NLS ground states on graphs

We investigate the existence of ground states for the subcritical NLS energy on metric graphs. In particular, we find out a topological assumption that guarantees the nonexistence of ground states, and give an example in which the assumption is not fulfilled and ground states actually exist. In order to obtain the result, we introduce a new rearrangement technique, adapted to the graph where it applies. Owing to such a technique, the energy level of the rearranged function is improved by conveniently mixing the symmetric and monotone rearrangement procedures.Comment: 24 pages, 4 figure

Dissecting the high-z interstellar medium through intensity mapping cross-correlations

We explore the detection, with upcoming spectroscopic surveys, of three-dimensional power spectra of emission line fluctuations produced in different phases of the Interstellar Medium (ISM) by ionized carbon, ionized nitrogen and neutral oxygen at redshift z>4. The emission line [CII] from ionized carbon at 157.7 micron, and multiple emission lines from carbon monoxide, are the main targets of planned ground-based surveys, and an important foreground for future space-based surveys like the Primordial Inflation Explorer (PIXIE). However, the oxygen [OI] (145.5 micron) line, and the nitrogen [NII] (121.9 micron and 205.2 micron) lines, might be detected in correlation with [CII] with reasonable signal-to-noise ratio (SNR). These lines are important coolants of both the neutral and the ionized medium, and probe multiple phases of the ISM. We compute predictions of the three-dimensional power spectra for two surveys designed to target the [CII] line, showing that they have the required sensitivity to detect cross-power spectra with the [OI] line, and the [NII] lines with sufficient SNR. The importance of cross-correlating multiple lines is twofold. On the one hand, we will have multiple probes of the different phases of the ISM, which is key to understand the interplay between energetic sources, the gas and dust at high redshift. This kind of studies will be useful for a next-generation space observatory such as the NASA Far-IR Surveyor. On the other end, emission lines from external galaxies are an important foreground when measuring spectral distortions of the Cosmic Microwave Background spectrum with future space-based experiments like PIXIE; measuring fluctuations in the intensity mapping regime will help constraining the mean amplitude of these lines, and will allow us to better handle this important foreground.Comment: 13 pages, 2 table, 7 figures, Accepted for publication in Ap

Nonlinear dynamics on branched structures and networks

Nonlinear dynamics on graphs has rapidly become a topical issue with many physical applications, ranging from nonlinear optics to Bose-Einstein condensation. Whenever in a physical experiment a ramified structure is involved, it can prove useful to approximate such a structure by a metric graph, or network. For the Schroedinger equation it turns out that the sixth power in the nonlinear term of the energy is critical in the sense that below that power the constrained energy is lower bounded irrespectively of the value of the mass (subcritical case). On the other hand, if the nonlinearity power equals six, then the lower boundedness depends on the value of the mass: below a critical mass, the constrained energy is lower bounded, beyond it, it is not. For powers larger than six the constrained energy functional is never lower bounded, so that it is meaningless to speak about ground states (supercritical case). These results are the same as in the case of the nonlinear Schrodinger equation on the real line. In fact, as regards the existence of ground states, the results for systems on graphs differ, in general, from the ones for systems on the line even in the subcritical case: in the latter case, whenever the constrained energy is lower bounded there always exist ground states (the solitons, whose shape is explicitly known), whereas for graphs the existence of a ground state is not guaranteed. For the critical case, our results show a phenomenology much richer than the analogous on the line.Comment: 47 pages, 44 figure. Lecture notes for a course given at the Summer School "MMKT 2016, Methods and Models of Kinetic Theory, Porto Ercole, June 5-11, 2016. To be published in Riv. Mat. Univ. Parm

The twin effects of globalization

Employees of"globalized"firms face a riskier, but potentially more rewarding, menu of labor market outcomes. The authors document this neglected tradeoff of globalization for a sample of Indian manufacturing firms. On the one hand, the employees of firms subject to foreign competition face a more uncertain stream of earnings and riskier employment prospects. On the other hand, they enjoy a more rapid career growth and have more opportunities to train and upgrade their skills. The negative uncertainty costs and the positive incentive effects of globalization are thus twin to each other. Concentrating on just one side of the coin gives a misleading picture of globalization.Small Scale Enterprise,Environmental Economics&Policies,Microfinance,Labor Policies,Economic Theory&Research,Environmental Economics&Policies,Economic Theory&Research,Microfinance,Private Participation in Infrastructure,Small Scale Enterprise

The Twin Effects of Globalization - Evidence from a Sample of Indian Manufacturing Firms

Employees of globalized firms face a riskier menu of labor market outcomes. They face a more uncertain stream of earnings and riskier employment prospects. However, they may also have stronger incentives to train and upgrade their skills and/or may benefit from more rapid careers. Hence, the costs of uncertainty and the benefits of skill upgrading associated with globalization may be twin to each other. We provide statistical evidence of this so far neglected trade-off for a sample of Indian manufacturing firms.globalization, uncertainty, training, labor markets, India