Instrumental design for capturing three‐dimensional moiré images

Hydrodynamically limited precision of gradient techniques in flow injection analysis

The error propagation among estimated parameters reflects the correlation among the parameters. We study the capability of machine learning of “learning” the correlation of estimated parameters. We show that machine learning can recover the relation between the uncertainties of different parameters, especially, as predicted by the error propagation formula. Gravitational lensing can be used to probe both astrophysics and cosmology. As a practical application, we show that the machine learning is able to intelligently find the error propagation among the gravitational lens parameters (effective lens mass M L and Einstein radius θ E ) in accordance with the theoretical formula for the singular isothermal ellipse (SIE) lens model. The relation of errors of lens mass and Einstein radius, (e.g., the ratio of standard deviations =σMLˆ/σθEˆ ) predicted by the deep convolution neural network are consistent with the error propagation formula of the SIE lens model. As a proof-of-principle test, a toy model of linear relation with Gaussian noise is presented. We found that the predictions obtained by machine learning indeed indicate the information about the law of error propagation and the distribution of noise. Error propagation plays a crucial role in identifying the physical relation among parameters, rather than a coincidence relation, therefore we anticipate our case study on the error propagation of machine learning predictions could extend to other physical systems on searching the correlation among parameters.

The Earth’s synthetic gravitational and density models can be used to validate numerical procedures applied for global (or large-scale regional) gravimetric forward and inverse modeling. Since the Earth’s lithospheric structure is better constrained by tomographic surveys than a deep mantle, most existing 3D density models describe only a lithospheric density structure, while 1D density models are typically used to describe a deep mantle density structure below the lithosphere-asthenosphere boundary. The accuracy of currently available lithospheric density models is examined in this study. The error analysis is established to assess the accuracy of modeling the sub-lithospheric mantle geoid while focusing on the largest errors (according to our estimates) that are attributed to lithospheric thickness and lithospheric mantle density uncertainties. Since a forward modeling of the sub-lithospheric mantle geoid also comprises numerical procedures of adding and subtracting gravitational contributions of similar density structures, the error propagation is derived for actual rather than random errors (that are described by the Gauss’ error propagation law). Possible systematic errors then either lessen or sum up after applying particular corrections to a geoidal geometry that are attributed to individual lithospheric density structures (such as sediments) or density interfaces (such as a Moho density contrast). The analysis indicates that errors in modeling of the sub-lithospheric mantle geoid attributed to lithospheric thickness and lithospheric mantle density uncertainties could reach several hundreds of meters, particularly at locations with the largest lithospheric thickness under cratonic formations. This numerical finding is important for the calibration and further development of synthetic density models of which mass equals the Earth’s total mass (excluding the atmosphere). Consequently, the (long-to-medium wavelength) gravitational field generated by a synthetic density model should closely agree with the Earth’s gravitational field.

In the classical geodetic data processing, a non- linear problem always can be converted to a linear least squares adjustment. However, the errors in Jacob matrix are often not being considered when using the least square method to estimate the optimal parameters from a system of equations. Furthermore, the identity weight matrix may not suitable for each element in Jacob matrix. The weighted total least squares method has been frequently applied in geodetic data processing for the case that the observation vector and the coefficient matrix are perturbed by random errors, which are zero mean and statistically in- dependent with inequality variance. In this contribution, we suggested an approach that employ the weighted total least squares to solve the nonlinear problems and to mitigate the affection of noise in Jacob matrix. The weight matrix of the vector from Jacob matrix is derived by the law of nonlinear error propagation. Two numerical examples, one is the triangulation adjustment and another is a simulation experiment, are given at last to validate the feasibility of the developed method.

Predictions of lifetime under load were made for five ceramic materials using strength and fracture mechanics techniques. The double-torsion technique was used to obtain fracture mechanics data, while the stressing-rate technique was used to obtain strength data. An error analysis based on the error propagation law was performed to determine confidence limits for the failure predictions. Agreement of lifetime predictions by the stressing-rate and fracture mechanics techniques were obtained for only two of the materials. The implications of these results with regard to microstructural effects on crack propagation and design applications are discussed.

In this study, threshold voltage (Vth) variability was investigated in silicon nanowire field-effect transistors (SNWFETs) with short gate-lengths of 15–22 nm and various channel diameters (DNW) of 7, 9, and 12 nm. Linear slope and nonzero y-intercept were observed in a Pelgrom plot of the standard deviation of Vth (σVth), which originated from random and process variations. Interestingly, the slope and y-intercept differed for each DNW, and σVth was the smallest at a median DNW of 9 nm. To analyze the observed DNW tendency of σVth, a novel modeling approach based on the error propagation law was proposed. The contribution of gate-metal work function, channel dopant concentration (Nch), and DNW variations (WFV, ∆Nch, and ∆DNW) to σVth were evaluated by directly fitting the developed model to measured σVth. As a result, WFV induced by metal gate granularity increased as channel area increases, and the slope of WFV in Pelgrom plot is similar to that of σVth. As DNW decreased, SNWFETs became robust to ∆Nch but vulnerable to ∆DNW. Consequently, the contribution of ∆DNW, WFV, and ∆Nch is dominant at DNW of 7 nm, 9 nm, and 12, respectively. The proposed model enables the quantifying of the contribution of various variation sources of Vth variation, and it is applicable to all SNWFETs with various LG and DNW.

By means of the least-squares canonical equations and the error propagation law only, the uncertainties in the parameters of the functional expression used to fit a set of experimental points, with both coordinates subject to error, are analytically determined.

