Connections on Naturally Reductive Spaces,Their Dirac Operator and Homogeneous Models in String Theory

 Given a reductive homogeneous space M=G/H endowed with a naturally reductive metric, we study the one-parameter family of connections ∇ ^t joining the canonical and the Levi-Civita connection (t=0, 1/2). We show that the Dirac operator D ^t corresponding to t=1/3 is the so-called ``cubic' Dirac operator recently introduced by B. Kostant, and derive the formula for its square for any t, thus generalizing the classical Parthasarathy formula on symmetric spaces. Applications include the existence of a new G-invariant first order differential operator on spinors and an eigenvalue estimate for the first eigenvalue of D <sup>1/3</sup>. This geometric situation can be used for constructing Riemannian manifolds which are Ricci flat and admit a parallel spinor with respect to some metric connection ∇ whose torsion T≠ 0 is a 3-form, the geometric model for the common sector of string theories. We present some results about solutions to the string equations and a detailed discussion of a 5-dimensional example. Received: 19 February 2002 / Accepted: 26 August 2002 Published online: 22 November 2002 RID="*" ID="*" This work was supported by the SFB 288 ``Differential geometry and quantum physics' of the Deutsche Forschungsgemeinschaft and the Max-Planck Society.     

Some analytical aspects in field theories with dynamical mass generation

The consequence of dynamical mass generation on the singularity structure of propagators is discussed. First the phenomena of dynamical mass generation is discussed in the framework of Euclidean gap equations, then a possible Minkowski solution is looked for. The examples are reviewed and studied for several models: Yukawa, QED, QCD and Wess-Zumino. It is argued that the absence of propagator pole goes hand in hand with the nontrivial solution for mass function. The consequences are discussed.     

Galvanomagnetic study of the quantum-well valence band of germanium in the Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript>/Ge/Ge<Subscript>1−x</Subscript>Si<Subscript>x</Subscript> potential well

The structure of the quantum-well valence band in a Ge(111) two-dimensional layer is calculated by the self-consistent method. It is shown that the effective mass characterizing the motion of holes along the germanium layer is almost one order of magnitude smaller than the mass for the motion of heavy holes along the [111] direction in a bulk material (this mass is responsible for the formation of quantum-well levels). This creates a unique situation in which a large number of subbands appear to be populated at moderate values of the layer thickness d _w and the hole concentration p _s . The depopulation of two or more upper subbands in a 38-nm-thick germanium layer at a hole concentration p _s = 5 × 10¹⁵ m^?2 is revealed from the results of measuring the magnetoresistance in a strong magnetic field aligned parallel to the germanium layers. The destruction of the quantum Hall state at a filling factor ν = 1 indicates that the two lower subbands merge together in a self-formed potential profile of the double quantum well. It is demonstrated that, in a quasi-two-dimensional hole gas, the latter effect should be sensitive to the layer strain.     

Visualization of concentration field in a vortex ring using acetone PLIF

To improve the understanding of flame propagation through a nonpremixed vortex ring, the characteristics of fuel concentration in a vortex ring have been investigated experimentally. The vortex ring was generated by the ejection of propane with a single stroke motion of a speaker. Planar laser-induced fluorescence (PLIF) technique was adopted by seeding acetone as a tracer to fuel stream, in which the PLIF signal intensity is directly proportional to the concentration of acetone. This technique provides non-intrusive and instantaneous measurement of concentration field. Results showed that fuel concentration and its gradient decreased with the evolution of a vortex ring. When a nonpremixed flame propagated through a vortex ring, the flame location coincides with the inner most spiral mixing layer of fuel and air in a vortex ring.     

Development of high-speed video cameras for Dynamic PIV

The most promising next generation Image Velocimtry (IV) is the high-speed Dynamic PIV. It requires the development of innovative high-speed video camera sensors. We started by specifying the required performance of these new sensors, for measurements in air and water flows. These criteria founded on the most recent developments in PIV algorithms and incorporate results from a large questionnaire survey of users of high-speed video cameras in Japan. The results suggest that the followings are required: (1) frame rate of 1,000,000 fps, (2) pixel count of 1,000,000 pixels, (3) frame storage capacity of 100–200 frames for tracing a single event and 10,000 frames for turbulent measurements, (4) gray levels of 4–8 bits for PTV; 12 bits for observation. Finally, we reviewed the state of the art of high-speed video-image sensors. Currently the standard parallel-readout sensors can operate at 1 Kfps with a pixel count of approximately 1 Kpixels. The In-situ Storage Image Sensor (ISIS) developed by the authors has recently achieved frame rates of 1 Mfps.     

Application of pressure sensitive paint measurement to a low-solidity cascade diffuser of a transonic centrifugal compressor

A pressure sensitive paint (PSP) measurement has been known as a pressure field measurement technique based on the oxygen quenching phenomenon of luminescence of specific luminophores. A PSP measurement was applied for pressure field measurement in a low-solidity circular cascade diffuser of a single-stage transonic centrifugal compressor with 5 in pressure ratio for HFC134a gas. The oxygen concentration was about 500 ppm. Ru (bath-phen) was adsorbed on a silica-gel thinlayer chromatography sheet, and the sheet was pasted onto the side-wall between the cascade vanes. A drastic change in luminescent intensity was recognized during a surge condition. Also the pressure variations based on luminescent intensity agreed well with the pressure fluctuations measured using a semiconductor pressure sensor with high-frequency-response. It was shown that a PSP measurement worked well to investigate the unsteady pressure fields in a circular cascade diffuser of a transonic centrifugal compressor. Moreover, the time response of PSP becomes clear as a problem to be overcome for the present.     

Interactive Compromise Programming

The purpose of this paper is to introduce a solution method for multiple objective linear programming (MOLP) problems. The method, called interactive compromise programming (ICP), offers a practical solution to MOLP problems by combining judgement with an automatic optimization technique in decision-making. This is realised by using the method of compromise programming and the method of a two-person zero-sum game in an iterative way. The method is illustrated by a numerical example.     

A DFT+U study of the catalytic activity of lanthanum nickelate

A density functional theory + Hubbard U (DFT+U) method is implemented to investigate the catalytic activity of lanthanum nickelate (LaNiO₃) for oxygen reduction reaction. Comparison of the surface energies of different LaNiO₃ surfaces shows that {001} surface has the lowest surface energy and hence maximum stability. Two possible terminations of the {001} surface namely LaO and NiO₂ are considered to carry out all our DFT calculations. Calculation of bond lengths of the atoms near the surface and adsorption energies for the reaction intermediates revealed that LaO terminated {001} surface is unstable for the process of OOH adsorption and hence not preferred for the oxygen reduction reaction. However, NiO₂ terminated {001} surface shows excellent catalytic activity for adsorption of all the reaction intermediates and hence is a favourable surface for reactions to occur. Superiority of the NiO₂ terminated {001} surface as catalyst over the LaO terminated one, is also confirmed from the total and partial density of states of the surfaces in presence of the adsorbates, which also shows that the desorption rate of the reaction intermediates is low in case of LaO terminated {001} surface compared to the NiO₂ terminated one.