Assumption Of Density Research Articles

A Selective Overview and Comparison of Robust Mixture Regression Estimators

SummaryMixture regression models have been widely used in business, marketing and social sciences to model mixed regression relationships arising from a clustered and thus heterogeneous population. The unknown mixture regression parameters are usually estimated by maximum likelihood estimators using the expectation–maximisation algorithm based on the normality assumption of component error density. However, it is well known that the normality‐based maximum likelihood estimation is very sensitive to outliers or heavy‐tailed error distributions. This paper aims to give a selective overview of the recently proposed robust mixture regression methods and compare their performance using simulation studies.

Characterizing the settleability of grit particles.

Grit chambers are installed at the headworks of a water resource recovery facility (WRRF) to reduce the impact of grit particles to the equipment and processes downstream. This settling process should thus be designed and operated in an efficient way. Despite the importance of knowing settling characteristics for design and operation of grit chambers, previous grit definitions have been based only on particle size characteristics, and not on settling velocities. Thus, this study presents an evaluation of the performance of two promising settling velocity characterization methods, ViCAs and elutriation, to characterize wastewater particles in view of the design and the optimization of the efficiency of the grit removal unit. PRACTITIONER POINTS: Settling characteristics are the governing parameter for grit chamber design. Since grit particles are vastly heterogeneous, it is preferred to measure these characteristics directly rather than to estimate them from particle size (and assumptions of density, form factor, …). More detailed settling information about grit particles can improve grit chamber design and estimation of removal performance. Adapted ViCAs and elutriation methods for faster settling particles allow studying the particle settling characteristics in a grit chamber. These methods are simple, fast, and cheap and only require small wastewater samples. A relationship was found between the influent TSS concentration and the location of the PSVD curve, with higher TSS concentrations corresponding to higher settling velocities. It was demonstrated that the dynamics of the wastewater characteristics under dry, wet, and snowmelt weather conditions influence grit settling characteristics.

Low Mach number limit of the three-dimensional full compressible Navier–Stokes–Korteweg equations

In this paper, we justify the low Mach number limit for the three-dimensional full compressible Navier–Stokes–Korteweg equations rigorously within the framework of smooth solution. Under the assumptions of small density and temperature perturbation, we show that for sufficiently small Mach number, the initial-value problem of the three-dimensional full compressible Navier–Stokes–Korteweg equations admits a unique smooth solution on the time interval where the smooth solution of the corresponding incompressible Navier–Stokes equations exists. Moreover, we obtain the convergence of smooth solutions for the full compressible Navier–Stokes–Korteweg equations toward those for the incompressible Navier–Stokes equations with a convergence rate.

A new mean ergodic theorem for tori and recurrences

Let$X$be a finite-dimensional connected compact abelian group equipped with the normalized Haar measure$\unicode[STIX]{x1D707}$. We obtain the following mean ergodic theorem over ‘thin’ phase sets. Fix$k\geq 1$and, for every$n\geq 1$, let$A_{n}$be a subset of$\mathbb{Z}^{k}\cap [-n,n]^{k}$. Assume that$(A_{n})_{n\geq 1}$has$\unicode[STIX]{x1D714}(1/n)$density in the sense that$\lim _{n\rightarrow \infty }(|A_{n}|/n^{k-1})=\infty$. Let$T_{1},\ldots ,T_{k}$be ergodic automorphisms of$X$. We have$$\begin{eqnarray}\frac{1}{|A_{n}|}\mathop{\sum }_{(n_{1},\ldots ,n_{k})\in A_{n}}f_{1}(T_{1}^{n_{1}}(x))\cdots f_{k}(T_{k}^{n_{k}}(x))\stackrel{L_{\unicode[STIX]{x1D707}}^{2}}{\longrightarrow }\int f_{1}\,d\unicode[STIX]{x1D707}\cdots \int f_{k}\,d\unicode[STIX]{x1D707},\end{eqnarray}$$for any$f_{1},\ldots ,f_{k}\in L_{\unicode[STIX]{x1D707}}^{\infty }$. When the$T_{i}$are ergodic epimorphisms, the same conclusion holds under the further assumption that$A_{n}$is a subset of$[0,n]^{k}$for every$n$. The density assumption on the$A_{i}$is necessary. Immediate applications include certain Poincaré style recurrence results.

