Nonlinear coherent transport of waves in disordered media

We present a diagrammatic theory for coherent backscattering from disordered dilute media in the nonlinear regime. The approach is non-perturbative in the strength of the nonlinearity. We show that the coherent backscattering enhancement factor is strongly affected by the nonlinearity, and corroborate these results by numerical simulations. Our theory can be applied to several physical scenarios like scattering of light in nonlinear Kerr media, or propagation of matter waves in disordered potentials.Comment: 4 pages, 3 figure

Synthetic magnetic fluxes on the honeycomb lattice

We devise experimental schemes able to mimic uniform and staggered magnetic fluxes acting on ultracold two-electron atoms, such as ytterbium atoms, propagating in a honeycomb lattice. The atoms are first trapped into two independent state-selective triangular lattices and are further exposed to a suitable configuration of resonant Raman laser beams. These beams induce hops between the two triangular lattices and make atoms move in a honeycomb lattice. Atoms traveling around each unit cell of this honeycomb lattice pick up a nonzero phase. In the uniform case, the artificial magnetic flux sustained by each cell can reach about two flux quanta, thereby realizing a cold atom analogue of the Harper model with its notorious Hofstadter's butterfly structure. Different condensed-matter phenomena such as the relativistic integer and fractional quantum Hall effects, as observed in graphene samples, could be targeted with this scheme.Comment: 12 pages, 14 figure

Mobile robot control on uneven and slippery ground: An adaptive approach based on a multi-model observer

International audienceThis paper proposes an algorithm dedicated to off-road mobile robot path tracking at high speed. In order to ensure a high accuracy, a predictive and adaptive approach is developed to face the various perturbations due to this context (mainly the bad grip conditions and the terrain geometry). The control law is based on previous work, and requires the knowledge of sideslip angles, which cannot be directly measured. As a result, an observer based on two levels of modeling (kinematic and dynamic) is proposed to ensure a relevant and fast estimation. If the kinematic part is independent from the terrain geometry, the dynamic model used in this paper requires to take explicitly into account the influence of the terrain geometry on mobile robot dynamic. It is achieved by the introduction of the lateral robot inclination, which is on-line estimated via a kalman filter and integrated in the dynamical model. The advantages of the proposed contribution to path tracking control are investigated through full-scale experiments achieved at high speed (up to 6m/s) on an uneven and grass field

Multicomponent Skyrmion lattices and their excitations

We study quantum Hall ferromagnets with a finite density topologically charged spin textures in the presence of internal degrees of freedom such as spin, valley, or layer indices, so that the system is parametrised by a $d$-component complex spinor field. In the absence of anisotropies, we find formation of a hexagonal Skyrmion lattice which completely breaks the underlying SU(d) symmetry. The ground state charge density modulation, which inevitably exists in these lattices, vanishes exponentially in $d$. We compute analytically the complete low-lying excitation spectrum, which separates into $d^{2}-1$ gapless acoustic magnetic modes and a magnetophonon. We discuss the role of effective mass anisotropy for SU(3)-valley Skyrmions relevant for experiments with AlAs quantum wells. Here, we find a transition, which breaks a six-fold rotational symmetry of a triangular lattice, followed by a formation of a square lattice at large values of anisotropy strength.Comment: 4.5 pages, 3 figure

Switchable Adhesion of Soft Composites Induced by a Magnetic Field

Switchable adhesives have the potential to improve the manufacturing and recycling of parts and to enable new modes of motility for soft robots. Here, we demonstrate magnetically-switchable adhesion of a two-phase composite to non-magnetic objects. The composite's continuous phase is a silicone elastomer, and the dispersed phase is a magneto-rheological fluid. The composite is simple to prepare, and to mould to different shapes. When a magnetic field is applied, the magneto-rheological fluid develops a yield stress, which dramatically enhances the composite's adhesive properties. We demonstrate up to a nine-fold increase of the pull-off force of non-magnetic objects in the presence of a 250 mT field

A generalization of Hausdorff dimension applied to Hilbert cubes and Wasserstein spaces

A Wasserstein spaces is a metric space of sufficiently concentrated probability measures over a general metric space. The main goal of this paper is to estimate the largeness of Wasserstein spaces, in a sense to be precised. In a first part, we generalize the Hausdorff dimension by defining a family of bi-Lipschitz invariants, called critical parameters, that measure largeness for infinite-dimensional metric spaces. Basic properties of these invariants are given, and they are estimated for a naturel set of spaces generalizing the usual Hilbert cube. In a second part, we estimate the value of these new invariants in the case of some Wasserstein spaces, as well as the dynamical complexity of push-forward maps. The lower bounds rely on several embedding results; for example we provide bi-Lipschitz embeddings of all powers of any space inside its Wasserstein space, with uniform bound and we prove that the Wasserstein space of a d-manifold has "power-exponential" critical parameter equal to d.Comment: v2 Largely expanded version, as reflected by the change of title; all part I on generalized Hausdorff dimension is new, as well as the embedding of Hilbert cubes into Wasserstein spaces. v3 modified according to the referee final remarks ; to appear in Journal of Topology and Analysi

Quantum modes on chaotic motion: analytically exact results

We discover a class of chaotic quantum systems for which we obtain some analytically exact eigenfunctions in closed form. These results have been possible due to connections shown between random matrix models, many-body theories, and dynamical systems. We believe that these results and connections will pave the way to a better understanding of quantum chaos

High-speed mobile robot control in off-road conditions: a multi-model based adaptive approach

International audienceThis paper is focused on the design of a control strategy for the path tracking of off-road mobile robots acting at high speed. In order to achieve high accuracy in such a context, uncertain and fast dynamics have to be explicitly taken into account. Since these phenomena (grip conditions, delays due to inertial and low-level control properties) are hardly measurable directly, the proposed approach relies on predictive and observer-based adaptive control techniques. In particular, the adaptive part is based on an observer loop, taking advantage of both kinematic and dynamic vehicle models. This multi-model based adaptive approach permits to adapt on-line the grip conditions (represented by cornering stiffnesses), enabling highly reactive sideslip angles observation and then accurate path tracking. The relevance of this approach is investigated through full scale experiments