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.

Frequency-Domain Identification of Radiation Forces for Floating Wind Turbines by Moment-Matching

The dynamics of a floating structure can be expressed in terms of Cummins’ equation, which is an integro-differential equation of the convolution class. In particular, this convolution operator accounts for radiation forces acting on the structure. Considering that the mere existence of this operator is highly inconvenient due to its excessive computational cost, it is commonly replaced by an approximating parametric model. Recently, the Finite Order Approximation by Moment-Matching (FOAMM) toolbox has been developed within the wave energy literature, allowing for an efficient parameterisation of this radiation force convolution term, in terms of a state-space representation. Unlike other parameterisation strategies, FOAMM is based on an interpolation approach, where the user can select a set of interpolation frequencies where the steady-state response of the obtained parametric representation exactly matches the behaviour of the target system. This paper illustrates the application of FOAMM to a UMaine semi-submersible-like floating structure.

Drift-Free Integration in Inductive Magnetic Field Measurements Achieved by Kalman Filtering

Sensing coils are inductive sensors commonly used to measure magnetic fields, such as those generated by electromagnets used in many kinds of industrial and scientific applications. Inductive sensors rely on integrating the output voltage at the coil’s terminals in order to obtain flux linkage, which may suffer from the magnification of low-frequency noise resulting in a drifting integrated signal. This article presents a method for the cancellation of integrator drift. The method is based on a first-order linear Kalman filter combining the data from the coil and a second sensor. Two case studies are presented. In the first one, the second sensor is a Hall probe, which senses the magnetic field directly. In a second case study, the magnet’s excitation current was used instead to provide a first-order approximation of the field. Experimental tests show that both approaches can reduce the measured field drift by three orders of magnitude. The Hall probe option guarantees, in addition, one order of magnitude better absolute accuracy than by using the excitation current.

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.

Sensitivity analysis of Wasserstein distributionally robust optimization problems

We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first-order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide an explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least-squares regression. We consider robustness of call option pricing and deduce a new Black–Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.

Environmental and anthropogenic gravity contributions at the Þeistareykir geothermal field, North Iceland

Continuous high-resolution gravimetry is increasingly used to monitor mass distribution changes in volcanic, hydrothermal or other complex geosystems. To quantify the often small target signals, gravity contributions from, e.g. atmospheric mass changes, global and local hydrology should be accounted for. We set up three iGrav superconducting gravity meters for continuous monitoring of the Þeistareykir geothermal field in North Island. Additionally, we installed a set of hydrometeorological sensors at each station for continuous observation of local pressure changes, soil moisture, snow and vertical surface displacement. We show that the contribution of these environmental parameters to the gravity signal does not exceed 10 µGal (1 µGal = 10–8 m s−2), mainly resulting from vertical displacement and snow accumulation. The seasonal gravity contributions (global atmosphere, local and global hydrology) are in the order of ± 2 µGal at each station. Using the environmental observations together with standard gravity corrections for instrumental drift and tidal effects, we comprehensively reduced the iGrav time-series. The gravity residuals were compared to groundwater level changes and geothermal mass flow rates (extraction and injection) of the Þeistareykir power plant. The direct response of the groundwater levels and a time-delayed response of the gravity signal to changes in extraction and injection suggest that the geothermal system is subject to a partially confined aquifer. Our observations indicate that a sustainable “equilibrium” state of the reservoir is reached at extraction flow rates below 240 kg s−1 and injection flow rates below 160 kg s−1. For a first-order approximation of the gravity contributions from extracted and injected masses, we applied a simplified forward gravity model. Comparison to the observed gravity signals suggest that most of the reinjected fluid is drained off through the nearby fracture system.

Recent developments on the realization of fractance device

A detailed analysis of the recent developments on the realization of fractance device is presented. A fractance device which is used to exhibit fractional order impedance properties finds applications in many branches of science and engineering. Realization of fractance device is a challenging job for the people working in this area. A term fractional order element, constant phase element, fractor, fractance, fractional order differintegrator, fractional order differentiator can be used interchangeably. In general, a fractance device can be realized in two ways. One is using rational approximations and the other is using capacitor physical realization principle. In this paper, an attempt is made to summarize the recent developments on the realization of fractance device. The various mathematical approximations are studied and a comparative analysis is also performed using MATLAB. Fourth order approximation is selected for the realization. The passive and active networks synthesized are simulated using TINA software. Various physical realizations of fractance device, their advantages and disadvantages are mentioned. Experimental results coincide with simulated results.