Massive higher spin fields coupled to a scalar: Aspects of interaction and causality

We consider in detail the most general cubic Lagrangian which describes an interaction between two identical higher spin fields in a triplet formulation with a scalar field, all fields having the same values of the mass. After performing the gauge fixing procedure we find that for the case of massive fields the gauge invariance does not guarantee the preservation of the correct number of propagating physical degrees of freedom. In order to get the correct number of degrees of freedom for the massive higher spin field one should impose some additional conditions on parameters of the vertex. Further independent constraints are provided by the causality analysis, indicating that the requirement of causality should be imposed in addition to the requirement of gauge invariance in order to have a consistent propagation of massive higher spin fields.     

A novel string-derived $Z^\prime$ with stable proton,light neutrinos and R-parity violation

The standard model indicates the realization of grand unified structures in nature, and it can only be viewed as an effective theory below a higher energy cutoff. While the renormalizable standard model forbids proton decay mediating operators due to accidental global symmetries, many extensions of the standard model introduce such dimension 4, 5 and 6 operators. Furthermore, quantum gravity effects are expected to induce proton instability, indicating that the higher energy cutoff scale must be above 10¹⁶ GeV. Quasi-realistic heterotic string models provide the arena to explore how perturbative quantum gravity affects the particle physics phenomenology. An appealing explanation for the proton longevity is provided by the existence of an Abelian gauge symmetry that suppresses the proton decay mediating operators. Additionally, such a low scale U(1) symmetry should feature the following: it should allow for the suppression of the left-handed neutrino masses by a seesaw mechanism; allow for fermion Yukawa couplings to the electroweak Higgs doublets; be anomaly free; and finally be family universal. These requirements render the existence of such U(1) symmetries in quasi-realistic heterotic string models highly non-trivial. We demonstrate the existence of a U(1) symmetry that satisfies all of the above requirements in a class of left–right symmetric heterotic string models in the free fermionic formulation. The existence of the extra in the energy range accessible to future experiments is motivated by the requirement of adequate suppression of proton decay mediation. We further show that, while the extra U(1) forbids dimension 4 baryon number violating operators, it allows dimension 4 lepton number violating operators and R-parity violation.     

Investigation of quasi-realistic heterotic string models with reduced Higgs spectrum

Quasi-realistic heterotic-string models in the free fermionic formulation typically contain an anomalous U(1) that leads to supersymmetry breaking. Supersymmetry is restored by imposing F- and D-flatness on the vacuum. A three generation free fermionic standard-like model which did not admit stringent F- and D-flat directions has been presented (Cleaver et al. in Phys. Rev. D 78, 046009, 2008) and it was argued that all the moduli in that model were fixed. The particular property of that model was the reduction of the untwisted Higgs spectrum by a combination of symmetric and asymmetric internal dimension boundary conditions with respect to the internal fermions associated with the compactified dimensions. This reduction occurred without the need or presence of flat directions. In this paper we extend the analysis of free fermionic models with reduced Higgs spectrum to models with the same internal space but with modified gauge groups: SO(10) or flipped SU(5) subgroup. We show that all the models studied in this paper do admit stringent flat directions. Currently, the only examples of models that do not admit stringent flat directions are the standard-like models of Cleaver et al. (Phys. Rev. D 78, 046009, 2008). We comment on the relationship between flat directions and reduced Higgs in free fermionic models as well as the possible connection between moduli stabilization and model phenomenology.     

Classification of heterotic Pati–Salam models

We extend the classification of free fermionic heterotic-string models to vacua in which the SO(10)$\mathit{SO}(10)$ GUT symmetry is broken at the string level to the Pati–Salam subgroup. Using our classification method we recently presented the first example of a quasi-realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the Generalised GSO (GGSO) projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of models that we classify is ²⁵¹∼¹⁰¹⁵$2^{51}\sim {10}^{15}$. We perform a statistical sampling in this space of models and extract 10¹¹ GGSO configurations with Pati–Salam gauge group. Our results demonstrate that one in every 10⁶ vacua correspond to a three generation exophobic model with the required Higgs states, needed to induce spontaneous breaking to the Standard Model.     

