Sanitation in the Hatchery

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Entropy of Open Lattice Systems

We investigate the behavior of the Gibbs-Shannon entropy of the stationary nonequilibrium measure describing a one-dimensional lattice gas, of L sites, with symmetric exclusion dynamics and in contact with particle reservoirs at different densities. In the hydrodynamic scaling limit, L to infinity, the leading order (O(L)) behavior of this entropy has been shown by Bahadoran to be that of a product measure corresponding to strict local equilibrium; we compute the first correction, which is O(1). The computation uses a formal expansion of the entropy in terms of truncated correlation functions; for this system the k-th such correlation is shown to be O(L^{-k+1}). This entropy correction depends only on the scaled truncated pair correlation, which describes the covariance of the density field. It coincides, in the large L limit, with the corresponding correction obtained from a Gaussian measure with the same covariance.Comment: Latex, 28 pages, 4 figures as eps file

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

Strategies for btagging calibration using collider data at CMS

The CMS Collaboration is studying several algorithms to identify jets coming from the hadronization of bottom quarks (b-jets) which are present in a wide range of physics processes of interests such as in the decay of top quarks, Higgs bosons and several non-Standard Model particles. All of these b-tagging algorithms rely upon the reconstruction of lower level objects like tracks, vertices, and jets, which might make it difficult for the Monte Carlo simulation to exactly reproduce the performance observed in data. Reliable methods to measure performance of these algorithms directly from collider data have been developed. The CMS b-tagging group is working on several strategies which should yield reliable results already with $10\;\rm{pb}^{-1}$ of integrated luminosity