Uniform molecular analysis using femtosecond laser mass spectrometry

The potential of femtosecond laser time-of-flight mass spectrometry (FLMS) for uniform quantitative analysis of molecules has been investigated. Various samples of molecular gases and vapours have been studied, using ultra-fast ( approximately 50 fs) laser pulses with very high intensity (up to 1.6 x 10(16) Wcm(-2)) for non-resonant multiphoton ionisation/tunnel ionisation. Some of these molecules have high ionisation potentials, requiring up to ten photons for non-resonant ionisation. The relative sensitivity factors (RSF) have been determined as a function of the laser intensity and it has been demonstrated that for molecules with very different masses and ionisation potentials, uniform ionisation has been achieved at the highest laser intensities. Quantitative laser mass spectrometry of molecules is therefore a distinct possibility. Copyright 1999 John Wiley & Sons, Ltd.     

Multicomponent phosphate invert glasses with improved processing

Owing to their structure of small phosphate units, phosphate invert glasses have high crystallisation tendencies, which make processing of the melt challenging. The aim was to improve their processing by (1) increasing the number of glass components and (2) incorporating intermediate oxides (TiO₂, MgO and ZnO). Glasses (P₂O₅–CaO–MgO–Na₂O) were produced by a melt-quench route. In series 1, TiO₂ was partially substituted for Na₂O, and the number of components was increased by partially substituting strontium for calcium, zinc for magnesium and potassium for sodium on a molar base. In series 2, the MgO + ZnO content in the multicomponent glass was varied between 0 and 20 mol% in exchange for CaO + SrO. Differential scanning calorimetry showed a significant increase of the processing window in the multicomponent glasses, explained by an increased energy barrier for crystallisation owing to increased entropy of mixing. The MgO + ZnO content also significantly improved the processing window from 117 K (0 mol% MgO + ZnO) to 185 K (20 mol%), owing to their large field strength. These results show that the processing of phosphate invert glasses for biomedical applications can be improved significantly by incorporating ions such as strontium or zinc which are also known to have therapeutic effects.     

Local Existence of Solutions of Self Gravitating Relativistic Perfect Fluids

This paper deals with the evolution of the Einstein gravitational fields which are coupled to a perfect fluid. We consider the Einstein–Euler system in asymptotically flat spacestimes and therefore use the condition that the energy density might vanish or tend to zero at infinity, and that the pressure is a fractional power of the energy density. In this setting we prove local in time existence, uniqueness and well-posedness of classical solutions. The zero order term of our system contains an expression which might not be a C ^∞ function and therefore causes an additional technical difficulty. In order to achieve our goals we use a certain type of weighted Sobolev space of fractional order. In Brauer and Karp (J Diff Eqs 251:1428–1446, 2011) we constructed an initial data set for these of systems in the same type of weighted Sobolev spaces. We obtain the same lower bound for the regularity as Hughes et al. (Arch Ratl Mech Anal 63(3):273–294, 1977) got for the vacuum Einstein equations. However, due to the presence of an equation of state with fractional power, the regularity is bounded from above.     

Eine Bedingung für vollständige Reduzibilität von Darstellungen gewöhnlicher und infinitesimaler Gruppen

Ohne Zusammenfassung     

Flux line lattice symmetries in the borocarbide superconductor LuNi2B2C

We compare the results of small angle neutron scattering on the flux line lattice (FLL) obtained in the borocarbide superconductor LuNi₂B₂C with the applied field along the c- and a-axes. For H‖c the temperature dependence of the FLL structural phase transition from square to hexagonal symmetry was investigated. Above 10 K the transition onset field. H ₂(T), rises sharply, bending away from H _c2(T) in contradiction to theoretical predictions of the two merging. For H‖a a first order FLL reorientation transition is observed at H _tr=3–3.5 kOe. Below H _tr the FLL nearest neighbor direction is parallel to the b-axis, and above H _tr to the c-axis. This transition cannot be explained using nonlocal corrections to the London model.     

