Biomedical subjects

Haye Hinrichsen

Publications and source records attributed to Haye Hinrichsen.

6 recordsLinked to original sources

PubMed2003

Epidemic processes with immunization.

We study a model of directed percolation (DP) with immunization, i.e., with different probabilities for the first infection and subsequent infections. The immunization effect leads to an additional non-Markovian term in the corresponding field theoretical action. We consider immunization as a small perturbation around the DP fixed point in d<6, where the non-Markovian term is relevant. The immunization causes the system to be driven away from the neighborhood of the DP critical point. In order to investigate the dynamical critical behavior of the model, we consider the limits of low and high first-infection rate, while the second-infection rate remains constant at the DP critical value. Scaling arguments are applied to obtain an expression for the survival probability in both limits. The corresponding exponents are written in terms of the critical exponents for ordinary DP and DP with a wall. We find that the survival probability does not obey a power-law behavior, decaying instead as a stretched exponential in the low first-infection probability limit and to a constant in the high first-infection probability limit. The theoretical predictions are confirmed by optimized numerical simulations in 1+1 dimensions.

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PubMed2003

Epidemic spreading with immunization and mutations.

The spreading of infectious diseases with and without immunization of individuals can be modeled by stochastic processes that exhibit a transition between an active phase of epidemic spreading and an absorbing phase, where the disease dies out. In nature, however, the transmitted pathogen may also mutate, weakening the effect of immunization. In order to study the influence of mutations, we introduce a model that mimics epidemic spreading with immunization and mutations. The model exhibits a line of continuous phase transitions and includes the general epidemic process (GEP) and directed percolation (DP) as special cases. Restricting to perfect immunization in two spatial dimensions, we analyze the phase diagram and study the scaling behavior along the phase transition line as well as in the vicinity of the GEP point. We show that mutations lead generically to a crossover from the GEP to DP. Using standard scaling arguments, we also predict the form of the phase transition line close to the GEP point. The protection gained by immunization is vitally decreased by the occurrence of mutations.

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PubMed2003

Logarithmic roughening in a growth process with edge evaporation.

Roughening transitions are often characterized by unusual scaling properties. As an example we investigate the roughening transition in a solid-on-solid growth process with edge evaporation [U. Alon, M. Evans, H. Hinrichsen, and D. Mukamel, Phys. Rev. Lett. 76, 2746 (1996)], where the interface is known to roughen logarithmically with time. Performing high-precision simulations we find appropriate scaling forms for various quantities. Moreover we present a simple approximation explaining why the interface roughens logarithmically.

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PubMed2003

Epitaxial growth with pulsed deposition: submonolayer scaling and Villain instability.

It has been observed experimentally that under certain conditions, pulsed laser deposition (PLD) produces smoother surfaces than ordinary molecular beam epitaxy (MBE). So far, the mechanism leading to the improved quality of surfaces in PLD is not yet fully understood. In the present work, we investigate the physical properties of a simple model for PLD, in which the transient mobility of adatoms and diffusion along edges is neglected. Analyzing the crossover from MBE to PLD, the scaling properties of the time-dependent nucleation density as well as the influence of Ehrlich-Schwoebel barriers, we find that there is indeed a range of parameters, where the surface quality in PLD is better than in MBE. However, since the improvement is weak and occurs only in a small range of parameters we conclude that deposition in pulses alone cannot explain the experimentally observed smoothness of PLD-grown surfaces.

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PubMed2002

Phase transition in a triplet process.

We argue that the reaction-diffusion process 3A-->4A,3A-->2A exhibits a different type of continuous phase transition from an active into an absorbing phase. Because of the upper critical dimension d(c)> or =4/3 we expect the phase transition in 1+1 dimensions to be characterized by nontrivial fluctuation effects.

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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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