A lower bound to the spectral threshold in curved tubes

We consider the Laplacian in curved tubes of arbitrary cross-section rotating together with the Frenet frame along curves in Euclidean spaces of arbitrary dimension, subject to Dirichlet boundary conditions on the cylindrical surface and Neumann conditions at the ends of the tube. We prove that the spectral threshold of the Laplacian is estimated from below by the lowest eigenvalue of the Dirichlet Laplacian in a torus determined by the geometry of the tube.Comment: LaTeX, 13 pages; to appear in R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sc

On the behavior of clamped plates under large compression

We determine the asymptotic behavior of eigenvalues of clamped plates under large compression by relating this problem to eigenvalues of the Laplacian with Robin boundary conditions. Using the method of fundamental solutions, we then carry out a numerical study of the extremal domains for the first eigenvalue, from which we see that these depend on the value of the compression, and start developing a boundary structure as this parameter is increased. The corresponding number of nodal domains of the first eigenfunction of the extremal domain also increases with the compression.This work was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia(Portugal) through the program “Investigador FCT” with reference IF/00177/2013 and the projectExtremal spectral quantities and related problems(PTDC/MAT-CAL/4334/2014).info:eu-repo/semantics/publishedVersio

Extreme Value Theory for Piecewise Contracting Maps with Randomly Applied Stochastic Perturbations

We consider globally invertible and piecewise contracting maps in higher dimensions and we perturb them with a particular kind of noise introduced by Lasota and Mackey. We got random transformations which are given by a stationary process: in this framework we develop an extreme value theory for a few classes of observables and we show how to get the (usual) limiting distributions together with an extremal index depending on the strength of the noise.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1407.041

Phenomenology of the Little Higgs model with X-Parity

In the popular littlest Higgs model, T-parity can be broken by Wess-Zumino-Witten (WZW) terms induced by a strongly coupled UV completion. On the other hand, certain models with multiple scalar multiplets (called moose models) permit the implementation of an exchange symmetry (X-parity) such that it is not broken by the WZW terms. Here we present a concrete and realistic construction of such a model. The little Higgs model with X-Parity is a concrete and realistic implementation of this idea. In this contribution, the properties of the model are reviewed and the collider phenomenology is discussed in some detail. We also present new results on the decay properties and LHC signatures of the light triplet scalars that are predicted by this model.Comment: 12 pages, to appear in in the proceedings of the International Workshop on Beyond the Standard Model Physics and LHC Signatures (BSM-LHC) and of the 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY09), Boston, USA, 2-4 and 5-10 Jun 200

Strong evidences for a nonextensive behavior of the rotation period in Open Clusters

Time-dependent nonextensivity in a stellar astrophysical scenario combines nonextensive entropic indices $q_{K}$ derived from the modified Kawaler's parametrization, and $q$, obtained from rotational velocity distribution. These $q$'s are related through a heuristic single relation given by $q\approx q_{0}(1-\Delta t/q_{K})$, where $t$ is the cluster age. In a nonextensive scenario, these indices are quantities that measure the degree of nonextensivity present in the system. Recent studies reveal that the index $q$ is correlated to the formation rate of high-energy tails present in the distribution of rotation velocity. On the other hand, the index $q_{K}$ is determined by the stellar rotation-age relationship. This depends on the magnetic field configuration through the expression $q_{K}=1+4aN/3$, where $a$ and $N$ denote the saturation level of the star magnetic field and its topology, respectively. In the present study, we show that the connection $q-q_{K}$ is also consistent with 548 rotation period data for single main-sequence stars in 11 Open Clusters aged less than 1 Gyr. The value of $q_{K}\sim$ 2.5 from our unsaturated model shows that the mean magnetic field topology of these stars is slightly more complex than a purely radial field. Our results also suggest that stellar rotational braking behavior affects the degree of anti-correlation between $q$ and cluster age $t$. Finally, we suggest that stellar magnetic braking can be scaled by the entropic index $q$.Comment: 6 pages and 2 figures, accepted to EPL on October 17, 201

A Little Higgs Model with Exact Dark Matter Parity

Based on a recent idea by Krohn and Yavin, we construct a little Higgs model with an internal parity that is not broken by anomalous Wess-Zumino-Witten terms. The model is a modification of the "minimal moose" models by Arkani-Hamed et al. and Cheng and Low. The new parity prevents large corrections to oblique electroweak parameters and leads to a viable dark matter candidate. It is shown how the complete Standard Model particle content, including quarks and leptons together with their Yukawa couplings, can be implemented. Successful electroweak symmetry breaking and consistency with electroweak precision constraints is achieved for natural paramters choices. A rich spectrum of new particles is predicted at the TeV scale, some of which have sizable production cross sections and striking decay signatures at the LHC.Comment: 25 pp. LaTeX; v2: improved discussion of precision constraints and references added; v3: summary of model structure added at beginning of sect. 2, version published in JHEP; v4: small correction in Fig.5; v5: correction to Fig.

Consequences of T-parity breaking in the Littlest Higgs model

In this paper we consider the effects of the T-parity violating anomalous Wess-Zumino-Witten-Term in the Littlest Higgs model. Apart from tree level processes, the loop induced decays of the heavy mirror particles into light standard model fermions lead to a new and rich phenomenology in particular at breaking scales f below 1 TeV. Various processes are calculated and their signatures at present and future colliders are discussed. As a byproduct we find an alternative production mechanism for the Higgs boson.Comment: 30 page