Self-consistent Estimates Research Articles

Statistics of the stress, strain-rate and spin fields in viscoplastic polycrystals

This paper provides estimates for the stress, strain-rate and spin field statistics in viscoplastic polycrystals. They are obtained by combining the fully optimized second-order (FOSO) homogenization method with the self-consistent estimate for linear polycrystalline aggregates. The FOSO linearization method allows the consistent estimation of the field statistics in nonlinear composites and polycrystals directly from those in suitably optimized linear comparison composites (LCC). For the LCC, a novel generalized approach is used to extract the field statistics of the stress, the strain-rate and also of the continuum-spin fields (including the second moments). Then, the stress-field statistics are used to extract the plastic-spin statistics, which, together with the continuum-spin statistics, provide consistent estimates for the microstructural-spin statistics. Applications to power-law viscoplastic FCC polycrystals and ice-like HCP polycrystals are considered, and the overall and intragranular field fluctuations are computed and found to increase with nonlinearity exponent and grain anisotropy. In particular, the covariance tensors of the continuum-spin fluctuations within the grains of viscoplastic polycrystals, which are characterized here for the first time by means of nonlinear homogenization methods, are found to be quite significant, even when the corresponding averages of the continuum-spin in the grains are negligible, and thus have a strong influence on the corresponding microstructural-spin fluctuations.

Performance Optimization for Drift-Robust Fidelity Improvement of Two-Qubit Gates

Quantum system characterization techniques represent the front line in the identification and mitigation of noise in quantum computing, but can be expensive in terms of quantum resources and time to repeatedly employ. Another challenging aspect is that parameters governing the performance of various operations tend to drift over time, and monitoring these is hence a difficult task. One of the most promising characterization techniques, gate set tomography (GST), provides a self-consistent estimate of the completely positive, trace-preserving (CPTP) maps for a complete set of gates, as well as preparation and measurement operators. We develop a method for performance optimization seeded by tomography (POST), which couples the power of GST with a classical optimization routine to achieve a consistent gate improvement in just a short number of steps within a given calibration cycle. By construction, the POST procedure finds the best available gate operation given the hardware, and is therefore robust to the effects of drift. Further, in comparison to other quantum error mitigation techniques, it builds upon a one-time application of GST. To demonstrate the performance of this method on a real quantum computer, we map out the operations of six qubit pairs on the superconducting \emph{ibmq\_poughkeepsie} quantum device. Under the restriction of logical-only control, we monitor the performance of the POST approach on a chosen CNOT gate over a period of six weeks. In this time, we achieve a consistent improvement in gate fidelity, averaging a fidelity increase of 21.1\% as measured by randomized benchmarking. The POST approach should find wide applicability as it is hardware agnostic, and can be applied at the upper logical level or at a deeper pulse control level.

Dust continuum, CO, and [C i] 1 − 0 lines: self-consistent H2 mass estimates and the possibility of globally CO-‘dark’ galaxies at z = 0.35

ABSTRACT We present Atacama Large Millimetre Array observations of a small but statistically complete sample of 12 250-μm-selected galaxies at z = 0.35 designed to measure their dust submillimeter continuum emission as well as their $\rm {^{12}CO(1-0)}$ and atomic carbon [C i](3P1−3P0) spectral lines. This is the first sample of galaxies with global measures of all three H2-mass tracers and that shows star formation rates (4–26 $\rm M_{\odot}$ yr−1) and infrared luminosities ($1\!-\!6\times 10^{11}\,\rm L_{\odot}$) typical of star-forming galaxies in their era. We find a surprising diversity of morphology and kinematic structure; one third of the sample have evidence for interaction with nearby smaller galaxies, several sources have disjoint dust and gas morphology. Moreover, two galaxies have very high $L^{\prime }_{\rm C\,{\small I}}$ / $L^{\prime }_{\rm {CO}}$ ratios for their global molecular gas reservoirs; if confirmed, such extreme intensity ratios in a sample of dust-selected, massive star-forming galaxies present a challenge to our understanding of interstellar medium. Finally, we use the emission of the three molecular gas tracers, to determine the carbon abundance, $\rm {X_{C\,{\small I}}}$ , and CO–$\rm {H_2}$ conversion αCO in our sample, using a weak prior that the gas-to-dust ratio is similar to that of the Milky Way for these massive and metal-rich galaxies. Using a likelihood method that simultaneously uses all three gas tracer measurements, we find mean values and errors on the mean of $\langle\alpha _{\rm {CO}}\rangle = 3.0\pm 0.5\, \rm {M}_{\odot }\, (\rm{K}\, \rm{kms}^{-1}\, \rm{pc}^2)^{-1}$ and $\langle \rm{X}_{\rm{CI}} \rangle =1.6\pm 0.1\times 10^{-5}$ (or $\alpha _{\rm{CI}} = 18.8\,\rm {M}_{\odot }\, (\rm{K}\, \rm{kms}^{-1}\, \rm{pc}^2)^{-1}$) and $\delta _{\rm {GDR}} = 128\pm 16$ (or $\alpha _{850} = 5.9\times 10^{12}\, \rm {W}\, \rm{Hz}^{-1}\,\rm {M}_{\odot }\,^{-1}$), where our starting assumption is that these metal-rich galaxies have an average gas-to-dust ratio similar to that of the Milky Way centred on $\rm{\delta} _{\rm {GDR}} =135$.

