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Pattern formation in microbial colonies of competing strains under purely space-limited population growth has recently attracted considerable research interest. We show that the reproduction time statistics of individuals has a significant impact on the sectoring patterns. Generalizing the standard Eden growth model, we introduce a simple one-parameter family of reproduction time distributions indexed by the variation coefficient &dgr; € [0,1], which includes deterministic (&dgr; = 0) and memory-less exponential distribution (&dgr; = 1) as extreme cases. We present convincing numerical evidence and heuristic arguments that the generalized model is still in the Kardar-Parisi-Zhang (KPZ) universality class, and the changes in patterns are due to changing prefactors in the scaling relations, which we are able to predict quantitatively. With the example of Saccharomyces cerevisiae, we show that our approach using the variation coefficient also works for more realistic reproduction time distributions. [ABSTRACT FROM AUTHOR]

The evolution of wide shear zones or shear bands was investigated experimentally and numerically for quasistatic dry granular flows in split bottom shear cells. We compare the behavior of materials consisting of beads, irregular grains, such as sand, and elongated particles. Shearing an initially random sample, the zone width was found to significantly decrease in the first stage of the process. The characteristic shear strain associated with this decrease is about unity and it is systematically increasing with shape anisotropy, i.e., when the grain shape changes from spherical to irregular (e.g., sand) and becomes elongated (pegs). The strongly decreasing tendency of the zone width is followed by a slight increase which is more pronounced for rodlike particles than for grains with smaller shape anisotropy (beads or irregular particles). The evolution of the zone width is connected to shear-induced packing density change and for nonspherical particles it also involves grain reorientation effects. The final zone width is significantly smaller for irregular grains than for spherical beads. [ABSTRACT FROM AUTHOR]

Many growth processes lead to intriguing stochastic patterns and complex fractal structures which exhibit local scale invariance properties. Such structures can often be described effectively by space-time trajectories of interacting particles, and their large scale behavior depends on the overall growth geometry. We establish an exact relation between statistical properties of structures in uniformly expanding and fixed geometries, which preserves the local scale invariance and is independent of other properties such as the dimensionality. This relation generalizes standard conformal transformations as the natural symmetry of self-affine growth processes. We illustrate our main result numerically for various structures of coalescing Lrvy flights and fractional Brownian motions, including also branching and finite particle sizes. One of the main benefits of this approach is a full, explicit description of the asymptotic statistics in expanding domains, which are often nontrivial and random due to amplification of initial fluctuations. [ABSTRACT FROM AUTHOR]

The alignment, ordering, and rotation of elongated granular particles was studied in shear flow. The time evolution of the orientation of a large number of particles was monitored in laboratory experiments by particle tracking using optical imaging and x-ray computed tomography. The experiments were complemented by discrete element simulations: The particles develop an orientational order. In the steady state the time- and ensemble-averaged direction of the main axis of the particles encloses a small angle with the streamlines! This shear alignment angle is independent of the applied shear rate, and it decreases with increasing grain aspect ratio. At the grain level the steady state is characterized by a net rotation of the particles, as dictated by the shear flow. The distribution of particle rotational velocities was measured both in the steady state and also during the initial transients. The average rotation speed of particles with their long axis perpendicular to the shear alignment angle is larger, while shear aligned particles rotate slower. The ratio of this fast/slow rotation increases with particle aspect ratio. During the initial transient starting from an unaligned initial condition, particles having an orientation just beyond the shear alignment angle rotate opposite to the direction dictated by the shear flow. [ABSTRACT FROM AUTHOR]

Shear induced alignment of elongated particles is studied experimentally and numerically. We show that shear alignment of ensembles of macroscopic particles is comparable even on a quantitative level to simple molecular systems, despite the completely different types of particle interactions. We demonstrate that for dry elongated grains the preferred orientation forms a small angle with the streamlines, independent of shear rate across three decades. For a given particle shape, this angle decreases with increasing aspect ratio of the particles. The shear-induced alignment results in a considerable reduction of the effective friction of the granular material. [ABSTRACT FROM AUTHOR]

