Studien Über inhomogene gekrümmte Strömungen

Zusammenfassung Im ersten Teil der Arbeit wurde das Verhalten zweier Luftströme mit verschiedenem Gesamtdruck in stabiler und labiler Schichtung und nebeneinander im Krümmer behandelt. Gesamtdruckverteilungen in den Längsschnitten zeigen die verschieden schnelle Ausbreitung der Mischungszone zwischen den beiden Luftströmen stabiler und labiler Schichtung im Krümmer und der im geraden Kanal.Im zweiten Teil wurde die Potentialströmung einer homogenen und einer stabilen Schichtung im Krümmer berechnet. Bei der Potentialströmung stabiler Schichtung wurde aus zwei verschiedenen Lösungen zweiter Näherung eine Linearkombination gemacht, da ein Hinzunehmen weiterer Glieder der Fourierreihe keine Verbesserung bringt. Die gerechnete Trennungsfläche der beiden Luftströme ist in den zugehörigen Längsschnitt (Abb. 5) des Kanals eingezeichnet. Sie zeigt eine sehr gute Übereinstimmung mit dem Experiment.Göttinger Dissertation. Referent: Prof. Dr.L. Prandtl.Die Versuche wurden im Kaiser Wilhelm-Institut für Strömungsforschung durchgeführt. Zu besonderem Dank bin ich Herrn ProfessorPrandtl verpflichtet, der die Anregung zu dieser Arbeit gab und sie in reichem Maße förderte.     

The size of Bose-Einstein effects in the statistical bootstrap model

We have determined the shift in Hagedorn temperature due to Bose statistics and calculated explicitly the cluster expansions of fireball level densities. This enabled us to investigate Bose effects in one-particle spectra and integrated correlations. Apart from the low secondary energy region of the one-particle distributions, the nonasymptotic behaviour of these quantities is little affected.     

Preliminary evidence for UA(1) breaking in QCD from lattice calculations

We suggest a simple definition of the topological charge density Q(x) in the lattice Yang-Mills theory and evaluate A≡∝d⁴x〈Q(x)Q(0)〉 in SU(2) by Monte Carlo simulation. The “data” interpolate well between the strong and weak coupling expansions, which we compute to order g^?12 and g⁶, respectively. After subtraction of the perturbative tail, our points exhibit the expected asymptotic freedom behaviour giving $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{≌(0.11±0.02)K}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, K being the SU(2) quarkless string tension. Although a larger value for $\text{A}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{K}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ would be preferable, we are led to conclude (at least tentatively) that the U_A(1) problem of QCD is indeed solved perturbatively in the quark loop expansion.     

Revisiting random walks in fractal media: on the occurrence of time discrete scale invariance

This paper addresses the kinetic behavior of random walks in fractal media. We perform extensive numerical simulations of both single and annihilating random walkers on several Sierpinski carpets, in order to study the time behavior of three observables: the average number of distinct sites visited by a single walker, the mean-square displacement from the origin, and the density of annihilating random walkers. We found that the time behavior of those observables is given by a power law modulated by soft logarithmic-periodic oscillations. We conjecture that logarithmic-periodic oscillations are a manifestation of a time domain discrete scale iNvariance (DSI) that occurs as a consequence of the spatial DSI of the substrate. Our conjecture implies that the logarithmic periods of oscillations in space and time domains are linked by a dynamic exponent z, through z=log(tau)/log(b(1)), where tau and b(1) are the fundamental scaling ratios of the DSI symmetry in the time and space domains, respectively. We use this relationship in order to compute z for different observables and fractals. Furthermore, we check the values obtained with independent measurements provided by the power-law behavior of the mean-square displacement with time [R(2)(t) proportional variant t(2/z)]. The very good agreement obtained between both computations of the z exponent gives strong support to the idea of an intimate interplay between spatial and time symmetry properties that we expect will have a quite general scope. We expect that the application of the outlined concepts in the field of dynamic processes in fractal media will stimulate further research.     

