Random sequential addition of hard atoms to the one‐dimensional integer lattice

1973 ◽  
Vol 59 (4) ◽  
pp. 1613-1615 ◽  
Author(s):  
B. Littlewood ◽  
J. L. Verrall
Keyword(s):  
Integer Lattice ◽  
One Dimensional ◽  
Random Sequential Addition ◽  
Sequential Addition ◽  
The One

On random sequential packing in the plane and a conjecture of palasti

1970 ◽  
Vol 7 (03) ◽  
pp. 667-698 ◽  
Author(s):  
B. Edwin Blaisdell ◽  
Herbert Solomon
Keyword(s):  
Physical Simulation ◽  
Random Packing ◽  
Three Dimensions ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Random Sequential Addition ◽  
Geometric Objects ◽  
Sequential Addition ◽  
The One ◽  
Packed Volume

The random packing of geometric objects in one-, two- or three-dimensions may afford useful insights into the structure of crystals, liquids, absorbates on crystals, and in higher dimensions, into problems of pattern recognition. Random packing has accordingly received increasing attention in recent years. Two principal packing procedures have been formulated and each gives rise to different packing ratios. In one case, all possible configurations of a sphere-packed volume are assumed to be equally likely. In the other and most widely reported case, there is random sequential addition of spheres to the volume until it is packed. This is the situation we study in this paper. Most of the work to date has been limited to the theoretical study of the one-dimensional lattice or to continuous cases particularly in the limit for long lines. The higher dimensional cases have resisted theoretical attack but have been studied by computer simulation by Palasti [12] and Solomon [14] and by physical simulation by Bernal and Scott (see [14]).

On random sequential packing in the plane and a conjecture of palasti

1970 ◽  
Vol 7 (3) ◽  
pp. 667-698 ◽  
Author(s):  
B. Edwin Blaisdell ◽  
Herbert Solomon
Keyword(s):  
Physical Simulation ◽  
Random Packing ◽  
Three Dimensions ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Random Sequential Addition ◽  
Geometric Objects ◽  
Sequential Addition ◽  
The One ◽  
Packed Volume

The random packing of geometric objects in one-, two- or three-dimensions may afford useful insights into the structure of crystals, liquids, absorbates on crystals, and in higher dimensions, into problems of pattern recognition. Random packing has accordingly received increasing attention in recent years. Two principal packing procedures have been formulated and each gives rise to different packing ratios. In one case, all possible configurations of a sphere-packed volume are assumed to be equally likely. In the other and most widely reported case, there is random sequential addition of spheres to the volume until it is packed. This is the situation we study in this paper. Most of the work to date has been limited to the theoretical study of the one-dimensional lattice or to continuous cases particularly in the limit for long lines. The higher dimensional cases have resisted theoretical attack but have been studied by computer simulation by Palasti [12] and Solomon [14] and by physical simulation by Bernal and Scott (see [14]).

scholarly journals PARRONDO GAMES WITH SPATIAL DEPENDENCE II

2012 ◽  
Vol 11 (04) ◽  
pp. 1250030 ◽  
Author(s):  
S. N. ETHIER ◽  
JIYEON LEE
Keyword(s):  
Spin System ◽  
Spatial Dependence ◽  
Integer Lattice ◽  
Periodic Pattern ◽  
One Dimensional ◽  
Random Mixture ◽  
The Mean ◽  
The One ◽  
Positive Integers ◽  
Special Case

Let game B be Toral's cooperative Parrondo game with (one-dimensional) spatial dependence, parameterized by N ≥ 3 and p0, p1, p2, p3 ∈ [0, 1], and let game A be the special case p0 = p1 = p2 = p3 = 1/2. In previous work we investigated μB and μ(1/2, 1/2), the mean profits per turn to the ensemble of N players always playing game B and always playing the randomly mixed game (1/2)(A + B). These means were computable for 3 ≤ N ≤ 19, at least, and appeared to converge as N → ∞, suggesting that the Parrondo region (i.e., the region in which μB ≤ 0 and μ(1/2, 1/2) > 0) has nonzero volume in the limit. The convergence was established under certain conditions, and the limits were expressed in terms of a parameterized spin system on the one-dimensional integer lattice. In this paper we replace the random mixture with the nonrandom periodic pattern Ar Bs, where r and s are positive integers. We show that μ[r, s], the mean profit per turn to the ensemble of N players repeatedly playing the pattern Ar Bs, is computable for 3 ≤ N ≤ 18 and r + s ≤ 4, at least, and appears to converge as N → ∞, albeit more slowly than in the random-mixture case. Again this suggests that the Parrondo region (μB ≤ 0 and μ[r, s] > 0) has nonzero volume in the limit. Moreover, we can prove this convergence under certain conditions and identify the limits.

