342 research outputs found
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
Traversals of Infinite Graphs with Random Local Orientations
We introduce the notion of a "random basic walk" on an infinite graph, give
numerous examples, list potential applications, and provide detailed
comparisons between the random basic walk and existing generalizations of
simple random walks. We define analogues in the setting of random basic walks
of the notions of recurrence and transience in the theory of simple random
walks, and we study the question of which graphs have a cycling random basic
walk and which a transient random basic walk.
We prove that cycles of arbitrary length are possible in any regular graph,
but that they are unlikely. We give upper bounds on the expected number of
vertices a random basic walk will visit on the infinite graphs studied and on
their finite analogues of sufficiently large size. We then study random basic
walks on complete graphs, and prove that the class of complete graphs has
random basic walks asymptotically visit a constant fraction of the nodes. We
end with numerous conjectures and problems for future study, as well as ideas
for how to approach these problems.Comment: This is my masters thesis from Wesleyan University. Currently my
advisor and I are selecting a journal where we will submit a shorter version.
We plan to split this work into two papers: one for the case of infinite
graphs and one for the finite case (which is not fully treated here
Circle Graph Obstructions
In this thesis we present a self-contained proof of Bouchet’s characterization of the class of circle graphs. The proof uses signed graphs and is analogous to Gerards’ graphic proof of Tutte’s excluded-minor characterization of the class of graphic matroids
A variational approach for viewpoint-based visibility maximization
We present a variational method for unfolding of the cortex based on a user-chosen point of view as an alternative to more traditional global flattening methods, which incur more distortion around the region of interest. Our approach involves three novel contributions. The first is an energy function and its corresponding gradient flow to measure the average visibility of a region of interest of a surface from a given viewpoint. The second is an additional energy function and flow designed to preserve the 3D topology of the evolving surface. This latter contribution receives significant focus in this thesis as it is crucial to obtain the desired unfolding effect derived from the first energy functional and flow. Without it, the resulting topology changes render the unconstrained evolution uninteresting for the purpose of cortical visualization, exploration, and inspection. The third is a method that dramatically improves the computational speed of the 3D topology-preservation approach by creating a tree structure of the triangulated surface and using a recursion technique.Ph.D.Committee Chair: Allen R. Tannenbaum; Committee Member: Anthony J. Yezzi; Committee Member: Gregory Turk; Committee Member: Joel R. Jackson; Committee Member: Patricio A. Vel
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Modèles particulaires turbulents pur suivre les surfaces libres
Two numerical particle models, the Smoothed Particle Hydrodynamics (SPH) and Moving Particle Semi-implicit (MPS) methods, coupled with a
sub-particle scale (SPS) turbulence model, are presented to simulate free surface flows. Both SPH and MPS methods have the advantages in that
the governing Navier¿Stokes equations are solved by Lagrangian approach and no grid is needed in the computation. Thus the free surface can be
easily and accurately tracked by particles without numerical diffusion. In this paper different particle interaction models for SPH and MPS methods
are summarized and compared. The robustness of two models is validated through experimental data of a dam-break flow. In addition, a series of
numerical runs are carried out to investigate the order of convergence of the models with regard to the time step and particle spacing. Finally the
efficiency of the incorporated SPS model is further demonstrated by the computed turbulence patterns from a breaking wave. It is shown that both
SPH and MPS models provide a useful tool for simulating free surface flows
Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization
International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM
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