Biomedical subjects

R B Stinchcombe

Publications and source records attributed to R B Stinchcombe.

9 recordsLinked to original sources

PubMed2005

Logarithmic coarsening and glassy behavior in a polymer model with mass-dependent diffusion.

We present a model of polymer growth and diffusion with frustration mechanisms for density increase and with diffusion rates of Arrhenius form with mass-dependent energy barriers Gamma(m) approximately (m-1)gamma. It shows nonuniversal logarithmic coarsening involving the exponent gamma. Strong-glass behavior is found in the typical times for disappearance of all polymers up to a given length, without reference to the equilibrium states of the macroscopic system. These features are predicted by numerical simulations, scaling theories, and an analytic solution of the master equation within an independent interval approximation, which also provides the cluster size distribution.

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PubMed2005

Quantum scaling approach to nonequilibrium models.

Stochastic nonequilibrium exclusion models are treated using a real space scaling approach. The method exploits the mapping between nonequilibrium and quantum systems, and it is developed to accommodate conservation laws and duality symmetries, yielding exact fixed points for a variety of exclusion models. In addition, it is shown how the asymmetric simple exclusion process in one dimension can be written in terms of a classical Hamiltonian in two dimensions using a Suzuki-Trotter decomposition.

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PubMed2005

Quantum approach to nucleation times of kinetic Ising ferromagnets.

Low temperature dynamics of Ising ferromagnets under finite magnetic fields are studied in terms of quantum spin representations of stochastic evolution operators. These are constructed for the Glauber dynamic as well as for its modification, introduced by Park [Phys. Rev. Lett. 92, 015701 (2004)]. In both cases the relaxation time after a field quench is evaluated both numerically and analytically using the spectrum gap of the corresponding operators. The numerical work employs standard recursive techniques following a symmetrization of the evolution operator accomplished by a nonunitary spin rotation. The analytical approach uses low temperature limits to identify dominant terms in the eigenvalue problem. It is argued that the relaxation times already provide a measure of actual nucleation lifetimes under finite fields. The approach is applied to square, triangular and honeycomb lattices.

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PubMed2005

Nonuniversal coarsening and universal distributions in far-from-equilibrium systems.

Anomalous coarsening in far-from-equilibrium one-dimensional systems is investigated by applying simulation and analytic techniques to minimal hard-core particle (exclusion) models. They contain mechanisms of aggregated particle diffusion, with rates epsilon<<1 , particle deposition into cluster gaps, but suppressed for the smallest gaps, and breakup of clusters that are adjacent to large gaps. Cluster breakup rates vary with the cluster length x as k x(alpha) . The domain growth law x approximately (epsilont)(z) , with z=1/ (2+alpha) for alpha>0 , is explained by a simple scaling picture involving the time for two particles to coalesce and a new particle to be deposited. The density of double vacancies, at which deposition and cluster breakup are allowed, scales as 1/ [t (epsilont)(z) ] . Numerical simulations for several values of alpha and epsilon confirm these results. A fuller approach is presented which employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. The equation for a one-variable scaling function explains the above average cluster length scaling. The probability distributions of cluster lengths x scale as P (x) = [1/ (epsilont)(z) ] g (y) , with y identical with x/ (epsilont)(z) , which is confirmed by simulation. However, those distributions show a universal tail with the form g (y) approximately exp (- y(3/2) ) , which is explained by the connection of the vacancy dynamics with the problem of particle trapping in an infinite sea of traps. The high correlation of surviving particle displacement in the latter problem explains the failure of the independent cluster approximation to represent those rare events.

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PubMed2004

Cluster growth in far-from-equilibrium particle models with diffusion, detachment, reattachment, and deposition.

Monolayer cluster growth in far-from-equilibrium systems is investigated by applying simulation and analytic techniques to minimal hard core particle (exclusion) models. The first model (I), for postdeposition coarsening dynamics, contains mechanisms of diffusion, attachment, and slow activated detachment (at rate epsilon<<1 ) of particles on a line. Simulation shows three successive regimes of cluster growth: fast attachment of isolated particles; detachment allowing further ( epsilont )(1/3) coarsening of average cluster size; and t(-1/2) approach to a saturation size varying as epsilon(-1/2) . Model II generalizes the first one in having an additional mechanism of particle deposition into cluster gaps, suppressed for the smallest gaps. This model exhibits early rapid filling, leading to slowing deposition due to the increasing scarcity of deposition sites, and then continued power law [ ( epsilont )(1/2) ] cluster size coarsening through the redistribution allowed by slow detachment. The basic ( epsilont )(1/3) domain growth laws and epsilon(-1/2) saturation in model I are explained by a simple scaling picture involving the time for a particle to detach and diffuse to the next cluster. A second, fuller approach is presented that employs a mapping of cluster configurations to a column picture and an approximate factorization of the cluster configuration probability within the resulting master equation. This allows, through the steady state solution of the corresponding equation for a cluster probability generating function, quantitative results for the saturation of model I in excellent agreement with the simulation results. For model II, it provides a one-variable scaling function solution for the coarsening probability distribution, and in particular quantitative agreement with the cluster length scaling and its amplitude.