Modelling error propagation in vector-based overlay analysis

Isobaric equilibrium data (P = 101.3 kPa) for the system cyclohexane-acetic acid-propionic acid have been measured by two different analytical techniques. Activity coefficients calculated by simultaneous solving of equations for the chemical and phase equilibria were subjected to a consistency test based on inaccuracies determined from the error propagation law, and were correlated by Wilson’s equation. The activity coefficients measured were compared with those calculated from binary vapour-liquid equilibrium data and with values predicted by the UNIFAC method.

Curved surfaces have a major influence on the propagation of sound in rooms. Convex surfaces always lead to attenuated reflections spread out over a larger area, while concave surfaces create either amplification or attenuation of reflections, depending on the source and receiver positions relative to the curved surface. Contemporary architecture often involves extensive use of both convex and concave surfaces. Therefore, acoustic consultants need to be able to quickly gain a thorough understanding of a given curved geometry, and judge to what extent the arising focusing will be either benign or problematic (due to focusing, inhomogeneous sound distribution or flutter echoes). The advent of NURBS-based 3D software (e.g. Rhino5) has made it possible to carry out very precise geometrical raytracing on curved surfaces, revealing their geometrical coverage. As a further refinement, a differential raytracing technique is proposed, allowing the straightforward calculation of the amplification or attenuation created by a given curved surface. This purely geometrical technique can also be applied to higher order reflections, in order to help identify flutter echo problems created by multiple reflection paths involving concave surfaces. Practical examples of halls with significant curved geometries will be given to illustrate the use of this approach, including Wigmore Hall, London and Wuxi Grand Theatre.

Heterogenous nucleation in a cave with an apex and iso-curvature lateral surface

Although artificial micromotors with unconventional shapes are emerging as a powerful tool in various applications, little research has been undertaken to clarify their propulsion mechanism, especially how the shape effect alters the bubble dynamics and hydrodynamic flows. In this study, we fabricated two types of bowl-shaped micromotors to investigate the distinct dynamics due to the shape effect of concave and convex surfaces, by coating a platinum (Pt) layer on either the concave surface or the convex surface of the micromotor. In the single-bubble propulsion mode at low fuel concentration, the concave-surface-Pt-coated micromotor moved unexpectedly slower than the convex-surface-Pt-coated micromotor, and the bubble growth on the concave surface was also much slower than that on the convex surface. It was elucidated that the confinement effect of the concave surface hindered fuel replenishment and thus the catalytic reaction. We further introduced the Kelvin impulse to explain why the concave shape eventually weakened the propulsion from hydrodynamic jet flows caused by bubble collapse. In the multi-bubble propulsion mode at high fuel concentration, the interaction among bubbles rendered a “more is less” phenomenon—increase in the fuel concentration did not enhance the maximum instantaneous propulsion speed. These findings inspire the development of new manipulation strategies utilizing the unconventional shape effect in micromotors.

Although artificial micromotors with unconventional shapes are emerging as a powerful tool in various applications, little research has been undertaken to clarify their propulsion mechanism, especially how the shape effect alters the bubble dynamics and hydrodynamic flows. In this study, we fabricated two types of bowl-shaped micromotors to investigate the distinct dynamics due to the shape effect of concave and convex surfaces, by coating a platinum (Pt) layer on either the concave surface or the convex surface of the micromotor. In the single-bubble propulsion mode at low fuel concentration, the concave-surface-Pt-coated micromotor moved unexpectedly slower than the convex-surface-Pt-coated micromotor, and the bubble growth on the concave surface was also much slower than that on the convex surface. It was elucidated that the confinement effect of the concave surface hindered fuel replenishment and thus the catalytic reaction. We further introduced the Kelvin impulse to explain why the concave shape eventually weakened the propulsion from hydrodynamic jet flows caused by bubble collapse. In the multi-bubble propulsion mode at high fuel concentration, the interaction among bubbles rendered a “more is less” phenomenon—increase in the fuel concentration did not enhance the maximum instantaneous propulsion speed. These findings inspire the development of new manipulation strategies utilizing the unconventional shape effect in micromotors.

Heat transfer investigations on methane-air premixed flame jet exiting from a circular nozzle and impinging over semi-cylindrical surfaces

Precipitation forecasting is an important mission in weather science. In recent years, data-driven precipitation forecasting techniques could complement numerical prediction, such as precipitation nowcasting, monthly precipitation projection and extreme precipitation event identification. In data-driven precipitation forecasting, the predictive uncertainty arises mainly from data and model uncertainties. Current deep learning forecasting methods could model the parametric uncertainty by random sampling from the parameters. However, the data uncertainty is usually ignored in the forecasting process and the derivation of predictive uncertainty is incomplete. In this study, the input data uncertainty, target data uncertainty and model uncertainty are jointly modeled in a deep learning precipitation forecasting framework to estimate the predictive uncertainty. Specifically, the data uncertainty is estimated a priori and the input uncertainty is propagated forward through model weights according to the law of error propagation. The model uncertainty is considered by sampling from the parameters and is coupled with input and target data uncertainties in the objective function during the training process. Finally, the predictive uncertainty is produced by propagating the input uncertainty and sampling the weights in the testing process. The experimental results indicate that the proposed joint uncertainty modeling and precipitation forecasting framework exhibits comparable forecasting accuracy with existing methods, while could reduce the predictive uncertainty to a large extent relative to two existing joint uncertainty modeling approaches. The developed joint uncertainty modeling method is a general uncertainty estimation approach for data-driven forecasting applications.