The Gould-Hopper Polynomials in the Novikov-Veselov equation

We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is studied using the GH polynomials and then the Lax pair is found. In particulr, when $N=3,4,5$, one can get the Gold-fish model. The smooth rational solutions of the NV equation are also constructed via the extended Moutard transformation and the GH polynomials. The asymptotic behavior is discussed and then the smooth rational solution of the Liouville equation is obtained.Comment: 22 pages, no figur

The VIPERS Multi-Lambda Survey. I. UV and NIR Observations, multi-color catalogues and photometric redshifts

We present observations collected in the CFHTLS-VIPERS region in the ultraviolet (UV) with the GALEX satellite (far and near UV channels) and the near infrared with the CFHT/WIRCam camera ($K_s$-band) over an area of 22 and 27 deg$^2$, respectively. The depth of the photometry was optimized to measure the physical properties (e.g., SFR, stellar masses) of all the galaxies in the VIPERS spectroscopic survey. The large volume explored by VIPERS will enable a unique investigation of the relationship between the galaxy properties and their environment (density field and cosmic web) at high redshift (0.5 < z < 1.2). In this paper, we present the observations, the data reductions and the build-up of the multi-color catalogues. The CFHTLS-T0007 (gri-{\chi}^2) images are used as reference to detect and measure the $K_s$-band photometry, while the T0007 u-selected sources are used as priors to perform the GALEX photometry based on a dedicated software (EMphot). Our final sample reaches $NUV_{AB}$~25 (at 5{\sigma}) and $K_{AB}$~22 (at 3{\sigma}). The large spectroscopic sample (~51,000 spectroscopic redshifts) allows us to highlight the robustness of our star/galaxy separation, and the reliability of our photometric redshifts with a typical accuracy $\sigma_z \le$ 0.04 and a catastrophic failure rate {\eta} < 2% down to i~23. We present various tests on the $K_s$ band completeness and photometric redshift accuracy by comparing with existing, overlapping deep photometric catalogues. Finally, we discuss the BzK sample of passive and active galaxies at high redshift and the evolution of galaxy morphology in the (NUV-r) vs (r-K_s) diagram at low redshift (z < 0.25) thanks to the high image quality of the CFHTLS. The images, catalogues and photometric redshifts for 1.5 million sources (down to $NUV \le$ 25 or $K_s \le$ 22) are released and available at this URL: http://cesam.lam.fr/vipers-mls/Comment: 14 pages, 16 figures. Accepted for publication in A&A. Version to be publishe

The VIPERS Multi-Lambda Survey. II. Diving with massive galaxies in 22 square degrees since z = 1.5

We investigate the evolution of the galaxy stellar mass function (SMF) and stellar mass density from redshift z=0.2 to z=1.5 of a $K_{AB}$<22-selected sample with highly reliable photometric redshifts and over an unprecedentedly large area. Our study is based on NIR observations carried out with WIRCam at CFHT over the footprint of the VIPERS spectroscopic survey and benefits from the high quality optical photometry from the CFHTLS and UV observations with the GALEX satellite. The accuracy of our photometric redshifts is $\sigma_z$ < 0.03 and 0.05 for the bright ($i_{AB}$22.5) samples, respectively. The SMF is measured with ~760,000 galaxies down to $K_s$=22 and over an effective area of ~22.4 deg$^2$, the latter of which drastically reduces the statistical uncertainties (i.e. Poissonian error & cosmic variance). We point out the importance of a careful control of the photometric calibration, whose impact becomes quickly dominant when statistical uncertainties are reduced, which will be a major issue for future generation of cosmological surveys with, e.g. EUCLID or LSST. By exploring the rest-frame (NUV-r) vs (r-$K_s$) color-color diagram separating star-forming and quiescent galaxies, (1) we find that the density of very massive log($M_*/ M_{\odot}$) > 11.5 galaxies is largely dominated by quiescent galaxies and increases by a factor 2 from z~1 to z~0.2, which allows for additional mass assembly via dry mergers, (2) we confirm a scenario where star formation activity is impeded above a stellar mass log($M^*_{SF} / M_{\odot}$) = 10.64$\pm$0.01, a value that is found to be very stable at 0.2 < z < 1.5, (3) we discuss the existence of a main quenching channel that is followed by massive star-forming galaxies, and finally (4) we characterise another quenching mechanism required to explain the clear excess of low-mass quiescent galaxies observed at low redshift.Comment: 22 pages, 20 figures. Accepted for publication in A&A. Version to be publishe

Darboux transformations for a 6-point scheme

We introduce (binary) Darboux transformation for general differential equation of the second order in two independent variables. We present a discrete version of the transformation for a 6-point difference scheme. The scheme is appropriate to solving a hyperbolic type initial-boundary value problem. We discuss several reductions and specifications of the transformations as well as construction of other Darboux covariant schemes by means of existing ones. In particular we introduce a 10-point scheme which can be regarded as the discretization of self-adjoint hyperbolic equation

Micellization of Sliding Polymer Surfactants

Following up a recent paper on grafted sliding polymer layers (Macromolecules 2005, 38, 1434-1441), we investigated the influence of the sliding degree of freedom on the self-assembly of sliding polymeric surfactants that can be obtained by complexation of polymers with cyclodextrins. In contrast to the micelles of quenched block copolymer surfactants, the free energy of micelles of sliding surfactants can have two minima: the first corresponding to small micelles with symmetric arm lengths, and the second corresponding to large micelles with asymmetric arm lengths. The relative sizes and concentrations of small and large micelles in the solution depend on the molecular parameters of the system. The appearance of small micelles drastically reduces the kinetic barrier signifying the fast formation of equilibrium micelles.Comment: Submitted to Macromolecule

