Reconstruction of α\alpha-attractor supergravity models of inflation

In this paper, we apply reconstruction techniques to recover the potential parameters for a particular class of single-field models, the $\alpha$-attractor (supergravity) models of inflation. This also allows to derive the inflaton vacuum expectation value at horizon crossing. We show how to use this value as one of the input variables to constrain the postaccelerated inflationary phase. We assume that the tensor-to-scalar ratio $r$ is of the order of $10^{-3}$ , a level reachable by the expected sensitivity of the next-generation CMB experiments.Comment: 10 pages, LaTeX, some typos correcte

Constraining auto-interaction terms in α-attractor supergravity models of inflation

The inflationary mechanism has become the paradigm of modern cosmology over the last thirty years. However, there are several aspects of inflationary physics that are still to be addressed, like the shape of the inflationary potential. Regarding this, the so-called α-attractor models show interesting properties. In this work, the reconstruction of the effective potential around the global minimum of these particular potentials is provided, assuming a detection of permille-order for the tensor-to-scalar-ratio by forthcoming cosmic microwave background or gravitational waves experiments

Lot-sizing with stock upper bounds and fixed charges

Here we study the discrete lot-sizing problem with an initial stock variable and an associated variable upper bound constraint. This problem is of interest in its own right, and is also a natural relaxation of the constant capacity lot-sizing problem with upper bounds and fixed charges on the stock variables. We show that the convex hull of solutions of the discrete lot-sizing problem is obtained as the intersection of two simpler sets, one involving just 0-1 variables and the second a mixing set with a variable upper bound constraint. For these two sets we derive both inequality descriptions and polynomial-size extended formulations of their respective convex hulls. Finally we carry out some limited computational tests on single-item constant capacity lot-sizing problems with upper bounds and fixed charges on the stock variables in which we use the extended formulations derived above to strengthen the initial mixed integer programming formulations.mixed integer programming, discrete lot-sizing, stock fixed costs, mixing sets

Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D

We prove the equivalence between the notion of Wasserstein gradient flow for a one-dimensional nonlocal transport PDE with attractive/repulsive Newtonian potential on one side, and the notion of entropy solution of a Burgers-type scalar conservation law on the other. The solution of the former is obtained by spatially differentiating the solution of the latter. The proof uses an intermediate step, namely the $L^2$ gradient flow of the pseudo-inverse distribution function of the gradient flow solution. We use this equivalence to provide a rigorous particle-system approximation to the Wasserstein gradient flow, avoiding the regularization effect due to the singularity in the repulsive kernel. The abstract particle method relies on the so-called wave-front-tracking algorithm for scalar conservation laws. Finally, we provide a characterization of the sub-differential of the functional involved in the Wasserstein gradient flow

Slow-roll Inflation for Generalized Two-Field Lagrangians

We study the slow-roll regime of two field inflation, in which the two fields are also coupled through their kinetic terms. Such Lagrangians are motivated by particle physics and by scalar-tensor theories studied in the Einstein frame. We compute the power spectra of adiabatic and isocurvature perturbations on large scales to first order in the slow-roll parameters. We discuss the relevance of the extra coupling terms for the amplitude and indexes of the power spectra. Beyond the consistency condition which involves the amplitude of gravitational waves, additional relations may be found in particular models based on such Lagrangians: as an example, we find an additional general consistency condition in implicit form for Brans-Dicke theory in the Einstein frame.Comment: 17 pages, 1 figure, accepted for publication in Phys. Rev.

Condensation phenomena in nonlinear drift equations

We study nonnegative, measure-valued solutions to nonlinear drift type equations modelling concentration phenomena related to Bose-Einstein particles. In one spatial dimension, we prove existence and uniqueness for measure solutions. Moreover, we prove that all solutions blow up in finite time leading to a concentration of mass only at the origin, and the concentrated mass absorbs increasingly the mass converging to the total mass as time goes to infinity. Our analysis makes a substantial use of independent variable scalings and pseudo-inverse functions techniques

Microscopic electronic configurations after ultrafast magnetization dynamics

We provide a model for the prediction of the electronic and magnetic configurations of ferromagnetic Fe after an ultrafast decrease or increase of magnetization. The model is based on the well-grounded assumption that, after the ultrafast magnetization change, the system achieves a partial thermal equilibrium. With statistical arguments it is possible to show that the magnetic configurations are qualitatively different in the case of reduced or increased magnetization. The predicted magnetic configurations are then used to compute the dielectric response at the 3p (M) absorption edge, which can be related to the changes observed in the experimental T-MOKE data. The good qualitative agreement between theory and experiment offers a substantial support to the existence of an ultrafast increase of magnetisation, which has been fiercely debated in the last years.Comment: Main text 10 pages including 7 figures. Supplemental material 5 pages including 1 figur

Rotational sensitivity of the "G-Pisa" gyrolaser

G-Pisa is an experiment investigating the possibility to operate a high sensitivity laser gyroscope with area less than $1 \rm m^2$ for improving the performances of the mirrors suspensions of the gravitational wave antenna Virgo. The experimental set-up consists in a He-Ne ring laser with a 4 mirrors square cavity. The laser is pumped by an RF discharge where the RF oscillator includes the laser plasma in order to reach a better stability. The contrast of the Sagnac fringes is typically above 50% and a stable regime has been reached with the laser operating both single mode or multimode. The effect of hydrogen contamination on the laser was also checked. A low-frequency sensitivity, below $1 \rm Hz$, in the range of $10^{-8} \rm {(rad / s)/ \sqrt{Hz}}$ has been measured.Comment: 6 pages, 6 figures, presented at the EFTF-IFCS joint conference 200