Modulational instability in dispersion-kicked optical fibers

We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been realized in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths much shorter than the period, which therefore approximate the ideal Dirac comb. Experimental spontaneous MI spectra recorded under quasi continuous wave excitation are in good agreement with the theory and with numerical simulations based on the generalized nonlinear Schr\"odinger equation

Condensate fraction in liquid 4He at zero temperature

We present results of the one-body density matrix (OBDM) and the condensate fraction n_0 of liquid 4He calculated at zero temperature by means of the Path Integral Ground State Monte Carlo method. This technique allows to generate a highly accurate approximation for the ground state wave function Psi_0 in a totally model-independent way, that depends only on the Hamiltonian of the system and on the symmetry properties of Psi_0. With this unbiased estimation of the OBDM, we obtain precise results for the condensate fraction n_0 and the kinetic energy K of the system. The dependence of n_0 with the pressure shows an excellent agreement of our results with recent experimental measurements. Above the melting pressure, overpressurized liquid 4He shows a small condensate fraction that has dropped to 0.8% at the highest pressure of p = 87 bar.Comment: 12 pages. 4 figures. Accepted for publication on "Journal of Low Temperature Physics

Heteroclinic structure of parametric resonance in the nonlinear Schr\"odinger equation

We show that the nonlinear stage of modulational instability induced by parametric driving in the {\em defocusing} nonlinear Schr\"odinger equation can be accurately described by combining mode truncation and averaging methods, valid in the strong driving regime. The resulting integrable oscillator reveals a complex hidden heteroclinic structure of the instability. A remarkable consequence, validated by the numerical integration of the original model, is the existence of breather solutions separating different Fermi-Pasta-Ulam recurrent regimes. Our theory also shows that optimal parametric amplification unexpectedly occurs outside the bandwidth of the resonance (or Arnold tongues) arising from the linearised Floquet analysis

Effects of the mean particle size in the deflagration index estimation for cornstarch dust

The National Fire Protection Association (NFPA) defines the dust explosions as a “credible risk”. Hence, to meet the challenge to prevent and protect from the catastrophic effects of these phenomena, it is fundamental to know what are the characteristics and the burning conditions regarding the combustible dusts that could have an effect on the explosion violence. The KSt, also known as deflagration index, is one of the relevant parameters in dust explosions, together with the maximum explosion overpressure generated in the test chamber, the minimumignition energy and so on. In particular, the deflagration index measures the relative explosion severity and it is used in the design of the dust venting protection equipment. However, one of the criticalities of such a parameter is that is strongly affected by the particle mean diameter. Hence, in the following, it will be preliminary presented the validation of a single particle spherical model able to predict the variation of the deflagration index with the increasing mean particle size knowing just one experimental KSt value

Safe optimization of potentially runaway processes using topology based tools and software

In chemical industries, fast and strongly exothermic reactions are often to be carried out to synthesize a number of intermediates and final desired products. Such processes can exhibit a phenomenon known as \u201cthermal runaway\u201d that consists in a reactor temperature loss of control. During the course of the years, lots of methods, aimed to detect the set of operating parameters (e.g., dosing times, initial reactor temperature, coolant temperature, etc..) at which such a dangerous phenomenon can occur, have been developed. Moreover, in the last few years, the attention has been posed on safe process optimization, that is how to compute the set of operating parameters able to ensure high reactor productivity and, contextually, safe conditions. To achieve this goal, with particular reference to industrial semibatch synthesis carried out using both isothermal and isoperibolic temperature control mode, a dedicated optimization software has been implemented. Such a software identifies the optimum set of operating parameters using a topological criterion able to bind the so-called \u201cQFS region\u201d (where reactants accumulation is low and all the heat released is readily removed by the cooling equipment) and, then, iteratively searching for the constrained system optimum. To manage the software, only a few experimental parameters are needed; essentially: heat(s) of reaction, apparent system kinetics (Arrhenius law), threshold temperature(s) above which unwanted side reactions, decompositions or boiling phenomena are triggered, heat transfer coefficients and reactants heat capacities. Such parameters can be obtained using simple calorimetric techniques (DSC, ARC, RC1, etc..). Over the optimization section, the software posses a simulation section where both normal and upset operating conditions (such as pumps failure and external fire) can be tested

Weakly Supervised Semantic Segmentation Using Constrained Dominant Sets

The availability of large-scale data sets is an essential pre-requisite for deep learning based semantic segmentation schemes. Since obtaining pixel-level labels is extremely expensive, supervising deep semantic segmentation networks using low-cost weak annotations has been an attractive research problem in recent years. In this work, we explore the potential of Constrained Dominant Sets (CDS) for generating multi-labeled full mask predictions to train a fully convolutional network (FCN) for semantic segmentation. Our experimental results show that using CDS's yields higher-quality mask predictions compared to methods that have been adopted in the literature for the same purpose

Finite-Dimensional Calculus

We discuss topics related to finite-dimensional calculus in the context of finite-dimensional quantum mechanics. The truncated Heisenberg-Weyl algebra is called a TAA algebra after Tekin, Aydin, and Arik who formulated it in terms of orthofermions. It is shown how to use a matrix approach to implement analytic representations of the Heisenberg-Weyl algebra in univariate and multivariate settings. We provide examples for the univariate case. Krawtchouk polynomials are presented in detail, including a review of Krawtchouk polynomials that illustrates some curious properties of the Heisenberg-Weyl algebra, as well as presenting an approach to computing Krawtchouk expansions. From a mathematical perspective, we are providing indications as to how to implement in finite terms Rota's "finite operator calculus".Comment: 26 pages. Added material on Krawtchouk polynomials. Additional references include