Statistical Scatter Research Articles

THE DEMOGRAPHICS OF BROAD-LINE QUASARS IN THE MASS-LUMINOSITY PLANE. I. TESTING FWHM-BASED VIRIAL BLACK HOLE MASSES

We jointly constrain the luminosity function (LF) and black hole mass function (BHMF) of broad-line quasars with forward Bayesian modeling in the quasar mass–luminosity plane, based on a homogeneous sample of ∼58, 000 Sloan Digital Sky Survey (SDSS) Data Release 7 quasars at z ∼ 0.3–5. We take into account the selection effect of the sample flux limit; more importantly, we deal with the statistical scatter between true BH masses and FWHM-based single-epoch virial mass estimates, as well as potential luminosity-dependent biases of these mass estimates. The LF is tightly constrained in the regime sampled by SDSS and makes reasonable predictions when extrapolated to ∼3 mag fainter. Downsizing is seen in the model LF. On the other hand, we find it difficult to constrain the BHMF to within a factor of a few at z ≳ 0.7 (with Mg ii and C iv-based virial BH masses). This is mainly driven by the unknown luminosity-dependent bias of these mass estimators and its degeneracy with other model parameters, and secondly driven by the fact that SDSS quasars only sample the tip of the active BH population at high redshift. Nevertheless, the most likely models favor a positive luminosity-dependent bias for Mg ii and possibly for C iv, such that at fixed true BH mass, objects with higher-than-average luminosities have overestimated FWHM-based virial masses. There is tentative evidence that downsizing also manifests itself in the active BHMF, and the BH mass density in broad-line quasars contributes an insignificant amount to the total BH mass density at all times. Within our model uncertainties, we do not find a strong BH mass dependence of the mean Eddington ratio, but there is evidence that the mean Eddington ratio (at fixed BH mass) increases with redshift.

Material defects as the basis of fatigue design

Microstructural inhomogeneities can exist in metals, such as precipitates and inclusions. These can be introduced purposely to strengthen the metal matrix (e.g.: CuAl2 in α-phase aluminium) or by faulty manufacture (e.g.: large inclusions). A major part of the history of metal fatigue has been to eliminate, or at least reduce, detrimental precipitates, inclusions and manufacture defects such as scratches, surface roughness and shrinkages in cast irons since these can initiate fatigue cracks. The deleterious nature of foreign bodies or other forms of inhomogeneities, e.g.: pores or de-bonded zones within a microstructure are related to their size, position, shape, orientation and physical properties.Small sizes of precipitates and inclusions are to be preferred to large ones; such defects being less detrimental inside a grain rather than at grain boundaries where they can simultaneously affect two or three near-neighbour grains. The orientation of a defect is dangerous should it be inclined to the future direction of Stage I and/or Stage II crack growth planes. An important duty of a metallurgist is to reduce the effectiveness of these different forms of micro-defects produced during manufacture whilst a mechanical engineer is required to derive a suitable form of fracture mechanics in order to account for their behaviour in a quantitative fatigue fracture analysis.In this paper, some important types of microstructural defects will be illustrated and discussed in terms of their size, position, shape, orientation and properties, together with their effect on the fatigue resistance of a material. This will be coupled with a fracture mechanics (FMs) approach that quantifies their behaviour in terms of their relationship to fatigue crack propagation. In this approach, the boundary condition between failure and non-failure is explored using FM as a threshold condition for a small crack coupled with the Vickers hardness HV of the material that represents the condition (ΔKth) for the onset of micro-plasticity (yielding) required for the growth of a crack from the defect and the non-propagation behaviour of the crack.Statistical scatters of microstructures, defects and inclusions are the major factors of statistical scatters of fatigue strength and fatigue life. Directions for optimizing microstructure to improve fatigue strength are explained from the viewpoint of equality control based on the statistics of extremes of defects and inclusions.A new efficient and reliable inclusion rating method for high strength steels based on the statistics of extremes using the phenomenon of hydrogen embrittlement is proposed.

Roughness and fractality of fracture surfaces as indicators of mechanical quantities of porous solids

Abstract The 3D profile surface parameter H q and fractal dimension D were tested as indicators of mechanical properties inferred from fracture surfaces of porous solids. High porous hydrated cement pastes were used as prototypes of porous materials. Both the profile parameter H q and the fractal dimension D showed capability to assess compressive strength from the fracture surfaces of hydrated pastes. From a practical point of view the 3D profile parameter H q seems to be more convenient as an indicator of mechanical properties, as its values suffer much less from statistical scatter than those of fractal dimensions.

