Biomedical subjects

Géza Odor

Publications and source records attributed to Géza Odor.

12 recordsLinked to original sources

PubMed2006

Phase transition of triplet reaction-diffusion models.

The phase transitions classes of reaction-diffusion systems with multiparticle reactions are an open challenging problem. Large scale simulations are applied for the 3A --> 4A, 3A --> 2A and the 3A --> 4A, 3A --> [formula : see text] triplet reaction models with site occupation restriction in one dimension. Static and dynamic mean-field scaling are observed with signs of logarithmic corrections suggesting d(c) = 1 upper critical dimension for this family of models.

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PubMed2006

Critical behavior of an even-offspringed branching and annihilating random-walk cellular automaton with spatial disorder.

A stochastic cellular automaton exhibiting a parity-conserving class transition has been investigated in the presence of quenched spatial disorder by large-scale simulations. Numerical evidence has been found that weak disorder causes irrelevant perturbation for the universal behavior of the transition and the absorbing phase of this model. This opens up the possibility for experimental observation of the critical behavior of a nonequilibrium phase transition to absorbing state. For very strong disorder the model breaks up into blocks with exponential-size distribution and continuously changing critical exponents are observed. For strong disorder the randomly distributed diffusion walls introduce another transition within the inactive phase of the model, in which residual particles survive the extinction. The critical dynamical behavior of this transition has been explored.

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PubMed2005

Cluster mean-field study of the parity-conserving phase transition.

The phase transition of the branching and annihilating random walk with even offspring is studied by N-cluster mean-field approximations on one-dimensional lattices. By allowing the system to reach zero branching rate a phase transition can be seen for any N < or = 12. Coherent anomaly extrapolations applied for the series of approximations results in nu(perpendicular) = 1.85(3) and beta=0.96(2).

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PubMed2004

Role of diffusion in branching and annihilation random walk models.

Different branching and annihilating random walk models are investigated by the cluster mean-field method and simulations in one and two dimensions. In the case of the A-->2A , 2A--> 0 model the cluster mean-field approximations show diffusion dependence in the phase diagram as was found recently by the nonperturbative renormalization group method [Phys. Rev. Lett. 92, 255703 (2004)]]. The same type of survey for the A-->2A , 4A--> 0 model results in a reentrant phase diagram, similar to that of the 2A-->3A , 4A--> 0 model [Phys. Rev. E 69, 036112 (2004)]]. Simulations of the A-->2A , 4A--> 0 model in one and two dimensions confirm the presence of both the directed percolation transitions at finite branching rates and the mean-field transition at zero branching rate. In two dimensions the directed percolation transition disappears for strong diffusion rates. These results disagree with the predictions of the perturbative renormalization group method.

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PubMed2004

Critical behavior of the two-dimensional 2A-->3A, 4A--> phi binary system.

The phase transitions of the recently introduced 2A-->3A, 4A--> phi reaction-diffusion model [G. Odor, Phys. Rev. E 69, 036112 (2004)]] are explored in two dimensions. This model exhibits site-occupation restriction and explicit diffusion of isolated particles. A reentrant phase diagram in the diffusion-creation rate space is confirmed, in agreement with cluster mean-field and one-dimensional results. For strong diffusion, a mean-field transition can be observed at zero branching rate characterized by an alpha=1/3 density decay exponent. In contrast, for weak diffusion the effective 2A-->3A-->4A--> phi reaction becomes relevant and the mean-field transition of the 2A-->3A, 2A--> phi model characterized by alpha=1/2 also appears for nonzero branching rates.

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PubMed2004

Phase transitions of the binary production 2A-->3A, 4A--> X model.

Phase transitions of the 2A-->3A, 4A--> X reaction-diffusion model is explored by dynamical, N-cluster approximations and by simulations. The model exhibits site occupation restriction and explicit diffusion of isolated particles. While the site mean-field approximation shows a single transition at zero branching rate introduced by Odor [G. Odor, Phys. Rev. E 67, 056114 (2003)], N>2 cluster approximations predict the appearance of another transition line for weak diffusion (D) as well. The latter phase transition is continuous, occurs at finite branching rate, and exhibits different scaling behavior. I show that the universal behavior of these transitions is in agreement with that of the diffusive pair contact process model both on the mean-field level and in one dimension. Therefore this model exhibiting annihilation by quadruplets does not fit in the recently suggested classification of universality classes of absorbing state transitions in one dimension [J. Kockelkoren and H. Chaté, Phys. Rev. Lett. 90, 125701 (2003)]. For high diffusion rates the effective 2A-->3A-->4A--> X reaction becomes irrelevant and the model exhibits a mean-field transition only. The two regions are separated by a nontrivial critical end point at D*.

