Chaotic dynamics of superconductor vortices in the plastic phase

We present numerical simulation results of driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics is readily understood in the framework of chaos theory. Intermittency "routes to chaos" have been clearly identified, and positive Lyapunov exponents and broad-band noise, both characteristic of chaos, are found to coincide with the differential resistance peak. Furthermore, the fractal dimension of the strange attractor reveals that the chaotic dynamics of vortices is low-dimensional.Comment: 5 pages, 3 figures Accepted for publication in Physical Review Letter

Chaos and plasticity in superconductor vortices: a low-dimensional dynamics

We present new results of numerical simulations for driven vortex lattices in presence of random disorder at zero temperature. We show that the plastic dynamics of vortices display dissipative chaos. Intermittency "routes to chaos" have been clearly identified below the differential resistance peak. The peak region is characterized by positive Lyapunov exponents characteristic of chaos, and low frequency broad-band noise. Furthermore we find a low fractal dimension of the strange attractor, which suggests that only a few dynamical variables are sufficient to model the complex plastic dynamics of vortices.Comment: 8 pages, 6 figures, accepted for publication in The Physical Review

Regression analysis with missing data and unknown colored noise: application to the MICROSCOPE space mission

The analysis of physical measurements often copes with highly correlated noises and interruptions caused by outliers, saturation events or transmission losses. We assess the impact of missing data on the performance of linear regression analysis involving the fit of modeled or measured time series. We show that data gaps can significantly alter the precision of the regression parameter estimation in the presence of colored noise, due to the frequency leakage of the noise power. We present a regression method which cancels this effect and estimates the parameters of interest with a precision comparable to the complete data case, even if the noise power spectral density (PSD) is not known a priori. The method is based on an autoregressive (AR) fit of the noise, which allows us to build an approximate generalized least squares estimator approaching the minimal variance bound. The method, which can be applied to any similar data processing, is tested on simulated measurements of the MICROSCOPE space mission, whose goal is to test the Weak Equivalence Principle (WEP) with a precision of $10^{-15}$. In this particular context the signal of interest is the WEP violation signal expected to be found around a well defined frequency. We test our method with different gap patterns and noise of known PSD and find that the results agree with the mission requirements, decreasing the uncertainty by a factor 60 with respect to ordinary least squares methods. We show that it also provides a test of significance to assess the uncertainty of the measurement.Comment: 12 pages, 4 figures, to be published in Phys. Rev.

Subcritical transition to turbulence in plane Couette flow

International audienceThe transition to turbulence in plane Couette flow was studied experimentally. The subcritical aspect of this transition is revealed by the stable coexistence of laminar and turbulent domains. By perturbing the flow, a critical Reynolds number has been determined, above which an artificially triggered turbulent spot can persist. The study of the spatiotemporal evolution of these spots shows, among other things, the existence of waves traveling away from the turbulent regions

Dynamic Modes of Microcapsules in Steady Shear Flow: Effects of Bending and Shear Elasticities

The dynamics of microcapsules in steady shear flow was studied using a theoretical approach based on three variables: The Taylor deformation parameter $\alpha_{\rm D}$, the inclination angle $\theta$, and the phase angle $\phi$ of the membrane rotation. It is found that the dynamic phase diagram shows a remarkable change with an increase in the ratio of the membrane shear and bending elasticities. A fluid vesicle (no shear elasticity) exhibits three dynamic modes: (i) Tank-treading (TT) at low viscosity $\eta_{\rm {in}}$ of internal fluid ($\alpha_{\rm D}$ and $\theta$ relaxes to constant values), (ii) Tumbling (TB) at high $\eta_{\rm {in}}$ ($\theta$ rotates), and (iii) Swinging (SW) at middle $\eta_{\rm {in}}$ and high shear rate $\dot\gamma$ ($\theta$ oscillates). All of three modes are accompanied by a membrane ($\phi$) rotation. For microcapsules with low shear elasticity, the TB phase with no $\phi$ rotation and the coexistence phase of SW and TB motions are induced by the energy barrier of $\phi$ rotation. Synchronization of $\phi$ rotation with TB rotation or SW oscillation occurs with integer ratios of rotational frequencies. At high shear elasticity, where a saddle point in the energy potential disappears, intermediate phases vanish, and either $\phi$ or $\theta$ rotation occurs. This phase behavior agrees with recent simulation results of microcapsules with low bending elasticity.Comment: 11 pages, 14 figure

Iterated maps for clarinet-like systems

The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime for string instruments. In this article, we study in more detail the properties of the corresponding non-linear iterations, with emphasis on the geometrical constructions that can be used to classify the various solutions (for instance with or without reed beating) as well as on the periodicity windows that occur within the chaotic region. In particular, we find a regime where period tripling occurs and examine the conditions for intermittency. We also show that, while the direct observation of the iteration function does not reveal much on the oscillation regime of the instrument, the graph of the high order iterates directly gives visible information on the oscillation regime (characterization of the number of period doubligs, chaotic behaviour, etc.)

Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice

We predict new generic types of vorticity-carrying soliton complexes in a class of physical systems including an attractive Bose-Einstein condensate in a square optical lattice (OL) and photonic lattices in photorefractive media. The patterns include ring-shaped higher-order vortex solitons and supervortices. Stability diagrams for these patterns, based on direct simulations, are presented. The vortex ring solitons are stable if the phase difference \Delta \phi between adjacent solitons in the ring is larger than \pi/2, while the supervortices are stable in the opposite case, \Delta \phi <\pi /2. A qualitative explanation to the stability is given.Comment: 9 pages, 4 figure

Exactly quantized dynamics of classical incommensurate sliders

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio v_cm/v_ext of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays pinned to exact "plateau" values for wide ranges of parameters, such as sliders corrugation amplitudes, external velocity, chain stiffness and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.Comment: 5 pags 4 fig

Chaotic, staggered and polarized dynamics in opinion forming: the contrarian effect

We revisit the no tie breaking 2-state Galam contrarian model of opinion dynamics for update groups of size 3. While the initial model assumes a constant density of contrarians a for both opinions, it now depends for each opinion on its global support. Proportionate contrarians are thus found to indeed preserve the former case main results. However, restricting the contrarian behavior to only the current collective majority, makes the dynamics more complex with novel features. For a density a<a_c=1/9 of one-sided contrarians, a chaotic basin is found in the fifty-fifty region separated from two majority-minority point attractors, one on each side. For 1/9<a< 0.301 only the chaotic basin survives. In the range a>0.301 the chaotic basin disappears and the majority starts to alternate between the two opinions with a staggered flow towards two point attractors. We then study the effect of both, decoupling the local update time sequence from the contrarian behavior activation, and a smoothing of the majority rule. A status quo driven bias for contrarian activation is also considered. Introduction of unsettled agents driven in the debate on a contrarian basis is shown to only shrink the chaotic basin. The model may shed light to recent apparent contradictory elections with on the one hand very tied results like in US in 2000 and in Germany in 2002 and 2005, and on the other hand, a huge majority like in France in 2002.Comment: 17 pages, 10 figure