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

Phase-locking modes in a bidimensional network of coupled water jets

International audienceIn this paper, we investigate the dynamics of a bidimensional network of coupled water jets impinging from below on a water/air interface. For each jet, a transition is observed at a critical flow rate value for which the surface bump at the vertical of the jet starts oscillating at a well-defined frequency. We infer that this oscillatory mode is the materialization at the surface of a helical instability of the submerged laminar jet. When coupled together, the bidimensionai network of oscillators exhibits monoperiodic collective modes whose spatial arrangements are similar to those encountered in crystals. A collection of phase-locking modes is observed for each geometry, and stability diagrams are constructed. Analysis of the coupling between the jets reveals a long distance coupling through surface waves. A tuning criterion is proposed to explain the bifurcation from one mode to another. Finally, the symmetries of the system are investigated using two different systematic schemes. The predictions are compared with the observations and some features of the particular topology of phase-locking modes are explained

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

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

Effect of annealing on the superconducting properties of a-Nb(x)Si(1-x) thin films

a-Nb(x)Si(1-x) thin films with thicknesses down to 25 {\AA} have been structurally characterized by TEM (Transmission Electron Microscopy) measurements. As-deposited or annealed films are shown to be continuous and homogeneous in composition and thickness, up to an annealing temperature of 500{\deg}C. We have carried out low temperature transport measurements on these films close to the superconductor-to-insulator transition (SIT), and shown a qualitative difference between the effect of annealing or composition, and a reduction of the film thickness on the superconducting properties of a-NbSi. These results question the pertinence of the sheet resistance R_square as the relevant parameter to describe the SIT.Comment: 9 pages, 12 figure

Direct transition to high-dimensional chaos through a global bifurcation

In the present work we report on a genuine route by which a high-dimensional (with d>4) chaotic attractor is created directly, i.e., without a low-dimensional chaotic attractor as an intermediate step. The high-dimensional chaotic set is created in a heteroclinic global bifurcation that yields an infinite number of unstable tori.The mechanism is illustrated using a system constructed by coupling three Lorenz oscillators. So, the route presented here can be considered a prototype for high-dimensional chaotic behavior just as the Lorenz model is for low-dimensional chaos.Comment: 7 page

Averaging For Solitons With Nonlinearity Management

We develop an averaging method for solitons of the nonlinear Schr{\"o}dinger equation with periodically varying nonlinearity coefficient. This method is used to effectively describe solitons in Bose-Einstein condensates, in the context of the recently proposed and experimentally realizable technique of Feshbach resonance management. Using the derived local averaged equation, we study matter-wave bright and dark solitons and demonstrate a very good agreement between solutions of the averaged and full equations.Comment: 6 pages, 5 figures, in pres

Cascaded self-compression of femtosecond pulses in filaments

Highly nonlinear wave propagation scenarios hold the potential to serve for energy concentration or pulse duration reduction of the input wave form, provided that a small range of input parameters be maintained. In particular when phenomena like rogue-wave formation or few-cycle optical pulses generation come into play, it becomes increasingly difficult to maintain control of the waveforms. Here we suggest an alternative approach towards the control of waveforms in a highly nonlinear system. Cascading pulse self-compression cycles at reduced nonlinearity limits the increase of input parameter sensitivity while still enabling an enhanced compression effect. This cascaded method is illustrated by experiments and in numerical simulations of the Nonlinear Schrödinger Equation, simulating the propagation of short optical pulses in a self-generated plasma

Vector solitons in (2+1) dimensions

We address the problem of existence and stability of vector spatial solitons formed by two incoherently interacting optical beams in bulk Kerr and saturable media. We identify families of (2+1)-dimensional two-mode self-trapped beams, with and without a topological charge, and describe their properties analytically and numerically.Comment: 3 pages, 5 figures, submitted to Opt. Let