877 research outputs found
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 ). 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 . 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
âItâs like my life but more, and better!â - Playing with the Cathaby Shark Girls: MMORPGs, young people and fantasy-based social play
This article is available open access through the publisherâs 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 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
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