Solution of 3-dimensional time-dependent viscous flows. Part 3: Application to turbulent and unsteady flows

A numerical scheme is developed for solving the time dependent, three dimensional compressible viscous flow equations to be used as an aid in the design of helicopter rotors. In order to further investigate the numerical procedure, the computer code developed to solve an approximate form of the three dimensional unsteady Navier-Stokes equations employing a linearized block implicit technique in conjunction with a QR operator scheme is tested. Results of calculations are presented for several two dimensional boundary layer flows including steady turbulent and unsteady laminar cases. A comparison of fourth order and second order solutions indicate that increased accuracy can be obtained without any significant increases in cost (run time). The results of the computations also indicate that the computer code can be applied to more complex flows such as those encountered on rotating airfoils. The geometry of a symmetric NACA four digit airfoil is considered and the appropriate geometrical properties are computed

Relaxing Lorentz invariance in general perturbative anomalies

We analyze the role of Lorentz symmetry in the perturbative non-gravitational anomalies for a single family of fermions. The theory is assumed to be translational invariant, power-counting renormalizable and based on a local action, but is allowed to have general Lorentz violating operators. We study the conservation of global and gauge currents associate with general internal symmetry groups and find, by using a perturbative approach, that Lorentz symmetry does not participate in the clash of symmetries that leads to the anomalies. We first analyze the triangle graphs and prove that there are regulators for which the anomalous part of the Ward identities exactly reproduces the Lorentz invariant case. Then we show, by means of a regulator independent argument, that the anomaly cancellation conditions derived in Lorentz invariant theories remain necessary ingredients for anomaly freedom.Comment: 18 pages, 1 figure. Few comments added. Article published in Physical Review

Constraints onOmega from the IRAS Redshift Surveys

We measure the anisotropy of the redshift-space power spectrum in the 1.2-Jy and QDOT redshift surveys of IRAS-selected galaxies. On large scales, this anisotropy is caused by coherent peculiar motions, and gravitational instability theory predicts a distortion of the power spectrum that depends only on the ratio $\beta \equiv f(\Omega)/b \approx \Omega^{0.6}/b$, where Omega is the cosmological density parameter and $b$ is the bias parameter. On small scales, the distortion is dominated by the random velocity dispersion in non-linear structures. We fit the observed anisotropy with an analytic model that incorporates two parameters, beta, and a small-scale velocity dispersion sigma_v. Tests on N-body simulations show that this model recovers beta quite accurately on the scales accessible to the existing IRAS redshift surveys. Applying our procedure to the 1.2-Jy and QDOT surveys, we find beta=0.52 +/- 0.13 and beta=0.54 +/- 0.3, respectively. These results imply Omega approximately 0.35 if galaxies trace mass, or a bias factor of about 2 if Omega=1.Comment: uufiles postscript here or plain postscript at ftp://dust0.dur.ac.uk/pub/preprints/cole_rsd.p

Three-dimensional unsteady viscous flow analysis over airfoil sections

A three-dimensional solution procedure for the approximate form of the Navier-Stokes equation was exercised in the two- and three-dimensional modes to compute the unsteady turbulent boundary layer on a flat plate corresponding to the data of Karlsson. The procedure is based on the use of a consistently split Linearized Block Implicit technique in conjunction with a QR operator scheme. New time-dependent upstream boundary conditions were developed that yielded realistic solutions for the interior in the vicinity of the upstream boundary. Comparisons of the computation employing these boundary conditions with the data indicate that both qualitative and quantitative agreement was obtained for the mean velocity and the in phase and out of phase components of the first harmonic of the velocity. In addition, the calculation gave results for the skin friction phase angle that had expected physical behavior for large distances downstream of the inflow boundary. For the three-dimensional case, the two-dimensional data of Karlsson was considered, but in a coordinate system skewed at 45 deg to the free stream direction. The results of the calculations were in excellent agreement with the data and the two-dimensional computations

Cosmic Evolution in Generalised Brans-Dicke Theory

We have studied the Generalised Brans-Dicke theory and obtained exact solutions of a(t),phi(t),and omega(t) for different epochs of the cosmic evolution .We discuss how inflation,decceleration,cosmic acceleration can result from this solution.The time variation of G(t) is also examined.Comment: 12 pages, no figure

Path-Integral Formulation of Pseudo-Hermitian Quantum Mechanics and the Role of the Metric Operator

We provide a careful analysis of the generating functional in the path integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator enters the expression for the generating functional.Comment: Published version, 4 page

Four Dimensional Supergravity from String Theory

A derivation of N=1 supergravity action from string theory is presented. Starting from a Nambu-Goto bosonic string, matter field is introduced to obtain a superstring in four dimension. The excitation quanta of this string contain graviton and the gravitino. Using the principle of equivalence, the action in curved space time are found and the sum of them is the Deser-Zumino N=1 supergravity action. The energy tensor is Lorentz invariant due to supersymmetry.Comment: 9 page

Low Energy Constants from High Energy Theorems

New constraints on resonance saturation in chiral perturbation theory are investigated. These constraints arise because each consistent saturation scheme must map to a representation of the full QCD chiral symmetry group. The low-energy constants of chiral perturbation theory are then related by a set of mixing angles. It is shown that vector meson dominance is a consequence of the fact that nature has chosen the lowest-dimensional nontrivial chiral representation. It is further shown that chiral symmetry places an upper bound on the mass of the lightest scalar in the hadron spectrum.Comment: 11 pages TeX and mtexsis.te

Convergence of density-matrix expansions for nuclear interactions

We extend density-matrix expansions in nuclei to higher orders in derivatives of densities and test their convergence properties. The expansions allow for converting the interaction energies characteristic to finite- and short-range nuclear effective forces into quasi-local density functionals. We also propose a new type of expansion that has excellent convergence properties when benchmarked against the binding energies obtained for the Gogny interaction.Comment: 4 pages, 3 figure