scholarly journals Deviation from Local Equilibrium Distribution in One-Dimensional Lattice Thermal Conduction

2006 ◽  
Vol 162 ◽  
pp. 220-227
Author(s):  
Shinji Takesue ◽  
Akira Ueda
Keyword(s):  
Thermal Conduction ◽  
Equilibrium Distribution ◽  
Local Equilibrium ◽  
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.

Physical nearest-neighbour models and non-linear time-series

1971 ◽  
Vol 8 (2) ◽  
pp. 222-232 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Equilibrium Distribution ◽  
Linear Models ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Non Linear

A general class of spatial-temporal Markov processes is defined leading to the standard spatial equilibrium distribution for nearest-neighbour models on a multi-dimensional lattice. Physical properties are obtainable from the marginal spatial spectral function. However, only the simplest one-dimensional case corresponds to a linear model with a readily derived spectrum. Non-linear models corresponding to two- and three-dimensional lattices are presented in their simplest terms, and a preliminary discussion of approximate solutions is included.

Physical nearest-neighbour models and non-linear time-series

1971 ◽  
Vol 8 (02) ◽  
pp. 222-232 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Equilibrium Distribution ◽  
Linear Models ◽  
Linear Time ◽  
Three Dimensional ◽  
Approximate Solutions ◽  
Nearest Neighbour ◽  
Spatial Equilibrium ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Non Linear

A general class of spatial-temporal Markov processes is defined leading to the standard spatial equilibrium distribution for nearest-neighbour models on a multi-dimensional lattice. Physical properties are obtainable from the marginal spatial spectral function. However, only the simplest one-dimensional case corresponds to a linear model with a readily derived spectrum. Non-linear models corresponding to two- and three-dimensional lattices are presented in their simplest terms, and a preliminary discussion of approximate solutions is included.

scholarly journals DIFFERENTIAL EQUATION APPROACH FOR ONE- AND TWO-DIMENSIONAL LATTICE GREEN'S FUNCTION

2007 ◽  
Vol 21 (02n03) ◽  
pp. 139-154 ◽  
Author(s):  
J. H. ASAD
Keyword(s):  
Differential Equation ◽  
Green’S Function ◽  
Recurrence Relation ◽  
Green's Function ◽  
Two Dimensional ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One ◽  
Lattice Green's Function ◽  
Lattice Green’S Function

A first-order differential equation of Green's function, at the origin G(0), for the one-dimensional lattice is derived by simple recurrence relation. Green's function at site (m) is then calculated in terms of G(0). A simple recurrence relation connecting the lattice Green's function at the site (m, n) and the first derivative of the lattice Green's function at the site (m ± 1, n) is presented for the two-dimensional lattice, a differential equation of second order in G(0, 0) is obtained. By making use of the latter recurrence relation, lattice Green's function at an arbitrary site is obtained in closed form. Finally, the phase shift and scattering cross-section are evaluated analytically and numerically for one- and two-impurities.

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