9,872 research outputs found
Local Causal States and Discrete Coherent Structures
Coherent structures form spontaneously in nonlinear spatiotemporal systems
and are found at all spatial scales in natural phenomena from laboratory
hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary
climate dynamics. Phenomenologically, they appear as key components that
organize the macroscopic behaviors in such systems. Despite a century of
effort, they have eluded rigorous analysis and empirical prediction, with
progress being made only recently. As a step in this, we present a formal
theory of coherent structures in fully-discrete dynamical field theories. It
builds on the notion of structure introduced by computational mechanics,
generalizing it to a local spatiotemporal setting. The analysis' main tool
employs the \localstates, which are used to uncover a system's hidden
spatiotemporal symmetries and which identify coherent structures as
spatially-localized deviations from those symmetries. The approach is
behavior-driven in the sense that it does not rely on directly analyzing
spatiotemporal equations of motion, rather it considers only the spatiotemporal
fields a system generates. As such, it offers an unsupervised approach to
discover and describe coherent structures. We illustrate the approach by
analyzing coherent structures generated by elementary cellular automata,
comparing the results with an earlier, dynamic-invariant-set approach that
decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures;
http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht
Improvement and analysis of a pseudo random bit generator by means of cellular automata
In this paper, we implement a revised pseudo random bit generator based on a
rule-90 cellular automaton. For this purpose, we introduce a sequence matrix
H_N with the aim of calculating the pseudo random sequences of N bits employing
the algorithm related to the automaton backward evolution. In addition, a
multifractal structure of the matrix H_N is revealed and quantified according
to the multifractal formalism. The latter analysis could help to disentangle
what kind of automaton rule is used in the randomization process and therefore
it could be useful in cryptanalysis. Moreover, the conditions are found under
which this pseudo random generator passes all the statistical tests provided by
the National Institute of Standards and Technology (NIST)Comment: 20 pages, 12 figure
A guided tour of asynchronous cellular automata
Research on asynchronous cellular automata has received a great amount of
attention these last years and has turned to a thriving field. We survey the
recent research that has been carried out on this topic and present a wide
state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat
Two dimensional outflows for cellular automata with shuffle updates
In this paper, we explore the two-dimensional behavior of cellular automata
with shuffle updates. As a test case, we consider the evacuation of a square
room by pedestrians modeled by a cellular automaton model with a static floor
field. Shuffle updates are characterized by a variable associated to each
particle and called phase, that can be interpreted as the phase in the step
cycle in the frame of pedestrian flows. Here we also introduce a dynamics for
these phases, in order to modify the properties of the model. We investigate in
particular the crossover between low- and high-density regimes that occurs when
the density of pedestrians increases, the dependency of the outflow in the
strength of the floor field, and the shape of the queue in front of the exit.
Eventually we discuss the relevance of these results for pedestrians.Comment: 20 pages, 5 figures. v2: 16 pages, 5 figures; changed the title,
abstract and structure of the paper. v3: minor change
Modelling microstructure evolution during equal channel angular pressing of magnesium alloys using cellular automata finite element method
Equal channel angular pressing (ECAP) is one of the most popular methods of obtaining ultrafine grained (UFG) metals. However, only relatively short billets can be processed by ECAP due to force limitation. A solution to this problem could be recently developed incremental variant of the process, so called I-ECAP. Since I-ECAP can deal with continuous billets, it can be widely used in industrial practice. Recently, many researchers have put an effort to obtain UFG magnesium alloys which, due to their low density, are very promising materials for weight and energy saving applications. It was reported that microstructure refinement during ECAP is controlled by dynamic recrystallization and the final mean grain size is dependent mainly on processing temperature. In this work, cellular automata finite element (CAFE) method was used to investigate microstructure evolution during four passes of ECAP and its incremental variant I-ECAP. The cellular automata space dynamics is determined by transition rules, whose parameters are strain, strain rate and temperature obtained from FE simulation. An internal state variable model describes total dislocation density evolution and transfers this information to the CA space. The developed CAFE model calculates the mean grain size and generates a digital microstructure prediction after processing, which could be useful to estimate mechanical properties of the produced UFG metal. Fitting and verification of the model was done using the experimental results obtained from I-ECAP of an AZ31B magnesium alloy and the data derived from literature. The CAFE simulation results were verified for the temperature range 200-250 °C and strain rate 0.01-0.5 s-1; good agreement with experimental data was achieved
Probabilistic initial value problem for cellular automaton rule 172
We consider the problem of computing a response curve for binary cellular
automata -- that is, the curve describing the dependence of the density of ones
after many iterations of the rule on the initial density of ones. We
demonstrate how this problem could be approached using rule 130 as an example.
For this rule, preimage sets of finite strings exhibit recognizable patterns,
and it is therefore possible to compute both cardinalities of preimages of
certain finite strings and probabilities of occurrence of these strings in a
configuration obtained by iterating a random initial configuration times.
Response curves can be rigorously calculated in both one- and two-dimensional
versions of CA rule 130. We also discuss a special case of totally disordered
initial configurations, that is, random configurations where the density of
ones and zeros are equal to 1/2.Comment: 13 pages, 3 figure
- …