Skeleton as a probe of the cosmic web: the 2D case

We discuss the skeleton as a probe of the filamentary structures of a 2D random field. It can be defined for a smooth field as the ensemble of pairs of field lines departing from saddle points, initially aligned with the major axis of local curvature and connecting them to local maxima. This definition is thus non local and makes analytical predictions difficult, so we propose a local approximation: the local skeleton is given by the set of points where the gradient is aligned with the local curvature major axis and where the second component of the local curvature is negative. We perform a statistical analysis of the length of the total local skeleton, chosen for simplicity as the set of all points of space where the gradient is either parallel or orthogonal to the main curvature axis. In all our numerical experiments, which include Gaussian and various non Gaussian realizations such as \chi^2 fields and Zel'dovich maps, the differential length is found within a normalization factor to be very close to the probability distribution function of the smoothed field. This is in fact explicitly demonstrated in the Gaussian case. This result might be discouraging for using the skeleton as a probe of non Gausiannity, but our analyses assume that the total length of the skeleton is a free, adjustable parameter. This total length could in fact be used to constrain cosmological models, in CMB maps but also in 3D galaxy catalogs, where it estimates the total length of filaments in the Universe. Making the link with other works, we also show how the skeleton can be used to study the dynamics of large scale structure.Comment: 15 pages, 11 figures, submitted to MNRA

Fluid-loaded metasurfaces

We consider wave propagation along fluid-loaded structures which take the form of an elastic plate augmented by an array of resonators forming a metasurface, that is, a surface structured with sub-wavelength resonators. Such surfaces have had considerable recent success for the control of wave propagation in electromagnetism and acoustics, by combining the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. We explore one aspect of recent interest in this field: graded metasurfaces, but within the context of fluid-loaded structures. Graded metasurfaces allow for selective spatial frequency separation and are often referred to as exhibiting rainbow trapping. Experiments, and theory, have been developed for acoustic, electromagnetic, and even elastic, rainbow devices but this has not been approached for fluid-loaded structures that support surface waves coupled with the acoustic field in a bulk fluid. This surface wave, coupled with the fluid, can be used to create an additional effect by designing a metasurface to mode convert from surface to bulk waves. We demonstrate that sub-wavelength control is possible and that one can create both rainbow trapping and mode conversion phenomena for a fluid-loaded elastic plate model.Comment: 13 pages, 10 figure

The three dimensional skeleton: tracing the filamentary structure of the universe

The skeleton formalism aims at extracting and quantifying the filamentary structure of the universe is generalized to 3D density fields; a numerical method for computating a local approximation of the skeleton is presented and validated here on Gaussian random fields. This method manages to trace well the filamentary structure in 3D fields such as given by numerical simulations of the dark matter distribution on large scales and is insensitive to monotonic biasing. Two of its characteristics, namely its length and differential length, are analyzed for Gaussian random fields. Its differential length per unit normalized density contrast scales like the PDF of the underlying density contrast times the total length times a quadratic Edgeworth correction involving the square of the spectral parameter. The total length scales like the inverse square smoothing length, with a scaling factor given by 0.21 (5.28+ n) where n is the power index of the underlying field. This dependency implies that the total length can be used to constrain the shape of the underlying power spectrum, hence the cosmology. Possible applications of the skeleton to galaxy formation and cosmology are discussed. As an illustration, the orientation of the spin of dark halos and the orientation of the flow near the skeleton is computed for dark matter simulations. The flow is laminar along the filaments, while spins of dark halos within 500 kpc of the skeleton are preferentially orthogonal to the direction of the flow at a level of 25%.Comment: 17 pages, 11 figures, submitted to MNRA

Enhanced sensing and conversion of ultrasonic Rayleigh waves by elastic metasurfaces

Recent years have heralded the introduction of metasurfaces that advantageously combine the vision of sub-wavelength wave manipulation, with the design, fabrication and size advantages associated with surface excitation. An important topic within metasurfaces is the tailored rainbow trapping and selective spatial frequency separation of electromagnetic and acoustic waves using graded metasurfaces. This frequency dependent trapping and spatial frequency segregation has implications for energy concentrators and associated energy harvesting, sensing and wave filtering techniques. Different demonstrations of acoustic and electromagnetic rainbow devices have been performed, however not for deep elastic substrates that support both shear and compressional waves, together with surface Rayleigh waves; these allow not only for Rayleigh wave rainbow effects to exist but also for mode conversion from surface into shear waves. Here we demonstrate experimentally not only elastic Rayleigh wave rainbow trapping, by taking advantage of a stop-band for surface waves, but also selective mode conversion of surface Rayleigh waves to shear waves. These experiments performed at ultrasonic frequencies, in the range of 400–600 kHz, are complemented by time domain numerical simulations. The metasurfaces we design are not limited to guided ultrasonic waves and are a general phenomenon in elastic waves that can be translated across scales

