A study of sound generation in subsonic rotors, volume 2

Computer programs were developed for use in the analysis of sound generation by subsonic rotors. Program AIRFOIL computes the spectrum of radiated sound from a single airfoil immersed in a laminar flow field. Program ROTOR extends this to a rotating frame, and provides a model for sound generation in subsonic rotors. The program also computes tone sound generation due to steady state forces on the blades. Program TONE uses a moving source analysis to generate a time series for an array of forces moving in a circular path. The resultant time series are than Fourier transformed to render the results in spectral form. Program SDATA is a standard time series analysis package. It reads in two discrete time series and forms auto and cross covariances and normalizes these to form correlations. The program then transforms the covariances to yield auto and cross power spectra by means of a Fourier transformation

AdS-Carroll Branes

Coset methods are used to determine the action of a co-dimension one brane (domain wall) embedded in (d+1)-dimensional AdS space in the Carroll limit in which the speed of light goes to zero. The action is invariant under the non-linearly realized symmetries of the AdS-Carroll spacetime. The Nambu-Goldstone field exhibits a static spatial distribution for the brane with a time varying momentum density related to the brane's spatial shape as well as the AdS-C geometry. The AdS-C vector field dual theory is obtained.Comment: 47 page

Gauging Nonlinear Supersymmetry

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local supersymmetries. The resulting action is an invariant form of the Einstein-Hilbert action, which in addition to the gravitational vierbein, also includes a massive gravitino field. Invariant interactions with matter and gauge fields are also constructed. The effective Lagrangian describing processes involving the emission or absorption of a single light gravitino is analyzed.Comment: 20 pages, no figure

The role of grain dynamics in determining the onset of sediment transport

Sediment transport occurs when the nondimensional fluid shear stress $\Theta$ at the bed surface exceeds a minimum value $\Theta_c$. A large collection of data, known as the Shields curve, shows that $\Theta_c$ is primarily a function of the shear Reynolds number ${\rm{Re}}_*$. It is commonly assumed that $\Theta>\Theta_c({\rm{Re}}_*)$ occurs when the ${\rm Re}_*$-dependent fluid forces are too large to maintain static equilibrium for a typical surface grain. A complimentary approach, which remains relatively unexplored, is to identify $\Theta_c({\rm{Re}}_*)$ as the applied shear stress at which grains cannot stop moving. With respect to grain dynamics, ${\rm{Re}}_*$ can be viewed as the viscous time scale for a grain to equilibrate to the fluid flow divided by the typical time for the fluid force to accelerate a grain over the characteristic bed roughness. We performed simulations of granular beds sheared by a model fluid, varying only these two time scales. We find that the critical Shields number $\Theta_c({\rm Re}_*)$ obtained from the model mimics the Shields curve and is insensitive to the grain properties, the model fluid flow, and the form of the drag law. Quantitative discrepancies between the model results and the Shields curve are consistent with previous calculations of lift forces at varying ${\rm Re}_*$. Grains at low ${\rm Re}_*$ find more stable configurations than those at high ${\rm{Re}}_*$ due to differences in the grain reorganization dynamics. Thus, instead of focusing on mechanical equilibrium of a typical grain at the bed surface, $\Theta_c({\rm{Re}}_*)$ may be better described by the stress at which mobile grains cannot find a stable configuration and stop moving.Comment: to appear in Phys. Rev. Fluid

Chemistry on the inside: green chemistry in mesoporous materials

An overview of the rapidly expanding area of tailored mesoporous solids is presented. The synthesis of a wide range of the materials is covered, both inorganically and organically modified. Their applications, in particular those relating to green chemistry, are also highlighted. Finally, potential future directions for these materials are discussed

A study of sound generation in subsonic rotors, volume 1

A model for the prediction of wake related sound generation by a single airfoil is presented. It is assumed that the net force fluctuation on an airfoil may be expressed in terms of the net momentum fluctuation in the near wake of the airfoil. The forcing function for sound generation depends on the spectra of the two point velocity correlations in the turbulent region near the airfoil trailing edge. The spectra of the two point velocity correlations were measured for the longitudinal and transverse components of turbulence in the wake of a 91.4 cm chord airfoil. A scaling procedure was developed using the turbulent boundary layer thickness. The model was then used to predict the radiated sound from a 5.1 cm chord airfoil. Agreement between the predicted and measured sound radiation spectra was good. The single airfoil results were extended to a rotor geometry, and various aerodynamic parameters were studied

Nonlinear realization of local symmetries of AdS space

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the local symmetries of AdS_{d+1} space due to the embedding of an AdS_d brane. The resulting action is an SO(2,d) invariant AdS form of the Einstein-Hilbert action, which in addition to the AdS_d gravitational vielbein, also includes a massive vector field localized on the brane. Its long wavelength dynamics is the same as a massive Abelian vector field coupled to gravity in AdS_d space.Comment: 17 page

Spectrum of the Schr\"odinger operator in a perturbed periodically twisted tube

We study Dirichlet Laplacian in a screw-shaped region, i.e. a straight twisted tube of a non-circular cross section. It is shown that a local perturbation which consists of "slowing down" the twisting in the mean gives rise to a non-empty discrete spectrum.Comment: LaTeX2e, 10 page