Least-squares Procedure Research Articles

A control-oriented model of turbulent jet ignition combustion in a rapid compression machine

Turbulent jet ignition combustion is a promising concept for achieving high thermal efficiency and low NOx (nitrogen oxides) emissions. A control-oriented turbulent jet ignition combustion model with satisfactory accuracy and low computational effort is usually a necessity for optimizing the turbulent jet ignition combustion system and developing the associated model-based turbulent jet ignition control strategies. This article presents a control-oriented turbulent jet ignition combustion model developed for a rapid compression machine configured for turbulent jet ignition combustion. A one-zone gas exchange model is developed to simulate the gas exchange process in both pre- and main-combustion chambers. The combustion process is modeled by a two-zone combustion model, where the ratio of the burned and unburned gases flowing between the two combustion chambers is variable. To simulate the influence of the turbulent jets on the rate of combustion in the main-combustion chamber, a new parameter-varying Wiebe function is proposed and used for the mass fraction burned calculation in the main-combustion chamber. The developed model is calibrated using the least-squares fitting and optimization procedures. Experimental data sets with different air-to-fuel ratios in both combustion chambers and different pre-combustion chamber orifice areas are used to calibrate and validate the model. The simulation results show good agreement with the experimental data for all the experimental data sets. This indicates that the developed combustion model is accurate for developing and validating turbulent jet ignition combustion control strategies. Future work will extend the rapid compression machine combustion model to engine applications.

Impedance-to-scattering matrix method for large silencer analysis using direct collocation

Large silencers used in industry usually have a very large cross section at the inlet and outlet. Higher-order modes will populate the inlet and outlet even at very low frequencies. A three-dimensional analysis tool, such as the finite element method or the boundary element method, must incorporate certain forms of modal expansion in order to consider the higher-order modes in the transmission loss computation. In this paper, the impedance matrix obtained from the sub-structured boundary element method is converted into the scattering matrix that relates the higher-order modes. Since there are always more boundary elements at the inlet and outlet than the total number of propagating modes, a least-squares procedure is used to convert the element-based impedance matrix into the modal expansion-based scattering matrix. The transmission loss of the silencer can then be computed from the scattering matrix if a certain form of the incident wave is assumed. Furthermore, a slightly rearranged form of the scattering matrix may also be used to combine subsystems in series connection.

Parallel algorithm for convection-diffusion system based on least-squares procedure.

Combining subspace correction method with least-squares finite element procedure, we construct a new overlapping domain decomposition parallel algorithm for solving the first-order time-dependent convection–diffusion system. This algorithm is fully parallel. We analyze the convergence of approximate solution, and study the dependence of the convergent rate on the spacial mesh size, time increment, iteration number and sub-domains overlapping degree. Both theoretical analysis and numerical results suggest that only one or two iterations are needed to reach to given accuracy at each time step.

Analysis of thermal deformation and influencing factors in shrink-fitting assembly of aluminum alloy drill pipe

In shrink-fitting assembly process of aluminum alloy drill pipe with steel joint, the relationship between cooling water velocity, initial heating temperature, and thermal deformation of the steel joint is an important factor to ensure the long-term reliability of the connection and the performance. In this article, the shrink-fitting assembly experiment of aluminum pipe with steel joint was conducted and the accurate experimental data were obtained for temperature field. A finite element method was then applied to simulate the temperature field of steel joint and compared with the experimental results. Based on the thermo-elasticity theories, an analytical solution was developed to calculate the thermal deformation in radial direction within the same cross section. A least-square fitting procedure was used to determine the thermal deformation of steel joint. A relationship diagram among these three factors was established, which is particularly important in predicting the minimum heating temperature of steel joint and the minimum cooling water velocity. Based on the above analysis, a method to select the initial heating temperature and the cooling water velocity was provided and the optimum values of the magnitude of interference, the initial heating temperature, and the cooling water velocity were obtained.

The impact of online reviews on exhibitor behaviour: evidence from movie industry

ABSTRACTThis paper explores the effects of online reviews in the empirical context of movie industry. Quality uncertainty and hedonic consumption render movies a particularly interesting category to study quality signals and social influence. Online consumer chatters about a movie are readily available in popular movie-related websites. These data, coupled with movie-specific sales and advertising information accessible online or from commercial sources, provide unique opportunity to explore the implication of word-of-mouth (WOM) for consumer behaviour and business strategy. We thus examine how online reviews impact on business strategies, in this case, exhibitor behaviour, through an empirical analysis of movie industry. First, online reviews are grouped into user reviews and critic reviews. We then use them respectively in two simultaneous equation systems, which regard online reviews, box office revenue and the number of screens as endogenous variables. Next, a three-stage least-square procedure is employed to estimate these two systems using a sample of 141 movies in the U.S. market. The results indicate that the online user reviews’ rating is positively associated with the number of screens, confirming that the online review is influential on exhibitor behaviour. The number of online reviews indirectly influences the number of screens through the box office revenue.

