Editorial

Plasmas and Polymers -     

A sequential method for a class of box constrained quadratic programming problems

The aim of this paper is to propose an algorithm, based on the optimal level solutions method, which solves a particular class of box constrained quadratic problems. The objective function is given by the sum of a quadratic strictly convex separable function and the square of an affine function multiplied by a real parameter. The convexity and the nonconvexity of the problem can be characterized by means of the value of the real parameter. Within the algorithm, some global optimality conditions are used as stopping criteria, even in the case of a nonconvex objective function. The results of a deep computational test of the algorithm are also provided. This paper has been partially supported by M.I.U.R.     

Numerical Scaling Invariance Applied to the van der Pol Model

In this study we use the van der Pol model to explain a novel numerical application of scaling invariance. The model in point is not invariant to a scaling group of transformations, but by introducing an embedding parameter we are able to recover it from an extended model which is invariant to an extended scaling group. As well known, within a similarity analysis we can define a family of solutions from a computed one, so that the solution of a target problem can be obtained by rescaling the solution of a reference problem. The main idea is to use scaling invariance and numerical analysis to find a reference problem easier to solve, from a numerical viewpoint, than the target problem. This allows us to save human efforts and computational resources every time we have to solve a challenging problem. We test our approach using three stiff solvers available within the most recent releases of MATLAB. Independently from the solver used, by employing the described scaling invariance we are able to significantly reduce the computational cost of the numerical solution of the van der Pol model.      

Second order homological obstructions on real algebraic manifolds

Let Y be a compact nonsingular real algebraic set whose homology classes (over Z/2) are represented by Zariski closed subsets. It is well known that every smooth map from a compact smooth manifold to Y is unoriented bordant to a regular map. In this paper, we show how to construct smooth maps from compact nonsingular real algebraic sets to Y not homotopic to any regular map starting from a nonzero homology class of Y of positive degree. We use these maps to obtain obstructions to the existence of local algebraic tubular neighborhoods of algebraic submanifolds of Rn and to study some algebro-homological properties of rational real algebraic manifolds.     

Nonlinear modelling of data in photomineralization kinetics of organic micropollutants by photocatalytic membranes immobilizing titanium dioxide in membrane reactors

Kinetic fitting of substrate disappearance and of total organic carbon (TOC) mineralization of organic micropollutants, in water and air, by photocatalytic membranes immobilizing titanium dioxide, was carried out. A model was used in which mineralization of substrate to CO₂ is supposed to occur, with kinetic constant k₁, through one single intermediate, mediating the behaviour of all the numerous real intermediates formed in the path to CO₂, kinetic constant of formation of the latter being k₂. A competitive Langmuirian‐type adsorption of both substrate and ‘intermediate’ was also supposed to be operative, as expressed by pseudo‐thermodynamic constants K₁ and K₂ respectively, these constants possessing a, partly at least, kinetic significance. Nonlinear models could be fitted to data by using the least‐squares method. The very satisfactory matching is shown for the laboratory‐scale mineralization kinetics of methane, as model molecule of aliphatic contaminants, both in the gas phase and in aqueous solution. Furthermore, in pilot plant experiments, using phenol, as model molecule of aromatics, modelling of quantum yields was carried out, as a function of concentration and of adsorbed radiant power. Kinetics of hydroxyl radicals reacting between themselves, leading to hydrogen peroxide, other than with substrate or intermediates leading to mineralization, was considered, paralleled by a second competition kinetics due to superoxide anion radical and its conjugate acid, equally leading to mineralization. In this model the contribution of hydroxyl radicals to mineralization decreases with irradiance, while the contribution of superoxide anion radical and its conjugate acid increases. If the regression equations of these two contributions are considered together, in a linear combination, the surface model perfectly fits the experimental data. Copyright © 2008 John Wiley & Sons, Ltd.     

