Asymptotic approximation of eigenvalues of vector equations

A vectorial extension of the Keller-Rubinow method of computing asymptotic approximations of eigenvalues in bounded domains is presented. The method is applied to the problem of a multimode step-profile cylindrical optical fibre, including the effects of polarisation. A comparison of the asymptotic results with the exact eigenvalues is made when these are available, and the agreement is shown to be good

Decorous lower bounds for minimum linear arrangement

Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this paper, we propose a linear-programming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances

Higgs couplings and new signals from Flavon-Higgs mixing effects within multi-scalar models

Testing the properties of the Higgs particle discovered at the LHC and searching for new physics signals, are some of the most important tasks of Particle Physics today. Current measurements of the Higgs couplings to fermions and gauge bosons, seem consistent with the Standard Model, and when taken as a function of the particle mass, should lay on a single line. However, in models with an extended Higgs sector the diagonal Higgs couplings to up-quarks, down-quarks and charged leptons, could lay on different lines, while non-diagonal flavor-violating Higgs couplings could appear too. We describe these possibilities within the context of multi-Higgs doublet models that employ the Froggatt-Nielsen (FN) mechanism to generate the Yukawa hierarchies. Furthermore, one of the doublets can be chosen to be of the inert type, which provides a viable dark matter candidate. The mixing of the Higgs doublets with the flavon field, can provide plenty of interesting signals, including: i) small corrections to the couplings of the SM-like Higgs, ii) exotic signals from the flavon fields, iii) new signatures from the heavy Higgs bosons. These aspects are studied within a specific model with 3+1 Higgs doublets and a singlet FN field. Constraints on the model are derived from the study of K and D mixing and the Higgs search at the LHC. For last, the implications from the latter aforementioned constraints to the FCNC top decay $t\to ch$ are presented too.Comment: 10 pages, 3 figures and 2 tables; v2: author added, text improved; v3: Title and Abstract slightly changed, 19 pages, references, tables and images added, additional clarifications; matches version published by Nucl. Phys.

A 3D Printed Toolbox for Opto-Mechanical Components

Nowadays is very common to find headlines in the media where it is stated that 3D printing is a technology called to change our lives in the near future. For many authors, we are living in times of a third industrial revolution. Howerver, we are currently in a stage of development where the use of 3D printing is advantageous over other manufacturing technologies only in rare scenarios. Fortunately, scientific research is one of them. Here we present the development of a set of opto-mechanical components that can be built easily using a 3D printer based on Fused Filament Fabrication (FFF) and parts that can be found on any hardware store. The components of the set presented here are highly customizable, low-cost, require a short time to be fabricated and offer a performance that compares favorably with respect to low-end commercial alternatives.Comment: 9 pages, 9 figure

Texture zeros and hierarchical masses from flavour (mis)alignment

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrization of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.Comment: 27 pages; v2 matches version accepted by NPB, discussion on Dirac CP phase for neutrinos adde