Stationärer Stoff- und Wärmeübergang an stationär quer angeströmten Zylindern

The steady forced convection mass and heat transfer from circular cylinders has been investigated. The full mass transport differential equation has been integrated numerically. The employed velocity distributions are known [1]. The most important result is reproduced in a correlation for the mass transfer, which regards the turbulence intensity in the flow of the cylinders. This mass transfer law is proofed theoretically and experimentally in the range of Schmidt numbers from Sc=0.73 up to S=3.3×10⁴; however it is valid for 0≤Sc∞. It can be used for all values of Re Sc greater than Re Sc=7.3×10^?5 and for all values of the Reynolds number less than the critical value, Re_kr. The critical Reynolds number, Re_kr, is a known function of the turbulence intensity [1]. For values of Re Sc less than Re Sc=7.3 x10^?5 the mass transfer can be predicted by an analytical equation that based on Oseen type linearization of the differential equation. The conditions are illustrated, which allow to calculate the quantities for heat transfer by means of the correlations for the mass transfer.     

Umströmung beschleunigter und verzögerter Partikeln

Zusammenfassung Die Bewegung von Partikeln ist in technischen Anlagen fast ausschließlich instationär. Insbesondere dann, wenn die Partikeln in Schwärmen auftreten, muß man aufgrund von Zusammenstößen zwischen den Partikeln oder von Partikeln mit einer festen Wand erwarten, daß im periodischen Wechsel Bewegungsabschnitte mit Beschleunigung und Verzögerung auftreten. Diese Bewegungsvorgänge sind für die Umströmung und folglich auch für damit verbundene Wärme- und Stoffübergangsprozesse sowie chemische Reaktionen von großer Bedeutung.Aus diesem Grunde wurden in Teil 1 dieses Berichtes die instationären Bewegungsvorgänge bei Beschleunigung näher untersucht. Besonderes Augenmerk sollte auf die Entstehung und die weitere Entwicklung der Wirbel gerichtet werden, die hinter den Partikeln auftreten.Die mathematische Beschreibung des Strömungsfeldes erfolgt für den Fall der linearen Partikelbewegung unter Vernachlässigung der Schwerkraft. Die numerische Lösung der Differentialgleichungen erfolgte mit Hilfe der Methode der finiten Elemente.Die berechneten Stromlinienfelder vermitteln einen umfassenden Einblick in die Umströmung der Partikeln. Sie lassen bei der Beschleuigung aus dem Ruhezustand die hinausgezögerte Entstehung und dann folgende Entwicklung der Wirbel erkennen. Sowohl die Länge der Wirbel als auch der Ablösepunkt der Strömung von der Partikeloberfläche wurden in Abhängigkeit von der Zeit dargestellt. Ferner wurde der Widerstandsbeiwert bestimmt. Die entsprechenden Ergebnisse für die verzögerte Bewegung von Partikeln werden in Teil 2 dieses Berichtes diskutiert.

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Fluid flow around accelerated and decelerated particlesPart 1

Fluid flow around particles or the motion of particles in a fluid is in general of unsteady state. Therefore the relative fluid motion around a particle with spherical shape has been studied applying theoretical-numerical methods.Unsteady state motion of the particles is due to collision when moving in swarms or when they collide with a wall. Prior to collision particle motion is decelerated and after collision they will be accelerated because of elastic properties of particle and wall materials. In many cases particle motion occurs in combination with heat transfer.It is well known, that, for steady state conditions, behind a particle vortex formation is observed. Vortex formation is expected to occur for unsteady state conditions in a different way. When the particle is accelerated, vortex formation is expected to be delayed. With decelerated motion vortex formation is expected to take place at a much smaller relative velocity and the vortex should envelope the particle for certain values of deceleration.The theoretical investigation is based on several assumptions. The particle is assumed to move with prescribed velocity on a linear path prior to constant acceleration or deceleration. Finite element methods are applied for solution of the differential equations describing the unsteady state motion.Streamlines give a comprehensive picture of the studied fluid motion. They reveal the expected delay of vortex formation for the case of acceleration and premature formation for the case of deceleration, when motion occurs at a Reynolds-number beyond a certain value. In this case, the vortex will move around the particle and finally completely envelope it. Below this value of the Reynolds-number the vortex, established under unsteady state motion, prior to onset of deceleration, will decade.From the determined fields of streamlines the length of the vortices and the angle of detachment of the fluid from particle surface have been determined for several values of acceleration and deceleration. From the calculated velocity fields the local shear stress and the local and mean values of the resistance factor have been derived.The paper is presented in two parts. The first part includes the physical fundamentals of unsteady state motion of particles, the numerical methods applied for the solution of the problems, and a discussion of results obtained for accelerated particles. The second part includes the discussion of results obtained for decelerated particles.