1,228 research outputs found
Groupoid Extensions of Mapping Class Representations for Bordered Surfaces
The mapping class group of a surface with one boundary component admits
numerous interesting representations including as a group of automorphisms of a
free group and as a group of symplectic transformations. Insofar as the mapping
class group can be identified with the fundamental group of Riemann's moduli
space, it is furthermore identified with a subgroup of the fundamental path
groupoid upon choosing a basepoint. A combinatorial model for this, the mapping
class groupoid, arises from the invariant cell decomposition of Teichm\"uller
space, whose fundamental path groupoid is called the Ptolemy groupoid. It is
natural to try to extend representations of the mapping class group to the
mapping class groupoid, i.e., construct a homomorphism from the mapping class
groupoid to the same target that extends the given representations arising from
various choices of basepoint.
Among others, we extend both aforementioned representations to the groupoid
level in this sense, where the symplectic representation is lifted both
rationally and integrally. The techniques of proof include several algorithms
involving fatgraphs and chord diagrams. The former extension is given by
explicit formulae depending upon six essential cases, and the kernel and image
of the groupoid representation are computed. Furthermore, this provides
groupoid extensions of any representation of the mapping class group that
factors through its action on the fundamental group of the surface including,
for instance, the Magnus representation and representations on the moduli
spaces of flat connections.Comment: 24 pages, 4 figures Theorem 3.6 has been strengthened, and Theorems
8.1 and 8.2 have been adde
Thermal roughening of {001} surfaces
Within the framework of a solid-on-solid model that incorporates nearest- (epsilon) and next-nearest-neighbor (delta) interactions we have determined the free energy of the high-symmetry steps on a (001) surface of a cubic crystal. We have found a simple expression that allows one to determine the thermal roughening temperature TR of a (001) surface (2e¿(epsilon/2+delta)/kbTR¿e¿(epsilon+2delta)/kbTR+2e¿(epsilon+delta)/kbTR=1). In a more refined analysis we have explicitly included step-edge overhangs. This results in a slightly lower thermal roughening temperature. Our results are also applicable to the two-dimensional Ising spin system
Finite type invariants and fatgraphs
We define an invariant of pairs M,G, where M is a 3-manifold
obtained by surgery on some framed link in the cylinder , S is a
connected surface with at least one boundary component, and G is a fatgraph
spine of S. In effect, is the composition with the maps of
Le-Murakami-Ohtsuki of the link invariant of Andersen-Mattes-Reshetikhin
computed relative to choices determined by the fatgraph G; this provides a
basic connection between 2d geometry and 3d quantum topology. For each fixed G,
this invariant is shown to be universal for homology cylinders, i.e.,
establishes an isomorphism from an appropriate vector space
of homology cylinders to a certain algebra of Jacobi diagrams. Via
composition for any pair of fatgraph spines
G,G' of S, we derive a representation of the Ptolemy groupoid, i.e., the
combinatorial model for the fundamental path groupoid of Teichmuller space, as
a group of automorphisms of this algebra. The space comes equipped
with a geometrically natural product induced by stacking cylinders on top of
one another and furthermore supports related operations which arise by gluing a
homology handlebody to one end of a cylinder or to another homology handlebody.
We compute how interacts with all three operations explicitly in
terms of natural products on Jacobi diagrams and certain diagrammatic
constants. Our main result gives an explicit extension of the LMO invariant of
3-manifolds to the Ptolemy groupoid in terms of these operations, and this
groupoid extension nearly fits the paradigm of a TQFT. We finally re-derive the
Morita-Penner cocycle representing the first Johnson homomorphism using a
variant/generalization of .Comment: 39 page
Comparison of performance of concussed and non-concussed individuals on Subtest VIII of the C-RTT
The purpose of this study was to investigate auditory comprehension in concussed and non-concussed individuals using Subtest VIII of the C-RTT. Thirty non-concussed individuals were matched as closely as possible on gender, age, education and history of concussion to a group of concussed individuals. A Mann-Whitney found that the two samples were significant different at p = .020, and a t-test found a significant difference at p = .008 on the Efficiency Score (ES) of Subtest VIII. The non-concussed individuals performed better than the concussed individuals. Efficiency Score may be useful in assessing comprehension in concussed individuals
Surface bubble nucleation phase space
Recent research has revealed several different techniques for nanoscopic gas
nucleation on submerged surfaces, with findings seemingly in contradiction with
each other. In response to this, we have systematically investigated the
occurrence of surface nanobubbles on a hydrophobised silicon substrate for
various different liquid temperatures and gas concentrations, which we
controlled independently. We found that nanobubbles occupy a distinct region of
this phase space, occurring for gas concentrations of approximately 100-110%.
Below the nanobubble phase we did not detect any gaseous formations on the
substrate, whereas micropancakes (micron wide, nanometer high gaseous domains)
were found at higher temperatures and gas concentrations. We moreover find that
supersaturation of dissolved gases is not a requirement for nucleation of
bubbles.Comment: 4 pages, 4 figure
Phase diagram of the random field Ising model on the Bethe lattice
The phase diagram of the random field Ising model on the Bethe lattice with a
symmetric dichotomous random field is closely investigated with respect to the
transition between the ferromagnetic and paramagnetic regime. Refining
arguments of Bleher, Ruiz and Zagrebnov [J. Stat. Phys. 93, 33 (1998)] an exact
upper bound for the existence of a unique paramagnetic phase is found which
considerably improves the earlier results. Several numerical estimates of
transition lines between a ferromagnetic and a paramagnetic regime are
presented. The obtained results do not coincide with a lower bound for the
onset of ferromagnetism proposed by Bruinsma [Phys. Rev. B 30, 289 (1984)]. If
the latter one proves correct this would hint to a region of coexistence of
stable ferromagnetic phases and a stable paramagnetic phase.Comment: Article has been condensed and reorganized; Figs 3,5,6 merged; Fig 4
omitted; Some discussion added at end of Sec. III; 9 pages, 5 figs, RevTeX4,
AMSTe
A two-qubit Bell inequality for which POVM measurements are relevant
A bipartite Bell inequality is derived which is maximally violated on the
two-qubit state space if measurements describable by positive operator valued
measure (POVM) elements are allowed rather than restricting the possible
measurements to projective ones. In particular, the presented Bell inequality
requires POVMs in order to be maximally violated by a maximally entangled
two-qubit state. This answers a question raised by N. Gisin.Comment: 7 pages, 1 figur
Stationary Properties of a Randomly Driven Ising Ferromagnet
We consider the behavior of an Ising ferromagnet obeying the Glauber dynamics
under the influence of a fast switching, random external field. Analytic
results for the stationary state are presented in mean-field approximation,
exhibiting a novel type of first order phase transition related to dynamic
freezing. Monte Carlo simulations performed on a quadratic lattice indicate
that many features of the mean field theory may survive the presence of
fluctuations.Comment: 5 pages in RevTex format, 7 eps/ps figures, send comments to
"mailto:[email protected]", submitted to PR
Vacancy-mediated diffusion of Co atoms embedded in Cu(001)
The diffusion of Co atoms in the Cu(001) surface has been studied using Scanning Tunneling Microscopy (STM). Like other impurities in the Cu(001) surface, the diffusion of Co is mediated by single surface vacancies. STM images reveal that diffusion of the embedded atoms takes place through multi-atom jumps separated by long time intervals, which is characteristic for this type of diffusion. The jump length and frequency are measured to establish the nature of the interaction between surface vacancies and the embedded Co atoms and to extract the relevant formation and diffusion energies
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