Lorentz Lattice Gases and Many-Dimensional Turing Machines

2002 ◽  
pp. 443-467 ◽  
Author(s):  
Leonid A. Bunimovich ◽  
Milena A. Khlabystova
Keyword(s):  
Lattice Gases ◽  
Turing Machines ◽  
Lorentz Lattice Gases

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.

Lorentz lattice gases: Basic theory

1988 ◽  
Vol 51 (5-6) ◽  
pp. 981-990 ◽  
Author(s):  
M. H. Ernst ◽  
P. M. Binder
Keyword(s):  
Basic Theory ◽  
Lattice Gases ◽  
Lorentz Lattice Gases

Novel phenomena in Lorentz lattice gases

1995 ◽  
Vol 219 (1-2) ◽  
pp. 56-87 ◽  
Author(s):  
E.G.D. Cohen ◽  
F. Wang
Keyword(s):  
Lattice Gases ◽  
Lorentz Lattice Gases

scholarly journals Chaos properties and localization in Lorentz lattice gases

1997 ◽  
Vol 56 (5) ◽  
pp. 5106-5122 ◽  
Author(s):  
C. Appert ◽  
M. H. Ernst
Keyword(s):  
Lattice Gases ◽  
Lorentz Lattice Gases

scholarly journals Applications of Temperley - Lieb algebras to Lorentz lattice gases

1998 ◽  
Vol 31 (43) ◽  
pp. L723-L729 ◽  
Author(s):  
M J Martins ◽  
B Nienhuis
Keyword(s):  
Lattice Gases ◽  
Lorentz Lattice Gases

Lorentz lattice gases, abnormal diffusion, and polymer statistics

1991 ◽  
Vol 62 (5-6) ◽  
pp. 1153-1171 ◽  
Author(s):  
X. P. Kong ◽  
E. G. D. Cohen
Keyword(s):  
Lattice Gases ◽  
Lorentz Lattice Gases ◽  
Polymer Statistics
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