Local Distribution Function Research Articles

X-ray galaxy clusters abundance and mass temperature scaling

The abundance of clusters of galaxies is known to be a potential source of cosmological constraints through their mass function. In the present work, we examine the information that can be obtained from the temperature distribution function of X-ray clusters. For this purpose, the mass-temperature ($M$-$T$) relation and its statistical properties are critical ingredients. Using a combination of cosmic microwave background (CMB) data from Planck and our estimations of X-ray cluster abundances, we use Markov chain Monte Carlo (MCMC) techniques to estimate the $\Lambda$CDM cosmological parameters and the mass to X-ray temperature scaling relation simultaneously. We determine the integrated X-ray temperature function of local clusters using flux-limited surveys. A local comprehensive sample was build from the BAX X-ray cluster database, allowing us to estimate the local temperature distribution function above $\sim$1 keV. We model the expected temperature function from the mass function and the $M$-$T$ scaling relation. We then estimate the cosmological parameters and the parameters of the $M$-$T$ relation (calibration and slope) simultaneously. The measured temperature function of local clusters in the range $\sim\!\!1$-$10$ keV is well reproduced once the calibration of the $M$-$T$ relation is treated as a free parameter, and therefore is self-consistent with respect to the $\Lambda$CDM cosmology. The best-fit values of the standard cosmological parameters as well as their uncertainties are unchanged by the addition of clusters data. The calibration of the mass temperature relation, as well as its slope, are determined with $\sim10\%$ statistical uncertainties. This calibration leads to masses that are $\sim\!\!75\%$ larger than X-ray masses used in Planck.

A Multistep Methodology for Building a Stochastic Model of Gold Grades in the Disseminated and Complex Deposit of Casas Novas in Alentejo, Southern Portugal

AbstractThis paper proposes a multistep approach for creating a 3D stochastic model of gold grades in a complex disseminated auriferous deposit located in the Alentejo region, southern Portugal. The approach involves the following steps: (i) the creation of a 3D low‐resolution vector object model of two geological domains that better discriminate gold grades; (ii) the definition of three intervals for gold grades (low, intermediate, and high values); (iii) the estimation of the probability of each grid block belonging to each interval constrained by the geological domains; (iv) the calculation of local conditional cumulative distribution functions (CCDFs) of gold grades, for each block, taking into account the geological domains and the borehole data; and finally (v) the simulation of images of gold grades. The results demonstrate the usefulness and accuracy of the proposed procedure, as they are in compliance with the conceptual model, the distribution laws are conditioned by the geological domains, and the transition of grades between domains is continuous.

Probabilistic modeling of hybrid transition structures

Abstract Within lightweight structures, often Fiber Reinforced Plastics (FRP) are used in combination with metallic materials. Most of these hybrid structures are manufactured by established methods like riveting, bolting or adhesive bonding. In order to avoid disadvantages like drilled FRP or large bond areas, the development of hybrid transition structures compatible to loads and material properties is required. To fulfill the requirements for enhanced lightweight design, novel, integral joint concepts are currently designed, dimensioned and produced by using textile, welding and casting techniques. Three concepts are under investigation which consist of different materials (titanium and Ti-alloys, glass fibers), manufacturing methods (casting, welding, textile techniques) and geometries. Various phase boundaries, materials and influences of the manufacturing processes have to be investigated that influence the structural behavior and its failure. Based on the results of Finite Element Models on the meso scale, further modeling is performed to include effects like material uncertainties and/or process influences. In this paper, a probabilistic computation procedure based on local survival probabilities and distribution functions is proposed and investigated. This approach allows to model the complex global failure behavior for each component or its interfaces as well as the whole hybrid transition zone. It also shows the interactions and consequences of certain component changes within the hybrid transition zone. First computations are carried out and compared with experiments.

