Suspensions Thermal Noise in the LIGO Gravitational Wave Detector

We present a calculation of the maximum sensitivity achievable by the LIGO Gravitational wave detector in construction, due to limiting thermal noise of its suspensions. We present a method to calculate thermal noise that allows the prediction of the suspension thermal noise in all its 6 degrees of freedom, from the energy dissipation due to the elasticity of the suspension wires. We show how this approach encompasses and explains previous ways to approximate the thermal noise limit in gravitational waver detectors. We show how this approach can be extended to more complicated suspensions to be used in future LIGO detectors.Comment: 28 pages, 13 figure

Three-dimensional flow instability in a lid-driven isosceles triangular cavity

Linear three-dimensional modal instability of steady laminar two-dimensional states developing in a lid-driven cavity of isosceles triangular cross-section is investigated theoretically and experimentally for the case in which the equal sides form a rectangular corner. An asymmetric steady two-dimensional motion is driven by the steady motion of one of the equal sides. If the side moves away from the rectangular corner, a stationary three-dimensional instability is found. If the motion is directed towards the corner, the instability is oscillatory. The respective critical Reynolds numbers are identified both theoretically and experimentally. The neutral curves pertinent to the two configurations and the properties of the respective leading eigenmodes are documented and analogies to instabilities in rectangular lid-driven cavities are discussed

On algebraic classification of quasi-exactly solvable matrix models

We suggest a generalization of the Lie algebraic approach for constructing quasi-exactly solvable one-dimensional Schroedinger equations which is due to Shifman and Turbiner in order to include into consideration matrix models. This generalization is based on representations of Lie algebras by first-order matrix differential operators. We have classified inequivalent representations of the Lie algebras of the dimension up to three by first-order matrix differential operators in one variable. Next we describe invariant finite-dimensional subspaces of the representation spaces of the one-, two-dimensional Lie algebras and of the algebra sl(2,R). These results enable constructing multi-parameter families of first- and second-order quasi-exactly solvable models. In particular, we have obtained two classes of quasi-exactly solvable matrix Schroedinger equations.Comment: LaTeX-file, 16 pages, submitted to J.Phys.A: Math.Ge

A New Algebraization of the Lame Equation

We develop a new way of writing the Lame Hamiltonian in Lie-algebraic form. This yields, in a natural way, an explicit formula for both the Lame polynomials and the classical non-meromorphic Lame functions in terms of Chebyshev polynomials and of a certain family of weakly orthogonal polynomialsComment: Latex2e with AMS-LaTeX and cite packages; 32 page

Natural inflation in 5D warped backgrounds

In light of the five-year data from the Wilkinson Microwave Anisotropy Probe (WMAP), we discuss models of inflation based on the pseudo Nambu-Goldstone potential predicted in five-dimensional gauge theories for different backgrounds: flat Minkowski, anti-de Sitter, and dilatonic spacetime. In this framework, the inflaton potential is naturally flat due to shift symmetries and the mass scales associated with it are related to 5D geometrical quantities.Comment: 10 pages, 8 figures; matches version to appear in Phys. Rev.

CMB anisotropy: deviations from Gaussianity due to non-linear gravity

Non-linear evolution of cosmological energy density fluctuations triggers deviations from Gaussianity in the temperature distribution of the cosmic microwave background. A method to estimate these deviations is proposed. N-body simulations -- in a $\Lambda$CDM cosmology -- are used to simulate the strongly non-linear evolution of cosmological structures. It is proved that these simulations can be combined with the potential approximation to calculate the statistical moments of the CMB anisotropies produced by non-linear gravity. Some of these moments are computed and the resulting values are different from those corresponding to Gaussianity.Comment: 6 latex pages with mn.sty, 3 eps figures. Accepted in MNRA