Red long-lasting phosphorescence (LLP) in β-TCP type Ca9.5Mn(PO4)7 compounds

Mn-ion doped calcium phosphates namely Ca₅(PO₄)₃(OH) hydroxyapatite (HAP), β-Ca₃(PO₄)₂ (β-TCP) as well as Ca_9.5Mn(PO₄)₇ whitlockite were synthesized and the optical properties of the Mn²⁺ cations were investigated. Annealing under reducing atmosphere enhances the emission of the divalent manganese species. Electron paramagnetic resonance (EPR) and optical spectroscopies confirm that Mn²⁺ ions are the active species. Orange and red emissions occur respectively for the Mn:HAP and Mn:TCP. For this latter, long-lasting phosphorescence (LLP) coming from the Mn²⁺ emission (⁴T₁ → ⁶A₁ transition) is observed at 640 nm but it appears that the traps depths are either two shallow or too deep to lead to an efficient long-lasting emission.     

Predicting and Detecting Symmetries in FOL Finite Model Search

Symmetries abound in logically formulated problems where many axioms are universally quantified, as this is the case in equational theories. Two complementary approaches have been used so far to dynamically tackle those symmetries: prediction and detection. The best-known predictive symmetry elimination method is the least number heuristic (lnh). A more recent predictive method, the extended least number heuristic (xlnh), focuses first on the enumeration of a bijection in the problem and easily exploits in the sequel the remaining isomorphisms. On the other hand, dynamic symmetry detection is costly in the general case (the problem is Graph Iso complete) but allows one to exploit more symmetries, and efficient (polytime) yet incomplete detection algorithms can be used on each node. This paper presents a generalization of xlnh that focuses on the enumeration of a unary function that does not require the function to be bijective, a general notion of symmetry for finite-model search in first-order logic together with an efficient symmetry detection algorithm, and a function-ordering heuristic that exploits the inherent structure of first-order logic theories to improve the search when using function-centric methods. A comprehensive study of the compared efficiency of all methods, in isolation and in combination, demonstrates the acceleration that can be expected in all cases. These ideas are implemented by using the known system SEM as an experimentation framework, to allow for accurate comparisons.     

Three-dimensional numerical simulation of free convection and entropy generation in a cubic cavity containing a heat source

The present article provides a three-dimensional numerical investigation of thermal convection and entropy generation. The lattice Boltzmann method, coupled with the finite difference approach, is applied to perform numerical simulations. The validation of these numerical approaches for thermal convection simulation and entropy calculation is performed by comparing our numerical results with those in the published literature for the case of benchmark problems. The physical geometry studied in this paper concerns a hot obstacle having the shape of a plus sign (+) placed in the center of a cubic enclosure. This cube is filled with air of a Prandtl number of 0.71 and characterized by two cold vertical walls. The heat exchange between the fluid and the hot body is studied as a function of the Rayleigh number (${10}^3\le \mathit{Ra}\le {10}^7$). The performed simulations show that the heat transfer rate can be increased by about 429% by switching from $\mathit{Ra}={10}^3$ to ${10}^7$. The entropy generation due to fluid friction, heat transfer, and total entropy are also calculated and discussed. For an irreversibility coefficient $\mathit{\phi }={10}^{-4}$, the analysis of the results showed that for low values of the Rayleigh number ($\mathit{Ra}={10}^3$), the entropy production due to temperature gradients predominates over that produced by viscous effects. In the cases of $\mathit{Ra}={10}^4$ and ${10}^5$, entropy generation is due to both fluid friction and heat transfer. However, when the Rayleigh number becomes large ($\mathit{Ra}{\ge 10}^6$), entropy generation due to viscosity predominates over entropy production related to heat exchange. These results have important implications for the optimization and design of heat transfer systems in various industrial applications.