We study the rheology of dense granular flows for frictionless spherocylinders by means of 3D numerical simulations. As in the case of spherical particles, the effective friction μ is an increasing function of the inertial number I, and we systematically investigate the dependence of μ on the particle aspect ratio Q, as well as that of the normal stress differences, the volume fraction, and the coordination number. We show in particular that the quasistatic friction coefficient is nonmonotonic with Q: from the spherical case Q=1, it first sharply increases, reaches a maximum around Q≃1.05, and then gently decreases until Q=3, passing its initial value at Q≃2. We provide a microscopic interpretation for this unexpected behavior through the analysis of the distribution of dissipative contacts around the particles: as compared to spheres, slightly elongated grains enhance contacts in their central cylindrical band, whereas at larger aspect ratios particles tend to align and dissipate by preferential contacts at their hemispherical caps. [ABSTRACT FROM AUTHOR]

More than 30 years ago Edwards and co-authors proposed a model to describe the statistics of granular packings by an ensemble of equiprobable jammed states. Experimental tests of this model remained scarce so far. We introduce a simple system to analyze statistical properties of jammed granular ensembles to test Edwards theory. Identical spheres packed in a nearly two-dimensional geometrical confinement were studied in experiments and numerical simulations. When tapped, the system evolves toward a ground state, but due to incompatible domain structures it gets trapped. Analytical calculations reproduce relatively well our simulation results, which allows us to test Edwards theory on a coupled system of two subsystems with different properties. We find that the joint system can only be described by the Edwards theory if considered as a single system due to the constraints in the stresses. The results show counterintuitive effects as in the coupled system the change in the order parameter is opposite to what is expected from the change in the compactivity.

We present simulations of coherent structures in compressible flows near the transition to turbulence using the dissipative particle dynamics method. The structures we find are remarkably consistent with experimental observations and direct numerical simulations (DNS) simulations of incompressible flows, despite a difference in Mach number of several orders of magnitude. The bifurcation from the laminar flow is bistable and shifts to higher Reynolds numbers when the fluid becomes more compressible. This work underlines the robustness of coherent structures in the transition to turbulence and illustrates the ability of particle-based methods to reproduce complex nonlinear instabilities.

We probe the nature of the jamming transition of frictional granular media by studying their vibrational properties as a function of the applied pressure p and friction coefficient mu. The density of vibrational states exhibits a crossover from a plateau at frequencies omega > or similar to omega*(p,mu) to a linear growth for omega < or similar to omega*(p,mu). We show that omega* is proportional to Deltaz, the excess number of contacts per grain relative to the minimally allowed, isostatic value. For zero and infinitely large friction, typical packings at the jamming threshold have Deltaz-->0, and then exhibit critical scaling. We study the nature of the soft modes in these two limits, and find that the ratio of elastic moduli is governed by the distance from isostaticity.

We study the origin of the scaling behavior in frictionless granular media above the jamming transition by analyzing their linear response. The response to local forcing is non-self-averaging and fluctuates over a length scale that diverges at the jamming transition. The response to global forcing becomes increasingly nonaffine near the jamming transition. This is due to the proximity of floppy modes, the influence of which we characterize by the local linear response. We show that the local response also governs the anomalous scaling of elastic constants and contact number.

We explore the macroscopic consequences of lattice anisotropy for diffusion limited aggregation (DLA) in three dimensions. Simple cubic and bcc lattice growths are shown to approach universal asymptotic states in a coherent fashion, and the approach is accelerated by the use of noise reduction. These states are strikingly anisotropic dendrites with a rich hierarchy of structure. For growth on an fcc lattice, our data suggest at least two stable fixed points of anisotropy, one matching the bcc case. Hexagonal growths, favoring six planar and two polar directions, appear to approach a line of asymptotic states with continuously tunable polar anisotropy. The more planar of these growths visually resembles real snowflake morphologies. Our simulations use a new and dimension-independent implementation of the DLA model. The algorithm maintains a hierarchy of sphere coverings of the growth, supporting efficient random walks onto the growth by spherical moves. Anisotropy was introduced by restricting growth to certain preferred directions.

