Biomedical subjects

G Odor

Publications and source records attributed to G Odor.

8 recordsLinked to original sources

PubMed2002

Phase transition of a two-dimensional binary spreading model.

We investigated the phase transition behavior of a binary spreading process in two dimensions for different particle diffusion strengths (D). We found that N>2 cluster mean-field approximations must be considered to get consistent singular behavior. The N=3,4 approximations result in a continuous phase transition belonging to a single universality class along the D subset (0,1) phase transition line. Large scale simulations of the particle density confirmed mean-field scaling behavior with logarithmic corrections. This is interpreted as numerical evidence supporting the bosonic field theoretical prediction that the upper critical dimension in this model is d(c)=2. The pair density scales in a similar way but with an additional logarithmic factor to the order parameter. At the D=0 end point of the transition line we found directed percolation criticality.

Journal Article↗

PubMed2001

Critical behavior of a lattice prey-predator model.

The critical properties of a simple prey-predator model are revisited. For some values of the control parameters, the model exhibits a line of directed percolationlike transitions to a single absorbing state. For other values of the control parameters one finds a second line of continuous transitions toward an infinite number of absorbing states, and the corresponding steady-state exponents are mean-field-like. The critical behavior of the special point T (bicritical point), where the two transition lines meet, belongs to a different universality class. A particular strategy for preparing the initial states used for the dynamical Monte Carlo method is devised to correctly describe the physics of the system near the second transition line. Relationships with a forest fire model with immunization are also discussed.

Journal Article↗

PubMed2001

Phase transition of the one-dimensional coagulation-production process.

Recently an exact solution has been found by M. Henkel and H. Hinrichsen [J. Phys. A 34, 1561 (2001)] for the one-dimensional coagulation-production process: 2A-->A, AØA-->3A with equal diffusion and coagulation rates. This model evolves into the inactive phase independently of the production rate with t(-1/2) density decay law. This paper shows that cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates as considered by the exact solution. Numerical evidence is given that the phase transition universality agrees with that of the annihilation-fission model with low diffusions.

Journal Article↗

PubMed2001

Universal behavior of one-dimensional multispecies branching and annihilating random walks with exclusion.

A directed percolation process with two symmetric particle species exhibiting exclusion in one dimension is investigated numerically. It is shown that if the species are coupled by branching (A-->AB, B-->BA), a continuous phase transition will appear at the zero-branching-rate limit belonging to the same universality class as that of the two component branching and annihilating random-walk model with two symmetric offsprings. This class persists even if the branching is biased towards one of the species. If the two systems are not coupled by branching but a hard-core interaction is allowed only the transition will occur at finite branching rate belonging to the usual (1+1)-dimensional directed percolation class.

Journal Article↗

PubMed2001

Critical branching-annihilating random walk of two species.

The effect of blocking between different species occurring in one dimension is investigated here numerically in the case of particles following branching and annihilating random walk. It is shown that two-dimensional simulations confirm the field theoretical results with logarithmic corrections. In one dimension, however, if particles exhibit hard core interaction I confirm the very recent predictions of Kwon et al. [Phys. Rev. Lett. 85, 1682 (2000)] that there are two different universality classes depending on the spatial symmetry of the offspring production characterized by beta(S)=0.5 and beta(A)=2. Elaborate analysis of simulation data shows that the order parameter exponent beta does not depend on initial conditions or on diffusion rates of species but strong correction to scaling is observed. By systematic numerical simulations the critical point properties have been explored and initial condition dependence of the dynamical exponents Z and alpha is shown. In the case of a random initial state the particle-density decay at the critical point follows the t(-1/4) law with logarithmic corrections with two offsprings.

Journal Article↗

PubMed2000

Critical behavior of the annihilating random walk of two species with exclusion in one dimension

The A+A-->0, B+B-->0 process, with exclusion between the different kinds, is investigated here numerically. Before treating this model explicitly, we study the generalized Domany-Kinzel cellular automaton model of Hinrichsen on the line of parameter space where only compact clusters can grow. The simplest version is treated with two absorbing phases in addition to the active one. The two kinds of kinks which arise in this case do not react, leading to kinetics differing from the standard annihilating random walk of two species. Time dependent simulations are presented here to illustrate differences caused by exclusion in scaling properties of the usually discussed characteristic quantities. The dependence on the density and composition of the initial state is most apparent. Making use of the parallelism between this process and directed percolation limited by a reflecting parabolic surface, we argue that the two kinds of kinks exert marginal perturbation on each other and lead to deviations from standard annihilating random walk behavior.

Journal Article↗

PubMed2000

Critical behavior of the one-dimensional annihilation-fission process 2A-->O, 2A-->3A

Numerical simulations and cluster mean-field approximations with coherent anomaly extrapolation show that the critical line of the 1d annihilation-fission process is separated into two regions. In both the small and high diffusion cases, the critical behavior is different from the well known universality classes of nonequilibrium phase transitions to absorbing states. The high diffusion region seems to be well described by the cyclically coupled directed percolation and annihilating random walk. Spreading exponents show nonuniversal behavior.

Journal Article↗

PubMed1999

Critical behavior of roughening transitions in parity-conserving growth processes.

We investigate a class of parity-conserving solid-on-solid models that describes the growth of an interface by the deposition and evaporation of dimers. As a key feature of the models, evaporation of dimers takes place only at the edges of terraces, leading to a roughening transition between a smooth and a rough phase. We consider several variants of growth models in order to identify universal and nonuniversal properties. Moreover, a parity-conserving polynuclear growth model is proposed. All variants display the same type of universal critical behavior at the roughening transition. Because of parity conservation, the critical behavior at the first few layers can be explained in terms of unidirectionally coupled branching annihilating random walks with an even number of offspring.

Journal Article↗