Predicting the sound absorption of natural materials: Best-fit inverse laws for the acoustic impedance and the propagation constant

Natural materials are becoming a valid option for sound absorption treatments. In particular, among them, natural fibers have received increasing attention given their good thermal insulation properties, lack of harmful effects on health, and availability in large quantities. This paper discusses an inverse method to predict the acoustical properties of nine natural fibers. Six vegetative fibers: kenaf, wood, hemp, coconut, straw, and cane; one animal fiber, sheep wool; recycled cardboard; and granular cork are investigated. The absorption coefficient and the flow resistance for samples of different thickness have been measured. Moving from the Delany-Bazley model, this study compares the impedance tube results with the theoretically predicted ones. Then, using a least-square fit procedure based on the Nelder-Mead method, the coefficients that best predict both the acoustic impedance and the propagation constant laws are calculated. The inverse approach used in this paper allows to determine different physical parameters and to obtain formulas to include the investigated natural fibers in software modelling for room acoustics applications.

Numerical upscaling in 2‐D heterogeneous poroelastic rocks: Anisotropic attenuation and dispersion of seismic waves

AbstractThe presence of stiffness contrasts at scales larger than the typical pore sizes but smaller than the predominant seismic wavelengths can produce seismic attenuation and velocity dispersion in fluid‐saturated porous rocks. This energy dissipation mechanism is caused by wave‐induced fluid pressure diffusion among the different components of the probed geological formations. In many cases, heterogeneities have elongated shapes and preferential orientations, which implies that the overall response of the medium is anisotropic. In this work, we propose a numerical upscaling procedure that permits to quantify seismic attenuation and phase velocity considering fluid pressure diffusion effects as well as generic anisotropy at the sample's scale. The methodology is based on a set of three relaxation tests performed on a 2‐D synthetic rock sample representative of the medium of interest. It provides a complex‐valued frequency‐dependent equivalent stiffness matrix through a least squares procedure. We also derive an approach for computing various poroelastic fields associated with the considered sample in response to the propagation of a seismic wave with arbitrary incidence angle. Using this approach, we provide an energy‐based estimation of seismic attenuation. A comprehensive numerical analysis indicates that the methodology is suitable for handling complex media and different levels of overall anisotropy. Comparisons with the energy‐based estimations demonstrate that the dynamic‐equivalent viscoelastic medium assumption made by the numerical upscaling procedure is reasonable even in the presence of high levels of overall anisotropy. This work also highlights the usefulness of poroelastic fields for the physical interpretation of seismic wave phenomena in strongly heterogeneous and complex media.

Statistical Mechanical Model for pH-Induced Protein Folding: Application to Apomyoglobin.

Despite the major role of pH in protein folding and stability, a quantitative understanding of the pH-induced protein folding mechanism remains elusive. Two conventional models, the Monod-Wyman-Changeux and Linderstrøm-Lang smeared charge models, respectively, have been used to analyze the formation/disruption of specific native structures and fluctuating non-native states. However, there are only a few models that can represent the overall kinetic events of folding/unfolding independent of the properties of relevant molecular species, which has hampered the efforts to systematically analyze pH-induced folding. Here, we constructed a statistical mechanical model that incorporates the protonation mechanism of conventional models along with a combined manual search and least-squares fitting procedure, which was used to investigate the folding of horse apomyoglobin over a wide pH range (2.2-6.7), with a time window ranging from ∼40 μs to ∼100 s, using continuous-/stopped-flow fluorescence at 8 °C. Quantitative analysis assuming a five-state sequential scheme indicated that (1) pH-induced folding/unfolding is represented by both specific binding and Coulombic interactions; (2) kinetic folding/unfolding intermediates share kinetic mechanisms with the equilibrium intermediate, indicating their equivalence; and (3) native-like properties are acquired successively during folding by intermediates and in transition states. This model could also be applied to a variety of association/dissociation processes.

