Solitary Waves in Nonlinear Beam Equations: Stability,Fission and Fusion

We continue work by the second author and co-workers onsolitary wave solutions of nonlinear beam equations and their stabilityand interaction properties. The equations are partial differentialequations that are fourth-order in space and second-order in time.First, we highlight similarities between the intricate structure ofsolitary wave solutions for two different nonlinearities; apiecewise-linear term versus an exponential approximation to thisnonlinearity which was shown in earlier work to possess remarkablystable solitary waves. Second, we compare two different numericalmethods for solving the time dependent problem. One uses a fixed griddiscretization and the other a moving mesh method. We use these methodsto shed light on the nonlinear dynamics of the solitary waves. Earlywork has reported how even quite complex solitary waves appear stable,and that stable waves appear to interact like solitons. Here we show twofurther effects. The first effect is that large complex waves can, as aresult of roundoff error, spontaneously decompose into two simplerwaves, a process we call fission. The second is the fusion of twostable waves into another plus a small amount of radiation.     

Synthesis of Bimodal PVC Latexes by Emulsion Polymerization: An Experimental and Modeling Study

The onset and extent of secondary particle formation in the seeded emulsion polymerization of vinyl chloride were investigated by performing a series of seeded polymerizations at different concentrations of seed latex and surfactant. It was found that, in general, both the onset and the extent of secondary particle formation are determined not only by the rate of homogeneous nucleation, but also by the rates of particle coagulation. A comparison of methods to compute the evolution of the particle size distribution in vinyl chloride emulsion polymerization was also carried out. For growth processes, the widely-used pseudo-bulk model gives correct answers. For processes involving particle formation, on the other hand, this model cannot be used because it neglects, among others, the effects of nucleation and coagulation on the radical number distribution. To surmount this problem, we propose to use the zero-one-two model, for which the full population balance equations are given here.     

Diketopyrrolopyrrole Bis-Phosphonate Conjugate: A New Fluorescent Probe for In Vitro Bone Imaging

The synthesis of a conjugate molecule between an unusual red-fluorescent diketopyrrolopyrrole (DPP) unit and a bis-phosphonate (BP) precursor by a click-chemistry strategy to target bone tissue and monitor the interaction is reported. After thorough investigation, conjugation through a triazole unit between a γ-azido rather than a β-azido BP and an alkyne-functionalized DPP fluorophore group turned out to be the winning strategy. Visualization of the DPP-BP conjugate on osteoclasts and specific antiresorption activity were successfully demonstrated.     

An Experimental Investigation of the Impact of Gas Phase Prepolymerization of Propylene

A systematic investigation is carried out on the gas phase of propylene during the initial instants of polymerization. The results confirm the positive impact of small amounts of mineral oil on the initial reaction rate and morphology. It is shown that polymerizing under conditions of mild temperature and pressure alone are not enough to achieve the same result. It is found that the presence of mineral oil, and low temperature of polymerization can be used to control the morphology of polymer particles and to obtain high activity in the main reaction. If enough oil is used, moderate to high temperatures of prepolymerization are acceptable in terms of controlling morphology but can compromise the activity of the main polymerization. It is also observed that the way in which the oil is introduced has an impact on the kinetics and particle morphology. Separate addition of oil from the precatalyst gives rise to relatively flat kinetics during prepolymerization and highest rate during main polymerization. To account for the activity enhancement, a selective quench‐labeling study employing methyl propargyl ether shows that the presence of mineral oil appears to increase the fraction of active titanium by a factor of almost 2.     