Convergence Detection in Direct Simulation Monte Carlo Calculations for Steady State Flows

AbstractA new criterion is presented to detect global convergence to steady state, and to identify local transient characteristics, during rarefied gas flow simulations performed using the direct simulation Monte Carlo (DSMC) method. Unlike deterministic computational fluid dynamics (CFD) schemes, DSMC is generally subject to large statistical scatter in instantaneous flow property evaluations, which prevents the use of residual tracking procedures as are often employed in CFD simulations. However, reliable prediction of the time to reach steady state is necessary for initialization of DSMC sampling operations. Techniques currently used in DSMC to identify steady state convergence are usually insensitive to weak transient behavior in small regions of relatively low density or recirculating flow. The proposed convergence criterion is developed with the goal of properly identifying such weak transient behavior, while adding negligible computational expense and allowing simple implementation in any existing DSMC code. Benefits of the proposed technique over existing convergence detection methods are demonstrated for representative nozzle/plume expansion flow, hypersonic blunt body flow and driven cavity flow problems.

ECG beat classification using features extracted from Teager energy functions in time and frequency domains

It is hypothesised that a key characteristic of ECG signal is its non-linear dynamic behaviour and that the non-linear component changes more significantly between normal and arrhythmia conditions than the linear component. This study makes an attempt to analyse ECG beats from an energy point of view by accounting for the features derived from non-linear component in time and frequency domains using Teager energy operator (TEO). The key feature of TEO is that it models the energy of the source that generated the signal rather than the energy of the signal itself. Hence any deviations in the regular rhythmic activity of the heart get reflected in the Teager energy function. To show the validity of appropriate choice of features, t-tests and scatter plot are used. The t-tests show significant statistical differences and scatter plot of mean of Teager energy in time domain against mean of Teager energy in frequency domain for the ECG beats evaluated on selected Manipal Institute of Technology–Beth Israel Hospital (MIT–BIH) database, which reveals an excellent separation of the features into five different classes: normal, left bundle branch block, right bundle branch block, premature ventricular contraction and paced beats. The neural network results achieved through only two non-linear features exhibit an average accuracy that exceeds 95%, average sensitivity of about 80% and average specificity of almost 100%.

Extension of a Modular Particle-Continuum Method to Vibrationally Excited, Hypersonic Flows

A modular particle-continuum method is extended to include vibrationally excited energy modes to simulate hypersonic steady-state flows that exhibit small regions of translational nonequilibrium in a mainly continuum flowfield. This method loosely couples an existing direct simulation Monte Carlo code to a Navier–Stokes solver (computational fluid dynamics) while allowing both time step and cell size to be completely decoupled between each method. A new information-transfer scheme that controls the inherently large statistical scatter of vibrational energies in low-temperature regions is described and tested. Two vibrational-relaxation models are implemented to test the sensitivity in agreement between direct simulation Monte Carlo and the modular particle-continuum method.By limiting the size of the direct simulationMonteCarlo region to only areas in translational nonequilibrium andmaintaining consistent physicalmodels in both computationalfluid dynamics anddirect simulationMonteCarlo modules, the modular particle-continuummethod is able to reproduce full direct simulationMonte Carlo results for flowwith globalKnudsen number of 0.01while decreasing the computational time required by a factor of about four.

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.

Irradiation creep of SA 304L and CW 316 stainless steels: Mechanical behaviour and microstructural aspects. Part I: Experimental results

Solution annealed 304L (SA 304L) and cold work 316 (CW 316) austenitic stainless steel irradiation creep behaviour have been studied thoroughly. Irradiations were carried out in fast breeder reactors BOR-60 (at 330 °C, up to 120 dpa) and EBR-II (at 375 °C, up to 10.5 dpa), and in the OSIRIS mixed spectrum reactor (at 330 °C, up to 9.8 dpa). After an incubation threshold, the irradiation creep of the austenitic stainless steels is linear in stress and in dose. Creep appears to be athermal in this temperature range. A significant difference in the behaviour is measured between the creep of SA 304L and CW 316. In order to study the anisotropy of loop population, which would be the signature of a possible stress induced preferential absorption (SIPA) mechanism for irradiation creep, special attention was given to the measurement of anisotropy of loop distribution between the four families. The anisotropy induced by an applied stress has been shown to be in the range of the statistical scatter in the situation where no stress is applied. TEM microstructural analyses performed on this sample show slight difference between the microstructure of specimens deformed under irradiation and the microstructure of specimens irradiated without stress under the same irradiation conditions.

