NUMERICAL STUDY OF THE Q-COLOR PROBLEM ON A LATTICE

1987 ◽  
Vol 01 (01) ◽  
pp. 111-119 ◽  
Author(s):  
XIYAO CHEN ◽  
C.Y. PAN
Keyword(s):  
Numerical Study ◽  
Strong Support ◽  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Zero Temperature ◽  
Color Problem ◽  
Exact Answer ◽  
Hypercubic Lattice ◽  
Good Agreement

By using the finite size extrapolation method and combined with a Monte Carlo simulation we have calculated the zero temperature entropy of the q-state Potts Antiferromagnet in two and three dimensions which is identical to the q-color problem in two and three dimensions. The model is laid on a hypercubic lattice. When q=3 (in two dimensions) the result is in good agreement with Lieb’s exact answer. When q>3 (in two and three dimensions) the results are in strong support of Mattis’ recent conjecture for the q-color problem. This method can also treat the d>3 cases without serious difficulties.

Q-COLOR PROBLEM IN D DIMENSIONS

1988 ◽  
Vol 02 (06) ◽  
pp. 1503-1511 ◽  
Author(s):  
C. Y. PAN ◽  
X. Y. CHEN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Cell Growth ◽  
Recursion Formula ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Four Dimensions ◽  
Color Problem ◽  
Hypercubic Lattice ◽  
Growth Method

Two methods are introduced to deal with the general q-color problem on a d-dimensional hypercubic lattice: one is the cell-growth method which gives an approximative solution of the problem in two and three dimensions, another is to combine the cell-growth method with the Monte Carlo simulation which leads to a recursion formula for the problem in d-dimensions. The results of both methods are in excellent agreement with Lieb's exact solution for the case of q = 3 in two dimensions and support Mattis' conjecture in the case of q > d, improve it in the case of 2 < q ≲ d. The validity of the recursion formula is supported by a Monte Carlo simulation up to four-dimensions.

Three-State Lattice-Gas Model of H-S on Pt(111)

1987 ◽  
Vol 111 ◽  
Author(s):  
Per Arne Rikvold ◽  
Joseph B. Collins ◽  
G. D. Hansen ◽  
J. D. Gunton ◽  
E. T. Gawlinski
Keyword(s):  
Adsorption Isotherms ◽  
Ground State ◽  
Lattice Gas ◽  
Nearest Neighbor ◽  
Numerical Study ◽  
Finite Size ◽  
Lateral Interaction ◽  
Finite Size Scaling ◽  
Enhanced Adsorption ◽  
Good Agreement

AbstractWe consider a three-state lattice-gas with nearest-neighbor interactions on a triangular lattice as a model for multicomponent chemi- and physisorption. By varying the lateral interaction constants between the adsorbate particles, this model can be made to exhibit either enhanced adsorption or poisoning (inhibited adsorption). We discuss here the conditions on the interaction constants that lead to poisoning. We present the results of a ground-state calculation and detailed numerical study of the phase diagram for a set of interactions that exhibits poisoning. We calculate the phase diagrams and adsorption isotherms by the finite-size scaling transfer-matrix method. We consider the result as a simple model for the coadsorption of Sulphur and Hydrogen on a Platinum (111) surface, with interaction constants estimated from experimental data. The resulting adsorption isotherms are in good agreement with experimental results.

scholarly journals Magnetohydrodynamic convection in molten gallium

1999 ◽  
Vol 378 ◽  
pp. 97-118 ◽  
Author(s):  
A. JUEL ◽  
T. MULLIN ◽  
H. BEN HADID ◽  
D. HENRY
Keyword(s):  
Magnetic Field ◽  
Free Convection ◽  
Numerical Study ◽  
Two Dimensions ◽  
Main Flow ◽  
Temperature Gradients ◽  
Two Dimensional ◽  
Steady Magnetic Field ◽  
The Magnetic Field ◽  
Good Agreement

We present the results of an experimental and numerical study of the effects of a steady magnetic field on sidewall convection in molten gallium. The magnetic field is applied in a direction which is orthogonal to the main flow which reduces the convection and good agreement is found for the scaling of this effect with the relevant parameters. Moreover, qualitatively similar changes in the structure of the bulk of the flow are observed in the experiment and the numerical simulations. In particular, the flow is restricted to two dimensions by the magnetic field, but it remains different to that found in two-dimensional free convection calculations. We also show that oscillations found at even greater temperature gradients can be suppressed by the magnetic field.

Softening Instability: Part II—Localization Into Ellipsoidal Regions

1988 ◽  
Vol 55 (3) ◽  
pp. 523-529 ◽  
Author(s):  
Zdeneˇk P. Bazˇant
Keyword(s):  
Strain Softening ◽  
Finite Size ◽  
Elastic Solid ◽  
Two Dimensions ◽  
The Body ◽  
Three Dimensions ◽  
Strain Diagram ◽  
Equilibrium Path ◽  
Special Cases ◽  
Localization Instability

Extending the preceding study of exact solutions for finite-size strain-softening regions in layers and infinite space, exact solution of localization instability is obtained for the localization of strain into an ellipsoidal region in an infinite solid. The solution exploits Eshelby’s theorem for eigenstrains in elliptical inclusions in an infinite elastic solid. The special cases of localization of strain into a spherical region in three dimensions and into a circular region in two dimensions are further solved for finite solids — spheres in 3D and circles in 2D. The solutions show that even if the body is infinite the localization into finite regions of such shapes cannot take place at the start of strain-softening (a state corresponding to the peak of the stress-strain diagram) but at a finite strain-softening slope. If the size of the body relative to the size of the softening region is decreased and the boundary is restrained, homogeneous strain-softening remains stable into a larger strain. The results also can be used as checks for finite element programs for strain-softening. The present solutions determine only stability of equilibration states but not bifurcations of the equilibrium path.

