Repositório RCAAP

Spatially distributed genetic populations that compete locally for resources and mate only with sufficiently close neighbors, may give rise to spontaneous pattern formation. Depending on the population parameters, like death rate per generation and size of the competition and mating neighborhoods, isolated groups of individuals, or demes, may appear. The existence of such groups in a population has consequences for genetic diversity and for speciation. In this paper we discuss the robustness of demes formation with respect to two important characteristics of the population: the way individuals recognize the demarcation of the local neighborhoods and the way competition for resources affects the birth rate in an overcrowed situation. Our results indicate that demes are expected to form only for sufficiently sharp demarcations and for sufficiently intense competition.

This paper describes the use of simple lattice models for studying the properties of structurally disordered systems like glasses and granulates. The models considered have crystalline states as ground states, finite connectivity, and are not subject to constrained evolution rules. After a short review of some of these models, the paper discusses how two particularly simple kinds of models, the Potts model and the exclusion models, evolve after a quench at low temperature to glassy states rather than to crystalline states.

We describe some of the recent results obtained for models with absorbing states. First, we present the nonequilibrium absorbing-state Potts model and discuss some of the factors that might affect the critical behaviour of such models. In particular we show that in two dimensions the further neighbour interactions might split the voter critical point into two critical points. We also describe some of the results obtained in the context of synchronization of chaotic dynamical systems. Moreover, we discuss the relation of the synchronization transition with some interfacial models.

The exact solution of the asymmetric exclusion problem and several of its generalizations is obtained by a matrix product ansatz. Due to the similarity of the master equation and the Schrodinger equation at imaginary times the solution of these problems reduces to the diagonalization of a one dimensional quantum Hamiltonian. Initially, we present the solution of the problem when an arbitrary mixture of molecules, each of then having an arbitrary size (s = 0; 1; 2; ...) in units of lattice spacing, diffuses asymmetrically on the lattice. The solution of the more general problem where we have the diffusion of particles belonging to N distinct classes of particles (c = 1; ... ; N), with hierarchical order and arbitrary sizes, is also presented. Our matrix product ansatz asserts that the amplitudes of an arbitrary eigenfunction of the associated quantum Hamiltonian can be expressed by a product of matrices. The algebraic properties of the matrices defining the ansatz depend on the particular associated Hamiltonian. The absence of contradictions in the algebraic relations defining the algebra ensures the exact integrability of the model. In the case of particles distributed in N > 2 classes, the associativity of this algebra implies the Yang-Baxter relations of the exact integrable model.

We present a general field-theoretic strategy to analyze three connected families of continuous phase transitions which occur in nonequilibrium steady-states. We focus on transitions taking place between an active state and one absorbing state, when there exist an infinite number of such absorbing states. In such transitions the order parameter is coupled to an auxiliary field. Three situations arise according to whether the auxiliary field is diffusive and conserved, static and conserved, or finally static and not conserved.

A wide variety of interacting particle assemblies driven by an external force are characterized by a transition between a blocked and a moving phase. The origin of this deblocking transition can be traced back to the presence of either external quenched disorder, or of internal constraints. The first case belongs to the realm of the depinning transition, which, for example, is relevant for flux-lines in type II superconductors and other elastic systems moving in a random medium. The second case is usually included within the so-called jamming scenario observed, for instance, in many glassy materials as well as in plastically deforming crystals. Here we review some aspects of the rich phenomenology observed in interacting particle models. In particular, we discuss front depinning, observed when particles are injected inside a random medium from the boundary, elastic and plastic depinning in particle assemblies driven by external forces, and the rheology of systems close to the jamming transition. We emphasize similarities and differences in these phenomena.

We review some results concerning the energetic and dynamical consequences of taking a generic hydrophobic model of a random polypeptide chain, where the effective hydrophobic interactions are represented by Hookean springs. Then we present a set of calculations on a microscopic model of hydrophobic interactions, investigating the behaviour of a hydrophobic chain in the vicinity of a hydrophobic boundary. We conclude with some speculations as to the thermodynamics of pre-biotic functions proteins may have discharged very early on in the evolutionary past.

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The manufacture of high resistance concrete or hard ceramics needs extremely dense granular packings. They can only be realised when the size distribution of grains is strongly polydisperse. Typically powerlaw distributions give the best results. We present a simple packing model for polydisperse distributions, namely a generalized reversible parking lot model. We also discuss the perfectly dense limit, namely Apollonian packings in three dimensions and show in particular the existence of space filling bearings rotating without slip and without torsion.

