Universal velocity distributions in an experimental granular fluid

We present experimental results on the velocity statistics of a uniformly heated granular fluid, in a quasi-2D configuration. We find the base state, as measured by the single particle velocity distribution $f(c)$, to be universal over a wide range of filling fractions and only weakly dependent on all other system parameters. There is a consistent overpopulation in the distribution's tails, which scale as $f\propto\exp(\mathrm{const.}\times c^{-3/2})$. More importantly, the high probability central region of $f(c)$, at low velocities, deviates from a Maxwell-Boltzmann by a second order Sonine polynomial with a single adjustable parameter, in agreement with recent theoretical analysis of inelastic hard spheres driven by a stochastic thermostat. To our knowledge, this is the first time that Sonine deviations have been measured in an experimental system.Comment: 13 pages, 15 figures, with minor corrections, submitted to Phys. Rev.

Minutes 1875

https://place.asburyseminary.edu/freemethodistminutesyearbooks/1013/thumbnail.jp

Shocks in supersonic sand

We measure time-averaged velocity, density, and temperature fields for steady granular flow past a wedge and calculate a speed of granular pressure disturbances (sound speed) equal to 10% of the flow speed. The flow is supersonic, forming shocks nearly identical to those in a supersonic gas. Molecular dynamics simulations of Newton's laws and Monte Carlo simulations of the Boltzmann equation yield fields in quantitative agreement with experiment. A numerical solution of Navier-Stokes-like equations agrees with a molecular dynamics simulation for experimental conditions excluding wall friction.Comment: 4 pages, 5 figure

Minutes 1877

https://place.asburyseminary.edu/freemethodistminutesyearbooks/1015/thumbnail.jp

A Continuum Description of Vibrated Sand

The motion of a thin layer of granular material on a plate undergoing sinusoidal vibrations is considered. We develop equations of motion for the local thickness and the horizontal velocity of the layer. The driving comes from the violent impact of the grains on the plate. A linear stability theory reveals that the waves are excited non-resonantly, in contrast to the usual Faraday waves in liquids. Together with the experimentally observed continuum scaling, the model suggests a close connection between the neutral curve and the dispersion relation of the waves, which agrees quite well with experiments. For strong hysteresis we find localized oscillon solutions.Comment: paper has been considerably extended (11 instead of 6 pages; 6 instead of 4 figures) much better agreement with experiment. obtain now oscillons in 1 dimensio

Phase Bubbles and Spatiotemporal Chaos in Granular Patterns

We use inelastic hard sphere molecular dynamics simulations and laboratory experiments to study patterns in vertically oscillated granular layers. The simulations and experiments reveal that {\em phase bubbles} spontaneously nucleate in the patterns when the container acceleration amplitude exceeds a critical value, about $7g$, where the pattern is approximately hexagonal, oscillating at one-fourth the driving frequency ($f/4$). A phase bubble is a localized region that oscillates with a phase opposite (differing by $\pi$) to that of the surrounding pattern; a localized phase shift is often called an {\em arching} in studies of two-dimensional systems. The simulations show that the formation of phase bubbles is triggered by undulation at the bottom of the layer on a large length scale compared to the wavelength of the pattern. Once formed, a phase bubble shrinks as if it had a surface tension, and disappears in tens to hundreds of cycles. We find that there is an oscillatory momentum transfer across a kink, and this shrinking is caused by a net collisional momentum inward across the boundary enclosing the bubble. At increasing acceleration amplitudes, the patterns evolve into randomly moving labyrinthian kinks (spatiotemporal chaos). We observe in the simulations that $f/3$ and $f/6$ subharmonic patterns emerge as primary instabilities, but that they are unstable to the undulation of the layer. Our experiments confirm the existence of transient $f/3$ and $f/6$ patterns.Comment: 6 pages, 12 figures, submitted to Phys. Rev. E on July 1st, 2001. for better quality figures, visit http://chaos.ph.utexas.edu/research/moo

Speech rhythm: a metaphor?

Is speech rhythmic? In the absence of evidence for a traditional view that languages strive to coordinate either syllables or stress-feet with regular time intervals, we consider the alternative that languages exhibit contrastive rhythm subsisting merely in the alternation of stronger and weaker elements. This is initially plausible, particularly for languages with a steep ‘prominence gradient’, i.e. a large disparity between stronger and weaker elements; but we point out that alternation is poorly achieved even by a ‘stress-timed’ language such as English, and, historically, languages have conspicuously failed to adopt simple phonological remedies that would ensure alternation. Languages seem more concerned to allow ‘syntagmatic contrast’ between successive units and to use durational effects to support linguistic functions than to facilitate rhythm. Furthermore, some languages (e.g. Tamil, Korean) lack the lexical prominence which would most straightforwardly underpin prominence alternation. We conclude that speech is not incontestibly rhythmic, and may even be antirhythmic. However, its linguistic structure and patterning allow the metaphorical extension of rhythm in varying degrees and in different ways depending on the language, and that it is this analogical process which allows speech to be matched to external rhythms

Transport Coefficients for Granular Media from Molecular Dynamics Simulations

Under many conditions, macroscopic grains flow like a fluid; kinetic theory pred icts continuum equations of motion for this granular fluid. In order to test the theory, we perform event driven molecular simulations of a two-dimensional gas of inelastic hard disks, driven by contact with a heat bath. Even for strong dissipation, high densities, and small numbers of particles, we find that continuum theory describes the system well. With a bath that heats the gas homogeneously, strong velocity correlations produce a slightly smaller energy loss due to inelastic collisions than that predicted by kinetic theory. With an inhomogeneous heat bath, thermal or velocity gradients are induced. Determination of the resulting fluxes allows calculation of the thermal conductivity and shear viscosity, which are compared to the predictions of granular kinetic theory, and which can be used in continuum modeling of granular flows. The shear viscosity is close to the prediction of kinetic theory, while the thermal conductivity can be overestimated by a factor of 2; in each case, transport is lowered with increasing inelasticity.Comment: 14 pages, 17 figures, 39 references, submitted to PRE feb 199

Stability of the Autism Diagnostic Interview—Revised from Pre-School to Elementary School Age in Children with Autism Spectrum Disorders

This study examined the stability of scores on the ADI-R from pre-school to elementary school age in children with autism spectrum disorders (ASD). Participants were 35 children who, at T1, all had a clinical diagnosis of ASD. On initial assessment (mean age 3.5 years; SD 0.6), all met ADI-R algorithm criteria for autism. ADI-R assessments were repeated at follow up (FU; mean age 10.5 years; SD 0.8). Changes in ADI-R total, domain and ADI-R algorithm item scores were assessed. Twentyeight children continued to score above the ADI-R cut-off for autism at FU, although significant decreases in ADI-R domain and item scores were also found. In conclusion, while classification of children according to ADI-R criteria, generally remained stable between pre-school and elementary school age, many children demonstrated significant improvements in symptom severity