Singular limit of Hele-Shaw flow and dispersive regularization of shock waves

We study a family of solutions to the Saffman-Taylor problem with zero surface tension at a critical regime. In this regime, the interface develops a thin singular finger. The flow of an isolated finger is given by the Whitham equations for the KdV integrable hierarchy. We show that the flow describing bubble break-off is identical to the Gurevich-Pitaevsky solution for regularization of shock waves in dispersive media. The method provides a scheme for the continuation of the flow through singularites.Comment: Some typos corrected, added journal referenc

Quantum Hall transitions: An exact theory based on conformal restriction

We revisit the problem of the plateau transition in the integer quantum Hall effect. Here we develop an analytical approach for this transition, based on the theory of conformal restriction. This is a mathematical theory that was recently developed within the context of the Schramm-Loewner evolution which describes the stochastic geometry of fractal curves and other stochastic geometrical fractal objects in 2D space. Observables elucidating the connection with the plateau transition include the so-called point-contact conductances (PCCs) between points on the boundary of the sample, described within the language of the Chalker-Coddington network model. We show that the disorder-averaged PCCs are characterized by classical probabilities for certain geometric objects in the plane (pictures), occurring with positive statistical weights, that satisfy the crucial restriction property with respect to changes in the shape of the sample with absorbing boundaries. Upon combining this restriction property with the expected conformal invariance at the transition point, we employ the mathematical theory of conformal restriction measures to relate the disorder-averaged PCCs to correlation functions of primary operators in a conformal field theory (of central charge $c=0$). We show how this can be used to calculate these functions in a number of geometries with various boundary conditions. Since our results employ only the conformal restriction property, they are equally applicable to a number of other critical disordered electronic systems in 2D. For most of these systems, we also predict exact values of critical exponents related to the spatial behavior of various disorder-averaged PCCs.Comment: Published versio

Viscous fingering and a shape of an electronic droplet in the Quantum Hall regime

We show that the semiclassical dynamics of an electronic droplet confined in the plane in a quantizing inhomogeneous magnetic field in the regime when the electrostatic interaction is negligible is similar to viscous (Saffman-Taylor) fingering on the interface between two fluids with different viscosities confined in a Hele-Shaw cell. Both phenomena are described by the same equations with scales differing by a factor of up to $10^{-9}$. We also report the quasiclassical wave function of the droplet in an inhomogeneous magnetic field.Comment: 4 pages, 1 eps figure include

Extended Seiberg-Witten Theory and Integrable Hierarchy

The prepotential of the effective N=2 super-Yang-Mills theory perturbed in the ultraviolet by the descendents of the single-trace chiral operators is shown to be a particular tau-function of the quasiclassical Toda hierarchy. In the case of noncommutative U(1) theory (or U(N) theory with 2N-2 fundamental hypermultiplets at the appropriate locus of the moduli space of vacua) or a theory on a single fractional D3 brane at the ADE singularity the hierarchy is the dispersionless Toda chain. We present its explicit solutions. Our results generalize the limit shape analysis of Logan-Schepp and Vershik-Kerov, support the prior work hep-th/0302191 which established the equivalence of these N=2 theories with the topological A string on CP^1 and clarify the origin of the Eguchi-Yang matrix integral. In the higher rank case we find an appropriate variant of the quasiclassical tau-function, show how the Seiberg-Witten curve is deformed by Toda flows, and fix the contact term ambiguity.Comment: 49 page

“It’s like my life but more, and better!” - Playing with the Cathaby Shark Girls: MMORPGs, young people and fantasy-based social play

This article is available open access through the publisher’s website at the link below. Copyright @ 2011 A B Academic Publishers.Digital technology has opened up a range of new on-line leisure spaces for young people. Despite their popularity, on-line games and Massive Multiplayer Online Role Playing Games in particular are still a comparatively under-researched area in the fields of both Education and more broadly Youth Studies. Drawing on a Five year ethnographic study, this paper considers the ways that young people use the virtual spaces offered by MMORPGs. This paper suggests that MMORPGs represent significant arenas within which young people act out a range of social narratives through gaming. It argues that MMORPG have become important fantasy spaces which offer young people possibilities to engage in what were formally material practices. Although this form of play is grounded in the everyday it also extends material practices and offers new and unique forms of symbolic experimentation, thus I argue that game-play narratives cannot be divorced from the everyday lives of their participants

Generic critical points of normal matrix ensembles

The evolution of the degenerate complex curve associated with the ensemble at a generic critical point is related to the finite time singularities of Laplacian Growth. It is shown that the scaling behavior at a critical point of singular geometry $x^3 \sim y^2$ is described by the first Painlev\'e transcendent. The regularization of the curve resulting from discretization is discussed.Comment: Based on a talk given at the conference on Random Matrices, Random Processes and Integrable Systems, CRM Montreal, June 200

The use of a ward's history in training psychiatric child care workers

The importance of the contribution of historical-cultural factors to an inpatient treatment setting's contemporaneous psycho-social climate has been given little attention in published discussions of ward staff problems and training. This report illustrates some ways in which such historical-cultural forces, embodied in social myths and entrenched traditions, operate. Examples are provided from a ward of disturbed adolescents, where young child care workers struggled as a group with the daily stresses of providing therapeutic milieu support to children ambivalently seeking and resisting external controls for their feelings and impulses. The process of incorporating the analysis of historical-cultural factors in an inservice training program is described.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/44275/1/10566_2005_Article_BF01642066.pd