Biomedical subjects

R A Blythe

Publications and source records attributed to R A Blythe.

4 recordsLinked to original sources

PubMed2006

Utterance selection model of language change.

We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time formulation of the model is expressed in terms of a Fokker-Planck equation. This equation is exactly soluble in the case of a single speaker and can be investigated analytically in the case of multiple speakers who communicate equally with all other speakers and give their utterances equal weight. Whilst the stationary properties of this system have much in common with the single-speaker case, time-dependent properties are richer. In the particular case where linguistic forms can become extinct, we find that the presence of many speakers causes a two-stage relaxation, the first being a common marginal distribution that persists for a long time as a consequence of ultimate extinction being due to rare fluctuations.

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PubMed2003

Survival probability of a diffusing particle in the presence of Poisson-distributed mobile traps.

The problem of a diffusing particle moving among diffusing traps is analyzed in general space dimension d. We consider the case where the traps are initially randomly distributed in space, with uniform density rho, and derive upper and lower bounds for the probability Q(t) (averaged over all particle and trap trajectories) that the particle survives up to time t. We show that, for 1< or =d< or =2, the bounds converge asymptotically to give Q(t) approximately exp(-lambda(d)t(d/2)) for 1< or =d<2, where lambda(d)=(2/pid)sin(pid/2)(4piD)(d/2)rho and D is the diffusion constant of the traps, and that Q(t) approximately exp(-4pirhoDt/ln t) for d=2. For d>2 bounds can still be derived, but they no longer converge for large t. For 1< or =d< or =2, these asymptotic forms are independent of the diffusion constant of the particle. The results are compared with simulation results obtained using a new algorithm [V. Mehra and P. Grassberger, Phys. Rev. E 65, 050101 (2002)] which is described in detail. Deviations from the predicted asymptotic forms are found to be large even for very small values of Q(t), indicating slowly decaying corrections whose form is consistent with the bounds. We also present results in d=1 for the case where the trap densities on either side of the particle are different. For this case we can still obtain exact bounds but they no longer converge.

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PubMed2002

Lee-Yang zeros and phase transitions in nonequilibrium steady states.

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here, one does not have a partition function; instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first- and the second-order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.

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PubMed2001

Slow crossover to Kardar-Parisi-Zhang scaling.

The Kardar-Parisi-Zhang (KPZ) equation is accepted as a generic description of interfacial growth. In several recent studies, however, values of the roughness exponent alpha have been reported that are significantly less than that associated with the KPZ equation. A feature common to these studies is the presence of holes (bubbles and overhangs) in the bulk and an interface that is smeared out. We study a model of this type in which the density of the bulk and sharpness of the interface can be adjusted by a single parameter. Through theoretical considerations and the study of a simplified model we determine that the presence of holes does not affect the asymptotic KPZ scaling. Moreover, based on our numerics, we propose a simple form for the crossover to the KPZ regime.

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