We consider the inverse problem of retrieving the coe cients of a second order boundary operator from Cauchy data associated with the Laplace operator at a measurement curve. We study the identifiability and reconstruction in the case of piecewise continuous parameters. We prove in particular the di↵erentiability of the Khon-Vogelius functional with respect to the discontinuity points and employ the result in a gradient type minimizing algorithm. We provide validating numerical results discussing in particular the case of unknown number of discontinuity points.
A new glass with a composition of 40P2O5-30ZnO-20LiCl-10BaF2 (in mol%), doped with 3.5Nd2O3-3.5Yb2O3, was fabricated by the quenching melt technique. The luminescence (PL) and gamma spectroscopy of the glass were investigated systematically. The spectroscopic parameters of the prepared glass, such as the optical energy gap, Judd–Ofelt parameters Ωk (where k = 2, 4 and 6), lifetimes and branching ratio of the Nd3+/Yb3+ level, were evaluated. Moreover, the shielding parameters, such as the linear and mass attenuation coefficients, mean free path and half-value layer, were evaluated. The prepared glass had a spectroscopic quality factor (Ω4/Ω6) of 0.84, which is about three-times larger than that of the most standard laser host, Nd3+:YAG. The energy of the 2P1/2 (Nd3+) level (~23,250 cm−1) was twice the energy of the Yb3+ transition (~10,290 cm−1). The value of the emission cross section (σem(λ)) of Nd3+:4F3/2→4I9/2 and Yb3+:2F5/2→2F7/2 were 2.23 × 10−24 cm2 and 2.88 × 10−24 cm2, respectively. The fabricated glass had a high emission cross section and low mean free path parameters, which makes the fabricated glass a potential candidate for multifunctional applications, such as laser emissions for medical purposes.
In the optical energy gap, visible and near-IR emission of halide phosphate glasses with a composition of 40P2O5-30ZnO-20LiCl-10BaF2 in mol% doped with 3.5 × 104 ppm Pr2O3, referred to as PZLBPr, were synthesized. The UV-VIS-NIR and spectroscopic properties of these glasses were also predicted. The current glasses had broadband emission photoluminescence covering a wavelength range of 1250 to 1700 nm when excited at 455 nm. These bands for near-infrared emission luminescence relate to the transitions 1G4 → 3H5, 1D2 → 1G4, and 3H4 → 3F3, 3F4 in the optical telecommunication window. The significant PL emission wideband was caused by the radiative transition from Pr3+: 1D2 to 1G4. At 445 nm excitation, these glasses exhibited emission bands that corresponded to blue/reddish orange spectral ranges in visible ranges. The prepared glass has a high lasing quality factor (Ω4/Ω6 = 0.9), high optical energy (4.72 eV), and quantum efficiency = 87.3% with FWHM = 156 nm of transition emission from the 1D2 → 1G4 level. As a result, broadband near infrared optical amplifiers can be fabricated from the prepared glasses.
A numerical modeling investigation of the spectral emission of laser-induced plasma in MgCl 2 -NaCl aqueous solution has been presented. A model based on equilibrium equations has been developed for the computation of the plasma composition and excited levels population. Physical interpretation is presented to comment on �rstly the evolution of atomic species number densities, and secondly on the population of the excited species emitting MgII and NaI resonant lines for temperatures ranging from 3000 K to 20 000 K. It is shown that MgII line reach a maximum of population on the issuing level, at norm temperature of 13800 K. Whereas, NaI line presents two norm temperatures, evaluated at 3300 K and 11700 K. is splitting of the NaI norm temperature is explained by the low-ionization potential and weak concentration of the sodium atom in this aqueous solution. us, the proposed model can be useful to predict the optimal plasma temperature for the detection of given chemical element, which is not easy to reveal experimentally.
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