Biomedical subjects
Publications and source records attributed to A J Bray.
The overlap length of a three-dimensional Ising spin glass on a cubic lattice with Gaussian interactions has been estimated numerically by transfer matrix methods and within a Migdal-Kadanoff renormalization group scheme. We find that the overlap length is large, explaining why it has been difficult to observe spin glass chaos in numerical simulations and experiment.
We consider a system of unbiased diffusing walkers (A(Phi)<-->(Phi)A) in one dimension with random initial conditions. We investigate numerically the relation between the fraction of walkers U(t) which have never encountered another walker up to time t, calling such walkers "uninfected" and the fraction of sites P(t) which have never been visited by a diffusing particle. We extend our study to include the A+B--> Phi diffusion-limited reaction in one dimension, with equal initial densities of A and B particles distributed homogeneously at t=0. We find U(t) approximately [P(t)]gamma, with gamma approximately 1.39, in both models, though there is evidence that a smaller value of gamma is required for t-->infinity.
The dynamics of the one-dimensional q-state Potts model, in the zero-temperature limit, can be formulated through the motion of random walkers which either annihilate (A+A-->Phi) or coalesce (A+A-->A) with a q-dependent probability. We consider all of the walkers in this model to be mutually infectious. Whenever two walkers meet, they experience mutual contamination. Walkers which avoid an encounter with another random walker up to time t remain uninfected. The fraction of uninfected walkers is known to obey a power-law decay U(t) approximately t(-phi(q)), with a nontrivial exponent phi(q) [C. Monthus, Phys. Rev. E 54, 4844 (1996); S. N. Majumdar and S. J. Cornell, ibid. 57, 3757 (1998)]. We probe the numerical values of phi(q) to a higher degree of accuracy than previous simulations and relate the exponent phi(q) to the persistence exponent theta(q) [B. Derrida, V. Hakim, and V. Pasquier, Phys. Rev. Lett. 75, 751 (1995)], through the relation phi(q)=gamma(q)theta(q) where gamma is an exponent introduced in [S. J. O'Donoghue and A. J. Bray, preceding paper, Phys. Rev. E 65, 051113 (2002)]. Our study is extended to include the coupled diffusion-limited reaction A+A-->B, B+B-->A in one dimension with equal initial densities of A and B particles. We find that the density of walkers decays in this model as rho(t) approximately t(-1/2). The fraction of sites unvisited by either an A or a B particle is found to obey a power law, P(t) approximately t(-theta) with theta approximately 1.33. We discuss these exponents within the context of the q-state Potts model and present numerical evidence that the fraction of walkers which remain uninfected decays as U(t) approximately t(-phi), where phi approximately 1.13 when infection occurs between like particles only, and phi approximately 1.93 when we also include cross-species contamination. We find that the relation between phi and theta in this model can also be characterized by an exponent gamma, where similarly, phi=gamma(theta).
We introduce the technique of aspect-ratio scaling to study the scale dependence of interfacial energies in Ising spin glasses, and we show how one can use it to determine the stiffness exponent theta in a clean way, with results that are independent of the domain-wall-forcing boundary conditions imposed on the system. In space dimension d = 2 we obtain theta = -0.282(3) for a Gaussian distribution of exchange interactions.
The persistence properties of a set of random walkers obeying the A+B--> Ø reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability P(t) that an annihilation process has not occurred at a given site has the asymptotic form P(t) approximately const+t(-straight theta), where straight theta is the persistence exponent (type I persistence). We argue that, for a density of particles rho>>1, this nontrivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, partial differential(t)straight phi= partial differential(xx)straight phi, where straight theta approximately 0.1207 [S. N. Majumdar, C. Sire, A. J. Bray, and S. J. Cornell, Phys. Rev. Lett. 77, 2867 (1996)]. In the case of an initial low density, rho(0)<<1, we find straight theta approximately 1/4 asymptotically. The probability that a site remains unvisited by any random walker (type II persistence) is also investigated and found to decay with a stretched exponential form, P(t) approximately exp(-constxrho(1/2)(0)t(1/4)), provided rho(0)<<1. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.
We introduce the concept of "discrete-time persistence," which deals with zero-crossings of a continuous stochastic process, X(T), measured at discrete times, T=n Delta T. For a Gaussian Markov process with relaxation rate mu, we show that the persistence (no crossing) probability decays as [rho(a)](n) for large n, where a = exp(-mu Delta T), and we compute rho(a) to high precision. We also define the concept of "alternating persistence," which corresponds to a<0. For a>1, corresponding to motion in an unstable potential (mu<0), there is a nonzero probability of having no zero-crossings in infinite time, and we show how to calculate it.
