Shift Equivalence of Measures and the Intrinsic Structure of Shocks in the Asymmetric Simple Exclusion Process

We investigate properties of non-translation-invariant measures, describing particle systems on \bbz, which are asymptotic to different translation invariant measures on the left and on the right. Often the structure of the transition region can only be observed from a point of view which is random---in particular, configuration dependent. Two such measures will be called shift equivalent if they differ only by the choice of such a viewpoint. We introduce certain quantities, called translation sums, which, under some auxiliary conditions, characterize the equivalence classes. Our prime example is the asymmetric simple exclusion process, for which the measures in question describe the microscopic structure of shocks. In this case we compute explicitly the translation sums and find that shocks generated in different ways---in particular, via initial conditions in an infinite system or by boundary conditions in a finite system---are described by shift equivalent measures. We show also that when the shock in the infinite system is observed from the location of a second class particle, treating this particle either as a first class particle or as an empty site leads to shift equivalent shock measures.Comment: Plain TeX, 2 figures; [email protected], [email protected], [email protected], [email protected]

Liouville Vortex And φ4\varphi^{4} Kink Solutions Of The Seiberg--Witten Equations

The Seiberg--Witten equations, when dimensionally reduced to \bf R^{2}\mit, naturally yield the Liouville equation, whose solutions are parametrized by an arbitrary analytic function $g(z)$. The magnetic flux $\Phi$ is the integral of a singular Kaehler form involving $g(z)$; for an appropriate choice of $g(z)$ , $N$ coaxial or separated vortex configurations with $\Phi=\frac{2\pi N}{e}$ are obtained when the integral is regularized. The regularized connection in the \bf R^{1}\mit case coincides with the kink solution of $\varphi^{4}$ theory.Comment: 14 pages, Late

Exact solutions for a mean-field Abelian sandpile

We introduce a model for a sandpile, with N sites, critical height N and each site connected to every other site. It is thus a mean-field model in the spin-glass sense. We find an exact solution for the steady state probability distribution of avalanche sizes, and discuss its asymptotics for large N.Comment: 10 pages, LaTe

Unfinished Business: a Review of the Implementation of the Provisions of United Nations General Assembly Resolutions 61/105 and 64/72, Related to the Management of Bottom Fisheries in Areas Beyond National Jurisdiction

In 2006 the General Assembly adopted resolution 61/105, based on a compromise proposal offered by deep-sea fishing nations, which committed States and regional fisheries management organisations [RFMOs] to take specific measures to protect vulnerable marine ecosystems [VMEs] from the adverse impacts of bottom fisheries in the high seas and to ensure the longterm sustainability of deep-sea fish stocks. These measures included conducting impact assessments to determine whether significant adverse impacts[SAIs] to VMEs would occur, managing fisheries to prevent SAIs on VMEs, and closing areas of the high seas to bottom fishing where VMEs are known or likely to occur, unless regulations are in place to prevent SAIs and to manage sustainably deep-sea fish stocks. Based on a review in 2009 of the actions taken by States and RFMOS, the UNGA adoptedresolution 64/72 that reaffirmed resolution 61/105 and strengthened the call for action through committing States, inter alia, to ensure that vessels do not engage in bottom fishing until impact assessments have been carried out and to not authorise bottom fishing activities until the measures in resolutions 64/72 and 61/105 have been adopted andimplemented

Research Notes : Australia : Designation of a core collection of perennial Glycine

Over the last decade, a large germplasm collection of the 12 currently recognized perennial species of Glycine has been assembled. This collection, now numbering more than 1400 accessions, is held in Canberra, Australia, and is recognized by the International Board of Plant Genetic Resources as the world base collection for perennial Glycine. The 12 species include five that have been described recently