We present numerical simulations of acoustic wave propagation in confined granular systems consisting of particles interacting with the three-dimensional Hertz-Mindlin force law. The response to a short mechanical excitation on one side of the system is found to be a propagating coherent wave front followed by random oscillations made of multiply scattered waves. We find that the coherent wave front is insensitive to details of the packing: force chains do not play an important role in determining this wave front. The coherent wave propagates linearly in time, and its amplitude and width depend as a power law on distance, while its velocity is roughly compatible with the predictions of macroscopic elasticity. As there is at present no theory for the broadening and decay of the coherent wave, we numerically and analytically study pulse propagation in a one-dimensional chain of identical elastic balls. The results for the broadening and decay exponents of this system differ significantly from those of the random packings. In all our simulations, the speed of the coherent wave front scales with pressure as p1/6; we compare this result with experimental data on various granular systems where deviations from the p1/6 behavior are seen. We briefly discuss the eigenmodes of the system and effects of damping are investigated as well.

Random walkers absorbing on a boundary sample the harmonic measure linearly and independently: we discuss how the recurrence times between impacts enable nonlinear moments of the measure to be estimated. From this we derive a technique to simulate dielectric breakdown model growth, which is governed nonlinearly by the harmonic measure. For diffusion-limited aggregation, recurrence times are shown to be accurate and effective in probing the multifractal growth measure in its active region. For the dielectric breakdown model our technique grows large clusters efficiently and we are led to significantly revise earlier exponent estimates. Previous results by two conformal mapping techniques were less converged than expected, and in particular a recent theoretical suggestion of superuniversality is firmly refuted.

The relation between packing geometry and force network statistics is studied for granular media. Based on simulations of two-dimensional packings of Hertzian spheres, we develop a geometrical framework relating the distribution of interparticle forces P(f) to the weight distribution P(w), which is measured in experiments. We apply this framework to reinterpret recent experimental data on strongly deformed packings and suggest that the observed changes of P(w) are dominated by changes in contact network while P(f) remains relatively unaltered. We furthermore investigate the role of packing disorder in the context of the q model and address the question of how force fluctuations build up as a function of the distance beneath the top surface.

We performed extensive numerical simulation of diffusion-limited aggregation in two-dimensional channel geometry. Contrary to earlier claims, the measured fractal dimension D=1.712+/-0.002 and its leading correction to scaling are the same as in the radial case. The average cluster, defined as the average conformal map, is similar but not identical to Saffman-Taylor fingers.

The influence of the local contact network on interparticle forces and effective particle weights is studied in simulations of two-dimensional packings of frictionless, Hertzian spheres. The weight distribution P(w) changes qualitatively when approaching a boundary and differs for regular and irregular packings, while the interparticle force distribution P(f) is robust. We provide examples where P(w) at the boundary, which is the quantity probed experimentally, deviates substantially from P(f) in the bulk. Discrepancies between the P(w)'s predicted by the q model and measured in experiments are due to differences in the contact geometry.

Off-lattice diffusion-limited aggregation (DLA) clusters grown with different levels of noise reduction are found to be consistent with a simple fractal fixed point. Cluster shapes and their ensemble variation exhibit a dominant slowest correction to scaling, and this also accounts for the apparent "multiscaling" in the DLA mass distribution. We interpret the correction to scaling in terms of renormalized noise. The limiting value of this variable is strikingly small and is dominated by fluctuations in cluster shape. Earlier claims of anomalous scaling in DLA were misled by the slow approach to this small fixed point value.