A self-consistent estimator for interval-valued data

In interval-valued data, the variable of interest is provided in the form of an interval with lower and upper bounds, not a single value. An univariate representation for the interval is not unique by its nature, in particular when interval-valued data are of the min-max (MM) type. Researchers focus on the marginal histogram distribution which is well suited to the measurement error (ME) type interval data. Two estimators, the empirical histogram estimator and nonparametric kernel estimator, have been proposed for the estimation of the marginal histogram in the literature. In this paper, we define a new univariate representation, named as a self-consistent marginal, for interval-valued data, and propose a self-consistent estimator (SCE) to estimate it. We theoretically and numerically investigate the properties of the SCE under various assumptions. We further illustrate the advantages of the SCE over the two existing estimators with empirical examples.

Self-consistent estimates of emission factors of carboncontaining pollutants from a typical gas flare

This study proposes an approach for estimating the emission of soot, carbon monoxide (CO) and carbondioxide (CO ) from a typical gas flare. The estimations depend on the quantity and varying composition of the 2 natural gas, flame dynamics (represented by the fire Froude number, Fr ) and the equivalence ratio, f, of the fuel- f air mixture. Soot emission estimates are presented as a function of fire Froude number for gases used in labbased test in order to validate the scheme and for two real-world fuel gas compositions. The mass-weighted carbon-hydrogen ratio (C:H) of the fuel gas compositions are 0.25 and 0.29 which are two extreme cases in terms of density. The soot yield of the lab-based test case was scaled up to estimate the soot yield of a full scale flare using the Richardson number as the scaling parameter. When all other variables are held constant at values characteristics of real-world flares, a difference of 16 % in the fuel-gas density, as indicated by the carbonhydrogen ratio, results in an increase of the emission factors (EF) of soot, CO and CO by factors of ~3, ~1.4 2 3 and ~1.7, measured in g/m , respectively. For both fuel gas compositions, the ratio of EF to EF at the fuel- soot CO lean region f < 1) is higher. The ratio lies in the range 0.031 – 0.13 and 0.0012 – 0.0055 for the fuel-lean (f < 1) and fuel-rich (f > 1) regions, respectively. The approach proposed and results obtained may be adopted to generate emissions inventories of emission species associated with gas flaring on regional and global scales.
 Keywords: gas flaring; soot; natural gas; emission factor; black carbon; equivalence ratio

Inferring the Dynamics of Underdamped Stochastic Systems.

Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into the physical laws governing the system. Here, we derive a principled framework to infer the dynamics of underdamped stochastic systems from realistic experimental trajectories, sampled at discrete times and subject to measurement errors. This framework yields an operational method, Underdamped Langevin Inference, which performs well on experimental trajectories of single migrating cells and in complex high-dimensional systems, including flocks with Viscek-like alignment interactions. Our method is robust to experimental measurement errors, and includes a self-consistent estimate of the inference error.

Generalized effective fields method in peridynamic micromechanics of random structure composites

We consider a static problem for statistically homogeneous matrix linear bond-based peridynamic composite materials (CMs). For the media subjected to remote homogeneous volumetric boundary loading, one proved that the effective behavior of this media is governed by conventional effective constitutive equation as in the local elasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional elasticity of composite materials (CMs) with their adaptation to peridynamics. This is extraction from the material properties a constituent of the matrix properties. Effective moduli are expressed through the introduced new notion of the average local polarization tensor. The average is performed over the surface of the extended inclusion phase rather than over an entire space. Any spatial derivatives of displacement fields are not required. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts. In particular, in the generalized effective field method (EFM) proposed, the effective field is evaluated from self-consistent estimations by the use of closing of a corresponding integral equation in the framework of the quasi-crystalline approximation. In so doing, the classical effective field hypothesis is relaxed, and the hypothesis of the ellipsoidal symmetry of the random structure of CMs is not used. One demonstrates some similarity and difference with respect to other methods (the dilute approximation and Mori-Tanaka approach) proposed before in micromechanics of peridynamic CMs. Comparative numerical analyses of these methods are performed for 1D case.

