Vol 419 ◽  
pp. 286-291 ◽  
Author(s):  
G.Y. Jiao ◽  
P.P. Li ◽  
R.J. Zhang
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Structures ◽  
Computing Time ◽  
Periodic Boundary Conditions ◽  
Numerical Results ◽  
General Boundary Condition ◽  
Matlab Code ◽  
Stent Expansion ◽  
Representative Model

The stent is commonly used to support blood vessels to avoid blood obstruction. Its tubular structure is a combination of micro periodic structures. The stent is expanded uniformly due to its internal pressure during the implantation process until plastic deformation occurs. In this article, the simulation of a representative model with application of the proposed periodic boundary conditions is performed by using ABAQUS/Explicit package and Matlab code. To make a comparison, the entire model of the same type stent with general boundary condition is also analyzed. The numerical results show that the deformation and stress distribution calculated by the representative model is a little higher than those of the entire model, but their overall results agree well with each other. Therefore, the numerical results of the entire stent can be obtained by a simple geometrical tessellation of the deformed representative models. The advantage of this method is that it can significantly reduce the modeling and computing time for analyzing expansion of vessel stent.

Molecular Dynamics Using Non-Variational Polarizable Force Fields: Theory, Periodic Boundary Conditions Implementation and Application to the Bond Capacity Model

2019 ◽  
Author(s):  
Pier Paolo Poier ◽  
Louis Lagardere ◽  
Jean-Philip Piquemal ◽  
Frank Jensen
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Force Fields ◽  
Periodic Boundary Conditions ◽  
Computational Effort ◽  
Polarizable Force Fields ◽  
Energy Models ◽  
Capacity Model ◽  
Energy Gradient ◽  
Polarization Models

<div> <div> <div> <p>We extend the framework for polarizable force fields to include the case where the electrostatic multipoles are not determined by a variational minimization of the electrostatic energy. Such models formally require that the polarization response is calculated for all possible geometrical perturbations in order to obtain the energy gradient required for performing molecular dynamics simulations. </p><div> <div> <div> <p>By making use of a Lagrange formalism, however, this computational demanding task can be re- placed by solving a single equation similar to that for determining the electrostatic variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p><div><div><div> </div> </div> </div> <p> </p><div> <div> <div> <p>variables themselves. Using the recently proposed bond capacity model that describes molecular polarization at the charge-only level, we show that the energy gradient for non-variational energy models with periodic boundary conditions can be calculated with a computational effort similar to that for variational polarization models. The possibility of separating the equation for calculating the electrostatic variables from the energy expression depending on these variables without a large computational penalty provides flexibility in the design of new force fields. </p> </div> </div> </div> </div> </div> </div> </div> </div> </div>

scholarly journals Sharp Lyapunov-type inequalities for second-order half-linear difference equations with different kinds of boundary conditions

2021 ◽  
Vol 115 (3) ◽  
Author(s):  
Robert Stegliński
Keyword(s):  
Difference Equation ◽  
Boundary Conditions ◽  
Difference Equations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Second Order ◽  
Linear Difference Equations ◽  
Order Difference ◽  
Second Order Difference Equation ◽  
Order Difference Equation

AbstractIn this work, we establish optimal Lyapunov-type inequalities for the second-order difference equation with p-Laplacian $$\begin{aligned} \Delta (\left| \Delta u(k-1)\right| ^{p-2}\Delta u(k-1))+a(k)\left| u(k)\right| ^{p-2}u(k)=0 \end{aligned}$$ Δ ( Δ u ( k - 1 ) p - 2 Δ u ( k - 1 ) ) + a ( k ) u ( k ) p - 2 u ( k ) = 0 with Dirichlet, Neumann, mixed, periodic and anti-periodic boundary conditions.

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