A computational study of a solver system for processing two-stage stochastic LPs with enhanced Benders decomposition

We report a computational study of two-stage SP models on a large set of benchmark problems and consider the following methods: (i) Solution of the deterministic equivalent problem by the simplex method and an interior point method, (ii) Benders decomposition (L-shaped method with aggregated cuts), (iii) Regularised decomposition of Ruszczy??ski (Math Program 35:309?C333, 1986), (iv) Benders decomposition with regularization of the expected recourse by the level method (Lemaréchal et al. in Math Program 69:111?C147, 1995), (v) Trust region (regularisation) method of Linderoth and Wright (Comput Optim Appl 24:207?C250, 2003). In this study the three regularisation methods have been introduced within the computational structure of Benders decomposition. Thus second-stage infeasibility is controlled in the traditional manner, by imposing feasibility cuts. This approach allows extensions of the regularisation to feasibility issues, as in Fábián and Sz?ke (Comput Manag Sci 4:313?C353, 2007). We report computational results for a wide range of benchmark problems from the POSTS and SLPTESTSET collections and a collection of difficult test problems compiled by us. Finally the scale-up properties and the performance profiles of the methods are presented.     

Emission mechanisms in stabilized iron-passivated porous silicon: Temperature and laser power dependences

Photoluminescence (PL) measurements of porous silicon (PS) and iron-porous silicon nanocomposites (PS/Fe) with stable optical properties versus temperature and laser power density have been investigated. The presence of iron in PS matrix is confirmed by Raman spectroscopy. The PL intensity of PS and PS/Fe increases at low temperature, the evolution of integrated PL intensity follows the modified Arrhenius model. The incorporation of iron in PS matrix reduces the activation energy traducing the existence of shallow levels related to iron atoms. Also, the temperature dependence of the porous silicon PL peak position follows a linear evolution at high temperature and a quadratic one at low temperature. Such evolution is due to the thermal carriers' redistribution and an energy transfer. Similarly, we have compared the laser power dependence of the PL in PS and PS/Fe layers. The results prove that the recombination process in PS is realised through the lower energy traps localised in the electronic gap. However, the observed emission in PS/Fe is essentially due to direct transitions. So, we can conclude that the presence of iron in PS matrix induces a strong modification of the PL mechanisms.     

Absence of percolation in graphs based on stationary point processes with degrees bounded by two

We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge-drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for signal-to-interference ratio graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional $k$-nearest neighbor graph of a two-dimensional homogeneous Poisson point process does not percolate for $k=2$.     

Ballistic performance of novel design of bulletproof plates inspired by biomimetic approaches

Metal and polymer matrix composite materials are preferred in bulletproof applications due to their high-impact resistance and lightness. Personal/demand-specific designs that have become possible with the developing additive manufacturing technologies have brought a new perspective to armor technologies. At the same time, parts with complex structures designed with biomimetic approaches can be easily manufactured with additive manufacturing. In this study, biomimetic armors obtained from standard Carbon fiber reinforced polymer (CFRP) and Inconel 718 materials were compared with traditional armor structures. Within the scope of the study, 9 × 19 mm² parabellum and 7.62 mm NATO bullets were impacted at 275 m/s and 600 m/s speeds on biomimetic and conventional armor consisting of three and five layers. Bullet velocities during impact, deformation of bullets, deformation of armor, and harmonic behavior are discussed. The results obtained were also used to calculate the damped impact energies. In the study, it was determined that biomimetic plates could absorb 22%–38% more impact energy. It has been determined that CFRP materials can absorb 45% more impact energy compared to Inconel 718.