Upper Bound on the Dark Matter Total Annihilation Cross Section

We consider dark matter annihilation into Standard Model particles and show that the least detectable final states, namely neutrinos, define an upper bound on the total cross section. Calculating the cosmic diffuse neutrino signal, and comparing it to the measured terrestrial atmospheric neutrino background, we derive a strong and general bound. This can be evaded if the annihilation products are dominantly new and truly invisible particles. Our bound is much stronger than the unitarity bound at the most interesting masses, shows that dark matter halos cannot be significantly modified by annihilations, and can be improved by a factor of 10--100 with existing neutrino experiments.Comment: 4 pages, 3 figures; version accepted for publication in PR

A Numerical Method for General Relativistic Magnetohydrodynamics

This paper describes the development and testing of a general relativistic magnetohydrodynamic (GRMHD) code to study ideal MHD in the fixed background of a Kerr black hole. The code is a direct extension of the hydrodynamic code of Hawley, Smarr, and Wilson, and uses Evans and Hawley constrained transport (CT) to evolve the magnetic fields. Two categories of test cases were undertaken. A one dimensional version of the code (Minkowski metric) was used to verify code performance in the special relativistic limit. The tests include Alfv\'en wave propagation, fast and slow magnetosonic shocks, rarefaction waves, and both relativistic and non-relativistic shock tubes. A series of one- and two-dimensional tests were also carried out in the Kerr metric: magnetized Bondi inflow, a magnetized inflow test due to Gammie, and two-dimensional magnetized constant-$l$ tori that are subject to the magnetorotational instability.Comment: 37 pages, 14 figures, submitted to ApJ. Animations can be viewed at http://www.astro.virginia.edu/~jd5v/grmhd/grmhd.htm

Experimental violation of a spin-1 Bell inequality using maximally-entangled four-photon states

We demonstrate the first experimental violation of a spin-1 Bell inequality. The spin-1 inequality is a calculation based on the Clauser, Horne, Shimony and Holt formalism. For entangled spin-1 particles the maximum quantum mechanical prediction is 2.552 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27 $\pm 0.02$ using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.Comment: 5 pages, 3 figures, Revtex4. Problem with figures resolve

Assumptions for a Market Share Theorem

Many marketing models use variants of the relationship: market share equals marketing effort divided by total marketing effort. Usually, share is defined within a customer group presumed to be reasonably homogeneous and overall share is obtained by weighting for the number in the group. Although the basic relationship can be assumed directly, certain insight is gained by deriving it from more fundamental assumptions as follows: For the given customer group, each competitive seller has a real-valued "attraction" with the following properties: (1) attraction is non-negative; (2) the attraction of a set of sellers is the sum of the attractions of the individual sellers; and (3) if the attractions of two sets of sellers are equal, the sellers have equal market shares in the customer groups. It is shown that, if the relation between share and attraction satisfies the above assumptions, is a continuous function, and is required to hold for arbitrary values of attraction and sets of sellers, then the relation is: Share equals attraction divided by total attraction. Insofar as various factors can be assembled into an attraction function that satisfies the assumptions of the theorem, the method for calculating share follows directly

Determining the galactic mass distribution using tidal streams from globular clusters

We discuss how to use tidal streams from globular clusters to measure the mass distribution of the Milky Way. Recent proper motion determinations for globular clusters from plate measurements and Hipparcos astrometry provide several good candidates for Galactic mass determinations in the intermediate halo, far above the Galactic disk, including Pal 5, NGC 4147, NGC 5024 (M53) and NGC 5466; the remaining Hipparcos clusters provide candidates for measurements several kpc above and below the disk. These clusters will help determine the profile and shape of the inner halo. To aid this effort, we present two methods of mass determination: one, a generalization of rotation-curve mass measurements, which gives the mass and potential from complete position-velocity observations for stream stars; and another using a simple chi^2 estimator, which can be used when only projected positions and radial velocities are known for stream stars. We illustrate the use of the latter method using simulated tidal streams from Pal 5 and find that fairly accurate mass determinations are possible even for relatively poor data sets. Follow-up observations of clusters with proper motion determinations may reveal tidal streams; obtaining radial velocity measurements would enable accurate measurements of the mass distribution in the inner Galaxy.Comment: 21 pages, 6 figures, published in A

Prolific pair production with high-power lasers

Prolific electron-positron pair production is possible at laser intensities approaching 10^{24} W/cm^2 at a wavelength of 1 micron. An analysis of electron trajectories and interactions at the nodes (B=0) of two counter-propagating, circularly polarised laser beams shows that a cascade of gamma-rays and pairs develops. The geometry is generalised qualitatively to linear polarisation and laser beams incident on a solid target.Comment: 4 pages, 1 figure, minor revisions, accepted for publication in Physical Review Letter

The EPR paradox, Bell's inequality, and the question of locality

Most physicists agree that the Einstein-Podolsky-Rosen-Bell paradox exemplifies much of the strange behavior of quantum mechanics, but argument persists about what assumptions underlie the paradox. To clarify what the debate is about, we employ a simple and well-known thought experiment involving two correlated photons to help us focus on the logical assumptions needed to construct the EPR and Bell arguments. The view presented in this paper is that the minimal assumptions behind Bell's inequality are locality and counterfactual definiteness, but not scientific realism, determinism, or hidden variables, as is often suggested. We further examine the resulting constraints on physical theory with an illustration from the many-worlds interpretation of quantum mechanics -- an interpretation that we argue is deterministic, local, and realist, but that nonetheless violates the Bell inequality.Comment: 28 pages; change of title, minor wording changes, move to TeX forma

Quantifying Compliance Costs for Small Businesses in New Zealand

This paper reports on a small-scale study of the compliance costs of small New Zealand businesses. Participating firms were asked to keep a record of both time spent and expenditure directly incurred over a thirteen-week period. This differs from previous studies that rely on a firm's recall of how much time has been spent on compliance over the previous year. The results suggest that New Zealand small businesses on average spend less time and money on compliance than has been indicated in previous studies. However a number offirms do perceive compliance to be a major issue and in some cases this perception prevents firms from expanding

Modeling the Large Scale Structures of Astrophysical Jets in the Magnetically Dominated Limit

We suggest a new approach that could be used for modeling both the large scale behavior of astrophysical jets and the magnetically dominated explosions in astrophysics. We describe a method for modeling the injection of magnetic fields and their subsequent evolution in a regime where the free energy is magnetically dominated. The injected magnetic fields, along with their associated currents, have both poloidal and toroidal components, and they are not force free. The dynamic expansion driven by the Lorentz force of the injected fields is studied using 3-dimensional ideal magnetohydrodynamic simulations. The generic behavior of magnetic field expansion, the interactions with the background medium, and the dependence on various parameters are investigated.Comment: Accepted to ApJ, May 10, 2006 issue, 12 figures total (3 color figures