Vibrations and diverging length scales near the unjamming transition

We numerically study the vibrations of jammed packings of particles interacting with finite-range, repulsive potentials at zero temperature. As the packing fraction $\phi$ is lowered towards the onset of unjamming at $\phi_{c}$, the density of vibrational states approaches a non-zero value in the limit of zero frequency. For $\phi>\phi_{c}$, there is a crossover frequency, $\omega^{*}$ below which the density of states drops towards zero. This crossover frequency obeys power-law scaling with $\phi-\phi_{c}$. Characteristic length scales, determined from the dominant wavevector contributing to the eigenmode at $\omega^{*}$, diverge as power-laws at the unjamming transition.Comment: Submitted to PRL, 4 pages + 7 .eps figure

Geometric origin of excess low-frequency vibrational modes in amorphous solids

Glasses have a large excess of low-frequency vibrational modes in comparison with crystalline solids. We show that such a feature is a necessary consequence of the geometry generic to weakly connected solids. In particular, we analyze the density of states of a recently simulated system, comprised of weakly compressed spheres at zero temperature. We account for the observed a) constancy of the density of modes with frequency, b) appearance of a low-frequency cutoff, and c) power-law increase of this cutoff with compression. We predict a length scale below which vibrations are very different from those of a continuous elastic body.Comment: 4 pages, 2 figures. Argument rewritten, identical result

Discrete stochastic models for traffic flow

We investigate a probabilistic cellular automaton model which has been introduced recently. This model describes single-lane traffic flow on a ring and generalizes the asymmetric exclusion process models. We study the equilibrium properties and calculate the so-called fundamental diagrams (flow vs.\ density) for parallel dynamics. This is done numerically by computer simulations of the model and by means of an improved mean-field approximation which takes into account short-range correlations. For cars with maximum velocity 1 the simplest non-trivial approximation gives the exact result. For higher velocities the analytical results, obtained by iterated application of the approximation scheme, are in excellent agreement with the numerical simulations.Comment: Revtex, 30 pages, full postscript version (including figures) available by anonymous ftp from "fileserv1.mi.uni-koeln.de" in the directory "pub/incoming/" paper accepted for publication in Phys.Rev.

Conservation Laws in Cellular Automata

If X is a discrete abelian group and B a finite set, then a cellular automaton (CA) is a continuous map F:B^X-->B^X that commutes with all X-shifts. If g is a real-valued function on B, then, for any b in B^X, we define G(b) to be the sum over all x in X of g(b_x) (if finite). We say g is `conserved' by F if G is constant under the action of F. We characterize such `conservation laws' in several ways, deriving both theoretical consequences and practical tests, and provide a method for constructing all one-dimensional CA exhibiting a given conservation law.Comment: 19 pages, LaTeX 2E with one (1) Encapsulated PostScript figure. To appear in Nonlinearity. (v2) minor changes/corrections; new references added to bibliograph

Massasauga Repatriation on a Restored Wet Prairie

The massasauga (Sistrurus catenatus) is a small rattlesnake that occurs from Texas to New York (Schmidt and Davis 1941, Conant and Collins 1991, Szymanski 1998). In Missouri, the Eastern massasauga rattlesnake (EMR; S. c. catenatus), a subspecies of the massasauga, occurs north and east of the Missouri River, is a former candidate for listing under the United States Endangered Species Act (Code of Federal Regulations 64 FR 57534; Szymanski 1998), and is listed as a state endangered species (Missouri Natural Heritage Program 2011). Missouri currently harbors five extant EMR populations (Johnson 2000, Durbian et al., unpublished report, J. Briggler, Missouri Department of Conservation, personal communication). The decline of this subspecies can be attributed to habitat loss and fragmentation, over utilization for commercial, recreational, scientific or educational purposes, predation due to habitat fragmentation, inadequacy of existing regulatory mechanisms, and indiscriminant or accidental killing (Szymanski 1988). In Missouri, the EMR utilizes a combination of mesic and xeric bottomland prairie habitats and is typically associated with wetlands (Seigel 1986, Johnson et al. 2000). Over the past century, 87% of the wetland habitat has been lost in Missouri (Dahl 1990); however, current restoration efforts will enable EMRs to repatriate sites that are adjacent to existing populations. Repatriation of restored habitat has been documented for many other species groups including amphibians (Lehtinen and Galatowitsch 2001) and birds (Gardali et al. 2006), however, we were unable to find evidence in the literature involving snakes. Therefore, our objective was to document repatriation of restored habitat by EMRs on Squaw Creek National Wildlife Refuge (SCNWR) located in northwestern Missouri

