Lattice Animals and Self-Organized Criticality

Fractals ◽  
1997 ◽  
Vol 05 (02) ◽  
pp. 199-213 ◽  
Author(s):  
A. Yu Shahverdian
Keyword(s):  
Weyl’S Theorem ◽  
Dynamical System Theory ◽  
Lattice Animals ◽  
Additional Time ◽  
One Dimensional ◽  
Self Organized ◽  
Special Cases ◽  
Self Organized Criticality ◽  
The One

The paper considers one model of SOC close to BTW and slider blocks models. In addition, it introduces an additional time parameter and imposes special restrictions on the avalanche geometrical structure. The generalization and modification of the avalanche's concept allows us to apply H. Weyl's theorem in the dynamical system theory so as to obtain the strong and exact results in this area. We introduce some combinatorial characteristic of clusters and use it as a tool for estimating the frequency of the avalanches. The results obtained give the asymptotically exact expressions for the asymptotical frequency as well as two special types of such extended avalanches. In some special cases, they reduce the determination of the frequency of the avalanches to combinatorial enumerative problem for lattice animals on the d-dimensional torus. The other two results are related to the one-dimensional model and establish the connection between the SOC and the theory of number partitions.

SELF-ORGANIZED CRITICALITY IN 1D TRAFFIC FLOW

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 279-283 ◽  
Author(s):  
TAKASHI NAGATANI
Keyword(s):  
Traffic Flow ◽  
Transition Probability ◽  
Annihilation Process ◽  
One Dimensional ◽  
Traffic Jams ◽  
Self Organized ◽  
Stochastic Transition ◽  
Self Organized Criticality ◽  
The One ◽  
Empty Wave

Annihilation process of traffic jams is investigated in a one-dimensional traffic flow on a highway. The one-dimensional fully asymmetric exclusion model with open boundaries for parallel update is extended to take into account stochastic transition of cars, where a car moves ahead with transition probability pt. Near pt=1, the system is driven asymptotically into a steady state exhibiting a self-organized criticality. Traffic jams with various lifetimes (or sizes) appear and disappear by colliding with an empty wave. The typical lifetime <m> of traffic jams scales as [Formula: see text], where ∆pt=1−pt. It is shown that the cumulative lifetime distribution Nm(∆pt) satisfies the scaling form [Formula: see text].

Electromagnetic effects in the theory of rods

1985 ◽  
Vol 314 (1530) ◽  
pp. 311-352 ◽  
Keyword(s):  
Nonlinear Equations ◽  
Constitutive Equations ◽  
Free Space ◽  
Thermal Effects ◽  
Direct Approach ◽  
One Dimensional ◽  
Special Cases ◽  
Electromagnetic Effects ◽  
The One

This paper is concerned with the nonlinear and linear thermomechanical theories of deformable rod-like bodies in which account is taken of electromagnetic effects. The development is made by a direct approach with the use of the one-dimensional formulation of a theory of directed media called a Cosserat curve . The first part of the paper deals with the formulation of appropriate nonlinear equations governing the motion of a rod in the presence of electromagnetic and thermal effects. In the second part of the paper, emphasis is placed on the linearized version of the theory, a general discussion of the linear constitutive equations and determination of the constitutive coefficients, along with applications in a number of special cases including a magnetic thermoelastic rod and a non-conducting rod in free space.

Numerical study of the one-dimensional Hubbard model in determination of trans-polyacetylene properties

2001 ◽  
Vol 296 (4) ◽  
pp. 377-387 ◽  
Author(s):  
S. Goumri-Said ◽  
R. Moussa ◽  
J.P. DuFour ◽  
L. Salomon ◽  
H. Aourag
Keyword(s):  
Hubbard Model ◽  
Numerical Study ◽  
One Dimensional ◽  
The One

Boundedness and Other Theories for Complex Systems

2013 ◽  
pp. 108-125
Keyword(s):  
Initial Conditions ◽  
Traditional Approach ◽  
Deterministic Chaos ◽  
Mathematical Object ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Universal Properties ◽  
The One ◽  
Global Invariant ◽  
Sensitivity To Initial Conditions

