Numerical experiments with an inexact Jacobian trust-region algorithm

We present the adaptation and implementation of a composite-step trust region algorithm, developed in (Walther, SIAM J. Optim. 19(1):307–325, 2008), that incorporates the approximation of the Jacobian of the equality constraints with a specialized quasi-Newton method. The forming and/or factoring of the exact Jacobian in each optimization step is avoided. Hence, the presented approach is especially well suited for equality constrained optimization problems where the Jacobian of the constraints is dense.     

Bicyclic Guanidine Promoted Mechanistically Divergent Depolymerization and Recycling of a Biobased Polycarbonate

We here report the organocatalytic and temperature-controlled depolymerization of biobased poly(limonene carbonate) providing access to its trans-configured cyclic carbonate as the major product. The base TBD (1,5,7-triazabicyclo[4.4.0]dec-5-ene) offers a unique opportunity to break down polycarbonates via end-group activation or main chain scission pathways as supported by various controls and computational analysis. These energetically competitive processes represent an unprecedented divergent approach to polycarbonate recycling. The trans limonene carbonate can be converted back to its polycarbonate via ring-opening polymerization using the same organocatalyst in the presence of an alcohol initiator, offering thus a potential circular and practical route for polycarbonate recycling.     

Carbon-based materials applied to the development of chemically modified sensors: Trends to environmental applications**

Nowadays, carbon-based materials applied to the development of chemically modified sensors have been highlighted once they can generate methods with high sensitivity, stability, conductivity, accuracy and low cost. Hence, these sensors have been used in environmental monitoring in aneco-friendlyy, sensitive, fast, efficient, inexpensive and robust way. In this review, firstly we described about carbon-based materials and their derivatives, followed by the chemically modified carbon-based sensors manufacturing overview and their applications in environmental analytical chemistry related to inorganic and organic compounds determinations. Future perspectives on trends of the carbon-based materials applications in the sensor modifications are also described.     

ZnO based planar and micropillar resonators

In this paper we report on planar and microscopic cylindrical resonators with ZnO as the cavity and active medium surrounded with ZrO₂/MgO Bragg reflectors. We have observed resonator behaviour of these structures and, for the planar resonators, exciton–polariton coupling with a mode splitting of about 50 meV.     

Phase transitions for random walk asymptotics on free products of groups

Suppose we are given finitely generated groups Γ₁,…,Γ_m equipped with irreducible random walks. Thereby we assume that the expansions of the corresponding Green functions at their radii of convergence contain only logarithmic or algebraic terms as singular terms up to sufficiently large order (except for some degenerate cases). We consider transient random walks on the free product Γ₁* … *Γ_m and give a complete classification of the possible asymptotic behaviour of the corresponding n‐step return probabilities. They either inherit a law of the form ?^nδn log n from one of the free factors Γ_i or obey a ?^nδn^?3/2‐law, where ? < 1 is the corresponding spectral radius and δ is the period of the random walk. In addition, we determine the full range of the asymptotic behaviour in the case of nearest neighbour random walks on free products of the form $\mathbb{Z}^{d_1}\ast \ldots \ast \mathbb{Z}^{d_m}Suppose we are given finitely generated groups Γ₁,…,Γ_m equipped with irreducible random walks. Thereby we assume that the expansions of the corresponding Green functions at their radii of convergence contain only logarithmic or algebraic terms as singular terms up to sufficiently large order (except for some degenerate cases). We consider transient random walks on the free product Γ₁* … *Γ_m and give a complete classification of the possible asymptotic behaviour of the corresponding n‐step return probabilities. They either inherit a law of the form ?^nδn log n from one of the free factors Γ_i or obey a ?^nδn^?3/2‐law, where ? < 1 is the corresponding spectral radius and δ is the period of the random walk. In addition, we determine the full range of the asymptotic behaviour in the case of nearest neighbour random walks on free products of the form $\mathbb{Z}^{d_1}\ast \ldots \ast \mathbb{Z}^{d_m}$. Moreover, we characterize the possible phase transitions of the non‐exponential types n log n in the case Γ₁ * Γ₂. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 2012     

