scholarly journals Glassy behaviour in short-range lattice models without quenched disorder

2002 ◽  
Vol 82 (5) ◽  
pp. 617-623 ◽  
Author(s):  
Mário J. de Oliveira ◽  
Alberto Petri
Keyword(s):  
Short Range ◽  
Lattice Models ◽  
Quenched Disorder

scholarly journals Glassy behaviour in short-range lattice models without quenched disorder

2002 ◽  
Vol 82 (5) ◽  
pp. 617-623 ◽  
Author(s):  
Mário J. De Oliveira ◽  
Alberto Petri
Keyword(s):  
Short Range ◽  
Lattice Models ◽  
Quenched Disorder

scholarly journals LATTICE THREE-SPECIES MODELS OF THE SPATIAL SPREAD OF RABIES AMONG FOXES

1999 ◽  
Vol 10 (06) ◽  
pp. 1025-1038 ◽  
Author(s):  
A. BENYOUSSEF ◽  
N. BOCCARA ◽  
H. CHAKIB ◽  
H. EZ-ZAHRAOUY
Keyword(s):  
Carrying Capacity ◽  
Short Range ◽  
Lattice Models ◽  
Infection Process ◽  
Spatial Spread ◽  
One Dimensional ◽  
Sense Of Direction ◽  
Speed Of Propagation ◽  
Automata Network ◽  
And Diffusion

Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.

scholarly journals Particles, conformal invariance and criticality in pure and disordered systems

2021 ◽  
Vol 94 (3) ◽  
Author(s):  
Gesualdo Delfino
Keyword(s):  
Conformal Invariance ◽  
Disordered Systems ◽  
Short Range ◽  
Recent Progress ◽  
Quenched Disorder ◽  
Exact Methods ◽  
Special Position ◽  
Infinite Dimensional ◽  
First Order ◽  
The Continuum

AbstractThe two-dimensional case occupies a special position in the theory of critical phenomena due to the exact results provided by lattice solutions and, directly in the continuum, by the infinite-dimensional character of the conformal algebra. However, some sectors of the theory, and most notably criticality in systems with quenched disorder and short-range interactions, have appeared out of reach of exact methods and lacked the insight coming from analytical solutions. In this article, we review recent progress achieved implementing conformal invariance within the particle description of field theory. The formalism yields exact unitarity equations whose solutions classify critical points with a given symmetry. It provides new insight in the case of pure systems, as well as the first exact access to criticality in presence of short range quenched disorder. Analytical mechanisms emerge that in the random case allow the superuniversality of some critical exponents and make explicit the softening of first-order transitions by disorder.Graphic abstract

scholarly journals Viscous fingering in the presence of weak disorder

2020 ◽  
Vol 15 ◽  
pp. 2
Author(s):  
Eldad Bettelheim ◽  
Oded Agam
Keyword(s):  
Correlation Function ◽  
Fractal Dimension ◽  
Harmonic Measure ◽  
Short Range ◽  
Viscous Fingering ◽  
Quenched Disorder ◽  
Weak Disorder ◽  
Box Counting ◽  
Point Correlation ◽  
Point Correlation Function

We consider the problem of viscous fingering in the presence of quenched disorder, that is both weak and short-range correlated. The two-point correlation function of the harmonic measure is calculated perturbatively, and is used in order to calculate the correction and the box-counting fractal dimension. We show that the disorder increases the fractal dimension, and that its effect decreases logarithmically with the size of the fractal.

scholarly journals Extinction of epidemics in lattice models with quenched disorder

2005 ◽  
Vol 72 (1) ◽  
Author(s):  
S. N. Taraskin ◽  
J. J. Ludlam ◽  
C. J. Neugebauer ◽  
C. A. Gilligan
Keyword(s):  
Lattice Models ◽  
Quenched Disorder

DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS

1991 ◽  
Vol 03 (02) ◽  
pp. 125-135 ◽  
Author(s):  
CHARLES RADIN
Keyword(s):  
Dynamical Systems ◽  
Statistical Mechanics ◽  
Continuous Spectrum ◽  
Ground State ◽  
Short Range ◽  
Ground States ◽  
Lattice Models ◽  
Positive Entropy ◽  
Classical Lattice ◽  
Classical Statistical Mechanics

We use strictly ergodic dynamical systems to describe two methods for constructing short range interactions of classical statistical mechanics models with unique ground states and unusual properties of disorder; in particular, these ground states can be mixing under translations (and therefore have purely continuous spectrum), and can have positive entropy. Because of the uniqueness of the ground state the disorder is not of the usual type associated with local degeneracy.

Domain coarsening by grain boundary migration in ordered Ni4Mo

1986 ◽  
Vol 44 ◽  
pp. 560-561
Author(s):  
K. Vasudevan ◽  
H. P. Kao ◽  
C. R. Brooks ◽  
E. E. Stansbury
Keyword(s):  
Grain Boundary ◽  
Grain Boundaries ◽  
Short Range ◽  
Boundary Migration ◽  
Grain Boundary Migration ◽  
Rapid Cooling ◽  
Temperature Range ◽  
Fee Structure ◽  
Domain Coarsening ◽  
Boundary Reaction

The Ni4Mo alloy has a short-range ordered fee structure (α) above 868°C, but transforms below this temperature to an ordered bet structure (β) by rearrangement of atoms on the fee lattice. The disordered α, retained by rapid cooling, can be ordered by appropriate aging below 868°C. Initially, very fine β domains in six different but crystallographically related variants form and grow in size on further aging. However, in the temperature range 600-775°C, a coarsening reaction begins at the former α grain boundaries and the alloy also coarsens by this mechanism. The purpose of this paper is to report on TEM observations showing the characteristics of this grain boundary reaction.

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