Trajectory analysis for non-Brownian inertial suspensions in simple shear flow

We analyse pair trajectories of equal-sized spherical particles in simple shear flow for small but finite Stokes numbers. The Stokes number, \mbox{\textit{St}} \,{=}\, \dot{\gamma} \tau_p, is a dimensionless measure of particle inertia; here, $\tau_p$ is the inertial relaxation time of an individual particle and $\dot{\gamma}$ is the shear rate. In the limit of weak particle inertia, a regular small-\mbox{\textit{St}} expansion of the particle velocity is used in the equations of motion to obtain trajectory equations to the desired order in \mbox{\textit{St}}. The equations for relative trajectories are then solved, to O(\mbox{\textit{St}}), in the dilute limit, including only pairwise interactions. Particle inertia is found to destroy the fore–aft symmetry of the zero-Stokes trajectories, and finite-\mbox{\textit{St}} open trajectories suffer net transverse displacements in the velocity gradient and vorticity directions. The vorticity displacement remains O(\mbox{\textit{St}}), while the scaling of the gradient displacement increases from O(\mbox{\textit{St}}) for far-field open trajectories, to O(\mbox{\textit{St}}^{{1}/{2}}) for open trajectories with O(\mbox{\textit{St}}^{{1}/{2}}) upstream gradient offsets. The gradient displacement also changes sign, being negative close to the plane of the reference sphere (the shearing plane) on account of dominant lubrication interactions, and then becoming positive at larger off-plane separations. The transverse displacements accompanying successive pair interactions lead to a diffusive behaviour for long times. The shear-induced diffusivity in the vorticity direction is O(\mbox{\textit{St}}^2\phi \dot{\gamma} a^2), while that in the gradient direction scales as O(\mbox{\textit{St}}^2 \ln \mbox{\textit{St}}\,\phi \dot{\gamma} a^2) and O(\mbox{\textit{St}}^2 \phi \ln (1/\phi) \dot{\gamma} a^2) in the limits \phi \,{\ll}\, \mbox{\textit{St}}^{{1}/{3}} and \mbox{\textit{St}}^{{1}/{3}} \,{\ll}\, \phi \,{\ll}\, 1, respectively. Further, the region of zero-Stokes closed trajectories is destroyed, and there exists a new attracting limit cycle whose location in the shearing plane is, at leading order, independent of \mbox{\textit{St}}. The extension of the present analysis to include a generic linear flow, and the implications of the finite-\mbox{\textit{St}} trajectory modifications for coagulating systems are discussed

Mapping and Distribution of Torpedograss and Evaluating the Effectiveness of Torpedograss Management Activities in Lake Okeechobee, Florida

Thousands of hectares of native plants and shallow open water habitat have been displaced in Lake Okeechobee’s marsh by the invasive exotic species torpedograss ( Panicum repens L.). The rate of torpedograss expansion, it’s areal distribution and the efficacy of herbicide treatments used to control torpedograss in the lake’s marsh were quantified using aerial color infra red (IR) photography.(PDF has 6 pages.

Complex oscillatory yielding of model hard sphere glasses

The yielding behaviour of hard sphere glasses under large amplitude oscillatory shear has been studied by probing the interplay of Brownian motion and shear-induced diffusion at varying oscillation frequencies. Stress, structure and dynamics are followed by experimental rheology and Browian Dynamics simulations. Brownian motion assisted cage escape dominates at low frequencies while escape through shear-induced collisions at high ones, both related with a yielding peak in\ $G^{\prime \prime}$. At intermediate frequencies a novel, for HS glasses, double peak in $G^{\prime \prime}$ is revealed reflecting both mechanisms. At high frequencies and strain amplitudes a persistent structural anisotropy causes a stress drop within the cycle after strain reversal, while higher stress harmonics are minimized at certain strain amplitudes indicating an apparent harmonic response.Comment: 4 figures placed at the end with following order: Figure 1, figure 3, figure 4 and figure

