Analytical and numerical prediction of harmonic sound power in the inlet of aero-engines with emphasis on transonic rotation speeds

Tone noise radiated through the inlet of a turbofan is mainly due to rotor-stator interactions at subsonic regimes (approach flight), and to the shock waves attached to each blade at supersonic helical tip speeds (takeoff). The axial compressor of a helicopter turboshaft engine is transonic as well and can be studied like turbofans at takeoff. The objective of the paper is to predict the sound power at the inlet radiating into the free field, with a focus on transonic conditions because sound levels are much higher. Direct numerical computation of tone acoustic power is based on a RANS (Reynolds averaged Navier–Stokes) solver followed by an integration of acoustic intensity over specified inlet cross-sections, derived from Cantrell and Hart equations (valid in irrotational flows). In transonic regimes, sound power decreases along the intake because of nonlinear propagation, which must be discriminated from numerical dissipation. This is one of the reasons why an analytical approach is also suggested. It is based on three steps: (i) appraisal of the initial pressure jump of the shock waves; (ii) 2D nonlinear propagation model of Morfey and Fisher; (iii) calculation of the sound power of the 3D ducted acoustic field. In this model, all the blades are assumed to be identical such that only the blade passing frequency and its harmonics are predicted (like in the present numerical simulations). However, transfer from blade passing frequency to multiple pure tones can be evaluated in a fourth step through a statistical analysis of irregularities between blades. Interest of the analytical method is to provide a good estimate of nonlinear acoustic propagation in the upstream duct while being easy and fast to compute. The various methods are applied to two turbofan models, respectively in approach (subsonic) and takeoff (transonic) conditions, and to a Turbomeca turboshaft engine (transonic case). The analytical method in transonic appears to be quite reliable by comparison with the numerical solution and with available experimental data.     

Cationic beta-cyclodextrin bilayer vesicles

Cationic amphiphilic beta-cyclodextrins, substituted with hydrophobic n-alkylthio chains at the primary hydroxyl side and hydrophilic omega-amino-oligo(ethylene glycol) units at the secondary side, form bilayer vesicles with a diameter of 30-35 nm (when alkyl = hexadecyl) or nanoparticles with a diameter of ca. 120 nm (when alkyl = hexyl) in water.     

Primordial Black Holes: Pair Creation, Lorentzian Condition, and Evaporation

The wave function of the universe is usuallytaken to be a functional of the threemetric on aspacelike section, , which is measured. It issometimes better, however, to work in the conjugaterepresentation, where the wave function depends on a quantityrelated to the second fundamental form of . Thismakes it possible to ensure that is part of aLorentzian universe by requiring that the argument of the wave function be purely imaginary. Wedemonstrate the advantages of this formalism first inthe well-known examples of the nucleation of a de Sitteror a Nariai universe. We then use it to calculate the pair creation rate for submaximal blackholes in de Sitter space, which had been thought tovanish semiclassically. We also study the quantumevolution of asymptotically de Sitter black holes. Forblack holes whose size is comparable to that of thecosmological horizon, this process differs significantlyfrom the evaporation of asymptotically flat black holes.Our model includes the one-loop effective action in the s-wave and large-N approximation.Black holes of the maximal mass are in equilibrium.Unexpectedly, we find that nearly maximal quantumSchwarzschild–de Sitter black holes antievaporate.However, there is a different perturbative mode thatleads to evaporation. We show that this mode will alwaysbe excited when a pair of maximal cosmological blackholes nucleates.     

Current partition in multiprobe conductors in the presence of slowly oscillating external potentials

In the presence of a static potential drop a carrier stream incident at a contact of the sample is partitioned into the other contacts according to the transmission probabilities of the sample. The bare response to oscillating potentials, on the other hand, violates current conservation due to the piling up of unscreened charges in the sample, and has to be modified by taking the induced screening potential into account. We present a novel derivation of the conductance response to oscillating external chemical potentials, find the response to an arbitrary internal potential in terms of functional derivatives with respect to the local potential of the scattering matrix of the conductor, and determine the screening potential for slowly oscillating potentials from the condition of local charge neutrality. We find that the current partitioning depends on ratios of local densities of states which reflect the injection and emission properties of the contacts of the sample.     

A canonical partition theorem for equivalence relations on Zt

A canonical version of the multidimensional version of van der Waerden's theorem on arithmetic progressions is proved.     

Ein Distributivitätskriterium für Verbände

Those one-place functions on a latticeL with values inL which can be obtained from the identityx and the constant functions by means of the fundamental operations ofL in a finite number of steps are called one-place polynomial functions. —It is shown that a latticeL is distributive iff all its one-place polynomial functions can be represented by words such that in every word the indeterminatex occurs at most once.     

On universality of blow-up profile for <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript> critical nonlinear Schrödinger equation

We consider finite time blow-up solutions to the critical nonlinear Schrödinger equation iu_t=-u-|u|^4/Nu with initial condition u₀H¹. Existence of such solutions is known, but the complete blow-up dynamic is not understood so far. For a specific set of initial data, finite time blow-up with a universal sharp upper bound on the blow-up rate has been proved in [22], [23].We establish in this paper the existence of a universal blow-up profile which attracts blow-up solutions in the vicinity of blow-up time. Such a property relies on classification results of a new type for solutions to critical NLS. In particular, a new characterization of soliton solutions is given, and a refined study of dispersive effects of (NLS) in L² will remove the possibility of self similar blow-up in energy space H¹.     

Isolation and characterization of kallosin A,a novel rearranged pseudopterane diterpenoid from the Caribbean sea plume Pseudopterogorgia kallos (Bielschowsky)

The Caribbean alcyonacean Pseudopterogorgia kallos is shown to contain a novel rearranged pseudopterane diterpene, kallosin A (1), possessing several unusual structural features. In addition to having two distinct 2(3H)- and 2(5H)-furanone moieties, kallosin A is based on a new carbon skeleton. The structural assignment of 1 was based mainly on 1D and 2D NMR spectral data and was further supported by accurate mass measurement and single-crystal X-ray diffraction analysis.     

Tetrahedral onsager crosses for solubility improvement and crystallization bypass

Pure organic molecules exhibiting a suitable concave rigid shape are expected to give porous glasses in the solid state. Such a feature opens new opportunities to avoid crystallization and to improve molecular solubility in relation to the high internal energy of these solid phases. To quantitatively explore the latter strategy, a series of rigid tetrahedral conjugated molecules nC and the corresponding models nR have been synthesized. Related to the present purpose, several properties have been investigated using UV absorption, steady-state fluorescence emission, differential scanning calorimetry, (1)H NMR translational self-diffusion, magic angle spinning (13)C NMR, and multiple-beam interferometry experiments. The present tetrahedral crosses are up to 8 orders of magnitude more soluble than the corresponding model compounds after normalization to the same molecular length. In addition, they give concentrated monomeric solutions that can be used to cover surfaces with homogeneous films whose thickness goes down to the nanometer range. Such attractive features make cross-like molecular architectures promising for many applications.