Biomedical subjects

Ivan T Georgiev

Publications and source records attributed to Ivan T Georgiev.

3 recordsLinked to original sources

PubMed2006

Fluctuations and correlations in lattice models for predator-prey interaction.

Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class. We discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator-prey model variant where the predation process includes next-nearest-neighbor interactions. We find that the corresponding stochastic model reproduces the above scenario in dimensions 1< d < or =4, in contrast with the mean-field theory, which predicts a first-order phase transition. However, the mean-field features are recovered upon allowing for nearest-neighbor particle exchange processes, provided these are sufficiently fast.

Adaptation, Physiological↗

PubMed2005

Voting and catalytic processes with inhomogeneities.

We consider the dynamics of the voter model and of the monomer-monomer catalytic process in the presence of many "competing" inhomogeneities and show, through exact calculations and numerical simulations, that their presence results in a non-trivial fluctuating steady state whose properties are studied and turn out to specifically depend on the dimensionality of the system, the strength of the inhomogeneities, and their separating distances. In fact, in arbitrary dimensions, we obtain an exact (yet formal) expression of the order parameters (magnetization and concentration of adsorbed particles) in the presence of an arbitrary number n of inhomogeneities ("zealots" in the voter language) and formal similarities with suitable electrostatic systems are pointed out. In the non-trivial cases n = 1,2, we explicitly compute the static and long-time properties of the order parameters and therefore capture the generic features of the systems. When n > 2 , the problems are studied through numerical simulations. In one spatial dimension, we also compute the expressions of the stationary order parameters in the completely disordered case, where n is arbitrary large. Particular attention is paid to the spatial dependence of the stationary order parameters and formal connections with electrostatics.

Journal Article↗

PubMed2003

Position-space renormalization-group approach for driven diffusive systems applied to the asymmetric exclusion model.

This paper introduces a position-space renormalization-group approach for nonequilibrium systems and applies the method to a driven stochastic one-dimensional gas with open boundaries. The dynamics are characterized by three parameters: the probability alpha that a particle will flow into the chain to the leftmost site, the probability beta that a particle will flow out from the rightmost site, and the probability p that a particle will jump to the right if the site to the right is empty. The renormalization-group procedure is conducted within the space of these transition probabilities, which are relevant to the system's dynamics. The method yields a critical point at alpha(c)=beta(c)=1/2, in agreement with the exact values, and the critical exponent nu=2.71, as compared with the exact value nu=2.00.

Journal Article↗