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PubMed2004

Disordered asymmetric simple exclusion process: mean-field treatment.

We provide two complementary approaches to the treatment of disorder in a fundamental nonequilibrium model, the asymmetric simple exclusion process. First, a mean-field steady-state mapping is generalized to the disordered case, where it provides a mapping of probability distributions and demonstrates how disorder results in a new flat regime in the steady-state current-density plot for periodic boundary conditions. This effect was earlier observed by Phys. Rev. E 58, 1911 (1998)] but we provide a treatment for more general distributions of disorder, including both numerical results and analytic expressions for the width 2 Delta(C) of the flat section. We then apply an argument based on moving shock fronts [Europhys. Lett. 48, 257 (1999)]] to show how this leads to an increase in the high-current region of the phase diagram for open boundary conditions. Second, we show how equivalent results can be obtained easily by taking the continuum limit of the problem and then using a disordered version of the well-known Cole-Hopf mapping to linearize the equation. Within this approach we show that adding disorder induces a localization transformation (verified by numerical scaling), and Delta(C) maps to an inverse localization length, helping to give a physical interpretation to the problem.

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PubMed2001

Correlation functions, free energies, and magnetizations in the two-dimensional random-field Ising model.

Transfer-matrix methods are used to calculate spin-spin correlation functions (G), Helmholtz free energies (f) and magnetizations (m) in the two-dimensional random-field Ising model close to the zero-field bulk critical temperature T(c 0), on long strips of width L=3-18 sites, for binary field distributions. Analysis of the probability distributions of G for varying spin-spin distances R shows that describing the decay of their averaged values by effective correlation lengths is a valid procedure only for not very large R. Connections between field and correlation function distributions at high temperatures are established, yielding approximate analytical expressions for the latter, which are used for computation of the corresponding structure factor. It is shown that, for fixed R/L, the fractional widths of correlation-function distributions saturate asymptotically with L-2.2. Considering an added uniform applied field h, a connection between f(h), m(h), the Gibbs free energy g(m) and the distribution function for the uniform magnetization in a zero uniform field, P0(m), is derived and first illustrated for pure systems, and then applied for nonzero random field. From finite-size scaling and crossover arguments, coupled with numerical data, it is found that the width of P0(m) varies against (nonvanishing, but small) random-field intensity H0 as H(-3/7)(0).

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PubMed1999

Length and time scale divergences at the magnetization-reversal transition in the Ising model.

The divergences of both the length and time scales, at the magnetization-reversal transition in the Ising model under a pulsed field, have been studied in the linearized limit of the mean field theory. Both the length and time scales are shown to diverge at the transition point and it has been checked that the nature of the time scale divergence agrees well with the result obtained from the numerical solution of the mean field equation of motion. Similar growths in length and time scales are also observed, as one approaches the transition point, using Monte Carlo simulations. However, these are not of the same nature as the mean field case. Nucleation theory provides a qualitative argument that explains the nature of the time scale growth. To study the nature of growth of the characteristic length scale, we have looked at the cluster size distribution of the reversed spin domains and have defined a pseudocorrelation length that has been observed to grow at the phase boundary of the transition.

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PubMed1999

Correlation functions in the two-dimensional random-field Ising model.

Transfer-matrix methods are used to study the probability distributions of spin-spin correlation functions G in the two-dimensional random-field Ising model, on long strips of width L=3-15 sites, for binary field distributions at generic distance R, temperature T, and field intensity h(0). For moderately high T, and h(0) of the order of magnitude used in most experiments, the distributions are singly peaked, though rather asymmetric. For low temperatures the single-peaked shape deteriorates, crossing over towards a double-delta ground-state structure. A connection is obtained between the probability distribution for correlation functions and the underlying distribution of accumulated field fluctuations. Analytical expressions are in good agreement with numerical results for R/L > or approximately 1, low T, h(0) not too small, and near G=1. From a finite-size ansatz at T=T(c)(h(0)=0), h(0)-->0, averaged correlation functions are predicted to scale with L(y)h(0), y=7/8. From numerical data we estimate y=0.875+/-0.025, in excellent agreement with theory. In the same region, the rms relative width W of the probability distributions varies for fixed R/L=1 as W approximately h(kappa)(0) f(L h(u)(0)) with kappa approximately 0.45, u approximately 0.8; f(x) appears to saturate when x-->infinity, thus implying W approximately h(kappa)(0) in d=2.

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