Coarsening systems under uniform shear display a long time regime characterized by the presence of highly stretched and thin domains. The question then arises whether thermal fluctuations may actually destroy this layered structure. To address this problem in the case of nonconserved dynamics, we study an anisotropic version of the Burgers equation, constructed to describe thermal fluctuations of an interface in the presence of a uniform shear flow. As a result, we find that stretched domains are only marginally stable against thermal fluctuations in d=2, whereas they are stable in d=3.
We show that the probability, P0(l), that the height of a fluctuating (d+1)-dimensional interface in its steady state stays above its initial value up to a distance l, along any linear cut in the d-dimensional space, decays as P0(l) approximately l(theta). Here straight theta is a "spatial" persistence exponent, and takes different values, straight theta(s) or straight theta(0), depending on how the point from which l is measured is specified. These exponents are shown to map onto corresponding temporal persistence exponents for a generalized d = 1 random-walk equation. The exponent straight theta(0) is nontrivial even for Gaussian interfaces.
In a recent publication [Phys. Rev. Lett. 81, 1142 (1998)] it was argued that a randomly forced particle that collides inelastically with a boundary can undergo inelastic collapse and come to rest in a finite time. Here we discuss the survival probability for the inelastic collapse transition. It is found that the collapse-time distribution behaves asymptotically as a power law in time, and that the exponent governing this decay is nonuniversal. An approximate calculation of the collapse-time exponent confirms this behavior and shows how inelastic collapse can be viewed as a generalized persistence phenomenon.
Corrections to scaling, associated with deviations of the order parameter from the scaling morphology in the initial state, are studied for systems with O(n) symmetry at zero temperature in phase-ordering kinetics. Including corrections to scaling, the equal time pair correlation function has the form C(r,t)=f0(r/L)+L(-omega)f1(r/L)+., where L is the coarsening length scale. The correction-to-scaling exponent omega and the correction-to-scaling function f1(x) are calculated for both nonconserved and conserved order parameter systems using the approximate Gaussian closure theory of Mazenko. In general omega is a nontrivial exponent which depends on both the dimensionality d of the system and the number of components n of the order parameter. Corrections to scaling are also calculated for the nonconserved one-dimensional XY model, where an exact solution is possible.
PURPOSE: To investigate the feasibility of using predilated thin-wall polytetrafluoroethylene (PTFE) secured by extra-large Palmaz stents for endoluminal repair of abdominal aortic aneurysms (AAA). METHODS: Thirty-two patients (26 males; aged 69 to 83 years) from three centers (two in Europe, one in Australia) were selected for endoluminal stent-grafting using predilated B-mm PTFE graft material fitted with extra-large Palmaz stents at the terminal ends. Aortoaortic tube grafts were implanted in 12 patients, while the remainder received aortomonoiliac endografts and femorofemoral bypass. Follow-up at 5 days and then biannually was by contrast-enhanced computed tomography (CT) or duplex scanning. RESULTS: There were 13 conversions to open surgery; these patients died within 30 days. Nineteen patients were discharged with functioning endografts within 5 days of treatment. Of these, two have had their grafts removed owing to infection in one and distal stent migration in the other. Two endoleaks have been detected in follow-up; one has been sealed by covered stenting. One twisted graft was repaired by Wallstent implantation. Seventeen patients remain well, one with persistent distal endoleak, but none shows an increase in AAA diameter on imaging over the 6- to 26-month (median 13) follow-up. CONCLUSIONS: These results represent the learning curves of three separate centers. Technical failure and complications were more common early in the study. Advantages of the technique include relative low cost and the ability to tailor the stent-graft to the individual aneurysm.
This paper explores the possibility that the formation of color blobs in primate striate cortex can be partly explained through the process of activity-based self-organization. We present a simulation of a highly simplified model of visual processing along the parvocellular pathway, that combines precortical color processing, excitatory and inhibitory cortical interactions, and Hebbian learning. The model self-organizes in response to natural color images and develops islands of unoriented, color-selective cells within a sea of contrast-sensitive, orientation-selective cells. By way of understanding this topography, a principal component analysis of the color inputs presented to the network reveals that the optimal linear coding of these inputs keeps color information and contrast information separate.