3,334 research outputs found
Higher categories, colimits, and the blob complex
We summarize our axioms for higher categories, and describe the blob complex.
Fixing an n-category C, the blob complex associates a chain complex B_*(W;C)$
to any n-manifold W. The 0-th homology of this chain complex recovers the usual
topological quantum field theory invariants of W. The higher homology groups
should be viewed as generalizations of Hochschild homology (indeed, when W=S^1
they coincide). The blob complex has a very natural definition in terms of
homotopy colimits along decompositions of the manifold W. We outline the
important properties of the blob complex, and sketch the proof of a
generalization of Deligne's conjecture on Hochschild cohomology and the little
discs operad to higher dimensions.Comment: 7 page
The centre of the extended Haagerup subfactor has 22 simple objects
We explain a technique for discovering the number of simple objects in
, the center of a fusion category , as well as the combinatorial data
of the induction and restriction functors at the level of Grothendieck rings.
The only input is the fusion ring and the dimension function .
The method is not guaranteed to succeed (it may give spurious answers besides
the correct one, or it may simply take too much computer time), but it seems it
often does. We illustrate by showing that there are 22 simple objects in the
center of the extended Haagerup subfactor [arXiv:0909.4099].Comment: 10 page
Tilted Interferometry Realizes Universal Quantum Computation in the Ising TQFT without Overpasses
We show how a universal gate set for topological quantum computation in the
Ising TQFT, the non-Abelian sector of the putative effective field theory of
the fractional quantum Hall state, can be implemented. This
implementation does not require overpasses or surgery, unlike the construction
of Bravyi and Kitaev, which we take as a starting point. However, it requires
measurements of the topological charge around time-like loops encircling moving
quasiaparticles, which require the ability to perform `tilted' interferometry
measurements.Comment: This manuscript has substantial overlap with cond-mat/0512066 which
contains more physics and less emphasis on the topology. The present
manuscript is posted as a possibly useful companion to the forme
Fermion condensation and super pivotal categories
We study fermionic topological phases using the technique of fermion
condensation. We give a prescription for performing fermion condensation in
bosonic topological phases which contain a fermion. Our approach to fermion
condensation can roughly be understood as coupling the parent bosonic
topological phase to a phase of physical fermions, and condensing pairs of
physical and emergent fermions. There are two distinct types of objects in
fermionic theories, which we call "m-type" and "q-type" particles. The
endomorphism algebras of q-type particles are complex Clifford algebras, and
they have no analogues in bosonic theories. We construct a fermionic
generalization of the tube category, which allows us to compute the
quasiparticle excitations in fermionic topological phases. We then prove a
series of results relating data in condensed theories to data in their parent
theories; for example, if is a modular tensor category containing
a fermion, then the tube category of the condensed theory satisfies
.
We also study how modular transformations, fusion rules, and coherence
relations are modified in the fermionic setting, prove a fermionic version of
the Verlinde dimension formula, construct a commuting projector lattice
Hamiltonian for fermionic theories, and write down a fermionic version of the
Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted
to three detailed examples of performing fermion condensation to produce
fermionic topological phases: we condense fermions in the Ising theory, the
theory, and the theory, and compute the
quasiparticle excitation spectrum in each of these examples.Comment: 161 pages; v2: corrected typos (including 18 instances of "the the")
and added some reference
Constitutive modeling of superalloy single crystals with verification testing
The goal is the development of constitutive equations to describe the elevated temperature stress-strain behavior of single crystal turbine blade alloys. The program includes both the development of a suitable model and verification of the model through elevated temperature-torsion testing. A constitutive model is derived from postulated constitutive behavior on individual crystallographic slip systems. The behavior of the entire single crystal is then arrived at by summing up the slip on all the operative crystallographic slip systems. This type of formulation has a number of important advantages, including the prediction orientation dependence and the ability to directly represent the constitutive behavior in terms which metallurgists use in describing the micromechanisms. Here, the model is briefly described, followed by the experimental set-up and some experimental findings to date
Exponential integration algorithms applied to viscoplasticity
Four, linear, exponential, integration algorithms (two implicit, one explicit, and one predictor/corrector) are applied to a viscoplastic model to assess their capabilities. Viscoplasticity comprises a system of coupled, nonlinear, stiff, first order, ordinary differential equations which are a challenge to integrate by any means. Two of the algorithms (the predictor/corrector and one of the implicits) give outstanding results, even for very large time steps
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