Diffusion in concentrated lattice gases: Intermediate incoherent dynamical scattering function for tagged particles on a square lattice

1990 ◽  
Vol 41 (5) ◽  
pp. 2784-2793 ◽  
Author(s):  
Ryszard Kutner ◽  
Klaus W. Kehr
Keyword(s):  
Lattice Gases ◽  
Square Lattice ◽  
Scattering Function

Theoretical Models of Cooperative Dynamics Near the Glass Transition

1990 ◽  
Vol 215 ◽  
Author(s):  
Josef Jäckle
Keyword(s):  
Glass Transition ◽  
Lattice Gas ◽  
Finite Size ◽  
Theoretical Models ◽  
Lattice Gases ◽  
Bootstrap Percolation ◽  
Square Lattice ◽  
High Particle Concentration ◽  
High Particle ◽  
Percolation Problem

AbstractIt is shown that diffusion in the hard-square and hard-octahedron lattice gases at high particle concentration has cooperative properties resembling molecular relaxation in undercooled liquids near the glass transition. For these models a characteristic length of cooperativity is introduced by an underlying percolation problem, which determines whether permanently blocked particles exist in lattices of finite size. The percolation problem belongs to a general class of bootstrap percolation models. Salient Monte Carlo results for the concentration and size dependence of self diffusion in the hard-square lattice gas are presented. Similarities with the n-spin facilitated kinetic Ising models are also pointed out.

INTERFACE INSTABILITY IN DRIVEN LATTICE GASES

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 954-958 ◽  
Author(s):  
G. SZABÓ ◽  
A. SZOLNOKI ◽  
T. ANTAL ◽  
I. BORSOS
Keyword(s):  
Lattice Gas ◽  
Nearest Neighbor ◽  
Interfacial Instability ◽  
Lattice Gases ◽  
Square Lattice ◽  
Wave Number ◽  
Material Transport ◽  
Interface Instability ◽  
Amplification Rate ◽  
Lattice Gas Models

In driven lattice-gas models, the enhanced material transport along the interfaces results in an instability of the planar interfaces and leads to the formation of multistrip states. To study the interfacial instability, Monte Carlo simulations are performed on different square lattice-gas models. The amplification rate of a periodic perturbation depends on the wave number k; it has a positive maximum at a characteristic value of k on the analogy of the Mullins-Sekerka instability. Significant differences have been found in the dependence of amplification rate on k when comparing the systems with nearest neighbor repulsive and nearest and next-nearest neighbor attractive interactions. The results agree qualitatively with theories neglecting the fluctuations.

MANY-DIMENSIONAL LORENTZ CELLULAR AUTOMATA AND TURING MACHINES

1996 ◽  
Vol 06 (06) ◽  
pp. 1127-1135 ◽  
Author(s):  
LEONID A. BUNIMOVICH
Keyword(s):  
Cellular Automata ◽  
Artificial Life ◽  
Lattice Gases ◽  
Square Lattice ◽  
Turing Machines ◽  
Natural Conditions ◽  
Vortex Sheets ◽  
Cubic Lattices ◽  
Higher Dimensional ◽  
Lorentz Lattice Gases

We study the class of cellular automata that generalizes the Lorentz lattice gases in statistical mechanics, the models of industrious ants in the theory of an artificial life and the so-called Tur-mites (many-dimensional Turing machines). We prove that on the square lattice ℤd, d = 2, the existence of a bounded orbit of a particle (ant, machine) determines all nondegenerate local scattering rules (states of a machine). For higher dimensional (d ≥ 3) cubic lattices we show that under some natural conditions all possible bounded orbits (vortices) can live only in some “vortex sheets” that have a dimension strictly less than d.

The temperature and frequency dependence of the inelastic neutron scattering from an Ising magnet

1968 ◽  
Vol 46 (7) ◽  
pp. 799-802 ◽  
Author(s):  
G. A. T. Allan ◽  
D. D. Betts
Keyword(s):  
Inelastic Scattering ◽  
Inelastic Neutron Scattering ◽  
Three Dimensional ◽  
Ising Models ◽  
Inelastic Neutron ◽  
Square Lattice ◽  
Two Dimensional ◽  
Scattering Function ◽  
Ising Magnet ◽  
Exact Energy

The magnetic inelastic scattering of neutrons from a spin-[Formula: see text] Ising system is considered. For the two-dimensional plane square lattice, the exact energy distribution of the scattering is obtained at all temperatures. It consists of a number of discrete levels, the envelope of which varies most markedly in the critical region. Some qualitative projections are also made concerning three-dimensional systems. For both two- and three-dimensional Ising models there can be no wave-vector dependence of the inelastic scattering function because there is correlation only between z components of the spins on different sites.

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