Instantaneous Rotation Research Articles

Quasi-periodicity of Supermassive Binary Black Hole Accretion Approaching Merger

Abstract In this paper we continue the first ever study of magnetized mini-disks coupled to circumbinary accretion in a supermassive binary black hole (SMBBH) approaching merger reported in Bowen et al. We extend this simulation from 3 to 12 binary orbital periods. We find that relativistic SMBBH accretion acts as a resonant cavity, where quasi-periodic oscillations tied to the frequency at which the black hole’s (BH’s) orbital phase matches a nonlinear m = 1 density feature, or “lump,” in the circumbinary accretion disk permeate the system. The rate of mass accretion onto each of the mini-disks around the BHs is modulated at the beat frequency between the binary frequency and the lump’s mean orbital frequency, i.e., , while the total mass accretion rate of this equal-mass binary is modulated at two different frequencies, and . The instantaneous rotation rate of the lump itself is also modulated at two frequencies close to the modulation frequencies of the total accretion rate, and . Because of the compact nature of the mini-disks in SMBBHs approaching merger, the inflow times within the mini-disks are comparable to the period on which their mass supply varies, so that their masses—and the accretion rates they supply to their BHs—are strongly modulated at the same frequency. In essence, the azimuthal symmetry of the circumbinary disk is broken by the dynamics of orbits near a binary, and this m = 1 asymmetry then drives quasi-periodic variation throughout the system, including both accretion and disk-feeding. In SMBBHs approaching merger, such time variability could introduce distinctive, increasingly rapid, fluctuations in their electromagnetic emission.

Autonomous Vehicles: Autodriver Algorithm and Vehicle Dynamics

A given road can be expressed mathematically in a global (or world) coordinate frame. Following the road can be substituted by following the loci of its curvature center and turning at the right circle of curvature. Considering that a vehicle in motion is always in turn about an instantaneous rotation center relative to the ground, an autonomous vehicle capable of following a given path by coinciding the rotation center of vehicle at every moment on the curvature center of the road could be designed. The dynamic reactions of the vehicle influence its path of motion and make its rotation center to depart from the desired path of the curvature center of the road. In this study, the Autodriver algorithm control strategy to front-wheel-steering vehicles has been developed and a control loop is introduced to compensate the present errors generated by the differences of the desired locating on the road and the real position of the vehicle.

Research Concerning the Correlations Between Some Experimental Results in the Case of a Sucker Rod Pumping Installation

In the paper are analyzed the correlations between the experimental results obtained for the instantaneous rotation speed of the cranks shaft of a conventional sucker rod pumping installation and the speed and the acceleration at the end of the polished rod. The correlations have been established by analyzing the kinematics of the mechanism of the sucker rod pumping unit. The experimental records have been processed with the program Total Well Management. A computer program for performing the simulations has been developed by the authors using Maple programming environment.

A novel application of pulse width modulation technique on hydroxy gas production

Software and hardware advancements on a hydroxy gas (HHO) production system is presented in this experimental study. A unique control system that enables to generate hydroxy gas at the specified volumetric flow rates with pulse width modulation (PWM) technique is developed and manufactured. The novelty of the method is automatic control of the hydroxy production according to the instantaneous demand, in other words, the adaptation of the HHO system to the operating principles of internal combustion engines (ICEs). A stepping motor represented the vehicle engine in order to get variable rotational speed values. The instantaneous rotation speed range of the motor divided into four sections as no rotation, low (1000–2001 rpm), middle (2001–4001 rpm) and high (>4001 rpm). A computer-driven microcontroller (MCU) card managed the entire system. The MCU card received motor speed input parameters and identified the PWM signal. Results of the study which are the electrical current, hydroxy gas flow and dry cell temperature ranges are presented in tables and graphs. The measured experimental data were 0–15 A, 0–1.56 L per minute and 24–48 °C for electrical current, hydroxy gas production and dry cell temperature ranges, respectively.

Author Correction: Atmospheric mountain wave generation on Venus and its influence on the solid planet’s rotation rate

In the version of this Article originally published, a statement regarding past measurements of the length of day and rotation rate of Venus was potentially misleading. The original statement has now been replaced in the online versions of this Article, to acknowledge that neither Magellan nor Venus Express measured an instantaneous rotation rate.

