Biomedical subjects

Joel L Lebowitz

Publications and source records attributed to Joel L Lebowitz.

7 recordsLinked to original sources

PubMed2006

Percolation in the harmonic crystal and voter model in three dimensions.

We investigate the site percolation transition in two strongly correlated systems in three dimensions: the massless harmonic crystal and the voter model. In the first case we start with a Gibbs measure for the potential U=(J2) summation operatorx,y[phi(x)-phi(y)]2, x,y Z3, J>0, and phi(x) R, a scalar height variable, and define occupation variables rhoh(x)=1 (0) for phi(x)>h (<h). The probability p of a site being occupied is then a function of h . In the voter model we consider a stationary measure in which each site is either occupied or empty, with probability p . In both cases the truncated pair correlation of the occupation variables, G(x-y) , decays asymptotically as mid |x-y|-1 . Using some Monte Carlo simulation methods and finite-size scaling we find accurate values of pc as well as the critical exponents for these systems. The latter are different from that of independent percolation in d=3 , as expected from the work of Weinrib and Halperin (WH) for the percolation transition of systems with G(r) approximately r-a [Phys. Rev. B 27, 413 (1983)]. In particular the correlation length exponent nu is very close to the predicted value of 2, supporting the conjecture by WH that nu=2/a is exact.

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PubMed2006

Canonical typicality.

It is well known that a system weakly coupled to a heat bath is described by the canonical ensemble when the composite S + B is described by the microcanonical ensemble corresponding to a suitable energy shell. This is true for both classical distributions on the phase space and quantum density matrices. Here we show that a much stronger statement holds for quantum systems. Even if the state of the composite corresponds to a single wave function rather than a mixture, the reduced density matrix of the system is canonical, for the overwhelming majority of wave functions in the subspace corresponding to the energy interval encompassed by the microcanonical ensemble. This clarifies, expands, and justifies remarks made by Schrödinger in 1952.

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PubMed2005

Population dynamics in spatially heterogeneous systems with drift: The generalized contact process.

We investigate the time evolution and stationary states of a stochastic, spatially discrete, population model (contact process) with spatial heterogeneity and imposed drift (wind) in one and two dimensions. We consider in particular a situation in which space is divided into two regions: an oasis and a desert (low and high death rates). Carrying out computer simulations we find that the population in the (quasi) stationary state will be zero, localized, or delocalized, depending on the values of the drift and other parameters. The phase diagram is similar to that obtained by Nelson and coworkers from a deterministic, spatially continuous model of a bacterial population undergoing convection in a heterogeneous medium.

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PubMed2005

Local mean field models of uniform to nonuniform density fluid-crystal transitions.

We investigate the existence of nontranslation invariant (periodic) density profiles, for systems interacting via translation invariant long-range potentials, as minimizers of local mean field free energy functionals. The existence of a second-order transition from a uniform to a nonuniform density at a specified temperature is proven for a class of model systems.

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PubMed2004

Pair approximation of the stochastic susceptible-infected-recovered-susceptible epidemic model on the hypercubic lattice.

We investigate the time evolution and steady states of the stochastic susceptible-infected-recovered-susceptible (SIRS) epidemic model on one- and two-dimensional lattices. We compare the behavior of this system, obtained from computer simulations, with those obtained from the mean-field approximation (MFA) and pair approximation (PA). The former (latter) approximates higher-order moments in terms of first- (second-) order ones. We find that the PA gives consistently better results than the MFA. In one dimension, the improvement is even qualitative.

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PubMed2004

Behavior of susceptible-infected-susceptible epidemics on heterogeneous networks with saturation.

We investigate saturation effects in susceptible-infected-susceptible models of the spread of epidemics in heterogeneous populations. The structure of interactions in the population is represented by networks with connectivity distribution P(k), including scale-free (SF) networks with power law distributions P(k) approximately k(-gamma). Considering cases where the transmission of infection between nodes depends on their connectivity, we introduce a saturation function C(k) which reduces the infection transmission rate lambda across an edge going from a node with high connectivity k. A mean-field approximation with the neglect of degree-degree correlation then leads to a finite threshold lambda(c) >0 for SF networks with 2<gamma</=3. We also find, in this approximation, the fraction of infected individuals among those with degree k for lambda close to lambda(c). We investigate via computer simulation the contact process on a heterogeneous regular lattice and compare the results with those obtained from mean-field theory with and without neglect of degree-degree correlations.

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PubMed2002

Hydrodynamics of binary fluid phase segregation.

Starting with the Vlasov-Boltzmann equation for a binary fluid mixture, we derive an equation for the velocity field u when the system is segregated into two phases (at low temperatures) with a sharp interface between them. u satisfies the incompressible Navier-Stokes equations together with a jump boundary condition for the pressure across the interface which, in turn, moves with a velocity given by the normal component of u. Numerical simulations of the Vlasov-Boltzmann equations for shear flows parallel and perpendicular to the interface in a phase segregated mixture support this analysis. We expect similar behavior in real fluid mixtures.

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