Global Wave-Front Properties for Fourier Integral Operators and Hyperbolic Problems

We illustrate the composition properties for an extended family of \({\text {SG}}\) Fourier integral operators. We prove continuity results on modulation spaces, and study mapping properties of global wave-front sets for such operators. These extend classical results to more general situations. For example, there are no requirements on homogeneity for the phase functions. Finally, we apply our results to the study of the propagation of singularities, in the context of modulation spaces, for the solutions to the Cauchy problems for the corresponding linear hyperbolic operators.     

Atmospheric chemistry of a model biodiesel fuel, CH3C(O)O(CH2)2OC(O)CH3: kinetics, mechanisms, and products of Cl atom and OH radical initiated oxidation in the presence and absence of NOx

Relative rate techniques were used to study the kinetics of the reactions of Cl atoms and OH radicals with ethylene glycol diacetate, CH3C(O)O(CH2)2OC(O)CH3, in 700 Torr of N2/O2 diluent at 296 K. The rate constants measured were k(Cl + CH3C(O)O(CH2)2OC(O)CH3) = (5.7 +/- 1.1) x 10(-12) and k(OH + CH3C(O)O(CH2)2OC(O)CH3) = (2.36 +/- 0.34) x 10(-12) cm3 molecule-1 s-1. Product studies of the Cl atom initiated oxidation of ethylene glycol diacetate in the absence of NO in 700 Torr of O2/N2 diluent at 296 K show the primary products to be CH3C(O)OC(O)CH2OC(O)CH3, CH3C(O)OC(O)H, and CH3C(O)OH. Product studies of the Cl atom initiated oxidation of ethylene glycol diacetate in the presence of NO in 700 Torr of O2/N2 diluent at 296 K show the primary products to be CH3C(O)OC(O)H and CH3C(O)OH. The CH3C(O)OCH2O* radical is formed during the Cl atom initiated oxidation of ethylene glycol diacetate, and two loss mechanisms were identified: reaction with O2 to give CH3C(O)OC(O)H and alpha-ester rearrangement to give CH3C(O)OH and HC(O) radicals. The reaction of CH3C(O)OCH2O2* with NO gives chemically activated CH3C(O)OCH2O* radicals which are more likely to undergo decomposition via the alpha-ester rearrangement than CH3C(O)OCH2O* radicals produced in the peroxy radical self-reaction.     

Atmospheric chemistry of CF3CH=CH2 and C4F9CH=CH2: products of the gas-phase reactions with Cl atoms and OH radicals

FTIR-smog chamber techniques were used to study the products of the Cl atom and OH radical initiated oxidation of CF3CH=CH2 in 700 Torr of N2/O2, diluent at 296 K. The Cl atom initiated oxidation of CF3CH=CH2 in 700 Torr of air in the absence of NOx gives CF3C(O)CH2Cl and CF3CHO in yields of 70+/-5% and 6.2+/-0.5%, respectively. Reaction with Cl atoms proceeds via addition to the >C=C< double bond (74+/-4% to the terminal and 26+/-4% to the central carbon atom) and leads to the formation of CF3CH(O)CH2Cl and CF3CHClCH2O radicals. Reaction with O2 and decomposition via C-C bond scission are competing loss mechanisms for CF3CH(O)CH2Cl radicals, kO2/kdiss=(3.8+/-1.8)x10(-18) cm3 molecule-1. The atmospheric fate of CF3CHClCH2O radicals is reaction with O2 to give CF3CHClCHO. The OH radical initiated oxidation of CxF2x+1CH=CH2 (x=1 and 4) in 700 Torr of air in the presence of NOx gives CxF2x+1CHO in a yield of 88+/-9%. Reaction with OH radicals proceeds via addition to the >C=C< double bond leading to the formation of CxF2x+1C(O)HCH2OH and CxF2x+1CHOHCH2O radicals. Decomposition via C-C bond scission is the sole fate of CxF2x+1CH(O)CH2OH and CxF2x+1CH(OH)CH2O radicals. As part of this work a rate constant of k(Cl+CF3C(O)CH2Cl)=(5.63+/-0.66)x10(-14) cm3 molecule-1 s-1 was determined. The results are discussed with respect to previous literature data and the possibility that the atmospheric oxidation of CxF2x+1CH=CH2 contributes to the observed burden of perfluorocarboxylic acids, CxF2x+1COOH, in remote locations.     

Comparison of T-piece and concentric mixing systems for continuous flow synthesis of anatase nanoparticles in supercritical isopropanol/water

T-piece and concentric counter-flow mixing systems are compared in continuous flow supercritical solvothermal synthesis of TiO₂ at identical system parameters. The phase pure anatase nanoparticle products were characterized with powder X-ray diffraction (PXRD), transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS), and the particle size, size distribution and absolute crystallinity mapped as a function of temperature, precursor concentration, flow rate and pressure for the two different continuous flow reactors. The particles synthesized with the T-piece geometry are smaller with a narrower size distribution, possibly indicating a more effective mixing, than particles synthesized at the same conditions with concentric counter-flow geometry. In general, an increased synthesis temperature leads to an increase in absolute crystallinity. For the particles synthesized with the concentric reactor geometry crossing of the critical point of the solvent causes a decrease in the particle size and size distribution, and conditions just above the critical temperature are demonstrated to be optimal for continuous solvothermal synthesis of anatase.     

