Cryogenic Sapphire Oscillator using a low-vibration design pulse-tube cryocooler: First results

A Cryogenic Sapphire Oscillator has been implemented at 11.2 GHz using a low-vibration design pulse-tube cryocooler. Compared with a state-of-the-art liquid helium cooled CSO in the same laboratory, the square root Allan variance of their combined fractional frequency instability is $\sigma_y = 1.4 \times 10^{-15}\tau^{-1/2}$ for integration times $1 < \tau < 10$ s, dominated by white frequency noise. The minimum $\sigma_y = 5.3 \times 10^{-16}$ for the two oscillators was reached at $\tau = 20$ s. Assuming equal contributions from both CSOs, the single oscillator phase noise $S_{\phi} \approx -96 \; dB \; rad^2/Hz$ at 1 Hz offset from the carrier.Comment: 5 pages, 5 figures, accepted in IEEE Trans on Ultrasonics, Ferroelectrics and Frequency Contro

On the global evolution of self-gravitating matter. Nonlinear interactions in Gowdy symmetry

We are interested in the evolution of a compressible fluid under its self-generated gravitational field. Assuming here Gowdy symmetry, we investigate the algebraic structure of the Euler equations satisfied by the mass density and velocity field. We exhibit several interaction functionals that provide us with a uniform control on weak solutions in suitable Sobolev norms or in bounded variation. These functionals allow us to study the local regularity and nonlinear stability properties of weakly regular fluid flows governed by the Euler-Gowdy system. In particular for the Gowdy equations, we prove that a spurious matter field arises under weak convergence, and we establish the nonlinear stability of weak solutions.Comment: 37 pages. v2: fix typos to match version published in 201

Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds

Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of the conservation laws is viewed as a vector-field on the manifold and depends on the unknown function as a parameter. We introduce notions of entropy solutions in the class of bounded measurable functions and in the class of measure-valued mappings. We establish the well-posedness theory for conservation laws on a manifold, by generalizing both Kruzkov's and DiPerna's theories originally developed in the Euclidian setting. The class of {\sl geometry-compatible} (as we call it) conservation laws is singled out as an important case of interest, which leads to robust $L^p$ estimates independent of the geometry of the manifold. On the other hand, general conservation laws solely enjoy the $L^1$ contraction property and leads to a unique contractive semi-group of entropy solutions. Our framework allows us to construct entropy solutions on a manifold via the vanishing diffusion method or the finite volume method.Comment: 30 pages. This is Part 1 of a serie

Cyclic spacetimes through singularity scattering maps. The laws of quiescent bounces

For spacetimes containing singularity hypersurfaces we propose a general notion of junction conditions based on a prescribed singularity scattering map, as we call it, and we introduce the notion of a cyclic spacetime (also called a multiverse) consisting of spacetime domains bounded by spacelike or timelike singularity hypersurfaces, across which our scattering map is applied. A local existence theory is established here while, in a companion paper, we construct plane-symmetric cyclic spacetimes. We study the singularity data space consisting of the suitably rescaled metric, extrinsic curvature, and matter fields which can be prescribed on each side of the singularity, and for the class of so-called quiescent singularities we establish restrictions that a singularity scattering map must satisfy. We obtain a full characterization of all scattering maps that are covariant and ultralocal, in a sense we define and, in particular, we distinguish between, on the one hand, three laws of bouncing cosmology of universal nature and, on the other hand, model-dependent junction conditions. The theory proposed in this paper applies to spacelike and timelike hypersurfaces and without symmetry restriction, and encompasses bouncing-cosmology scenarios, both in string theory and in loop quantum cosmology, and puts strong restrictions on their possible explicit realizations.Comment: 56 pages. Construction of plane symmetric cyclic spacetimes moved to a separate pape

Universal scattering laws for bouncing cosmology

Bouncing cosmologies can arise from various gravity theories. We model them through a singularity scattering map, as we call it, relating large scale geometries before and after the bounce. By classifying all suitably local maps we uncover universal laws (scaling of Kasner exponents, canonical transformation of matter). We study the singularity scattering map for Bianchi I bounces in string theory, loop quantum cosmology and modified matter models: our classification then determines how general spatial inhomogeneities and anisotropies (without BKL oscillations) are transmitted through bounces.Comment: 5 page