Upper Bound on the Products of Particle Interactions in Cellular Automata

Particle-like objects are observed to propagate and interact in many spatially extended dynamical systems. For one of the simplest classes of such systems, one-dimensional cellular automata, we establish a rigorous upper bound on the number of distinct products that these interactions can generate. The upper bound is controlled by the structural complexity of the interacting particles---a quantity which is defined here and which measures the amount of spatio-temporal information that a particle stores. Along the way we establish a number of properties of domains and particles that follow from the computational mechanics analysis of cellular automata; thereby elucidating why that approach is of general utility. The upper bound is tested against several relatively complex domain-particle cellular automata and found to be tight.Comment: 17 pages, 12 figures, 3 tables, http://www.santafe.edu/projects/CompMech/papers/ub.html V2: References and accompanying text modified, to comply with legal demands arising from on-going intellectual property litigation among third parties. V3: Accepted for publication in Physica D. References added and other small changes made per referee suggestion

Probabilistic cellular automata with conserved quantities

We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation conditions for deterministic cellular automata. Conservation condition for PCA can also be written in the form of a current conservation law. For deterministic nearest-neighbour CA the current can be computed exactly. Local structure approximation can partially predict the equilibrium current for non-deterministic cases. For linear segments of the fundamental diagram it actually produces exact results.Comment: 17 pages, 2 figure

Non-deterministic density classification with diffusive probabilistic cellular automata

We present a probabilistic cellular automaton (CA) with two absorbing states which performs classification of binary strings in a non-deterministic sense. In a system evolving under this CA rule, empty sites become occupied with a probability proportional to the number of occupied sites in the neighborhood, while occupied sites become empty with a probability proportional to the number of empty sites in the neighborhood. The probability that all sites become eventually occupied is equal to the density of occupied sites in the initial string.Comment: 4 pages, 4 figure

Cellular automaton rules conserving the number of active sites

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure

Persistence, extinction and spatio-temporal synchronization of SIRS cellular automata models

Spatially explicit models have been widely used in today's mathematical ecology and epidemiology to study persistence and extinction of populations as well as their spatial patterns. Here we extend the earlier work--static dispersal between neighbouring individuals to mobility of individuals as well as multi-patches environment. As is commonly found, the basic reproductive ratio is maximized for the evolutionary stable strategy (ESS) on diseases' persistence in mean-field theory. This has important implications, as it implies that for a wide range of parameters that infection rate will tend maximum. This is opposite with present results obtained in spatial explicit models that infection rate is limited by upper bound. We observe the emergence of trade-offs of extinction and persistence on the parameters of the infection period and infection rate and show the extinction time having a linear relationship with respect to system size. We further find that the higher mobility can pronouncedly promote the persistence of spread of epidemics, i.e., the phase transition occurs from extinction domain to persistence domain, and the spirals' wavelength increases as the mobility increasing and ultimately, it will saturate at a certain value. Furthermore, for multi-patches case, we find that the lower coupling strength leads to anti-phase oscillation of infected fraction, while higher coupling strength corresponds to in-phase oscillation.Comment: 12page

The “Mirage” Sensor in a Industrial Environment: Optical and Thermal Losses Determinations

Since the first “Mirage” experiment run in the laboratory of ESPCI in 1979 [1], this method has been used by many other laboratories for the determination of optical and thermal properties and for non destructive evaluation [2] [3] [4]

Physics of brain dynamics: Fokker-Planck analysis reveals changes in EEG delta-theta interactions in anaesthesia

We use drift and diffusion coefficients to reveal interactions between different oscillatory processes underlying a complex signal and apply the method to EEG delta and theta frequencies in the brain. By analysis of data recorded from rats during anaesthesia, we consider the stability and basins of attraction of fixed points in the phase portrait of the deterministic part of the retrieved stochastic process. We show that different classes of dynamics are associated with deep and light anaesthesia, and we demonstrate that the predominant directionality of the interaction is such that theta drives delt

Anomalous Thermal Diffusivity of Amorphous Semiconductor Superlattices

Since the development of amorphous semiconductor superlattice films, the great interesting in fundamental and technological is attracted by their special properties and applications. The optical and electronic properties of the films have been studied by conventional spectroscope, photoluminescence and photoconductance techniques etc. Some anomalous phenomena, such as, the quantum size effect and the permenent photoconductivity (PPC) effect, have been discovered [1–2]. Recently the investigations of the characteristics and parameters of amorphous semiconductor superlattice films by photoacoustic and photothermal techniques are being got attention [3,4]. In this paper, we describe the study of the thermal diffusivity of a series samples of amorphous semiconductor superlattices a-Si:H/a-SiNx:H. The thermal diffusivity of the samples is experimentally measured by using mirage detection technique [5,6]. Up to date, the mirage detection method has been used successfully to determine the thermal diffusivity of both transparent and opaque materials. Specially it is available to measure directly the thermal parameters of thin films which are usually difficalt to be, evaluated. In the theoretical calculation, one dimensional model with “ the thormal resistors in series “ and ” the weighted average ” is used. Comparing the experimental and theoretical results, we find that both are in good agreement for the most of the samples. However, some anomalous thermal diffusivity phenomena have been observed in some special samples

Heterodyne detection of multiply scattered monochromatic light with a multipixel detector

International audienceA new technique is presented for measuring the spectral broadening of light that has been multiply scattered from scatterers in motion. In our method the scattered light is detected by a heterodyne receiver that uses a CCD as a multipixel detector. We obtain the frequency spectrum of the scattered light by sweeping the heterodyne local oscillator frequency. Our detection scheme combines a high optical etendue (product of the surface by the detection solid angle) with an optimal detection of the scattered photons (shot noise). Using this technique, we measure, in vivo, the frequency spectrum of the light scattered through the breast of a female volunteer