Two and three particle distribution functions of one‐dimensional lattice fluids

1985 ◽  
Vol 82 (8) ◽  
pp. 3779-3785 ◽  
Author(s):  
Elijah Johnson
Keyword(s):  
Particle Distribution ◽  
Distribution Functions ◽  
Dimensional Lattice ◽  
One Dimensional

One-Diohliensilonall A + B = 0 Reactmion with One Immobile Species

1992 ◽  
Vol 290 ◽  
Author(s):  
Panos Argyrakisa ◽  
Raoul Kopelman
Keyword(s):  
Monte Carlo ◽  
Particle Distribution ◽  
Rate Coefficient ◽  
Reaction Order ◽  
Distribution Functions ◽  
Relative Mobility ◽  
Subtle Difference ◽  
Density Profiles ◽  
Dimensional Lattice ◽  
One Dimensional

AbstractThe elementary batch reaction A + B = 0 is re-examined via Monte-Carlo simulations on a one-dimensional lattice. The relative mobility of the A and B species is varied in this model, but the initial densities of the A and B are always the same. We calculate the rates, the density profiles, and the particle distribution functions. The rate power law is conserved, i.e., the well-known 1/4 behavior is established for all mobilities. The rate coefficient is the only mobility-dependent quantity. The interparticle distribution functions show that the aggregation depends on the relative mobility but the segregation does not. This subtle difference has no effect on the asymptotic reaction order, which is close to 5.

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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