Numerical Estimates Research Articles

A new general biased estimator in linear measurement error model

Numerous biased estimators are known to circumvent the multicollinearity problem in linear measurement error models. This article proposes a general biased estimator with the ridge regression and the Liu estimators as special cases. The efficiency of the suggested estimator is compared with ridge regression and Liu estimators under the mean squared error matrix criterion. In addition, a Monte Carlo simulation study and a numerical evaluation have been conducted to elucidate the superiority of the new general biased estimator over other estimators.

Verification of strain energy splits of phase field fracture model using Westergaard’s problem under mixed-mode loading

One challenge in verifying strain energy splits in phase field fracture models is the lack of reference problems with exact solutions in mixed-mode loading that could serve as benchmark problems. In this work, different strain energy splits used in the variational phase field model have been applied to the classical Westergaard’s problem. In contrast to other benchmark problems used in the literature, the proposed problem not only includes the singular term as a boundary condition but also implicitly considers all terms. To the authors’ knowledge, this is the first time in the literature that this reference problem has been used to rigorously verify the accuracy of different energy splits of the phase field model. Several critical factors such as the pre-crack definition, mesh size, mixed mode ratio and the length scale parameter have been analysed. A good correlation between the numerical estimations and the analytical predictions was found for some pre-crack definition approaches under mode I. However, we demonstrated that the compatible regularisation length scale and mesh size are significantly lower under mode II loading (i.e., when the crack kinks) than under mode I.

Response surface methodology-based new model to optimize heat transfer and shear stress for ferrites/motor oil hybrid nanofluid

PurposeThis study aims to optimize heat transfer efficiency and minimize friction factor and entropy generation in hybrid nanofluid flows through porous media. By incorporating factors such as melting effect, buoyancy, viscous dissipation and no-slip velocity on a stretchable surface, the aim is to enhance overall performance. Additionally, sensitivity analysis using response surface methodology is used to evaluate the influence of key parameters on response functions.Design/methodology/approachAfter deriving suitable Lie-group transformations, the modeled equations are solved numerically using the “spectral local linearization method.” This approach is validated through rigorous numerical comparisons and error estimations, demonstrating strong alignment with prior studies.FindingsThe findings reveal that higher Darcy numbers and melting parameters are associated with decreased entropy (35.86% and 35.93%, respectively) and shear stress, increased heat transmission (16.4% and 30.41%, respectively) in hybrid nanofluids. Moreover, response surface methodology uses key factors, concerning the Nusselt number and shear stress as response variables in a quadratic model. Notably, the model exhibits exceptional accuracy with $R^2$ values of 99.99% for the Nusselt number and 100.00% for skin friction. Additionally, optimization results demonstrate a notable sensitivity to the key parameters.Research limitations/implicationsLubrication is a vital method to minimize friction and wear in the automobile sector, contributing significantly to energy efficiency, environmental conservation and carbon reduction. The incorporation of nickel and manganese zinc ferrites into SAE 20 W-40 motor oil lubricants, as defined by the Society of Automotive Engineers, significantly improves their performance, particularly in terms of tribological attributes.Originality/valueThis work stands out for its focus on applications such as hybrid electromagnetic fuel cells and nano-magnetic material processing. While these applications are gaining interest, there is still a research gap regarding the effects of melting on heat transfer in a NiZnFe_2O_4-MnZnFe_2O_4/20W40 motor oil hybrid nanofluid over a stretchable surface, necessitating a thorough investigation that includes both numerical simulations and statistical analysis.

