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ROTOR-ROUTER AGGREGATION ON THE LAYERED SQUARE LATTICE
ROTOR-ROUTER AGGREGATION LAYERED SQUARE LATTICE
2015/8/14
In rotor-router aggregation on the square lattice Z2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the clus...
Discrete breathers on symmetry-determined invariant manifolds for scalar models on the plane square lattice
Discrete breathers symmetry-determined invariant manifolds scalar models plane square lattice
2011/7/5
A group-theoretical approach for studying localized periodic and quasiperiodic vibrations in 2D
and 3D lattice dynamical models is developed. This approach is demonstrated for the scalar mod-
els on...
Enumeration of closed random walks in the square lattice according to their areas
Enumeration of closed random square lattice
2011/2/22
We study the area distribution of closed walks of length n, begin-ning and ending at the origin. The concept of area of a walk in the square lattice is generalized and the usefulness of the new concep...
T=0 Partition Functions for Potts Antiferromagnets on Square Lattice Strips with (Twisted) Periodic Boundary Conditions
Functions Potts Antiferromagnets Periodic Boundary Conditions
2010/11/2
We present exact calculations of the zero-temperature partition function for the q-state Potts antiferromagnet (equivalently, the chromatic polynomial) for two families of arbitrarily long strip graph...