A 3D Multidirectional Piezoelectric Energy Harvester using Rope-Driven Mechanism for Low Frequency and Ultralow Intensity Vibration Environment

Though numerous piezoelectric vibration energy harvesters (PVEHs) have been designed and investigated to provide power supply for wireless sensors or wearable devices, it remains a challenge for traditional PVEHs to work effectively in an environment of low frequency, low acceleration and multidirectional vibrations. This work presents a PVEH using a low-frequency energy-capturing resonant system formed by a rolling ball in a hemispherical shell and driven by a rope. Due to the symmetry of the sphere, the ball can be excited at multiple directions in 3D space, and the piezoelectric beam can be pulled by the ball through a rope in multiple directions. Thus, the efficient multidirectional energy harvesting under low frequency (< 10 Hz) and ultralow intensity (< 0.1 g) vibrations could be realized. A mass-spring-damper equivalent model was built to understand the operation mechanism of the proposed PVEH. The results show that the proposed PVEH has a potential to collect energy in any direction in 3D space, and could achieve a good angle bandwidth with 360° for φ and 240° for β under the excitation of a = 0.04 g, f = 6.8 Hz with the acceleration defined in the spherical coordinate system. The developed PVEH can generate 6.5 μW under a low-intensity excitation (0.03 g), and the normalized power density can reach 22.63 μW/(cm3g2Hz). Moreover, the minimum start-up acceleration analysis of the proposed PVEH indicates that the PVEH can capture multidirectional energy from vibrations as low as 0.01 g. In addition, both simulation and experimental study on rope redundancy and ball mass show that they can be used to adjust the device performance easily without structure re-fabrication. Overall, this study demonstrates a new mechanism that could effectively harvest low frequency, ultralow intensity and multidirectional vibration

Three-Dimensional Modeling and Control of a Tethered UAV-Buoy System

This work presents the nonlinear dynamical model and motion controller of a system consisting of an unmanned aerial vehicle (UAV) that is tethered to a floating buoy in the three-dimensional (3D) space. Detailed models of the UAV, buoy, and the coupled tethered system dynamics are presented in a marine environment that includes surface-water currents and oscillating gravity waves, in addition to wind gusts. This work extends the previously modeled planar (vertical) motion of this novel robotic system to allow its free motion in all three dimensions. Furthermore, a Directional Surge Velocity Control System (DSVCS) is hereby proposed to allow both the free movement of the UAV around the buoy when the cable is slack, and the manipulation of the buoy’s surge velocity when the cable is taut. Using a spherical coordinate system centered at the buoy, the control system commands the UAV to apply forces on the buoy at specific azimuth and elevation angles via the tether, which yields a more appropriate realization of the control problem as compared to the Cartesian coordinates where the traditional x- , y- , and z -coordinates do not intuitively describe the tether’s tension and orientation. The proposed robotic system and controller offer a new method of interaction and collaboration between UAVs and marine systems from a locomotion perspective. The system is validated in a virtual high-fidelity simulation environment, which was specifically developed for this purpose, while considering various settings and wave scenarios.

Generating accurate 3D gaze vectors using synchronized eye tracking and motion capture

Assessing gaze behaviour during real-world tasks is difficult; dynamic bodies moving through dynamic worlds make finding gaze fixations challenging. Current approaches involve laborious coding of pupil positions overlaid on video. One solution is to combine eye tracking with motion tracking to generate 3D gaze vectors. When combined with tracked or known object locations, fixation detection can be automated. Here we use combined eye and motion tracking and explore how linear regression models generate accurate 3D gaze vectors. We compare spatial accuracy of models derived from four short calibration routines across three data types: the performance of calibration routines were assessed using calibration data, a validation task that demands short fixations on task-relevant locations, and an object interaction task we used to bridge the gap between laboratory and "in the wild" studies. Further, we generated and compared models using spherical and cartesian coordinate systems and monocular (Left or Right) or binocular data. Our results suggest that all calibration routines perform similarly, with the best performance (i.e., sub-centimeter errors) coming from the task (i.e., the most "natural") trials when the participant is looking at an object in front of them. Further, we found that spherical coordinate systems generate more accurate gaze vectors with no differences in accuracy when using monocular or binocular data. Overall, we recommend recording one-minute calibration datasets, using a binocular eye tracking headset (for redundancy), a spherical coordinate system when depth is not considered, and ensuring data quality (i.e., tracker positioning) is high when recording datasets.

Fluid Flow in Composite Regions Past a Solid Sphere

A steady, 2-D, incompressible, viscous fluid flow past a stationary solid sphere of radius 'a' has been considered. The flow of fluid occurs in 3 regions, namely fluid, porous and fluid regions. The governing equations for fluid flow in the clear and porous regions are Stokes and Brinkman equations, respectively. These governing equations are written in terms of stream function in the spherical coordinate system and solved using the similarity transformation method. The variation in flow patterns by means of streamlines has been analyzed for the obtained exact solution. The nature of the streamlines and the corresponding tangential and normal velocity profiles are observed graphically for the different values of porous parameter 'σ'. From the obtained results, it is noticed that an increase in porous parameters suppresses the fluid flow in the porous region due to less permeability; as a result, the fluid moves away from the solid sphere. It also decreases the velocity of the fluid in the porous region due to the suppression of the fluid as 'σ' increases. Hence the parabolic velocity profile is noticed near the solid sphere.

