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International audience; Indentation is a standard, widely used technique in mechanical assays and theoretical analysis. It unveils the fundamental modes of deformation and predicts the response of the material under more complex loads. Here we present an experimental setup for testing thin-film materials by studying the lateral indentation of a narrow opening cut into a film, triggering a cascade of buckling events. The force response F is dominated by bending and stretching effects for small displacements and slowly varies with indenter displacement $F\sim d^{2/5}$ , to finally reach a wrinkled state that results in a robust nonlinear asymptotic relation, $F\sim d^4$. Experiments with films of various thicknesses and material properties, and numerical simulations confirm our analysis and help to define an order parameter that accounts for the different response regimes observed in experiments and simulations.

We present an implementation of the analytical string theory recently applied to the description of glasses. These are modeled as continuum media with embedded elastic string heterogeneities, randomly located and randomly oriented, which oscillate around a straight equilibrium position with a fundamental frequency depending on their length. The existence of a length distribution reflects then in a distribution of oscillation frequencies which is responsible for the Boson Peak in the glass density of states. Previously, it has been shown that such a description can account for the elastic anomalies reported at frequencies comparable with the Boson Peak. Here we start from the generalized hydrodynamics to determine the dynamic correlation function $S(k,\omega)$ associated with the coherent, dispersive and attenuated, sound waves resulting from a sound-string interference. Once the vibrational density of states has been measured, we can use it for univocally fixing the string length distribution inherent to a given glass. The density-density correlation function obtained using such distribution is strongly constrained, and able to account for the experimental data collected on two prototypical glasses: glycerol and silica. The obtained string length distribution is compatible with the typical size of elastic heterogeneities previously reported for silica and supercooled liquids, and the atomic motion associated to the string dynamics is consistent with the soft modes recently identified in large scale numerical simulations as non-phonon modes responsible for the Boson Peak. The theory is thus in agreement with the most recent advances in the understanding of the glass specific dynamics and offers an appealing simple understanding of the microscopic origin of the latter, while raising new questions on the universality or material-specificity of the string distribution properties., Comment: 15 pages, 8 figures

International audience; We review experimental and theoretical results on the computing properties of single spiking micropillar lasers and present numerical studies of propagation and computing in chains of evanescently coupled micropillar lasers. Single mi-cropillar lasers are shown to behave as ultrafast optical neurons with sub-nanosecond spike times. They also possess absolute and relative refractory times, spike latency and show temporal summation. With delayed optical feedback, they emulate an autapse. These basic neural properties can be used for simple photonic computing. We show by numerical simulations of a chain of coupled spiking micropillar lasers that basic logical operations can be implemented in photonic circuits, as well as temporal pattern recognition based on the collision properties of pulses in this chain.

International audience; This study investigates the tearing of a thin notched sheet when two points on the sheet are pulled apart. The concepts that determine the crack trajectory are reviewed in the general anisotropic case, in which the energy of the fracture depends on the fracture direction. When observed as a flat sheet a purely geometric "tearing vector" is defined through the location of the crack tip and the pulling points. Both the Griffiths's criterion and the "maximum energy release rate criterion" (MERR) predict a fracture path that is parallel to the tearing vector in the isotropic case. However, for the anisotropic case, the application of the MERR leads to a crack path that deviates from the tearing vector, following a propagation direction that tends to minimize the fracture energy. In the case of strong anisotropy, it is more difficult to obtain an analytical prediction of the tearing trajectory. Thus, simple geometrical arguments are provided to give a derivation of a differential equation accounting for crack trajectory, according to the natural coordinates of the pulling, and in the case that the anisotropy is sufficiently weak. The solution derived from this analysis is in good agreement with previous experimental observations.

Driven damped coupled oscillators exhibit complex spatiotemporal dynamics. An archetype model is the driven damped sine-Gordon equation, which can describe several physical systems such as coupled pendula, extended Josephson junction, optical systems and driven magnetic wires. Close to resonance an enveloped model in the form Lugiato-Lefever equation can be derived from the driven damped sine-Gordon equation. We compare the dynamics obtained from both models. Unexpectedly, qualitatively similar dynamical behaviors are obtained for both models including homogeneous steady states, localized structures, and pattern waves. For large forcing, both systems share similar spatiotemporal chaos.

