Resilience of the standard predictions for primordial tensor modes

We show that the prediction for the primordial tensor power spectrum cannot be modified at leading order in derivatives. Indeed, one can always set to unity the speed of propagation of gravitational waves during inflation by a suitable disformal transformation of the metric, while a conformal one can make the Planck mass time-independent. Therefore, the tensor amplitude unambiguously fixes the energy scale of inflation. Using the Effective Field Theory of Inflation, we check that predictions are independent of the choice of frame, as expected. The first corrections to the standard prediction come from two parity violating operators with three derivatives. Also the correlator $$ is standard and only receives higher derivative corrections. These results hold also in multifield models of inflation and in alternatives to inflation and make the connection between a (quasi) scale-invariant tensor spectrum and inflation completely robust.Comment: 5 pages, reference added, version accepted in PR

Scattering for nonlinear Schrodinger equation under partial harmonic confinement

We consider the nonlinear Schrodinger equation under a partial quadratic confinement. We show that the global dispersion corresponding to the direction(s) with no potential is enough to prove global in time Strichartz estimates, from which we infer the existence of wave operators thanks to suitable vector-fields. Conversely, given an initial Cauchy datum, the solution is global in time and asymptotically free, provided that confinement affects one spatial direction only. This stems from anisotropic Morawetz estimates, involving a marginal of the position density.Comment: 26 pages. Some typos fixed, especially in Section

Analytical approximations to the spectra of quark-antiquark potentials

A method, recently devised to obtain analytical approximations to certain classes of integrals, is used in combination with the WKB expansion to derive accurate analytical expressions for the spectrum of quantum potentials. The accuracy of our results is verified by comparing them both with the literature on the subject and with the numerical results obtained with a Fortran code. As an application of the method that we propose, we consider the meson spectroscopy with various phenomenological potentials.Comment: 12 pages, 4 figures, 1 tabl

Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy

We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy. It allows us to define a matrix Harry Dym hierarchy of commuting Hamiltonian flows in two fields that projects onto the scalar Harry Dym hierarchy. We also show that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.Comment: Revised version, 22 pages; a section on reciprocal transformations added. To appear in J. Math. Phys

Exploring educational mobility in Europe

This paper is concerned with the investigation of the intergenerational mobility of education in several European countries and its changes across birth cohorts (1940-1980) using a new mobility index that considers the total degree of mobility as the weighted sum of mobility with respect to both parents. Moreover, this mobility index enables the analysis of the role of family characteristics as mediating factors in the statistical association between individual and parental education. We find that Nordic countries display lower levels of educational persistence but that the degree of mobility increases over time only in those countries with low initial levels. Moreover, the results suggest that the degree of mobility with respect to fathers and mothers converges to the same level and that family characteristics account for an important part of the statistical association between parental education and children’s schooling; a particular finding is that the most important elements of family characteristics are the family’s socio-economic status and educational assortative mating of the parents.Educational Economics, Intergenerational Mobility, Europe, Birth Cohorts, Family

Multi-physics phenomena influencing the performance of the car horn

Usually cars are equipped with disk horns. In these devices electromagnetic energy is converted into mechanical energy of two nuclei that vibrate and impact each other \u2013 the impacts excite the disk that radiates sound. This paper aims at understanding the results of acoustic tests carried out on horns with different excitation voltages and different mounting brackets. Since many non-linear phenomena are inherent in the vibrations of the nuclei, a detailed model of the electromechanical system is developed. Results show the dependence of operating frequency on the input voltage and the role played by the various mechanical and electrical parameters on the dynamics of the horn. Particular nonlinear effects, like sub-harmonic excitation, are presented and discussed. A general agreement between experimental results and numerical simulations is found

Spherical collapse in quintessence models with zero speed of sound

We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshift.Comment: 38 pages; small changes, including modification of the window function. JCAP published versio