Systematic measurements of transient fields for W,Os and Pt ions traversing Fe

Transient magnetic fields were measured for W, Os and Pt ions traversing iron hosts with average velocities in the range from approximately 1.6v ₀ to 4.8v ₀ (v ₀=c/137, Bohr velocity). Transient fields for W and Os in Fe are consistent with behaviour found for lighter rare-earth ions and are about 20% stronger than those for Pt in Fe over the majority of the velocity range examined. A measurement was made to confirm that possible heavy-ion beam induced attenuations of the transient field are negligible for low-velocity Pt ions excited by Ni beams. Results are discussed in terms of both empirical and model-based parameterizations of the transient field strength.     

Complete solution of the XXZ-model on finite rings

The thermodynamical properties of the XXZ-model are studied by means of a complete diagonalization of the XXZ-Hamiltonian on rings withN=4,6...16 sites. Based on a finite size analysis we are able to extract the universal term in the free energy as it is predicted by conformal invariance. We also study the finite site scaling properties of the density of states in a properly chosen scaling variable for the excitation energies. The thermal averages of the modulus of the momentum and of the reflection parity appear to be independent of the temperature in the thermodynamical limit.     

Seven and nine quasi-particleK-isomers in175Hf

NewK-isomers with very high spin (up to 57/2) have been found in¹⁷⁵Hf. This is the highest spin isomer seen in deformed nuclei and involves 9 quasi-particles. The predominant decay to the I=55/2 state in aK ^π=35/2^?, 5 quasi-particle rotational band further demonstrates the surprising breakdown of theK-selection rules, reported previously in neighbouring nuclei.     

Anisotropic relaxations introduced by Cd impurities in rutile TiO(2): first-principles calculations and experimental Support

We present an ab initio study of the relaxations introduced in TiO (2) when a Cd impurity substitutes a Ti atom and an experimental test of this calculation by a perturbed-angular-correlation (PAC) measurement of the orientation of the electric-field gradient (EFG) tensor at the Cd site. The ab initio calculation predicts strong anisotropic relaxations of the nearest oxygen neighbors of the impurity and a change of the orientation of the largest EFG tensor component, V(33 ), from the [001] to the [110] direction upon substitution of a Ti atom by a Cd impurity. The last prediction is confirmed by the PAC experiment that shows that V(33 ) at the Cd site is parallel to either the [110] or the [1 1;0] crystal axis.     

Bethe's Equation Is Incomplete for the XXZ Model at Roots of Unity

We demonstrate for the six vertex and XXZ model parameterized by = –(q+q^-1)/2±1 that when q^2N=1 for integer N2 the Bethe's ansatz equations determine only the eigenvectors which are the highest weights of the infinite dimensional sl₂ loop algebra symmetry group of the model. Therefore in this case the Bethe's ansatz equations are incomplete and further conditions need to be imposed in order to completely specify the wave function. We discuss how the evaluation parameters of the finite dimensional representations of the sl₂ loop algebra can be used to complete this specification.     

ICP-MS-based characterization of inorganic nanoparticles—sample preparation and off-line fractionation strategies

Validated and easily applicable analytical tools are required to develop and implement regulatory frameworks and an appropriate risk assessment for engineered nanoparticles (ENPs). Concerning metal-based ENPs, two main aspects are the quantification of the absolute mass concentration and of the “dissolved” fraction in, e.g., (eco)toxicity and environmental studies. To provide information on preparative aspects and on potential uncertainties, preferably simple off-line methods were compared to determine (1) the total concentration of suspensions of five metal-based ENP materials (Ag, TiO₂, CeO₂, ZnO, and Au; two sizes), and (2) six methods to quantify the “dissolved” fraction of an Ag ENP suspension. Focusing on inductively coupled plasma–mass spectrometry, the total concentration of the ENP suspensions was determined by direct measurement, after acidification and after microwave-assisted digestion. Except for Au 10 nm, the total concentrations determined by direct measurements were clearly lower than those measured after digestion (between 61.1 % for Au 200 nm and 93.7 % for ZnO). In general, acidified suspensions delivered better recoveries from 89.3 % (ZnO) to 99.3 % (Ag). For the quantification of dissolved fractions two filtration methods (ultrafiltration and tangential flow filtration), centrifugation and ion selective electrode were mainly appropriate with certain limitations, while dialysis and cloud point extraction cannot be recommended. With respect to precision, time consumption, applicability, as well as to economic demands, ultrafiltration in combination with microwave digestion was identified as best practice.