Efficient implementation of periodic boundary conditions in Monte Carlo simulation

2018 ◽  
Vol 40 (5) ◽  
pp. 734-739
Author(s):  
Dzmitry V. Shakhno ◽  
Aleh V. Shakhno ◽  
Eugene Paulechka
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Efficient Implementation

Unphysical Frozen States in Monte Carlo Simulation of 2D Ising Model

1998 ◽  
Vol 09 (06) ◽  
pp. 881-886 ◽  
Author(s):  
Andres R. R. Papa
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Ising Model ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Periodic Boundary ◽  
Random Access ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
Ising Systems

We show that for two-dimensional square Ising systems unphysical frozen states are obtained by just changing the instant of application of periodic boundary conditions during Monte Carlo simulations. The strange behavior is observed up to sample sizes currently used in literature. The anomalous results appear to be associated to the simultaneous use of type writer updating algorithms; they disappear when random access routines are implemented.

Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions

1996 ◽  
Vol 53 (4) ◽  
pp. 1814-1832 ◽  
Author(s):  
Louisa M. Fraser ◽  
W. M. C. Foulkes ◽  
G. Rajagopal ◽  
R. J. Needs ◽  
S. D. Kenny ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Size Effects ◽  
Quantum Monte Carlo ◽  
Periodic Boundary ◽  
Finite Size ◽  
Periodic Boundary Conditions ◽  
Coulomb Interactions ◽  
Finite Size Effects ◽  
Monte Carlo Calculations

Grand ensemble Monte Carlo study of crystallization in sub-monolayer adsorption at a solid vapour interface

1978 ◽  
Vol 31 (5) ◽  
pp. 933 ◽  
Author(s):  
JE Lane ◽  
TH Spurling
Keyword(s):  
Monte Carlo ◽  
Adsorption Isotherm ◽  
Thermodynamic Properties ◽  
Boundary Conditions ◽  
Iterative Procedure ◽  
Periodic Boundary ◽  
Monte Carlo Study ◽  
Periodic Boundary Conditions ◽  
Ensemble Monte Carlo ◽  
Monolayer Adsorption

A grand ensemble Monte Carlo procedure is used to examine the thermodynamic properties of a crystal-like layer of krypton adsorbed at sub-monolayer coverages on graphite at 90.12 K. The effect of the periodic boundary conditions on these properties is discussed and used to develop a thermodynamically consistent iterative procedure to estimate the transition pressure and thereby fix the adsorption isotherm.

SUMMATION OF LOGARITHMIC INTERACTIONS IN PERIODIC MEDIA

1996 ◽  
Vol 07 (06) ◽  
pp. 873-881 ◽  
Author(s):  
NIELS GRØNBECH-JENSEN
Keyword(s):  
Monte Carlo ◽  
Boundary Conditions ◽  
Monte Carlo Simulations ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Dimensional System ◽  
Two Dimensional ◽  
Trigonometric Functions ◽  
Periodic Media ◽  
Two Dimensional System

We present a set of expressions for evaluating energies and forces between particles interacting logarithmically in a finite two-dimensional system with periodic boundary conditions. The formalism can be used for fast and accurate, dynamical or Monte Carlo, simulations of interacting line charges or interactions between point and line charges. The expressions are shown to converge to usual computer accuracy (~10–16) by adding only few terms in a single sum of standard trigonometric functions.

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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