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

Structural signatures of the unjamming transition at zero temperature

We study the pair correlation function $g(r)$ for zero-temperature, disordered, soft-sphere packings just above the onset of jamming. We find distinct signatures of the transition in both the first and split second peaks of this function. As the transition is approached from the jammed side (at higher packing fraction) the first peak diverges and narrows on the small-$r$ side to a delta-function. On the high-$r$ side of this peak, $g(r)$ decays as a power-law. In the split second peak, the two subpeaks are both singular at the transition, with power-law behavior on their low-$r$ sides and step-function drop-offs on their high-$r$ sides. These singularities at the transition are reminiscent of empirical criteria that have previously been used to distinguish glassy structures from liquid ones.Comment: 8 pages, 13 figure

Homiletics

Homiletics

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

Quickest Paths in Simulations of Pedestrians

This contribution proposes a method to make agents in a microscopic simulation of pedestrian traffic walk approximately along a path of estimated minimal remaining travel time to their destination. Usually models of pedestrian dynamics are (implicitly) built on the assumption that pedestrians walk along the shortest path. Model elements formulated to make pedestrians locally avoid collisions and intrusion into personal space do not produce motion on quickest paths. Therefore a special model element is needed, if one wants to model and simulate pedestrians for whom travel time matters most (e.g. travelers in a station hall who are late for a train). Here such a model element is proposed, discussed and used within the Social Force Model.Comment: revised version submitte

Scaling behavior in the β\beta-relaxation regime of a supercooled Lennard-Jones mixture

We report the results of a molecular dynamics simulation of a supercooled binary Lennard-Jones mixture. By plotting the self intermediate scattering functions vs. rescaled time, we find a master curve in the $\beta$-relaxation regime. This master curve can be fitted well by a power-law for almost three decades in rescaled time and the scaling time, or relaxation time, has a power-law dependence on temperature. Thus the predictions of mode-coupling-theory on the existence of a von Schweidler law are found to hold for this system; moreover, the exponents in these two power-laws are very close to satisfying the exponent relationship predicted by the mode-coupling-theory. At low temperatures, the diffusion constants also show a power-law behavior with the same critical temperature. However, the exponent for diffusion differs from that of the relaxation time, a result that is in disagreement with the theory.Comment: 8 pages, RevTex, four postscript figures available on request, MZ-Physics-10

The Kasteleyn model and a cellular automaton approach to traffic flow

We propose a bridge between the theory of exactly solvable models and the investigation of traffic flow. By choosing the activities in an apropriate way the dimer configurations of the Kasteleyn model on a hexagonal lattice can be interpreted as space-time trajectories of cars. This then allows for a calculation of the flow-density relationship (fundamental diagram). We further introduce a closely-related cellular automaton model. This model can be viewed as a variant of the Nagel-Schreckenberg model in which the cars do not have a velocity memory. It is also exactly solvable and the fundamental diagram is calculated.Comment: Latex, 13 pages including 3 ps-figure

Phase Transitions in Two-Dimensional Traffic Flow Models

We introduce two simple two-dimensional lattice models to study traffic flow in cities. We have found that a few basic elements give rise to the characteristic phase diagram of a first-order phase transition from a freely moving phase to a jammed state, with a critical point. The jammed phase presents new transitions corresponding to structural transformations of the jam. We discuss their relevance in the infinite size limit.Comment: RevTeX 3.0 file. Figures available upon request to e-address [email protected] (or 'dopico' or 'molera' or 'anxo', same node