scholarly journals ON THE S MATRIX OF THE SUBLEADING MAGNETIC DEFORMATION OF THE TRICRITICAL ISING MODEL IN TWO DIMENSIONS

1992 ◽  
Vol 07 (21) ◽  
pp. 5281-5305 ◽  
Author(s):  
F. COLOMO ◽  
G. MUSSARDO ◽  
A. KOUBEK
Keyword(s):  
Ising Model ◽  
Finite Size ◽  
Numerical Data ◽  
Two Dimensions ◽  
Conformal Space ◽  
Crossing Symmetry ◽  
S Matrix ◽  
Space Approach ◽  
Good Agreement

We compute the S matrix of the tricritical Ising model perturbed by the subleading magnetic operator using Smirnov’s RSOS reduction of the Izergin-Korepin model. The massive model contains kink excitations which interpolate between two degenerate asymmetric vacua. As a consequence of the different structure of the two vacua, the crossing symmetry is implemented in a nontrivial way. We use finite-size techniques to compare our results with the numerical data obtained by the truncated conformal space approach and find good agreement.

A Comparative Numerical Study of Particle Mixing on Different Grate Designs Through the Discrete Element Method

2006 ◽  
Vol 129 (4) ◽  
pp. 593-600 ◽  
Author(s):  
Harald Kruggel-Emden ◽  
Erdem Simsek ◽  
Siegmar Wirtz ◽  
Viktor Scherer
Keyword(s):  
Granular Flow ◽  
Numerical Study ◽  
Discrete Element ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Mixing Process ◽  
Particle Mixing ◽  
Mixing Parameters ◽  
Discrete Element Simulations ◽  
Over Time

Based on LEAT’s discrete element codes, granular flow and mixing on conveying equipment are studied in two and three dimensions. Discrete element simulations, which are briefly introduced, provide detailed information on particle positions and velocities over time. This information is used to derive quantities characterizing the dynamic process of mixing. The main focus of the study presented is the mixing process of inhomogeneous particle ensembles on different grate types. For this purpose, the introduced mixing parameters are used to compare the mixing in a 3D situation with the corresponding 2D approximation on identical grates and to compare different grate designs in two dimensions.

MONTE CARLO STUDIES OF THE THREE-DIMENSIONAL ISING MODEL IN EQUILIBRIUM

2001 ◽  
Vol 12 (07) ◽  
pp. 911-1009 ◽  
Author(s):  
MARTIN HASENBUSCH
Keyword(s):  
Monte Carlo ◽  
Ising Model ◽  
Monte Carlo Simulations ◽  
Three Dimensional ◽  
Finite Size ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Amplitude Ratios ◽  
Interface Tension ◽  
Monte Carlo Studies

We review Monte Carlo simulations of the Ising model and similar models in three dimensions that were performed in the last decade. Only recently, Monte Carlo simulations provide more accurate results for critical exponents than field theoretic methods, such as the ∊-expansion. These results were obtained with finite size scaling and "improved actions". In addition, we summarize Monte Carlo results for universal amplitude ratios, the interface tension, and the dimensional crossover from three to two dimensions.

Numerical Study on Uniaxial Compression Failure of Brittle Material with a Single Flaw

2015 ◽  
Vol 1119 ◽  
pp. 683-687
Author(s):  
Jia Shen Tian ◽  
Cheng Zhao
Keyword(s):  
Uniaxial Compression ◽  
Numerical Study ◽  
Failure Process ◽  
Fracture Analysis ◽  
Two Dimensions ◽  
Analysis Software ◽  
Numerical Investigations ◽  
Compression Failure ◽  
Single Flaw ◽  
Good Agreement

Numerical investigations on failure process of rock-like materials with a single flaw were carried out under uniaxial compression based on the fracture analysis software: Fracture Analysis Code in Two Dimensions (FRANC2D/L). The change of the displacements and stress distribution were recorded around the crack. Comparative analysis is made among samples containing different angled flaw, which has great influnce on the process of crack initiation and propagetion, and with the increase of flaw angle from 30° to 75°, peak strength of the specimen increases linearly, basically. Which are in good agreement with those of experiments.

FINITE TEMPERATURE ENTROPY OF THE ANTIFERROMAGNETIC POTTS MODEL

1988 ◽  
Vol 02 (06) ◽  
pp. 1495-1501 ◽  
Author(s):  
X. Y. CHEN ◽  
C. Y. PAN
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Potts Model ◽  
Finite Temperature ◽  
Three Dimensions ◽  
Universal Relation ◽  
Zero Temperature ◽  
Disorder Transition ◽  
Color Problem ◽  
Antiferromagnetic Potts Model

Monte Carlo simulation is used to deal with the finite temperature entropy of the q-state antiferromagnetic Potts model which is the extension of the general q-color problem (at zero temperature). The finite temperature entropy of the model in two and three dimensions is obtained which is consistent with the zero temperature results. A possible universal relation of the model to determine when the order-disorder transition happens is proposed.

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