One-Dimensional Lattice Dynamics of the Diffusion-Limited Reaction A+A→A+S: Transient Behavior

We use a Boolean cellular automaton model to describe the diffusion-limited dynamics of the irreversible reaction A+AA+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which explicit expressions for the particle concentration and the two-point correlation can be obtained. It is shown that the long-time dynamics is in agreement with the off-lattice solution. The early-time behavior, however, predicts a slower decay of the concentration.     

Chaotic dynamics in biological information processing: A heuristic outline

Summary A given but otherwise random environmental time series impinging on the input of a certain biological processor passes through with overwhelming probability practically undetected. A very small percentage of environmental stimuli, though, is ?captured? by the processor's nonlinear dissipative operator asinitial conditions, that is, assolutions of the processor's dissipative dynamics. The processor, then, is in such cases instrumental in compressing or abstracting those stimuli, thereby making the external world to collapse from a previous regime of a ?pure state? of suspended animation onto a set of stable eigenfunctions or ?categories?—chaotic strange attractors. The characteristics of this cognitive set depend on the operator involved and the hierarchical level where the abstraction takes place. In this paper we model the physics of such a cognitive process and the role that the thalamo-cortical pacemaker of the (human) brain plays in both stimulating the individual attractors and permutating them on a time division multiplexing basis. A synthesis of the Markovian processes taking place within each individual attractor-memory and the Markovian or semi-Markovian process involving the intermittent jumping among the different attractor-memories are discussed.

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Riassunto Una data ma casuale serie temporale ambientale che influisce sull'immissione di un determinato processore biologico passa con schiacciante probabilità praticamente inosservata. Una piccolissima percentuale di stimoli ambientali, tuttavia, è catturata dall'operatore dissipativo non lineare del processore comecondizioni iniziali, cioè comesoluzioni della dinamica dissipativa del processore. Il processore è quindi, in tali casi, strumentale nel comprimere o estrarre quegli stimoli, facendo perciò collassare il mondo esterno da un precedente regime di ?stato puro? ad animazione sospesa ad un gruppo di autofunzioni stabili o ?categorie?—attrattori caotici strani. Le caratteristiche di questo gruppo cognitivo dipendono dall'operatore coinvolto e dal livello gerarchico in cui l'estrazione ha luogo. In questo lavoro si modella la fisica di tale processo cognitivo e il ruolo che lo stimolatore talamo-corticale del cervello (umano) ha sia nello stimolare gli attrattori individuali che nel permutarli su una base che manda segnali multiplex a divisione temporale. Si discute una sintesi dei processi markoviani che hanno luogo all'interno di ogni attrattore-memoria individuale e il processo markoviano o semimarkoviano che interessa il salto intermittente tra i diversi attrattori-memoria.

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Резюме Временная последовательность на входе некоторого биологического процессора может иметь практически недетектируемую вероятность. Очень небольшой процент стимулов окружающей среды ?захватывается? нелинейным диссипативным оператором процессора как начальные условия, т.е. представляется как решение диссипативпой динамики процессора. Затем процессор обрабатывает внешние стимулы, вынуждая внешний мир коллапсировать из предыдущего режима ?чистого состояния? приостановленного оживления в систему собственных функций или ?категорий?. Характеристики зтой познавательной системы зависят от используемого оператора и иерархического уровня, на котором происходит абстрагирование. В зтой статье мы моделируем физику такого познавательного процесса. Обсуждается синтез марковских процессов, происходящий внутри отдельного злемента ?атрактор-память?, и марковский или полумарковский процесс, включающий пережежающиеся прыжки между различными злементами ?атракторпамять?.

     

Extraktionsapparate

Ohne Zusammenfassung     

Super-selection rules modulating complexity: an overview

Complex systems comprising a large number of elements are potentially capable of finding themselves in a huge variety of states arising by combining the states of their parts. If such a combinatorial explosion were indeed materializing, the observed behavior would resemble to random noise. It is therefore essential that physically relevant complex systems be capable of developing mechanisms for selecting a meaningful subset of states out of the large set of a priori available states. In this communication some generic mechanisms for reducing complexity are analyzed and illustrated on case studies.     

Temporal coherence of oscillatory modes of non-linear reactive processes: local theory

The dynamical ordering that arises for the case of spatially homogeneous multi-component non-linear reactive processes as a result of a continuous transition, sufficiently far from an instability, to a temporal dissipative structure (an oscillatory mode) is studied near threshold. A local theory characterizing the transition is presented in terms of a modulus of continuity and a critical index through the use of a derivable and well-defined class of potential-like hermitian forms.     

Stability criteria and fluctuations around nonequilibrium states

A stochastic formulation of the stability of, nonequilibrium states is discussed. An entropy balance equation, including the effect of both the macroscopic evolution and of the fluctuations is derived. In the linear region of thermodynamics Prigogine's minimum entropy production, theorem is extended to include the effect of fluctuations. The latter are shown to reïnforce the return of the system to its steady state distribution.     

Word frequency and entropy of symbolic sequences: a dynamical perspective

Symbolic sequences generated by nonlinear dynamics, a German text and a piece of classical music are investigated. The higher order block entropies and the mean uncertainty are calculated using both analytical and numerical methods. The existence of weak long memory effects and the corresponding scaling of the entropies are explored. The hypothesis is developed that for language-like processes the block entropies increase in a sublinear way with the word length n, i.e. H_n a n^μ with exponents in the range μ 1/4−1/2. Correspondingly the effective number of words follows a stretched exponential law.     

Recurrence time statistics in chaotic dynamics. I. Discrete time maps

The dynamics of transitions between the cells of a finite-phase-space partition in a variety of systems giving rise to chaotic behavior is analyzed, with special emphasis on the statistics of recurrence times. In the case of one-dimensional piecewise Markow maps the recurrence problem is cast into a-renewal process. In the presence of intermittency, transitions between cells define a non-Markovian, non-renewal process reflected in the presence of power-law probability distributions and of divergent variances and mean values.