BOSONIC CENTRAL LIMIT THEOREM FOR THE ONE-DIMENSIONAL XY MODEL

2002 ◽  
Vol 14 (07n08) ◽  
pp. 675-700 ◽  
Author(s):  
TAKU MATSUI
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Ground States ◽  
Integer Lattice ◽  
Gibbs States ◽  
Xy Model ◽  
One Dimensional ◽  
The Central Limit Theorem ◽  
The One

We prove the central limit theorem for Gibbs states and ground states of quasifree Fermions (bilinear Hamiltonians) and those of the off critical XY model on a one-dimensional integer lattice.

Exploring the Multidimensional Facets of Authoritarianism: Authoritarian Aggression and Social Dominance Orientation

2008 ◽  
Vol 67 (1) ◽  
pp. 51-60 ◽  
Author(s):  
Stefano Passini
Keyword(s):  
Social Dominance ◽  
Factor Model ◽  
Three Dimensional ◽  
Social Dominance Orientation ◽  
Model Fit ◽  
Regression Analyses ◽  
One Dimensional ◽  
Confirmatory Factor ◽  
The One ◽  
Better Than

The relation between authoritarianism and social dominance orientation was analyzed, with authoritarianism measured using a three-dimensional scale. The implicit multidimensional structure (authoritarian submission, conventionalism, authoritarian aggression) of Altemeyer’s (1981, 1988) conceptualization of authoritarianism is inconsistent with its one-dimensional methodological operationalization. The dimensionality of authoritarianism was investigated using confirmatory factor analysis in a sample of 713 university students. As hypothesized, the three-factor model fit the data significantly better than the one-factor model. Regression analyses revealed that only authoritarian aggression was related to social dominance orientation. That is, only intolerance of deviance was related to high social dominance, whereas submissiveness was not.

Adiabatic large polarons in anisotropic molecular crystals

2011 ◽  
Vol 35 (1) ◽  
pp. 15-27
Author(s):  
Zoran Ivić ◽  
Željko Pržulj
Keyword(s):  
Energy Transfer ◽  
Effective Mass ◽  
Molecular Crystals ◽  
Single Chain ◽  
Proper Understanding ◽  
One Dimensional ◽  
Interchain Coupling ◽  
Large Polaron ◽  
The One

Adiabatic large polarons in anisotropic molecular crystals We study the large polaron whose motion is confined to a single chain in a system composed of the collection of parallel molecular chains embedded in threedimensional lattice. It is found that the interchain coupling has a significant impact on the large polaron characteristics. In particular, its radius is quite larger while its effective mass is considerably lighter than that estimated within the one-dimensional models. We believe that our findings should be taken into account for the proper understanding of the possible role of large polarons in the charge and energy transfer in quasi-one-dimensional substances.

Modelling Techniques in Applied Glaciology: Numerical Modelling of Avalanches

1983 ◽  
Vol 4 ◽  
pp. 297-297
Author(s):  
G. Brugnot
Keyword(s):  
Finite Difference Method ◽  
Transverse Velocity ◽  
Longitudinal Velocity ◽  
Momentum Conservation ◽  
Dimensional Model ◽  
One Dimensional ◽  
Modelling Techniques ◽  
Reference Grid ◽  
The One ◽  
Near Future

We consider the paper by Brugnot and Pochat (1981), which describes a one-dimensional model applied to a snow avalanche. The main advance made here is the introduction of the second dimension in the runout zone. Indeed, in the channelled course, we still use the one-dimensional model, but, when the avalanche spreads before stopping, we apply a (x, y) grid on the ground and six equations have to be solved: (1) for the avalanche body, one equation for continuity and two equations for momentum conservation, and (2) at the front, one equation for continuity and two equations for momentum conservation. We suppose the front to be a mobile jump, with longitudinal velocity varying more rapidly than transverse velocity.We solve these equations by a finite difference method. This involves many topological problems, due to the actual position of the front, which is defined by its intersection with the reference grid (SI, YJ). In the near future our two directions of research will be testing the code on actual avalanches and improving it by trying to make it cheaper without impairing its accuracy.

Sign in / Sign up

Export Citation Format

Share Document