Exact nearest neighbor statistics for λ‐bell particles on a one‐dimensional lattice

1977 ◽  
Vol 18 (6) ◽  
pp. 1200-1205 ◽  
Author(s):  
R. B. McQuistan
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Exact Nearest Neighbor

Thermal conduction in a quasi-stationary one-dimensional lattice system

2019 ◽  
Vol 33 (17) ◽  
pp. 1950178
Author(s):  
Mohammad Khorrami ◽  
Amir Aghamohammadi
Keyword(s):  
Heat Transfer ◽  
Ising Model ◽  
Diffusion Equation ◽  
Thermal Conduction ◽  
Nearest Neighbor ◽  
Entropy Change ◽  
Neighbor Interaction ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Special Case

A system of nearest-neighbor interaction on a one-dimensional lattice is investigated, which has a quasi-stationary (and position-dependent) temperature profile. The rates of heat transfer and entropy change, as well as the diffusion equation for the temperature are studied. A q-state Potts model, and its special case, a two-state Ising model, are considered as an example.

ATTRACTORS FOR STOCHASTIC LATTICE DYNAMICAL SYSTEMS

2006 ◽  
Vol 06 (01) ◽  
pp. 1-21 ◽  
Author(s):  
PETER W. BATES ◽  
HANNELORE LISEI ◽  
KENING LU
Keyword(s):  
Initial Data ◽  
Nearest Neighbor ◽  
Invariant Set ◽  
Neighbor Interaction ◽  
Forward Flow ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Nonlinear Reaction ◽  
Lattice Dynamical Systems ◽  
Bounded Sets

We consider a one-dimensional lattice with diffusive nearest neighbor interaction, a dissipative nonlinear reaction term and additive independent white noise at each node. We prove the existence of a compact global random attractor within the set of tempered random bounded sets. An interesting feature of this is that, even though the spatial domain is unbounded and the solution operator is not smoothing or compact, pulled back bounded sets of initial data converge under the forward flow to a random compact invariant set.

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