A comparison between the concept of boundedness on the one hand, and the theory of self-organized criticality (SOC) and the deterministic chaos on the other hand, is made. The focus is put on the methodological importance of the general frame through which an enormous class of empirical observations is viewed. The major difference between the concept of boundedness and the theory of self organized criticality is that under boundedness, the response comprises both specific and universal part, and thus a system has well defined “identity,” while SOC assumes response as a global invariant which has only universal properties. Unlike the deterministic chaos, the boundedness is free to explain the sensitivity to initial conditions independently from the mathematical object that generates them. Alongside, it turns out that the traditional approach to the deterministic chaos has its ample understanding under the concept of boundedness.

Integration of one-dimensional equations of motions

2020 ◽  
pp. 79-90
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Potential Energy ◽  
Field Change ◽  
One Dimensional ◽  
System A ◽  
Small Correction ◽  
The Law ◽  
The One ◽  
The Given ◽  
Equations Of Motions

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

Structural determination of the group K capsular polysaccharide of Neisseriameningitidis: a 2D-NMR analysis

1985 ◽  
Vol 63 (10) ◽  
pp. 2781-2786 ◽  
Author(s):  
Francis Michon ◽  
Jean Robert Brisson ◽  
René Roy ◽  
Harold J. Jennings ◽  
Fraser E. Ashton
Keyword(s):  
Capsular Polysaccharide ◽  
2D Nmr ◽  
Ion Exchange Chromatography ◽  
Exchange Chromatography ◽  
Electronic Effects ◽  
Nmr Studies ◽  
Polysaccharide Antigen ◽  
One Dimensional ◽  
The One

The capsular polysaccharide antigen of Neisseriameningitidis group K was isolated by Cetavlon precipitation and purified by ion-exchange chromatography. The structure of the K polysaccharide was determined to a large extent by comprehensive proton and carbon-13 nuclear magnetic resonance (nmr) studies. In these studies one-dimensional and two-dimensional experiments were carried out directly on the K polysaccharide. The K polysaccharide is composed of the following repeating unit: -4)β-D-ManpNAcA(1→3) [4-OAc]β-D-ManpNAcA(1→. Except for the one-bond couplings between their anomeric carbons and protons [Formula: see text], all the nmr spectroscopic evidence was consistent with both 2-acetamido-2-deoxy-D-mannopyranosyluronic acid residues adopting the 4C1 (D) conformation and having the β-D-configuration. This ambiguity in [Formula: see text] is probably due to through-space electronic effects generated by the presence of contiguous carboxylated sugar residues in the K polysaccharide. The O-acetyl substituents of the K polysaccharide are essential for its antigenicity to group K polysaccharide-specific antibodies.

The general Lie group and similarity solutions for the one-dimensional Vlasov–Maxwell equations

1985 ◽  
Vol 33 (2) ◽  
pp. 219-236 ◽  
Author(s):  
Dana Roberts
Keyword(s):  
Lie Group ◽  
Maxwell Equations ◽  
Transformation Group ◽  
Spatial Dimension ◽  
Similarity Solutions ◽  
One Dimensional ◽  
Special Cases ◽  
General Similarity ◽  
The One ◽  
The Individual

The general Lie point transformation group and the associated reduced differential equations and similarity forms for the solutions are derived here for the coupled (nonlinear) Vlasov–Maxwell equations in one spatial dimension. The case of one species in a background is shown to admit a larger group than the multi-species case. Previous exact solutions are shown to be special cases of the above solutions, and many of the new solutions are found to constrain the form of the distribution function much more than, for example, the BGK solutions do. The individual generators of the Lie group are used to find the possible subgroups. Finally, a simple physical argument is given to show that the asymptotic solution (t→∞) for a one-species, one-dimensional plasma is one of the general similarity solutions.

Sign in / Sign up

Export Citation Format

Share Document