Darboux Transformations for SUSY Integrable Systems

Several types of Darboux transformations for supersymmetric integrable systems such as the Manin-Radul KdV, Mathieu KdV and SUSY sine-Gordon equations are considered. We also present solutions such as supersolitons and superkinks.Comment: 13 pages. LaTeX209 with LamuPhys and EPSF packages, 3 figures. Contribution to the proceedings of the "Integrable Models and Supersymmetry" meeting held at Chicago on July'9

The VIMOS Public Extragalactic Redshift Survey (VIPERS): PCA-based automatic cleaning and reconstruction of survey spectra

Identifying spurious reduction artefacts in galaxy spectra is a challenge for large surveys. We present an algorithm for identifying and repairing residual spurious features in sky-subtracted galaxy spectra with application to the VIPERS survey. The algorithm uses principal component analysis (PCA) applied to the galaxy spectra in the observed frame to identify sky line residuals imprinted at characteristic wavelengths. We further model the galaxy spectra in the rest-frame using PCA to estimate the most probable continuum in the corrupted spectral regions, which are then repaired. We apply the method to 90,000 spectra from the VIPERS survey and compare the results with a subset where careful editing was performed by hand. We find that the automatic technique does an extremely good job in reproducing the time-consuming manual cleaning and does it in a uniform and objective manner across a large data sample. The mask data products produced in this work are released together with the VIPERS second public data release (PDR-2).Comment: Find the VIPERS data release at http://vipers.inaf.i

The galaxy-halo connection from a joint lensing, clustering and abundance analysis in the CFHTLenS/VIPERS field

We present new constraints on the relationship between galaxies and their host dark matter halos, measured from the location of the peak of the stellar-to-halo mass ratio (SHMR), up to the most massive galaxy clusters at redshift $z\sim0.8$ and over a volume of nearly 0.1~Gpc$^3$. We use a unique combination of deep observations in the CFHTLenS/VIPERS field from the near-UV to the near-IR, supplemented by $\sim60\,000$ secure spectroscopic redshifts, analysing galaxy clustering, galaxy-galaxy lensing and the stellar mass function. We interpret our measurements within the halo occupation distribution (HOD) framework, separating the contributions from central and satellite galaxies. We find that the SHMR for the central galaxies peaks at $M_{\rm h, peak} = 1.9^{+0.2}_{-0.1}\times10^{12} M_{\odot}$ with an amplitude of $0.025$, which decreases to $\sim0.001$ for massive halos ($M_{\rm h} > 10^{14} M_{\odot}$). Compared to central galaxies only, the total SHMR (including satellites) is boosted by a factor 10 in the high-mass regime (cluster-size halos), a result consistent with cluster analyses from the literature based on fully independent methods. After properly accounting for differences in modelling, we have compared our results with a large number of results from the literature up to $z=1$: we find good general agreement, independently of the method used, within the typical stellar-mass systematic errors at low to intermediate mass (${M}_{\star} < 10^{11} M_{\odot}$) and the statistical errors above. We have also compared our SHMR results to semi-analytic simulations and found that the SHMR is tilted compared to our measurements in such a way that they over- (under-) predict star formation efficiency in central (satellite) galaxies.Comment: 31 pages, 18 figures, 4 table. Accepted for publication in MNRAS. Online material available at http://www.cfhtlens.or

HSC-CLAUDS survey: The star formation rate functions since z ~ 2 and comparison with hydrodynamical simulations

Star formation rate functions (SFRFs) give an instantaneous view of the distribution of star formation rates (SFRs) in galaxies at different epochs. They are a complementary and more stringent test for models than the galaxy stellar mass function, which gives an integrated view of the past star formation activity. However, the exploration of SFRFs has been limited thus far due to difficulties in assessing the SFR from observed quantities and probing the SFRF over a wide range of SFRs. We overcome these limitations thanks to an original method that predicts the infrared luminosity from the rest-frame UV/optical color of a galaxy and then its SFR over a wide range of stellar masses and redshifts. We applied this technique to the deep imaging survey HSC-CLAUDS combined with near-infrared and UV photometry. We provide the first SFR functions with reliable measurements in the high- and low-SFR regimes up to $z=2$ and compare our results with previous observations and four state-of-the-art hydrodynamical simulations.Comment: 29 pages, 19 figure

CFHTLenS and RCSLenS cross-correlation with Planck lensing detected in fourier and configuration space

We measure the cross-correlation signature between the Planck cosmic microwave background (CMB) lensing map and the weak lensing observations from both the Red-sequence Cluster Lensing Survey and the Canada–France–Hawaii Telescope Lensing Survey. In addition to a Fourier analysis, we include the first configuration-space detection, based on the estimators 〈κCMBκgal〉 and 〈κCMBγt〉. Combining 747.2 deg2 from both surveys, we find a detection significance that exceeds 4.2σ in both Fourier- and configuration-space analyses. Scaling the predictions by a free parameter A, we obtain APlanckCFHT=0.68±0.31 and APlanckRCS=1.31±0.33⁠. In preparation for the next generation of measurements similar to these, we quantify the impact of different analysis choices on these results. First, since none of these estimators probes the exact same dynamical range, we improve our detection by combining them. Secondly, we carry out a detailed investigation on the effect of apodization, zero-padding and mask multiplication, validated on a suite of high-resolution simulations, and find that the latter produces the largest systematic bias in the cosmological interpretation. Finally, we show that residual contamination from intrinsic alignment and the effect of photometric redshift error are both largely degenerate with the characteristic signal from massive neutrinos, however the signature of baryon feedback might be easier to distinguish. The three lensing data sets are publicly available