Stability criteria of the Vlasov equation and quasi-stationary states of the HMF model

We perform a detailed study of the relaxation towards equilibrium in the Hamiltonian Mean-Field (HMF) model, a prototype for long-range interactions in $N$-particle dynamics. In particular, we point out the role played by the infinity of stationary states of the associated $N ~$ Vlasov dynamics. In this context, we derive a new general criterion for the stability of any spatially homogeneous distribution, and compare its analytical predictions with numerical simulations of the Hamiltonian, finite $N$, dynamics. We then propose and verify numerically a scenario for the relaxation process, relying on the Vlasov equation. When starting from a non stationary or a Vlasov unstable stationary initial state, the system shows initially a rapid convergence towards a stable stationary state of the Vlasov equation via non stationary states: we characterize numerically this dynamical instability in the finite $N$ system by introducing appropriate indicators. This first step of the evolution towards Boltzmann-Gibbs equilibrium is followed by a slow quasi-stationary process, that proceeds through different stable stationary states of the Vlasov equation. If the finite $N$ system is initialized in a Vlasov stable homogenous state, it remains trapped in a quasi-stationary state for times that increase with the nontrivial power law $N^{1.7}$. Single particle momentum distributions in such a quasi-stationary regime do not have power-law tails, and hence cannot be fitted by the $q$-exponential distributions derived from Tsallis statistics.Comment: To appear in Physica

The Power Spectrum, Bias Evolution, and the Spatial Three-Point Correlation Function

We calculate perturbatively the normalized spatial skewness, $S_3$, and full three-point correlation function (3PCF), $\zeta$, induced by gravitational instability of Gaussian primordial fluctuations for a biased tracer-mass distribution in flat and open cold-dark-matter (CDM) models. We take into account the dependence on the shape and evolution of the CDM power spectrum, and allow the bias to be nonlinear and/or evolving in time, using an extension of Fry's (1996) bias-evolution model. We derive a scale-dependent, leading-order correction to the standard perturbative expression for $S_3$ in the case of nonlinear biasing, as defined for the unsmoothed galaxy and dark-matter fields, and find that this correction becomes large when probing positive effective power-spectrum indices. This term implies that the inferred nonlinear-bias parameter, as usually defined in terms of the smoothed density fields, might depend on the chosen smoothing scale. In general, we find that the dependence of $S_3$ on the biasing scheme can substantially outweigh that on the adopted cosmology. We demonstrate that the normalized 3PCF, $Q$, is an ill-behaved quantity, and instead investigate $Q_V$, the variance-normalized 3PCF. The configuration dependence of $Q_V$ shows similarly strong sensitivities to the bias scheme as $S_3$, but also exhibits significant dependence on the form of the CDM power spectrum. Though the degeneracy of $S_3$ with respect to the cosmological parameters and constant linear- and nonlinear-bias parameters can be broken by the full configuration dependence of $Q_V$, neither statistic can distinguish well between evolving and non-evolving bias scenarios. We show that this can be resolved, in principle, by considering the redshift dependence of $\zeta$.Comment: 41 pages, including 12 Figures. To appear in The Astrophysical Journal, Vol. 521, #

Probability distribution of density fluctuations in the non-linear regime

We present a general procedure for obtaining the present density fluctuation probability distribution given the statistics of the initial conditions. The main difficulties faced with regard to this problem are those related to the non-linear evolution of the density fluctuations and those posed by the fact that the fields we are interested in are the result of filtering an underlying field with structure down to scales much smaller than that of filtering. The solution to the latter problem is discussed here in detail and the solution to the former is taken from a previous work. We have checked the procedure for values of the rms density fluctuation as large as 3/2 and several power spectra and found that it leads to results in excellent agreement with those obtained in numerical simulations. We also recover all available exact results from perturbation theory.Comment: Accepted to be published in Ap

SZ and CMB reconstruction using Generalized Morphological Component Analysis

In the last decade, the study of cosmic microwave background (CMB) data has become one of the most powerful tools to study and understand the Universe. More precisely, measuring the CMB power spectrum leads to the estimation of most cosmological parameters. Nevertheless, accessing such precious physical information requires extracting several different astrophysical components from the data. Recovering those astrophysical sources (CMB, Sunyaev-Zel'dovich clusters, galactic dust) thus amounts to a component separation problem which has already led to an intense activity in the field of CMB studies. In this paper, we introduce a new sparsity-based component separation method coined Generalized Morphological Component Analysis (GMCA). The GMCA approach is formulated in a Bayesian maximum a posteriori (MAP) framework. Numerical results show that this new source recovery technique performs well compared to state-of-the-art component separation methods already applied to CMB data.Comment: 11 pages - Statistical Methodology - Special Issue on Astrostatistics - in pres

On the Unusual Depletions toward Sk 155, or What Are the Small Magellanic Cloud Dust Grains Made of?