Thermoelastic bounds and self-consistent estimation for the overall properties of composites

In the present work, static thermoelastic bounds for a composite with spheroidal isotropic inclusions embedded in an isotropic matrix are calculated. Using the Green’s function derived for the thermoelastic case by Valdiviezo-Mijangos, et al., (2009) and the variational formulation for anisotropic composites developed by Willis (1992), thermoelastic bounds are explicitly obtained. In the case of the thermal expansion coefficient, the results are also compared with experimental data as well as with the Rosen-Hashin bounds. A good agreement among the bounds, the self-consistent method and the experimental data is shown.

Learning Force Fields from Stochastic Trajectories

When monitoring the dynamics of stochastic systems, such as interacting particles agitated by thermal noise, disentangling deterministic forces from Brownian motion is challenging. Indeed, we show that there is an information-theoretic bound, the capacity of the system when viewed as a communication channel, that limits the rate at which information about the force field can be extracted from a Brownian trajectory. This capacity provides an upper bound to the system's entropy production rate, and quantifies the rate at which the trajectory becomes distinguishable from pure Brownian motion. We propose a practical and principled method, Stochastic Force Inference, that uses this information to approximate force fields and spatially variable diffusion coefficients. It is data efficient, including in high dimensions, robust to experimental noise, and provides a self-consistent estimate of the inference error. In addition to forces, this technique readily permits the evaluation of out-of-equilibrium currents and the corresponding entropy production with a limited amount of data.

Elastostatic field distributions in polycrystals and cracked media

ABSTRACTThis work addresses the problem of the reconstruction of the local fields distribution occurring in heterogeneous linear elastic solids. The constitutive heterogeneities are crystals and cracks. Through comparisons with FFT computations, it is shown that self-consistent estimates together with an assumption of normal distribution at the phase scale provide an accurate description of the elastostatic field histograms in polycrystals without cracks. In the case of inter and transgranular cracks, full-field FFT simulations indicate that the field histograms present van Hove singularities. Their natures are determined analytically in the low-density regime, in the case of an homogeneous medium containing cracks.

Estimating the Term Structure with Linear Regressions: Getting to the Roots of the Problem

Abstract Linear estimators of the affine term structure model are inconsistent since they cannot reproduce the factors used in estimation. This is a serious handicap empirically, giving a worse fit than the conventional ML estimator that ensures consistency. We show that a simple self-consistent estimator can be constructed using the eigenvalue decomposition of a regression estimator. The remaining parameters of the model follow analytically. Estimates from this model are virtually indistinguishable from that of the ML estimator. We apply the method to estimate various models of U.S. Treasury yields. These exercises greatly extend the range of models that can be estimated.

Improved Estimates of Geocenter Variability from Time-Variable Gravity and Ocean Model Outputs

Geocenter variations relate the motion of the Earth’s center of mass with respect to its center of figure, and represent global-scale redistributions of the Earth’s mass. We investigate different techniques for estimating of geocenter motion from combinations of time-variable gravity measurements from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On missions, and bottom pressure outputs from ocean models. Here, we provide self-consistent estimates of geocenter variability incorporating the effects of self-attraction and loading, and investigate the effect of uncertainties in atmospheric and oceanic variation. The effects of self-attraction and loading from changes in land water storage and ice mass change affect both the seasonality and long-term trend in geocenter position. Omitting the redistribution of sea level affects the average annual amplitudes of the x, y, and z components by 0.2, 0.1, and 0.3 mm, respectively, and affects geocenter trend estimates by 0.02, 0.04 and 0.05 mm/yr for the the x, y, and z components, respectively. Geocenter estimates from the GRACE Follow-On mission are consistent with estimates from the original GRACE mission.