Performance index in assessing the physiological state of trees in urban ecosystems

Based on PAM and PEA measurements of fluorescence of bark chloroplasts, we have compared the information capacity of the methods for assessing the physiological state of Tilia cordata Mill. by the maximal quantum efficiency of PS II photochemistry (Fv/Fm) and by the performance index (PI). The measurements were made on annual shoots of linden trees growing in different environs. It was shown that the chlorophyll content in the bark of shoots growing near a busy urban street was twice less than in controls growing out of town. For the trees in the unfavorable environment, a small decrease in (Fv/Fm) was registered, and there was a significant statistical scatter in these values as compared with controls. The PI and its constituent parameters calculated from fluorescence induction curves (PEA method) are more informative and allow recognizing changes in the primary energy conversion processes in PS II when they are still small. Thus, PI can be used as a sensitive, robust, and rapid test to evaluate the physiological state of trees and other plant objects even under minor environmental changes.

Cross-calibration of the X-ray instruments onboard theChandra, INTEGRAL, RXTE,Suzaku, Swift, and XMM-Newtonobservatories using G21.5–0.9

Context. The Crab nebula has been used as a celestial calibration source of the X-ray flux and spectral shape for many years by X-ray astronomy missions. However, the object is often too bright for current and future missions equipped with instruments with improved sensitivity. Aims. We use G21.5-0.9 as a viable, fainter substitute to the Crab, which is another pulsar-wind nebula with a time-constant powerlaw spectrum with a flux of a few milli Crab in the X-ray band. Using this source, we conduct a cross-calibration study of the instruments onboard currently active observatories: Chandra ACIS, Suzaku XIS, Swift XRT, XMM-Newton EPIC (MOS and pn) for the soft-band, and INTEGRAL IBIS-ISGRI, RXTE PCA, and Suzaku HXD-PIN for the hard band. Methods. We extract spectra from all the instruments and fit them under the same astrophysical assumptions. We compare the spectral parameters of the G21.5-0.9 model: power-law photon index, H-equivalent column density of the interstellar photoelectric absorption, flux in the soft (2-8 keV) or hard (15-50 keV) energy band. Results. We identify the systematic differences in the best-fit parameter values unattributable to the statistical scatter of the data alone. We interpret these differences as due to residual cross-calibration problems. The differences can be as large as 20% and 9% for the soft-band flux and power-law index, respectively, and 46% for the hard-band flux. The results are plotted and tabulated as a useful reference for future calibration and scientific studies using multiple missions.

Statistical scatter of fracture toughness in the ductile–brittle transition of a structural steel

The statistical scatter of fracture toughness in the ductile–brittle transition temperature range was experimentally examined on a 500 MPa class low carbon steel. Fracture toughness tests were replicatedly performed at −60 °C, −20 °C and −10 °C. The tests at −60 °C resulted in a single modal Weibull distribution with a shape parameter of 4 for the critical stress intensity factor converted from J-integral, whereas the Weibull distributions of the critical stress intensity factor at −20 °C and −10 °C showed a bilinear pattern with an elbow point, which caused a wider scatter than that at −60 °C. Such scatter transition behavior was discussed with reference to stable crack initiation. A model of the statistical scatter transition has been proposed in this work and the model reasonably explains the experimental results.

Statistical Analysis of High-Cycle Fatigue Behavior of Friction Stir Welded AA5083-H321

A review of the literature revealed that high-cycle fatigue data associated with friction stir-welded (FSW) joints of AA5083-H321 (a solid-solution-strengthened and strain-hardened/stabilized Al-Mg-Mn alloy) are characterized by a relatively large statistical scatter. This scatter is closely related to the intrinsic variability of the FSW process and to the stochastic nature of the workpiece material microstructure/properties as well as to the surface condition of the weld. Consequently, the use of statistical methods and tools in the analysis of FSW joints is highly critical. A three-step FSW-joint fatigue-strength/life statistical-analysis procedure is proposed in this study. Within the first step, the type of the most appropriate probability distribution function is identified. The parameters of the selected probability distribution function, along with their confidence limits, are computed in the second step. In the third step, a procedure is developed for assessment of the statistical significance of the effect of the FSW process parameters and fatigue specimen surface conditions. The procedure is then applied to a set of stress-amplitude versus number of cycles to failure experimental data in which the tool translational speed was varied over four levels, while the fatigue specimen surface condition was varied over two levels. The results obtained showed that a two-parameter weibull distribution function with its scale factor being dependent on the stress amplitude is the most appropriate choice for the probability distribution function. In addition, it is found that, while the tool translational speed has a first-order effect on the AA5083-H321 FSW-joint fatigue strength/life, the effect of the fatigue specimen surface condition is less pronounced.