Quantum-Mechanical Substantiation of the Periodic System of Isotopes. Models of Nuclear Orbitals

The topic of this article lies in the field of problems: substantiating the periodic system of isotopes and the principle of multilevel periodicity using quantum mechanical calculations, combining strong and electromagnetic interactions, and searching for the fundamental cause of periodicity in general. This article is a theoretical section and a continuation of the article: "Periodic system of isotopes", in which the system was checked against 10 types of experimental data, the periodic change of properties at the level of nuclei and the vertical symmetry of subgroups of isotopes were found. Periodic system of isotopes was constructed with the help of a special algorithm, the principle of multilevel periodicity of the atom, from the electrons to the nucleus. As a description of the multilevel periodicity, this paper presents a unified system of quantum numbers, which is used to describe both electron and nucleon shells (binomial probabilistic interpretation). With the binomial interpretation the problem of a particle in a one-dimensional potential well has been solved; quantummechanical calculations for the probability functions of the orbitals and periods of both electrons and nucleons have been performed - characteristic equations have been obtained, the projections of electronic orbitals have been reproduced and the binomial interpretation has been shown to correspond to the family of spherical harmonics. For the electron orbitals the calculation and analysis of solutions of the Schrödinger equation for the binomial interpretation of quantum numbers have been performed. The spatial nature of quantum numbers, for this interpretation, in the form of degrees of freedom is shown. Based on the principle of multilevel periodicity, expressions are derived and planar projections of nucleon nucleon orbitals are constructed, and similarity of the forms with electron orbitals is analyzed and revealed. A critical analysis of the modern spherical coordinate system was made, possible errors in the construction of electron orbitals were shown and, taking into account the drawbacks, two alternative spherical coordinate systems were proposed, for which Lame coefficients were calculated and Laplace equations were derived. As a search for the fundamental cause of multilevel periodicity, a spatial model with changing degrees of freedom 0-n is presented, its manifestation in nature (crystal forms) is found; a number of experiments are proposed; the predictions about the applicability of the multilevel periodicity principle in quark theory are made

Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications.

FDTD analysis of ELF radio wave propagation in the spherical Earth-ionosphere waveguide and its validation based on analytical solutions

The FDTD model of electromagnetic wave propagation in the Earth-ionosphere cavity was developed under assumption of axisymmetric system, solving the reduced Maxwell’s equations in a 2D spherical coordinate system. The model was validated on different conductivity profiles for the electric and magnetic field components for various locations on Earth along the meridian. The characteristic electric and magnetic altitudes, the phase velocity and attenuation rate were calculated. We compared the results of numerical and analytical calculations and found good agreement between them. The undertaken FDTD modeling enables us to analyze the Schumann resonances and the propagation of individual lightning discharges occurring at various distances from the receiver. The developed model is particularly useful when analyzing ELF measurements.

Traces of Anisotropic Quasi-Regular Structure in the SDSS Data

The aim of this study is to search for quasi-periodical structures at moderate cosmological redshifts z ≲ 0.5. We mainly use the SDSS DR7 data on the luminous red galaxies (LRGs)with redshifts 0.16 ≤ z ≤ 0.47. At first, we analyze features (peaks) in the power spectra of radial (shell-like) distributions using separate angular sectors in the sky and calculate the power spectra within each sector. As a result, we found some signs of a large-scale anisotropic quasi-periodic structure detectable through 6 sectors out of a total of 144 sectors. These sectors are distinguished by large amplitudes of dominant peaks in their radial power spectra at wavenumbers k within a narrow interval of 0.05 < k < 0.07 h Mpc−1. Then, passing from a spherical coordinate system to a Cartesian one, we found a special direction such that the total distribution of LRG projections on it contains a significant (≳5σ) quasi-periodical component. We assume that we are dealing with a signature of a quasi-regular structure with a characteristic scale 116 ± 10 h−1 Mpc. Our assumption is confirmed by a preliminary analysis of the SDSS DR12 data.

Quantitative Study of Loess Microstructure At Micrometer Scale Via X-Ray Computed Tomography

The macroscopic properties of loess are significantly controlled by its microstructure. Quantitative analysis of loess microstructure is essential for modeling the microstructure and further incorporating the microstructural effects into geotechnical practice. However, loess has a multi-scale microstructure ranging from nanometer to millimeter scales, and researches at the particle resolution are still inadequate. This study systematically investigates the micrometer-scale microstructure of loess from Jingyang, China, via X-ray computed tomography and the image segmentation method that was explored for loess. The statistical analyses of three-dimensional (3D) microstructure reveal that the particle size follows the Weibull distribution, and the distributions of pore and pore throat sizes obey the gamma distribution. Most particles are blade-shaped, with a peak length ratio of (1.53–1.64):1.28:1. The particles are oriented in the polar directions but not azimuthally, in a spherical coordinate system, exhibiting a transversely isotropic structure. The quantitative microstructures of the loess and paleosol samples were slightly different irrespective of the large aggregates developed in paleosol sample. Moreover, the representative elementary volume obtained through porosity is also applicable for the analysis of microstructural parameters such as size distribution, shape factor, orientation angle, and pore connectivity. Besides, the two-dimensional (2D) distributions of the particle, pore, and pore throat sizes agree with the 3D distributions, except that the former were marginally smaller. However, the 2D sectional analysis of shape, arrangement, and pore connectivity cannot adequately represent the 3D characteristics.