Vortex amplifier internal geometry and its effect on performance

Consideration of the internal geometry of a vortex amplifier reveals eight geometrical ratios that describe the device. The effects of each of these ratios on the performance of a vortex amplifier are considered and experimental results presented. The most significant ratios when designing for vortex amplifier performance are identified     

Three-dimensional boundary-layer transition on a cone at Mach 3.5

A boundary-layer transition study on a sharp, 5° half-angle cone at various angles of attack was conducted at Mach 3.5. Transition data were obtained with and without significantly reduced freestream acoustic disturbance levels. A progressive downstream and upstream motion of the transition front on the windward and leeward rays, respectively, of the cone with angle of attack was observed for the high noise level data in agreement with data trends obtained in conventional (noisy) wind tunnels. However, the downstream movement was not observed to the same degree for the low noise level data in the present study. Transition believed to be crossflow dominated was found to be less receptive to freestream acoustic disturbances than first-mode (Tollmien-Schlichting) dominated transition. The previously-developed crossflow transition Reynolds number criterion, _tr,max 200, was found to be inadequate for the current case. An improved criterion is offered, which includes compressibility and flow-geometry effects.     

A very complicated structure of resonances in a nonlinear system with cyclic symmetry: Nonlinear forced localization

The fundamental and subharmonic resonances of a nonlinear cyclic assembly are examined using the asymptotic method of multiple-scales. The system consists of a number of identical cantilever beams coupled by means of weak linear stiffnesses. Assuming beam inextensionality, geometric nonlinearities arise due to longitudinal inertia and the nonlinear relation between beam curvature and transverse displacement. The governing nonlinear partial differential equations are discretized by a Galerkin procedure and the resulting set of coupled ordinary differential equations is solved using an asymptotic analysis. The unforced assembly is known to possess localized nonlinear normal modes, which give rise to a very complicated topological structure of fundamental and subharmonic response curves. In contrast to the linear system which exhibits as many forced resonances as its number of degrees of freedom, the nonlinear system is found to possess a number of additional resonance branches which have no counterparts in linear theory. Some of the additional resonances are spatially localized, corresponding to motions of only a small subset of periodic elements. The analytical results are verified by numerical Poincaré maps, and the forced localization features of the nonlinear assembly are demonstrated by considering its response to impulsive excitations.     

Wetting front instability in unsaturated porous media: A three-dimensional study in initially dry sand

Three-dimensional fingers caused by gravity driven, wetting front instability in unsaturated porous media were explored through laboratory experimentation. Two sets of experiments were conducted using initially dry sand in large 30 cm diameter columns to guide analytical development for finger velocity and diameter. The first set consisted of ponding water on a two-layer sand system with a fine sand overlying a coarse sand. Here, a complicated pattern of interaction among fingers was found to occur. In the second set, water was applied directly to the coarse layer as 2 cm diameter area sources, enabling systematic study of individual finger structure. Based on dimensional analysis and the experimental results, general relationships were found for finger velocity and cross-sectional area as a function of both the flux through the finger and hydraulic properties of the coarse layer represented by the sorptivity, saturated conductivity, and initial and saturated moisture contents. Unlike the two-dimensional case, air entrapment was an important factor in explaining the experimental results.     

Unsteady flows in elastico-viscous liquids

Summary Consideration is given to two problems involving the unsteady motion of a sphere in aMaxwell liquid. In both problems the full solutions are obtained and compared in each case to the solution obtained using an approximation procedure. Good agreement is obtained for large values of the elastic parameter. The approximation reduces the mathematics considerably and thus allows experimentalists to determine the elastic parameter involved.With 2 figures     

Hypercontractivity for Semigroups of Unital Qubit Channels

Hypercontractivity is proved for products of qubit channels that belong to self-adjoint semigroups. The hypercontractive bound gives necessary and sufficient conditions for a product of the form ${e^{-t_1 H_1}\otimes \cdots \otimes e^{- t_n H_n}}$ to be a contraction from L ^p to L ^q , where L ^p is the algebra of 2 ⁿ -dimensional matrices equipped with the normalized Schatten norm, and each generator H _j is a self-adjoint positive semidefinite operator on the algebra of 2-dimensional matrices. As a particular case the result establishes the hypercontractive bound for a product of qubit depolarizing channels.     

Single molecules reveal the dynamics of heterogeneities in a polymer at the glass transition

The notion of heterogeneous dynamics in glasses, that is, the spatial and temporal variations of structural relaxation rates, explains many of the puzzling features of glass dynamics. The nature and the dynamics of these heterogeneities, however, have been very controversial. Single rhodamine B molecules in poly(vinyl acetate) at the glass transition reorient through sudden jumps. With a statistical search for the most likely break points in the logarithm of the ratio of the two perpendicular fluorescence polarizations, we determine the times of these angular jumps. We interpret these jumps as an indication for individual glass rearrangements in the vicinity of the probe molecule. Time-series analysis of the resulting sequence of waiting times between jumps shows that dynamic heterogeneities in the matrix exist, but are short lived. From the correlation of the logarithm of the waiting time between subsequent jumps, we determine an upper limit for the lifetime of heterogeneities in the sample. The correlation time of τ(het) = 32 s is three times shorter than the orientational correlation time of the probe molecule, τ(orient) = 90 s, in the sample at this temperature, but 13 times longer than the structural relaxation time, τ(α) = 2.5 s, estimated for this sample from dielectric experiments. We present a model for glass dynamics in which each rearrangement in one region causes a random change in the barrier height for subsequent rearrangements in a neighboring region. This model, which equates the dynamics of the heterogeneities with the dynamics of the glass itself and thus implies a factor of one between heterogeneity lifetime and structural relaxation time, successfully reproduces the statistics of the experimentally observed waiting time sequences.     

The triflic acid-mediated cyclisation of N-benzylcinnamanilides

N-Benzylcinnamanilides cyclise with triflic acid to form 1-benzyl-4-aryl-2,4-dihydro-1H-quinolin-2-ones and 2,5-diaryl-benzazepin-3-ones. The product ratio is determined by the preferred orientation of the amide and by the electronics of the substituents. With ortho-substituted anilides, N-debenzylation also occurs to give 4-aryl-2,4-dihydro-1H-quinoline-2-ones.     

Synthesis and Study of Cationic,Two‐Coordinate Triphenylphosphine– Gold–π Complexes

Cationic, two‐coordinate triphenylphosphine–gold(I)–π complexes of the form [(PPh₃)Au(π ligand)]⁺ SbF₆^? (π ligand=4‐methylstyrene, 1? SbF₆), 2‐methyl‐2‐butene ( 3? SbF₆), 3‐hexyne ( 6? SbF₆), 1,3‐cyclohexadiene ( 7? SbF₆), 3‐methyl‐1,2‐butadiene ( 8? SbF₆), and 1,7‐diphenyl‐3,4‐heptadiene ( 10? SbF₆) were generated in situ from reaction of [(PPh₃)AuCl], AgSbF₆, and π ligand at ?78 °C and were characterized by low‐temperature, multinuclear NMR spectroscopy without isolation. The π ligands of these complexes were both weakly bound and kinetically labile and underwent facile intermolecular exchange with free ligand (ΔG^≠≈9 kcal mol^?1 in the case of 6? SbF₆) and competitive displacement by weak σ donors, such as trifluoromethane sulfonate. Triphenylphosphine–gold(I)–π complexes were thermally unstable and decomposed above ?20 °C to form the bis(triphenylphosphine) gold cation [(PPh₃)₂Au]⁺SbF₆^? ( 2? SbF₆).