Bispectrum non-Gaussian covariance in redshift space

We provide an analytical description of the galaxy bispectrum covariance and the power spectrum-bispectrum cross-covariance in redshift space that captures the dominant non-Gaussian contributions at mildly non-linear scales, particularly those arising from the squeezed configurations.The Gaussian prediction for the variance of the halo bispectrum monopole significantly underestimates numerical estimates particularly for squeezed triangles, that is bispectrum triangular configurations where one side is much smaller than the other two, whereas the effect is relatively less important when considering the quadrupole.We propose an expression for the missing non-Gaussian contribution valid at mildly non-linear scales in the squeezed limit that requires an accurate modeling of the bispectrum alone. We validate our model against the numerical covariance estimated from a large suite of mock catalogs and find that it accurately predicts the variance as well as the dominant off-diagonal terms. We also present an expression for the cross-covariance between power spectrum and bispectrum multipoles and likewise find it to provide a good description of the numerical results.

Directionality of gravitational and thermal diffusive transport in geologic fluid storage.

Diffusive transport has implications for the long-term status of underground storage of hydrogen (H_{2}) fuel and carbon dioxide (CO_{2}), technologies which are being pursued to mitigate climate change and advance the energy transition. Once injected underground, CO_{2} and H_{2} will exist in multiphase fluid-water-rock systems. The partially soluble injected fluids can flow through the porous rock in a connected plume, become disconnected and trapped as ganglia surrounded by groundwater within the storage rock pore space, and also dissolve and migrate through the aqueous phase once dissolved. Recent analyses have focused on the concentration gradients induced by differing capillary pressure between fluid ganglia which can drive diffusive transport ("Ostwald ripening"). However, studies have neglected or excessively simplified important factors, namely the nonideality of gases under geologic conditions, the opposing equilibrium state of dissolved CO_{2} and H_{2} driven by the partial molar density of dissolved solutes, and entropic and thermodiffusive effects resulting from geothermal gradients. We conduct an analysis from thermodynamic first principles and use this to provide numerical estimates for CO_{2} and H_{2} at conditions relevant to underground storage reservoirs. We show that while diffusive transport in isothermal systems is upwards for both gases, as indicated by previous analysis, entropic contributions to the free energy are so significant as to cause a reversal in the direction of diffusive transport in systems with geothermal gradients. For CO_{2}, even geothermal gradients less than 10^{∘}C/km (far less than typical gradients of 25^{∘}C/km) are sufficient to induce downwards diffusion at depths relevant to storage. Diffusive transport of H_{2} is less affected but still reverses direction under typical gradients, e.g., 30^{∘}C/km, at a depth of 1000m. This reversal occurs independent of the solute's thermophobicity or thermophilicity in aqueous solutions. The entropic contribution also modifies the magnitude of flux where geothermal gradients are present, with the largest diffusive fluxes estimated for CO_{2} with a 30^{∘}C/km gradient, despite the higher diffusion coefficient of H_{2}. We find a maximum flux on the order of 10^{-13} mol/(cm^{2}s) for CO_{2} in the 30^{∘}C/km scenario; significantly lower than literature estimates for maximum convective fluxes in moderate to high permeability formations. Contrary to previous studies, we find that in diffusion and convection will likely work in concert-both driving CO_{2} downwards, and both driving H_{2} upwards-for conditions representative of their respective storage reservoirs.

Probing the Quark Orbital Angular Momentum at Electron-Ion Colliders Using Exclusive π^{0} Production.

We propose to detect signals from quark orbital angular momentum (OAM) through exclusive π^{0} production in electron- (longitudinally polarized) proton collisions. Our analysis demonstrates that the sin2ϕ azimuthal angular correlation between the transverse momentum of the scattered electron and the recoil proton serves as a sensitive probe of quark OAM. Additionally, we present a numerical estimate of the asymmetry associated with this correlation for the kinematics accessible at the Electron-Ion Colliders in the U.S. and China. This study aims to pave the way for the first experimental study of quark OAM in relation to the Jaffe-Manohar spin sum rule.