Dynamical masses and mass-to-light ratios of resolved massive star clusters – I. NGC 419 and NGC 1846

ABSTRACT As an introduction of a kinematic survey of Magellanic Cloud (MC) star clusters, we report on the dynamical masses and mass-to-light ratios (M/L) of NGC 419 (Small Magellanic Cloud) and NGC 1846 (Large Magellanic Cloud). We have obtained more than one hundred high-resolution stellar spectra in and around each cluster using the multi-object spectrograph M2FS on the Magellan/Clay Telescope. Line-of-sight velocities and positions of the stars observed in each cluster were used as input to an expectation-maximization algorithm used to estimate cluster membership probabilities, resulting in samples of 46 and 52 likely members (PM ≥ 50 per cent) in NGC 419 and NGC 1846, respectively. This process employed single-mass King models constrained by the structural parameters of the clusters and provided self-consistent dynamical mass estimates for both clusters. Our best-fitting results show that NGC 419 has a projected central velocity dispersion of $2.44^{+0.37}_{-0.21}$ km s−1, corresponding to a total mass of $7.6^{+2.5}_{-1.3}\times 10^4\ {\rm M}_{\odot }$ and V-band M/L ratio of $0.22^{+0.08}_{-0.05}$ in solar units. For NGC 1846, the corresponding results are $2.04^{+0.28}_{-0.24}$ km s−1, $5.4^{+1.5}_{-1.4}\times 10^4\ {\rm M}_{\odot }$, and $0.32^{+0.11}_{-0.11}$. The mean metallicities of NGC 419 and NGC 1846 are found to be $\rm [Fe/H]=-0.84\pm 0.19$ and −0.70 ± 0.08, respectively, based on the spectra of likely cluster members. We find marginal statistical evidence of rotation in both clusters, though in neither cluster does rotation alter our mass estimates significantly. We critically compare our findings with those of previous kinematic studies of these two clusters in order to evaluate the consistency of our observational results and analytic tools.

Self-consistent Estimation of Dissipated Power Allocation of OLED in view of Electromagnetic Wave Mode Analysis

Self-consistent Estimation of Dissipated Power Allocation of OLED in view of Electromagnetic Wave Mode Analysis

The thermoelastic response of cracked polycrystals with hexagonal symmetry

ABSTRACTThe influence of a population of randomly oriented cracks on the macroscopic thermal and linear-elastic response of a hexagonal polycrystal is addressed using a self-consistent method. Coupling between micro-cracks and crystal anisotropy is taken into account through the effective medium where all inhomogeneities are embedded. In the absence of cracks, the proposed approach reduces to the self-consistent estimate of Berryman (2005). The accuracy of the present method is first assessed using numerical, Fourier-based computations. In the absence of crystal anisotropy, the estimates for the effective elastic properties are close to that obtained numerically for a homogeneous body containing disk-shaped cracks, with Boolean spatial dispersion. Various other analytical estimates and bounds, that are available for homogeneous cracked bodies, are also considered and compared to the present approach. Second, the combined role of crystal anisotropy and micro-cracks is investigated analytically, specifically when the in-plane shear modulus of the crystal becomes zero. The cracks-density percolation threshold is found to diminish abruptly in this limit. This ‘advanced’ percolation threshold is concomitant to the onset of large, weakly loaded regions surrounding cracks in strongly anisotropic crystals.

Thermoelastic properties of microcracked polycrystals. Part II: The case of jointed polycrystalline TATB

The thermoelastic responses of a cracked TATB polycrystal is modeled using Fourier-based numerical computations and linear homogenization estimates. The numerical method is based on a Fourier scheme previously investigated (Gasnier et al., 2018) and the homogenization schemes include a new self-consistent estimate recently developed for cracked polycrystals. The effect of various populations of intergranular and transgranular microcracks are compared, with special attention to thermal behavior in the percolating regime. A model of micro-cracks is proposed for the TATB material in its initial state and the variations of the volumetric expansion coefficient of the TATB polycrystal under thermal cycles, during cooling and heating, are interpreted.

Fully optimized second-order homogenization estimates for the macroscopic response and texture evolution of low-symmetry viscoplastic polycrystals

