6,566 research outputs found
Combed 3-Manifolds with Concave Boundary, Framed Links, and Pseudo-Legendrian Links
We provide combinatorial realizations, according to the usual objects/moves
scheme, of the following three topological categories: (1) pairs (M,v) where M
is a 3-manifold (up to diffeomorphism) and v is a (non-singular vector) field,
up to homotopy; here possibly the boundary of M is non-empty and v may be
tangent to the boundary, but only in a concave fashion, and homotopy should
preserve tangency type; (2) framed links L in M, up to framed isotopy; (3)
triples (M,v,L), with (M,v) as above and L transversal to v, up to
pseudo-Legendrian isotopy (transversality-preserving simultaneous homotopy of v
and isotopy of L). All realizations are based on the notion of branched
standard spine, and build on results previously obtained. Links are encoded by
means of diagrams on branched spines, where the diagram is smooth with respect
to the branching. Several motivations for being interested in combinatorial
realizations of the topological categories considered in this paper are given
in the introduction. The encoding of links is suitable for the comparison of
the framed and the pseudo-Legendrian categories, and some applications are
given in connection with contact structures, torsion and finite-order
invariants. An estension of Trace's notion of winding number of a knot diagram
is introduced and discussed.Comment: 38 pages, 33 figure
Volume and homology of one-cusped hyperbolic 3-manifolds
Let M be a complete, finite-volume, orientable hyperbolic manifold having
exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a
genus-2 surface group, and that either (a) H_1(M;Z_p) has dimension at least 5
for some prime p, or (b) H_1(M;Z_2) has dimension at least 4, and the subspace
of H^2(M;Z_2) spanned by the image of the cup product has dimension at most 1,
then vol M > 5.06 If we assume that H_1(M;Z_2) has dimension at least 7, and
that the compact core of M does not contain a genus-2 closed incompressible
surface, then vol M > 5.06.Comment: 31 pages. This version agrees with the published version of the
paper, except that an error in the published abstract has been corrected. In
particular, the result which applies to manifolds with mod 2 homology of
dimension at least 7 is stronger and has a shorter proof than the
corresponding result in version
Real-time monitoring of proton exchange membrane fuel cell stack failure
Uneven pressure drops in a 75-cell 9.5-kWe proton exchange membrane fuel cell stack with a U-shaped flow configuration have been shown to cause localised flooding. Condensed water then leads to localised cell heating, resulting in reduced membrane durability. Upon purging of the anode manifold, the resulting mechanical strain on the membrane can lead to the formation of a pin-hole/membrane crack and a rapid decrease in open circuit voltage due to gas crossover. This failure has the potential to cascade to neighbouring cells due to the bipolar plate coupling and the current density heterogeneities arising from the pin-hole/membrane crack. Reintroduction of hydrogen after failure results in cell voltage loss propagating from the pin-hole/membrane crack location due to reactant crossover from the anode to the cathode, given that the anode pressure is higher than the cathode pressure. Through these observations, it is recommended that purging is avoided when the onset of flooding is observed to prevent irreparable damage to the stack
Combinatorial Hopf algebra of superclass functions of type
We provide a Hopf algebra structure on the space of superclass functions on
the unipotent upper triangular group of type D over a finite field based on a
supercharacter theory constructed by Andr\'e and Neto. Also, we make further
comments with respect to types B and C. Type A was explores by M. Aguiar et. al
(2010), thus this paper is a contribution to understand combinatorially the
supercharacter theory of the other classical Lie types.Comment: Last section modified. Recent development added and correction with
respect to previous version state
Spectral geometry as a probe of quantum spacetime
Employing standard results from spectral geometry, we provide strong evidence
that in the classical limit the ground state of three-dimensional causal
dynamical triangulations is de Sitter spacetime. This result is obtained by
measuring the expectation value of the spectral dimension on the ensemble of
geometries defined by these models, and comparing its large scale behaviour to
that of a sphere (Euclidean de Sitter). From the same measurement we are also
able to confirm the phenomenon of dynamical dimensional reduction observed in
this and other approaches to quantum gravity -- the first time this has been
done for three-dimensional causal dynamical triangulations. In this case, the
value for the short-scale limit of the spectral dimension that we find is
approximately 2. We comment on the relevance of these results for the
comparison to asymptotic safety and Horava-Lifshitz gravity, among other
approaches to quantum gravity.Comment: 25 pages, 6 figures. Version 2: references to figures added,
acknowledgment added
Existence for Competitive Equilibrium by Means of Generalized Quasivariational Inequalities
A competitive economic equilibrium model integrated with exchange, consumption, and production is considered. Our goal is to give an existence result when the utility functions are concave, proper, and upper semicontinuous. To this aim we are able to characterize the equilibrium by means of a suitable generalized quasi-variational inequality; then we give the existence of equilibrium by using the variational approach
Cosmological measurements, time and observables in (2+1)-dimensional gravity
We investigate the relation between measurements and the physical observables
for vacuum spacetimes with compact spatial surfaces in (2+1)-gravity with
vanishing cosmological constant. By considering an observer who emits lightrays
that return to him at a later time, we obtain explicit expressions for several
measurable quantities as functions on the physical phase space of the theory:
the eigentime elapsed between the emission of a lightray and its return to the
observer, the angles between the directions into which the light has to be
emitted to return to the observer and the relative frequencies of the lightrays
at their emission and return. This provides a framework in which conceptual
questions about time, observables and measurements can be addressed. We analyse
the properties of these measurements and their geometrical interpretation and
show how they allow an observer to determine the values of the Wilson loop
observables that parametrise the physical phase space of (2+1)-gravity. We
discuss the role of time in the theory and demonstrate that the specification
of an observer with respect to the spacetime's geometry amounts to a gauge
fixing procedure yielding Dirac observables.Comment: 38 pages, 11 eps figures, typos corrected, references update
Construction, Management and Visualization of 3D Models of Large Archeological and Architectural Sites for E-Heritage GIS Systems
In this paper we present an integrated system developed in order to record, construct, pre-process, manage,
visualize and visually navigate 3D models reality based of large archeological and architectural sites for
eHeritage GIS systems. The framework integrates structured geometrical and documentary information
resulting from multiple sources with the aim to enhance the knowledge of those sites within the frame of its
historical evolution and its institutional management in a 3D GIS/DB. The developed applications were
designed for different types of users, with a largely scalable interface, able to support different output
devices and to work at different levels of iconicity. The system allows a full comprehension of the buildings
in their own context, permitting to discover unknown relationships, to evaluate their architectural occupancy
and to quickly access a complex system of information. The framework has been tested in two different
systems - designed and developed to satisfy both internal (cataloguing, documentation, preservation,
management of archaeological heritage) and external (communication through the web portal) purposes:
the first, in Pompeii, developed in order to have a web-based system that uses Open Source software and
complies with national and international standards; the second one, a prototype designed to make available
on the Google Earth platform the complete Palladian corpus documentation implemented by the CISAAP
Laser-heater assisted plasma channel formation in capillary discharge waveguides
A method of creating plasma channels with controllable depth and transverse
profile for the guiding of short, high power laser pulses for efficient
electron acceleration is proposed. The plasma channel produced by the
hydrogen-filled capillary discharge waveguide is modified by a ns-scale laser
pulse, which heats the electrons near the capillary axis. This interaction
creates a deeper plasma channel within the capillary discharge that evolves on
a ns-time scale, allowing laser beams with smaller spot sizes than would
otherwise be possible in the unmodified capillary discharge.Comment: 5 pages, 3 figure
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