Force on a sphere via the generalized reciprocal theorem

An approach based on the generalized reciprocal theorem is presented to derive the well-known result for the drag force exerted on a rigid sphere translating in a viscous fluid in an arbitrary manner. The use of generalized reciprocal theorem allows one to bypass the calculation of stress distribution over the particle surface in order to compute the force

Shellability of noncrossing partition lattices

We give a case-free proof that the lattice of noncrossing partitions associated to any finite real reflection group is EL-shellable. Shellability of these lattices was open for the groups of type $D_n$ and those of exceptional type and rank at least three.Comment: 10 page

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

Competing Explanations of U.S. Defense Industry Consolidation in the 1990s and Their Policy Implications

Was the consolidation of defense industry in the 1990s driven by U.S. Department of Defense (DOD) directives, or was it driven instead by the same forces that drove consolidation in many other sectors of the U.S. economy in the 1990s? To better understand the roles of DOD policy and economy-wide forces in shaping the U.S. defense industry, we test for structural breaks in defense industry and spending data and compare our findings to those relating to other sectors and the general economy. We identify structural breaks in the defense-related data in the early 1980s and throughout the 1990s, roughly consistent with changes in the U.S. economy, including broader merger trends. Overall, our results are more consistent with the view that economy-wide factors drove defense industry consolidation, largely independent of the DOD policy changes that occurred early in the 1990s.

Draft Genome Sequence of Rhizobium rhizogenes Strain ATCC 15834.

Here, we present the draft genome of Rhizobium rhizogenes strain ATCC 15834. The genome contains 7,070,307 bp in 43 scaffolds. R. rhizogenes, also known as Agrobacterium rhizogenes, is a plant pathogen that causes hairy root disease. This hairy root induction has been used in biotechnology for the generation of transgenic root cultures

Searching Gravitational Waves from Pulsars, Using Laser Beam Interferometers

We use recent population synthesis results to investigate the distribution of pulsars in the frequency space, having a gravitational strain high enough to be detected by the future generations of laser beam interferometers. We find that until detectors become able to recover the entire population, the frequency distribution of the 'detectable' population will be very dependent on the detector noise curve. Assuming a mean equatorial deformation $\epsilon =10^{-6}$, the optimal frequency is around 450 Hz for interferometers of the first generation (LIGO or VIRGO) and shifts toward 85 Hz for advanced detectors. An interesting result for future detection stategies is the significant narrowing of the distribution when improving the sensitivity: with an advanced detector, it is possible to have 90% of detection probability while exploring less than 20% of the parameter space (7.5% in the case of $\epsilon =10^{-5}$). In addition, we show that in most cases the spindown of 'detectable' pulsars represents a period shift of less than a tens of nanoseconds after one year of observation, making them easier to follow in the frequency space.Comment: 5 pages, 3 figures accepted for publication in Astronomy & Astrophysic

Numerical investigation of black hole interiors

Gravitational perturbations which are present in any realistic stellar collapse to a black hole, die off in the exterior of the hole, but experience an infinite blueshift in the interior. This is believed to lead to a slowly contracting lightlike scalar curvature singularity, characterized by a divergence of the hole's (quasi-local) mass function along the inner horizon. The region near the inner horizon is described to great accuracy by a plane wave spacetime. While Einstein's equations for this metric are still too complicated to be solved in closed form it is relatively simple to integrate them numerically. We find for generic regular initial data the predicted mass inflation type null singularity, rather than a spacelike singularity. It thus seems that mass inflation indeed represents a generic self-consistent picture of the black hole interior.Comment: 6 pages LaTeX, 3 eps figure

h-vectors of generalized associahedra and non-crossing partitions

A case-free proof is given that the entries of the $h$-vector of the cluster complex $\Delta (\Phi)$, associated by S. Fomin and A. Zelevinsky to a finite root system $\Phi$, count elements of the lattice \nc of noncrossing partitions of corresponding type by rank. Similar interpretations for the $h$-vector of the positive part of $\Delta (\Phi)$ are provided. The proof utilizes the appearance of the complex $\Delta (\Phi)$ in the context of the lattice \nc, in recent work of two of the authors, as well as an explicit shelling of $\Delta (\Phi)$.Comment: 20 pages, 1 figur