Theory of relaxation processes in polymers. The dynamics of three-dimensional lattice models of polymer chains

1969 ◽  
Vol 11 (11) ◽  
pp. 2725-2736 ◽  
Author(s):  
Yu.Ya. Gotlib ◽  
A.A. Darinskii
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Polymer Chains ◽  
Relaxation Processes ◽  
Dimensional Lattice

Solvable Three-Dimensional Lattice Models

1963 ◽  
Vol 132 (3) ◽  
pp. 1085-1092 ◽  
Author(s):  
Bruce W. Knight ◽  
Gerald A. Peterson
Keyword(s):  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice

Walk of a Point Defect in a Model with Macroscopic Ground State Degeneracy

1997 ◽  
Vol 11 (07) ◽  
pp. 293-296 ◽  
Author(s):  
A. V. Bakaev ◽  
V. I. Kabanovich
Keyword(s):  
Point Defect ◽  
Ground State ◽  
State Energy ◽  
Hard Spheres ◽  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice ◽  
Cubic Lattices ◽  
Ground State Degeneracy ◽  
Antiferromagnetic Potts Model

Walks of the point defect in the two- and three-dimensional lattice models of colored hard spheres mimicking the q-state antiferromagnetic Potts model are considered. The walks are generated by moves of neighboring vertices which conserve the ground state energy. Various "traps" confining the walks are observed, while for the models with q≥4 and q≥5 on the square and cubic lattices respectively nonvanishing probabilities that all lattice vertices are attainable in a walk are found.

scholarly journals Continued Classification of 3D Lattice Models in the Positive Octant

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Axel Bacher ◽  
Manuel Kauers ◽  
Rika Yatchak
Keyword(s):  
Asymptotic Behaviour ◽  
Generating Function ◽  
Asymptotic Form ◽  
Three Dimensional ◽  
Lattice Models ◽  
Dimensional Lattice ◽  
Lattice Walks ◽  
Small Set ◽  
International Audience

International audience We continue the investigations of lattice walks in the three-dimensional lattice restricted to the positive octant. We separate models which clearly have a D-finite generating function from models for which there is no reason to expect that their generating function is D-finite, and we isolate a small set of models whose nature remains unclear and requires further investigation. For these, we give some experimental results about their asymptotic behaviour, based on the inspection of a large number of initial terms. At least for some of them, the guessed asymptotic form seems to tip the balance towards non-D-finiteness.

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