Residual‐based stabilization of the finite element approximation to the acoustic perturbation equations for low Mach number aeroacoustics

The acoustic perturbation equations (APE) are suitable to predict aerodynamic noise in the presence of a non‐uniform mean flow. As for any hybrid computational aeroacoustics approach, a first computational fluid dynamics simulation is carried out from which the mean flow characteristics and acoustic sources are obtained. In a second step, the APE are solved to get the acoustic pressure and particle velocity fields. However, resorting to the finite element method (FEM) for that purpose is not straightforward. Whereas mixed finite elements satisfying an appropriate inf–sup compatibility condition can be built in the case of no mean flow, that is, for the standard wave equation in mixed form, these are difficult to implement and their good performance is yet to be checked for more complex wave operators. As a consequence, strong simplifying assumptions are usually considered when solving the APE with FEM. It is possible to avoid them by resorting to stabilized formulations. In this work, a residual‐based stabilized FEM is presented for the APE at low Mach numbers, which allows one to deal with the APE convective and reaction terms in its full extent. The key of the approach resides in the design of the matrix of stabilization parameters. The performance of the formulation and the contributions of the different terms in the equations are tested for an acoustic pulse propagating in sheared‐solenoidal mean flow, and for the aeolian tone generated by flow past a two‐dimensional cylinder. Copyright © 2016 John Wiley & Sons, Ltd.     

Perimidine-based synthetic receptors for determination of copper(II) in water solution

Perimidine-based chelators 1 and 2 were prepared, and their structures were confirmed by ¹H and ¹³C NMR, MS spectroscopy and elemental analysis. These compounds were studied as specific synthetic receptors for the recognition of transition metal ions. They exhibited high affinity and selectivity towards Cu(II) ions. The conditional binding constants, linear dynamic range and detection limit were determined by UV–vis spectroscopy. These parameters demonstrated high potential of the prepared synthetic receptors for the recognition and determination of Cu(II) ions. The minimum detectable concentrations of Cu(II) ions for the synthetic receptors 1 and 2 were 270 and 75 nM (R ² = 0.9915 and 0.9964) in aqueous medium (water/DMSO; 99:1 (v/v)), respectively.     

Lie algebra type noncommutative phase spaces are Hopf algebroids

For a noncommutative configuration space whose coordinate algebra is the universal enveloping algebra of a finite-dimensional Lie algebra, it is known how to introduce an extension playing the role of the corresponding noncommutative phase space, namely by adding the commuting deformed derivatives in a consistent and nontrivial way; therefore, obtaining certain deformed Heisenberg algebra. This algebra has been studied in physical contexts, mainly in the case of the kappa-Minkowski space-time. Here, we equip the entire phase space algebra with a coproduct, so that it becomes an instance of a completed variant of a Hopf algebroid over a noncommutative base, where the base is the enveloping algebra.     

Algebraic preconditioning for Biot-Barenblatt poroelastic systems

Poroelastic systems describe fluid flow through porous medium coupled with deformation of the porous matrix. In this paper, the deformation is described by linear elasticity, the fluid flow is modelled as Darcy flow. The main focus is on the Biot-Barenblatt model with double porosity/double permeability flow, which distinguishes flow in two regions considered as continua. The main goal is in proposing block diagonal preconditionings to systems arising from the discretization of the Biot-Barenblatt model by a mixed finite element method in space and implicit Euler method in time and estimating the condition number for such preconditioning. The investigation of preconditioning includes its dependence on material coefficients and parameters of discretization.     

Strongly orthogonal geminals: size-extensive and variational reference states

Properties and some applications of strongly orthogonal geminals (APSG) are reviewed emphasizing the motivations for their use and their shortcomings. An overview presents some techniques capable of improving the APSG function.