1,208 research outputs found
Anomalous Scale Dimensions from Timelike Braiding
Using the previously gained insight about the particle/field relation in
conformal quantum field theories which required interactions to be related to
the existence of particle-like states associated with fields of anomalous
scaling dimensions, we set out to construct a classification theory for the
spectra of anomalous dimensions. Starting from the old observations on
conformal superselection sectors related to the anomalous dimensions via the
phases which appear in the spectral decomposition of the center of the
conformal covering group we explore the possibility
of a timelike braiding structure consistent with the timelike ordering which
refines and explains the central decomposition. We regard this as a preparatory
step in a new construction attempt of interacting conformal quantum field
theories in D=4 spacetime dimensions. Other ideas of constructions based on the
- or the perturbative SYM approach in their relation to the
present idea are briefly mentioned.Comment: completely revised, updated and shortened replacement, 24 pages
tcilatex, 3 latexcad figure
Most vital segment barriers
We study continuous analogues of "vitality" for discrete network flows/paths,
and consider problems related to placing segment barriers that have highest
impact on a flow/path in a polygonal domain. This extends the graph-theoretic
notion of "most vital arcs" for flows/paths to geometric environments. We give
hardness results and efficient algorithms for various versions of the problem,
(almost) completely separating hard and polynomially-solvable cases
Molecular dynamics simulations of complex shaped particles using Minkowski operators
The Minkowski operators (addition and substraction of sets in vectorial
spaces) has been extensively used for Computer Graphics and Image Processing to
represent complex shapes. Here we propose to apply those mathematical concepts
to extend the Molecular Dynamics (MD) Methods for simulations with
complex-shaped particles. A new concept of Voronoi-Minkowski diagrams is
introduced to generate random packings of complex-shaped particles with tunable
particle roundness. By extending the classical concept of Verlet list we
achieve numerical efficiencies that do not grow quadratically with the body
number of sides. Simulations of dissipative granular materials under shear
demonstrate that the method complies with the first law of thermodynamics for
energy balance.Comment: Submitted to Phys. Rev.
2D multi-objective placement algorithm for free-form components
This article presents a generic method to solve 2D multi-objective placement
problem for free-form components. The proposed method is a relaxed placement
technique combined with an hybrid algorithm based on a genetic algorithm and a
separation algorithm. The genetic algorithm is used as a global optimizer and
is in charge of efficiently exploring the search space. The separation
algorithm is used to legalize solutions proposed by the global optimizer, so
that placement constraints are satisfied. A test case illustrates the
application of the proposed method. Extensions for solving the 3D problem are
given at the end of the article.Comment: ASME 2009 International Design Engineering Technical Conferences &
Computers and Information in Engineering Conference, San Diego : United
States (2009
On the Power of Manifold Samples in Exploring Configuration Spaces and the Dimensionality of Narrow Passages
We extend our study of Motion Planning via Manifold Samples (MMS), a general
algorithmic framework that combines geometric methods for the exact and
complete analysis of low-dimensional configuration spaces with sampling-based
approaches that are appropriate for higher dimensions. The framework explores
the configuration space by taking samples that are entire low-dimensional
manifolds of the configuration space capturing its connectivity much better
than isolated point samples. The contributions of this paper are as follows:
(i) We present a recursive application of MMS in a six-dimensional
configuration space, enabling the coordination of two polygonal robots
translating and rotating amidst polygonal obstacles. In the adduced experiments
for the more demanding test cases MMS clearly outperforms PRM, with over
20-fold speedup in a coordination-tight setting. (ii) A probabilistic
completeness proof for the most prevalent case, namely MMS with samples that
are affine subspaces. (iii) A closer examination of the test cases reveals that
MMS has, in comparison to standard sampling-based algorithms, a significant
advantage in scenarios containing high-dimensional narrow passages. This
provokes a novel characterization of narrow passages which attempts to capture
their dimensionality, an attribute that had been (to a large extent) unattended
in previous definitions.Comment: 20 page
Two-dimensional models as testing ground for principles and concepts of local quantum physics
In the past two-dimensional models of QFT have served as theoretical
laboratories for testing new concepts under mathematically controllable
condition. In more recent times low-dimensional models (e.g. chiral models,
factorizing models) often have been treated by special recipes in a way which
sometimes led to a loss of unity of QFT. In the present work I try to
counteract this apartheid tendency by reviewing past results within the setting
of the general principles of QFT. To this I add two new ideas: (1) a modular
interpretation of the chiral model Diff(S)-covariance with a close connection
to the recently formulated local covariance principle for QFT in curved
spacetime and (2) a derivation of the chiral model temperature duality from a
suitable operator formulation of the angular Wick rotation (in analogy to the
Nelson-Symanzik duality in the Ostertwalder-Schrader setting) for rational
chiral theories. The SL(2,Z) modular Verlinde relation is a special case of
this thermal duality and (within the family of rational models) the matrix S
appearing in the thermal duality relation becomes identified with the
statistics character matrix S. The relevant angular Euclideanization'' is done
in the setting of the Tomita-Takesaki modular formalism of operator algebras.
I find it appropriate to dedicate this work to the memory of J. A. Swieca
with whom I shared the interest in two-dimensional models as a testing ground
for QFT for more than one decade.
This is a significantly extended version of an ``Encyclopedia of Mathematical
Physics'' contribution hep-th/0502125.Comment: 55 pages, removal of some typos in section
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