An analysis of the noise reduction of orthotropic cylindrical shells Final report

Statistical energy and classical methods for calculating noise reduction of orthotropic cylindrical shell

Non-perturbative calculations for the effective potential of the PTPT symmetric and non-Hermitian (−gϕ4)(-g\phi^{4}) field theoretic model

We investigate the effective potential of the $PT$ symmetric $(-g\phi^{4})$ field theory, perturbatively as well as non-perturbatively. For the perturbative calculations, we first use normal ordering to obtain the first order effective potential from which the predicted vacuum condensate vanishes exponentially as $G\to G^+$ in agreement with previous calculations. For the higher orders, we employed the invariance of the bare parameters under the change of the mass scale $t$ to fix the transformed form totally equivalent to the original theory. The form so obtained up to $G^3$ is new and shows that all the 1PI amplitudes are perurbative for both $G\ll 1$ and $G\gg 1$ regions. For the intermediate region, we modified the fractal self-similar resummation method to have a unique resummation formula for all $G$ values. This unique formula is necessary because the effective potential is the generating functional for all the 1PI amplitudes which can be obtained via $\partial^n E/\partial b^n$ and thus we can obtain an analytic calculation for the 1PI amplitudes. Again, the resummed from of the effective potential is new and interpolates the effective potential between the perturbative regions. Moreover, the resummed effective potential agrees in spirit of previous calculation concerning bound states.Comment: 20 page

Spatially resolved spectroscopy of Coma cluster early-type galaxies IV. Completing the dataset

The long-slit spectra obtained along the minor axis, offset major axis and diagonal axis are presented for 12 E and S0 galaxies of the Coma cluster drawn from a magnitude-limited sample studied before. The rotation curves, velocity dispersion profiles and the H_3 and H_4 coefficients of the Hermite decomposition of the line of sight velocity distribution are derived. The radial profiles of the Hbeta, Mg, and Fe line strength indices are measured too. In addition, the surface photometry of the central regions of a subsample of 4 galaxies recently obtained with Hubble Space Telescope is presented. The data will be used to construct dynamical models of the galaxies and study their stellar populations.Comment: 40 pages, 7 figures, 6 tables. Accepted for publication in ApJ

Nonlinear Integral-Equation Formulation of Orthogonal Polynomials

The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P(x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial solutions is orthogonal with respect to the measure x w(x). The nonlinear integral equation can be used to specify all orthogonal polynomials in a simple and compact way. This integral equation provides a natural vehicle for extending the theory of orthogonal polynomials into the complex domain. Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex domai

On the eigenproblems of PT-symmetric oscillators

We consider the non-Hermitian Hamiltonian H= -\frac{d^2}{dx^2}+P(x^2)-(ix)^{2n+1} on the real line, where P(x) is a polynomial of degree at most n \geq 1 with all nonnegative real coefficients (possibly P\equiv 0). It is proved that the eigenvalues \lambda must be in the sector | arg \lambda | \leq \frac{\pi}{2n+3}. Also for the case H=-\frac{d^2}{dx^2}-(ix)^3, we establish a zero-free region of the eigenfunction u and its derivative u^\prime and we find some other interesting properties of eigenfunctions.Comment: 21pages, 9 figure

Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics in the presence of a Running Dilaton and Space-Time Defects

The interplay of dilatonic effects in dilaton cosmology and stochastic quantum space-time defects within the framework of string/brane cosmologies is examined. The Boltzmann equation describes the physics of thermal dark-matter-relic abundances in the presence of rolling dilatons. These dilatons affect the coupling of stringy matter to D-particle defects, which are generic in string theory. This coupling leads to an additional source term in the Boltzmann equation. The techniques of asymptotic matching and boundary-layer theory, which were recently applied by two of the authors (CMB and SS) to a Boltzmann equation, are used here to find the detailed asymptotic relic abundances for all ranges of the expectation value of the dilaton field. The phenomenological implications for the search of supersymmetric dark matter in current colliders, such as the LHC, are discussed

Asymptotic Analysis of the Boltzmann Equation for Dark Matter Relics

This paper presents an asymptotic analysis of the Boltzmann equations (Riccati differential equations) that describe the physics of thermal dark-matter-relic abundances. Two different asymptotic techniques are used, boundary-layer theory, which makes use of asymptotic matching, and the delta expansion, which is a powerful technique for solving nonlinear differential equations. Two different Boltzmann equations are considered. The first is derived from general relativistic considerations and the second arises in dilatonic string cosmology. The global asymptotic analysis presented here is used to find the long-time behavior of the solutions to these equations. In the first case the nature of the so-called freeze-out region and the post-freeze-out behavior is explored. In the second case the effect of the dilaton on cold dark-matter abundances is calculated and it is shown that there is a large-time power-law fall off of the dark-matter abundance. Corrections to the power-law behavior are also calculated.Comment: 15 pages, no figure

Bulgeless Giant Galaxies Challenge our Picture of Galaxy Formation by Hierarchical Clustering

We dissect giant Sc-Scd galaxies with Hubble Space Telescope photometry and Hobby-Eberly Telescope spectroscopy. We use HET's High Resolution Spectrograph (resolution = 15,000) to measure stellar velocity dispersions in the nuclear star clusters and pseudobulges of the pure-disk galaxies M33, M101, NGC 3338, NGC 3810, NGC 6503, and NGC 6946. We conclude: (1) Upper limits on the masses of any supermassive black holes are MBH <= (2.6+-0.5) * 10**6 M_Sun in M101 and MBH <= (2.0+-0.6) * 10**6 M_Sun in NGC 6503. (2) HST photometry shows that the above galaxies contain tiny pseudobulges that make up <~ 3 % of the stellar mass but no classical bulges. We inventory a sphere of radius 8 Mpc centered on our Galaxy to see whether giant, pure-disk galaxies are common or rare. In this volume, 11 of 19 galaxies with rotation velocity > 150 km/s show no evidence for a classical bulge. Four may contain small classical bulges that contribute 5-12% of the galaxy light. Only 4 of the 19 giant galaxies are ellipticals or have classical bulges that contribute 1/3 of the galaxy light. So pure-disk galaxies are far from rare. It is hard to understand how they could form as the quiescent tail of a distribution of merger histories. Recognition of pseudobulges makes the biggest problem with cold dark matter galaxy formation more acute: How can hierarchical clustering make so many giant, pure-disk galaxies with no evidence for merger-built bulges? This problem depends strongly on environment: the Virgo cluster is not a puzzle, because >2/3 of its stellar mass is in merger remnants.Comment: 28 pages, 16 Postscript figures, 2 tables; requires emulateapj.sty and apjfonts.sty; accepted for publication in ApJ; for a version with full resolution figures, see http://chandra.as.utexas.edu/~kormendy/kdbc.pd