QUADRATURE METHODS FOR HIGHLY OSCILLATORY SINGULAR INTEGRALS

We address the evaluation of highly oscillatory integrals,with power-law and logarithmic singularities.Such problems arise in numerical methods in engineering.Notably,the evaluation of oscillatory integrals dominates the run-time for wave-enriched boundary integral formulations for wave scattering,and many of these exhibit singularities.We show that the asymptotic behaviour of the integral depends on the integrand and its derivatives at the singular point of the integrand,the stationary points and the endpoints of the integral.A truncated asymptotic expansion achieves an error that decays faster for increasing frequency.Based on the asymptotic analysis,a Filon-type method is constructed to approximate the integral.Unlike an asymptotic expansion,the Filon method achieves high accuracy for both small and large frequency.Complex-valued quadrature involves interpolation at the zeros of polynomials orthogonal to a complex weight function.Numerical results indicate that the complex-valued Gaussian quadrature achieves the highest accuracy when the three methods are compared.However,while it achieves higher accuracy for the same number of function evaluations,it requires signi cant additional cost of computation of orthogonal polynomials and their zeros.     

Optimization of Biocompatibility for a Hydrophilic Biological Molecule Encapsulation System

Despite considerable advances in recent years, challenges in delivery and storage of biological drugs persist and may delay or prohibit their clinical application. Though nanoparticle-based approaches for small molecule drug encapsulation are mature, encapsulation of proteins remains problematic due to destabilization of the protein. Reverse micelles composed of decylmonoacyl glycerol (10MAG) and lauryldimethylamino-N-oxide (LDAO) in low-viscosity alkanes have been shown to preserve the structure and stability of a wide range of biological macromolecules. Here, we present a first step on developing this system as a future platform for storage and delivery of biological drugs by replacing the non-biocompatible alkane solvent with solvents currently used in small molecule delivery systems. Using a novel screening approach, we performed a comprehensive evaluation of the 10MAG/LDAO system using two preparation methods across seven biocompatible solvents with analysis of toxicity and encapsulation efficiency for each solvent. By using an inexpensive hydrophilic small molecule to test a wide range of conditions, we identify optimal solvent properties for further development. We validate the predictions from this screen with preliminary protein encapsulation tests. The insight provided lays the foundation for further development of this system toward long-term room-temperature storage of biologics or toward water-in-oil-in-water biologic delivery systems.     

Perfect matchings and Hamiltonian cycles in the preferential attachment model

In this paper, we study the existence of perfect matchings and Hamiltonian cycles in the preferential attachment model. In this model, vertices are added to the graph one by one, and each time a new vertex is created it establishes a connection with m random vertices selected with probabilities proportional to their current degrees. (Constant m is the only parameter of the model.) We prove that if , then asymptotically almost surely there exists a perfect matching. Moreover, we show that there exists a Hamiltonian cycle asymptotically almost surely, provided that . One difficulty in the analysis comes from the fact that vertices establish connections only with vertices that are “older” (ie, are created earlier in the process). However, the main obstacle arises from the fact that edges in the preferential attachment model are not generated independently. In view of that, we also consider a simpler setting—sometimes called uniform attachment—in which vertices are added one by one and each vertex connects to m older vertices selected uniformly at random and independently of all other choices. We first investigate the existence of perfect matchings and Hamiltonian cycles in the uniform attachment model, and then extend the argument to the preferential attachment version.     

Multi-parameter diagnostics for high-resolution in-situ measurements of single coal particle combustion

To study volatile combustion processes of single coal particles non-intrusive simultaneous multi-parameter measurements were performed. The experiment was carried out in a fully premixed flat flame burner with well-defined boundary conditions. For flame visualization high-speed luminescence imaging was combined with high-resolution high-speed OH-PLIF. To address particle size and shape a stereoscopic high-resolution backlight-illumination system was set up. Due to simultaneous recording of individual particle events the volatile combustion duration related to particle size, shape and velocity was measured. A comparison of luminescence imaging and OH-PLIF for flame visualization was investigated to define their application areas in coal combustion. The stereoscopic backlight-illumination setup was benchmarked to a well characterized bituminous coal. With a pixel resolution of ～2.5 µm fine particle contours were resolved. The particle diameter and eccentricity were evaluated by an ellipse approximation. The experimental setup can be used to investigate different coal ranks and biomass in N₂/O₂ and CO₂/O₂ atmospheres in future.     

