Ly-alpha forest: efficient unbiased estimation of second-order properties with missing data

Context. One important step in the statistical analysis of the Ly-alpha forest data is the study of their second order properties. Usually, this is accomplished by means of the two-point correlation function or, alternatively, the K-function. In the computation of these functions it is necessary to take into account the presence of strong metal line complexes and strong Ly-alpha lines that can hidden part of the Ly-alpha forest and represent a non negligible source of bias. Aims. In this work, we show quantitatively what are the effects of the gaps introduced in the spectrum by the strong lines if they are not properly accounted for in the computation of the correlation properties. We propose a geometric method which is able to solve this problem and is computationally more efficient than the Monte Carlo (MC) technique that is typically adopted in Cosmology studies. The method is implemented in two different algorithms. The first one permits to obtain exact results, whereas the second one provides approximated results but is computationally very efficient. The proposed approach can be easily extended to deal with the case of two or more lists of lines that have to be analyzed at the same time. Methods. Numerical experiments are presented that illustrate the consequences to neglect the effects due to the strong lines and the excellent performances of the proposed approach. Results. The proposed method is able to remarkably improve the estimates of both the two-point correlation function and the K-function.Comment: A&A accepted, 12 pages, 15 figure

Branching mechanism of intergranular crack propagation in three dimensions

We investigate the process of slow intergranular crack propagation by the finite element method model, and show that branching is induced by partial arresting of crack front owing to the geometrical randomness of grain boundaries. A possible scenario for branching instability of crack propagation in disordered continuum medium is also discussed.Comment: 4 pages, submitted to Phys.Rev.E; v2:corrected typos v3: final version to be publishe

Computer simulation of crystallization kinetics with non-Poisson distributed nuclei

The influence of non-uniform distribution of nuclei on crystallization kinetics of amorphous materials is investigated. This case cannot be described by the well-known Johnson-Mehl-Avrami (JMA) equation, which is only valid under the assumption of a spatially homogeneous nucleation probability. The results of computer simulations of crystallization kinetics with nuclei distributed according to a cluster and a hardcore distribution are compared with JMA kinetics. The effects of the different distributions on the so-called Avrami exponent $n$ are shown. Furthermore, we calculate the small-angle scattering curves of the simulated structures which can be used to distinguish experimentally between the three nucleation models under consideration.Comment: 14 pages including 7 postscript figures, uses epsf.sty and ioplppt.st

Flow Regime Identification in a Bubble Column based on Both Statistical and Chaotic Parameters Applied to Computed Tomography Data

The Kolmogorov Entropy (KE) Algorithm Was Applied Successfully to Single Source Γ-Ray Computed Tomography (CT) Data Measured in a 0.162 M ID Bubble Column Equipped with a Perforated Plate Distributor (163 Holes · Ø 1.32 Mm). Dried Air Was Used as the Gas Phase and Therminol LT (ΡL = 886 Kg M-3, ΜL = 0.88 · 10-3 Pa S, Σ = 17 · 10-3 N M-1) Was Used as a Liquid Phase. Three Different Pressures, P, of 0.1, 0.4, and 1.0 MPa Were Examined. at Each Pressure the Superficial Gas Velocity, UG, Was Increased Stepwise by Steps of 0.01 Ms-1 Up to 0.2 Ms-1. the Average Absolute Deviation (AAD) Was Also Used as a Robust Statistical Criterion for Regime Transition. at All Three Pressures, based on the Sudden Changes in Both the AAD and KE Values, the Boundaries of the Following Five Regimes Were Identified: Dispersed Bubble Regime, First and Second Transition Regimes, Coalesced Bubble Regime Consisting of Four Regions (Called 4-Region Flow), and Coalesced Bubble Regime Consisting of Three Regions (Called 3-Region Flow). the Existence of These Regimes Has Already Been Documented. as the Pressure Increases, the Transition Velocity between the Dispersed Bubble and First Transition Regimes and the Transition Velocity between Coalesced Bubble (4-Region Flow) and Coalesced Bubble (3-Region Flow) Regimes Shift to Higher UG Values. on the Other Hand, at P = 0.4 MPa the Second Transition Regime Starts Earlier. in Addition, P = 1 MPa the Transition to Coalesced Bubble (4-Region Flow) is Delayed. © 2006 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Prediction of the Kolmogorov Entropy Derived from Computed Tomography Data in a Bubble Column Operated under the Transition Regime and Ambient Pressure

The Kolmogorov Entropy (KE) Algorithm Was Successfully Applied to Single Source Γ-Ray Computed Tomography (CT) Data Measured by Three Scintillation Detectors in a 0.162 M-ID Bubble Column Equipped with a Perforated Plate Distributor (163 Holes X ∅ 1.32. 10-3 M). the Aerated Liquid Height Was Set at 1.8 M. Dried Air Was Used as a Gas Phase, While Therminol LT (PL = 886 Kg M-3, ΜL = 0.88.10-3 Pa S, Σ = 17.10-3 N M-1) Was Used as a Liquid Phase. at Ambient Pressure, the Superficial Gas Velocity, ΜG, Was Increased Stepwise with an Increment of 0.01 M S-1 Up to 0.2 M S-1. based on the Sudden Changes in the KE Values, the Boundaries of the Following Five Regimes Were Successfully Identified: Dispersed Bubble Regime (ΜG \u3c 0.02 M S-1), First Transition Regime (0.02 ≤ UG \u3c 0.08 M S-1), Second Transition Regime (0.08 ≤ UG \u3c 0.1 M S-1), Coalesced Bubble Regime Consisting of Four Regions (Called 4-Region Flow; 0.1 ≤ UG \u3c 0.12 M S-1), and Coalesced Bubble Regime Consisting of Three Regions (Called 3-Region Flow; UG \u3e 0.12 M S-1). the KE Values Derived from Three Scintillation Detectors in the First Transition Regime Were Successfully Correlated to Both Bubble Frequency and Bubble Impact. the Latter Was Found to Be Inversely Proportional to the Bubble Froude Number. the KE Model Implies that the Bubble Size in This Particular Flow Regime is a Weak Function of the Orifice Reynolds Number (Db = 7.1.10-3 Re0-0.05). © 2007 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim

Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres

Hyperuniform many-particle distributions possess a local number variance that grows more slowly than the volume of an observation window, implying that the local density is effectively homogeneous beyond a few characteristic length scales. Previous work on maximally random strictly jammed sphere packings in three dimensions has shown that these systems are hyperuniform and possess unusual quasi-long-range pair correlations, resulting in anomalous logarithmic growth in the number variance. However, recent work on maximally random jammed sphere packings with a size distribution has suggested that such quasi-long-range correlations and hyperuniformity are not universal among jammed hard-particle systems. In this paper we show that such systems are indeed hyperuniform with signature quasi-long-range correlations by characterizing the more general local-volume-fraction fluctuations. We argue that the regularity of the void space induced by the constraints of saturation and strict jamming overcomes the local inhomogeneity of the disk centers to induce hyperuniformity in the medium with a linear small-wavenumber nonanalytic behavior in the spectral density, resulting in quasi-long-range spatial correlations. A numerical and analytical analysis of the pore-size distribution for a binary MRJ system in addition to a local characterization of the n-particle loops governing the void space surrounding the inclusions is presented in support of our argument. This paper is the first part of a series of two papers considering the relationships among hyperuniformity, jamming, and regularity of the void space in hard-particle packings.Comment: 40 pages, 15 figure

Mark correlations: relating physical properties to spatial distributions

Mark correlations provide a systematic approach to look at objects both distributed in space and bearing intrinsic information, for instance on physical properties. The interplay of the objects' properties (marks) with the spatial clustering is of vivid interest for many applications; are, e.g., galaxies with high luminosities more strongly clustered than dim ones? Do neighbored pores in a sandstone have similar sizes? How does the shape of impact craters on a planet depend on the geological surface properties? In this article, we give an introduction into the appropriate mathematical framework to deal with such questions, i.e. the theory of marked point processes. After having clarified the notion of segregation effects, we define universal test quantities applicable to realizations of a marked point processes. We show their power using concrete data sets in analyzing the luminosity-dependence of the galaxy clustering, the alignment of dark matter halos in gravitational $N$-body simulations, the morphology- and diameter-dependence of the Martian crater distribution and the size correlations of pores in sandstone. In order to understand our data in more detail, we discuss the Boolean depletion model, the random field model and the Cox random field model. The first model describes depletion effects in the distribution of Martian craters and pores in sandstone, whereas the last one accounts at least qualitatively for the observed luminosity-dependence of the galaxy clustering.Comment: 35 pages, 12 figures. to be published in Lecture Notes of Physics, second Wuppertal conference "Spatial statistics and statistical physics

Formation energy and interaction of point defects in two-dimensional colloidal crystals

The manipulation of individual colloidal particles using optical tweezers has allowed vacancies to be created in two-dimensional (2d) colloidal crystals, with unprecedented possibility of real-time monitoring the dynamics of such defects (Nature {\bf 413}, 147 (2001)). In this Letter, we employ molecular dynamics (MD) simulations to calculate the formation energy of single defects and the binding energy between pairs of defects in a 2d colloidal crystal. In the light of our results, experimental observations of vacancies could be explained and then compared to simulation results for the interstitial defects. We see a remarkable similarity between our results for a 2d colloidal crystal and the 2d Wigner crystal (Phys. Rev. Lett. {\bf 86}, 492 (2001)). The results show that the formation energy to create a single interstitial is $12$ lower than that of the vacancy. Because the pair binding energies of the defects are strongly attractive for short distances, the ground state should correspond to bound pairs with the interstitial bound pairs being the most probable.Comment: 5 pages, 2 figure

Modeling Heterogeneous Materials via Two-Point Correlation Functions: I. Basic Principles

Heterogeneous materials abound in nature and man-made situations. Examples include porous media, biological materials, and composite materials. Diverse and interesting properties exhibited by these materials result from their complex microstructures, which also make it difficult to model the materials. In this first part of a series of two papers, we collect the known necessary conditions on the standard two-point correlation function S2(r) and formulate a new conjecture. In particular, we argue that given a complete two-point correlation function space, S2(r) of any statistically homogeneous material can be expressed through a map on a selected set of bases of the function space. We provide new examples of realizable two-point correlation functions and suggest a set of analytical basis functions. Moreover, we devise an efficient and isotropy- preserving construction algorithm, namely, the Lattice-Point algorithm to generate realizations of materials from their two- point correlation functions based on the Yeong-Torquato technique. Subsequent analysis can be performed on the generated images to obtain desired macroscopic properties. These developments are integrated here into a general scheme that enables one to model and categorize heterogeneous materials via two-point correlation functions.Comment: 37 pages, 26 figure