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.

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.

scholarly journals Mixing and demixing of binary mixtures of polar chiral active particles

Soft Matter ◽  
2018 ◽  
Vol 14 (21) ◽  
pp. 4388-4395 ◽  
Author(s):  
Bao-quan Ai ◽  
Zhi-gang Shao ◽  
Wei-rong Zhong
Keyword(s):  
Binary Mixture ◽  
Boundary Conditions ◽  
Binary Mixtures ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
Active Particles

We study a binary mixture of polar chiral (counterclockwise or clockwise) active particles in a two-dimensional box with periodic boundary conditions.

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.

scholarly journals Global Attractors of Sixth Order PDEs Describing the Faceting of Growing Surfaces

2015 ◽  
Vol 28 (1) ◽  
pp. 49-67 ◽  
Author(s):  
M. D. Korzec ◽  
P. Nayar ◽  
P. Rybka
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Initial Conditions ◽  
Periodic Boundary Conditions ◽  
Global Attractors ◽  
Sixth Order ◽  
Two Dimensional ◽  
One Dimensional ◽  
Crystalline Surface ◽  
Dimensional Version

Abstract A spatially two-dimensional sixth order PDE describing the evolution of a growing crystalline surface h(x, y, t) that undergoes faceting is considered with periodic boundary conditions, as well as its reduced one-dimensional version. These equations are expressed in terms of the slopes $$u_1=h_{x}$$ u 1 = h x and $$u_2=h_y$$ u 2 = h y to establish the existence of global, connected attractors for both equations. Since unique solutions are guaranteed for initial conditions in $$\dot{H}^2_{per}$$ H ˙ p e r 2 , we consider the solution operator $$S(t): \dot{H}^2_{per} \rightarrow \dot{H}^2_{per}$$ S ( t ) : H ˙ p e r 2 → H ˙ p e r 2 , to gain our results. We prove the necessary continuity, dissipation and compactness properties.

DEGENERATE CRYSTALLINE PHASE IN A TWO-DIMENSIONAL SYSTEM OF HARD DIMERS

1991 ◽  
Vol 05 (28) ◽  
pp. 1843-1851 ◽  
Author(s):  
K.W. WOJCIECHOWSKI
Keyword(s):  
Monte Carlo ◽  
Thermodynamic Stability ◽  
Crystalline Phase ◽  
Solid Phase ◽  
Dimensional System ◽  
Two Dimensional ◽  
Close Packed Structure ◽  
Packed Structure ◽  
Two Dimensional System ◽  
Disordered Crystal

Monte Carlo simulations showing thermodynamic stability of a non-periodic solid phase in a system of two-dimensional hard, homonuclear dimers are reviewed briefly. The thermodynamic stability of this phase, called degenerate (or disordered) crystal, follows from a huge degeneracy of the close packed structure of the dimers. The degenerate crystalline phase and its various analogues constitute intermediate steps on a path joining periodically ordered crystalline states with completely disordered states of matter.

Two-dimensional periodic boundary conditions for demagnetization interactions in micromagnetics

2010 ◽  
Vol 49 (1) ◽  
pp. 84-87 ◽  
Author(s):  
Weiwei Wang ◽  
Congpu Mu ◽  
Bin Zhang ◽  
Qingfang Liu ◽  
Jianbo Wang ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary ◽  
Periodic Boundary Conditions ◽  
Two Dimensional
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