Decomposition of 3-connected cubic graphs

AbstractWe solve a conjecture of Foulds and Robinson (1979) on decomposable triangulations in the plane, in the more general context of a decomposition theory of cubic 3-connected graphs. The decomposition gives us a natural way to obtain some known results about specific homeomorphic subgraphs and the extremal diameter of 3-connected cubic graphs

Deligne-Beilinson cohomology and abelian link invariants: torsion case

For the abelian Chern-Simons field theory, we consider the quantum functional integration over the Deligne-Beilinson cohomology classes and present an explicit path-integral non-perturbative computation of the Chern-Simons link invariants in $SO(3)\simeq\mathbb{R}P^3$, a toy example of 3-manifold with torsion

The Non-Homologous Nature of Solar Diameter Variations

We show in this paper that the changes of the solar diameter in response to variations of large scale magnetic fields and turbulence are not homologous. For the best current model, the variation at the photospheric level is over 1000 times larger than the variation at a depth of 5 Mm, which is about the level at which f-mode solar oscillations determine diameter variations. This model is supported by observations that indicate larger diameter changes for high degree f-modes than for low degree f-modes, since energy of the former are concentrated at shallower layers than the latter.Comment: 11 pages, 3 figures, aastex style, accepted for publication by ApJ

Three-manifold invariant from functional integration

We give a precise definition and produce a path-integral computation of the normalized partition function of the abelian U(1) Chern-Simons field theory defined in a general closed oriented 3-manifold. We use the Deligne-Beilinson formalism, we sum over the inequivalent U(1) principal bundles over the manifold and, for each bundle, we integrate over the gauge orbits of the associated connection 1- forms. The result of the functional integration is compared with the abelian U(1) Reshetikhin-Turaev surgery invariant

Abelian BF theory and Turaev-Viro invariant

The U(1) BF Quantum Field Theory is revisited in the light of Deligne-Beilinson Cohomology. We show how the U(1) Chern-Simons partition function is related to the BF one and how the latter on its turn coincides with an abelian Turaev-Viro invariant. Significant differences compared to the non-abelian case are highlighted.Comment: 47 pages and 6 figure

On P_4-tidy graphs

We study the P_4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P_4-domination in perfect graphs. This class strictly contains the P_4-extendible graphs and the P_4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P_4-tidy graphs and P_4-lite graphs are closely related. Note that the class of P_4-lite graphs is a class of brittle graphs strictly containing the P_4-sparse graphs defined by Hoang in [14]. McConnel & Spinrad [2] and independently Cournier & Habib [5] have shown that the modular decomposition tree of any graph is computable in linear time. For recognizing in linear time P_4-tidy graphs, we apply a method introduced by Giakoumakis in [9] and Giakoumakis & Fouquet in [6] using modular decomposition of graphs and we propose linear algorithms for optimization problems on such graphs, as clique number, stability number, chromatic number and scattering number. We show that the Hamiltonian Path Problem is linear for this class of graphs. Our study unifies and generalizes previous results of Jamison & Olariu ([18], [21], [22]), Hochstattler & Schindler[16], Jung [25] and Hochstattler & Tinhofer [15]

Symmetries and observables in topological gravity

After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between different approaches to topological gravity. Though the main focus of our work is on the vielbein formalism, we also discuss the metric approach and its relationship with the former formalism.Comment: 34 pages; a few explanations added in subsection 2.2.1, published version of pape

The acceleration and storage of radioactive ions for a neutrino factory

The term beta-beam has been coined for the production of a pure beam of electron neutrinos or their antiparticles through the decay of radioactive ions circulating in a storage ring. This concept requires radioactive ions to be accelerated to a Lorentz gamma of 150 for 6He and 60 for 18Ne. The neutrino source itself consists of a storage ring for this energy range, with long straight sections in line with the experiment(s). Such a decay ring does not exist at CERN today, nor does a high-intensity proton source for the production of the radioactive ions. Nevertheless, the existing CERN accelerator infrastructure could be used as this would still represent an important saving for a beta-beam facility. This paper outlines the first study, while some of the more speculative ideas will need further investigations.Comment: Accepted for publication in proceedings of Nufact02, London, 200

A Class of Topological Actions

We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be extended to situations involving distributions as is appropriate in the context of quantized fields.Comment: 41 pages, no figure

Stellar jitter from variable gravitational redshift: implications for RV confirmation of habitable exoplanets

A variation of gravitational redshift, arising from stellar radius fluctuations, will introduce astrophysical noise into radial velocity measurements by shifting the centroid of the observed spectral lines. Shifting the centroid does not necessarily introduce line asymmetries. This is fundamentally different from other types of stellar jitter so far identified, which do result from line asymmetries. Furthermore, only a very small change in stellar radius, ~0.01%, is necessary to generate a gravitational redshift variation large enough to mask or mimic an Earth-twin. We explore possible mechanisms for stellar radius fluctuations in low-mass stars. Convective inhibition due to varying magnetic field strengths and the Wilson depression of starspots are both found to induce substantial gravitational redshift variations. Finally, we investigate a possible method for monitoring/correcting this newly identified potential source of jitter and comment on its impact for future exoplanet searches.Comment: 6 pages, 1 figure, 1 tabl