The Suyama-Yamaguchi consistency relation in the presence of vector fields

We consider inflationary models in which vector fields are responsible for part or eventually all of the primordial curvature perturbation \zeta. Such models are phenomenologically interesting since they naturally introduce anisotropies in the probability distribution function of the primordial fluctuations that can leave a measurable imprint in the cosmic microwave background. Assuming that non-Gaussianity is generated due to the superhorizon evolution, we use the \delta N formalism to do a complete tree level calculation of the non-Gaussianity parameters f_{NL} and \tau_{NL} in the presence of vector fields. We isolate the isotropic pieces of the non-Gaussianity parameters, which anyway have contributions from the vector fields, and show that they obey the Suyama-Yamaguchi consistency relation \tau^{iso}_{NL}>=(6/5f^{iso}_{NL})^2. Other ways of defining the non-Gaussianity parameters, which could be observationally relevant, are stated and the respective Suyama-Yamaguchi-like consistency relations are obtained.Comment: LaTeX file, 11 pages. v2: a few minor changes, references added and updated. v3: version to be published in Modern Physics Letters

Feynman-like Rules for Calculating n-Point Correlators of the Primordial Curvature Perturbation

A diagrammatic approach to calculate n-point correlators of the primordial curvature perturbation \zeta was developed a few years ago following the spirit of the Feynman rules in Quantum Field Theory. The methodology is very useful and time-saving, as it is for the case of the Feynman rules in the particle physics context, but, unfortunately, is not very well known by the cosmology community. In the present work, we extend such an approach in order to include not only scalar field perturbations as the generators of \zeta, but also vector field perturbations. The purpose is twofold: first, we would like the diagrammatic approach (which we would call the Feynman-like rules) to become widespread among the cosmology community; second, we intend to give an easy tool to formulate any correlator of \zeta for those cases that involve vector field perturbations and that, therefore, may generate prolonged stages of anisotropic expansion and/or important levels of statistical anisotropy. Indeed, the usual way of formulating such correlators, using the Wick's theorem, may become very clutter and time-consuming.Comment: LaTeX file, 26 pages. v2: A short discussion added regarding the role of the diagrams in high precision cosmology as well as in those cases where the loop contributions are larger than the tree level terms, generating large and observable levels of (anisotropic) non-gaussianity; references added, conclusions unchanged. v3: version to appear in Journal of Cosmology and Astroparticle Physic

The different varieties of the Suyama-Yamaguchi consistency relation and its violation as a signal of statistical inhomogeneity

We present the different consistency relations that can be seen as variations of the well known Suyama-Yamaguchi (SY) consistency relation \tau_{NL} \geqslant ((6/5) f_{NL})^2. It has been claimed that the following variation: \tau_{NL} ({\bf k}_1, {\bf k_3}) \geqslant (6/5)^2 f_{NL} ({\bf k}_1) f_{NL} ({\bf k}_3), which we call "the fourth variety", in the collapsed (for \tau_{NL}) and squeezed (for f_{NL}) limits is always satisfied independently of any physics; however, the proof depends sensitively on the assumption of scale-invariance which only applies for cosmological models involving Lorentz-invariant scalar fields (at least at tree level), leaving room for a strong violation of this variety of the consistency relation when non-trivial degrees of freedom, for instance vector fields, are in charge of the generation of \zeta. With this in mind as a motivation, we explicitly state under which conditions the SY consistency relation has been claimed to hold in its different varieties (implicitly) presented in the literature; as a result, we show for the first time that the variety \tau_{NL} ({\bf k}_1, {\bf k}_1) \geqslant ((6/5) f_{NL} ({\bf k}_1))^2, which we call "the fifth variety", is always satisfied even when there is strong scale-dependence as long as statistical homogeneity holds: thus, an observed violation of this specific variety would prevent the comparison between theory and observation, shaking this way the foundations of cosmology as a science. Later, we concern about the existence of non-trivial degrees of freedom, concretely vector fields for which the levels of non-gaussianity have been calculated for very few models, finding that the fourth variety of the SY consistency relation is indeed strongly violated for some specific wavevector configurations while the fifth variety continues to be well satisfied. (Abridged)Comment: LaTex file, 12 pages, 4 figures. v2: minor cosmetic changes, references added and updated, version to be published in Journal of Cosmology and Astroparticle Physic

Dental Treatment under General Anesthesia in Healthy and Medically Compromised/Developmentally Disabled Children: A Comparative Study

Aim: To compare the type, number of procedures and working time of dental treatment provided under dental general anesthesia (DGA) in healthy and medically compromised/developmentally disabled children (MCDD children). Design: This cross-sectional prospective study involved 80 children divided into two groups of 40 children each. Group 1 consisted of healthy and Group 2 consisted of MCDD children. Results: Healthy children needed more working time than MCDD children, the means being 161±7.9 and 84±5.7 minutes, respectively (P= 0.0001). Operative dentistry and endodontic treatments showed a significant statistical difference (P= 0.0001). The means of procedures were 17±5.0 for healthy children and 11±4.8 for MCDD children (P= 0.0001). Conclusions: Healthy children needed more extensive dental treatment than MCDD children under DGA. The information from this sample of Mexican children could be used as reference for determining trends both within a facility as well as in comparing facilities in cross-population studies

Analytical results for a Bessel function times Legendre polynomials class integrals

When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make unnecessary numerical quadrature techniques or localized approximations. The solution is presented using the properties of the Bessel and associated Legendre functions.Comment: 4 page

Modulated model predictive control with optimized overmodulation

Finite Set Model Predictive Control (FS-MPC) has many advantages, such as a fast dynamic response and an intuitive implementation. For these reasons, it has been thoroughly researched during the last decade. However, the wave form produced by FS-MPC has a switching component whose spread spectrum remains a major disadvantage of the strategy. This paper discusses a modulated model predictive control that guarantees a spectrum switching frequency in the linear modulation range and extends its optimized response to the overmodulation region. Due to the equivalent high gain of the predictive control, and to the limit on the voltage actuation of the power converter, it is expected that the actuation voltage will enter the overmodulation region during large reference changes or in response to load impacts. An optimized overmodulation strategy that converges towards FS-MPC’s response for large tracking errors is proposed for this situation. This technique seamlessly combines PWM’s good steadystate switching performance with FS-MPC’s high dynamic response during large transients. The constant switching frequency is achieved by incorporating modulation of the predicted current vectors in the model predictive control of the currents in a similar fashion as conventional Space-Vector Pulse Width Modulation (SV-PWM) is used to synthesize an arbitrary voltage reference. Experimental results showing the proposed strategy’s good steady-state switching performance, its FS-MPC-like transient response and the seamless transition between modes of operation are presented for a permanent magnet synchronous machine drive

Polymer brush collapse under shear flow

Shear responsive surfaces offer potential advances in a number of applications. Surface functionalisation using polymer brushes is one route to such properties, particularly in the case of entangled polymers. We report on neutron reflectometry measurements of polymer brushes in entangled polymer solutions performed under controlled shear, as well as coarse-grained computer simulations corresponding to these interfaces. Here we show a reversible and reproducible collapse of the brushes, increasing with the shear rate. Using two brushes of greatly different chain lengths and grafting densities, we demonstrate that the dynamics responsible for the structural change of the brush are governed by the free chains in solution rather than the brush itself, within the range of parameters examined. The phenomenon of the brush collapse could find applications in the tailoring of nanosensors, and as a way to dynamically control surface friction and adhesion