Biomedical subjects

G M Schütz

Publications and source records attributed to G M Schütz.

8 recordsLinked to original sources

PubMed2004

Molecular traffic control in single-file networks with fast catalysts.

As a model for molecular traffic control we investigate the diffusion of hard core particles in crossed single-file systems. We consider a square lattice of single-files being connected to external reservoirs. The (vertical) alpha channels, carrying only A particles, are connected to reservoirs with constant density rho(A). B particles move along the (horizontal) beta channels, which are connected to reservoirs of density rho(B). We allow the irreversible transition A-->B at intersections. We are interested in the stationary density profile in the alpha and beta channels, which is the distribution of the occupation probabilities over the lattice. We calculate the stationary currents of the system and show that for sufficiently long channels the currents (as a function of the reservoir densities) show in the limit of large transition rates nonanalytic behavior. The results obtained by direct solution of the master equation are verified by kinetic Monte Carlo simulations.

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PubMed2003

Hysteresis in one-dimensional reaction-diffusion systems.

We introduce a simple nonequilibrium model for a driven diffusive system with nonconservative reaction kinetics in one dimension. The steady state exhibits a phase with broken ergodicity and hysteresis which has no analog in systems investigated previously. We identify the main dynamical mode, viz., the random motion of a shock in an effective potential, which provides a unified framework for understanding phase coexistence as well as ergodicity breaking. This picture also leads to the exact phase diagram of the system.

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PubMed2003

Phase-separation transition in one-dimensional driven models.

A class of models of two-species driven diffusive systems which is shown to exhibit phase separation in d=1 dimensions is introduced. Unlike previously studied models exhibiting similar phenomena, here the relative density of the two species is fluctuating within the macroscopic domain of the phase separtated state. The nature of the phase transition from the homogeneous to the phase-separated state is discussed in view of a recently introduced criterion for phase separation in one-dimensional driven systems.

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PubMed2003

Localization of shocks in driven diffusive systems without particle number conservation.

We study the formation of localized shocks in one-dimensional driven diffusive systems with spatially homogeneous creation and annihilation of particles (Langmuir kinetics). We show how to obtain hydrodynamic equations that describe the density profile in systems with uncorrelated steady state as well as in those exhibiting correlations. As a special example of the latter case, the Katz-Lebowitz-Spohn model is considered. The existence of a localized double density shock is demonstrated in one-dimensional driven diffusive systems. This corresponds to phase separation into regimes of three distinct densities, separated by localized domain walls. Our analytical approach is supported by Monte Carlo simulations.

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PubMed2002

Criterion for phase separation in one-dimensional driven systems.

A general criterion for the existence of phase separation in driven density-conserving one-dimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steady-state currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zero-range processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.

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PubMed2001

Exact time-dependent correlation functions for the symmetric exclusion process with open boundary.

As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density rho(*) and which initially is in a nonequilibrium state with bulk density rho(0). We calculate the exact time-dependent two-point density correlation function C(k,l)(t) identical with - and the mean and variance of the integrated average net flux of particles N(t)-N(0) that have entered (or left) the system up to time t. We find that the boundary region of the semi-infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient. The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions. Some implications for the relaxational dynamics of entangled polymers and for single-file diffusion in colloidal systems are discussed.

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PubMed2001

Minimal current phase and universal boundary layers in driven diffusive systems.

We investigate boundary-driven phase transitions in open driven diffusive systems. The generic phase diagram for systems with short-ranged interactions is governed by a simple extremal principle for the macroscopic current, which results from an interplay of density fluctuations with the motion of shocks. In systems with more than one extremum in the current-density relation, one finds a minimal current phase even though the boundaries support a higher current. The boundary layers of the critical minimal current and maximal current phases are argued to be of a universal form. The predictions of the theory are confirmed by Monte Carlo simulations of the two-parameter family of stochastic particle hopping models of Katz, Lebowitz, and Spohn and by analytical results for a related cellular automaton with deterministic bulk dynamics. The effect of disorder in the particle jump rates on the boundary layer profile is also discussed.

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PubMed1999

Transport in the XX chain at zero temperature: emergence of flat magnetization profiles.

We study the connection between magnetization transport and magnetization profiles in zero-temperature XX chains. The time evolution of the transverse magnetization m(x,t) is calculated using an inhomogeneous initial state that is the ground state at fixed magnetization but with m reversed from -m(0) for x<0 to m(0) for x>0. In the long-time limit, the magnetization evolves into a scaling form m(x,t)=Phi(x/t) and the profile develops a flat part (m=Phi=0) in the (x/t) 1/2 while it expands with the maximum velocity c(0)=1 for m(0)-->0. The states emerging in the scaling limit are compared to those of a homogeneous system where the same magnetization current is driven by a bulk field, and we find that the expectation values of various quantities (energy, occupation number in the fermionic representation) agree in the two systems.

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