We study the patterns observed in the vicinity of a Faraday instability, in the limit of a very thin layer of viscous fluid. We numerically solve our previous model [N.O. Rojas et al., Phys. Rev. Lett. 104, 187801 (2010)] and compare our predictions to experiments. Our model captures quantitatively the threshold of instability. The direct simulation of our system permits us to predict the patterns observed in experiments.

We derive a set of non-linear amplitude equations that predicts the presence of nonlinear patterns in a vertically oscillated one dimensional viscous fluid layer.

International audience; The coherent propagation of elastic waves in a solid filled with a random distribution of pinned dislocation segments is studied to all orders in perturbation theory. It is shown that, within the independent scattering approximation, the perturbation series that generates the mass operator is a geometric series that can thus be formally summed. A divergent quantity is shown to be renormalizable to zero at low frequencies. At higher frequencies said quantity can be expressed in terms of a cut-off with dimensions of length, related to the dislocation length, and physical quantities can be computed in terms of two parameters, to be determined by experiment. The approach used in this problem is compared and contrasted with the scattering of de Broglie waves by delta-function potentials as described by the Schrödinger equation.

In this article, we present a deflection measurement setup for Atomic Force Microscopy (AFM). It is based on a quadrature phase differential interferometer: we measure the optical path difference between a laser beam reflecting above the cantilever tip and a reference beam reflecting on the static base of the sensor. A design with very low environmental susceptibility and another allowing calibrated measurements on a wide spectral range are described. Both enable a very high resolution (down to $\SI{2.5E-15}{m/\sqrt{Hz}}$), illustrated by thermal noise measurements on AFM cantilevers. They present an excellent long-term stability, and a constant sensitivity independent of the optical phase of the interferometer. A quick review shows that our precision is equaling or out-performing the best results reported in the literature, but for a much larger deflection range, up to a few $\SI{}{\micro m}$.

We study the self-modulation of a circularly polarized Alfv\'en wave in a strongly magnetized relativistic electron-positron plasma with finite temperature. This nonlinear wave corresponds to an exact solution of the equations, with a dispersion relation that has two branches. For a large magnetic field, the Alfv\'en branch has two different zones, which we call the normal dispersion zone (where $d\ensuremath{\omega}/dkg0$) and the anomalous dispersion zone (where $d\ensuremath{\omega}/dkl0$). A nonlinear Schr\"odinger equation is derived in the normal dispersion zone of the Alfv\'en wave, where the wave envelope can evolve as a periodic wave train or as a solitary wave, depending on the initial condition. The maximum growth rate of the modulational instability decreases as the temperature is increased. We also study the Alfv\'en wave propagation in the anomalous dispersion zone, where a nonlinear wave equation is obtained. However, in this zone the wave envelope can evolve only as a periodic wave train.

Equipe 101 : Nanomagnétisme et électronique de spin; International audience; We report on a method to fabricate laterally modulated Co films using the artificially induced nano-wrinkled surface of a polydimethylsiloxane polymeric film as template. Large area patterning of self-organized parallel wrinkles is formed displaying a submicrometer wavelength. The subsequent deposition of a Co layer on this wavy surface yields a uniaxial magnetic anisotropy imposed by the wrinkles' morphology. Measurement of the remanent magnetization and coercive field as a function of the field angle confirms the uniaxial nature of the anisotropy and reveals a reversal mechanism more complex than pure coherent rotation. The magnetostatic origin of the anisotropy is analyzed.

A time-periodic magnetic field applied transversally to the hard axis of an extended easy-plane ferromagnetic sample can produce parametric resonance. For the 2:1 resonance, the prototype order-parameter-equation derived from the Landau–Lifshitz–Gilbert dynamical model for the precessional motion is the parametrically driven damped nonlinear Schrodinger equation. Unfortunately this standard approximation fails to meet the stability feature of the synchronized precession states, and we propose some amendment. Localized solutions supported by the uniform states are characterized and classified into two types: motionless and propagative states, rising through a non-variational Ising–Bloch transition. We propose and investigate a dynamical model ruling this transition.

Thin fluid films can have surprising behavior depending on the boundary conditions enforced, the energy input and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime.

We present a unifying description close to a spatial bifurcation of localized states, appearing as large amplitude peaks nucleating over a pattern of lower amplitude. Localized states are pinned over a lattice spontaneously generated by the system itself. We show that the phenomenon is generic and requires only the coexistence of two spatially periodic states. At the onset of the spatial bifurcation, a forced amplitude equation is derived for the critical modes, which accounts for the appearance of localized peaks.

