Iterative operator‐splitting methods for nonlinear differential equations and applications

In this article, we consider iterative operator‐splitting methods for nonlinear differential equations with bounded and unbounded operators. The main feature of the proposed idea is the embedding of Newton's method for solving the split parts of the nonlinear equation at each step. The convergence properties of such a mixed method are studied and demonstrated. We confirm with numerical applications the effectiveness of the proposed scheme in comparison with the standard operator‐splitting methods by providing improved results and convergence rates. We apply our results to deposition processes. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1026–1054, 2011     

Simultaneous determination of perfluoroalkyl phosphonates, carboxylates, and sulfonates in drinking water

A trace analytical method based on high performance liquid chromatography coupled to quadrupole time-of-flight high resolution mass spectrometry was developed for simultaneous determination of perfluoroalkyl phosphonates (PFPAs, carbon chain lengths C6,8,10), perfluoroalkyl carboxylates (PFCAs, C5-12), and perfluoroalkyl sulfonates (PFSAs, C4,6,8,10) in drinking water (tap water). Analytes were enriched on a mixed mode co-polymeric sorbent (C8+quaternary amine) using solid phase extraction. Chromatographic separation was achieved on a Zorbax Extend C18 reversed phase column using a mobile phase gradient consisting of water, methanol, and acetonitrile containing 2mM ammonium acetate and 5 mM 1-methyl piperidine. The mass spectrometer was operated in electrospray negative ion mode. Use of 1-methyl piperidine in the mobile phase resulted in a significant increase in instrument sensitivity for PFPAs through improved chromatographic resolution, background suppression, and increased ionization efficiency. Method detection limits for extraction of 500 mL tap water were in the ranges of 0.095-0.17 ng/L, 0.027-0.17 ng/L, and 0.014-0.052 ng/L for PFPAs, PFCAs, and PFSAs, respectively. Whole method recoveries at a spiking level of 0.5 ng/L to 500 mL HPLC grade water were 40-56%, 56-97%, and 55-77% for PFPAs, PFCAs, and PFSAs, respectively. A matrix effect (signal enhancement) was observed in the detection of PFPAs in tap water extracts, leading to calculated recoveries of 249-297% at a 0.5 ng/L spiking level. This effect resulted in an additional improvement of method sensitivity for PFPAs. To compensate for the matrix effect, PFPAs in tap water were quantified using matrix-matched and extracted calibration standards. The method was successfully applied to the analysis of drinking water collected from six European countries. PFPAs were not detected except for perfluorooctyl phosphonate (PFOPA) at close to the detection limit of 0.095 ng/L in two water samples from Amsterdam, the Netherlands. Highest levels were found for perfluorobutane sulfonate (PFBS, 18.8 ng/L) and perfluorooctanoate (PFOA, 8.6 ng/L) in samples from Amsterdam as well as for perfluorooctane sulfonate (PFOS, 8.8 ng/L) in tap water from Stockholm, Sweden.     

Neighborhood Relationships of Widely Distributed and Irregularly Shaped Particles in Partially Dewatered Filter Cakes

A more thorough understanding of the properties of bulk material structures in solid–liquid separation processes is essential to understand better and optimize industrially established processes, such as cake filtration, whose process outcome is mainly dependent on the properties of the bulk material structure. Here, changes of bulk properties like porosity and permeability can originate from local variations in particle size, especially for non-spherical particles. In this study, we mix self-similar fractions of crushed, irregularly shaped Al₂O₃ particles (20 to 90 µm and 55 to 300 µm) to bimodal distributions. These mixtures vary in volume fraction of fines (0, 20, 30, 40, 50, 60 and 100 vol.%). The self-similarity of both systems serves the improved parameter correlation in the case of multimodal distributed particle systems. We use nondestructive 3D X-ray microscopy to capture the filter cake microstructure directly after mechanical dewatering, whereby we give particular attention to packing structure and particle–particle relationships (porosity, coordination number, particle size and corresponding hydraulic isolated liquid areas). Our results reveal widely varying distributions of local porosity and particle contact points. An average coordination number (here 5.84 to 6.04) is no longer a sufficient measure to describe the significant bulk porosity variation (in our case, 40 and 49%). Therefore, the explanation of the correlation is provided on a discrete particle level. While individual particles?<?90 µm had only two or three contacts, others?>?100 µm took up to 25. Due to this higher local coordination number, the liquid load of corresponding particles (liquid volume/particle volume) after mechanical dewatering increases from 0.48 to 1.47.