Transition from deterministic to stochastic deformation

Theory predicts that deformation that occurs by emission of strain bursts falls into two regimes, one in which the burst emission remains a stochastic process as strain increases, and another in which the emission of bursts settles into a deterministic process for large strains. The stochastic regime occurs when the burst emission rate decreases with strain, and in this case, large statistical scatter persists in the stress–strain response on repeated measurements. The deterministic regime occurs when the emission rate increases with strain, and the scatter in the corresponding stress–stress behaviour diminishes at large strains. The strength at the same strain in the stochastic regime is also higher than in the deterministic regime. Factors that affect the burst emission rate include the number of sources as well as the stress dependence of the efficiency of the sources.

On the use of structure functions to study blazar variability: caveats and problems

The extensive use of the structure function (SF) in the field of blazar variability suggests that characteristics time-scales are embedded in the light curves of these objects. We argue that for blazar variability studies, the SF results are sometimes erroneously interpreted leading to misconceptions about the actual source properties. Based on extensive simulations we caution that spurious breaks will appear in the SFs of almost all light curves, even though these light curves may contain no intrinsic characteristic time-scales. i.e. having a featureless underlying power-spectral-density (PSD). We show that the time-scales of the spurious SF-breaks depend mainly on the length of the artificial data set and also on the character of the variability i.e. the shape of the PSD. The SF is often invoked in the framework of shot-noise models to determine the temporal properties of individual shots. We caution that although the SF may be fitted to infer the shot parameters, the resultant shot-noise model is usually inconsistent with the observed PSD. As any model should fit the data in both the time and the frequency domain the shot-noise model, in these particular cases, can not be valid. Moreover, we show that the lack of statistical independence between adjacent SF points, in the standard SF formulation, means that it is not possible to perform robust statistical model fitting following the commonly used least-squares fitting methodology. The latter yields uncertainties in the fitting parameters (i.e. slopes, breaks) that are far too small with respect to their true statistical scatter. Finally, it is also commonly thought that SFs are immune to the sampling problems, such as data gaps, which affects the estimators of the PSDs. However we show that SFs are also troubled by gaps which can induce artefacts.

Fatigue Model for Composites Based on the Cycle-by-cycle Probability of Failure: Implications and Applications

Further implications of a fatigue model based on the cycle-by-cycle probability of failure are presented. A model for the residual strength is developed based on a linear relation between the residual strength at any cycle level and its derivative. This model is shown to be in excellent agreement with published test results. The model is also shown to lead to a constant cycle-by-cycle probability of failure under constant amplitude loading thus verifying the assumption of constant probability of failure made previously. The model is then used to construct constant life (Goodman) diagrams for composite structures and its predictions are compared to published test results. The model follows the test data well but needs further improvement for negative R values. The approach is then extended to the determination of the truncation level required for a structure to meet a certain fatigue life. The truncation level is a function of R ratio and the amount of statistical scatter for static tension and compression tests. Using representative values for the scatter, the predicted truncation level of 38% is shown to cover most applications. Possible reasons for discrepancies and areas where more work is needed are identified.

Can micro-compression testing provide stress–strain data for thin films?: A comparative study using Cu, VN, TiN and W coatings

Micro-compression testing using an instrumented micro- or nanoindenter equipped with a flat punch is a promising approach to measure the stress–strain response of miniaturized materials and to complement hardness and modulus measurements gained by nanoindendation. Focussed ion beam milling is employed to fabricate micron-sized compression pillars from 1µm thick single crystal Cu(001), TiN(001), and VN(001) films grown on MgO(001), and from a 6.7µm thick polycrystalline W coating deposited on Si(001). In situ micro-compression tests in a scanning electron microscope reveal reproducible stress–strain curves for W, a considerable statistical scatter in the flow stress for Cu and VN, and failure of TiN pillars by cleavage. A linear work-hardening rate of 2.7±1.2GPa is determined for the polycrystalline W coating. The results are critically discussed taking into account material defects and the stiffness of the film-substrate system.