The second-degree gravity coefficients of Phobos from two Mars Express flybys

ABSTRACT Several close spacecraft flybys of Phobos have been performed over the past 40 yr in order to determine the gravity field of this tiny Martian moon. In this work, the second-degree coefficients of the gravity field of Phobos were derived from the radio tracking data of two combined Mars Express flybys (2010 and 2013), by applying a least squares regularized inverse technique, that introduces as an a priori the gravity field retrieved from a shape model based on constant density hypothesis. A gravitational mass estimate of $(7.0765\pm 0.0075)\times 10^5 \, \mathrm{m^3\, s}^{-2}$ and second-degree gravity coefficients C20 = −0.1378 ± 0.0348 and C22 = 0.0166 ± 0.0153(3σ) were derived. The estimated C20 value, in contrast to the value of C20 computed from the shape model under the constant density assumption, supports an inhomogeneous distribution inside Phobos at a confidence interval of 95 per cent (1.96σ). This result indicates a denser mass in the equatorial region or lighter mass in polar areas.

Inflation, (p)reheating and neutrino anomalies: production of sterile neutrinos with secret interactions

A number of experimental anomalies involving neutrinos hint towards the existence of at least an extra (a very light) sterile neutrino. However, such a species, appreciably mixing with the active neutrinos, is disfavored by different cosmological observations like Big Bang Nucleosynthesis (BBN), Cosmic Microwave Background (CMB) and Large Scale Structure (LSS). Recently, it was shown that the presence of additional interactions in the sterile neutrino sector via light bosonic mediators can make the scenario cosmologically viable by suppressing the production of the sterile neutrinos from active neutrinos via matter-like effect caused by the mediator. This mechanism works assuming the initial population of this sterile sector to be negligible with respect to that of the Standard Model (SM) particles, before the production from active neutrinos. However, there is fair chance that such bosonic mediators may couple to the inflaton and can be copiously produced during (p)reheating epoch. Consequently, they may ruin this assumption of initial small density of the sterile sector. In this article we, starting from inflation, investigate the production of such a sterile sector during (p)reheating in a large field inflationary scenario and identify the parameter region that allows for a viable early Universe cosmology.

Evaluation of Abel Inversion Method Assisted By an Improved IRI Model

AbstractThe most significant error of the radio occultation ionospheric retrieval is brought by the spherical symmetric assumption of electron density in Abel inversion. We developed an improved inversion method that attaches additional horizontal constraints based on a background model in Guo et al. (2015, https://doi.org/10.1016/j.jastp.2014.12.008) and found the effect of the method depends greatly on the accuracy of the background model. In this study, an improved ionospheric model, which applies radio occultation ‐based F2‐layer parameters and an adaptive topside model into the International Reference Ionosphere (IRI), is employed as a new choice of background model. The improved inversion is evaluated in several aspects in the middle‐ and low‐latitudinal regions during equinox season (from 19 March to 18 April in 2008 and 2012) and throughout the year. Results show that the artificial plasma caves underneath the equatorial ionization anomaly crests caused by Abel inversion is to some extent eliminated during the daytime, and the negative electron densities in the E layer are also reduced by the improved method. The comparison between Constellation Observing System for Meteorology, Ionosphere, and Climate events and colocated incoherent scatter radar (ISR)/ionosonde observations indicates comparable accuracy of both methods. Moreover, the Global Ionosphere Maps is introduced as true reference of the vertical total electron density content. The mean vertical total electron density content errors derived through the improved inversion method are less than that of Abel inversion in the global scope.

Possible roles of fall speed parameters of different graupel densities on microphysics and electrification in an idealized thunderstorm

