76 research outputs found
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 , while in the second one each site on average has
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 in the latter for .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 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
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