Magneto-Mechanical Enhancement of Elastic Moduli in Magnetoactive Elastomers with Anisotropic Microstructures

Magnetoactive elastomers (MAEs) have gained significant attention in recent years due to their wide range of engineering applications. This paper investigates the important interplay between the particle microstructure and the sample shape of MAEs. A simple analytical expression is derived based on geometrical arguments to describe the particle distribution inside MAEs. In particular, smeared microstructures are considered instead of a discrete particle distribution. As a consequence of considering structured particle arrangements, the elastic free energy is anisotropic. It is formulated with the help of the rule of mixtures. We show that the enhancement of elastic moduli arises not only from the induced dipole–dipole interactions in the presence of an external magnetic field but also considerably from the change in the particle microstructure.

Parametric Analysis of the Edge Capacitance of Uniform Slots and Application to Frequency-Variation Permittivity Sensors

This paper presents a parametric analysis relative to the effects of the dielectric constant of the substrate, substrate thickness and slot width on the edge capacitance of a slot-based resonator. The interest is to find the conditions (ranges of the previously cited parameters) compatible with the presence of a quasi-magnetic wall in the plane of the slot (or plane of the metallization). If such magnetic wall is present (or roughly present), the electric field in the plane of the slot is tangential (or quasi-tangential) to it and the edge capacitance can be considered to be the parallel combination of the capacitances at both sides of the slot. Moreover, variations in one of such capacitances, e.g., caused by a change in the material on top of the slot, or by a modification of the dielectric constant of the substrate do not affect the opposite capacitance. Under the magnetic wall approximation, the capacitance of certain electrically small slot-based resonators can be easily linked to the dielectric constant of the material present on top of it. The consequence is that such resonators can be used as sensing elements in a permittivity sensor and the dielectric constant of the so-called material under test (MUT) can be determined from the measured resonance frequency and a simple analytical expression. In this paper, the results of this parametric analysis are validated by considering several sensing structures based on dumbbell defect ground structure (DB-DGS) resonators of different dimensions.

A New Type of Shape-Invariant Beams with Structured Coherence: Laguerre-Christoffel-Darboux Beams

A new class of sources presenting structured coherence properties is introduced and analyzed. They are obtained as the incoherent superposition of coherent Laguerre-Gaussian modes with suitable coefficients. This ensures that the shape of the intensity profile and the spatial coherence features of the propagated beams are invariant during paraxial approximation. A simple analytical expression is obtained for the cross-spectral density of the sources of this class, regardless of the number of superposed modes. Properties of these sources are analyzed and described by several examples.

An Approximate Analytical Solution Of Nonlinear Equations In N-Aminopiperidine Synthesis: New Approach Of Homotopy Perturbation Method)

the synthesis of N-aminopiperidine (NAPP) using hydroxylamine-O-sulfonic acid (HOSA) is based on system of nonlinear rate equations. The new approach to homotopy perturbation method is applied to solve the nonlinear equations. A simple analytical expression for concentrations of hydroxylamine-O-sulfonique acid (HOSA), piperidine (PP), N-aminopiperidine (NAPP), sodium hydroxide (NaOH) and diazene (N2H2) along with NAPP yield is obtained and is compared with numerical result. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation. The obtained analytical result of NAPP yield is compared with the experimental results. The influence of reagents ratio p and rate constants ratio r on yield has been discussed.

Quantifying Face Mask Comfort

Face mask usage is one of the most effective ways to limit SARS-CoV-2 transmission, but a mask is only useful if user compliance is high. Through anonymous surveys, we show that mask discomfort is the primary source of noncompliance in mask wearing. Further, through these surveys, we identify three critical parameters that dictate mask comfort: air resistance, water vapor permeability, and face temperature change. To validate these parameters in a physiological context, we performed experiments to measure the respiratory rate and change in face temperature while wearing different types of commonly used masks. Finally, using values of these parameters from experiments and the literature, and surveys asking users to rate the comfort of various masks, three machine learning algorithms were trained and tested to generate overall comfort scores for those masks. Although all three models tested performed with an accuracy of approximately 70%, the multiple linear regression model also provides a simple analytical expression to predict the comfort scores for any face mask provided the input parameters. As face mask usage is crucial during the COVID-19 pandemic, the ability of this quantitative framework to predict mask comfort is likely to improve user experience and prevent discomfort-induced noncompliance.