Developing coarse-grained potentials for the prediction of multi-properties of trans-1,4-polybutadiene melt

In this paper, we combined structure-based and thermodynamic quantities-based coarse-graining (CG) approaches and adopted the bulk density, local conformational distributions and radial distribution function of the underlying atomistic model system as the target properties to derive the CG force field (FF) for the polymer system of trans-1,4-polybutadiene. The resultant CG FF exhibits good observable representability. In addition to the overall chain size, the extracted bulk modulus, isothermal compressibility, storage and loss moduli from CG model systems are of the same level of magnitude as the atomistic results, suggesting that this hybrid CG approach improves the reproduction capability of the CG model on mechanical property, pressure-dependent density fluctuations, and viscoelasticity. Upon the introduction of a standard dissipative particle dynamics (DPD) thermostat to remedy the removed degrees of freedom and reduced friction during CG, the CG model can completely mimic the dynamics of the atomistic model. Furthermore, we found that the standard DPD thermostat approach is applicable to the steady shear flow simulation at low and moderate rates and the relevant dissipative factor derived by matching diffusion coefficients can only quantitatively reproduce the shear viscosity at low shear rates. Overall, these findings demonstrate the ability of combined CG methods in optimizing CG FF to reproduce multi-properties of polymers.

Anomalous Localization of Electrochemical Activity in Reversible Charge Transfer at a Weierstrass Fractal Electrode: Local Electrochemical Impedance Spectroscopy.

The knowledge of local electrochemical activity over an electrode surface is of utmost importance in understanding several processes like electrocatalysis, dendrite growth, and corrosion. For a redox system with unequal diffusivities, we have developed a second order perturbation theory in the surface profile for the local electrochemical impedance spectroscopy (LEIS) for a reversible charge transfer system at an electrode with arbitrary surface profile corrugations. Detailed analysis of LEIS is performed for the simple roughness model of the sinusoidal surface and the realistic roughness model of the finite fractal Weierstrass function as surface corrugation. At a low roughness surface, local electrochemical activity is localized at peaks and depleted at valleys. However, at moderate and high roughness surfaces, there is anomalous bifurcation beside peak positions, making local electrochemical activity localized at cliff (high slope) locations. Maximum depletion is observed at valleys and remains more depleted at valleys as compared to peak positions of the surface even at a high aspect ratio of roughness and frequency of the external signal. Complex multifurcations behavior of local activity and inactivity occur in Weierstrass corrugation for moderate and high roughness. The localization phenomenon of impedance on a Weierstrass fractal surface depends upon the fractal dimension size of finest feature and mean square width of roughness. The influence of various features of a Weierstrass surface is also studied through local impedance distribution functions.

The rich are different: evidence from the RAVE survey for stellar radial migration

Using the RAdial Velocity Experiment fourth data release (RAVE DR4), and a new metallicity calibration that will be also taken into account in the future RAVE DR5, we investigate the existence and the properties of supersolar metallicity stars ([M/H] ≳ +0.1 dex) in the sample, and in particular in the solar neighbourhood. We find that RAVE is rich in supersolar metallicity stars, and that the local metallicity distribution function declines remarkably slowly up to +0.4 dex. Our results show that the kinematics and height distributions of the supersolar metallicity stars are identical to those of the [M/H] ≲ 0 thin-disc giants that we presume were locally manufactured. The eccentricities of the supersolar metallicity stars indicate that half of them are on a roughly circular orbit (e ≤ 0.15), so under the assumption that the metallicity of the interstellar medium at a given radius never decreases with time, they must have increased their angular momenta by scattering at corotation resonances of spiral arms from regions far inside the solar annulus. The likelihood that a star will migrate radially does not seem to decrease significantly with increasing amplitude of vertical oscillations within range of oscillation amplitudes encountered in the disc.

A new approach to soil classification mapping based on the spatial distribution of soil properties

This study presents a new approach to classifying types of soil based on the probability classes of the relevant set of attributes. Two key ideas are addressed in this study: (i) the use of stochastic simulations to generate a local cumulative distribution function or extreme classes of each attribute and (ii) the use of a multidimensional scaling (MDS) technique to visualize and quantify the relative importance of each attribute in the classification process. After the simulated realizations, the weighted “distances” attributes extreme values (probability classes) of each grid node are calculated and the MDS algorithm is applied for the spatial representation of the grid nodes in a new Cartesian reference frame based on the “distances” of the probability classes of attributes. This allows the classification of soil types based on the clusters in the MDS space, after expert validation. In the second step, a sensitivity analysis of the attributes is performed with MDS: each attribute is made “neutral” one at a time, by assuming the median rather than the extreme values in each grid node before the distance evaluation, and the consequent impact on the shape and centroid displacement of the clusters (soil types) in the MDS reference frame is calculated. Hence, the spatial uncertainty of the soil type/classes and the influence of various properties are evaluated in the MDS reference frame. This method is applied to soils in a region of Brazilian in which the previous classification of soil types has been a crucial tool for precision agriculture management. Using the MDS algorithm, the selected attributes (horizon, textural gradient, colors, saturation, sand content, and clay content) were represented in a two-dimensional plot and grouped into eight clusters distinguished from each other by their characteristics. A sensitivity analysis shows that the horizon and saturation attributes had the greatest influence on determination of the clusters, i.e., the soil types.