Mechanical behaviour of 3D printed carbon fibre reinforced composite metastructure with various filling rates

This paper evaluated the influence of filling rate and printing direction on the mechanical properties of composite metastructure via experimental and numerical approaches. A representative volume element (RVE) and finite element method were adopted to estimate the tensile and flexural properties and verify the applicability of these methods in the 3D printing of composite metastructure. Results showed that apparent tensile and flexural properties drop with decreasing filling rates. The tensile and flexural strength reached 70.7 MPa and 131.1 MPa for solid specimens. The bending test for samples with different printing directions showed that the printing direction of the core has no noticeable effect on flexural strength, but the +45°/-45° sample exhibited the highest modulus. The numerical estimation showed similar trend compared to experimental results for both tensile and flexural properties. Such an attempt indicates the feasibility of designing a composite metastructure with an optimum weight-strength relationship.

TWO APPROACHES TO THE FORMATION OF A QUANTITATIVE MEASURE OF STABILITY BASED ON MULTIPLE ESTIMATES OF THE PARAMETERS OF AN ENSEMBLE OF TRANSIENT PROCESSES

The article is devoted to the further development of the theory of stability of dynamic systems, namely of quantitative methods of stability assessment. A review and critical analysis of various approaches, which allow to introduce a quantitative measure of stability of dynamic systems to one degree or another, is given. The limitations of the existing methods, which are primarily related to the assessment of the behavior of the transient processes of individual trajectories, as well as the difficulty of obtaining an assessment of the behavior of the ensemble of transient processes when trying to apply the methods of N. D. Moiseyev. are substantiated. A method of quantitative assessment of a dynamic system stability based on the numerical estimates of the behavior of the area of initial deviations from the equilibrium position on the trajectories of the dynamic system is substantiated. Based on the Liouville formula, it is shown that changes in the volume of the area of the initial deviations on the trajectories of the system does not depend on the form of the latter one. This allowed to limit the area of initial deviations in the shape of a hypersphere and to obtain a simple expression for a quantitative measure of the stability of a linear stationary dynamic system, the geometric sense of which is to estimate the rate of change of the volume of the control surface. The article proposes and substantiates the criterion of uniformity of deformation of the area of initial deviations. The essence of the problem is that in the transient process, the values of some components of the phase vector may reach unacceptable deviations from the equilibrium position. A theoretical estimate of deformation non-uniformity for linear systems is obtained, which is taken to be the deviation of the trace of the ellipsoid matrix from the deviations of the trace of the hypersphere matrix of the corresponding volume. A method for a quantitative measure of the stability based on an integral quadratic functional calculated on a set of transient processes of initial deviations in the form of a set of ellipsoids with a normalized volume is proposed and substantiated. Diagonal positive normalized matrices are considered as a set of matrices of the integral quadratic criterion. A simple algorithm for calculation of the multiple integral quadratic criterion is proposed.

Influence of temperature and momentum on heavy quark energy loss

We investigated the correlation between temperature and momentum, as well as the impact of temperature and momentum on energy loss in quark-gluon plasma (QGP), along with the primary mechanisms of energy dissipation. Our findings reveal that the threshold momentum increases with rising temperatures, indicating a greater possibility to energy loss at higher temperatures and momenta. Numerical estimates of the losses show that the energy loss in the hot matter is greater than the energy loss in the cold matter. Upon considering energy loss due to polarization, radiation, and collision, we observe that under low transverse momentum conditions, polarization dominates the energy loss, whereas under high transverse momentum conditions, radiation takes precedence. In addition, we found that heavy quarks with lower mass are more prone to energy loss because of the faster thermalization rate.

