Biomedical subjects

Róbert Juhász

Publications and source records attributed to Róbert Juhász.

4 recordsLinked to original sources

PubMed2006

Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks.

We consider nonequilibrium phase transitions, such as epidemic spreading, in weighted scale-free networks, in which highly connected nodes have a relatively smaller ability to transfer infection. We solve the dynamical mean-field equations and discuss finite-size scaling theory. The theoretical predictions are confronted with the results of large scale Monte Carlo simulations on the weighted Barabási-Albert network. Local scaling exponents are found different at a typical site and at a node with very large connectivity.

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PubMed2005

Partially asymmetric zero-range process with quenched disorder.

We consider the one-dimensional partially asymmetric zero-range process where the hopping rates as well as the easy direction of hopping are random variables. For this type of disorder there is a condensation phenomenon in the thermodynamic limit: the particles typically occupy one single site and the fraction of particles outside the condensate is vanishing. We use extreme value statistics and an asymptotically exact strong disorder renormalization group method to explore the properties of the steady state. In a finite system of L sites the current vanishes as J approximately L(-z), where the dynamical exponent, z, is exactly calculated. For 0 < z < 1 the transport is realized by N(a) approximately L(1-z) active particles, which move with a constant velocity, whereas for z > 1 the transport is due to the anomalous diffusion of a single Brownian particle. Inactive particles are localized at a second special site and their number in rare realizations is macroscopic. The average density profile of inactive particles has a width of xi approximately delta(-2) in terms of the asymmetry parameter delta. In addition to this, we have investigated the approach to the steady state of the system through a coarsening process and found that the size of the condensate grows as n(L) approximately t(1/(1+z)) for large times. For the unbiased model z is formally infinite and the coarsening is logarithmically slow.

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PubMed2005

Partially asymmetric exclusion models with quenched disorder.

We consider the one-dimensional partially asymmetric exclusion process with random hopping rates, in which a fraction of particles (or sites) have a preferential jumping direction against the global drift. In this case, the accumulated distance traveled by the particles, x, scales with the time, t, as x approximately t(1/z), with a dynamical exponent z>0. Using extreme value statistics and an asymptotically exact strong disorder renormalization group method, we exactly calculate z(PW) for particlewise disorder, which is argued to be related as z(SW)=z(PW)/2 for sitewise disorder. In the symmetric case with zero mean drift, the particle diffusion is ultraslow, logarithmic in time.

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PubMed2002

Percolation in a random environment.

We consider bond percolation on the square lattice with perfectly correlated random probabilities. According to scaling considerations, mapping to a random walk problem and the results of Monte Carlo simulations the critical behavior of the system with varying degree of disorder is governed by new, random fixed points with anisotropic scaling properties. For weaker disorder both the magnetization and the anisotropy exponents are nonuniversal, whereas for strong enough disorder the system scales into an infinite randomness fixed point in which the critical exponents are exactly known.

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