A Modeling Approach for Predicting the Resolution Capability in Terrestrial Laser Scanning

The minimum size of objects or geometrical features that can be distinguished within a laser scanning point cloud is called the resolution capability (RC). Herein, we develop a simple analytical expression for predicting the RC in angular direction for phase-based laser scanners. We start from a numerical approximation of the mixed-pixel bias which occurs when the laser beam simultaneously hits surfaces at grossly different distances. In correspondence with previous literature, we view the RC as the minimum angular distance between points on the foreground and points on the background which are not (severely) affected by a mixed-pixel bias. We use an elliptical Gaussian beam for quantifying the effect. We show that the surface reflectivities and the distance step between foreground and background have generally little impact. Subsequently, we derive an approximation of the RC and extend it to include the selected scanning resolution, that is, angular increment. We verify our model by comparison to the resolution capabilities empirically determined by others. Our model requires parameters that can be taken from the data sheet of the scanner or approximated using a simple experiment. We describe this experiment herein and provide the required software on GitHub. Our approach is thus easily accessible, enables the prediction of the resolution capability with little effort and supports assessing the suitability of a specific scanner or of specific scanning parameters for a given application.

Dynamical taxonomy of the coupled solar radiation pressure and oblateness problem and analytical deorbiting configurations

Recent works demonstrated that the dynamics caused by the planetary oblateness coupled with the solar radiation pressure can be described through a model based on singly averaged equations of motion. The coupled perturbations affect the evolution of the eccentricity, inclination and orientation of the orbit with respect to the Sun–Earth line. Resonant interactions lead to non-trivial orbital evolution that can be exploited in mission design. Moreover, the dynamics in the vicinity of each resonance can be analytically described by a resonant model that provides the location of the central and hyperbolic invariant manifolds which drive the phase space evolution. The classical tools of the dynamical systems theory can be applied to perform a preliminary mission analysis for practical applications. On this basis, in this work we provide a detailed derivation of the resonant dynamics, also in non-singular variables, and discuss its properties, by studying the main bifurcation phenomena associated with each resonance. Last, the analytical model will provide a simple analytical expression to obtain the area-to-mass ratio required for a satellite to deorbit from a given altitude in a feasible timescale.

Some New Facts about the Unit-Rayleigh Distribution with Applications

The unit-Rayleigh distribution is a one-parameter distribution with support on the unit interval. It is defined as the so-called unit-Weibull distribution with a shape parameter equal to two. As a particular case among others, it seems that it has not been given special attention. This paper shows that the unit-Rayleigh distribution is much more interesting than it might at first glance, revealing closed-form expressions of important functions, and new desirable properties for application purposes. More precisely, on the theoretical level, we contribute to the following aspects: (i) we bring new characteristics on the form analysis of its main probabilistic and reliability functions, and show that the possible mode has a simple analytical expression, (ii) we prove new stochastic ordering results, (iii) we expose closed-form expressions of the incomplete and probability weighted moments at the basis of various probability functions and measures, (iv) we investigate distributional properties of the order statistics, (v) we show that the reliability coefficient can have a simple ratio expression, (vi) we provide a tractable expansion for the Tsallis entropy and (vii) we propose some bivariate unit-Rayleigh distributions. On a practical level, we show that the maximum likelihood estimate has a quite simple closed-form. Three data sets are analyzed and adjusted, revealing that the unit-Rayleigh distribution can be a better alternative to standard one-parameter unit distributions, such as the one-parameter Kumaraswamy, Topp–Leone, one-parameter beta, power and transmuted distributions.

The Application of the Integral Momentum Balance on the Pressure Drop of a Sudden Contraction

A new approach based on the momentum balance to calculate the pressure drop in turbulent flow through sharp-edged axisymmetric sudden contractions is presented. The momentum balance needs the velocity as well as the pressure distributions on the boundaries of the control volume. These distributions are obtained by a series of numerical simulations with different settings for the discharge, as well as the contraction ratio. The numerical model itself is validated by the comparison of the simulated and measured pressure drops in a laboratory experiment at different positions. To get easily applicable hydraulic formulations for the pressure drop depending on the discharge and the contraction ratio, the missing momentum and pressure coefficients are determined from the simulated velocity and pressure distributions. Only the pressure coefficient shows a dependency on the contraction ratio. After fitting the dependency by a simple analytical expression, a new formulation for the hydraulics of a sharp-edged sudden contraction based solely on momentum balance was obtained. The comparison with own experimental results as well as the classical parameterization of Idelchik show in both cases very good agreement.

Localization by an external magnetic field of electrons on the ions of hydrogen-like donors in non-degenerate semiconductors

In the quasi-classical approximation of quantum mechanics a model for the localization of conduction electrons on the ions of hydrogen-like donors in an external magnetic field was developed. The thermal ionization energy of donors in lightly doped and moderately compensated crystals of gallium arsenide and indium antimonide of n-type was calculated depending on the induction of the external magnetic field. In contrast to the known theoretical works (which use variational methods for solving the Schrödinger equation), a simple analytical expression is proposed for the ionization energy of the donor in the magnetic field, which quantitatively agrees with the known experimental data. It is shown that the magnitude of the magnetic field induced by the orbital motion of the electron around the ion core of the donor is negligible compared to the external field and does not contribute to the ionization energy of donors.