Measuring Abstraction Levels of Sculptural Objects

Abstract Freestanding sculpture can be scored for abstraction using order scales such as the three-rank ‘realistic,’ ‘mixed,’ and ‘abstract.’ Subjective but invaluable, the ranks support ordering but not arithmetic. Numeric limitations can be addressed via information-theoretic metrics that measure collective uncertainty about a sculpture; to this end 60 participants view 25 images of sculpture via an internet questionnaire. They (i) score each depicted object and (ii) type a caption stating what impression the object evokes. Captions for the image are simplified to their English simple subject, sorted into classification categories and counted. A metric converts an image’s categories and counts into viewers’ uncertainty. The investigation examines four-rank and five-rank scales plus metrics CC (category count), H (entropy) and EC ≡ 2H (equalized category count). Medians of scores or uncertainties reduce variability as appropriate. Comparisons of scores vs uncertainties show the two generally correlate well. Results also highlight inherent design tradeoffs. Scale/metric pairings affect both ranks (which should be statistically distinct) and rank/uncertainty correlations. Two good combinations are [four-rank; median CC] and [five-rank; median EC]. Metric CC is easy to compute and correlates slightly better than EC, although the latter supports five evenly separated ranks. Shifting focus to image scatterplots, the pair [four-rank median score; CC] yields a very strong correlation. Once uncertainties are linked to ranks to ‘calibrate’ them, one gets a quantitative sense of the rank order scale. The augmented framework offers the speed and ease of scoring along with valid numeric estimates of uncertainty unavailable from ranks alone.

A‐prori layer height determination for wire arc additive manufacturing based on weld geometry

AbstractThe application of wire arc additive manufacturing (WAAM) for the production of large size components is currently limited, due to strong distortion and unprecise filling behavior. The resulting geometric and metallurgical irregularities pose a challenge to the process. The current approach of a layered structure cannot be adopted without adjustments when using wire arc additive manufacturing. Reasons include incompleteness, material accumulation and deformation. The combination of experimental weld geometry‐determination and its numerical estimation is presented here as solution to this challenge. The procedure is based on the measurement of a weld bead cross‐section‐area. By convolution of a path matrix with a weld‐geometry‐function, the planned path is filled with the seam geometry. Subsequent summation of multiple matrices results in a height profile showing discontinuities and accumulations. Further validation tests show a good agreement between the method and experimentally determined problem areas. The presented optimisation procedure can be extended with material parameters. A local compensation for deformation can be achieved.

Analytical solutions for nonequilibrium bioheat transfer in tumor during magnetic nanoparticles hyperthermia

Abstract This paper presents mathematical responses for the dual-phase-lag (DPL) hypothesis, which accounts for nonequilibrium heat transfer during magnetic nanoparticle hyperthermia in tumor. To get this precision, volume averaging is used for the local instantaneous energy formulation for tissues and blood. This study proposes a hybrid numerical strategy to solve this problem by combining change of variables, improved discretization techniques, and Laplace transforms. Using the Arrhenius formulas, the range of denatured proteins is used to assess the degree of heat damages to the tumor and healthy tissues. The impacts of porosity, the blood perfusion and metabolism on the temperature and the thermal injuries are studied. The numerical estimations of temperature and the resulting of thermal injuries are shown on a graph, and a comparison with earlier research establishes the results’ validity.

Potential and limitations of noise-based surface-wave tomography for numerical site effect estimation: a case study in the French Rhône valley

Potential and limitations of noise-based surface-wave tomography for numerical site effect estimation: a case study in the French Rhône valley

Experimental and numerical estimation of thermal conductivity of bio-based building composite materials with an enhanced thermal capacity