The dust in the Small Magellanic Cloud (SMC), an ideal analog of primordial galaxies at high redshifts, differs markedly from that in the Milky Way by exhibiting a steeply rising far-ultraviolet extinction curve, an absence of the 2175 Angstrom extinction feature, and a local minimum at ~12 micron in its infrared emission spectrum, suggesting the lack of ultrasmall carbonaceous grains (i.e. polycyclic aromatic hydrocarbon molecules) which are ubiquitously seen in the Milky Way. While current models for the SMC dust all rely heavily on silicates, recent observations of the SMC sightline toward Sk 155 indicated that Si and Mg are essentially undepleted and the depletions of Fe range from mild to severe, suggesting that metallic grains and/or iron oxides, instead of silicates, may dominate the SMC dust. However, in this Letter we apply the Kramers-Kronig relation to demonstrate that neither metallic grains nor iron oxides are capable of accounting for the observed extinction; silicates remain as an important contributor to the extinction, consistent with current models for the SMC dust.Comment: 12 pages, 3 figures; The Astrophysical Journal Letters, in pres

Coulomb-U and magnetic moment collapse in δ\delta-Pu

The around-the-mean-field version of the LDA+U method is applied to investigate electron correlation effects in $\delta$-Pu. It yields a non-magnetic ground state of $\delta-$Pu, and provides a good agreement with experimental equilibrium volume, bulk modulus and explains important features of the photoelectron spectra

Algebraic Correlation Function and Anomalous Diffusion in the HMF model

In the quasi-stationary states of the Hamiltonian Mean-Field model, we numerically compute correlation functions of momenta and diffusion of angles with homogeneous initial conditions. This is an example, in a N-body Hamiltonian system, of anomalous transport properties characterized by non exponential relaxations and long-range temporal correlations. Kinetic theory predicts a striking transition between weak anomalous diffusion and strong anomalous diffusion. The numerical results are in excellent agreement with the quantitative predictions of the anomalous transport exponents. Noteworthy, also at statistical equilibrium, the system exhibits long-range temporal correlations: the correlation function is inversely proportional to time with a logarithmic correction instead of the usually expected exponential decay, leading to weak anomalous transport properties

The Angular Three-Point Correlation Function in the Quasilinear Regime

We calculate the normalized angular three-point correlation function (3PCF), $q$, as well as the normalized angular skewness, $s_3$, assuming the small-angle approximation, for a biased mass distribution in flat and open cold-dark-matter (CDM) models with Gaussian initial conditions. The leading-order perturbative results incorporate the explicit dependence on the cosmological parameters, the shape of the CDM transfer function, the linear evolution of the power spectrum, the form of redshift distribution function, and linear and nonlinear biasing, which may be evolving. Results are presented for different redshift distributions, including that appropriate for the APM Galaxy Survey, as well as for a survey with a mean redshift of $\bar{z} \simeq 1$ (such as the VLA FIRST Survey). Qualitatively, many of the results found for $s_3$ and $q$ are similar to those obtained in a related treatment of the spatial skewness and 3PCF (Buchalter & Kamionkowski 1999), such as a leading-order correction to the standard result for $s_3$ in the case of nonlinear bias (as defined for unsmoothed density fields), and the sensitivity of the configuration dependence of $q$ to both cosmological and biasing models. We show that since angular CFs are sensitive to clustering over a range of redshifts, the various evolutionary dependences included in our predictions imply that measurements of $q$ in a deep survey might better discriminate between models with different histories, such as evolving vs. non-evolving bias, that can have similar spatial CFs at low redshift. Our calculations employ a derived equation---valid for open, closed, and flat models---for obtaining the angular bispectrum from the spatial bispectrum in the small-angle approximation.Comment: 45 pages, including 11 Figures, submitted to the Astrophysical Journa

Superlubricity mechanism of diamond-like carbon with glycerol. Coupling of experimental and simulation studies

We report a unique tribological system that produces superlubricity under boundary lubrication conditions with extremely little wear. This system is a thin coating of hydrogen-free amorphous Diamond-Like-Carbon (denoted as ta-C) at 353 K in a ta-C/ta-C friction pair lubricated with pure glycerol. To understand the mechanism of friction vanishing we performed ToF-SIMS experiments using deuterated glycerol and 13C glycerol. This was complemented by first-principles-based computer simulations using the ReaxFF reactive force field to create an atomistic model of ta-C. These simulations show that DLC with the experimental density of 3.24 g/cc leads to an atomistic structure consisting of a 3D percolating network of tetrahedral (sp3) carbons accounting for 71.5% of the total, in excellent agreement with the 70% deduced from our Auger spectroscopy and XANES experiments. The simulations show that the remaining carbons (with sp2 and sp1 character) attach in short chains of length 1 to 7. In sliding simulations including glycerol molecules, the surface atoms react readily to form a very smooth carbon surface containing OH-terminated groups. This agrees with our SIMS experiments. The simulations find that the OH atoms are mostly bound to surface sp1 atoms leading to very flexible elastic response to sliding. Both simulations and experiments suggest that the origin of the superlubricity arises from the formation of this OH-terminated surface

Large deviation techniques applied to systems with long-range interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by Ellis, Physica D 133, 106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibri um effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the alpha-Ising model in one-dimension with $0\leq\alpha<1$