Biomedical subjects

George C M A Ehrhardt

Publications and source records attributed to George C M A Ehrhardt.

4 recordsLinked to original sources

PubMed2006

Phenomenological models of socioeconomic network dynamics.

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between "similar" nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean-field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.

Journal Article↗

PubMed2005

Segregation mechanisms in a numerical model of a binary granular mixture.

A simple phenomenological numerical model of a binary granular mixture is developed and investigated numerically. We attempt to model a recently reported experimental system where a horizontally vibrated binary monolayer was found to exhibit a transition from a mixed to a segregated state as the filling fraction of the mixture was increased. This numerical model is found to reproduce much of the experimentally observed behavior, most importantly the transition from the mixed to the segregated state. We use the numerical model to investigate granular segregation mechanisms and explain the experimentally observed behavior.

Journal Article↗

PubMed2002

Persistence of a continuous stochastic process with discrete-time sampling: non-Markov processes.

We consider the problem of "discrete-time persistence," which deals with the zero crossings of a continuous stochastic process X(T) measured at discrete times T=nDeltaT. For a Gaussian stationary process the persistence (no crossing) probability decays as exp(-theta(D)T)=[rho(a)](n) for large n, where a=exp(-DeltaT/2) and the discrete persistence exponent theta(D) is given by theta(D)=(ln rho)/(2 ln a). Using the "independent interval approximation," we show how theta(D) varies with DeltaT for small DeltaT and conclude that experimental measurements of persistence for smooth processes, such as diffusion, are less sensitive to the effects of discrete sampling than measurements of a randomly accelerated particle or random walker. We extend the matrix method developed by us previously [Phys. Rev. E 64, 015101(R) (2001)] to determine rho(a) for a two-dimensional random walk and the one-dimensional random-acceleration problem. We also consider "alternating persistence," which corresponds to a<0, and calculate rho(a) for this case.

Journal Article↗

PubMed2002

Series expansion calculation of persistence exponents.

We consider an arbitrary Gaussian stationary process X(T) with known correlator C(T), sampled at discrete times Tn = nDeltaT. The probability that (n+1) consecutive values of X have the same sign decays as Pn approximately exp(-theta(D)Tn). We calculate the discrete persistence exponent theta(D) as a series expansion in the correlator C(DeltaT) up to fourteenth order, and extrapolate to DeltaT = 0 using constrained Padé approximants to obtain the continuum persistence exponent thetas. For the diffusion equation our results are in exceptionally good agreement with recent numerical estimates.

Journal Article↗