Richness-mass relation self-calibration for galaxy clusters

This work attains a threefold objective: first, we derived the richness-mass scaling in the local Universe from data of 53 clusters with individual measurements of mass. We found a 0.46+-0.12 slope and a 0.25+-0.03 dex scatter measuring richness with a previously developed method. Second, we showed on a real sample of 250 0.06<z<0.9 clusters, most of which are at z<0.3, with spectroscopic redshift that the colour of the red sequence allows us to measure the clusters' redshift to better than Delta z=0.02. Third, we computed the predicted prior of the richness-mass scaling to forecast the capabilities of future wide-field-area surveys of galaxy clusters to constrain cosmological parameters. We computed the uncertainty and the covariance matrix of the (evolving) richness-mass scaling of a PanStarrs 1+Euclid-like survey accounting for a large suite of sources of errors. We find that the richness-mass scaling parameters, which are the input ingredients of cosmological forecasts using cluster counts, can be determined 10^5 times better than estimated in previous works that did not use weak-lensing mass estimates. The better knowledge of the scaling parameters likely has a strong impact on the relative importance of the different probes used to constrain cosmological parameters. Richness-mass scaling parameters were recovered, but only if the cluster mass function and the weak-lensing redshift-dependent selection function were accounted for in the fitting of the mass-richness scaling. This emphasizes the limitations of often adopted simplifying assumptions, such as having a mass-complete redshift-independent sample. The fitting code used for computing the predicted prior, including the treatment of the mass function and of the weak-lensing selection function, is provided in the appendix. [Abridged]Comment: A&A, in pres

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

Collapsing dynamics of attractive Bose-Einstein condensates

The self-similar collapse of 3D and quasi-2D atom condensates with negative scattering length is examined. 3D condensates are shown to blow up following the scenario of {\it weak collapse}: The inner core of the condensate diverges with an almost zero particle number, while its tail distribution spreads out to large distances with a constant density profile. For this case, the 3-body recombination arrests the collapse, but it weakly dissipates the atoms. The confining trap then reforms the condensate at later times. In contrast, 2D condensates undergo a {\it strong collapse}: The atoms stay mainly located at center and recombination sequentially absorbs a significant amount of particles.Comment: 4 pages, submitted for publicatio

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.

Multidimensional solitons in a low-dimensional periodic potential

Using the variational approximation(VA) and direct simulations, we find stable 2D and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction ($z$) and periodic in the others (but the quasi-1D potentials cannot stabilize 3D solitons). The family of solitons includes single- and multi-peaked ones. The results apply to Bose-Einstein condensates (BECs) in optical lattices (OLs), and to spatial or spatiotemporal solitons in layered optical media. This is the first prediction of {\em mobile} 2D and 3D solitons in BECs, as they keep mobility along $z$. Head-on collisions of in-phase solitons lead to their fusion into a collapsing pulse. Solitons colliding in adjacent OL-induced channels may form a bound state (BS), which then relaxes to a stable asymmetric form. An initially unstable soliton splits into a three-soliton BS. Localized states in the self-repulsive GPE with the low-dimensional OL are found too.Comment: 4 pages, 5 figure

The fundamental solution of the unidirectional pulse propagation equation

The fundamental solution of a variant of the three-dimensional wave equation known as "unidirectional pulse propagation equation" (UPPE) and its paraxial approximation is obtained. It is shown that the fundamental solution can be presented as a projection of a fundamental solution of the wave equation to some functional subspace. We discuss the degree of equivalence of the UPPE and the wave equation in this respect. In particular, we show that the UPPE, in contrast to the common belief, describes wave propagation in both longitudinal and temporal directions, and, thereby, its fundamental solution possesses a non-causal character.Comment: accepted to J. Math. Phy

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