Application of finite element techniques in predicting the acoustic properties of turbofan inlets

An analytical technique was developed for predicting the acoustic performance of turbofan inlets carrying a subsonic axisymmetric steady flow. The finite element method combined with the method of weighted residuals is used in predicting the acoustic properties of variable area, annular ducts with or without acoustic treatments along their walls. An approximate solution for the steady inviscid flow field is obtained using an integral method for calculating the incompressible potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique was assessed by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard walled annular cylinder with a constant mean flow

The transition temperature of the dilute interacting Bose gas for NN internal degrees of freedom

We calculate explicitly the variation $\delta T_c$ of the Bose-Einstein condensation temperature $T_c$ induced by weak repulsive two-body interactions to leading order in the interaction strength. As shown earlier by general arguments, $\delta T_c/T_c$ is linear in the dimensionless product $an^{1/3}$ to leading order, where $n$ is the density and $a$ the scattering length. This result is non-perturbative, and a direct perturbative calculation of the amplitude is impossible due to infrared divergences familiar from the study of the superfluid helium lambda transition. Therefore we introduce here another standard expansion scheme, generalizing the initial model which depends on one complex field to one depending on $N$ real fields, and calculating the temperature shift at leading order for large $N$. The result is explicit and finite. The reliability of the result depends on the relevance of the large $N$ expansion to the situation N=2, which can in principle be checked by systematic higher order calculations. The large $N$ result agrees remarkably well with recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter

Acoustic properties of turbofan inlets

The acoustic field within a duct containing a nonuniform steady flow was predicted. This analysis used the finite element method to calculate the velocity potential within the duct

Multicritical behavior of two-dimensional anisotropic antiferromagnets in a magnetic field

We study the phase diagram and multicritical behavior of anisotropic Heisenberg antiferromagnets on a square lattice in the presence of a magnetic field along the easy axis. We argue that, beside the Ising and XY critical lines, the phase diagram presents a first-order spin-flop line starting from T=0, as in the three-dimensional case. By using field theory we show that the multicritical point where these transition lines meet cannot be O(3) symmetric and occurs at finite temperature. We also predict how the critical temperature of the transition lines varies with the magnetic field and the uniaxial anisotropy in the limit of weak anisotropy.Comment: 21 pages, 8 fig

Distributions of absolute central moments for random walk surfaces

We study periodic Brownian paths, wrapped around the surface of a cylinder. One characteristic of such a path is its width square, $w^2$, defined as its variance. Though the average of $w^2$ over all possible paths is well known, its full distribution function was investigated only recently. Generalising $w^2$ to $w^{(N)}$, defined as the $N$-th power of the {\it magnitude} of the deviations of the path from its mean, we show that the distribution functions of these also scale and obtain the asymptotic behaviour for both large and small $w^{(N)}$

Breakdown of the perturbative renormalization group at certain quantum critical points

It is shown that the presence of multiple time scales at a quantum critical point can lead to a breakdown of the loop expansion for critical exponents, since coefficients in the expansion diverge. Consequently, results obtained from finite-order perturbative renormalization-group treatments may be not be an approximation in any sense to the true asymptotic critical behavior. This problem manifests itself as a non-renormalizable field theory, or, equivalently, as the presence of a dangerous irrelevant variable. The quantum ferromagnetic transition in disordered metals provides an example.Comment: 4pp, 1 eps fi

Disorder-Induced Shift of Condensation Temperature for Dilute Trapped Bose Gases

We determine the leading shift of the Bose-Einstein condensation temperature for an ultracold dilute atomic gas in a harmonic trap due to weak disorder by treating both a Gaussian and a Lorentzian spatial correlation for the quenched disorder potential. Increasing the correlation length from values much smaller than the geometric mean of the trap scale and the mean particle distance to much larger values leads first to an increase of the positive shift to a maximum at this critical length scale and then to a decrease.Comment: Author information under http://www.theo-phys.uni-essen.de/tp/ags/pelster_di

Anomalous Density-of-States Fluctuations in Two-Dimensional Clean Metals

It is shown that density-of-states fluctuations, which can be interpreted as the order-parameter susceptibility \chi_OP in a Fermi liquid, are anomalously strong as a result of the existence of Goldstone modes and associated strong fluctuations. In a 2-d system with a long-range Coulomb interaction, a suitably defined \chi_OP diverges as 1/T^2 as a function of temperature in the limit of small wavenumber and frequency. In contrast, standard statistics suggest \chi_OP = O(T), a discrepancy of three powers of T. The reasons behind this surprising prediction, as well as ways to observe it, are discussed.Comment: 4 pp, revised version contains a substantially expanded derivatio

Searching for RR Lyrae stars in the Canis Major Overdensity

The Canis Major overdensity (CMa) was initially proposed to be the remnant of a tidally disrupting dSph galaxy. Since its nature is still subject of debate, the goal of the present work was to conduct a large-scale RR Lyrae survey in CMa, in order to see if there is an overdensity of these stars. The survey spans a total area of ~34 sq. deg. with observations in V and R filters, made with the 1.0m Jurgen Stock Schmidt telescope at the National Astronomical Observatory of Venezuela. Current results in a subregion, including spectroscopic observations, show that the small number of RR Lyrae stars found can be accounted for by the halo and thick disk components of our Galaxy.Comment: 2 pages, 1 figure, to appear in the proceedings of IAU Symposium No241 "Stellar Populations as Building Blocks of Galaxies