Mapping the Stability Diagram of a Quadrupole Mass Spectrometer with a Static Transverse Magnetic Field Applied

Previous experimental and theoretical work identified that the application of a static magnetic (B) field can improve the resolution of a quadrupole mass spectrometer (QMS) and this simple method of performance enhancement offers advantages for field deployment. Presented here are further data showing the effect of the transverse magnetic field upon the QMS performance. For the first time, the asymmetry in QMS operation with B _x and B _y is considered and explained in terms of operation in the fourth quadrant of the stability diagram. The results may be explained by considering the additional Lorentz force (v x B) experienced by the ion trajectories in each case. Using our numerical approach, we model not only the individual ion trajectories for a transverse B field applied in x and y but also the mass spectra and the effect of the magnetic field upon the stability diagram. Our theoretical findings, confirmed by experiment, show an improvement in resolution and ion transmission by application of magnetic field for certain operating conditions.

Absence of wandering domains for some real entire functions with bounded singular sets

Let $f$ be a real entire function whose set $S(f)$ of singular values is real and bounded. We show that, if $f$ satisfies a certain function-theoretic condition (the “sector condition”), then $f$ has no wandering domains. Our result includes all maps of the form $z\mapsto \lambda \frac{\sinh (z)}{z} + a$ with $\lambda >0$ and $a\in \mathbb{R }$ . We also show the absence of wandering domains for certain non-real entire functions for which $S(f)$ is bounded and $f^n|_{S(f)}\rightarrow \infty $ uniformly. As a special case of our theorem, we give a short, elementary and non-technical proof that the Julia set of the exponential map $f(z)=e^z$ is the entire complex plane. Furthermore, we apply similar methods to extend a result of Bergweiler, concerning Baker domains of entire functions and their relation to the postsingular set, to the case of meromorphic functions.     

Transition wave in a supported heavy beam

We consider a heavy, uniform, elastic beam rested on periodically distributed supports as a simplified model of a bridge. The supports are subjected to a partial destruction propagating as a failure wave along the beam. Three related models are examined and compared: (a) a uniform elastic beam on a distributed elastic foundation, (b) an elastic beam in which the mass is concentrated at a discrete set of points corresponding to the discrete set of the elastic supports and (c) a uniform elastic beam on a set of discrete elastic supports. Stiffness of the support is assumed to drop when the stress reaches a critical value. In the formulation, it is also assumed that, at the moment of the support damage, the value of the ‘added mass’, which reflects the dynamic response of the support, is dropped too. Strong similarities in the behavior of the continuous and discrete-continuous models are detected. Three speed regimes, subsonic, intersonic and supersonic, where the failure wave is or is not accompanied by elastic waves excited by the moving jump in the support stiffness, are considered and related characteristic speeds are determined. With respect to these continuous and discrete-continuous models, the conditions are found for the failure wave to exist, to propagate uniformly or to accelerate. It is also found that such beam-related transition wave can propagate steadily only at the intersonic speeds. It is remarkable that the steady-state speed appears to decrease as the jump of the stiffness increases.     

Iterative solver approach for turbine interactions: application to wind or marine current turbine farms

This paper presents a numerical investigation for the computation of wind or marine current turbines in a farm. A 3D unsteady Lagrangian vortex method is used together with a panel method in order to take into account for the turbines. In order to enforce the boundary condition onto the panel elements, a linear matrix system is defined. Solving general linear matrix systems is a topic with important scientific literature. But the main concern here is the application to a dedicated matrix which is non-sparse, non-symmetric, neither diagonally dominant nor positive-definite. Several iterative approaches were tested and compared. But after some numerical tests, a Bi-CGSTAB method was finally chosen. The main advantage of the presented method is the use of a specific preconditioner well suited for the desired application. The chosen implementation proved to be very efficient with only 3 iterations of our preconditioned Bi-CGSTAB algorithm whatever the turbine geometrical configuration. Although developed for wind or marine turbines, the proposed algorithm is absolutely not restricted to these cases, and can be applied to many others. At the end of the paper, some applications (specifically, wake computations) in a farm are presented, along with a quantitative assessment of the computational time savings brought by the iterative approach.     

The distribution of age-of-information performance measures for message processing systems

Queueing Systems - The idea behind the recently introduced “age-of-information” performance measure of a network message processing system is that it indicates our knowledge regarding...