An efficient discontinuous Galerkin method for aeroacoustic propagation

An efficient discontinuous Galerkin formulation is applied to the solution of the linearized Euler equations and the acoustic perturbation equations for the simulation of aeroacoustic propagation in two‐dimensional and axisymmetric problems, with triangular and quadrilateral elements. To improve computational efficiency, a new strategy of variable interpolation order is proposed in addition to a quadrature‐free approach and parallel implementation. Moreover, an accurate wall boundary condition is formulated on the basis of the solution of the Riemann problem for a reflective wall. Time discretization is based on a low dissipation formulation of a fourth‐order, low storage Runge–Kutta scheme. Along the far‐field boundaries a perfectly matched layer boundary condition is used. For the far‐field computations, the integral formulation of Ffowcs Williams and Hawkings is coupled with the near‐field solver. The efficiency and accuracy of the proposed variable order formulation is assessed for realistic geometries, namely sound propagation around a high‐lift airfoil and the Munt problem. Copyright © 2011 John Wiley & Sons, Ltd.     

Semi‐preparative LC‐SPE‐cryoflow NMR for impurity identifications: use of mother liquor as a better source of impurities

Unambiguous structural elucidation of active pharmaceutical ingredients (API) impurities is a particularly challenging necessity of pharmaceutical development, particularly if the impurities are low level (0.1% level). In many cases, this requires acquiring high‐quality NMR data on a pure sample of each impurity. High‐quality, high signal‐to‐noise (S/N) one‐ and two‐dimensional NMR data can be obtained using liquid chromatography‐solid phase extraction‐cryoflow NMR (LC‐SPE‐cryoflow NMR) with a combination of semi‐preparative column for separation and mother liquor as a source of concentrated impurities. These NMR data, in conjunction with mass spectrometry data, allowed for quick and unambiguous structural elucidations of four impurities found at low level in the crystallized API but found at appreciable levels in the mother liquor that was used as the source for these impurities. These data show that semi‐preparative columns can be used at lower than ideal flow rates to facilitate trapping of HPLC components for LC‐SPE‐cryoflow NMR analysis without compromising chromatographic resolution. Also, despite the complex chromatography encountered with the use of mother liquor as a source of impurities, acceptably pure analytes were obtained for acquiring NMR data for unambiguous structure elucidations. Copyright © 2013 John Wiley & Sons, Ltd.     

Low coercive field and conducting nanocomposite formed by Fe3O4 and poly(thiophene)

Magnetite and poly(thiophene) composites have been produced by in situ monomer oxidation. Fourier transform infrared (FTIR) and X-ray diffraction (XRD) confirmed the presence of Fe₃O₄ as particle agglomerates ranging from 15 to ca. 54 nm in size. Transmission electron micrographs (TEMs) revealed a face-to-face structure in both the pure magnetite and the nanocomposite. Typical superparamagnetic (ferrimagnetic) curves have been observed, whereas the relatively weak magnetic field employed in measurement, 200 Oe, was sufficient to split the curves completely. Zero field cooling (ZFC) and field cooling (FC) curves coincide only above room temperature, indicating that the characteristic blocking temperature (T_B) for superparamagnetic particles in this assembly is above room temperature.     

Beyond a solvent: the roles of 1-butyl-3-methylimidazolium chloride in the acid-catalysis for cellulose depolymerisation

In this report, 1-butyl-3-methylimidazolium chloride ([C₄C₁im]Cl) is demonstrated to enhance the kinetics of acid-catalysed hydrolysis of 1,4-β-glucans in binary solvent mixtures. [C₄C₁im]Cl plays other roles in the reaction beyond acting as a solvent for cellulose, as currently accepted. In fact, the presence of the IL increases the Hammett acidity of the catalyst dissolved in the reaction medium. The kinetic data from cellobiose and cellulose hydrolysis directly correlate with the acid strength found for p-toluenesulfonic acid in the different reaction media studied here. The current report identifies neglected, but yet very important phenomena occurring in cellulose depolymerisation.     

Exact Penalty Functions for Nonlinear Integer Programming Problems

In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem in a continuous space.     

Solving Max-Cut to optimality by intersecting semidefinite and polyhedral relaxations

We present a method for finding exact solutions of Max-Cut, the problem of finding a cut of maximum weight in a weighted graph. We use a Branch-and-Bound setting that applies a dynamic version of the bundle method as bounding procedure. This approach uses Lagrangian duality to obtain a “nearly optimal” solution of the basic semidefinite Max-Cut relaxation, strengthened by triangle inequalities. The expensive part of our bounding procedure is solving the basic semidefinite relaxation of the Max-Cut problem, which has to be done several times during the bounding process. We review other solution approaches and compare the numerical results with our method. We also extend our experiments to instances of unconstrained quadratic 0–1 optimization and to instances of the graph equipartition problem. The experiments show that our method nearly always outperforms all other approaches. In particular, for dense graphs, where linear programming-based methods fail, our method performs very well. Exact solutions are obtained in a reasonable time for any instance of size up to n = 100, independent of the density. For some problems of special structure we can solve even larger problem classes. We could prove optimality for several problems of the literature where, to the best of our knowledge, no other method is able to do so. Supported in part by the EU project Algorithmic Discrete Optimization (ADONET), MRTN-CT-2003-504438.     

Concave programming for minimizing the zero-norm over polyhedral sets

Given a non empty polyhedral set, we consider the problem of finding a vector belonging to it and having the minimum number of nonzero components, i.e., a feasible vector with minimum zero-norm. This combinatorial optimization problem is NP-Hard and arises in various fields such as machine learning, pattern recognition, signal processing. One of the contributions of this paper is to propose two new smooth approximations of the zero-norm function, where the approximating functions are separable and concave. In this paper we first formally prove the equivalence between the approximating problems and the original nonsmooth problem. To this aim, we preliminarily state in a general setting theoretical conditions sufficient to guarantee the equivalence between pairs of problems. Moreover we also define an effective and efficient version of the Frank-Wolfe algorithm for the minimization of concave separable functions over polyhedral sets in which variables which are null at an iteration are eliminated for all the following ones, with significant savings in computational time, and we prove the global convergence of the method. Finally, we report the numerical results on test problems showing both the usefulness of the new concave formulations and the efficiency in terms of computational time of the implemented minimization algorithm.