Cellular Automaton Simulation of Polymers

1991 ◽  
Vol 248 ◽  
Author(s):  
M. A. Smith ◽  
Y. Bar-Yam ◽  
Y. Rabin ◽  
N. Margolus ◽  
T. Toffoli ◽  
...  
Keyword(s):  
Parallel Processing ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Large Scale ◽  
Dynamic Properties ◽  
Two Dimensions ◽  
Excluded Volume ◽  
Complex Behavior ◽  
Dynamical Models ◽  
Space Partitioning

AbstractIn order to improve our ability to simulate the complex behavior of polymers, we introduce dynamical models in the class of Cellular Automata (CA). Space partitioning methods enable us to overcome fundamental obstacles to large scale simulation of connected chains with excluded volume by parallel processing computers. A highly efficient, two-space algorithm is devised and tested on both Cellular Automata Machines (CAMs) and serial computers. Preliminary results on the static and dynamic properties of polymers in two dimensions are reported.

Outline

2010 ◽  
pp. 1-16
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Large Scale ◽  
Social Economic ◽  
Psychological Phenomena ◽  
New Methods ◽  
Large Numbers ◽  
Contemporary Science ◽  
Scale Behavior ◽  
Vast Range

Ever more frequently, contemporary science finds itself in situations in which the only way it can address the complexity of nature is to develop new methods. One of the most common models is the Cellular Automaton - a system in which large numbers of particles, distributed on a lattice, developing according to deterministic local rules, generate unpredictable large scale behavior. Cellular Automata (from now on CAs) provide important insights into a vast range of physical, biological, social, economic and psychological phenomena.

A Study of the Keep-Right-Except-to-Pass Traffic Rule on Cellular Automata

2014 ◽  
Vol 989-994 ◽  
pp. 2470-2473
Author(s):  
Wen Bin Cao
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Traffic Flow ◽  
Large Scale ◽  
Cellular Automaton Model ◽  
Driving Safety ◽  
Average Speed ◽  
Object A ◽  
Flow Through ◽  
Traffic Rule

Traffic rule is set to enable the safety and efficiency of the traffic. This paper takes the keep-right-except-to-pass rule as the research object. A three-lane cellular automaton model is proposed to simulate traffic flow. Through computer simulating, we analyze the relationships among traffic flow, overtaking ratio, average speed and density. The result shows that the rule although can increase the traffic flow and the average speed, the effect is not very evident, while this rule instead can increase driving safety in a large scale.

Cellular Automata Metrics

2010 ◽  
pp. 114-149
Author(s):  
Eleonora Bilotta ◽  
Pietro Pantano
Keyword(s):  
Complex System ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Initial Conditions ◽  
Biological Systems ◽  
Complexity Science ◽  
Complex Behavior ◽  
Multiple Components ◽  
Complex Phenomena

There have been many attempts to understand complexity and to represent it in terms of computable quantities. To date, however, these attempts have had little success. Although we find complexity in a broad range of scientific domains, precise definitions escape our grasp (Bak, 1996; Morin, 2001; Prigogine & Stengers, 1984). One of the key models in complexity science is the Cellular Automaton (CA), a class of system in which small changes in the initial conditions or in local rules can provoke unpredictable behavior (Wolfram, 1984; Wolfram, 2002; Langton, 1986; 1990). The key issue, here as in other kinds of complex system, is to discover the rules governing the emergence of complex phenomena. If such rules were known we could use them to model and predict the behavior of complex physical and biological systems. Taking it for granted that complex behavior is the result of interactions among multiple components of a larger system; we can ask a number of fundamental questions.

scholarly journals Mining stochastic cellular automata to solve density classification task in two dimensions

DYNA ◽  
2020 ◽  
Vol 87 (215) ◽  
pp. 39-46
Author(s):  
Nestor Diaz ◽  
Irene Tischer
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Full Range ◽  
Critical Density ◽  
Two Dimensions ◽  
Classification Task ◽  
Parallel Genetic Algorithm ◽  
Local Rule ◽  
Stochastic Cellular Automata ◽  
Global Coordination

