Initial noise predictions for rudimentary landing gear

A four-wheel “rudimentary” landing gear (RLG) truck was designed for public-domain research, with a level of complexity which is manageable in current numerical simulations, and a weak Reynolds-number sensitivity. Experimental measurements of wall-pressure fluctuations are allowing a meaningful test of unsteady simulations with emphasis on noise generation. We present three Detached-Eddy Simulations (DES) using up to 18 million points in the high-order NTS code. The first is incompressible with the model placed in the wind tunnel, as requested for the 2010 workshop on Benchmark problems for Airframe Noise Computations (BANC-I), intended for force and surface-pressure studies. The second and third are at Mach 0.115 and Mach 0.23, with only one wall, a “ceiling” analogous to a wing (but infinite and inviscid), and are used to exercise far-field noise prediction by coupling the Detached-Eddy Simulations and a Ffowcs-Williams/Hawkings calculation. The results include wall-pressure, and far-field-noise intensities and spectra. The wall pressure signals in the three simulations are very similar and, in a comparison published separately, agree well with experiment and other simulations. In the absence of experimental noise data, the attention is focused on internal quality checks, by varying the permeable Ffowcs-Williams/Hawkings calculation surface and then by using only the solid surface. An unexpected finding at these Mach numbers is an apparent strong role for quadrupoles, revealed by a typical deficit of 3 dB in the solid-surface results, relative to the permeable-surface results. The solid-surface approach has variants, related to the presence of the ceiling (a plane of symmetry), which can increase this error further; there is little consensus on the exact configuration of the solid surfaces in the Ffowcs-Williams/Hawkings calculation procedure. Tentative theoretical arguments suggest that a balance somewhat in favor of quadrupoles over dipoles is plausible at Mach 0.115. However, the scaling of sound with Mach number does not follow the eighth power, as quadrupoles do in theory: it is closer to the sixth power. This trend gives a muddled theoretical picture, but agrees with the scaling observed in experiments. If it is confirmed, this finding will complicate airframe-noise calculations, and prevent the attribution of noise to a given component of the aircraft. Progress in airframe-noise simulations appears real, but systematic grid-refinement studies and noise comparisons with experiment or other simulations have yet to occur, and the theoretical uncertainty is high.     

Computation of weak steady shock reflections by means of an unstructured shock-fitting solver

Weak steady Mach reflections are numerically simulated using unstructured grids by means of either “shock-fitting” or “shock-capturing” techniques. It is shown that shock-fitting allows using coarser meshes than those required by shock-capturing, since the latter needs mesh refinement in the direction normal to the discontinuities, which is not needed using the former approach. The shock-fitted solution is also free from the numerical disturbances that arise along the captured discontinuities and pollute the captured solution in the smooth flowfield region. Finally, the shock-fitting solutions show the presence of a small region next to the Mach stem and the reflected shock downstream of the triple point, characterized by very high gradients.     

Wigner function and Bell’s inequalities for even and odd coherent states

The Wigner function and the symplectic tomogram of an entangled quantum state, which is a superposition of the photon’s coherent states (even and odd coherent states), is studied. Photon statistics and violation of Bell’s inequality for the photon state are discussed.     

Some open problems concerning relatively free and free profinite semigroups

Besides constituting an important and often crucial tool in studying semigroup varieties and pseudovarieties, relatively free and free profinite semigroups have proved to be of interest from many other natural standpoints. We present three groups of new problems concerning certain relatively free and free profinite semigroups and give background and motivation for them. The problems deal with the first-order theories of free profinite semigroups, the structure of free Burnside semigroups with commuting idempotents and of free Burnside inverse semigroups, and the representation of finitely generated free bands by order preserving transformations of a finite chain. April 19, 2001     

Complexation and chiral recognition thermodynamics of 6-amino-6-deoxy-beta-cyclodextrin with anionic, cationic, and neutral chiral guests: counterbalance between van der Waals and coulombic interactions

The stability constant (K), standard free energy (Delta G degrees), enthalpy (Delta H degrees), and entropy changes (T Delta S degrees) for the complexation of 6-amino-6-deoxy-beta-cyclodextrin with more than 50 negatively or positively charged as well as neutral guests, including 22 enantiomer pairs, have been determined in aqueous phosphate buffer (pH 6.9) at 298.15 K by titration microcalorimetry. The thermodynamic parameters obtained in this study and the relevant data for native beta-cyclodextrin indicate that the complexation and chiral discrimination behavior of the cationic host with charged guests are governed by the critical counterbalance between the electrostatic interactions of the charged groups in host and guest and the conventional intracavity interactions of the hydrophobic moiety of guest, such as hydrophobic, van der Waals, solvation/desolvation, and hydrogen-bonding interactions.     

Parametric amplification at low-frequency pumping and generation of four-mode entangled states

We show that parametric amplification at low-frequency pumping can be implemented in aperiodic nonlinear photonic crystals. In this process, the intensities of the waves with frequencies higher than the pumping frequency increase with increase in the interaction length as in the case of the standard process of parametric amplification at high-frequency pumping. The process under consideration includes a nondegenerate parametric down-conversion followed by two parametric up-conversions in the same pumping wave. As a result, generation at four new frequencies arises. Quantum analysis of the process demonstrates the presence of entanglement in the states of four modes. Talk presented at the oral issue of J. Russ. Laser Res. dedicated to the memory of Professor Vladimir A. Isakov, Professor Alexander S. Shumovsky, and Professor Andrei V. Vinogradov held in Moscow February 21–22, 2008.     

On Sylow Subgraphs of Vertex-Transitive Self-Complementary Graphs

One of the basic facts of group theory is that each finite groupcontains a Sylow p-subgroup for each prime p which divides theorder of the group. In this note we show that each vertex-transitiveself- complementary graph has an analogous property. As a consequenceof this fact, we obtain that each prime divisor p of the orderof a vertex-transitive self-complementary graph satisfies thecongruence p^m 1(mod 4), where p^m is the highest power of pwhich divides the order of the graph. 1991 Mathematics SubjectClassification 05C25, 20B25.     

Electrodialysis performance when recycling dilute nickel solutions directly into a plating bath

This work was performed to determine membrane performance characteristics when using low current electrodialysis to recover and recycle nickel (salts) from dilute waste waters. Results showed that nickel at typical plating rinse concentrations (3000 p.p.m.) can be transferred electrically across commercially available membranes, and directly into a concentrated Watt's nickel plating bath (72,000 p.p.m.). Recovery at approximately 90% current efficiency was possible at current densities as low as 3.0 mA/cm². Nickel and co-transported water were routinely recycled as a relatively concentrated solution which would not cause dilution, since it was well above plating bath strength at all but the lowest current densities.