Microscopic theory for the glass transition in a system without static correlations

We study the orientational dynamics of infinitely thin hard rods of length L, with the centers-of-mass fixed on a simple cubic lattice with lattice constant a.We approximate the influence of the surrounding rods onto dynamics of a pair of rods by introducing an effective rotational diffusion constant D(l),l=L/a. We get D(l) ~ [1-v(l)], where v(l) is given through an integral of a time-dependent torque-torque correlator of an isolated pair of rods. A glass transition occurs at l_c, if v(l_c)=1. We present a variational and a numerically exact evaluation of v(l).Close to l_c the diffusion constant decreases as D(l) ~ (l_c-l)^\gamma, with \gamma=1. Our approach predicts a glass transition in the absence of any static correlations, in contrast to present form of mode coupling theory.Comment: 6 pages, 3 figure

Short Time Behavior in De Gennes' Reptation Model

To establish a standard for the distinction of reptation from other modes of polymer diffusion, we analytically and numerically study the displacement of the central bead of a chain diffusing through an ordered obstacle array for times $t < O(N^2)$. Our theory and simulations agree quantitatively and show that the second moment approaches the $t^{1/4}$ often viewed as signature of reptation only after a very long transient and only for long chains (N > 100). Our analytically solvable model furthermore predicts a very short transient for the fourth moment. This is verified by computer experiment.Comment: 4 pages, revtex, 4 ps file

Critical behaviour of the Rouse model for gelling polymers

It is shown that the traditionally accepted "Rouse values" for the critical exponents at the gelation transition do not arise from the Rouse model for gelling polymers. The true critical behaviour of the Rouse model for gelling polymers is obtained from spectral properties of the connectivity matrix of the fractal clusters that are formed by the molecules. The required spectral properties are related to the return probability of a "blind ant"-random walk on the critical percolating cluster. The resulting scaling relations express the critical exponents of the shear-stress-relaxation function, and hence those of the shear viscosity and of the first normal stress coefficient, in terms of the spectral dimension $d_{s}$ of the critical percolating cluster and the exponents $\sigma$ and $\tau$ of the cluster-size distribution.Comment: 9 pages, slightly extended version, to appear in J. Phys.

Dynamics of gelling liquids: a short survey

The dynamics of randomly crosslinked liquids is addressed via a Rouse- and a Zimm-type model with crosslink statistics taken either from bond percolation or Erdoes-Renyi random graphs. While the Rouse-type model isolates the effects of the random connectivity on the dynamics of molecular clusters, the Zimm-type model also accounts for hydrodynamic interactions on a preaveraged level. The incoherent intermediate scattering function is computed in thermal equilibrium, its critical behaviour near the sol-gel transition is analysed and related to the scaling of cluster diffusion constants at the critical point. Second, non-equilibrium dynamics is studied by looking at stress relaxation in a simple shear flow. Anomalous stress relaxation and critical rheological properties are derived. Some of the results contradict long-standing scaling arguments, which are shown to be flawed by inconsistencies.Comment: 21 pages, 3 figures; Dedicated to Lothar Schaefer on the occasion of his 60th birthday; Changes: added comments on the gel phase and some reference

Anomalous scaling of passively advected magnetic field in the presence of strong anisotropy

Inertial-range scaling behavior of high-order (up to order N=51) structure functions of a passively advected vector field has been analyzed in the framework of the rapid-change model with strong small-scale anisotropy with the aid of the renormalization group and the operator-product expansion. It has been shown that in inertial range the leading terms of the structure functions are coordinate independent, but powerlike corrections appear with the same anomalous scaling exponents as for the passively advected scalar field. These exponents depend on anisotropy parameters in such a way that a specific hierarchy related to the degree of anisotropy is observed. Deviations from power-law behavior like oscillations or logarithmic behavior in the corrections to structure functions have not been found.Comment: 15 pages, 18 figure

Describing interruptions, multi-tasking and task-switching in the community pharmacy: A qualitative study in England