Schatten–von Neumann properties for Fourier integral operators with non-smooth symbols,I

We consider Fourier integral operators with symbols in modulation spaces and non-smooth phase functions whose second orders of derivatives belong to certain types of modulation space. We prove continuity and Schatten–von Neumann properties of such operators when acting on L ².     

Gabor pairs,and a discrete approach to wave-front sets

We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of “continuous type”. This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f.     

Implementation of a ”data filter” for the UK National Marine Monitoring Programme

The implementation of a strategy for the assessment of the validity of environmental monitoring data – a ”data filter”– is described. The approach was developed through the UK National Marine AQC Scheme for application to data collected during the UK National Marine Monitoring Programme. Data reported for the year 1999, by nine laboratories, for 74 determinand-matrix combinations were assessed on the basis of the completeness of their supporting quality assurance and quality control information. The approach to the establishment of criteria of acceptability for quality information is described. Received: 28 August 2001 Accepted: 29 November 2001     

Thermogravimetric and dilatometric studies using Stepwise Isothermal Analysis and related techniques

The Stepwise Isothermal Analysis (SIA) technique, which was introduced by the author in the late seventies has proved to be very useful both in thermogravimetric and dilatometric studies. By this technique the heating and cooling programme is controlled by the rate of the reactions taking place in the sample, for instance thermal decompositions (TG) or sintering (dilatometry). By an advanced computer programme this control is achieved in the following way: The sample is heated at a constant heating rate until the reaction rate. i. e. the slope of the weight/length versus time curve, exceeds a preset limit at which point the heating is stopped. The reaction thereafter proceeds isothermally until the rate again becomes smaller than the limit where the heating is resumed. By this techniques the reactions thus characteristically take place in isothermal steps.This technique is especially useful in studies of thermal decompositions and it is believed that the decomposition températures determined by SIA is much more accurate than those determined by other techniques even for materials involving consecutive and close-lying reactions. One typical application of this technique is establishment of optimum conditions for removal of organic binders from ceramic powder compacts prepared for instance by dry pressing or injection moulding.The SIA technique is also very useful in kinetic studies and with the advanced computer systems available today rather sophisticated control and analysis of the data can be obtained. One example, which will also be discussed in the presentation, is a study of the decomposition of Ce-carbonate using first the standard technique described above by which the reaction mechanism could be established and then followed by the so-called Forced Stepwise Isothermal Analysis technique (FSIA) by which the activation energy could be obtained.Finally the SIA technique is also very useful in dilatometric sintering studies and to demonstrate this the result obtained both using SIA and the related constant shrinkage rate technique in a study of the initial sintering stage of CeO₂ will be presented.

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Zusammenfassung Das vom Autor Ende der siebziger Jahre eingeführte Verfahren der Stufenweisen Isothermischen Analyse (SIA) erwies sich sowohl bei thermogravimetrischen als auch bei dilatometrischen Untersuchungen als sehr nutzvoll. Bei diesem Verfahren wir das Heiz- und Kühlprogramm durch die Geschwindigkeit der in der Probe ablaufenden Reaktion- z.B. der thermischen Zersetzung (TG) oder des Sintern (Dilatometrie) — gesteuert. Diese Steuerung wird durch ein Computerprogramm auf folgende Weise erreicht: Die Probe wird mit einer konstanten Aufheizgeschwindigkeit aufgeheizt, bis die Reaktionsgeschwindigkeit, d.h. der Anstieg der Gewichts/Längen — Zeitkurve, einen gewissen Grenzwert überschreitet, wodurch der Aufheizvorgang gestoppt wird. Die Reaktion wird anschlie\end isotherm fortgesetzt, bis die Geschwindigkeit wieder kleiner als der Grenzwert wird, zu diesem Zeitpunkt setzt die Aufheizung wieder ein. Durch dieses Verfahren erfolgt die Reaktion somit in isothermen Stufen.Dieses Verfahren ist besonders bei der Untersuchung von thermischen Zersetzungen nutzvoll und man nimmt an, da\ die mittels SIA ermittelte Zersetzungstemperatur wesentlich genauer ist als im Falle von anderen Verfahren, besonders bei Substanzen mit konsekutiven und nahe beieinanderliegenden Reaktionen. Eine typische Anwendung dieses Verfahrens ist die Ermittlung der Optimumbedingungen für die Entfernung organischer Bindemittel aus Keramikpulverpre\lingen, die z.B. durch Trockenpressen oder Spritzgie\en hergestellt wurden. Ein Anwendungsbeispiel dafür wird hier diskutiert.Auch bei kinetischen Untersuchungen ist das SIA Verfahren sehr nutzvoll und mit den heute erhältlichen Computersystemen ist eine anspruchsvollere überwachung und Analyse der Angaben ist möglich. Ein ebenfalls in vorliegender Arbeit diskutiertes Beispiel ist die Untersuchung der Zersetzung von Ceriumkarbonat, wobei zuerst die obenbeschriebene Standardmethode angewendet wird, wodurch der Reaktionsmechanismus abgeschätzt werden kann. Im Anschlu\ erfolgt eine sogenannte Erzwungene Stufenweise Isotherme Analyse (FSIA), wodurch die Aktivierungsenergie ermittelt werden kann.Letztendlich ist das SIA Verfahren auch bei dilatometrischen Sinteruntersuchungen sehr nutzbringend. Um dies darzustellen, wird bei einer Untersuchung des ursprünglichen Sinterzustandes von CeO₂, sowohl das durch SIA als auch das durch das Verfahren der konstanten Abschreckgeschwindigkeit≓ erhaltene Ergebnis dargestellt.