Measurement of a 2D fast-ion velocity distribution function by tomographic inversion of fast-ion D-alpha spectra

We present the first measurement of a local fast-ion 2D velocity distribution function f(v‖, v⊥). To this end, we heated a plasma in ASDEX Upgrade by neutral beam injection and measured spectra of fast-ion Dα (FIDA) light from the plasma centre in three views simultaneously. The measured spectra agree very well with synthetic spectra calculated from a TRANSP/NUBEAM simulation. Based on the measured FIDA spectra alone, we infer f(v‖, v⊥) by tomographic inversion. Salient features of our measurement of f(v‖, v⊥) agree reasonably well with the simulation: the measured as well as the simulated f(v‖, v⊥) are lopsided towards negative velocities parallel to the magnetic field, and they have similar shapes. Further, the peaks in the simulation of f(v‖, v⊥) at full and half injection energies of the neutral beam also appear in the measurement at similar velocity-space locations. We expect that we can measure spectra in up to seven views simultaneously in the next ASDEX Upgrade campaign which would further improve measurements of f(v‖, v⊥) by tomographic inversion.

Role of Environmental and Antibiotic Stress on Staphylococcus epidermidis Biofilm Microstructure

Cellular clustering and separation of Staphylococcus epidermidis surface adherent biofilms were found to depend significantly on both antibiotic and environmental stress present during growth under steady flow. Image analysis techniques common to colloidal science were applied to image volumes acquired with high-resolution confocal laser scanning microscopy to extract spatial positions of individual bacteria in volumes of size ~30 × 30 × 15 μm(3). The local number density, cluster distribution, and radial distribution function were determined at each condition by analyzing the statistics of the bacterial spatial positions. Environmental stressors of high osmotic pressure (776 mM NaCl) and sublethal antibiotic dose (1.9 μg/mL vancomycin) decreased the average bacterial local number density 10-fold. Device-associated bacterial biofilms are frequently exposed to these environmental and antibiotic stressors while undergoing flow in the bloodstream. Characteristic density phenotypes associated with low, medium, and high local number densities were identified in unstressed S. epidermidis biofilms, while stressed biofilms contained medium- and low-density phenotypes. All biofilms exhibited clustering at length scales commensurate with cell division (~1.0 μm). However, density phenotypes differed in cellular connectivity at the scale of ~6 μm. On this scale, nearly all cells in the high- and medium-density phenotypes were connected into a single cluster with a structure characteristic of a densely packed disordered fluid. However, in the low-density phenotype, the number of clusters was greater, equal to 4% of the total number of cells, and structures were fractal in nature with d(f) =1.7 ± 0.1. The work advances the understanding of biofilm growth, informs the development of predictive models of transport and mechanical properties of biofilms, and provides a method for quantifying the kinetics of bacterial surface colonization as well as biofilm fracture and fragmentation.

Quantitative Prediction of Effective Toughness at Random Heterogeneous Interfaces

The propagation of an adhesive crack through an anisotropic heterogeneous interface is considered. Tuning the local toughness distribution function and spatial correlation is numerically shown to induce a transition between weak to strong pinning conditions. While the macroscopic effective toughness is given by the mean local toughness in the case of weak pinning, a systematic toughness enhancement is observed for strong pinning (the critical point of the depinning transition). A self-consistent approximation is shown to account very accurately for this evolution, without any free parameter.

使用极坐标格子玻尔兹曼方法研究冲击过程——复杂系统中非平衡效应的探索

本文使用极坐标高速可压格子玻尔兹曼模型研究冲击过程。其中离散速度模型是由Watari和Tsutahara提出的D2V97，对流项采用修正的Warming-Beam格式处理。分别模拟研究了冲击波在环形区域和圆形区域中向内传播过程中物理量的变化规律，并通过离散速度分布函数的速度矩分析了冲击波波阵面附近的非平衡效应。为了从更基本层面理解界面行为，给出了波阵面处真实分布函数在速度空间的示意图。 The Polar Coordinate Lattice Boltzmann (PCLB) model is used to investigate the shocking processes. The discrete velocity model used in this PCLB is the D2V97 presented by Watari and Tsutahara. The convective term is treated with a modified Warming-Beam scheme. Two shocking processes are investigated. In one case, the evolution of a shock wave travels inwards within an annular area is studied. In the other case, the evolution of a shock wave travels inwards within a circular area is studied. The non-equilibrium effects around the shock fronts are investigated by ana- lyzing the simulated results of velocity moments of local discrete distribution function. To further understand the inter- face from a more fundamental level, we give the sketch of the actual distribution function in velocity space around the shock front.

