Parallel distributed-memory simplex for large-scale stochastic LP problems

We present a parallelization of the revised simplex method for large extensive forms of two-stage stochastic linear programming (LP) problems. These problems have been considered too large to solve with the simplex method; instead, decomposition approaches based on Benders decomposition or, more recently, interior-point methods are generally used. However, these approaches do not provide optimal basic solutions, which allow for efficient hot-starts (e.g., in a branch-and-bound context) and can provide important sensitivity information. Our approach exploits the dual block-angular structure of these problems inside the linear algebra of the revised simplex method in a manner suitable for high-performance distributed-memory clusters or supercomputers. While this paper focuses on stochastic LPs, the work is applicable to all problems with a dual block-angular structure. Our implementation is competitive in serial with highly efficient sparsity-exploiting simplex codes and achieves significant relative speed-ups when run in parallel. Additionally, very large problems with hundreds of millions of variables have been successfully solved to optimality. This is the largest-scale parallel sparsity-exploiting revised simplex implementation that has been developed to date and the first truly distributed solver. It is built on novel analysis of the linear algebra for dual block-angular LP problems when solved by using the revised simplex method and a novel parallel scheme for applying product-form updates.     

ESR and XRD investigation of effects induced by gamma radiation on PVA-TiO2 membranes

The effects of gamma radiation on the local structure of PVA membranes containing TiO₂ were investigated by ESR and XRD methods. An intense ESR signal is observed after irradiation at 16 KGy dose. This signal appears only for irradiated samples and it is associated with the breaking of the polymeric chain, followed by local reorganization of the polymeric segments and the apparition of the unpaired electrons and free radicals. The intensity of the signal decreases with the concentration of TiO₂, indicating a shielding effect of the dopand. That the modification of local order of the polymeric chains has been modified after irradiation is confirmed by XRD method.     

Effect of spark discharges on the trajectories of insulating particles in roll-type corona-electrostatic separators. Experimental and numerical study

Corona-electrostatic separation is a multi-variable process that has been thoroughly studied in connection with its various applications in the recycling industry. The aim of the present paper is to point out one parasitic phenomenon that adversely affects the efficiency of the separation: the sparks generated at the passage of conductive particles through the electric field zone. The experiments were carried out on a laboratory roll-type corona electrostatic separators, and the sparks were generated by introducing 16 calibrated copper pins in 40-g samples of granular insulating material (PVC; typical granule size: 1.5 mm) that were fed at a constant rate onto the surface of the grounded rotating roll electrode. The distribution of the PVC granules in the 14 boxes of the collector was altered by the occurrence of the spark discharges, as they were accompanied by the annealing of the electric field between the electrodes. The numerical simulation of insulating granules charging and movement under the action of the electric field enabled a better understanding of the interactions between the spark discharges and the other factors that influence their trajectories and affect the efficiency of the separation: roll-speed, particle size and ambient humidity. The particle dynamics equations were solved using an iterative scheme by using the electric field calculated in any point with the commercial software TRICOMP. The good agreement between the predictions made by these simulations and the experimental findings confirms the ability of the mathematical model to reflect the complexity of the physical phenomena.     

Hierarchical approach for survivable network design

A central design challenge facing network planners is how to select a cost-effective network configuration that can provide uninterrupted service despite edge failures. In this paper, we study the Survivable Network Design (SND) problem, a core model underlying the design of such resilient networks that incorporates complex cost and connectivity trade-offs. Given an undirected graph with specified edge costs and (integer) connectivity requirements between pairs of nodes, the SND problem seeks the minimum cost set of edges that interconnects each node pair with at least as many edge-disjoint paths as the connectivity requirement of the nodes. We develop a hierarchical approach for solving the problem that integrates ideas from decomposition, tabu search, randomization, and optimization. The approach decomposes the SND problem into two subproblems, Backbone design and Access design, and uses an iterative multi-stage method for solving the SND problem in a hierarchical fashion. Since both subproblems are NP-hard, we develop effective optimization-based tabu search strategies that balance intensification and diversification to identify near-optimal solutions. To initiate this method, we develop two heuristic procedures that can yield good starting points. We test the combined approach on large-scale SND instances, and empirically assess the quality of the solutions vis-à-vis optimal values or lower bounds. On average, our hierarchical solution approach generates solutions within 2.7% of optimality even for very large problems (that cannot be solved using exact methods), and our results demonstrate that the performance of the method is robust for a variety of problems with different size and connectivity characteristics.     

Simultaneous thermal and contraction/expansion analyses of cast iron solidification process

Journal of Thermal Analysis and Calorimetry - Simultaneous thermal and contraction/expansion analysis of hypoeutectic grey (lamellar graphite) and ductile (nodular graphite) cast irons...     

Application of thermal analysis in solidification pattern control of La-inoculated grey cast irons

Journal of Thermal Analysis and Calorimetry - The new generation of acid-lined medium-frequency coreless induction furnaces revolutionized the iron foundries, resulting higher overheating and lower...     

Eigenvalue problems in Orlicz–Sobolev spaces for rapidly growing operators in divergence form

Eigenvalue problems involving the p-Laplacian and rapidly growing operators in divergence form are studied in an Orlicz–Sobolev setting. An asymptotic analysis of these problems leads to a full characterization of the spectrum of an exponential type perturbation of the Laplace operator.     

The Effect of Calcium-Silicate Cements on Reparative Dentinogenesis Following Direct Pulp Capping on Animal Models

Dental pulp vitality is a desideratum for preserving the health and functionality of the tooth. In certain clinical situations that lead to pulp exposure, bioactive agents are used in direct pulp-capping procedures to stimulate the dentin-pulp complex and activate reparative dentinogenesis. Hydraulic calcium-silicate cements, derived from Portland cement, can induce the formation of a new dentin bridge at the interface between the biomaterial and the dental pulp. Odontoblasts are molecularly activated, and, if necessary, undifferentiated stem cells in the dental pulp can differentiate into odontoblasts. An extensive review of literature was conducted on MedLine/PubMed database to evaluate the histological outcomes of direct pulp capping with hydraulic calcium-silicate cements performed on animal models. Overall, irrespective of their physico-chemical properties and the molecular mechanisms involved in pulp healing, the effects of cements on tertiary dentin formation and pulp vitality preservation were positive. Histological examinations showed different degrees of dental pulp inflammatory response and complete/incomplete dentin bridge formation during the pulp healing process at different follow-up periods. Calcium silicate materials have the ability to induce reparative dentinogenesis when applied over exposed pulps, with different behaviors, as related to the animal model used, pulpal inflammatory responses, and quality of dentin bridges.     

On a class of nonlinear problems involving a p(x)-Laplace type operator

We study the boundary value problem in Ω, u = 0 on ∂Ω, where Ω is a smooth bounded domain in ℝ ^N . Our attention is focused on two cases when , where m(x) = max{p ₁(x), p ₂(x)} for any x ∈ or m(x) < q(x) < N · m(x)/(N − m(x)) for any x ∈ . In the former case we show the existence of infinitely many weak solutions for any λ > 0. In the latter we prove that if λ is large enough then there exists a nontrivial weak solution. Our approach relies on the variable exponent theory of generalized Lebesgue-Sobolev spaces, combined with a ℤ₂-symmetric version for even functionals of the Mountain Pass Theorem and some adequate variational methods.