Isomorph Invariance of Higher-Order Structural Measures in Four Lennard–Jones Systems

In the condensed liquid phase, both single- and multicomponent Lennard–Jones (LJ) systems obey the “hidden-scale-invariance” symmetry to a good approximation. Defining an isomorph as a line of constant excess entropy in the thermodynamic phase diagram, the consequent approximate isomorph invariance of structure and dynamics in appropriate units is well documented. However, although all measures of the structure are predicted to be isomorph invariant, with few exceptions only the radial distribution function (RDF) has been investigated. This paper studies the variation along isomorphs of the nearest-neighbor geometry quantified by the occurrence of Voronoi structures, Frank–Kasper bonds, icosahedral local order, and bond-orientational order. Data are presented for the standard LJ system and for three binary LJ mixtures (Kob–Andersen, Wahnström, NiY2). We find that, while the nearest-neighbor geometry generally varies significantly throughout the phase diagram, good invariance is observed along the isomorphs. We conclude that higher-order structural correlations are no less isomorph invariant than is the RDF.     

Shedding Light on the Interactions of Hydrocarbon Ester Substituents upon Formation of Dimeric Titanium(IV) Triscatecholates in DMSO Solution

The dissociation of hierarchically formed dimeric triple lithium bridged triscatecholate titanium(IV) helicates with hydrocarbyl esters as side groups is systematically investigated in DMSO. Primary alkyl, alkenyl, alkynyl as well as benzyl esters are studied in order to minimize steric effects close to the helicate core. The ¹H NMR dimerization constants for the monomer–dimer equilibrium show some solvent dependent influence of the side chains on the dimer stability. In the dimer, the ability of the hydrocarbyl ester groups to aggregate minimizes their contacts with the solvent molecules. Due to this, most solvophobic alkyl groups show the highest dimerization tendency followed by alkenyls, alkynyls and finally benzyls. Furthermore, trends within the different groups of compounds can be observed. For example, the dimer is destabilized by internal double or triple bonds due to π–π repulsion. A strong indication for solvent supported London dispersion interaction between the ester side groups is found by observation of an even/odd alternation of dimerization constants within the series of n-alkyls, n-Ω-alkenyls or n-Ω-alkynyls. This corresponds to the interaction of the parent hydrocarbons, as documented by an even/odd melting point alternation.     

Characterizing Polyoxovanadate-Alkoxide Clusters Using Vanadium K-Edge X-Ray Absorption Spectroscopy

A number of technologies would benefit from developing inorganic compounds and materials with specific electronic and magnetic exchange properties. Unfortunately, designing compounds with these properties is difficult because metal⋅⋅⋅metal coupling schemes are hard to predict and control. Fully characterizing communication between metals in existing compounds that exhibit interesting properties could provide valuable insight and advance those predictive capabilities. One such class of molecules are the series of Lindqvist iron-functionalized and hexavanadium polyoxovanadate-alkoxide clusters, which we characterized here using V K-edge X-ray absorption spectroscopy. Substantial changes in the pre-edge peak intensities were observed that tracked with the V 3d-electron count. The data also suggested substantial delocalization between the vanadium cations. Meanwhile, the Fe^III cations were electronically isolated from the polyoxovanadate core.     

Synthesis and Characterisation of Hierarchically Structured Titanium Silicalite-1 Zeolites with Large Intracrystalline Macropores

The successful synthesis of hierarchically structured titanium silicalite-1 (TS-1) with large intracrystalline macropores by steam-assisted crystallisation of mesoporous silica particles is reported. The macropore topology was imaged in 3D by using electron tomography and synchrotron radiation-based ptychographic X-ray computed tomography, revealing interconnected macropores within the crystals accounting for about 30 % of the particle volume. The study of the macropore formation mechanism revealed that the mesoporous silica particles act as a sacrificial macropore template during the synthesis. Silicon-to-titanium ratio of the macroporous TS-1 samples was successfully tuned from 100 to 44. The hierarchically structured TS-1 exhibited high activity in the liquid phase epoxidation of 2-octene with hydrogen peroxide. The hierarchically structured TS-1 surpassed a conventional nano-sized TS-1 sample in terms of alkene conversion and showed comparable selectivity to the epoxide. The flexible synthesis route described here can be used to prepare hierarchical zeolites with improved mass transport properties for other selective oxidation reactions.