Semiquantitative method for the evaluation of grease barrier coatings

Many tests are known for testing the grease barrier performance of coatings in paper or paperboard. Some are manifested in standard procedures such as TAPPI, ASTM, or ISO, but as many procedures were developed and modified by companies and research groups. Mainly the test methods are based on visually detecting the amount of oil, which is in most cases dyed for better contrast, penetrating through the coating, meaning the procedures are based on a subjective visual evaluation and thus often not linked for instance to a statistical meaningful physical value. We found that by using a slightly modified ASTM D 722 test the L* a* b* color coordinates determined with a commercial handheld spectrophotometer are related to the grease barrier performance of an organic coating. By applying this new method the penetration time of an oil/dye mixture could be correlated to the lightness L* and chromaticity b* and fitted by an exponential function. Furthermore, the coating was slightly modified and an improvement or worsening of the grease barrier could be detected clearly outside of the statistical scatter of a control series. We call this method semiquantitative, since the level of grease barrier of a coating is not measured directly by a quantitative value, but color coordinates are correlated in a series to the effectiveness of the grease barrier.

The Impact of Planimetric Configuration on Structurally Damaged Residential Buildings

This study was conducted to determine a significant relationship between planimetric configuration and vulnerability of hazardous buildings located in seismic zones by developing design and construction efficiency indicators. Case study examples were chosen from residential buildings in Bolu, Düzce and Kaynaşlı in Turkey, which were damaged by the 1999 earthquakes. Utilizing field survey drawings, efficiency quotients; compactness quotients; construction efficiency ratios; aspect ratios and height-to-base ratios were defined as planimetric configuration indicators. The significant relationship between these aspects and the damage level of buildings were determined through statistical analyses and scatter charts. Planimetric configuration—including building geometry, cantilever projections and layout of columns—was reviewed according to the Turkish Earthquake Code. Findings revealed certain dependencies for efficiency ratios, which would satisfactorily predict the seismic vulnerability of buildings based on planimetric configuration. Researchers in the field of architecture who are engaged in earthquake-resistant design may use the general methodology. In addition, architects and structural engineers can use this approach presented here to evaluate their design.

An improved Quiet Direct Simulation method for Eulerian fluids using a second-order scheme

In this paper, a second-order scheme for the Quiet Direct Simulation (QDS) of Eulerian fluids is proposed. The QDS method replaces the random sampling method used in Direct Simulation Monte Carlo (DSMC) methods with a technique whereby particles are moved, have their properties distributed onto a mesh, are destroyed and then are recreated deterministically from the properties stored on the mesh using Gauss–Hermite quadrature weights and abscissas. Particles are permitted to move in physically realistic directions so flux exchange is not limited to cells sharing an adjacent interface as in conventional, direction decoupled finite volume solvers. In this paper the method is extended by calculating the fluxes of mass, momentum and energy between cells assuming a linear variation of density, temperature and velocity in each cell and using these fluxes to update the mass, velocity and internal energy carried by each particle. This Euler solver has several advantages including large dynamic range, no statistical scatter in the results, true direction fluxes to all nearby neighbors and is computationally inexpensive. The second-order method is found to reduce the numerical diffusion of QDS as demonstrated in several verification studies. These include unsteady shock tube flow, a two-dimensional blast wave and of the development of Mach 3 flow over a forward facing step in a wind tunnel, which are compared with previous results from the literature wherever is possible. Finally the implementation of QUIETWAVE, a rapid method of simulating blast events in urban environments, is introduced and the results of a test case are presented.

Modeling of processes in gases in shock tubes with consideration for internal degrees of freedom by using the direct simulation Monte Carlo method

Parallel calculations within the framework of the direct simulation Monte Carlo method were performed on multiprocessor computers using the block decomposition of the simulation region. At the initial moment, the driver section of the shock was filled with a gas with a molecular mass identical to that of H2 while the driven section was filled with a mixture of gases with molecular masses identical to those of Xe, O2, He, and H2 and a ratio of molar concentrations of 1: 10: 169: 20. Simulations were performed using a simplified description of the rotational and vibrational degrees of freedom of the molecules. A model with energy sink was used. The width of smearing of the post-shock flow boundary adjacent to contact surface was determined and shown be to time-independent within the statistical scatter over the entire duration of simulations. It was revealed that the concentrations of O2, Xe, and He in the post-shock flow region adjacent to the contact surface were substantially higher over the entire time of flow existence. This effect was not observed when the internal degrees of freedom were disregarded.