Statistical Tests for CHDM and \LambdaCDM Cosmologies

We apply several statistical estimators to high-resolution N-body simulations of two currently viable cosmological models: a mixed dark matter model, having $\Omega_\nu=0.2$ contributed by two massive neutrinos (C+2\nuDM), and a Cold Dark Matter model with Cosmological Constant (\LambdaCDM) with $\Omega_0=0.3$ and h=0.7. Our aim is to compare simulated galaxy samples with the Perseus-Pisces redshift survey (PPS). We consider the n-point correlation functions (n=2-4), the N-count probability functions P_N, including the void probability function P_0, and the underdensity probability function U_\epsilon (where \epsilon fixes the underdensity threshold in percentage of the average). We find that P_0 (for which PPS and CfA2 data agree) and P_1 distinguish efficiently between the models, while U_\epsilon is only marginally discriminatory. On the contrary, the reduced skewness and kurtosis are, respectively, S_3\simeq 2.2 and S_4\simeq 6-7 in all cases, quite independent of the scale, in agreement with hierarchical scaling predictions and estimates based on redshift surveys. Among our results, we emphasize the remarkable agreement between PPS data and C+2\nuDM in all the tests performed. In contrast, the above \LambdaCDM model has serious difficulties in reproducing observational data if galaxies and matter overdensities are related in a simple way.Comment: 12 pages, 10 figures, LaTeX (aaspp4 macro), in press on ApJ, Vol. 479, April 199

Effect of interchain separation on the photoinduced absorption spectra of polycarbazolyldiacetylenes

The photoinduced absorption spectra of a novel polycarbazolyldiacetylene with long aliphatic chains on the carbazolyl side groups are measured and compared with those of the unsubstituted polyDCHD. The two polymers in the blue form exhibit very similar electronic absorption spectra and Raman frequencies. This fact indicates that the conjugation length of the polydiacetylene backbone is not too affected by the long substituents. In contrast, the near steady-state photoinduced absorption spectra show that different photogeneration mechanisms are involved in the two polymers. This result can be ascribed to the role played by the interchain distance in the dynamics of the relaxation processes in polydiacetylenes

A New Dark Matter Candidate: Non-thermal Sterile Neutrinos

We propose a new and unique dark matter candidate: $\sim 100$ eV to $\sim 10$ keV sterile neutrinos produced via lepton number-driven resonant MSW (Mikheyev-Smirnov-Wolfenstein) conversion of active neutrinos. The requisite lepton number asymmetries in any of the active neutrino flavors range from 10$^{-3}$ to 10$^{-1}$ of the photon number - well within primordial nucleosynthesis bounds. The unique feature here is that the adiabaticity condition of the resonance strongly favors the production of lower energy sterile neutrinos. The resulting non-thermal (cold) energy spectrum can cause these sterile neutrinos to revert to non-relativistic kinematics at an early epoch, so that free-streaming lengths at or below the dwarf galaxy scale are possible. Therefore, the main problem associated with light neutrino dark matter candidates can be circumvented in our model.Comment: Latex 11 pages + 1 figur

Ray Tracing Simulations of Weak Lensing by Large-Scale Structure

We investigate weak lensing by large-scale structure using ray tracing through N-body simulations. Photon trajectories are followed through high resolution simulations of structure formation to make simulated maps of shear and convergence on the sky. Tests with varying numerical parameters are used to calibrate the accuracy of computed lensing statistics on angular scales from about 1 arcminute to a few degrees. Various aspects of the weak lensing approximation are also tested. For fields a few degrees on a side the shear power spectrum is almost entirely in the nonlinear regime and agrees well with nonlinear analytical predictions. Sampling fluctuations in power spectrum estimates are investigated by comparing several ray tracing realizations of a given model. For survey areas smaller than a degree on a side the main source of scatter is nonlinear coupling to modes larger than the survey. We develop a method which uses this effect to estimate the mass density parameter Omega from the scatter in power spectrum estimates for subregions of a larger survey. We show that the power spectrum can be measured accurately from realistically noisy data on scales corresponding to 1-10 Mpc/h. Non-Gaussian features in the one point distribution function of the weak lensing convergence (reconstructed from the shear) are also sensitive to Omega. We suggest several techniques for estimating Omega in the presence of noise and compare their statistical power, robustness and simplicity. With realistic noise Omega can be determined to within 0.1-0.2 from a deep survey of several square degrees.Comment: 59 pages, 22 figures included. Matches version accepted for Ap

On measuring the covariance matrix of the nonlinear power spectrum from simulations

We show how to estimate the covariance of the power spectrum of a statistically homogeneous and isotropic density field from a single periodic simulation, by applying a set of weightings to the density field, and by measuring the scatter in power spectra between different weightings. We recommend a specific set of 52 weightings containing only combinations of fundamental modes, constructed to yield a minimum variance estimate of the covariance of power. Numerical tests reveal that at nonlinear scales the variance of power estimated by the weightings method substantially exceeds that estimated from a simple ensemble method. We argue that the discrepancy is caused by beat-coupling, in which products of closely spaced Fourier modes couple by nonlinear gravitational growth to the beat mode between them. Beat-coupling appears whenever nonlinear power is measured from Fourier modes with a finite spread of wavevector, and is therefore present in the weightings method but not the ensemble method. Beat-coupling inevitably affects real galaxy surveys, whose Fourier modes have finite width. Surprisingly, the beat-coupling contribution dominates the covariance of power at nonlinear scales, so that, counter-intuitively, it is expected that the covariance of nonlinear power in galaxy surveys is dominated not by small scale structure, but rather by beat-coupling to the largest scales of the survey.Comment: 19 pages, 4 figures. To appear in Monthly Notices of the Royal Astronomical Society. Revised to match accepted versio