AbstractGraupel is often parametrized as “medium‐density” ice particles with a bulk density of 400 kg m−3 and corresponding fixed fall speed parameters in numerical models. In natural clouds, however, graupel has an extensive range of densities, and its fall speed is closely related to its density ρg. In this study, the possible responses of the microphysical and electrical structures of a simulated thunderstorm to varying ρg and its corresponding fall speed parameters were examined using the Advanced Research Weather and Forecasting Model (ARW‐WRF) with an explicit charging and discharge lightning scheme. Six sensitivity tests were performed with different ρg and corresponding fall speed parameters. ρg ranges from 350–850 kg m−3, to represent relatively low‐ (350, 450 kg m−3), medium‐ (550, 650 kg m−3), and high‐ (750, 850 kg m−3) density assumptions. In low‐density cases, the ice water path (IWP) could be comparable with the liquid water path (LWP), while the LWP exceeds the contribution of the IWP to the total water path (TWP) in high‐density cases. The results show that melting rates and precipitation were enhanced when ρg was increased from low to high values, resulting in a smaller size and lighter mean mass due to a shorter residence time and faster fall speed.Different assumptions about graupel density also resulted in different electrical structures in the simulated clouds. The clouds produced in the low‐ and medium‐density cases are mainly charged with conventional tripole or positive dipole structures, while the ones formed in the high‐density cases present “bottom‐heavy” tripole structures. The upper positive regions become weaker, with reduced negative noninductive charging rates, as graupel falls faster and less graupel is negatively charged at higher altitude. It is also found that a faster fall speed of graupel does not necessarily mean stronger flash density, although lightning activities are correlated with higher fall speed.

Large deviation principle for random matrix products

Under a Zariski density assumption, we extend the classical theorem of Cramer on large deviations of sums of i.i.d. real random variables to random matrix products.

Early twenty-first century glacier mass losses in the Indus Basin constrained by density assumptions

Glaciers in the upper Indus supply more than half of the river water, are experiencing significant melting with a debated fate. The recent melting rate is still contained by considerable uncertainties, hindering to estimate precise glacier mass change. Here we present geodetic mass balance results for the whole Indus Basin using SRTM and ALOS 30 m elevation data, improved glacier inventory, optimized glacier surface density, and validation through in-situ differential GPS and ICESat data. Our glacier inventory and derived by improving RGI6.0 boundaries and separated into debris cover and debris free parts. The derived surface elevation changes were converted into annual mass balances using separated density assumptions (four criteria) for debris-covered ice (900 ± 60 kg m−3), debris-free ice (below 20° and 25° slopes (850 ± 60 kg m−3) and above 20° and 25° slopes (600 ± 60 kg m−3)), respectively. The resulting mass balance biased between −0.20 and 0.09 m water equivalent (w.e.) a-1 using an average (850 ± 60 kg m−3) density assumption throughout the Indus Basin. In the western Himalaya and Hindu Kush, the glacier mass losses are less affected by the average density assumption compared to the Karakoram. The western (Hunza) and central (Shigar) Karakoram glaciers show negligible mass losses of −0.02 ± 0.12 and −0.01 ± 0.13 m w.e. a−1 in contrast to the relatively more negative mass balance (−0.26 ± 0.21 m w.e. a−1) in the eastern (Shyok) Karakoram. All the sub-basins exhibit negative mass balances, with the most negative values ranging from −0.34 ± 0.31 to 0.44 ± 0.27 m w.e. a−1 in the Ravi, Chenab and Jhelum sub-basins of the Himalaya. The whole Indus Basin contributes approximately +0.014 ± 0.016 mm a−1 to the global mean sea-level equivalent.

Reprint of “Effects of asteroid property distributions on expected impact rates”

Assessments of the risk posed by asteroid impacts depend implicitly upon estimates of how frequently asteroids of different sizes and properties are expected to strike Earth. These impact rates are generally based upon populations of near-Earth objects as a function of absolute magnitude, which are then translated to equivalent size frequencies by assuming an average albedo. However, this simplified approach neglects the broad distribution of sizes and properties among objects of a given absolute magnitude. In this study, we use a probabilistic asteroid impact risk model to more rigorously investigate the effects of asteroid property distributions on estimated impact rates as a function of diameter, energy, mass, and blast damage radius. We also use impact damage modeling results to compare the effects of the new distribution-based results on expected casualty rates for two sample risk assessment cases. The current study focuses on mid-sized objects with diameters of 20–300m, which could cause substantial local ground damage but are unlikely to produce larger-scale regional or global effects. Particular emphasis is placed on sizes similar to the 1908 Tunguska event, which provides a unique source of evidence for such impacts and is often used as a reference point for damage potential and impact rates in the literature. Results demonstrate that accounting for realistic distributions of asteroid properties can significantly reduce expected impact intervals for these size ranges compared to estimates based on mean albedo, density, and velocity assumptions. These lower impact intervals, in turn, result in higher expected casualty estimates in impact risk assessment applications.