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PubMed2003

Multispecies annihilating random walk transition at zero branching rate: cluster scaling behavior in a spin model.

Numerical and theoretical studies of a one-dimensional spin model with locally broken spin symmetry are presented. The multispecies annihilating random walk transition found at zero branching rate previously is investigated now concerning the cluster behavior of the underlying spins. Generic power-law behaviors are found, besides the phase transition point, also in the active phase with fulfillment of the hyperscaling law. On the other hand scaling laws connecting bulk and cluster exponents are broken--a possibility in no contradiction with basic scaling assumptions because of the missing absorbing phase.

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PubMed2003

Phase transition classes in triplet and quadruplet reaction-diffusion models.

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n=3,4 parents, whereas explicit diffusion of single particles (A) is present are investigated in low dimensions by the mean-field approximation and simulations. The mean-field approximation of general nA-->(n+k)A, mA-->(m-l)A type of lattice models is solved and a different kind of critical behavior is pointed out. In d=2 dimensions, the 3A-->4A, 3A-->2A model exhibits a continuous mean-field type of phase transition, that implies d(c)<2 upper critical dimension. For this model in d=1 extensive simulations support a mean-field type of phase transition with logarithmic corrections unlike the recent study of Park et al. [Phys. Rev E 66, 025101 (2002)]. On the other hand, the 4A-->5A, 4A-->3A quadruplet model exhibits a mean-field type of phase transition with logarithmic corrections in d=2, while quadruplet models in one-dimensional show robust, nontrivial transitions suggesting d(c)=2. Furthermore, I show that a parity conserving model 3A-->5A, 2A--> zero in d=1 has a continuous phase transition with different kinds of exponents. These results are in contradiction with the recently suggested implications of a phenomenological, multiplicative noise Langevin equation approach and with the simulations on suppressed bosonic systems by Kockelkoren and Chaté [Phys. Rev. Lett. 90, 125701 (2003)].

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PubMed2003

Critical behavior of the one-dimensional diffusive pair contact process.

The phase transition of the one-dimensional diffusive pair contact process is investigated by N cluster mean-field approximations and high precision simulations. The N=3,4 cluster approximations exhibit smooth transition line to absorbing state by varying the diffusion rate D with beta(2)=2 mean-field order parameter exponent of the pair density. This contradicts with former N=2 results, where two different mean-field behavior was found along the transition line. Extensive dynamical simulations on L=10(5) lattices give estimates for the order parameter exponents of the particles for 0.05<or=D<or=0.7. These data may support former two distinct class findings. However, the gap between low- and high-D exponents is narrower than previously estimated and the possibility for interpreting numerical data as a single class behavior with exponents alpha=0.21(1), beta=0.40(1) assuming logarithmic corrections is shown. Finite-size scaling results are also presented.

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PubMed2002

One-dimensional nonequilibrium kinetic Ising models with local spin symmetry breaking: N-component branching annihilating random-walk transition at zero branching rate.

The effects of locally broken spin symmetry are investigated in one-dimensional nonequilibrium kinetic Ising systems via computer simulations and cluster-mean-field calculations. Besides a line of directed percolation transitions, a line of transitions belonging to N-component, two-offspring branching annihilating random-walk class (N-BARW2) is revealed in the phase diagram at zero branching rate. In this way a spin model for N-BARW2 transitions is proposed.

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PubMed2002

Multicomponent binary spreading process.

I investigate numerically the phase transitions of two-component generalizations of binary spreading processes in one dimension. In these models pair annihilation AA --> emptyset, BB --> emptyset, explicit particle diffusion, and binary pair production processes compete with each other. Several versions with spatially different production are explored, and it is shown that for the cases 2A --> 3A, 2B--> 3B and 2A --> 2AB, 2B--> 2BA a phase transition occurs at zero production rate (sigma=0), which belongs to the class of N-component, asymmetric branching and annihilating random walks, characterized by the order parameter exponent beta=2. In the model with particle production AB --> ABA, BA --> BAB a phase transition point can be located at sigma(c)=0.3253 which belongs to the class of one-component binary spreading processes.

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PubMed2001

Pair contact process with a particle source.

We study the phase diagram and critical behavior of the one-dimensional pair contact process (PCP) with a particle source using cluster approximations and extensive simulations. The source creates isolated particles only, not pairs, and so couples not to the order parameter (the pair density) but to a nonordering field, whose state influences the evolution of the order parameter. While the critical point p(c) shows a singular dependence on the source intensity, the critical exponents appear to be unaffected by the presence of the source, except possibly for a small change in beta. In the course of our paper, we obtain high-precision values for the critical exponents of the standard PCP, confirming directed-percolationlike scaling.

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