     

Realization of a Framework for Simulation-Based Large-Scale Shape Optimization Using Vertex Morphing

Journal of Optimization Theory and Applications - There is a significant tendency in the industry for automation of the engineering design process. This requires the capability of analyzing an...     

Pulsed laser surface fragmentation and mid-infrared laser spectroscopy for remote detection of explosives

Stand-off technology for the remote detection of explosives and their traces on contaminated surfaces is a field of research that has recently gained much interest. Optical methods are well established in applications for counterterrorism because they facilitate analysis without contact between human being and hazardous materials. In this paper, to our knowledge for the first time, a remote stand-off detection system is developed by combination of pulsed laser fragmentation and pulsed mid-infrared laser absorption spectroscopy. Since the absorption of explosives is more efficient for infrared wavelengths laser radiation in the eye safe region around λ=1.47 μm rather than the conventional Nd:YAG laser line at λ=1.06 μm is preferred for the fragmentation. Generated product gases such as nitric oxide are probed by a synchronized distributed feedback quantum cascade laser (DFB-QCL) at λ≈5.3 μm. The ratio of NO and NO₂ is a measure to distinguish between energetic and non-energetic materials. PACS 42.62.Fi; 07.07.DF; 42.55.Px     

Furo[2,3‐d]pyrimidines and Oxazolo[5,4‐d]pyrimidines as Inhibitors of Receptor Tyrosine Kinases (RTK)

Receptor tyrosine kinases such as VEGFR2 (vascular endothelial growth factor receptor 2, KDR) or EGFR (epidermal growth factor receptor) play crucial roles in a variety of diseases, such as cancer. Recently, some pyrrolopyrimidines were shown to be potent EGFR inhibitors. Therefore, new types of oxazolo[5,4‐d]pyrimidines and furo[2,3‐d]pyrimidines were synthesized (Schemes 1 and 2). Appropriately substituted derivatives of these classes of compounds inhibited VEGFR2 and EGFR with IC₅₀ values in the low nanomolar range (see Table). Generally, the furopyrimidines were somewhat more active than the oxazolopyrimidines. The best inhibitors, 20m, 20p , and 20r , had an IC₅₀ of 3 nM towards EGFR and showed a good selectivity, being distinctly less active towards VEGFR2.     

Vortex penetration depth of κ-(ET)2Cu[N(CN)2]Br

The magnetic field dependence of the in-plane penetration depth λ_|(H) for single crystal κ-(ET)₂Cu[N(CN)₂]Br has been measured at 3, 9.6, and 36 MHz. Over a limited range, λ_| scales with a characteristic field H^*(T) that coincides with a shoulder in the λ_| vs. H curves. Above that field, λ_| increases sharply toward a second inflection point at H^**(T) that coincides with is close to the irreversibility line measured by magnetization. For fields larger than H^** the penetration depth diverges, suggesting that the vortex lattice has melted. The field dependence at one frequency agrees qualitatively with a model of pinned vortices at low fields giving way to flux flow at higher fields. However, the observed frequency dependence deviates significantly from the predictions of this model, suggesting that collective effects play a major role. Our technique also yields a new measurement for the interplane penetration depth λ 300 μm, implying an anisotropy λ/λ_| > 200.     

Hamiltonian dynamics on convex symplectic manifolds

We study the dynamics of Hamiltonian diffeomorphisms on convex symplectic manifolds. To this end we first establish an explicit isomorphism between the Floer homology and the Morse homology of such a manifold, and then use this isomorphism to construct a biinvariant metric on the group of compactly supported Hamiltonian diffeomorphisms analogous to the metrics constructed by Viterbo, Schwarz and Oh. These tools are then applied to prove and reprove results in Hamiltonian dynamics. Our applications comprise a uniform lower estimate for the slow entropy of a compactly supported Hamiltonian diffeomorphism, the existence of infinitely many non-trivial periodic points of a compactly supported Hamiltonian diffeomorphism of a subcritical Stein manifold, new cases of the Weinstein conjecture, and, most noteworthy, new existence results for closed trajectories of a charge in a magnetic field on almost all small energy levels. We shall also obtain some new Lagrangian intersection results. Partially supported by the Swiss National Foundation. Supported by the Swiss National Foundation and the von Roll Research Foundation.