Absolute Antioxidant Activity of Five Phenol-Rich Essential Oils

Essential oils (EOs) have promising antioxidant activities which are gaining interest as natural alternatives to synthetic antioxidants in the food and cosmetic industries. However, quantitative data on chain-breaking activity and on the kinetics of peroxyl radical trapping are missing. Five phenol-rich EOs were analyzed by GC-MS and studied by oxygen-uptake kinetics in inhibited controlled autoxidations of reference substrates (cumene and squalene). Terpene-rich Thymus vulgaris (thymol 4%; carvacrol 33.9%), Origanum vulgare, (thymol 0.4%; carvacrol 66.2%) and Satureja hortensis, (thymol 1.7%; carvacrol 46.6%), had apparent k_inh (30 °C, PhCl) of (1.5 ± 0.3) × 10⁴, (1.3 ± 0.1) × 10⁴ and (1.1 ± 0.3) × 10⁴ M⁻¹s⁻¹, respectively, while phenylpropanoid-rich Eugenia caryophyllus (eugenol 80.8%) and Cinnamomum zeylanicum, (eugenol 81.4%) showed apparent k_inh (30 °C, PhCl) of (5.0 ± 0.1) × 10³ and (4.9 ± 0.3) × 10³ M⁻¹s⁻¹, respectively. All EOs already granted good antioxidant protection of cumene at a concentration of 1 ppm (1 mg/L), the duration being proportional to their phenolic content, which dictated their antioxidant behavior. They also afforded excellent protection of squalene after adjusting their concentration (100 mg/L) to account for the much higher oxidizability of this substrate. All investigated EOs had k_inh comparable to synthetic butylated hydroxytoluene (BHT) were are eligible to replace it in the protection of food or cosmetic products.     

Bulk and shear mechanical loss of titania-doped tantala

We report on the mechanical loss from bulk and shear stresses in thin film, ion beam deposited, titania-doped tantala. The numerical values of these mechanical losses are necessary to fully calculate the Brownian thermal noise in precision optical cavities, including interferometric gravitational wave detectors like LIGO. We found the values from measuring the normal mode mechanical quality factors, Q's, in the frequency range of about 2000-10,000 Hz, of silica disks coated with titania-doped tantala coupled with calculating the elastic energy in shear and bulk stresses in the coating using a finite element model. We fit the results to both a frequency independent and frequency dependent model and find ${?}_{\mathrm{shear}}=(8.3\pm 1.1)\times {10}^{?4}$, ${?}_{\mathrm{bulk}}=(6.6\pm 3.8)\times {10}^{?4}$ with a frequency independent model and ${?}_{\mathrm{shear}}\left(f\right)=(5.0\pm 0.7)\times {10}^{?4}+(5.4\pm 1.1)\times {10}^{?8}f$, ${?}_{\mathrm{bulk}}\left(f\right)=(11\pm 2.8)\times {10}^{?4}?(8.7\pm 4.7)\times {10}^{?8}f$ with a frequency dependent (linear) model. The ratio of these values suggest that modest improvement in the coating thermal noise may be possible in future gravitational wave detector optics made with titania-doped tantala as the high index coating material by optimizing the coating design to take advantage of the two different mechanical loss angles.     

One-Dimensional Fluids with Positive Potentials

We study a class of one-dimensional classical fluids with penetrable particles interacting through positive, purely repulsive, pair-potentials. Starting from some lower bounds to the total potential energy, we draw results on the thermodynamic limit of the given model.     

Parallel transport and defects on nematic shells

Nematic shells are thin films of nematic liquid crystal deposited on the boundary of colloidal particles, where liquid crystal molecules may freely glide, while remaining tangent to the surface substrate. The surface nematic order is described here by an appropriate tensor field Q, which vanishes wherever a defect occurs in the molecular order. We show how the classical concept of parallel transport on a manifold introduced by Levi-Civita can be adapted to this setting to define the topological charge m of a defect. We arrive at a simple formula to compute m from a generic representation of Q. In a number of separate appendices, we revisit in a unified language several, apparently disparate applications of Levi-Civita’s parallel transport.