The paper tackles the important problem of estimating and predicting the thermal conductivity of bio-based building materials that can help decarbonize the building sector. Knowledge and the possibility to optimize their insulating properties is the first criterion for determining the ability of their use in the building sector. The novel yet not well-studied hemp shives and magnesium binder composites with improved thermal mass by microencapsulated phase change material (PCM) were considered. The samples of composites without PCM having different densities as well as with different amounts of microencapsulated PCM and the same density were manufactured and tested experimentally in different states, i.e., dry and after conditioning at relative humidity (RH) of 50, 75, and 90 %, and in the case of samples with PCM also at different average measurement temperatures selected with respect to the phase change range of the PCM. A novel method of predicting bio-based composites' effective thermal conductivity tensor was also developed. The method is based on the numerical solution of the heat conduction equation at the micro-scale considering real composite microstructure. The method was tuned using micro-computed tomography (μCT) data with the microstructure of composites without PCM and then applied to predict the thermal conductivities of composites with PCM, utilizing computational domains with an artificially distributed PCM in the binder. The experimental testing of composites without PCM revealed an apparent effect of increasing thermal conductivity with rising sample density and RH applied during conditioning. With an increase in density from 394 to 576 kg/m3, their thermal conductivities varied from 0.105 to 0.159 W/m/K for the dry state and from 0.157 to 0.241 W/m/K for RH 90 %. A similar effect of sample state and RH was observed for composites with microencapsulated PCM, which had the highest thermal conductivity, equal to 0.265 W/m/K, for the lowest PCM amount and RH 90 %. Moreover, a decrease in composites' effective thermal conductivity with an increase in PCM fraction was observed, except for the lowest PCM fraction, for which it increased. It also rose with increasing the average measurement temperature. The developed micro-scale-based numerical method allowed for predicting the thermal conductivities of composites with accuracies below 4.1 and 7.2 % for composites without and with PCM, respectively, except for the composite with the lowest amount of PCM, which behaved differently. Thus, its suitability for designing and optimizing bio-based composites was shown.

Failure assessment of eccentric circular holes under compressive loading

AbstractThe present work aims to investigate the failure size effect on flattened disks containing an eccentric circular hole under mode I loading conditions. For this purpose, uniaxial compression tests are carried out on polymethyl methacrylate (PMMA) samples with holes. Depending on the hole radius and eccentricity, the energy release rate is either an increasing or decreasing function of the crack length, thus affecting the stability of crack propagation. Experimental results are interpreted and discussed through the coupled stress and energy criterion of Finite Fracture Mechanics. The approach lies on the assumption of a finite crack advance and it is implemented through the numerical estimation of the stress field and the Incremental Energy Release Rate functions. Finally, stability and crack speed propagation are discussed under the assumption of Linear Elastic Fracture Mechanics. Theoretical predictions reveal in agreement with experimental results thus demonstrating that the Coupled Criterion effectively captures the failure condition.

Transoceanic pathogen transfer in the age of sail and steam

In the centuries following Christopher Columbus's 1492 voyage to the Americas, transoceanic travel opened unprecedented pathways in global pathogen circulation. Yet no biological transfer is a single, discrete event. We use mathematical modeling to quantify historical risk of shipborne pathogen introduction, exploring the respective contributions of journey time, ship size, population susceptibility, transmission intensity, density dependence, and pathogen biology. We contextualize our results using port arrivals data from San Francisco, 1850 to 1852, and from a selection of historically significant voyages, 1492 to 1918. We offer numerical estimates of introduction risk across historically realistic ranges of journey time and ship population size, and show that both steam travel and shipping regimes that involved frequent, large-scale movement of people substantially increased risk of transoceanic pathogen circulation.

A compensation method for PMSM sensorless control with parameter identification considering SMO observation error

AbstractSensorless control of permanent magnet synchronous motor (PMSM) can increase the reliability of electric actuators of more electrical aircraft. Numerical online parameter estimation method will enhance the performance for sensorless control methods based on sliding mode observer (SMO). However, numerical online parameter identification methods typically assume zero rotor position estimation error to ensure full rank of the identification equation set. This assumption actually leads to errors in parameter identification, resulting in steady‐state errors in rotor position estimation. This paper focuses on a compensation method for PMSM online parameter identification that takes into account rotor position estimation error. This method is used for sensorless control based on SMO, using model reference adaptive systems for online parameter identification, and no additional parameter adjustment required. Validation is conducted on a PMSM experimental platform with maximum load of 15kW. The experimental results of 1000 r/min steady state operation proved the effectiveness of the method, and the dynamic experiments with 5 and 15kW loads proved that the method has no significant adverse effect on the system dynamics.