Far-infrared spectra of dimethyl-ether and its 13C enriched isotopologues: The fundamental band of the C–O–C in plane bending mode, ν7

We recorded the ν7 fundamental band of dimethyl-ether around 400cm−1 for the normal and 13C-enriched isotopologues using the Fourier transform spectrometer at the SOLEIL Synchrotron facility. For all three species P, Q and R branch-transitions up to J=20 and Ka=5 were assigned and the band origins and rotational parameters of Watson’s A-reduced Hamiltonian have been determined by the least-squares fitting procedure. The line splitting due to the torsional tunneling is observed for low J transitions, which is attributed to the ro-vibrational interaction with the excited torsional states.

Least-Squares Estimation of the Common Pole-Zero Filter of Acoustic Feedback Paths in Hearing Aids

In adaptive feedback cancellation both the convergence speed and the computational complexity depend on the number of adaptive parameters used to model the acoustic feedback paths. To reduce the number of adaptive parameters, it has been proposed to model the acoustic feedback paths as the convolution of a time-invariant common pole-zero filter and time-varying all-zero filters, enabling to track fast changes. In this paper, a novel procedure to estimate the common pole-zero filter of acoustic feedback paths is presented. In contrast to previous approaches which minimize the so-called equation-error, we propose to approximate the desired output-error minimization by employing a weighted least-squares procedure motivated by the Steiglitz--McBride iteration. The estimation of the common pole-zero filter is formulated as a semidefinite programming problem, to which a constraint based on the Lyapunov theory is added in order to guarantee the stability of the estimated pole-zero filter. Experimental results using measured acoustic feedback paths from a two microphone behind-the-ear hearing aid show that the proposed optimization procedure using the Lyapunov constraint outperforms existing optimization procedures in terms of modelling accuracy and added stable gain.

Accurate Automatic Detection of Densely Distributed Cell Nuclei in 3D Space

To measure the activity of neurons using whole-brain activity imaging, precise detection of each neuron or its nucleus is required. In the head region of the nematode C. elegans, the neuronal cell bodies are distributed densely in three-dimensional (3D) space. However, no existing computational methods of image analysis can separate them with sufficient accuracy. Here we propose a highly accurate segmentation method based on the curvatures of the iso-intensity surfaces. To obtain accurate positions of nuclei, we also developed a new procedure for least squares fitting with a Gaussian mixture model. Combining these methods enables accurate detection of densely distributed cell nuclei in a 3D space. The proposed method was implemented as a graphical user interface program that allows visualization and correction of the results of automatic detection. Additionally, the proposed method was applied to time-lapse 3D calcium imaging data, and most of the nuclei in the images were successfully tracked and measured.

Determination of optimized frequency and frequency ratio values from over-determined sets of clock comparison data

We summarize a recently developed method for analyzing over-determined sets of clock frequency comparison data to derive optimized values for the frequency ratios between each of the contributing standards. This least-squares adjustment procedure, based on the approach used by CODATA to derive a self-consistent set of values for the fundamental physical constants, is used to deduce optimized frequency and frequency ratio values from the international body of clock comparison data available in September 2015.

A third-order compact gas-kinetic scheme on unstructured meshes for compressible Navier–Stokes solutions

In this paper, for the first time a third-order compact gas-kinetic scheme is proposed on unstructured meshes for the compressible viscous flow computations. The possibility to design such a third-order compact scheme is due to the high-order gas evolution model, where a time-dependent gas distribution function at cell interface not only provides the fluxes across a cell interface, but also presents a time accurate solution for flow variables at cell interface. As a result, both cell averaged and cell interface flow variables can be used for the initial data reconstruction at the beginning of next time step. A weighted least-square procedure has been used for the initial reconstruction. Therefore, a compact third-order gas-kinetic scheme with the involvement of neighboring cells only can be developed on unstructured meshes. In comparison with other conventional high-order schemes, the current method avoids the Gaussian point integration for numerical fluxes along a cell interface and the multi-stage Runge–Kutta method for temporal accuracy. The third-order compact scheme is numerically stable under CFL condition CFL≈0.5. Due to its multidimensional gas-kinetic formulation and the coupling of inviscid and viscous terms, even with unstructured meshes, the boundary layer solution and vortex structure can be accurately captured by the current scheme. At the same time, the compact scheme can capture strong shocks as well.

