Is Random Close Packing of Spheres Well Defined?

Despite its long history, there are many fundamental issues concerning random packings of spheres that remain elusive, including a precise definition of random close packing (RCP). We argue that the current picture of RCP cannot be made mathematically precise and support this conclusion via a molecular dynamics study of hard spheres using the Lubachevsky-Stillinger compression algorithm. We suggest that this impasse can be broken by introducing the new concept of a maximally random jammed state, which can be made precise.Comment: 6 pages total, 2 figure

Granular circulation in a cylindrical pan: simulations of reversing radial and tangential flows

Granular flows due to simultaneous vertical and horizontal excitations of a flat-bottomed cylindrical pan are investigated using event-driven molecular dynamics simulations. In agreement with recent experimental results, we observe a transition from a solid-like state, to a fluidized state in which circulatory flow occurs simultaneously in the radial and tangential directions. By going beyond the range of conditions explored experimentally, we find that each of these circulations reverse their direction as a function of the control parameters of the motion. We numerically evaluate the dynamical phase diagram for this system and show, using a simple model, that the solid-fluid transition can be understood in terms of a critical value of the radial acceleration of the pan bottom; and that the circulation reversals are controlled by the phase shift relating the horizontal and vertical components of the vibrations. We also discuss the crucial role played by the geometry of the boundary conditions, and point out a relationship of the circulation observed here and the flows generated in vibratory conveyors.Comment: 10 pages, 8 figure

Testing the Collective Properties of Small-World Networks through Roughness Scaling

Motivated by a fundamental synchronization problem in scalable parallel computing and by a recent criterion for ``mean-field'' synchronizability in interacting systems, we study the Edwards-Wilkinson model on two variations of a small-worldnetwork. In the first version each site has exactly one random link of strength $p$, while in the second one each site on average has $p$ links of unit strength. We construct a perturbative description for the width of the stationary-state surface (a measure of synchronization), in the weak- and sparse-coupling limits, respectively, and verify the results by performing exact numerical diagonalization. The width remains finite in both cases, but exhibits anomalous scaling with $p$ in the latter for $d\leq 2$.Comment: 4 pages, 3 figure

One dimensional drift-diffusion between two absorbing boundaries: application to granular segregation

Motivated by a novel method for granular segregation, we analyze the one dimensional drift-diffusion between two absorbing boundaries. The time evolution of the probability distribution and the rate of absorption are given by explicit formulae, the splitting probability and the mean first passage time are also calculated. Applying the results we find optimal parameters for segregating binary granular mixtures.Comment: RevTeX, 5 pages, 6 figure

Extremal-point Densities of Interface Fluctuations

We introduce and investigate the stochastic dynamics of the density of local extrema (minima and maxima) of non-equilibrium surface fluctuations. We give a number of exact, analytic results for interface fluctuations described by linear Langevin equations, and for on-lattice, solid-on-solid surface growth models. We show that in spite of the non-universal character of the quantities studied, their behavior against the variation of the microscopic length scales can present generic features, characteristic to the macroscopic observables of the system. The quantities investigated here present us with tools that give an entirely un-orthodox approach to the dynamics of surface morphologies: a statistical analysis from the short wavelength end of the Fourier decomposition spectrum. In addition to surface growth applications, our results can be used to solve the asymptotic scalability problem of massively parallel algorithms for discrete event simulations, which are extensively used in Monte-Carlo type simulations on parallel architectures.Comment: 30 pages, 5 ps figure

Roughening of the (1+1) interfaces in two-component surface growth with an admixture of random deposition

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the universal scaling function of the interface width for this model and show that the RD admixture acts as a dilatation mechanism to the fundamental time and height scales, but leaves the KPZ correlations intact. This observation is generalized to other growth models. It is shown that the flat-substrate initial condition is responsible for the existence of an early non-scaling phase in the interface evolution. The length of this initial phase is a non-universal parameter, but its presence is universal. In application to parallel and distributed computations, the important consequence of the derived scaling is the existence of the upper bound for the desynchronization in a conservative update algorithm for parallel discrete-event simulations. It is shown that such algorithms are generally scalable in a ring communication topology.Comment: 16 pages, 16 figures, 77 reference

Synchronization Landscapes in Small-World-Connected Computer Networks

Motivated by a synchronization problem in distributed computing we studied a simple growth model on regular and small-world networks, embedded in one and two-dimensions. We find that the synchronization landscape (corresponding to the progress of the individual processors) exhibits Kardar-Parisi-Zhang-like kinetic roughening on regular networks with short-range communication links. Although the processors, on average, progress at a nonzero rate, their spread (the width of the synchronization landscape) diverges with the number of nodes (desynchronized state) hindering efficient data management. When random communication links are added on top of the one and two-dimensional regular networks (resulting in a small-world network), large fluctuations in the synchronization landscape are suppressed and the width approaches a finite value in the large system-size limit (synchronized state). In the resulting synchronization scheme, the processors make close-to-uniform progress with a nonzero rate without global intervention. We obtain our results by ``simulating the simulations", based on the exact algorithmic rules, supported by coarse-grained arguments.Comment: 20 pages, 22 figure