A crossing probability for critical percolation in two dimensions

Langlands et al. considered two crossing probabilities, pi_h and pi_{hv}, in their extensive numerical investigations of critical percolation in two dimensions. Cardy was able to find the exact form of pi_h by treating it as a correlation function of boundary operators in the Q goes to 1 limit of the Q state Potts model. We extend his results to find an analogous formula for pi_{hv} which compares very well with the numerical results.Comment: 8 pages, Latex2e, 1 figure, uuencoded compressed tar file, (1 typo changed

The development and application of time resolved PIV at the University of Strathclyde

This paper describes the development of time resolved particle image velocimetry (PIV) within the Department of Mechanical Engineering at the University of Strathclyde. The Department's first PIV systems were developed on a limited budget and used existing and second hand equipment. The original technique which, employed 16mm high speed cinematography, is described. The introduction and development of low cost systems employing high speed digital video (HSDV) is discussed and, finally, the Department's new time resolved PIV system, supplied by Dantec Dynamics, is introduced. For each of the PIV systems that have been developed a critical analysis of their functionality is given and samples of the data that they have been produced are shown. Data are presented from systems such as de-rotated centrifugal impellers, air bubbles growing in columns of water, pulsatile jets and vortex shedding

On Artin's L-Functions

Paper by R. P. Langland

Boundary states for a free boson defined on finite geometries

Langlands recently constructed a map that factorizes the partition function of a free boson on a cylinder with boundary condition given by two arbitrary functions in the form of a scalar product of boundary states. We rewrite these boundary states in a compact form, getting rid of technical assumptions necessary in his construction. This simpler form allows us to show explicitly that the map between boundary conditions and states commutes with conformal transformations preserving the boundary and the reality condition on the scalar field.Comment: 16 pages, LaTeX (uses AMS components). Revised version; an analogy with string theory computations is discussed and references adde

On elliptic factors in real endoscopic transfer I

This paper is concerned with the structure of packets of representations and some refinements that are helpful in endoscopic transfer for real groups. It includes results on the structure and transfer of packets of limits of discrete series representations. It also reinterprets the Adams-Johnson transfer of certain nontempered representations via spectral analogues of the Langlands-Shelstad factors, thereby providing structure and transfer compatible with the associated transfer of orbital integrals. The results come from two simple tools introduced here. The first concerns a family of splittings of the algebraic group G under consideration; such a splitting is based on a fundamental maximal torus of G rather than a maximally split maximal torus. The second concerns a family of Levi groups attached to the dual data of a Langlands or an Arthur parameter for the group G. The introduced splittings provide explicit realizations of these Levi groups. The tools also apply to maps on stable conjugacy classes associated with the transfer of orbital integrals. In particular, they allow for a simpler version of the definitions of Kottwitz-Shelstad for twisted endoscopic transfer in certain critical cases. The paper prepares for spectral factors in twisted endoscopic transfer that are compatible in a certain sense with the standard factors discussed here. This compatibility is needed for Arthur's global theory. The twisted factors themselves will be defined in a separate paper.Comment: 48 pages, to appear in Progress in Mathematics, Volume 312, Birkha\"user. Also renumbering to match that of submitted versio

The Tails of the Crossing Probability

The scaling of the tails of the probability of a system to percolate only in the horizontal direction $\pi_{hs}$ was investigated numerically for correlated site-bond percolation model for $q=1,2,3,4$.We have to demonstrate that the tails of the crossing probability far from the critical point have shape $\pi_{hs}(p) \simeq D \exp(c L[p-p_{c}]^{\nu})$ where $\nu$ is the correlation length index, $p=1-\exp(-\beta)$ is the probability of a bond to be closed. At criticality we observe crossover to another scaling $\pi_{hs}(p) \simeq A \exp (-b {L [p-p_{c}]^{\nu}}^{z})$. Here $z$ is a scaling index describing the central part of the crossing probability.Comment: 20 pages, 7 figures, v3:one fitting procedure is changed, grammatical change

Illustrating phallic worship: uses of material objects and the production of sexual knowledge in eighteenth-century antiquarianism and early twentieth-century sexual science

This is the final version of the article. Available from Taylor & Francis via the DOI in this record.This article reveals previously overlooked connections between eighteenth-century antiquarianism and early twentieth-century sexual science by presenting a comparative reading of two illustrated books: An Account of the Remains of the Worship of Priapus, by British antiquarian scholar Richard Payne Knight (1750–1824), and Die Weltreise eines Sexualforschers (The World Journey of a Sexologist), by German sexual scientist Magnus Hirschfeld (1868–1935). A close analysis of these publications demonstrates the special status of material artefacts and the strategic engagement with visual evidence in antiquarian and scientific writings about sex. Through its exploration of the similarities between antiquarian and sexual scientific thought, the article demonstrates the centrality of material culture to the production of sexual knowledge in the Western world. It also opens up new perspectives on Western intellectual history and on the intellectual origins of sexual science. While previous scholarship has traced the beginnings of sexual science back to nineteenth-century medical disciplines, this article shows that sexual scientists drew upon different forms of evidence and varied methodologies to produce sexual knowledge and secure scientific authority. As such, sexual science needs to be understood as a field with diverse intellectual roots that can be traced back (at least) to the eighteenth century.All authors gratefully acknowledge financial support from the Wellcome Trust [grant numbers NC110388, 106654/Z/14/Z and 106653/Z/14/Z]

Critical Percolation in Finite Geometries

The methods of conformal field theory are used to compute the crossing probabilities between segments of the boundary of a compact two-dimensional region at the percolation threshold. These probabilities are shown to be invariant not only under changes of scale, but also under mappings of the region which are conformal in the interior and continuous on the boundary. This is a larger invariance than that expected for generic critical systems. Specific predictions are presented for the crossing probability between opposite sides of a rectangle, and are compared with recent numerical work. The agreement is excellent.Comment: 10 page

Mesoscopic description of reactions under anomalous diffusion: A case study

Reaction-diffusion equations deliver a versatile tool for the description of reactions in inhomogeneous systems under the assumption that the characteristic reaction scales and the scales of the inhomogeneities in the reactant concentrations separate. In the present work we discuss the possibilities of a generalization of reaction-diffusion equations to the case of anomalous diffusion described by continuous-time random walks with decoupled step length and waiting time probability densities, the first being Gaussian or Levy, the second one being an exponential or a power-law lacking the first moment. We consider a special case of an irreversible or reversible A ->B conversion and show that only in the Markovian case of an exponential waiting time distribution the diffusion- and the reaction-term can be decoupled. In all other cases, the properties of the reaction affect the transport operator, so that the form of the corresponding reaction-anomalous diffusion equations does not closely follow the form of the usual reaction-diffusion equations