Nonlinear Single-Armed Spiral Density Waves in Nearly Keplerian Disks

Single-armed, stationary density waves can propagate in very weakly self-gravitating gas disks dominated by a central mass. Examples include circumstellar disks of protostars and molecular disks in galactic nuclei. We explore the linear and nonlinear dynamics of such waves. Variational methods yield nonlinear versions of the dispersion relation, angular momentum flux, and propagation velocity in the tight-winding limit. The pitch angle increases with amplitude until the tight-winding approximation breaks down. We also find a series of nonlinear logarithmic spirals which is exact in the limit of small disk mass and which extends to large pitch angle.Comment: 16 pages, 3 figures. Uses mn.sty and mncite.sty. Accepted by MNRA

Price Fix Away?: Does the Supreme Court’s Decision in Leegin Creative Leather Products Strengthen the Ability of Businesses to Engage in Vertical Price Restraints with Impunity?

The United States Supreme Court in recent years has taken an increased interest in patent law, making a number of key decisions in the areas of injunctions1, licensing2, patentable subject matter3, and the standards of determining obviousness.4 In the current 2007-2008 term, the Court has already granted certiorari to consider the boundaries of the patent exhaustion doctrine; a case closely watched by legal commentators and observers.5 The Court's attention has also been drawn to the intersection of intellectual property law and antitrust law, with two cases in that legal realm having been recently decided. In Illinois Tool Works v. Independent Ink, the Court considered whether the presumption that patent owners have market power in the subject matter of their patents is "applicable in the antitrust context when a seller conditions its sale of a patented product . . . on the purchase of a second product."

A non-perturbative analysis of symmetry breaking in two-dimensional phi^4 theory using periodic field methods

We describe the generalization of spherical field theory to other modal expansion methods. The main approach remains the same, to reduce a d-dimensional field theory into a set of coupled one-dimensional systems. The method we discuss here uses an expansion with respect to periodic-box modes. We apply the method to phi^4 theory in two dimensions and compute the critical coupling and critical exponents. We compare with lattice results and predictions via universality and the two-dimensional Ising model.Comment: 12 pages, 4 figures, version to appear in Physics Letters

Twin Deficit Revisited: Evidence From India, Pakistan And Mexico

In recent years twin deficit has been a subject of investigation for several authors including Darrat (1988), Day (1998), Evans (1986).  In the decade of 1980s when US deficits behaved much like twins rather than distant cousins, there was a great interest in further research.  Several attempts have been made to explain the reasons of expected casuality between trade and budget deficits.  This paper attempts to test this casuality for trade and budget deficits for the annual data of India, Pakistan and Mexico

BPS Magnetic Monopole Bags

We explore the characteristics of spherical bags made of large numbers of BPS magnetic monopoles. There are two extreme limits. In the Abelian bag, $N$ zeros of the Higgs field are arranged in a quasiregular lattice on a sphere of radius $R_{\rm cr} \sim N/v$, where $v$ is the Higgs vacuum expectation value. The massive gauge fields of the theory are largely confined to a thin shell at this radius that separates an interior with almost vanishing magnetic and Higgs fields from an exterior region with long-range Coulomb magnetic and Higgs fields. In the other limiting case, which we term a non-Abelian bag, the $N$ zeros of the Higgs field are all the origin, but there is again a thin shell of radius $R_{\rm cr}$. In this case the region enclosed by this shell can be viewed as a large monopole core, with small Higgs field but nontrivial massive and massless gauge fields.Comment: 19 pages, 1 figur

Are All Static Black Hole Solutions Spherically Symmetric?

The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples demonstrating that static black holes need not be spherically symmetric exist in theories, such as the standard electroweak model, with electrically charged massive vector fields. In such theories, a magnetically charged Reissner-Nordstrom solution with sufficiently small horizon radius is unstable against the development of a nonzero vector field outside the horizon. General arguments show that, for generic values of the magnetic charge, this field cannot be spherically symmetric. Explicit construction of the solution shows that it in fact has no rotational symmetry at all.Comment: 6 pages, plain TeX. Submitted to GRF Essay Competitio