Cellular automaton rules conserving the number of active sites

This paper shows how to determine all the unidimensional two-state cellular automaton rules of a given number of inputs which conserve the number of active sites. These rules have to satisfy a necessary and sufficient condition. If the active sites are viewed as cells occupied by identical particles, these cellular automaton rules represent evolution operators of systems of identical interacting particles whose total number is conserved. Some of these rules, which allow motion in both directions, mimic ensembles of one-dimensional pseudo-random walkers. Numerical evidence indicates that the corresponding stochastic processes might be non-Gaussian.Comment: 14 pages, 5 figure

Using Absorption Imaging to Study Ion Dynamics in an Ultracold Neutral Plasma

We report optical absorption imaging of ultracold neutral plasmas.Images are used to measure the ion absorption spectrum, which is Doppler-broadened. Through the spectral width, we monitor ion equilibration in the first 250ns after plasma formation. The equilibration leaves ions on the border between the weakly coupled gaseous and strongly coupled liquid states. On a longer timescale of microseconds, we observe radial acceleration of ions resulting from pressure exerted by the trapped electron gas.Comment: 4 pages, 4 figure

Heat transport in model jammed solids

We calculate numerically the normal modes of vibrations in 3D jammed packings of soft spheres as a function of the packing fraction and obtain the energy diffusivity, a spectral measure of transport that controls sound propagation and thermal conductivity. The crossover frequency between weak and strong phonon scattering is controlled by the coordination and shifts to zero as the system is decompressed towards the critical packing fraction at which rigidity is lost. Below the crossover, the diffusivity displays a power-law divergence with inverse frequency, which suggests that the vibrational modes are primarily transverse waves, weakly scattered by disorder. Above it, a large number of modes appear whose diffusivity plateaus at a nearly constant value independent of the inter-particle potential, before dropping to zero above the Anderson localization frequency. The thermal conductivity of a marginally jammed solid just above the rigidity threshold is calculated and related to the one measured experimentally at room temperature for most glasses.Comment: 15 pages, 7 figure

Spectroscopic determination of the s-wave scattering lengths of 86Sr and 88Sr

We report the use of photoassociative spectroscopy to determine the ground state s-wave scattering lengths for the main bosonic isotopes of strontium, 86Sr and 88Sr. Photoassociative transitions are driven with a laser red-detuned by up to 1400 GHz from the 1S0-1P1 atomic resonance at 461 nm. A minimum in the transition amplitude for 86Sr at -494+/-5 GHz allows us to determine the scattering lengths 610a0 < a86 < 2300a0 for 86Sr and a much smaller value of -1a0 < a88 < 13a0 for 88Sr.Comment: 4 pages, 3 figures, submitted to Physical Review Letter

Absorption Imaging and Spectroscopy of Ultracold Neutral Plasmas

Absorption imaging and spectroscopy can probe the dynamics of an ultracold neutral plasma during the first few microseconds after its creation. Quantitative analysis of the data, however, is complicated by the inhomogeneous density distribution, expansion of the plasma, and possible lack of global thermal equilibrium for the ions. In this article we describe methods for addressing these issues. Using simple assumptions about the underlying temperature distribution and ion motion, the Doppler-broadened absorption spectrum obtained from plasma images can be related to the average temperature in the plasma.Comment: 14 pages, 8 figure