Assembly and Disassembly Mechanics of a Cylindrical Snap Fit

Snap fit is a common mechanical mechanism. It uses the physical asymmetry that is easy to assemble but difficult to disassemble to provide a simple and fast link between objects. The ingenious combination of geometric shape, bending elasticity and friction of the snap fit is the mechanism behind the easy to assemble but difficult to disassemble disassemble. Yoshida and Wada (2020) has done a groundbreaking work in the analysis of the elastic snap fit. During our study of their paper, while we really enjoyed their research, unfortunately we detected several questioning formulations. After careful checking, we found that those formulations are not typographical, therefore it is necessary to make corrections. This paper reformulates the linear elasticity of a cylindrical snap fit, obtains an exact solution and proposes an accurate relation between the opening angle and bending tangent angle. Under the first order approximation, our formulations can reduced to the results of Yoshida and Wada and hence confirms the scientific correctness of Yoshida and Wada's work. Furthermore, this paper also derives a correct vertical displacement expression, and propose a new way of disassembly by bending for the first time and formulate a scaling law by data fitting. All formulations are validated by finite element simulation and experiment. The research here is helpful to the design of elastic snap fit or adjustable mechanical mechanism and metamaterial cell.

Surface sum-frequency generation from chiral medium by elliptically polarized light beyond plane-wave approximation and coplanar geometry of incidence

Aiming to study the nonlinear response of the surface of isotropic chiral medium, we obtained analytical expression relating the transverse amplitudes of the spatial Fourier-spectra of two incident arbitrary polarized fundamental beams and one signal reflected beam at the sum-frequency within the first-order approximation by their divergence angles. The calculations, carried out in paraxial approximation, simultaneously take into account the spatial dispersion of the bulk of the medium, its near-surface heterogeneity and the transverse finiteness of the three interacting light beams with arbitrary amplitude profiles and orientation in space. A special compact form for the final formulas was found, which makes use of effective nonlinear transformation tensors, the components of which are solely determined by the geometry of incidence of the beams and the material constants of the medium. A possibility of ``switching off'' the certain mechanisms of nonlinear response by choosing the specific polarization states of the incident beams is discussed.

On The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is UnknownOn The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is Unknown

Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known population meanof auxiliary variable. In this paper, a new class of almost unbiased imputation method that uses as an estimate of is suggested. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.

Exponential-Ratio-Type Imputation Class of Estimators using Nonconventional Robust Measures of Dispersions

Human-assisted surveys, such as medical and social science surveys, are frequently plagued by non-response or missing observations. Several authors have devised different imputation algorithms to account for missing observations during analyses. Nonetheless, several of these imputation schemes' estimators are based on known auxiliary variable parameters that can be influenced by outliers. In this paper, we suggested new classes of exponential-ratio-type imputation method that uses parameters that are robust against outliers. Using the Taylor series expansion technique, the MSE of the class of estimators presented was derived up to first order approximation. Conditions were also specified for which the new estimators were more efficient than the other estimators studied in the study. The results of numerical examples through simulations revealed that the suggested class of estimators is more efficient.

Modified Class of Estimator for Finite Population Mean Under Two-Phase Sampling Using Regression Estimation Approach

This study proposed modified a class of estimator in simple random sampling for the estimation of population mean of the study variable using as axillary information. The biases and MSE of suggested estimators were derived up to the first order approximation using Taylor’s series expansion approach. Theoretically, the suggested estimators were compared with the existing estimators in the literature. The mean square errors (MSE) and percentage relative efficiency (PRE) of proposed estimators and that of some existing estimators were computed numerically and the results revealed that the members of the proposed class of estimator were more efficient compared to their counterparts and can produce better estimates than other estimators considered in the study.

The cosmological background and the “external field” in modified gravity (MOG)

We investigate the contributions of the Friedmann–Lemaître–Robertson–Walker metric of the standard cosmology as an asymptotic boundary condition on the first-order approximation of the gravitational field in Moffat’s theory of modified gravity (MOG). We also consider contributions due to the fact that the MOG theory does not satisfy the shell theorem or Birkhoff’s theorem, resulting in what is known as the “external field effect” (EFE). We show that while both these effects add small contributions to the radial acceleration law, the result is orders of magnitude smaller than the radial acceleration in spiral galaxies.

Density Modelling in Mixed Convection Flow in a Vertical Parallel Plate Channel

In this paper, a novel way of modelling the density in buoyancy term of mixed convection flow problem is presented using equation of state and Boussinesq approximation without first-order approximation of density with respect to temperature. The presented density model is used to investigate the laminar mixed convection flow in a vertical parallel plate channel under symmetric constant wall heat flux. The results obtained are compared with the results obtained using first-order approximation of density with Boussinesq approximation, and also compared with the results obtained using variable thermophysical properties with negligible viscous dissipation. Investigation is performed on the basis of flow and thermal fields for Re=150 and 300, Ri=0.1 to 25. It is found that the presented density model produces relatively better results, which is able to describe the case of developing flow under constant heat flux condition that is not evident if Boussinesq approximation with first-order approximation of density is used. An appearance of recirculatory cells when reverse flow takes place is also witnessed in vertical channel flow with constant heat flux boundary condition which was not reported earlier.

Logarithmic Ratio-Type Estimator of Population Coefficient of Variation

The estimation of population coefficient of variation is one of the challenging aspects in sampling survey techniques for the past decades and much effort has been employed to develop estimators to produce its efficient estimate. In this paper, we proposed logarithmic ratio type estimator for the estimating population coefficient of variation using logarithm transformation on the both population and sample variances of the auxiliary character. The expression for the mean squared error (MSE) of the proposed estimator has been derived using Taylor series first order approximation approach. Efficiency conditions of the proposed estimator over other estimators in the study has also been derived. The empirical study was conducted using two-sets of populations and the results showed that the proposed estimator is more efficient. This result implies that, the estimate of proposed estimator will be closer to the true parameter than the estimates of other estimators in the study.

Application of Cubature Information Filter for Underwater Target Path Estimation

Bearings-only tracking plays a pivotal role in passive underwater surveillance. Using noisy sonar bearing measurements, the target motion parameters (TMP) are extensively estimated using the extended Kalman filter (EKF) because of its simplicity and low computational load. The EKF utilizes the first order approximation of the nonlinear system in estimation of the TMP that degrades the accuracy of estimation due to the elimination of the higher order terms. In this paper, the cubature Kalman filter (CKF) that captures the system nonlinearity upto third order is proposed to estimate the TMP. The CKF is further extended using the information filter (IF) to provide decentralized data fusion, hence the filter is termed as cubature information filter (CIF). The results are generated using Matlab with Gaussian assumption of noise in measurements. Monte-Carlo simulation is done and the results demonstrate that the CIF accuracy is same as that of UKF and this indicates the usefulness of the algorithm for state estimation in underwater with the required accuracy.

Regression-type Imputation Class of Estimators using Auxiliary Attributes

Several imputation schemes and estimators have been proposed by different authors in sample survey. However, these estimators utilized quantitative information of auxiliary characters. In this study, some imputation methods were studied using qualitative information of auxiliary characters and two new imputation schemes using auxiliary attribute have been suggested. The mean squared errors of the proposed estimators were derived up to first order approximation using Taylor series approach. Numerical illustrations with two populations were conducted and the results revealed that the proposed estimator is more efficient.