Interplay among entanglement, measurement incompatibility, and nonlocality

Nonlocality, manifested by the violation of Bell inequalities, indicates entanglement within a joint quantum system. A natural question is how much entanglement is required for a given nonlocal behavior. Here, we explore this question by quantifying entanglement using a family of generalized Clauser–Horne–Shimony–Holt-type Bell inequalities. Given a Bell-inequality violation, we derive analytical lower bounds on the entanglement of formation, a measure related to entanglement dilution. The bounds also lead to an analytical estimation of the negativity of entanglement. In addition, we consider one-way distillable entanglement tied to entanglement distillation and derive tight numerical estimates. With the additional assumptions of qubit-qubit systems, we find that the relationship between entanglement and measurement incompatibility is not simply a trade-off under a fixed nonlocal behavior. Furthermore, we apply our results to two realistic scenarios—non-maximally entangled and Werner states. We show that one can utilize the nonlocal statistics by optimizing the Bell inequality for better entanglement estimation.

Examining the Impact of Structural Uncertainty Across 10 Type 2 Diabetes Models: Results From the 2022 Mount Hood Challenge

ObjectivesThe Mount Hood Diabetes Challenge Network aimed to examine the impact of model structural uncertainty on the estimated cost-effectiveness of interventions for type 2 diabetes. MethodsTen independent modeling groups completed a blinded simulation exercise to estimate the cost-effectiveness of 3 interventions in 2 type 2 diabetes populations. Modeling groups were provided with a common baseline population, cost and utility values associated with different model health states, and instructions regarding time horizon and discounting. We collated the results to identify variation in predictions of net monetary benefit (NMB) and the drivers of those differences. ResultsOverall, modeling groups agreed which interventions had a positive NMB (ie, were cost-effective), Although estimates of NMB varied substantially—by up to £23 696 for 1 intervention. Variation was mainly driven through differences in risk equations for complications of diabetes and their implementation between models. The number of modeled health states was also a significant predictor of NMB. ConclusionsThis exercise demonstrates that structural uncertainty between different health economic models affects cost-effectiveness estimates. Although it is reassuring that a decision maker would likely reach similar conclusions on which interventions were cost-effective using most models, the range in numerical estimates generated across different models would nevertheless be important for price-setting negotiations with intervention developers. Minimizing the impact of structural uncertainty on healthcare decision making therefore remains an important priority. Model registries, which record and compare the impact of structural assumptions, offer one potential avenue to improve confidence in the robustness of health economic modeling.

Design and characteristic analysis of flame cutting nozzles for ultralarge-thickness steel ingots

The cutting thickness of the flame cutting nozzle mainly depends on the characteristics of the cutting oxygen jet, and in the process of designing and manufacturing a flame cutting nozzle with an ultralarge thickness, it is impossible to carry out multiple experiments to optimize the design due to the difficulty in testing, safety, manufacturing cost, environmental pollution, and other problems. In this paper, the Laval-type cutting oxygen orifice channel was first designed by theoretical calculation, the pressure, velocity, Mach number, and density distribution characteristics of the cutting oxygen jet were investigated by numerical simulation, and the reliability and adaptability of the numerical simulation results were verified by experiments. Then, the numerical simulation comparison and estimation method of jet characteristics with the general-purpose G301-7# nozzle was used to study the cutting oxygen orifice channel of the ultralarge thickness flame cutting nozzle. The results show that under the condition of a 19 mm throat diameter and 10 atm inlet pressure, it was estimated that the length of cutting oxygen flow from the design nozzle can reach 1800 mm and the cutting thickness can reach 2500 mm based on the density value; the length of cutting oxygen flow can reach 2000 mm and the cutting thickness can reach 3800 mm based on the velocity value; the length of cutting oxygen flow can reach 1600 mm according to the value of the oxygen quality fraction; and the cutting thickness can reach 2800 mm based on the oxygen mass fraction content. Finally, trial production of the nozzle design, verification of the cutting test, the nozzle with a cutting thickness of 2500 mm at an oxygen pressure of 7 atm, and the cutting quality were all good.