Background: There is growing evidence base around interruptions and distractions in the community pharmacy setting. There is also evidence to suggest these practices may be associated with dispensing errors. Up to date, qualitative research on this subject is limited. Objective: To explore interruptions and distractions in the community setting; utilising an ethnographic approach to be able to provide a detailed description of the circumstances surrounding such practices. Setting: Community pharmacies in England, July to October 2011. Method: An ethnographic approach was taken. Non participant, unstructured observations were utilised to make records of pharmacists’ every activities. Case studies were formed by combining field notes with detailed information on pharmacists and their respective pharmacy businesses. Content analysis was undertaken both manually and electronically, utilising NVivo 10. Results: Response rate was 12% (n=11). Over fifteen days, a total of 123 hours and 58 minutes of observations were recorded in 11 separate pharmacies of 11 individual pharmacists. The sample was evenly split by gender (female n=6; male n=5) and pharmacy ownership (independent n=5; multiple n=6). Employment statuses included employee pharmacists (n=6), owners (n=4) and a locum (n=1). Average period of registration as a pharmacist was 19 years (range 5-39 years). Average prescriptions busyness of pharmacies ranged from 2,600 – 24,000 items dispensed per month. Two key themes were: “Interruptions and task-switching” and “distractions and multi-tasking.” All observed pharmacists’ work was dominated by interruptions, task-switches, distractions and multi-tasking, often to manage a barrage of conflicting demands. These practices were observed to be part of a deep-rooted culture in the community setting. Directional work maps illustrated the extent and direction of task switching employed by pharmacists. Conclusions: In this study pharmacists’ working practices were permeated by interruptions and multi-tasking. These practices are inefficient and potentially reduce patient safety in terms of dispensing accuracy

Effects of differential mobility on biased diffusion of two species

Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility, and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species.Comment: 15 pages, 4 figure

Sand in the wheels, or oiling the wheels, of international finance? : New Labour's appeal to a 'new Bretton Woods'

Tony Blair’s political instinct typically is to associate himself only with the future. As such, his explicit appeal to ‘the past’ in his references to New Labour’s desire to establish a “new Bretton Woods” is sufficient in itself to arouse some degree of analytical curiosity (see Blair 1998a). The fact that this appeal was made specifically in relation to Bretton Woods is even more interesting. The resonant image of the international economic context established by the original Bretton Woods agreements invokes a style and content of policy-making which Tony Blair typically dismisses as neither economically nor politically consistent with his preferred vision of the future (see Blair 2000c, 2001b)

Prophet Inequalities for IID Random Variables from an Unknown Distribution

A central object in optimal stopping theory is the single-choice prophet inequality for independent, identically distributed random variables: given a sequence of random variables X1, . . . , Xn drawn independently from a distribution F , the goal is to choose a stopping time τ so as to maximize α such that for all distributions F we have E[Xτ ] ≥ α · E[maxt Xt ]. What makes this problem challenging is that the decision whether τ = t may only depend on the values of the random variables X1, . . . , Xt and on the distribution F . For a long time the best known bound for the problem had been α ≥ 1 − 1/e ≈ 0.632, but quite recently a tight bound of α ≈ 0.745 was obtained. The case where F is unknown, such that the decision whether τ = t may depend only on the values of the random variables X1, . . . , Xt , is equally well motivated but has received much less attention. A straightforward guarantee for this case of α ≥ 1/e ≈ 0.368 can be derived from the solution to the secretary problem, where an arbitrary set of values arrive in random order and the goal is to maximize the probability of selecting the largest value. We show that this bound is in fact tight. We then investigate the case where the stopping time may additionally depend on a limited number of samples from F , and show that even with o(n) samples α ≤ 1/e. On the other hand, n samples allow for a significant improvement, while O(n2) samples are equivalent to knowledge of the distribution: specifically, with n samples α ≥ 1 − 1/e ≈ 0.632 and α ≤ ln(2) ≈ 0.693, and with O(n2) samples α ≥ 0.745 − ε for any ε > 0

Biofeedback fixation training method for improving eccentric vision in patients with loss of foveal function secondary to different maculopathies

© 2019, The Author(s). Purpose: Fixation stability (FS) of the preferred retinal locus (PRL) may be improved by biofeedback fixation training (BFT) with microperimetry. Such training can be done on the patient’s PRL or in different retinal loci with better functional characteristics. We studied both options and compared the outcomes. Methods: Sixty-seven consecutive patients with bilateral central vision loss, poor FS and visual acuity (VA) lower than 0.3 LogMAR were recruited for BFT with microperimeter. Patients were assigned into 2 groups. In group A, BFT was performed on the patient’s spontaneous PRL. In group B, PRL was located between 2 adjacent loci with the highest light sensitivity and the lowest distance from the fovea. Two sets of 12 weekly BFT sessions were performed. Primary outcomes were: FS, VA and reading speed. Results: Outcomes were statistically significantly better in group B. Mean percentage of FS at therapy end improved from 32 to 35% for group A and from 40 to 55% in group B. Mean VA improved from 1 to 0.86 in group A and from 1 to 0.84 in group B. Reading speed (wpm) improved from 56 to 58 in group A and from 63 to 89 in group B. Conclusions: This study describes a reliable methodology of improving eccentric fixation stability using BFT in microperimetry, when the fixation training locus is individualized as the retinal area with best functional characteristics. Further studies are needed to validate its value in a larger scale of patients, at different stages of the disease, and its persistence over time