Hydrodynamic stress on fractal aggregates of spheres

We calculate the average hydrodynamic stress on fractal aggregates of spheres using Stokesian dynamics. We find that for fractal aggregates of force-free particles, the stress does not grow as the cube of the radius of gyration, but rather as the number of particles in the aggregate. This behavior is only found for random aggregates of force-free particles held together by hydrodynamic lubrication forces. The stress on aggregates of particles rigidly connected by interparticle forces grows as the radius of gyration cubed. We explain this behavior by examining the transmission of the tension along connecting lines in an aggregate and use the concept of a persistance length in order to characterize this stress transmission within an aggregate

Vacuum Polarisation and the Black Hole Singularity

In order to investigate the effects of vacuum polarisation on mass inflation singularities, we study a simple toy model of a charged black hole with cross flowing radial null dust which is homogeneous in the black hole interior. In the region $r^2 \ll e^2$ we find an approximate analytic solution to the classical field equations. The renormalized stress-energy tensor is evaluated on this background and we find the vacuum polarisation backreaction corrections to the mass function $m(r)$. Asymptotic analysis of the semiclassical mass function shows that the mass inflation singularity is much stronger in the presence of vacuum polarisation than in the classical case.Comment: 12 pages, RevTe

Short- and intermediate-time behavior of the linear stress relaxation in semiflexible polymers

The linear viscoelasticity of semiflexible polymers is studied through Brownian Dynamics simulations covering a broad range of chain stiffness and time scales. Our results agree with existing theoretical predictions in the flexible and stiff limits; however, we find that over a wide intermediate-time window spanning several decades, the stress relaxation is described by a single power law t^(-alpha), with the exponent alpha apparently varying continuously from 1/2 for flexible chains, to 5/4 for stiff ones. Our study identifies the limits of validity of the t^(-3/4) power law at short times predicted by recent theories. An additional regime is identified, the "ultrastiff" chains, where this behavior disappears. In the absence of Brownian motion, the purely mechanical stress relaxation produces a t^(-3/4) power law for both short and intermediate times

Target enrichment of ultraconserved elements from arthropods provides a genomic perspective on relationships among Hymenoptera

Gaining a genomic perspective on phylogeny requires the collection of data from many putatively independent loci collected across the genome. Among insects, an increasingly common approach to collecting this class of data involves transcriptome sequencing, because few insects have high-quality genome sequences available; assembling new genomes remains a limiting factor; the transcribed portion of the genome is a reasonable, reduced subset of the genome to target; and the data collected from transcribed portions of the genome are similar in composition to the types of data with which biologists have traditionally worked (e.g., exons). However, molecular techniques requiring RNA as a template are limited to using very high quality source materials, which are often unavailable from a large proportion of biologically important insect samples. Recent research suggests that DNA-based target enrichment of conserved genomic elements offers another path to collecting phylogenomic data across insect taxa, provided that conserved elements are present in and can be collected from insect genomes. Here, we identify a large set (n$=$1510) of ultraconserved elements (UCE) shared among the insect order Hymenoptera. We use in silico analyses to show that these loci accurately reconstruct relationships among genome-enabled Hymenoptera, and we design a set of baits for enriching these loci that researchers can use with DNA templates extracted from a variety of sources. We use our UCE bait set to enrich an average of 721 UCE loci from 30 hymenopteran taxa, and we use these UCE loci to reconstruct phylogenetic relationships spanning very old ($\geq$220 MYA) to very young ($\leq$1 MYA) divergences among hymenopteran lineages. In contrast to a recent study addressing hymenopteran phylogeny using transcriptome data, we found ants to be sister to all remaining aculeate lineages with complete support

Cosmic Censorship: As Strong As Ever

Spacetimes which have been considered counter-examples to strong cosmic censorship are revisited. We demonstrate the classical instability of the Cauchy horizon inside charged black holes embedded in de Sitter spacetime for all values of the physical parameters. The relevant modes which maintain the instability, in the regime which was previously considered stable, originate as outgoing modes near to the black hole event horizon. This same mechanism is also relevant for the instability of Cauchy horizons in other proposed counter-examples of strong cosmic censorship.Comment: 4 pages RevTeX style, 1 figure included using epsfi

The Journey West: The Mormon Pioneer Journals of Horace K. Whitney with Insights by Helen Mar Kimball Whitney

Review of: The Journey West: The Mormon Pioneer Journals of Horace K. Whitney with Insights by Helen Mar Kimball Whitney, edited by Richard E. Bennett