Flame propagation in random media

We introduce a phase-field model to describe the dynamics of a self-sustaining propagating combustion front within a medium of randomly distributed reactants. Numerical simulations of this model show that a flame front exists for reactant concentration $c > c^* > 0$, while its vanishing at $c^*$ is consistent with mean-field percolation theory. For $c > c^*$, we find that the interface associated with the diffuse combustion zone exhibits kinetic roughening characteristic of the Kardar-Parisi-Zhang equation.Comment: 4, LR541

Competition Among Companies: Coexistence and Extinction

We study a spatially homogeneous model of a market where several agents or companies compete for a wealth resource. In analogy with ecological systems the simplest case of such models shows a kind of "competitive exclusion" principle. However, the inclusion of terms corresponding for instance to "company efficiency" or to (ecological) "intracompetition" shows that, if the associated parameter overcome certain threshold values, the meaning of "strong" and "weak" companies should be redefined. Also, by adequately adjusting such a parameter, a company can induce the "extinction" of one or more of its competitors.Comment: 5 pages, 3 figures include

Ecological model of extinctions

We present numerical results based on a simplified ecological system in evolution, showing features of extinction similar to that claimed for the biosystem on Earth. In the model each species consists of a population in interaction with the others, that reproduces and evolves in time. Each species is simultaneously a predator and a prey in a food chain. Mutations that change the interactions are supposed to occur randomly at a low rate. Extinctions of populations result naturally from the predator-prey dynamics. The model is not pinned in a fitness variable, and natural selection arises from the dynamics.Comment: 16 pages (LaTeX type, RevTeX style), including 6 figures in gif format. To be published in Phys. Rev. E (prob. Dic. 96

Computer simulations of history of life: speciation, emergence of complex species from simpler organisms, and extinctions

We propose a generic model of eco-systems, with a {\it hierarchical} food web structure. In our computer simulations we let the eco-system evolve continuously for so long that that we can monitor extinctions as well as speciations over geological time scales. {\it Speciation} leads not only to horizontal diversification of species at any given trophic level but also to vertical bio-diversity that accounts for the emergence of complex species from simpler forms of life. We find that five or six trophic levels appear as the eco-system evolves for sufficiently long time, starting initially from just one single level. Moreover, the time intervals between the successive collections of ecological data is so short that we could also study ``micro''-evolution of the eco-system, i.e., the birth, ageing and death of individual organisms.Comment: 7 pages, including 4 EPS figures, REVTE

Risk of Population Extinction from Periodic and Abrupt Changes of Environment

A simulation model of a population having internal (genetic) structure is presented. The population is subject to selection pressure coming from the environment which is the same in the whole system but changes in time. Reproduction has a sexual character with recombination and mutation. Two cases are considered - oscillatory changes of the environment and abrupt ones (catastrophes). We show how the survival chance of a population depends on maximum allowed size of the population, the length of the genotypes characterising individuals, selection pressure and the characteristics of the climate changes, either their period of oscillations or the scale of the abrupt shift.Comment: 8 pages, 25 references, 10 figures; preliminary version to be submitted to Physica

Unified "micro"- and "macro-" evolution of eco-systems: Self-organization of a dynamic network

Very recently we have developed a dynamic network model for eco-systems that achieved ``unification'' of ``micro'' and ``macro''-evolution. We now propose an extension of our model so as to stabilize the eco-system and describe {\it speciation} in a more realistic manner.Comment: 7 pages with 3 figures; for Max Born Symposium, Poland, Sept. 200

DLCQ of Fivebranes, Large N Screening, and L^2 Harmonic Forms on Calabi Manifolds

We find one explicit L^2 harmonic form for every Calabi manifold. Calabi manifolds are known to arise in low energy dynamics of solitons in Yang-Mills theories, and the L^2 harmonic form corresponds to the supersymmetric ground state. As the normalizable ground state of a single U(N) instanton, it is related to the bound state of a single D0 to multiple coincident D4's in the non-commutative setting, or equivalently a unit Kaluza-Klein mode in DLCQ of fivebrane worldvolume theory. As the ground state of nonabelian massless monopoles realized around a monopole-``anti''-monopole pair, it shows how the long range force between the pair is screened in a manner reminiscent of large N behavior of quark-anti-quark potential found in AdS/CFT correspondence.Comment: LaTeX, 23 page

The efficiency of individual optimization in the conditions of competitive growth

The paper aims to discuss statistical properties of the multi-agent based model of competitive growth. Each of the agents is described by growth (or decay) rule of its virtual "mass" with the rate affected by the interaction with other agents. The interaction depends on the strategy vector and mutual distance between agents and both are subjected to the agent's individual optimization process. Steady-state simulations yield phase diagrams with the high and low competition phases (HCP and LCP, respectively) separated by critical point. Particular focus has been made on the indicators of the power-law behavior of the mass distributions with respect to the critical regime. In this regime the study has revealed remarkable anomaly in the optimization efficiency

Scaling, Propagation, and Kinetic Roughening of Flame Fronts in Random Media

We introduce a model of two coupled reaction-diffusion equations to describe the dynamics and propagation of flame fronts in random media. The model incorporates heat diffusion, its dissipation, and its production through coupling to the background reactant density. We first show analytically and numerically that there is a finite critical value of the background density, below which the front associated with the temperature field stops propagating. The critical exponents associated with this transition are shown to be consistent with mean field theory of percolation. Second, we study the kinetic roughening associated with a moving planar flame front above the critical density. By numerically calculating the time dependent width and equal time height correlation function of the front, we demonstrate that the roughening process belongs to the universality class of the Kardar-Parisi-Zhang interface equation. Finally, we show how this interface equation can be analytically derived from our model in the limit of almost uniform background density.Comment: Standard LaTeX, no figures, 29 pages; (to appear in J. Stat. Phys. vol.81, 1995). Complete file available at http://www.physics.helsinki.fi/tft/tft.html or anonymous ftp at ftp://rock.helsinki.fi/pub/preprints/tft

Why are probabilistic laws governing quantum mechanics and neurobiology?

We address the question: Why are dynamical laws governing in quantum mechanics and in neuroscience of probabilistic nature instead of being deterministic? We discuss some ideas showing that the probabilistic option offers advantages over the deterministic one.Comment: 40 pages, 8 fig