2,369 research outputs found
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 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
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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 Î-Ray Computed Tomography (CT) Data Measured in a 0.162 M ID Bubble Column Equipped with a Perforated Plate Distributor (163 Holes · Ă 1.32 Mm). Dried Air Was Used as the Gas Phase and Therminol LT (ÎĄL = 886 Kg M-3, ÎL = 0.88 · 10-3 Pa S, ÎŁ = 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 Î-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 â
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, ÎL = 0.88.10-3 Pa S, ÎŁ = 17.10-3 N M-1) Was Used as a Liquid Phase. at Ambient Pressure, the Superficial Gas Velocity, ÎG, 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 (ÎG \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
-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
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
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