Competition and cooperation:aspects of dynamics in sandpiles

In this article, we review some of our approaches to granular dynamics, now well known to consist of both fast and slow relaxational processes. In the first case, grains typically compete with each other, while in the second, they cooperate. A typical result of {\it cooperation} is the formation of stable bridges, signatures of spatiotemporal inhomogeneities; we review their geometrical characteristics and compare theoretical results with those of independent simulations. {\it Cooperative} excitations due to local density fluctuations are also responsible for relaxation at the angle of repose; the {\it competition} between these fluctuations and external driving forces, can, on the other hand, result in a (rare) collapse of the sandpile to the horizontal. Both these features are present in a theory reviewed here. An arena where the effects of cooperation versus competition are felt most keenly is granular compaction; we review here a random graph model, where three-spin interactions are used to model compaction under tapping. The compaction curve shows distinct regions where 'fast' and 'slow' dynamics apply, separated by what we have called the {\it single-particle relaxation threshold}. In the final section of this paper, we explore the effect of shape -- jagged vs. regular -- on the compaction of packings near their jamming limit. One of our major results is an entropic landscape that, while microscopically rough, manifests {\it Edwards' flatness} at a macroscopic level. Another major result is that of surface intermittency under low-intensity shaking.Comment: 36 pages, 23 figures, minor correction

Statistics of quantum transmission in one dimension with broad disorder

We study the statistics of quantum transmission through a one-dimensional disordered system modelled by a sequence of independent scattering units. Each unit is characterized by its length and by its action, which is proportional to the logarithm of the transmission probability through this unit. Unit actions and lengths are independent random variables, with a common distribution that is either narrow or broad. This investigation is motivated by results on disordered systems with non-stationary random potentials whose fluctuations grow with distance. In the statistical ensemble at fixed total sample length four phases can be distinguished, according to the values of the indices characterizing the distribution of the unit actions and lengths. The sample action, which is proportional to the logarithm of the conductance across the sample, is found to obey a fluctuating scaling law, and therefore to be non-self-averaging, in three of the four phases. According to the values of the two above mentioned indices, the sample action may typically grow less rapidly than linearly with the sample length (underlocalization), more rapidly than linearly (superlocalization), or linearly but with non-trivial sample-to-sample fluctuations (fluctuating localization).Comment: 26 pages, 4 figures, 1 tabl

Surface Properties of Aperiodic Ising Quantum Chains

We consider Ising quantum chains with quenched aperiodic disorder of the coupling constants given through general substitution rules. The critical scaling behaviour of several bulk and surface quantities is obtained by exact real space renormalization.Comment: 4 pages, RevTex, reference update

How useful is the DSM-5 severity indicator in bulimia nervosa? A clinical study including a measure of impairment

The severity criterion used in DSM-5 for bulimia nervosa (BN) was investigated in 214 individuals referred for treatment at a regional eating disorders service in the UK. In addition to comparing eating disorder symptoms, impairment secondary to these symptoms was also assessed. According to guidance in DSM-5, 94 individuals were classified as mild (43.9%), 70 as moderate (32.7%), 32 as severe (15.0%), and 8 as extreme (3.7%) levels of BN severity. Due to small numbers in the latter two groups, it was necessary to combine these to form one ‘severe/extreme’ group. Analyses on these three groups suggested no group effect on demographic variables but differences were seen on measures of eating pathology, psychological distress, and psychosocial impairment between the mild group and other groups. Individuals in the moderate and severe/extreme groups scored comparably on most measures of pathology and impairment. The results are broadly consistent with past studies on community samples although together question the demarcation between moderate and more severe groups of individuals with BN

Structure of the stationary state of the asymmetric target process

We introduce a novel migration process, the target process. This process is dual to the zero-range process (ZRP) in the sense that, while for the ZRP the rate of transfer of a particle only depends on the occupation of the departure site, it only depends on the occupation of the arrival site for the target process. More precisely, duality associates to a given ZRP a unique target process, and vice-versa. If the dynamics is symmetric, i.e., in the absence of a bias, both processes have the same stationary-state product measure. In this work we focus our interest on the situation where the latter measure exhibits a continuous condensation transition at some finite critical density $\rho_c$, irrespective of the dimensionality. The novelty comes from the case of asymmetric dynamics, where the target process has a nontrivial fluctuating stationary state, whose characteristics depend on the dimensionality. In one dimension, the system remains homogeneous at any finite density. An alternating scenario however prevails in the high-density regime: typical configurations consist of long alternating sequences of highly occupied and less occupied sites. The local density of the latter is equal to $\rho_c$ and their occupation distribution is critical. In dimension two and above, the asymmetric target process exhibits a phase transition at a threshold density $\rho_0$ much larger than $\rho_c$. The system is homogeneous at any density below $\rho_0$, whereas for higher densities it exhibits an extended condensate elongated along the direction of the mean current, on top of a critical background with density $\rho_c$.Comment: 30 pages, 16 figure

Metastability in zero-temperature dynamics: Statistics of attractors

The zero-temperature dynamics of simple models such as Ising ferromagnets provides, as an alternative to the mean-field situation, interesting examples of dynamical systems with many attractors (absorbing configurations, blocked configurations, zero-temperature metastable states). After a brief review of metastability in the mean-field ferromagnet and of the droplet picture, we focus our attention onto zero-temperature single-spin-flip dynamics of ferromagnetic Ising models. The situations leading to metastability are characterized. The statistics and the spatial structure of the attractors thus obtained are investigated, and put in perspective with uniform a priori ensembles. We review the vast amount of exact results available in one dimension, and present original results on the square and honeycomb lattices.Comment: 21 pages, 6 figures. To appear in special issue of JPCM on Granular Matter edited by M. Nicodem

Conformal invariance and linear defects in the two-dimensional Ising model

Using conformal invariance, we show that the non-universal exponent eta_0 associated with the decay of correlations along a defect line of modified bonds in the square-lattice Ising model is related to the amplitude A_0=xi_n/n of the correlation length \xi_n(K_c) at the bulk critical coupling K_c, on a strip with width n, periodic boundary conditions and two equidistant defect lines along the strip, through A_0=(\pi\eta_0)^{-1}.Comment: Old paper, for archiving. 5 pages, 4 figures, IOP macro, eps

Statistics of leaders and lead changes in growing networks

We investigate various aspects of the statistics of leaders in growing network models defined by stochastic attachment rules. The leader is the node with highest degree at a given time (or the node which reached that degree first if there are co-leaders). This comprehensive study includes the full distribution of the degree of the leader, its identity, the number of co-leaders, as well as several observables characterizing the whole history of lead changes: number of lead changes, number of distinct leaders, lead persistence probability. We successively consider the following network models: uniform attachment, linear attachment (the Barabasi-Albert model), and generalized preferential attachment with initial attractiveness.Comment: 28 pages, 14 figures, 1 tabl