Characterisation of the turbulent electromotive force and its magnetically-mediated quenching in a global EULAG-MHD simulation of solar convection

We perform a mean-field analysis of the EULAG-MHD millenium simulation of global magnetohydrodynamical convection presented in Passos and Charbonneau (2014). The turbulent electromotive force (emf) operating in the simulation is assumed to be linearly related to the cyclic axisymmetric mean magnetic field and its first spatial derivatives. At every grid point in the simulation’s meridional plane, this assumed relationship involves 27 independent tensorial coefficients. Expanding on Racine et al. (2011), we extract these coefficients from the simulation data through a least-squares minimization procedure based on singular value decomposition. The reconstructed α-tensor shows good agreement with that obtained by Racine et al. (2011), who did not include derivatives of the mean-field in their fit, as well as with the α-tensor extracted by Augustson et al. (2015) from a distinct ASH MHD simulation. The isotropic part of the turbulent magnetic diffusivity tensor β is positive definite and reaches values of 5.0×107m2s−1 in the middle of the convecting fluid layers. The spatial variations of both αϕϕ and βϕϕ component are well reproduced by expressions obtained under the Second Order Correlation Approximation, with a good matching of amplitude requiring a turbulent correlation time about five times smaller than the estimated turnover time of the small-scale turbulent flow. By segmenting the simulation data into epochs of magnetic cycle minima and maxima, we also measure α- and β-quenching. We find the magnetic quenching of the α-effect to be driven primarily by a reduction of the small-scale flow’s kinetic helicity, with variations of the current helicity playing a lesser role in most locations in the simulation domain. Our measurements of turbulent diffusivity quenching are restricted to the βϕϕ component, but indicate a weaker quenching, by a factor of ≃1.36, than of the α-effect, which in our simulation drops by a factor of three between the minimum and maximum phases of the magnetic cycle.

Accurate double many-body expansion potential energy surface of HS2A2A′) by scaling the external correlation**Project supported by the National Natural Science Foundation of China (Grant No. 11304185), the Taishan Scholar Project of Shandong Province, China, the Shandong Provincial Natural Science Foundation, China (Grant No. ZR2014AM022), the Shandong Province Higher Educational Science and Technology Program, China (Grant No. J15LJ03), the China Postdoctoral

A globally accurate single-sheeted double many-body expansion potential energy surface is reported for the first excited state of HS2 by fitting the accurate ab initio energies, which are calculated at the multireference configuration interaction level with the aug-cc-pVQZ basis set. By using the double many-body expansion-scaled external correlation method, such calculated ab initio energies are then slightly corrected by scaling their dynamical correlation. A grid of 2767 ab initio energies is used in the least-square fitting procedure with the total root-mean square deviation being 1.406 kcal·mol−1. The topographical features of the HS2(A2A′) global potential energy surface are examined in detail. The attributes of the stationary points are presented and compared with the corresponding ab initio results as well as experimental and other theoretical data, showing good agreement. The resulting potential energy surface of HS2(A2A′) can be used as a building block for constructing the global potential energy surfaces of larger S/H molecular systems and recommended for dynamic studies on the title molecular system.

Generalised Rank Regression Estimator with Standard Error Adjusted Lasso

SummaryOne of the standard variable selection procedures in multiple linear regression is to use a penalisation technique in least‐squares (LS) analysis. In this setting, many different types of penalties have been introduced to achieve variable selection. It is well known that LS analysis is sensitive to outliers, and consequently outliers can present serious problems for the classical variable selection procedures. Since rank‐based procedures have desirable robustness properties compared to LS procedures, we propose a rank‐based adaptive lasso‐type penalised regression estimator and a corresponding variable selection procedure for linear regression models. The proposed estimator and variable selection procedure are robust against outliers in both response and predictor space. Furthermore, since rank regression can yield unstable estimators in the presence of multicollinearity, in order to provide inference that is robust against multicollinearity, we adjust the penalty term in the adaptive lasso function by incorporating the standard errors of the rank estimator. The theoretical properties of the proposed procedures are established and their performances are investigated by means of simulations. Finally, the estimator and variable selection procedure are applied to the Plasma Beta‐Carotene Level data set.

Stress measurement using area detectors: a theoretical and experimental comparison of different methods in ferritic steel using a portable X-ray apparatus

Using area detectors for stress determination by diffraction methods in a single exposure greatly simplifies the measurement process and permits the design of portable systems without complex sample cradles or moving parts. An additional advantage is the ability to see the entire or a large fraction of the Debye ring and thus determine texture and grain size effects before analysis. The two methods most commonly used to obtain stress from a single Debye ring are the so-called $$\cos \alpha $$ and full-ring fitting methods, which employ least-squares procedures to determine the stress from the distortion of a Debye ring by probing a set of scattering vector simultaneously. The widely applied $$\sin ^2\psi $$ method, in contrast, requires sample rotations to probe a different subset of scattering vector orientations. In this paper, we first present a description of the different methods under the same formalism and using a unified set of coordinates that are suited to area detectors normal to the incident beam, highlighting the similarities and differences between them. We further characterize these methods by means of in situ measurements in carbon steel tube samples, using a portable detector in reflection geometry. We show that, in the absence of plastic flow, the different methods yield basically the same results and are equivalent. An analysis of possible sources of errors and their impact in the final stress values is also presented.

