Biomedical subjects

Hans-Karl Janssen

Publications and source records attributed to Hans-Karl Janssen.

5 recordsLinked to original sources

PubMed2003

Logarithmic corrections in dynamic isotropic percolation.

Based on the field theoretic formulation of the general epidemic process, we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine these corrections for some of the most interesting time dependent observables in dynamic percolation at the critical point up to and including the next to leading correction. For clusters emanating from a local seed at the origin, we calculate the number of active sites, the radius of gyration, as well as the survival probability.

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PubMed2003

Logarithmic corrections to scaling in critical percolation and random resistor networks.

We study the critical behavior of various geometrical and transport properties of percolation in six dimensions. By employing field theory and renormalization group methods we analyze fluctuation induced logarithmic corrections to scaling up to and including the next-to-leading order correction. Our study comprehends the percolation correlation function, i.e., the probability that two given points are connected, and some of the fractal masses describing percolation clusters. To be specific, we calculate the mass of the backbone, the red bonds, and the shortest path. Moreover, we study key transport properties of percolation as represented by the random resistor network. We investigate the average two-point resistance as well as the entire family of multifractal moments of the current distribution.

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PubMed2003

Percolating granular superconductors.

We investigate diamagnetic fluctuations in percolating granular superconductors. Granular superconductors are known to have a rich phase diagram including normal, superconducting, and spin-glass phases. Focusing on the normal-superconducting and the normal-spin-glass transition at low temperatures, we study the diamagnetic susceptibility chi((1)) and the mean square fluctuations of the total magnetic moment chi((2)) of large clusters. Our work is based on a random Josephson network model that we analyze with the powerful methods of renormalized field theory. We investigate the structural properties of the Feynman diagrams contributing to the renormalization of chi((1)) and chi((2)). This allows us to determine the critical behavior of chi((1)) and chi((2)) to arbitrary order in perturbation theory.

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PubMed2002

Multifractal current distribution in random-diode networks.

Recently it has been shown analytically that electric currents in a random-diode network are distributed in a multifractal manner [O. Stenull and H. K. Janssen, Europhys. Lett. 55, 691 (2001)]. In the present paper we investigate the multifractal properties of a random diode network at the critical point by numerical simulations. We analyze the currents running on a directed percolation cluster and confirm the field-theoretic predictions for the scaling behavior of moments of the current distribution. It is pointed out that a random diode network is a particularly good candidate for a possible experimental realization of directed percolation.

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PubMed2002

Multifractal properties of resistor diode percolation.

Focusing on multifractal properties we investigate electric transport on random resistor diode networks at the phase transition between the nonpercolating and the directed percolating phase. Building on first principles such as symmetries and relevance we derive a field theoretic Hamiltonian. Based on this Hamiltonian we determine the multifractal moments of the current distribution that are governed by a family of critical exponents [psi(l)]. We calculate the family [psi(l)] to two-loop order in a diagrammatic perturbation calculation augmented by renormalization group methods.

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