An existence result for a nonlinear transmission problems

Let $\Omega^o$ and $\Omega^i$ be open bounded subsets of $\mathbb{R}^n$ of class $C^{1,\alpha}$ such that the closure of $\Omega^i$ is contained in $\Omega^o$. Let $f^o$ be a function in $C^{1,\alpha}(\partial\Omega^o)$ and let $F$ and $G$ be continuous functions from $\partial\Omega^i\times\mathbb{R}$ to $\mathbb{R}$. By exploiting an argument based on potential theory and on the Leray-Schauder principle we show that under suitable and completely explicit conditions on $F$ and $G$ there exists at least one pair of continuous functions $(u^o, u^i)$ such that $$\left\{ \begin{array}{ll} \Delta u^o=0&\text{in }\Omega^o\setminus\mathrm{cl}\Omega^i\,,\\ \Delta u^i=0&\text{in }\Omega^i\,,\\ u^o(x)=f^o(x)&\text{for all }x\in\partial\Omega^o\,,\\ u^o(x)=F(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,,\\ \nu_{\Omega^i}\cdot\nabla u^o(x)-\nu_{\Omega^i}\cdot\nabla u^i(x)=G(x,u^i(x))&\text{for all }x\in\partial\Omega^i\,, \end{array} \right.$$ where the last equality is attained in certain weak sense. In a simple example we show that such a pair of functions $(u^o, u^i)$ is in general neither unique nor local unique. If instead the fourth condition of the problem is obtained by a small nonlinear perturbation of a homogeneous linear condition, then we can prove the existence of at least one classical solution which is in addition locally unique

Development and calibration of a structural simulation method of CF-SMC composite parts processed by compression molding

The need for the reduction in CO2 production in automotive field increasingly leads manufacturers to consider fiber-reinforced composite materials that are however costly to processes. Discontinuous fiber composite materials, like CF – SMC, are a competitive candidate because they are transformed by the high productivity compression molding technology. On the negative side, their structural complexity introduces high variability in the mechanical performance that needs to be considered at the design stage. This contribution describes the development of a structural modeling strategy for parts made of CF-SMC processed by compression molding. It is based the statistical material model proposed by Feraboli implemented here in a FEA-based structural analysis procedure. After validation and calibration of a specific CF-SMC material, the proposed procedure is applied to the simulation of the structural response of a compression molded part of complex geometry subjected to know loading condition

High brightness 100 W-50 μm delivery blue laser diode module

Blue laser diodes are emerging as the next revolution in laser material processing, especially for high reflective materials, such as copper and gold. The paper presents the most recent evolution of a family of medium-high power and high brightness devices specifically conceived for micro-machining applications. The modules make use of a proprietary architecture based on the combination of commercial laser diodes in TO9 package. The diodes are first organized in rows staggered along the fast axis, then the rows are multiplexed along the fast axis; finally, wavelength and polarization multiplexing are exploited to achieve up to 100W of power into a 50 μm/0.22NA fiber

Excitons and charged excitons in semiconductor quantum wells

A variational calculation of the ground-state energy of neutral excitons and of positively and negatively charged excitons (trions) confined in a single-quantum well is presented. We study the dependence of the correlation energy and of the binding energy on the well width and on the hole mass. The conditional probability distribution for positively and negatively charged excitons is obtained, providing information on the correlation and the charge distribution in the system. A comparison is made with available experimental data on trion binding energies in GaAs-, ZnSe-, and CdTe-based quantum well structures, which indicates that trions become localized with decreasing quantum well width.Comment: 9 pages, 11 figure

Magnetic field dependence of the energy of negatively charged excitons in semiconductor quantum wells

A variational calculation of the spin-singlet and spin-triplet state of a negatively charged exciton (trion) confined to a single quantum well and in the presence of a perpendicular magnetic field is presented. We calculated the probability density and the pair correlation function of the singlet and triplet trion states. The dependence of the energy levels and of the binding energy on the well width and on the magnetic field strength was investigated. We compared our results with the available experimental data on GaAs/AlGaAs quantum wells and find that in the low magnetic field region (B<18 T) the observed transition are those of the singlet and the dark triplet trion (with angular momentum $L_z=-1$), while for high magnetic fields (B>25 T) the dark trion becomes optically inactive and possibly a transition to a bright triplet trion (angular momentum $L_z=0$) state is observed.Comment: 9 pages, 10 figures submitted to Phys. Rev.

Frequency Dynamics in Fully Non-Synchronous Electrical Grids: A Case Study of an Existing Island

The operation of a power system with 100% converter-interfaced generation poses several questions and challenges regarding various aspects of the design and the control of the system. Existing literature on the integration of renewable energy sources in isolated systems mainly focuses on energy aspects or steady-state issues, and only a few studies examine the dynamic issues of autonomous networks operated with fully non-synchronous generation. A lack of research can be found in particular in the determination of the required amount of grid-forming power, the selection of the number and rated power of the units which should implement the grid-forming controls, and the relative locations of the grid-forming converters. The paper aims to address those research gaps starting from a theoretical point of view and then by examining the actual electrical network of an existing island as a case study. The results obtained from the investigations indicate specific observations and design opportunities, which are essential for securing the synchronization and the stability of the grid. Possible solutions for a fully non-synchronous operation of autonomous systems, in terms of dynamic characteristics and frequency stability, are presented and discussed

Active shape correction of a thin glass/plastic X-ray mirror

Optics for future X-ray telescopes will be characterized by very large aperture and focal length, and will be made of lightweight materials like glass or plastic in order to keep the total mass within acceptable limits. Optics based on thin slumped glass foils are currently in use in the NuSTAR telescope and are being developed at various institutes like INAF/OAB, aiming at improving the angular resolution to a few arcsec HEW. Another possibility would be the use of thin plastic foils, being developed at SAO and the Palermo University. Even if relevant progresses in the achieved angular resolution were recently made, a viable possibility to further improve the mirror figure would be the application of piezoelectric actuators onto the non-optical side of the mirrors. In fact, thin mirrors are prone to deform, so they require a careful integration to avoid deformations and even correct forming errors. This however offers the possibility to actively correct the residual deformation. Even if other groups are already at work on this idea, we are pursuing the concept of active integration of thin glass or plastic foils with piezoelectric patches, fed by voltages driven by the feedback provided by X-rays, in intra-focal setup at the XACT facility at INAF/OAPA. In this work, we show the preliminary simulations and the first steps taken in this project