Einstein-Cartan theory as a theory of defects in space-time

The Einstein-Cartan theory of gravitation and the classical theory of defects in an elastic medium are presented and compared. The former is an extension of general relativity and refers to four-dimensional space-time, while we introduce the latter as a description of the equilibrium state of a three-dimensional continuum. Despite these important differences, an analogy is built on their common geometrical foundations, and it is shown that a space-time with curvature and torsion can be considered as a state of a four-dimensional continuum containing defects. This formal analogy is useful for illustrating the geometrical concept of torsion by applying it to concrete physical problems. Moreover, the presentation of these theories using a common geometrical basis allows a deeper understanding of their foundations.Comment: 18 pages, 7 EPS figures, RevTeX4, to appear in the American Journal of Physics, revised version with typos correcte

Scaling in a continuous time model for biological aging

In this paper we consider a generalization to the asexual version of the Penna model for biological aging, where we take a continuous time limit. The genotype associated to each individual is an interval of real numbers over which Dirac $\delta$--functions are defined, representing genetically programmed diseases to be switched on at defined ages of the individual life. We discuss two different continuous limits for the evolution equation and two different mutation protocols, to be implemented during reproduction. Exact stationary solutions are obtained and scaling properties are discussed.Comment: 10 pages, 6 figure

Von-Neumann's and related scaling laws in Rock-Paper-Scissors type models

We introduce a family of Rock-Paper-Scissors type models with $Z_N$ symmetry ($N$ is the number of species) and we show that it has a very rich structure with many completely different phases. We study realizations which lead to the formation of domains, where individuals of one or more species coexist, separated by interfaces whose (average) dynamics is curvature driven. This type of behavior, which might be relevant for the development of biological complexity, leads to an interface network evolution and pattern formation similar to the ones of several other nonlinear systems in condensed matter and cosmology.Comment: 5 pages, 6 figures, published versio

Spontaneous emergence of spatial patterns ina a predator-prey model

We present studies for an individual based model of three interacting populations whose individuals are mobile in a 2D-lattice. We focus on the pattern formation in the spatial distributions of the populations. Also relevant is the relationship between pattern formation and features of the populations' time series. Our model displays travelling waves solutions, clustering and uniform distributions, all related to the parameters values. We also observed that the regeneration rate, the parameter associated to the primary level of trophic chain, the plants, regulated the presence of predators, as well as the type of spatial configuration.Comment: 17 pages and 15 figure

A symplectic realization of the Volterra lattice

We examine the multiple Hamiltonian structure and construct a symplectic realization of the Volterra model. We rediscover the hierarchy of invariants, Poisson brackets and master symmetries via the use of a recursion operator. The rational Volterra bracket is obtained using a negative recursion operator.Comment: 8 page

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Synchronization and Stability in Noisy Population Dynamics

We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered, random perturbations tend to destabilize the populations, leading to extinction. If the number of patches is small, stabilization in the presence of noise is maintained at the expense of synchronization. As the number of patches increases, both the stability and the synchrony among patches increase. However, a residual asynchrony, large compared with the noise amplitude, seems to persist even in the limit of infinite number of patches. Therefore, the mechanism of stabilization by asynchrony recently proposed by R. Abta et. al., combining noise, diffusion and nonlinearities, seems to be more general than first proposed.Comment: 3 pages, 3 figures. To appear in Phys. Rev.

First and second order optimality conditions for optimal control problems of state constrained integral equations

This paper deals with optimal control problems of integral equations, with initial-final and running state constraints. The order of a running state constraint is defined in the setting of integral dynamics, and we work here with constraints of arbitrary high orders. First and second-order necessary conditions of optimality are obtained, as well as second-order sufficient conditions

Oscillatory behaviour in a lattice prey-predator system

Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behaviour is absent in lower-dimensional models. Finite-size analysis indicate that amplitude of these oscillations is finite even in the thermodynamic limit. In our opinion, this is the first example of a microscopic model with stochastic dynamics which exhibits oscillatory behaviour without any external driving force. We suggest that oscillations in our model are induced by some kind of stochastic resonance.Comment: 7 pages, 10 figures, Phys.Rev.E (Nov. 1999

Rare Events Statistics in Reaction--Diffusion Systems

We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian, encoding the system's evolution. To this end we formulate corresponding canonical dynamical system and investigate its phase portrait. The method is presented for a number of pedagogical examples.Comment: 12 pages, 6 figure