The Large Scale Energy Landscapes of Randomly Pinned Objects

We discuss the large scale effective potential for elastic objects (manifolds) in the presence of a random pinning potential, from the point of view of the Functional Renormalisation Group (FRG) and of the replica method. Both approaches suggest that the energy landscape at large scales is a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined.Comment: 14 pages, two postcript figures attache

D-Jogger: Syncing Music with Walking

(Abstract to follow

Slow invariant manifolds as curvature of the flow of dynamical systems

Considering trajectory curves, integral of n-dimensional dynamical systems, within the framework of Differential Geometry as curves in Euclidean n-space, it will be established in this article that the curvature of the flow, i.e. the curvature of the trajectory curves of any n-dimensional dynamical system directly provides its slow manifold analytical equation the invariance of which will be then proved according to Darboux theory. Thus, it will be stated that the flow curvature method, which uses neither eigenvectors nor asymptotic expansions but only involves time derivatives of the velocity vector field, constitutes a general method simplifying and improving the slow invariant manifold analytical equation determination of high-dimensional dynamical systems. Moreover, it will be shown that this method generalizes the Tangent Linear System Approximation and encompasses the so-called Geometric Singular Perturbation Theory. Then, slow invariant manifolds analytical equation of paradigmatic Chua's piecewise linear and cubic models of dimensions three, four and five will be provided as tutorial examples exemplifying this method as well as those of high-dimensional dynamical systems

Canards from Chua's circuit

The aim of this work is to extend Beno\^it's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.Comment: arXiv admin note: text overlap with arXiv:1408.489

CLT for Crossings of random trigonometric Polynomials

International audienceWe establish a central limit theorem for the number of roots of the equation $X_N(t) =u$ when $X_N(t)$ is a Gaussian trigonometric polynomial of degree $N$. The case $u=0$ was studied by Granville and Wigman. We show that for some size of the considered interval, the asymptotic behavior is different depending on whether $u$ vanishes or not. Our mains tools are: a) a chaining argument with the stationary Gaussain process with covariance $\sin(t)/t$, b) the use of Wiener chaos decomposition that explains some singularities that appear in the limit when $u \neq 0$

Control of magnetotactic bacterium in a micro-fabricated maze

We demonstrate the closed-loop control of a magnetotactic bacterium (MTB), i.e., Magnetospirillum magnetotacticum, within a micro-fabricated maze using a magneticbased manipulation system. The effect of the channel wall on the motion of the MTB is experimentally analyzed. This analysis is done by comparing the characteristics of the transient- and steady-states of the controlled MTB inside and outside a microfabricated maze. In this analysis, the magnetic dipole moment of our MTB is characterized using a motile technique (the u-turn technique), then used in the realization of a closed-loop control system. This control system allows the MTB to reach reference positions within a micro-fabricated maze with a channel width of 10 μm, at a velocity of 8 μm/s. Further, the control system positions the MTB within a region-of-convergence of 10 μm in diameter. Due to the effect of the channel wall, we observe that the velocity and the positioning accuracy of the MTB are decreased and increased by 71% and 44%, respectively

Finding Black Holes with Microlensing

The MACHO and OGLE collaborations have argued that the three longest duration bulge microlensing events are likely caused by nearby black holes, given the small velocities measured with microlensing parallax and nondetection of the lenses. However, these events may be due to lensing by more numerous lower mass stars at greater distances. We find a posteriori probabilities of 76%, 16%, and 4% that the three longest events are black holes, assuming a Salpeter initial mass function (IMF) and a 40 M cutoff for neutron star progenitors; the numbers depend strongly on the assumed mass function but favor a black hole for the longest event for most standard IMFs. The longest events (>600 days) have an a priori 26% probability of being black holes for a standard mass function. We propose a new technique for measuring the lens mass function using the mass distribution of long events measured with the Advanced Camera for Surveys on the Hubble Space Telescope, the Very Large Telescope Interferometer, the Space Interferometry Mission, or the Global Astrometric Interferometer for Astrophysics.Comment: final version with additional significant correction