Observer design for the Doyle–Fuller–Newman Li-ion battery model without electrolyte dynamics

Abstract An observer is designed for the Doyle-Fuller-Newman electrochemical model of a Li-ion battery under the assumption of constant ion exchange current density and MacInnes’ equation being concentration independent. For this nonlinear system, the observer is shown to experience both exponential convergence and a degree of robustness. This result extends the class of electrochemical model for battery observer design, generating improved estimates for the state-of-charge and for the spatial variation of the overpotential across an electrode.

Protoplanetary Disk Masses from Radiative Transfer Modeling: A Case Study in Taurus

Abstract Measuring the masses of protoplanetary disks is crucial for understanding their planet-forming potential. Typically, dust masses are derived from (sub-)millimeter flux density measurements plus assumptions for the opacity, temperature, and optical depth of the dust. Here we use radiative transfer models to quantify the validity of these assumptions with the aim of improving the accuracy of disk dust mass measurements. We first carry out a controlled exploration of disk parameter space. We find that the disk temperature is a strong function of disk size, while the optical depth depends on both disk size and dust mass. The millimeter-wavelength spectral index can be significantly shallower than the naive expectation due to a combination of optical depth and deviations from the Rayleigh–Jeans regime. We fit radiative transfer models to the spectral energy distributions (SEDs) of 132 disks in the Taurus-Auriga region using a Markov chain Monte Carlo approach. We used all available data to produce the most complete SEDs used in any extant modeling study. We perform the fitting twice: first with unconstrained disk sizes and again imposing the disk size–brightness relation inferred for sources in Taurus. This constraint generally forces the disks to be smaller, warmer, and more optically thick. From both sets of fits, we find disks to be ∼1–5 times more massive than when derived using (sub-)millimeter measurements and common assumptions. With the uncertainties derived from our model fitting, the previously measured dust mass–stellar mass correlation is present in our study but only significant at the 2σ level.

A Mathematical Approach to Consider Solid Compressibility in the Compression of Pharmaceutical Powders

In-die compression analysis is an effective method for the characterization of powder compressibility. However, physically unreasonable apparent solid fractions above one or apparent in-die porosities below zero are often calculated for higher compression stresses. One important reason for this is the neglect of solid compressibility and hence the assumption of a constant solid density. In this work, the solid compressibility of four pharmaceutical powders with different deformation behaviour is characterized using mercury porosimetry. The derived bulk moduli are applied for the calculation of in-die porosities. The change of in-die porosity due to the consideration of solid compressibility is for instance up to 4% for microcrystalline cellulose at a compression stress of 400 MPa and thus cannot be neglected for the calculation of in-die porosities. However, solid compressibility and further uncertainties from, for example the measured solid density and from the displacement sensors, are difficult or only partially accessible. Therefore, a mathematic term for the calculation of physically reasonable in-die porosities is introduced. This term can be used for the extension of common mathematical models, such as the models of Heckel and of Cooper & Eaton. Additionally, an extended in-die compression function is introduced to precisely describe the entire range of in-die porosity curves and to enable the successful differentiation and quantification of the compression behaviour of the investigated pharmaceutical powders.

Introducing a modified exact difference method for incorporating unsteady and non-uniform force terms in lattice kinetic models

The exact difference method (EDM) of Kupershtokh (2004), in this work, is modified to accurately incorporate unsteady non-uniform force terms into lattice kinetic models. We use the characteristic scheme for integrating the Boltzmann equation along with the trapezoidal rule to estimate the integration results. The method is based on discretizing the total derivative of the equilibrium distribution function (EDF) in the EDM, using a central second-order scheme, instead of a first order method. It is shown that the assumption of constant density in calculating the total derivative of the EDF is not necessary in the limit of incompressible fluid flows. Using the Chapman–Enskog analysis, it is shown that the present method can be applied to both the standard lattice Boltzmann method and the recently introduced constant speed kinetic model (CSKM) of Zadehgol and Ashrafizaadeh (2014). The following benchmark flows are simulated: (i) Womersley flow, (ii) Hartmann flow, (iii) unsteady Taylor–Green vortex flow, and (iv) the circular interface, using the CSKM, and the results are in excellent agreement with the analytical solutions.