A viability theorem for set-valued states in a Hilbert space

Applications in robust control problems and shape evolution motivate the mathematical interest in control problems whose states are compact (possibly non-convex) sets rather than vectors. This leads to evolutions in a basic set which can be supplied with a metric (like the well-established Pompeiu–Hausdorff distance), but it does not have an obvious linear structure. This article extends differential inclusions with state constraints to compact-valued states in a separable Hilbert space H. The focus is on sufficient conditions such that a given constraint set (of compact subsets) is viable a.k.a. weakly invariant. Our main result extends the tangential criterion in the well-known viability theorem (usually for differential inclusions in a vector space) to the metric space of non-empty compact subsets of H.     

Donor-like defects in ZnO substrate materials and ZnO thin films

We have investigated donor-like defects in ZnO substrate material grown by three different methods, and in epitaxial ZnO thin films grown on sapphire by pulsed laser deposition. Temperature dependent Hall effect measurements yield information about dominant donors. The thermal activation energies lie in a wide range from about 20 meV to about 370 meV. Deep level transient spectroscopy is used to obtain parameters of deep donor-like defects. For that, a high-speed diode contact configuration was laid out for the epitaxial thin films in order to determine the defect parameters with high precision. The identified levels are E1, E3 and E4, though the level E4 is observed only in single crystals grown by seeded chemical vapor transport. PACS 72.10.Fk; 72.80.Ey; 73.50.-h     

Extended X-ray absorption fine structure studies of thulium doped GaN epilayers

The local structure of Tm³⁺ ions incorporated into GaN epilayers was studied by means of Extended X-ray Absorption Fine Structure. The samples were doped either in situ during growth by Molecular Beam Epitaxy or by ion implantation of layers grown by Metal Organic Chemical Vapour Deposition. The implantation was done at ion energy of 300 keV and different nominal fluences of 3×10¹⁵, 4×10¹⁵ cm⁻² and 5×10¹⁵ cm⁻². The concentration of Tm in the samples studied was measured by Wavelength Dispersive X-ray analysis. For the in situ doped sample with concentration of 0.5%, and for all of the implanted samples, Tm was found on the Ga site in GaN. The ion implanted sample and an in situ doped sample with a similar concentration of Tm showed the same local structure, which suggests that the lattice site occupied by Tm does not depend on the doping method. When the average Tm concentration for in situ doped samples is increased to 1.2% and 2.0%, Tm is found to occupy the Ga substitutional site and the presence of a substantial number of Tm ions in the second coordination sphere indicates dopant clustering in the films. The formation of pure TmN clusters was found in an in situ doped sample with a dopant concentration of 3.4%.     

Size-fractionated characterization and quantification of nanoparticle release rates from a consumer spray product containing engineered nanoparticles

This study describes methods developed for reliable quantification of size- and element-specific release of engineered nanoparticles (ENP) from consumer spray products. A modified glove box setup was designed to allow controlled spray experiments in a particle-minimized environment. Time dependence of the particle size distribution in a size range of 10–500 nm and ENP release rates were studied using a scanning mobility particle sizer (SMPS). In parallel, the aerosol was transferred to a size-calibrated electrostatic TEM sampler. The deposited particles were investigated using electron microscopy techniques in combination with image processing software. This approach enables the chemical and morphological characterization as well as quantification of released nanoparticles from a spray product. The differentiation of solid ENP from the released nano-sized droplets was achieved by applying a thermo-desorbing unit. After optimization, the setup was applied to investigate different spray situations using both pump and gas propellant spray dispensers for a commercially available water-based nano-silver spray. The pump spray situation showed no measurable nanoparticle release, whereas in the case of the gas spray, a significant release was observed. From the results it can be assumed that the homogeneously distributed ENP from the original dispersion grow in size and change morphology during and after the spray process but still exist as nanometer particles of size <100 nm. Furthermore, it seems that the release of ENP correlates with the generated aerosol droplet size distribution produced by the spray vessel type used. This is the first study presenting results concerning the release of ENP from spray products.