We study the viscoelastic properties and the relaxation process in a gelling system by means of a minimal statistical mechanics model. The model is based on percolation and bond-fluctuation dynamics. By opportunely varying some model parameter we are able to describe a crossover from the chemical gelation behaviour to dynamics more typical of colloidal systems. The results suggest a novel connection linking classical gelation, as originally described by Flory, to more recent results on colloidal systems.

Studying simple artificial peptides, we show that recently developed simulation techniques enable efficient investigations of secondary structure formation and folding in small peptides.

This paper describes an innovative technique, the gradient pattern analysis (GPA), for analysing spatially extended dynamics. The measures obtained from GPA are based on the spatio-temporal correlations between large and small amplitude fluctuations of the structure represented as a dynamical gradient pattern. By means of four gradient moments it is possible to quantify the relative fluctuations and scaling coherence at a dynamical numerical lattice and this is a set of proper measures of the pattern complexity and equilibrium. The GPA technique is applied for the first time in 3D-simulated molecular chains with the objective of characterizing small symmetry breaking, amplitude and phase disorder due to spatio-temporal fluctuations driven by the spatially extended dynamics of a relaxation regime.

We review mean-field and fluctuation-dominated behaviors exhibited by the Seceder Model, which moves an evolving population to various critical states of self-organized segregation, delicately balancing opposed sociological pressures of conformity & dissent, and giving rise to rich ideological condensation phenomena. The secession exponent and finite societal Seceder limits are examined.

A 1 = L-expansion for percolation problems is proposed, where L is the lattice finite length. The square lattice with 27 different sizes L = 18; 22;... 1594 is considered. Certain spanning probabilities were determined by Monte Carlo simulations, as continuous functions of the site occupation probability p. We estimate the critical threshold pc by applying the quoted expansion to these data. Also, the universal spanning probability at p c for an annulus with aspect ratio r = 1=2 is estimated as C = 0.876657(45).

We study the plausibility of the handicap principle, using a bit-string model to represent both the genoma and the phenotype of the individuals of a population. We find that the distribution of genoma of population selforganizes due to the natural selection. The phenotype represents some trait of the interaction of individuals with others and with the environment so, it also suffers the pressure of natural selection. The handicap is introduced in sexual selection. At time of reproduction, females compare males according to the phenotype, choosing the one who has a phenotype representing the greatest handicap. Our results show that in this way females are able to see the quality of their possible mates and males have no possibility to cheat due to pressure of natural selection.

One species is simulated to split into two separate species via random mutations, even if both populations live together in the same environment. This speciation is achieved in the Penna bitstring model of biological ageing, with modified Verhulst factors, and in part by additional bitstrings regulating phenotype and mate selection.

In this paper we review the trajectory of a model proposed by Stauffer and Weisbuch in 1992 to describe the evolution of the immune repertoire and present new results about its dynamical behavior. Ten years later this model, which is based on the ideas of the immune network as proposed by Jerne, has been able to describe a multi-connected network and could be used to reproduce immunization and aging experiments performed with mice. The immunization protocol is simulated by introducing small and large perturbations (damages), and in this work we discuss the role of both. Besides its biological implications, the physical aspects of the complex dynamics of this network is very interesting per se. In a very recent paper we studied the aging effects by using auto-correlation functions, and the results obtained apparently indicated that the small perturbations would be more important than the large ones, since their cumulative effects may change the attractor of the dynamics. However our new results indicate that both types of perturbations are important. It is the cooperative effects between both that lead to the complex behavior which allows to reproduce experimental results.

The combined influence of linear damping and noise on a dynamical finite-time-singularity model is considered for a single degree of freedom. The noise resolves the finite-time-singularity and replaces it by a first-passagetime distribution with a peak at the singularity and a long time tail. The damping introduces a characteristic cross-over time. In the early time regime the first-passage-time distribution shows a power law behavior with scaling exponent depending on the ratio of the non linear coupling strength to the noise strength. In the late time regime the damping prevails. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.

Recently a multifractal object, Qmf, was proposed to allow the study of percolation properties in a multifractal support. The area and the number of neighbors of the blocks of Qmf show a non-trivial behavior. The value of the probability of occupation at the percolation threshold, p c, is a function of r, a parameter of Qmf which is related to its anisotropy. We investigate the relation between p c and the average number of neighbors of the blocks as well as the anisotropy of Qmf.

Bootstrap percolation models describe systems as diverse as magnetic materials, fluid flow in rocks and computer storage systems. The models have a common feature of requiring not just a simple connectivity of neighbouring sites, but rather an environment of other suitably occupied sites. Different applications as well as the connection with the mathematical literature on these models is presented. Visualizations that show the compact nature of the clusters are provided.