Perturbations of the local gravity field due to mass distribution on precise measuring instruments: a numerical method applied to a cold atom gravimeter

We present a numerical method, based on a FEM simulation, for the determination of the gravitational field generated by massive objects, whatever geometry and space mass density they have. The method was applied for the determination of the self gravity effect of an absolute cold atom gravimeter which aims at a relative uncertainty of 10-9. The deduced bias, calculated with a perturbative treatment, is finally presented. The perturbation reaches (1.3 \pm 0.1) \times 10-9 of the Earth's gravitational field.Comment: 12 pages, 7 figure

Comparison between two mobile absolute gravimeters: optical versus atomic interferometers

We report a comparison between two absolute gravimeters: the LNE-SYRTE cold atoms gravimeter and FG5#220 of Leibniz Universit\"at of Hannover. They rely on different principles of operation: atomic and optical interferometry. Both are movable which enabled them to participated to the last International Comparison of Absolute Gravimeters (ICAG'09) at BIPM. Immediately after, their bilateral comparison took place in the LNE watt balance laboratory and showed an agreement of 4.3 +/- 6.4 {\mu}Gal

Influence of chirping the Raman lasers in an atom gravimeter: phase shifts due to the Raman light shift and to the finite speed of light

We present here an analysis of the influence of the frequency dependence of the Raman laser light shifts on the phase of a Raman-type atom gravimeter. Frequency chirps are applied to the Raman lasers in order to compensate gravity and ensure the resonance of the Raman pulses during the interferometer. We show that the change in the Raman light shift when this chirp is applied only to one of the two Raman lasers is enough to bias the gravity measurement by a fraction of $\mu$Gal ($1~\mu$Gal~=~$10^{-8}$~m/s$^2$). We also show that this effect is not compensated when averaging over the two directions of the Raman wavevector $k$. This thus constitutes a limit to the rejection efficiency of the $k$-reversal technique. Our analysis allows us to separate this effect from the effect of the finite speed of light, which we find in perfect agreement with expected values. This study highlights the benefit of chirping symmetrically the two Raman lasers

The electric double layer has a life of its own

Using molecular dynamics simulations with recently developed importance sampling methods, we show that the differential capacitance of a model ionic liquid based double-layer capacitor exhibits an anomalous dependence on the applied electrical potential. Such behavior is qualitatively incompatible with standard mean-field theories of the electrical double layer, but is consistent with observations made in experiment. The anomalous response results from structural changes induced in the interfacial region of the ionic liquid as it develops a charge density to screen the charge induced on the electrode surface. These structural changes are strongly influenced by the out-of-plane layering of the electrolyte and are multifaceted, including an abrupt local ordering of the ions adsorbed in the plane of the electrode surface, reorientation of molecular ions, and the spontaneous exchange of ions between different layers of the electrolyte close to the electrode surface. The local ordering exhibits signatures of a first-order phase transition, which would indicate a singular charge-density transition in a macroscopic limit

Self-Motions of General 3-RPR Planar Parallel Robots

This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the expressions for the singularity loci of 3-RPR planar parallel robots are determined. Then, the global behaviour at all singularities is geometrically described by studying the degeneracy of the direct kinematic model. Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted. Finally, a practical example is discussed and experimental validations performed on an actual robot prototype are presented

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Mid-Infrared Spectroscopy of Uranus from the Spitzer Infrared Spectrometer: 2. Determination of the Mean Composition of the Upper Troposphere and Stratosphere

Mid-infrared spectral observations Uranus acquired with the Infrared Spectrometer (IRS) on the Spitzer Space Telescope are used to determine the abundances of C2H2, C2H6, CH3C2H, C4H2, CO2, and tentatively CH3 on Uranus at the time of the 2007 equinox. For vertically uniform eddy diffusion coefficients in the range 2200-2600 cm2 s-1, photochemical models that reproduce the observed methane emission also predict C2H6 profiles that compare well with emission in the 11.6-12.5 micron wavelength region, where the nu9 band of C2H6 is prominent. Our nominal model with a uniform eddy diffusion coefficient Kzz = 2430 cm2 sec-1 and a CH4 tropopause mole fraction of 1.6x10-5 provides a good fit to other hydrocarbon emission features, such as those of C2H2 and C4H2, but the model profile for CH3C2H must be scaled by a factor of 0.43, suggesting that improvements are needed in the chemical reaction mechanism for C3Hx species. The nominal model is consistent with a CH3D/CH4 ratio of 3.0+-0.2x10-4. From the best-fit scaling of these photochemical-model profiles, we derive column abundances above the 10-mbar level of 4.5+01.1/-0.8 x 10+19 molecule-cm-2 for CH4, 6.2 +- 1.0 x 10+16 molecule-cm-2 for C2H2 (with a value 24% higher from a different longitudinal sampling), 3.1 +- 0.3 x 10+16 molecule-cm-2 for C2H6, 8.6 +- 2.6 x 10+13 molecule-cm-2 for CH3C2H, 1.8 +- 0.3 x 10+13 molecule-cm-2 for C4H2, and 1.7 +- 0.4 x 10+13 molecule-cm-2 for CO2 on Uranus. Our results have implications with respect to the influx rate of exogenic oxygen species and the production rate of stratospheric hazes on Uranus, as well as the C4H2 vapor pressure over C4H2 ice at low temperatures