scholarly journals Diffusion of small clusters on metal (100) surfaces: Exact master-equation analysis for lattice-gas models

1999 ◽  
Vol 59 (4) ◽  
pp. 3224-3233 ◽  
Author(s):  
J. R. Sanchez ◽  
J. W. Evans
Keyword(s):  
Master Equation ◽  
Lattice Gas ◽  
Equation Analysis ◽  
Lattice Gas Models ◽  
Small Clusters

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

UNIFORM ERGODIC THEOREMS ON APERIODIC LINEARLY REPETITIVE TILINGS AND APPLICATIONS

2008 ◽  
Vol 20 (05) ◽  
pp. 597-623 ◽  
Author(s):  
ADNENE BESBES
Keyword(s):  
Lattice Gas ◽  
Weak Form ◽  
Ergodic Theorems ◽  
Self Similarity ◽  
Lattice Gas Models

The paper is concerned with aperiodic linearly repetitive tilings. For such tilings, we establish a weak form of self-similarity that allows us to prove general (sub)additive ergodic theorems. Finally, we provide applications to the study of lattice gas models.

Lattice gas models for nonideal gas fluids

1991 ◽  
Vol 47 (1-2) ◽  
pp. 97-111 ◽  
Author(s):  
Shiyi Chen ◽  
Hudong Chen ◽  
Gary D. Doolen ◽  
Y.C. Lee ◽  
H. Rose ◽  
...  
Keyword(s):  
Lattice Gas ◽  
Nonideal Gas ◽  
Lattice Gas Models

Boltzmann master equation analysis of preequilibrium neutron emission from heavy-ion collisions at 35 MeV/nucleon

1988 ◽  
Vol 38 (4) ◽  
pp. 1746-1756 ◽  
Author(s):  
B. A. Remington ◽  
M. Blann ◽  
A. Galonsky ◽  
L. Heilbronn ◽  
F. Deak ◽  
...  
Keyword(s):  
Master Equation ◽  
Heavy Ion Collisions ◽  
Neutron Emission ◽  
Heavy Ion ◽  
Ion Collisions ◽  
Equation Analysis

Spatial Correlations in Growing Films

2000 ◽  
Vol 619 ◽  
Author(s):  
M.C. Bartelt
Keyword(s):  
Size Distribution ◽  
Lattice Gas ◽  
Mean Field ◽  
Film Deposition ◽  
Nucleation Theory ◽  
Spatial Correlations ◽  
Island Size ◽  
Pit Formation ◽  
Free Region ◽  
Lattice Gas Models

ABSTRACTDetailed analyses of non-equilibrium lattice-gas models of island nucleation and growth during film deposition (or etching) have been invaluable in elucidating basic issues in nucleation theory, deviations from mean-field predictions, and experimental observations. Particularly interesting and useful is the behavior of spatial correlations in the adlayer which develop during island (or pit) formation. In particular, a strong depletion in the population of island pairs at separations smaller than the average follows from depletion in the density of diffusing adspecies near islands. This feature delays percolation of clusters of coalesced islands. Another recently discovered and more subtle feature is a strong correlation between the width of the island-free region surrounding an island and the size and growth rate of that island. This direct correlation between island sizes and separations controls the shape of the island size distribution. If incorporated into rate-equation descriptions, it recovers the exact form of the scaling function for the island size distribution.

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