STRUCTURE OF 2-AMINO-4-(3-BROMOPHENYL)-7,7-DIMETHYL-5-OXO-5,6,7,8-TETRAHYDRO-4H-CHROMENE-3-CARBONITRILE

The title compound, 2-amino-4-(3-bromophenyl)-7,7-dimethyl-5-oxo-5,6,7,8-tetrahydro-4 H -chromene-3-carbonitrile (C 18 H 17 BrN 2 O 2 ), was synthesized, in 86% yield, by one-pot multicomponent reaction of 3-bromobenzaldehyde, malononitrile and dimedone using 10 mol % urea as an organo-catalyst at room temperature. It crystallizes in the monoclinic space group C 2/c with the unit-cell parameters: a= 23.557(2), b= 9.2963(7), c= 15.7502(12) A, β = 93.430(8) o and Z = 8. The crystal structure was solved by direct methods using single-crystal X-ray diffraction data collected at room temperature and refined by full-matrix least-squares procedures to a final R-value of 0.0585 for 1411 observed reflections. The packing between the molecules within the unit cell is stabilized by N-H..O and N-H…N type of intermolecular hydrogen interactions.

The daily computed weighted averaging basic reproduction number [formula omitted] for MERS-CoV in South Korea

In this paper, we propose the daily computed weighted averaging basic reproduction number R0,k,ωn for Middle East respiratory syndrome coronavirus (MERS-CoV) outbreak in South Korea, May to July 2015. We use an SIR model with piecewise constant parameters β (contact rate) and γ (removed rate). We use the explicit Euler’s method for the solution of the SIR model and a nonlinear least-square fitting procedure for finding the best parameters. In R0,k,ωn, the parameters n, k, and w denote days from a reference date, the number of days in averaging, and a weighting factor, respectively. We perform a series of numerical experiments and compare the results with the real-world data. In particular, using the predicted reproduction number based on the previous two consecutive reproduction numbers, we can predict the future behavior of the reproduction number.

Simultaneous muscle water T2 and fat fraction mapping using transverse relaxometry with stimulated echo compensation.

Skeletal muscle inflammation/necrosis and fat infiltration are strong indicators of disease activity and progression in many neuromuscular disorders. They can be assessed by muscle T2 relaxometry and water-fat separation techniques, respectively. In the present work, we exploited differences between water and fat T1 and T2 relaxivities by applying a bi-component extended phase graph (EPG) fitting approach to simultaneously quantify the muscle water T2 and fat fraction from standard multi-slice multi-echo (MSME) acquisitions in the presence of stimulated echoes. Experimental decay curves were adjusted to the theoretical model using either an iterative non-negative least-squares (NNLS) procedure or a pattern recognition approach. Twenty-two patients (age, 49 ± 18 years) were selected to cover a large range of muscle fat infiltration. Four cases of chronic or subchronic juvenile dermatomyositis (age, 8 ± 3 years) were investigated before and 3 months following steroid treatment. For control, five healthy volunteers (age, 25 ± 2 years) were recruited. All subjects underwent the MSME sequence and EPG fitting procedure. The EPG fitting algorithm allowed a precise estimation of water T2 and fat fraction in diseased muscle, even in the presence of large B1(+) inhomogeneities. In the whole cohort of patients, there was no overall correlation between water T2 values obtained with the proposed method and the fat fraction estimated inside muscle tissues (R(2) = 0.02). In the patients with dermatomyositis, there was a significant decrease in water T2 (-4.09 ± 3.7 ms) consequent to steroid treatment. The pattern recognition approach resulted in a 20-fold decrease in processing time relative to the iterative NNLS procedure. The fat fraction derived from the EPG fitting approach correlated well with the fat fraction derived from a standard three-point Dixon method (≈1.5% bias). The bi-component EPG fitting analysis is a precise tool to monitor muscle tissue disease activity and is able to handle bias introduced by fat infiltration and B1(+) inhomogeneities.