The use of T2 distribution to study tumor extent and heterogeneity in head and neck cancer

Demarcation of the extent of malignant tissue is essential for planning a course of radiotherapy. MR images may provide additional information for delineating the target volume because of the large difference in the proton magnetic resonance relaxation times between normal and malignant tissues. In 13 patients with head and neck tumors the distribution of the proton spin-spin relaxation times, T2, at 1.5 Tesla were evaluated throughout the physician designated target volume and normal surrounding tissue. The T2 values within the tumor were always elevated compared with normal tissue, the highest values being in the nominal center of the tumor and decreasing toward the periphery. The regional distribution of T2 values within the tumor is a measure of the tissue heterogeneity within the tumor volume. In addition, the large differences in T2 relaxation times between normal and disease tissues were used in a computer algorithm to automatically demarcate the boundary of abnormal tissue in each axial MRI section. This potentially could significantly expedite the time required to identify the target volume on multiple sections and thus remove one of the major time constraints for 3D treatment planning.     

A novel derivative for the assessment of urinary and salivary nitrate using gas chromatography/mass spectrometry

Previous gas chromatography/mass spectrometry (GC/MS) methods for determining nitrate in biological samples involve either hazardous chemicals or produce multiple isomers that can be difficult to quantitate. Modification of these methods, by the nitration of mesitylene instead of benzene and in the presence of trifluoroacetic anhydride rather than sulphuric acid, should enable simple isotopic quantitation for use in tracer studies, for example, in the measurement of nitric oxide production. Desiccated urine and saliva samples, in addition to aqueous labelled and unlabelled nitrate standards, were treated with trifluoroacetic anhydride and mesitylene at 70°C for 1 h, cooled, then sequentially washed with deionised water and aqueous sodium bicarbonate. The solution of nitromesitylene in mesitylene was separated, dried and analysed by GC/MS. The full mass spectra exhibited abundant ions at m/z 165 and 166 corresponding to the unlabelled and labelled molecular species of nitromesitylene, respectively. Selected ion monitoring of these masses for a series of gravimetrically prepared standards indicated good agreement with isotopic enrichments in the range 0.0625–5 mole % excess, and at nitrate concentrations within the physiological range of 0.078–2 mmol/L. Derivatised samples were stable with respect to isotopic enrichments and nitrate concentrations at −20°C for up to 21 days and exhibited excellent repeatability. Nitration of mesitylene proved to be a simple and rapid method for the measurement of isotope ratios in aqueous nitrates by GC/MS, which has applications in tracer studies and in concentration determinations by isotope dilution techniques for nitric oxide production. Copyright © 2008 John Wiley & Sons, Ltd.     

Structure and morphology of the reaction fronts during the formation of MgAl2O4 thin films by solid state reaction between R-cut sapphire substrates and MgO films

The thin-film spinel-forming solid state reaction between Al₂O₃ and MgO has been studied under initially non-coherent conditions. MgO films in (001) orientation on -cut sapphire single crystals were heated at 1100°C for 30 min or 1h. The film/substrate reaction proceeds via cation counterdiffusion as was revealed by a marker experiment. The MgAl₂O₄ films formed were predominantly (001) oriented, with an additional systematic tilt of about 5° of the spinel lattice around the [010] axis. The structure of the Al₂O₃ /MgAl₂O₄(001) and MgAl₂O₄(001)/MgO(001) reaction fronts has been investigated on cross section samples by high-resolution electron microscopy. It appeared that after starting from an incoherent interface, the Al₂O₃ /MgAl₂O₄(001) front assumes an almost fully coherent structure during the reaction. As a result the lattice misfit is reduced to 1%, and interfacial ledges are formed. The latter most probably play an active role in the necessary c.p.h. f.c.c. reconstruction of the oxygen sublattice. The MgAl₂O₄(001)/MgO(001) reaction front consists of coherent regions divided by misfit dislocations. During the reaction the former run ahead whereas the latter lag behind. As a result the morphology of the reaction front is bowed. The results confirm earlier observations of Carter and Schmalzried of the semicoherent Al₂O₃(00.1)/CoAl₂O₄(111) interface, thus strongly supporting the conclusion of a fundamental new phase transformation mechanism specific to oxide systems.Presented at the workshop on High-Voltage and High-Resolution Electron Microscopy, February 21–24, 1994, Stuttgart, Germany.