Stability conditions and positivity of invariants of fibrations

We study three methods that prove the positivity of a natural numerical invariant associated to $1-$parameter families of polarized varieties. All these methods involve different stability conditions. In dimension 2 we prove that there is a natural connection between them, related to a yet another stability condition, the linear stability. Finally we make some speculations and prove new results in higher dimension.Comment: Final version, to appear in the Springer volume dedicated to Klaus Hulek on the occasion of his 60-th birthda

Observation of single collisionally cooled trapped ions in a buffer gas

Individual Ba ions are trapped in a gas-filled linear ion trap and observed with a high signal-to-noise ratio by resonance fluorescence. Single-ion storage times of ~5 min (~1 min) are achieved using He (Ar) as a buffer gas at pressures in the range 8e-5 - 4e-3 torr. Trap dynamics in buffer gases are experimentally studied in the simple case of single ions. In particular, the cooling effects of light gases such as He and Ar and the destabilizing properties of heavier gases such as Xe are studied. A simple model is offered to explain the observed phenomenology.Comment: 5 pages, 4 figures, accepted for publication in Phys. Rev. A. Minor text and figure change

Birefringence of interferential mirrors at normal incidence Experimental and computational study

In this paper we present a review of the existing data on interferential mirror birefringence. We also report new measurements of two sets of mirrors that confirm that mirror phase retardation per reflection decreases when mirror reflectivity increases. We finally developed a computational code to calculate the expected phase retardation per reflection as a function of the total number of layers constituting the mirror. Different cases have been studied and we have compared computational results with the trend of the experimental data. Our study indicates that the origin of the mirror intrinsic birefringence can be ascribed to the reflecting layers close to the substrate.Comment: To be published in Applied Physics

Planetary Dynamics and Habitable Planet Formation In Binary Star Systems

Whether binaries can harbor potentially habitable planets depends on several factors including the physical properties and the orbital characteristics of the binary system. While the former determines the location of the habitable zone (HZ), the latter affects the dynamics of the material from which terrestrial planets are formed (i.e., planetesimals and planetary embryos), and drives the final architecture of the planets assembly. In order for a habitable planet to form in a binary star system, these two factors have to work in harmony. That is, the orbital dynamics of the two stars and their interactions with the planet-forming material have to allow terrestrial planet formation in the habitable zone, and ensure that the orbit of a potentially habitable planet will be stable for long times. We have organized this chapter with the same order in mind. We begin by presenting a general discussion on the motion of planets in binary stars and their stability. We then discuss the stability of terrestrial planets, and the formation of potentially habitable planets in a binary-planetary system.Comment: 56 pages, 29 figures, chapter to appear in the book: Planets in Binary Star Systems (Ed. N. Haghighipour, Springer publishing company

Hydrotropism: analysis of the root response to a moisture gradient

Hydrotropism is a genuine response of roots to a moisture gradient to avoid drought. An experimental system for the induction of hydrotropic root response in petri dishes was designed by pioneering groups in the field. This system uses split agar plates containing an osmolyte only in a region of the plate in order to generate a water potential gradient. Arabidopsis seedlings are placed on the MS agar plate so that their root tips are near the junction between plain MS medium and the region supplemented with the osmolyte. This elicits a hydrotropic response in Arabidopsis roots that can be measured as the root curvature angle

Coincidence analysis to search for inspiraling compact binaries using TAMA300 and LISM data

Japanese laser interferometric gravitational wave detectors, TAMA300 and LISM, performed a coincident observation during 2001. We perform a coincidence analysis to search for inspiraling compact binaries. The length of data used for the coincidence analysis is 275 hours when both TAMA300 and LISM detectors are operated simultaneously. TAMA300 and LISM data are analyzed by matched filtering, and candidates for gravitational wave events are obtained. If there is a true gravitational wave signal, it should appear in both data of detectors with consistent waveforms characterized by masses of stars, amplitude of the signal, the coalescence time and so on. We introduce a set of coincidence conditions of the parameters, and search for coincident events. This procedure reduces the number of fake events considerably, by a factor $\sim 10^{-4}$ compared with the number of fake events in single detector analysis. We find that the number of events after imposing the coincidence conditions is consistent with the number of accidental coincidences produced purely by noise. We thus find no evidence of gravitational wave signals. We obtain an upper limit of 0.046 /hours (CL $= 90$) to the Galactic event rate within 1kpc from the Earth. The method used in this paper can be applied straightforwardly to the case of coincidence observations with more than two detectors with arbitrary arm directions.Comment: 28 pages, 17 figures, Replaced with the version to be published in Physical Review

Optical Conductivity and Electronic Structure of CeRu4Sb12 under High Pressure

Optical conductivity [s(w)] of Ce-filled skutterudite CeRu4Sb12 has been measured at high pressure to 8 GPa and at low temperature, to probe the pressure evolution of its electronic structures. At ambient pressure, a mid-infrared peak at 0.1 eV was formed in s(w) at low temperature, and the spectral weight below 0.1 eV was strongly suppressed, due to a hybridization of the f electron and conduction electron states. With increasing external pressure, the mid-infrared peak shifts to higher energy, and the spectral weight below the peak was further depleted. The obtained spectral data are analyzed in comparison with band calculation result and other reported physical properties. It is shown that the electronic structure of CeRu4Sb12 becomes similar to that of a narrow-gap semiconductor under external pressure.Comment: 8 pages, 9 figure

Majorations explicites de fonctions de Hilbert-Samuel géométrique et arithmétique

International audienceBy using the $\mathbb R$-filtration approach of Arakelov geometry, one establishes explicit upper bounds for geometric and arithmetic Hilbert-Samuel function for line bundles on projective varieties and hermitian line bundles on arithmetic projective varieties

Sources of nonlinearities, chatter generation and suppression in metal cutting

The mechanics of chip formation has been revisited in order to understand functional relationships between the process and the technological parameters. This has led to the necessity of considering the chip-formation process as highly nonlinear, with complex interrelations between its dynamics and thermodynamics. In this paper a critical review of the state of the art of modelling and the experimental investigations is outlined with a view to how the nonlinear dynamics perception can help to capture the major phenomena causing instabilities (chatter) in machining operations. The paper is concluded with a case study, where stability of a milling process is investigated in detail, using an analytical model which results in an explicit relation for the stability limit. The model is very practical for the generation of the stability lobe diagrams, which is time consuming when using numerical methods. The extension of the model to the stability analysis of variable pitch cutting tools is also given. The application and verification of the method are demonstrated by several examples