scholarly journals LOCALIZATION IN TWO-DIMENSIONAL SU(2) LATTICE GAUGE THEORY AND A NEW MULTIGRID METHOD

1995 ◽  
Vol 06 (01) ◽  
pp. 85-104 ◽  
Author(s):  
M. BÄKER
Keyword(s):  
Anderson Localization ◽  
Periodic Boundary ◽  
Multigrid Method ◽  
Lattice Gauge Theory ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
Localization Problem ◽  
Multigrid Algorithm ◽  
Slowing Down ◽  
Lattice Gauge

We show numerically that the lowest eigenmodes of the two-dimensional Laplace operator with SU(2) gauge couplings and periodic boundary conditions are strongly localized. A connection is drawn to the Anderson localization problem. A new multigrid algorithm, capable of dealing with these modes, shows no critical slowing down for this problem independent of the disorder.

A NOTE ON INTERFACES WITH PERIODIC BOUNDARIES

1992 ◽  
Vol 03 (05) ◽  
pp. 889-896 ◽  
Author(s):  
B. BUNK
Keyword(s):  
Free Energy ◽  
Gauge Theory ◽  
Boundary Conditions ◽  
Periodic Boundary ◽  
Lattice Gauge Theory ◽  
Periodic Boundary Conditions ◽  
Large Area ◽  
Universal Form ◽  
Lattice Gauge ◽  
Numerical Coefficient

The partition funtion of a fluctuating interface is argued to approach a universal form at large area, including the numerical coefficient, provided that the interface has periodic boundary conditions und continuum behavior. This is demonstrated by explicit calculations, using effective actions with different regularisations. The result is applied to an analysis of the vortex free energy in SU(2) lattice gauge theory.

scholarly journals CLUSTER ALGORITHMS FOR NONLINEAR SIGMA MODELS

1992 ◽  
Vol 03 (01) ◽  
pp. 213-219 ◽  
Author(s):  
ULLI WOLFF
Keyword(s):  
Lattice Gauge Theory ◽  
Percolation Cluster ◽  
Cluster Technique ◽  
Slowing Down ◽  
Monte Carlo Algorithms ◽  
Lattice Gauge ◽  
Running Coupling ◽  
Running Coupling Constant ◽  
Cluster Monte Carlo ◽  
Theory Calculation

Percolation cluster Monte Carlo algorithms for nonlinear σ-models on the lattice are reviewed with special emphasis on their possible generalizations. While they have been found to practically eliminate critical slowing down for the standard O(n) invariant vector models, their extension to other physically similar models — like RPn−1 and SU(n)×SU(n) chiral models — is less straight forward than one might have thought. I outline the present situation in this area of research. In the second part of my talk I described a numerical calculation of a physical running coupling constant in the O(3) model. This represents an application of the cluster technique in a preparatory study for a later lattice gauge theory calculation. This material can be found in Ref. 11.

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.

Effect of Permeability on Convergence Rates of Multigrid Solutions of Laminar Flows in Porous Media

2003 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Multigrid Method ◽  
Convergence Rates ◽  
Computational Effort ◽  
Laminar Flows ◽  
Two Dimensional ◽  
Multigrid Algorithm ◽  
Finite Volume Discretization ◽  
Medium Permeability ◽  
Correction Scheme ◽  
Grid Level

The present work investigates the efficiency of the multigrid method when applied to solve laminar flow in a two-dimensional tank filled with a porous material. The numerical method includes finite volume discretization with the flux blended deferred correction scheme on structure orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different numbers of sweeps in each grid level. Up to four grids, for both multigrid V- and W-cycles, are considered. Effects of medium permeability on converged rates are presented. Results indicate that W-cycles perform better in reducing the required computational effort and that the lower the permeability, faster solutions are obtained.

scholarly journals HOLOGRAPHIC GEOMETRIC ENTROPY AT FINITE TEMPERATURE FROM BLACK HOLES IN GLOBAL ANTI-DE SITTER SPACES

2012 ◽  
Vol 27 (09) ◽  
pp. 1250048 ◽  
Author(s):  
IBRAHIMA BAH ◽  
LEOPOLDO A. PANDO ZAYAS ◽  
CÉSAR A. TERRERO-ESCALANTE
Keyword(s):  
Field Theory ◽  
Black Holes ◽  
Conformal Field Theory ◽  
Periodic Boundary ◽  
Entanglement Entropy ◽  
Periodic Boundary Conditions ◽  
Two Dimensional ◽  
De Sitter ◽  
Conformal Field ◽  
The Difference

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdSp for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS3, the calculation reproduces precisely the geometric entropy of an interval of length l in a two-dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS4 and AdS5 the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS4 and AdS5.

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.

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.

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