Shock propagation in the one‐dimensional lattice at a nonzero initial temperature

1978 ◽  
Vol 49 (7) ◽  
pp. 3933-3940 ◽  
Author(s):  
Jad H. Batteh ◽  
John D. Powell
Keyword(s):  
Initial Temperature ◽  
Shock Propagation ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One

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.

The spread of flame across a liquid surface II. Steady-state conditions

1968 ◽  
Vol 308 (1492) ◽  
pp. 55-68 ◽  
Keyword(s):  
Steady State ◽  
Gas Phase ◽  
Flame Spread ◽  
Initial Temperature ◽  
Liquid Surface ◽  
Flash Point ◽  
One Dimensional ◽  
Flammable Liquids ◽  
The One ◽  
Qualitative Picture

The one-dimensional spread of flame along the surface of flammable liquids confined in a parallel-sided channel has been studied and the effects of physical dimensions and initial temperature upon its rate established. When the initial temperature of the liquid is below the closed flash point, flame spread depends upon the transfer of heat to the liquid sufficient to raise its surface temperature to the flash-point value and a qualitative picture of the mechanism by which this takes place is developed. When the initial temperature is above the flash point, flame spread is dependent upon conditions in the gas phase above the liquid and these are defined.

scholarly journals Correlation length critical exponent as a function of the percolation radius for one-dimensional chains in bond problems

2021 ◽  
Vol 2094 (2) ◽  
pp. 022038
Author(s):  
T V Yakunina ◽  
V N Udodov
Keyword(s):  
Critical Exponent ◽  
Percolation Threshold ◽  
Correlation Length ◽  
Adjacency Matrix ◽  
Nearest Neighbors ◽  
Percolation Model ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
The One

Abstract A one-dimensional lattice percolation model is constructed for the problem of constraints flowing along non-nearest neighbors. In this work, we calculated the critical exponent of the correlation length in the one-dimensional bond problem for a percolation radius of up to 6. In the calculations, we used a method without constructing a covering lattice or an adjacency matrix (to find the percolation threshold). The values of the critical exponent of the correlation length were obtained in the one-dimensional bond problem depending on the size of the system and at different percolation radii. Based on original algorithms that operate on a computer faster than standard ones (associated with the construction of a covering lattice), these results are obtained with corresponding errors.

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