Mechanical Design and Control Strategy for Hip Joint Power Assisting.

The basic requirements for mechanical design and control strategy are adapting to human joint movements and building an interaction model between human and robot. In this paper, a 3-UPS parallel mechanism is adopted to realize that the instantaneous rotation center of the assistive system coincides with human joint movement center, and a force sensory system is used to detect human movement intention and build the modeling of control strategy based on the interactive force. Then, based on the constructed experimental platform, the feasibility of movement intention detection and power assisting are verified through the experimental results.

Use of the correlated EEMD and time-spectral kurtosis for bearing defect detection under large speed variation

Vibration-based diagnosis is in common use for the health monitoring of rolling element bearing (REB). This paper is concerned with a new defect detection method of the REB under large speed variation by using the correlated ensemble empirical mode decomposition (EEMD) and time-spectral kurtosis (TSK), which are accomplished in two phases. During the first phase, vibration signals are decomposed into intrinsic mode functions (IMFs) with the EEMD, which are then correlated with the original signal in order to determine the shaft IMFs, and hence the distinct instantaneous rotation frequencies (IRFs). During the second phase, the TSK is adopted to determine the fault IMFs, which are further used to reconstruct the fault signal. As a result, the non-stationary signal in the time domain is transformed into the cyclostationary signal in the angular domain with respect to the IRFs by resampling with equal angle increments. Simulations and experiments are carried out to validate the feasibility of the proposed method. It is shown that proposed method offers a potential improvement over the conventional short time Fourier transform and order tracking-based method.

CUSP-SINGULARITY OF THE TRAJECTORY OF THE QUBIT’S BLOCH VECTOR UNDER AN EXTERNAL PERIODIC LIGHT FIELD

The quantum dynamics of a two-level quantum-mechanical system subjected to the external monochromatic action beyond the rotating wave approximation was investigated. It was shown that under the condition of exact resonance on the trajectories of the Bloch vectors, special points are manifested under different initial conditions. These points are classified as cusps singularities. It is revealed that at such points, the instantaneous rotation axis, relative to which the Bloch vector rotates, reverses its direction. There is a movement stop. For a nonzero frequency detuning, the cusp singularities vanish. A numerical analysis of the singularities of the trajectories of the Bloch vector without rotating wave approximation was supplemented by a study based on the use of the Floquet methods. Within the framework of this approach, recurrence relations for the spectral components of the probability amplitudes were obtained and analyzed. An analytic expression was found for the two values of quasi-energies within a fourth order of magnitude in the interaction energy. It was shown that to obtain a singular behavior of the trajectories of the Bloch vector, it is sufficient to confine by four spectral harmonics in the Floquet expansion. The results obtained are important for achieving the accuracy when performing coherent transformations with two-level systems in the cases where the rotating wave approximation is inapplicable.

Monitoring of Bridges by a Laser Pointer: Dynamic Measurement of Support Rotations and Elastic Line Displacements: Methodology and First Test.

Deck inclination and vertical displacements are among the most important technical parameters to evaluate the health status of a bridge and to verify its bearing capacity. Several methods, both conventional and innovative, are used for structural rotations and displacement monitoring; however, none of these allow, at the same time, precision, automation, static and dynamic monitoring without using high cost instrumentation. The proposed system uses a common laser pointer and image processing. The elastic line inclination is measured by analyzing the single frames of an HD video of the laser beam imprint projected on a flat target. For the image processing, a code was developed in Matlab® that provides instantaneous rotation and displacement of a bridge, charged by a mobile load. An important feature is the synchronization of the load positioning, obtained by a GNSS receiver or by a video. After the calibration procedures, a test was carried out during the movements of a heavy truck maneuvering on a bridge. Data acquisition synchronization allowed us to relate the position of the truck on the deck to inclination and displacements. The inclination of the elastic line at the support was obtained with a precision of 0.01 mrad. The results demonstrate the suitability of the method for dynamic load tests, and the control and monitoring of bridges.

