Parallel Algorithm for Unconstrained Optimization Based on Decomposition Techniques

We present a numerical implementation of the parallel gradient distribution (PGD) method for the solution of large-scale unconstrained optimization problems. The proposed parallel algorithm is characterized by a parallel phase which exploits the portions of the gradient of the objective function assigned to each processor; then, a coordination phase follows which, by a synchronous interaction scheme, optimizes over the partial results obtained by the parallel phase. The parallel and coordination phases are implemented using a quasi-Newton limited-memory BFGS approach. The computational experiments, carried out on a network of UNIX workstations by using the parallel software tool PVM, show that parallelization efficiency was problem dependent and ranged between 0.15 and 8.75. For the 150 problems solved by PGD on more than one processor, 85 cases had parallelization efficiency below 1, while 65 cases had a parallelization efficiency above 1.     

Recent theories of gas sorption in polymers

Theories and models are presented for gas sorption in polymers above and below the glass transition temperature. With the exception of predictive theories that do not represent the data well, the models are fit to data for the carbon dioxide/silicone rubber and carbon dioxide/polycarbonate systems for the purposes of comparison. During the past decade, a number of new models and theories have been proposed specifically for gas sorption in glassy polymers. Each new model attempts to incorporate aspects of the gas sorption process that are unique to polymers below the glass transition temperature. This review discusses these recent advances, the assumptions used in their development and their advantages and disadvantages.     

Properties of balanced and perfect matrices

In this paper we define wheel matrices and characterize some properties of matrices that are perfect but not balanced. A consequence of our results is that if a matrixA is perfect then we can construct a polynomial number of submatricesA _I,,A _n ofA such thatA is balanced if and only if all the submatricesA ₁,,A _n ofA are perfect. This implies that if the problem of testing perfection is polynomially solvable, then so is the problem of testing balancedness.Partial support under NSF Grants DMS-8606188, ECS-8800281 and DDM-8800281.     

Diffraction engineering in arrays of photonic crystal waveguides

Light propagation in uniform arrays of photonic crystal waveguides is studied. We demonstrate that, in stark contrast to the case of conventional waveguide arrays, diffraction can be tailored both in magnitude and sign by varying only the spacing between adjacent waveguides. Diffraction management in ultracompact arrays of straight photonic crystal waveguides is demonstrated by solving Maxwell's equations through the time-domain finite-element method.     

The Three-Wave Resonant Interaction Equations: Spectral and Numerical Methods

The spectral theory of the integrable partial differential equations which model the resonant interaction of three waves is considered with the purpose of numerically solving the direct spectral problem for both vanishing and non vanishing boundary values. Methods of computing both the continuum spectrum data and the discrete spectrum eigenvalues are given together with examples of such computations. The explicit spectral representation of the Manley-Rowe invariants is also displayed.     

Water distribution networks design under uncertainty

Water distribution networks are important systems that provide citizens with an essential public service which is crucial for the normal development of most basic activities of life. Despite many water distribution network problems have been extensively investigated in the literature, the presence of uncertainty in the data has often been neglected. This paper studies the challenging problem of designing an isolation system for water distribution networks under different failure scenarios. To solve the problem, three heuristic methods are presented and analyzed on a real case study taken from the literature. Numerical results show the merits of the suggested techniques for solving the problem.     

Chemical composition and bioactivity of Citrus medica L. cv. Diamante essential oil obtained by hydrodistillation, cold-pressing and supercritical carbon dioxide extraction

The chemical composition of the essential oil of Citrus medica L. cv. Diamante peel obtained by hydrodistillation, cold-pressing and supercritical carbon dioxide extraction techniques was determined by GC/MS analysis. Forty-six components were fully characterised. Limonene and γ-terpinene were the major components of the oils obtained by hydrodistillation (HD) and cold-pressing (CP), while citropten was the major constituent in the oil obtained by supercritical carbon dioxide extraction (SFE). Acetylcholinesterase (AChE) and butyrylcholinesterase (BChE) inhibitory activities were evaluated. The essential oil obtained by hydrodistillation exerted the highest inhibitory activity against BChE (IC?? value of 154.6 μg mL?1) and AChE (IC?? value of 171.3 μg mL?1. Interestingly, the oil obtained by cold-pressing exhibited a selective inhibitory activity against AChE. The essential oils have also been evaluated for the inhibition of NO production in LPS induced RAW 264.7 macrophages. The oil obtained by hydrodistillation exerted a significant inhibition of NO production with an IC?? value of 17 μg mL?1 (IC?? of positive control 53 μg mL?1).     

Modified edge finite elements for photonic crystals

We consider Maxwell’s equations with periodic coefficients as it is usually done for the modeling of photonic crystals. Using Bloch/Floquet theory, the problem reduces in a standard way to a modification of the Maxwell cavity eigenproblem with periodic boundary conditions. Following [8], a modification of edge finite elements is considered for the approximation of the band gap. The method can be used with meshes of tetrahedrons or parallelepipeds. A rigorous analysis of convergence is presented, together with some preliminary numerical results in 2D, which fully confirm the robustness of the method. The analysis uses well established results on the discrete compactness for edge elements, together with new sharper interpolation estimates.