Parameterized reduced order modeling of misaligned stacked disks rotor assemblies

Light and flexible rotating parts of modern turbine engines operating at supercritical speeds necessitate application of more accurate but rather computationally expensive 3D FE modeling techniques. Stacked disks misalignment due to manufacturing variability in the geometry of individual components constitutes a particularly important aspect to be included in the analysis because of its impact on system dynamics. A new parametric model order reduction algorithm is presented to achieve this goal at affordable computational costs. It is shown that the disks misalignment leads to significant changes in nominal system properties that manifest themselves as additional blocks coupling neighboring spatial harmonics in Fourier space. Consequently, the misalignment effects can no longer be accurately modeled as equivalent forces applied to a nominal unperturbed system. The fact that the mode shapes become heavily distorted by extra harmonic content renders the nominal modal projection-based methods inaccurate and thus numerically ineffective in the context of repeated analysis of multiple misalignment realizations. The significant numerical bottleneck is removed by employing an orthogonal projection onto the subspace spanned by first few Fourier harmonic basis vectors. The projected highly sparse systems are shown to accurately approximate the specific misalignment effects, to be inexpensive to solve using direct sparse methods and easy to parameterize with a small set of measurable eccentricity and tilt angle parameters. Selected numerical examples on an industrial scale model are presented to illustrate the accuracy and efficiency of the algorithm implementation.     

Spin-spin coupling edition in chiral liquid crystal NMR solvent

The application of the G-SERFph pulse sequence is presented on enantiomeric mixtures dissolved in a chiral liquid crystal. It aims at editing, within one single 2D spectrum, every proton coupling which is experienced by a given proton site in the molecule, and leads to real phased T-edited spectroscopy (T=J+2D). This NMR experiment is based on the combination of homonuclear semi-selective refocusing techniques with a spatial frequency encoding of the sample. This approach, which consists in handling selectively each coupling in separate cross sections of the sample, is applied to the visualization of enantiomers dissolved in a chiral liquid crystalline phase. Advantages and limits of this methodology are widely discussed.     

Modified z-gradient filtering as a mean to obtain phased deuterium autocorrelation 2D NMR spectra in oriented solvents

We describe a modified z-gradient filter scheme specifically designed to obtain pure absorption mode deuterium 2D NMR spectra recorded in oriented solvents. The proposed technique is investigated by analysing the evolution of the density operator for a spin I=1. The method is applied to the recently designed Q-COSY and Q-resolved 2D experiments to simplify the analysis of chiral molecules dissolved in weakly orienting chiral liquid crystals. The efficiency of this z-gradient filtering technique is illustrated using the perdeuterated 1-butanol, a prochiral molecule of average Cs symmetry, dissolved in an organic solution of poly-gamma-benzyl-L-glutamate (PBLG). The experimental results as well as the advantages of the new experiments compared with the previous ones are described and discussed.     

Schrödinger Operators with Random Sparse Potentials. Existence of Wave Operators

We consider the connection problem for the Heun differential equation, which is a Fuchsian differential equation that has four regular singular points. We consider the case in which the parameters in this equation satisfy a certain set of conditions coming from the eigenvalue problem of the non-commutative harmonic oscillators. As an application, we describe eigenvalues with multiplicities greater than 1 and the corresponding odd eigenfunctions of the non-commutative harmonic oscillators. The existence of a rational or a certain algebraic solution of the Heun equation implies that the corresponding eigenvalues has multiplicities greater than 1.The research of the author is supported in part by a Grant-in-Aid for Scientific Research (B) (No. 15340005) from the Ministry of Education, Culture, Sports, Science and Technology.Mathematics Subject classifications (2000). primary, 34M35, secondary, 33E20.This revised version was published online in March 2005 with corrections to the cover date.     

Microwave-resonance-induced resistivity: evidence of ultrahot surface-state electrons on liquid 3He

Measurements of the dc resistivity of surface-state electrons on liquid helium exposed to microwave radiation are reported. It is shown that the resonant microwave excitation of surface-state electrons is accompanied by a strong increase in their resistivity, which is opposite to the result expected from the previously used two-level model. We show that even a very small fraction of electrons excited to the first excited state and decaying back due to vapor-atom scattering strongly heat the electron system, causing a population of higher subbands. The calculated resistivity change is in good agreement with the observed data.     

Intrinsic magnetic properties of In2O3 and transition metal-doped-In2O3

This paper reports on the influence of the sintering temperature and atmosphere and transition-metal doping on the magnetic properties of nanocrystalline and bulk In₂O₃. Undoped nanocrystalline In₂O₃ is diamagnetic whatever the sintering temperature and atmosphere. All single-phase transition-metal-doped In₂O₃ samples are paramagnetic, with a paramagnetic effective moment originating from weakly interacting transition metal ions. No trace of ferromagnetism has been detected even with samples sintered under argon, except extrinsic ferromagnetism for samples with magnetic dopant concentrations exceeding the solubility limit.     

Properties of nanocrystalline TiO2 synthesized in premixed flames stabilized on a rotating surface

The properties of TiO₂ nanoparticles synthesized using the flame stabilized on a rotating surface method (FSRS) are investigated. The method uses a laminar, premixed, stagnation flame, combining particle synthesis and film deposition in a single step. The current study examines the effects of flame properties on particle characteristics. Synthesized particles were characterized using X-ray diffractometry, Transmission Electron Microscopy and UV–vis spectrometry in order to quantify the effects of equivalence ratio and precursor loading on particle size, crystallinity and optical band-gap. Results show that flame stoichiometry significantly affects crystal phase, but it has little to no effect on particle size and light absorption band edge. In addition, precursor loading impacts both the particle size and the crystal phase. The study demonstrates the potential of the FSRS method for producing tailored nanoscale TiO₂ particles for a variety of applications.     

Time‐resolved Raman studies on Al2O3: Cr3+: lifetime measurements of the excited‐state transition Ē → 2Ā

A time‐resolved intensified charge coupled device‐based Raman microspectrometer system dedicated to the study of solid samples is described, offering good optical, temporal and spatial resolution. The advantages of this approach are demonstrated on Al₂O₃:Cr³⁺, obtaining for the first time the temporal evolution of the excited state transition Ē → 2Ā. Moreover, the time dependence of the luminescence due to the chromium ion was also determined by the same Raman device. Copyright © 2010 John Wiley & Sons, Ltd.     

Stationary Flow Past a Semi-Infinite Flat Plate: Analytical and Numerical Evidence for a Symmetry-Breaking Solution

We consider the question of the existence of stationary solutions for the Navier Stokes equations describing the flow of a incompressible fluid past a semi-infinite flat plate at zero incidence angle. By using ideas from the theory of dynamical systems we analyze the vorticity equation for this problem and show that a symmetry-breaking term fits naturally into the downstream asymptotic expansion of a solution. Finally, in order to check that our asymptotic expressions can be completed to a symmetry-breaking solution of the Navier–Stokes equations we solve the problem numerically by using our asymptotic results to prescribe artificial boundary conditions for a sequence of truncated domains. The results of these numerical computations a clearly compatible with the existence of such a solution. Mathematics Subject Classification (2000). 76D05, 76D25, 76M10, 41A60, 35Q35 Supported in part by the Fonds National Suisse.