A simple nonlinear equation for structural relaxation in glasses

A wide range of glassy and disordered materials exhibit complex, non-exponential, structural relaxation (aging). We propose a simple nonlinear rate equation d\delta/dt = a [1-exp (b\delta)], where '\delta' is the normalized deviation of a macroscopic variable from its equilibrium value, to describe glassy relaxation. Analysis of extensive experimental data shows that this equation quantitatively captures structural relaxation, where 'a' and 'b' are both temperature-, and more importantly, history-dependent parameters. This analysis explicitly demonstrates that structural relaxation cannot be accurately described by a single non-equilibrium variable. Relaxation rates extracted from the data imply the existence of cooperative rearrangements on a super-molecular scale.Comment: 5 pages, 4 figure

A descriptive study of delinquent boys who are socially isolated within the context of an approved school.

A thesis submitted for the degree of Doctor of Medicine in the University of Witwatersrand Johannesburg.WHSLYP201

Navier-Stokes hydrodynamics of thermal collapse in a freely cooling granular gas

We employ Navier-Stokes granular hydrodynamics to investigate the long-time behavior of clustering instability in a freely cooling dilute granular gas in two dimensions. We find that, in circular containers, the homogeneous cooling state (HCS) of the gas loses its stability via a sub-critical pitchfork bifurcation. There are no time-independent solutions for the gas density in the supercritical region, and we present analytical and numerical evidence that the gas develops thermal collapse unarrested by heat diffusion. To get more insight, we switch to a simpler geometry of a narrow-sector-shaped container. Here the HCS loses its stability via a transcritical bifurcation. For some initial conditions a time-independent inhomogeneous density profile sets in, qualitatively similar to that previously found in a narrow-channel geometry. For other initial conditions, however, the dilute gas develops thermal collapse unarrested by heat diffusion. We determine the dynamic scalings of the flow close to collapse analytically and verify them in hydrodynamic simulations. The results of this work imply that, in dimension higher than one, Navier-Stokes hydrodynamics of a dilute granular gas is prone to finite-time density blowups. This provides a natural explanation to the formation of densely packed clusters of particles in a variety of initially dilute granular flows.Comment: 18 pages, 19 figure

How super-tough gels break

Fracture of highly stretched materials challenges our view of how things break. We directly visualize rupture of tough double-network (DN) gels at >50\% strain. During fracture, crack tip shapes obey a $x\sim y^{1.6}$ power-law, in contrast to the parabolic profile observed in low-strain cracks. A new length-scale $\ell$ emerges from the power-law; we show that $\ell$ scales directly with the stored elastic energy, and diverges when the crack velocity approaches the shear wave speed. Our results show that DN gels undergo brittle fracture, and provide a testing ground for large-strain fracture mechanics

Dissociation of brain activation in autism and schizotypal personality disorder during social judgements

Background There are overlaps between autism and schizophrenia but these are particularly pronounced, especially in social domains, for higher functioning individuals with autism spectrum disorders (ASD) or schizotypal personality disorder (SPD). It is not known whether these overlapping social deficits result from shared or distinct brain mechanisms. We therefore compared social cognition in ASD and SPD using functional magnetic resonance imaging (fMRI). Methods Twenty-one individuals with SPD, 28 with ASD and 33 controls were compared with respect to clinical symptoms using the Positive and Negative Syndrome Scale; social cognition, using a social judgment task and Ekman 60 faces task; and brain activation using an fMRI task of social judgment. Results The ASD and SPD groups showed few differences in symptoms or social cognition. However, fMRI showed that, compared to ASD, the SPD group showed significantly greater activation during social compared to gender judgments in the amygdala and 3 clusters: right posterior cerebellum, extending into fusiform and inferior temporal gyri; left posterior cerebellum; and left intraparietal sulcus extending through medial portions of the temporal gyri into the fusiform gyrus (all P < .05 family-wise error corrected). Control activations lay between the ASD and SPD groups. Conclusions Although social cognitive deficits in ASD and SPD appear superficially similar they are the result of different brain mechanisms. These findings have implications for therapeutic interventions targeted at social dysfunction in these conditions

Experimental Study of Energy Transfer by Inertial Waves During the Build up of Turbulence in a Rotating System

We study the transition from fluid at rest to turbulence in a rotating water cylinder. We show that the energy, injected at a given height, is transported by inertial wave packets through the fluid volume. These waves propagate at velocities consistent with those calculated from linearized theory, even when they possess large amplitudes. A clear "front" in the temporal evolution of the energy power spectrum is detected, defining a time scale for energy transport at the linear wave speed in the system. Nonlinear energy transfer between modes is governed by a different time scale that can be much longer than the linear one. These observations suggest that the energy distribution and statistics in rotating turbulent fields that are driven by intermittent energy sources may be different from those described by the inverse energy cascade in two-dimensional turbulence.Comment: 11 pages, 5 figure

Topological structure and dynamics of three-dimensional active nematics.

Topological structures are effective descriptors of the nonequilibrium dynamics of diverse many-body systems. For example, motile, point-like topological defects capture the salient features of two-dimensional active liquid crystals composed of energy-consuming anisotropic units. We dispersed force-generating microtubule bundles in a passive colloidal liquid crystal to form a three-dimensional active nematic. Light-sheet microscopy revealed the temporal evolution of the millimeter-scale structure of these active nematics with single-bundle resolution. The primary topological excitations are extended, charge-neutral disclination loops that undergo complex dynamics and recombination events. Our work suggests a framework for analyzing the nonequilibrium dynamics of bulk anisotropic systems as diverse as driven complex fluids, active metamaterials, biological tissues, and collections of robots or organisms