In this paper, we present a finite-strain homogenization model for the macroscopic response of viscoplastic polycrystals deforming by crystallographic slip. The model makes use of the recently developed fully optimized second-order (FOSO) variational homogenization method, together with self-consistent estimates for the instantaneous response of a linear comparison composite (LCC) with optimally selected properties, to generate corresponding estimates for nonlinear viscoplastic polycrystals. The estimates are guaranteed to be exact to second order in the heterogeneity contrast, and to satisfy all known bounds. Unlike earlier second-order methods, the FOSO method has the distinct advantage that the macroscopic behavior and field statistics in the nonlinear composite can be conveniently extracted directly from the corresponding quantities in the LCC. Moreover, consistent homogenization estimates for the average strain-rate and spin fields in the grains are used to derive the evolution equations for the morphological and crystallographic textures of the polycrystals at large deformations. The FOSO method is then used for the first time to investigate the effects of rate sensitivity and grain anisotropy on the macroscopic response and field statistics of untextured (low-symmetry) HCP polycrystals. Comparisons with full-field simulations and earlier homogenization models show that the FOSO method is the most accurate to date. In addition, the FOSO method is used to predict the texture evolution for ice-like HCP polycrystals subjected to finite-strain loading conditions. It is found that the method is able to capture the strong basal texture that is observed experimentally in these materials under compression, leading to strong geometric softening/hardening effects, as well as strong viscous anisotropy in the overall response.

A multi-scale homogenization model for fine-grained porous viscoplastic polycrystals: I – Finite-strain theory

We make use of the recently developed iterated second-order homogenization method to obtain finite-strain constitutive models for the macroscopic response of porous polycrystals consisting of large pores randomly distributed in a fine-grained polycrystalline matrix. The porous polycrystal is modeled as a three-scale composite, where the grains are described by single-crystal viscoplasticity and the pores are assumed to be large compared to the grain size. The method makes use of a linear comparison composite (LCC) with the same substructure as the actual nonlinear composite, but whose local properties are chosen optimally via a suitably designed variational statement. In turn, the effective properties of the resulting three-scale LCC are determined by means of a sequential homogenization procedure, utilizing the self-consistent estimates for the effective behavior of the polycrystalline matrix, and the Willis estimates for the effective behavior of the porous composite. The iterated homogenization procedure allows for a more accurate characterization of the properties of the matrix by means of a finer “discretization” of the properties of the LCC to obtain improved estimates, especially at low porosities, high nonlinearties and high triaxialities. In addition, consistent homogenization estimates for the average strain rate and spin fields in the pores and grains are used to develop evolution laws for the substructural variables, including the porosity, pore shape and orientation, as well as the “crystallographic” and “morphological” textures of the underlying matrix. In Part II of this work has appeared in Song and Ponte Castañeda (2018b), the model will be used to generate estimates for both the instantaneous effective response and the evolution of the microstructure for porous FCC and HCP polycrystals under various loading conditions.

Parameter dependences of the separatrix density in nitrogen seeded ASDEX Upgrade H-mode discharges

The upstream separatrix electron density is an important interface parameter for core performance and divertor power exhaust. It has been measured in ASDEX Upgrade H-mode discharges by means of Thomson scattering using a self-consistent estimate of the upstream electron temperature under the assumption of Spitzer–Härm electron conduction. Its dependence on various plasma parameters has been tested for different plasma conditions in H-mode. The leading parameter determining ne,sep was found to be the neutral divertor pressure, which can be considered as an engineering parameter since it is determined mainly by the gas puff rate and the pumping speed. The experimentally found parameter dependence of ne,sep, which is dominated by the divertor neutral pressure, could be approximately reconciled by 2-point modelling.

Metal Abundances of KISS Galaxies. VI. New Metallicity Relations for the KISS Sample of Star-forming Galaxies

Abstract We present updated metallicity relations for the spectral database of star-forming galaxies (SFGs) found in the KPNO International Spectroscopic Survey (KISS). New spectral observations of emission-line galaxies obtained from a variety of telescope facilities provide oxygen abundance information. A nearly fourfold increase in the number of KISS objects with robust metallicities relative to our previous analysis provides for an empirical abundance calibration to compute self-consistent metallicity estimates for all SFGs in the sample with adequate spectral data. In addition, a sophisticated spectral energy distribution fitting routine has provided robust calculations of stellar mass. With these new and/or improved galaxy characteristics, we have developed luminosity–metallicity (L–Z) relations, mass–metallicity (M *–Z) relations, and the so-called fundamental metallicity relation (FMR) for over 1450 galaxies from the KISS sample. This KISS M *–Z relation is presented for the first time and demonstrates markedly lower scatter than the KISS L–Z relation. We find that our relations agree reasonably well with previous publications, modulo modest offsets due to differences in the strong emission line metallicity calibrations used. We illustrate an important bias present in previous L–Z and M *–Z studies involving direct-method (T e ) abundances that may result in systematically lower slopes in these relations. Our KISS FMR shows consistency with those found in the literature, albeit with a larger scatter. This is likely a consequence of the KISS sample being biased toward galaxies with high levels of activity.