Density Classification Task (DCT) is a well-known problem that researchers have been tackling for more than two decades, where the main goal is to build a cellular automaton whose local rule gives rise to emergent global coordination. We describe the methods used to identify new cellular automata that solve this problem. The design of our cellular automata was carried out by a parallel genetic algorithm, specifically instantiated for this task. Our approach identifies both the neighborhood and its stochastic rule using a dataset of initial configurations that covers in a predefined and balanced way the full range of densities in DCT. We compare our results with some models currently available in the field. In some cases, our models show better performance than the best solution reported in the literature, with efficacy of 0.842 for datasets with uniform distribution around the critical density. The best-known cellular automaton achieves 0.832 in the same datasets. Tests are carried out in datasets of diverse lattice sizes and sampling conditions; we focused the analysis on the performance of our model around critical densities. Finally, by a statistical non-parametric test, we demonstrate that there are no significant differences between our identified cellular automata and the best-known model.

Simulating Self-Regeneration and Self-Replication Processes Using Movable Cellular Automata with a Mutual Equilibrium Neighborhood

2020 ◽  
Vol 29 (4) ◽  
pp. 741-757
Author(s):  
Kateryna Hazdiuk ◽  
◽  
Volodymyr Zhikharevich ◽  
Serhiy Ostapov ◽  
◽  
...  
Keyword(s):  
Cellular Automata ◽  
Cellular Automaton ◽  
Three Dimensional ◽  
Computer Models ◽  
The Self ◽  
Model Construction ◽  
Natural Phenomena ◽  
Different Types ◽  
Movable Cellular Automata ◽  
Self Replication

This paper deals with the issue of model construction of the self-regeneration and self-replication processes using movable cellular automata (MCAs). The rules of cellular automaton (CA) interactions are found according to the concept of equilibrium neighborhood. The method is implemented by establishing these rules between different types of cellular automata (CAs). Several models for two- and three-dimensional cases are described, which depict both stable and unstable structures. As a result, computer models imitating such natural phenomena as self-replication and self-regeneration are obtained and graphically presented.

A STUDY OF BIFURCATIONS IN A CIRCULAR REAL CELLULAR AUTOMATON

1993 ◽  
Vol 03 (02) ◽  
pp. 293-321 ◽  
Author(s):  
JÜRGEN WEITKÄMPER
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Cellular Automata ◽  
Cellular Automaton ◽  
Parallel Computers ◽  
Discrete Dynamical Systems ◽  
Two Dimensional ◽  
Bifurcation Structure ◽  
Logistic Mapping ◽  
Henon Mapping

Real cellular automata (RCA) are time-discrete dynamical systems on ℝN. Like cellular automata they can be obtained from discretizing partial differential equations. Due to their structure RCA are ideally suited to implementation on parallel computers with a large number of processors. In a way similar to the Hénon mapping, the system we consider here embeds the logistic mapping in a system on ℝN, N>1. But in contrast to the Hénon system an RCA in general is not invertible. We present some results about the bifurcation structure of such systems, mostly restricting ourselves, due to the complexity of the problem, to the two-dimensional case. Among others we observe cascades of cusp bifurcations forming generalized crossroad areas and crossroad areas with the flip curves replaced by Hopf bifurcation curves.

TRANSFER-MATRIX STUDY OF NEGATIVE-FUGACITY SINGULARITY OF HARD-CORE LATTICE GAS

1999 ◽  
Vol 10 (04) ◽  
pp. 517-529 ◽  
Author(s):  
SYNGE TODO
Keyword(s):  
Large Scale ◽  
Lattice Gas ◽  
Central Charge ◽  
Hard Core ◽  
Universality Class ◽  
Two Dimensions ◽  
Square Lattice ◽  
Lattice Gas Models ◽  
Renormalization Technique ◽  
Phenomenological Renormalization

A singularity on the negative-fugacity axis of the hard-core lattice gas is investigated in terms of numerical diagonalization of large-scale transfer matrices. For the hard-square lattice gas, the location of the singular point [Formula: see text] and the critical exponent ν are accurately determined by the phenomenological renormalization technique as -0.11933888188(1) and 0.416667(1), respectively. It is also found that the central charge c and the dominant scaling dimension xσ are -4.399996(8) and -0.3999996(7), respectively. Similar analyses for other hard-core lattice-gas models in two dimensions are also performed, and it is confirmed that the universality between these models does hold. These results strongly indicate that the present singularity belongs to the same universality class as the Yang–Lee edge singularity.

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