Kinetic equation for the processes of local reorganization of molecular systems with charged species

A molecular dynamic theory based on the lattice-gas model for the local reorganization of multi-component systems containing charged species is considered. Expressions for the mono- and bimolecular stages of the elementary processes that describe chemical reactions and displacements and rotations of molecules in dense gases and liquids are derived, with consideration given to direct and indirect effects of the initiation of electron and proton transfer. The proposed kinetic equations describe small-scale restructuring of solutions containing components of different sizes under the influence of changes in the external parameters of the molecular system at the kinetic stage of evolution of the system. The theory retains the effects of direct spatial correlations in the distribution of all the components of the mixture with the help of pair distribution functions in the quasi-chemical approximation. The dynamics of the local reorganization of molecules includes the kinetic equations for the local densities and pair distribution functions. The equations derived are intended to describe liquid-phase reactions, ion charge exchange, mutual diffusion of components of different sizes in multicomponent solutions, extraction processes at liquid phase boundaries, and photochemical processes in condensed phases.

Computational simulation of metal ion propagation from plasma to substrates with uneven surfaces

The influence of the unevenness of substrates immersed into plasma on plasma–surface interactions was studied by the combination of multidimensional fluid modelling and particle simulation connected together in iterative hybrid code. The fluid part of our model consisted of continuity equations for all charged species and Poisson's equation. The non self-consistent particle simulation technique was used both for the calculation of local electron energy distribution function and for the derivation of quantities characterising plasma–surface interaction. This approach enabled us to study in detail the structure of the plasma near metal substrates with complex geometries, i.e. planar substrates covered by a variety of hemispherical protrusions. The main attention was devoted to the influence of substrate unevenness in both macroscopic and microscopic spatial scales on both metal ions and ions of background gas propagation to the substrate.

Spatio-temporal patterns of Cu contamination in mosses using geostatistical estimation

Several recent studies have reported temporal trends in metal contamination in mosses, but such assessments did not evaluate uncertainty in temporal changes, therefore providing weak statistical support for time comparisons. Furthermore, levels of contaminants in the environment change in both space and time, requiring space-time modelling methods for map estimation. We propose an indicator of spatial and temporal variation based on space-time estimation by indicator kriging, where uncertainty at each location is estimated from the local distribution function, thereby calculating variability intervals for comparison between several biomonitoring dates. This approach was exemplified using copper concentrations in mosses from four Portuguese surveys (1992, 1997, 2002 and 2006). Using this approach, we identified a general decrease in copper contamination, but spatial patterns were not uniform, and from the uncertainty intervals, changes could not be considered significant in the majority of the study area.

Phase diagram of mixed Cu(InxCr1−x)P2S6crystals

Mixed Cu(In${}_{x}$Cr${}_{1\ensuremath{-}x}$)P${}_{2}$S${}_{6}$ crystals of ferrielectric CuInP${}_{2}$S ${}_{6}$ and antiferroelectric CuCrP${}_{2}$S${}_{6}$ were investigated by means of broadband dielectric spectroscopy (10 mHz--3 GHz), for several values of $x$. The phase boundary between the ferrielectric phase and the dipolar glass state was found to lie between 0.5 and 0.7, and a similar boundary between the dipolar glass state and the antiferroelectric phase is observed to be located between 0.4 and 0.2. The dipole freezing results in a broad distribution of the relaxation times. The parameters of the double-well potentials, the local polarization distribution function, and glass order parameter have been extracted from the dielectric measurements. From these results the complete phase diagram has been constructed.

Local Field Distributions in Systems with Dipolar Interaction

We investigate systematically the local field distribution functions of up-spins for systems of dipolar interaction, with particular emphasis on Ising-type lattice systems. It is found that as the fraction increases, the shape of the distribution function changes from Lorentzian to Gaussian. In addition, sub-peaks can be induced in the distribution function by non-cubic lattice structures. This is in stark contrast with a dilute gas system, where the distribution has only one Lorentzian peak for any up-spin fraction.

