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

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

Kinematically Redundant Octahedral Motion Platform for Virtual Reality Simulations

We propose a novel design of a parallel manipulator of Stewart Gough type for virtual reality application of single individuals; i.e. an omni-directional treadmill is mounted on the motion platform in order to improve VR immersion by giving feedback to the human body. For this purpose we modify the well-known octahedral manipulator in a way that it has one degree of kinematical redundancy; namely an equiform reconfigurability of the base. The instantaneous kinematics and singularities of this mechanism are studied, where especially "unavoidable singularities" are characterized. These are poses of the motion platform, which can only be realized by singular configurations of the mechanism despite its kinematic redundancy.Comment: 13 pages, 6 figure

Canonical polyadic decomposition of complex-valued multi-way arrays based on simultaneous Schur decomposition

International audienceIn this paper, we propose a new semi-algebraic algorithm to compute the Canonical Polyadic (CP) decomposition of complex-valued multi-way arrays. The proposed algorithm is based on the Simultaneous Schur Decomposition (SSD) of particular matrices derived from the array to process. This CP algorithm solves some convergence problems of classical iterative techniques and its identifiability assumptions are less restrictive than those of other semi-algebraic methods. We also propose a new Jacobi-like algorithm to calculate the SSD of several complex-valued matrices. Finally the usefulness of the proposed method is illustrated in the context of fluorescence spectroscopy and epileptic source localization

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

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

Rotation symmetry axes and the quality index in a 3D octahedral parallel robot manipulator system

The geometry of a 3D octahedral parallel robot manipulator system is specified in terms of two rigid octahedral structures (the fixed and moving platforms) and six actuation legs. The symmetry of the system is exploited to determine the behaviour of (a new version of) the quality index for various motions. The main results are presented graphically

Estimation of Fiber Orientations Using Neighborhood Information

Data from diffusion magnetic resonance imaging (dMRI) can be used to reconstruct fiber tracts, for example, in muscle and white matter. Estimation of fiber orientations (FOs) is a crucial step in the reconstruction process and these estimates can be corrupted by noise. In this paper, a new method called Fiber Orientation Reconstruction using Neighborhood Information (FORNI) is described and shown to reduce the effects of noise and improve FO estimation performance by incorporating spatial consistency. FORNI uses a fixed tensor basis to model the diffusion weighted signals, which has the advantage of providing an explicit relationship between the basis vectors and the FOs. FO spatial coherence is encouraged using weighted l1-norm regularization terms, which contain the interaction of directional information between neighbor voxels. Data fidelity is encouraged using a squared error between the observed and reconstructed diffusion weighted signals. After appropriate weighting of these competing objectives, the resulting objective function is minimized using a block coordinate descent algorithm, and a straightforward parallelization strategy is used to speed up processing. Experiments were performed on a digital crossing phantom, ex vivo tongue dMRI data, and in vivo brain dMRI data for both qualitative and quantitative evaluation. The results demonstrate that FORNI improves the quality of FO estimation over other state of the art algorithms.Comment: Journal paper accepted in Medical Image Analysis. 35 pages and 16 figure

A terrestrial search for dark contents of the vacuum, such as dark energy, using atom interferometry

We describe the theory and first experimental work on our concept for searching on earth for the presence of dark content of the vacuum (DCV) using atom interferometry. Specifically, we have in mind any DCV that has not yet been detected on a laboratory scale, but might manifest itself as dark energy on the cosmological scale. The experimental method uses two atom interferometers to cancel the effect of earth's gravity and diverse noise sources. It depends upon two assumptions: first, that the DCV possesses some space inhomogeneity in density, and second that it exerts a sufficiently strong non-gravitational force on matter. The motion of the apparatus through the DCV should then lead to an irregular variation in the detected matter-wave phase shift. We discuss the nature of this signal and note the problem of distinguishing it from instrumental noise. We also discuss the relation of our experiment to what might be learned by studying the noise in gravitational wave detectors such as LIGO.The paper concludes with a projection that a future search of this nature might be carried out using an atom interferometer in an orbiting satellite. The apparatus is now being constructed