Determination of nearest neighbor degeneracy on a one‐dimensional lattice

1976 ◽  
Vol 17 (1) ◽  
pp. 69-72 ◽  
Author(s):  
C. C. Yan
Keyword(s):  
Nearest Neighbor ◽  
Dimensional Lattice ◽  
One Dimensional

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.

Ab initio Simulation of 1D Pattern Formation of Adsorbates on the Ge(100)-2 × 1 Surface

2013 ◽  
Vol 1551 ◽  
pp. 81-86
Author(s):  
Bonggeun Shong ◽  
Stacey F. Bent
Keyword(s):  
Pattern Formation ◽  
Density Functional ◽  
Nearest Neighbor ◽  
Energy Surface ◽  
Functional Theory ◽  
Ab Initio Simulation ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Kinetic Coefficients ◽  
Simulation Results

ABSTRACTIt is known that methanol and ethylene form distinct one-dimensional patterns along the dimer row on the Ge(100)-2 × 1 surface. A unified explanation for the pattern formation is attempted in this study through theoretical methods. Kinetic parameters of the precursor-mediated adsorption of the two molecules are calculated using density functional theory methods. The potential energy surface along the reaction channel was found to vary according to nearest-neighbor occupation. Monte Carlo simulations were performed with calculated kinetic coefficients and assumptions of a one-dimensional lattice with nearest neighbor interactions. The simulation results effectively reproduce the coverage-dependent evolution of longer-range adsorption patterns.

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