Towards a fully kinetic 3D electromagnetic particle-in-cell model of streamer formation and dynamics in high-pressure electronegative gases

Streamer and leader formation in high pressure devices is dynamic process involving a broad range of physical phenomena. These include elastic and inelastic particle collisions in the gas, radiation generation, transport and absorption, and electrode interactions. Accurate modeling of these physical processes is essential for a number of applications, including high-current, laser-triggered gas switches. Towards this end, we present a new 3D implicit particle-in-cell simulation model of gas breakdown leading to streamer formation in electronegative gases. The model uses a Monte Carlo treatment for all particle interactions and includes discrete photon generation, transport, and absorption for ultra-violet and soft x-ray radiation. Central to the realization of this fully kinetic particle treatment is an algorithm that manages the total particle count by species while preserving the local momentum distribution functions and conserving charge [D. R. Welch, T. C. Genoni, R. E. Clark, and D. V. Rose, J. Comput. Phys. 227, 143 (2007)]. The simulation model is fully electromagnetic, making it capable of following, for example, the evolution of a gas switch from the point of laser-induced localized breakdown of the gas between electrodes through the successive stages of streamer propagation, initial electrode current connection, and high-current conduction channel evolution, where self-magnetic field effects are likely to be important. We describe the model details and underlying assumptions used and present sample results from 3D simulations of streamer formation and propagation in SF6.

Constraining the star formation rate in the solar neighbourhood with star clusters

This paper investigates the star formation rate (SFR) in the Solar neighbourhood. First, we build the local age distribution function (ADF) with an updated sample of 442 star clusters located at less than 1\,kpc from the Sun. Next, we define the SFR, compute the individual mass evolution of a population of artificial clusters covering the broad range of parameters observed in actual clusters, and assume 100\,\ms\ as the low-mass limit for effective cluster observation. This leads to a simulated ADF, which is compared to the low-noise Solar neighbourhood ADF. The best match corresponds to a non-constant SFR presenting two conspicuous excesses for ages $\le9$\,Myr and between 220-600\,Myr (the local starburst). The average formation rate is $\bar{SFR}\approx(2500\pm500)\,\mmy$, corresponding to the average surface formation rate $\bar{\ssfr}\approx(790\pm160)\,\mmk$. These values are consistent with the formation rate inferred from embedded clusters (ECs), but much lower ($\la16%$) than that implied by field stars. Both the local starburst and the recent star formation period require $SFR\sim2\times\bar{SFR}$ to be described. The simulations show that $91.2\pm2.7%$ of the clusters created in the Solar neighbourhood do not survive the first 10\,Myr, which is consistent with the rate of EC dissolution.

Kinetic equations for processes of local rearrangement of molecular systems

A dynamic theory of the local rearrangement of multicomponent molecular systems based on the lattice-gas model is constructed. Kinetic equations describing the small-scale restructuring of solutions containing components of different sizes under the influence of the external parameters of the system are derived. The intermolecular interactions between the reactants and the solvent specified in the form of an atom-atom potentials are described in the quasi-chemical approximation. This approach reflects the direct effects of spatial correlations in the distribution of all components of the mixture by means of pair distribution functions. The dynamics of the local rearrangement of the molecules is described by the equations for local density and pair distribution function. The theory is also capable of describing the mutual diffusion of components of different sizes in multicomponent solutions and the processes of swelling of polymers under the action of low-molecular substances dissolved in them. The problems of detailed description of the rates of elementary stages in dense gases and liquids by taking into account the direct dynamic effects of colliding molecules and the cooperative movement of polymer units during the relaxation of amorphous polymer matrices are examined.

Modeling of initial crystallization in the alloys Al–10Ni and Al–5Ni–2.7Y at high undercoolings

Formation and growth of crystallization centers of aluminum in amorphous alloys Al–10Ni and Al–5Ni–2.7Y have been studied by a method of the molecular dynamics. Local radial pair distribution functions were calculated for studying of structure. Growth kinetics of the comparatively large aluminum crystals in the binary system is studied. Latencies of appearance of the first crystallization centre are found. The energies of interatomic interaction averaged locally and also in the bulk of the amorphous phase are determined. It is researched how the size of the crystallization centre influences its structure and the local interaction energy. Formation of icosahedrons and their lifetimes are in consideration.