Three-region inequalities for the second order elliptic equation with discontinuous coefficients and size estimate

In this paper, we would like to derive a quantitative uniqueness estimate, the three-region inequality, for the second order elliptic equation with jump discontinuous coefficients. The derivation of the inequality relies on the Carleman estimate proved in our previous work. We then apply the three-region inequality to study the size estimate problem with one boundary measurement.Comment: 16 pages, 1 figur

VUV-Vis optical characterization of Tetraphenyl-butadiene films on glass and specular reflector substrates from room to liquid Argon temperature

The use of efficient wavelength-shifters from the vacuum-ultraviolet to the photosensor's range of sensitivity is a key feature in detectors for Dark Matter search and neutrino physics based on liquid argon scintillation detection. Thin film of Tetraphenyl-butadiene (TPB) deposited onto the surface delimiting the active volume of the detector and/or onto the photosensor optical window is the most common solution in current and planned experiments. Detector design and response can be evaluated and correctly simulated only when the properties of the optical system in use (TPB film + substrate) are fully understood. Characterization of the optical system requires specific, sometimes sophisticated optical methodologies. In this paper the main features of TPB coatings on different, commonly used substrates is reported, as a result of two independent campaigns of measurements at the specialized optical metrology labs of ENEA and University of Tor Vergata. Measured features include TPB emission spectra with lineshape and relative intensity variation recorded as a function of the film thickness and for the first time down to LAr temperature, as well as optical reflectance and transmittance spectra of the TPB coated substrates in the wavelength range of the TPB emission

CFD MODELING OF SOLAR COLLECTOR WITH NANO-FLUID DIRECT ABSORPTION FOR CIVIL APPLICATION

Direct solar absorption has been considered often in the past as a possible configuration of solar thermal collectors for residential and small commercial applications. Of course, a direct absorption could improve the performance of solar collectors by skipping one step of the heat transfer mechanism of standard devices and by modifying the temperature distribution inside the collector. In fact, classical solar thermal collectors have a metal sheet as absorber, designed such that water has the minimum temperature in each transversal section, in order to collect as much as possible the solar thermal energy. On the other hand, in a direct configuration, the hottest part of the system is the operating fluid and this allows to have a more efficient conversion. Nanofluids, i.e. fluids with a suspension of nano-particles, as carbon nano-horns, could be a good and innovative family of absorbing fluids, for their higher absorption coefficient with respect to the base fluid and stability under moderate temperature gradients. Moreover, carbon nanohorns offer the significant advantage to be non-toxic unlike other carbon nanoparticles (e.g. carbon nanotubes). In this work, an original 3D model of the absorption phenomena in nano-fluids flowing in a cylindrical tube is coupled with a CFD analysis of the flow and temperature field. Recent measurements of the optical properties of nano-fluids with different concentrations have been used for the radiation heat transfer modeling and included in the fluid dynamic modeling as well. Heat losses due to conduction, convection and radiation at the boundaries are included in the model. The results are compared with the typical performance of flat solar collectors present on the marke

Entanglement entropy in collective models

We discuss the behavior of the entanglement entropy of the ground state in various collective systems. Results for general quadratic two-mode boson models are given, yielding the relation between quantum phase transitions of the system (signaled by a divergence of the entanglement entropy) and the excitation energies. Such systems naturally arise when expanding collective spin Hamiltonians at leading order via the Holstein-Primakoff mapping. In a second step, we analyze several such models (the Dicke model, the two-level BCS model, the Lieb-Mattis model and the Lipkin-Meshkov-Glick model) and investigate the properties of the entanglement entropy in the whole parameter range. We show that when the system contains gapless excitations the entanglement entropy of the ground state diverges with increasing system size. We derive and classify the scaling behaviors that can be met.Comment: 11 pages, 7 figure

A direct D-bar reconstruction algorithm for recovering a complex conductivity in 2-D

A direct reconstruction algorithm for complex conductivities in $W^{2,\infty}(\Omega)$, where $\Omega$ is a bounded, simply connected Lipschitz domain in $\mathbb{R}^2$, is presented. The framework is based on the uniqueness proof by Francini [Inverse Problems 20 2000], but equations relating the Dirichlet-to-Neumann to the scattering transform and the exponentially growing solutions are not present in that work, and are derived here. The algorithm constitutes the first D-bar method for the reconstruction of conductivities and permittivities in two dimensions. Reconstructions of numerically simulated chest phantoms with discontinuities at the organ boundaries are included.Comment: This is an author-created, un-copyedited version of an article accepted for publication in [insert name of journal]. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at 10.1088/0266-5611/28/9/09500