Experimental evidence of bouncing localized structures in a nonlinear optical system is reported., Comment: 4 pages

17 pages; International audience; We show that in a liquid-crystal-light-valve with optical feedback the Fréedericksz transition displays a subcritical character. Experimentally, we determine the extension of the bistable region and we study the propagation of fronts connecting the different metastable states. Theoretically, we derive an amplitude equation, valid close to the Fréedericksz transition point, which accounts for the subcritical character of the bifurcation. When, in the space of parameters, we move far from the Fréedericksz transition point, we adopt a mean-field model which is able to capture the qualitative features of all the successive branches of bistability. Close to the points of nascent bistability, by including diffraction effects we show the appearance of localized structures. Highly symmetric configurations of localized structures may be observed in the experiment by imposing a N-order rotation angle in the feedback loop. For increase of the input light intensity complex spatio-temporal dynamics arise, with either periodic or irregular oscillations in the position of the localized states. Rings dynamics is also observed, by the introduction of a small nonlocal shift in the feedback loop.

International audience; réedericksz transition can become subcritical in the presence of a feedback mechanism that leads to the dependence of the local electric field onto the liquid crystal re-orientation angle. We have characterized experimentally the first-order Fréedericksz transition in a Liquid Crystal Light Valve with optical feedback. The bistability region is determined, together with the Fréedericksz transition point and the Maxwell point. We show the propagation of fronts connecting the different metastable states and we estimate the front velocity. Theoretically, we derive an amplitude equation, valid close to the Fréedericksz transition point, which accounts for the subcritical character of the bifurcation.

International audience; In this article we review the conditions for the appearance of localized states in a nonlinear optical system, with particular reference to the liquid crystal light valve (LCLV) experiment. The localized structures here described are of dissipative type; that is, they represent the localized solutions of a pattern-forming system. We discuss their features of stable addressable localized states, and we show that they dispose themselves on the nodes of highly symmetric lattices, as obtained by the introduction of an N-order rotation angle in the optical feedback loop. The stability is lost either on increase of the input light intensity or by the introduction of an extra small angle of rotation. The complex spatio-temporal dynamics that follows is characterized by oscillations in the position of the localized states. We discuss the origin of this permanent dynamics in relation to the non-variational character of the LCLV system, underlining the general character of such complex behaviours of localized states.

International audience; Standing surface waves that interact with a confined, vertical, vorticity field with zero net circulation are studied both analytically and experimentally. The surface waves are generated by vertical vibration, and constant vorticity injection is achieved by a rotating disk flush mounted in the cell. Experimental results are indicative of a local wave-vortex interaction (no dislocation), and a simple theoretical model is able to explain them in quantitative detail.

Previous results on the scattering of surface waves by vertical vorticity on shallow water are generalized to the case of dispersive water waves. Dispersion effects are treated perturbatively around the shallow water limit, to first order in the ratio of depth to wavelength. The dislocation of the incident wavefront, analogous to the Aharonov-Bohm effect, is still observed. At short wavelengths the scattering is qualitatively similar to the nondispersive case. At moderate wavelengths, however, there are two markedly different scattering regimes according to wether the capillary length is smaller or larger than $\sqrt{3}$ times depth. The dislocation is characterized by a parameter that depends both on phase and group velocity. The validity range of the calculation is the same as in the shallow water case: wavelengths small compared to vortex radius, and low Mach number. The implications of these limitations are carefully considered., Comment: 30 pages, 11 figures

International audience; Surface waves interacting with a vertical vortex are studied both analytically and experimentally. There are similarities as well as differences with the Aharonov-Bohm effect: among the former, a dislocation in the wave fronts that is proportional to the vortex circulation, and among the latter, a significant change in the symmetry of the scattered wave.

When a surface wave interacts with a vertical vortex in shallow water the latter induces a dislocation in the incident wavefronts that is analogous to what happens in the Aharonov-Bohm effect for the scattering of electrons by a confined magnetic field. In addition to this global similarity between these two physical systems there is scattering. This paper reports a detailed calculation of this scattering, which is quantitatively different from the electronic case in that a surface wave penetrates the inside of a vortex while electrons do not penetrate a solenoid. This difference, together with an additional difference in the equations that govern both physical systems lead to a quite different scattering in the case of surface waves, whose main characteristic is a strong asymmetry in the scattering cross section. The assumptions and approximations under which these effects happen are carefully considered, and their applicability to the case of scattering of acoustic waves by vorticity is noted., Comment: 19 pages, 5 figures