A Semi-Parametric Mode Regression with Censored Data

In this work we suppose that the random vector (X, Y) satisfies the regression model Y = m(X) + ϵ, where m(·) belongs to some parametric class {\({m_\beta}(\cdot):\beta \in \mathbb{K}\)} and the error ϵ is independent of the covariate X. The response Y is subject to random right censoring. Using a nonlinear mode regression, a new estimation procedure for the true unknown parameter vector β0is proposed that extends the classical least squares procedure for nonlinear regression. We also establish asymptotic properties for the proposed estimator under assumptions of the error density. We investigate the performance through a simulation study.

Effects of asteroid property distributions on expected impact rates

Assessments of the risk posed by asteroid impacts depend implicitly upon estimates of how frequently asteroids of different sizes and properties are expected to strike Earth. These impact rates are generally based upon populations of near-Earth objects as a function of absolute magnitude, which are then translated to equivalent size frequencies by assuming an average albedo. However, this simplified approach neglects the broad distribution of sizes and properties among objects of a given absolute magnitude. In this study, we use a probabilistic asteroid impact risk model to more rigorously investigate the effects of asteroid property distributions on estimated impact rates as a function of diameter, energy, mass, and blast damage radius. We also use impact damage modeling results to compare the effects of the new distribution-based results on expected casualty rates for two sample risk assessment cases. The current study focuses on mid-sized objects with diameters of 20–300 m, which could cause substantial local ground damage but are unlikely to produce larger-scale regional or global effects. Particular emphasis is placed on sizes similar to the 1908 Tunguska event, which provides a unique source of evidence for such impacts and is often used as a reference point for damage potential and impact rates in the literature. Results demonstrate that accounting for realistic distributions of asteroid properties can significantly reduce expected impact intervals for these size ranges compared to estimates based on mean albedo, density, and velocity assumptions. These lower impact intervals, in turn, result in higher expected casualty estimates in impact risk assessment applications.

Probabilistic assessment of Tunguska-scale asteroid impacts

The Tunguska meteor airburst has been extensively studied and modeled in attempts to deduce its size, properties, and impact characteristics. However, most of the existing modeling and simulation studies have investigated a small subset of cases based on assumptions of representative densities, velocities, or other properties. In this study, we use a probabilistic asteroid impact risk model to assess the entry, burst, and ground damage from 50 million Tunguska-scale asteroid impacts, covering a full range of potential impactor properties. The impact cases are sampled from probabilistic distributions representing our current knowledge of asteroid properties, entry trajectories, and size frequencies. The results provide a broader characterization of the range and relative likelihood of asteroid properties that could yield Tunguska-scale impacts. Results show that Tunguska-like events can be produced by a broad range of impact scenarios, and prevailing size and energy estimates of 50–80 m or 10–20 Mt remain within the relatively likely property ranges. However, our results suggest that objects with slightly larger initial energies of 20–30 Mt and diameters 70–80 m are more likely to cause Tunguska-scale damage areas than objects on the smaller end of the potential size range. Even when relative size frequencies are accounted for, the greater damage potential of larger objects outweighs their rarity, while the low damage potential of small objects counteracts their frequency.

Modeling the trapped field distribution in a polycrystalline bulk superconductor based on a critical state model

The trapped field distribution of a polycrystalline bulk superconductor induced by perpendicular magnetic field is theoretically analyzed based on the critical state model. A rational model is presented to describe the current pattern changes near a low-angle grain boundary (GB) that is observed in others’ experiment. The current pattern that varies with the ratio between GB critical current density and grain critical current density is analyzed based on the constant critical current density assumption. In addition, the magnetic field that trapped in the prism both on magnetization ascent and descent stage have been discussed in detail on the basis of the current distribution that we deduce above. The results of this work can also be useful for AC loss analysis and stress calculating of polycrystalline superconductors.

Are there any models with homogeneous energy density?

By applying a recent method --based on a tetrad formalism in General Relativity and the orthogonal splitting of the Riemann tensor-- to the simple spherical static case, we found that the only static solution with homogeneous energy density is the Schwarzschild solution and that there are no spherically symmetric dynamic solutions consistent with the homogeneous energy density assumption. Finally, a circular equivalence is shown among the most frequent conditions considered in the spherical symmetric case: homogeneous density, isotropy in pressures, conformally flatness and shear-free conditions. We demonstrate that, due to the regularity conditions at the center of the matter distribution, the imposition of two conditions necessarily leads to the static case.