Conditional reliability of bulk carriers damaged by ship collisions

Time-variant reliability analysis of a bulk carrier in damage conditions, after a collision event, is performed by Monte Carlo simulation. Two different collision models are applied, the former based on the deterministic format actually embodied in the Harmonized Common Structural Rules for Oil Tankers and Bulk Carriers, the latter based on a probabilistic format, derived by the recently developed GOALDS database statistics for collision and grounding events. A modified incremental-iterative method is applied, to account for instantaneous neutral axis rotation, due to asymmetrically damaged cross-sections, as for collision events. Time-variant residual strength statistical properties are preliminarily determined by Monte Carlo simulation, up to 25-year ship lifetime, accounting for corrosion wastages of all structural members contributing to hull girder strength, welding residual stresses and material properties randomness. Finally, time-variant reliability analysis is performed, to investigate the incidence of the applied collision damage models on hull girder annual failure probabilities in sagging and hogging conditions. Reliability analysis is performed for the Capesize single side bulk carrier, benchmarked in the 2012 ISSC report and assumed as reference ship in current analysis. Obtained results are fully investigated and discussed.

Motion decomposition, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling

Widespread approaches to generalizing geometrically linear constitutive relations to the case of large displacement gradients have been considered. These approaches are based on the replacement of the material derivatives of stress and strain tensors by frame-indifferent corotational or convective derivatives. The correctness of choosing the indifferent derivatives is analyzed from a more general viewpoint of motion decomposition into rigid and strain-induced motion. It is shown that the use of the Zaremba-Jaumann derivative in constitutive relations corresponds to motion decomposition by the Cauchy-Helmholtz theorem according to which instantaneous rigid rotation of a material particle with small neighborhood is described by the vorticity tensor. The relations derived with the use of the so-called "logarithmic spin" are analyzed. It is noted that the spin tensors entering into these relations are not associated with the material fibers (in particular with the symmetry axes of anisotropic materials) during the entire studied process of deformation. Hence these spins do not describe the rotation of the reference frame (crystallographic one for metals) in which the material property tensor is defined. A new method of motion decomposition is proposed on the basis of a two-level (macro and meso) approach for single and polycrystalline metals. The mesoscopic spin is determined by the rotation rate of the corotational coordinate system associated with the crystallographic direction and crystallographic plane. Mesoscopic constitutive relations are formulated using the proposed spin. The spin of a representative macrovolume is determined by averaging the spins of the crystallites contained in this volume. This spin is used to formulate rate-type elastic constitutive equations. Examples are given to illustrate the stress state determination for loading along closed strain paths and two-segment paths for isotropic and anisotropic (with cubic symmetry, hcp) elastic materials, and an elastoviscoplastic fcc crystallite. The determination is carried out by using the corotational derivatives in the constitutive relations which are obtained by different motion decomposition methods.

Frequency dependence of susceptibility in magnets with uniaxial and triaxial anisotropy

AbstractCharacterization of minerals in rocks and soils provides a window into environmental processes and improves the interpretation of paleomagnetic measurements. Mineral composition, size, and shape can be constrained using magnetic measurements. For small minerals, a promising measurement is the frequency dependence of magnetic susceptibility. The size and shape dependence of the in‐phase componentand out‐of‐phase componentare derived for arbitrarily oriented superparamagnetic and single‐domain magnets with uniaxial and triaxial anisotropy. In a fluctuating field, a single magnet has a thermal response parallel to the easy axis and instantaneous rotation of the moment perpendicular to it. The size and temperature variations have the same form as in earlier theories in which all the magnets are aligned with the field and can be easily adapted to the methods of Shcherbakov and Fabian (2005) and Egli (2009) for finding size distributions using multiple temperatures and frequencies. These inversions are inherently nonunique and complicated by non‐SD contributions, but some robust constraints can be put on the volume distribution if the commonly used ratioχfdis 10% or greater. The anisotropy of the out‐of‐phase component (opAMS) has the same sense as thermoremanent magnetization (TRM) and can be used to correct the paleofield direction. Along with the anisotropy of the in‐phase component (ipAMS), it can be used to gain quantitative information on the deformation of the host rock. For the line/plane, or March, deformation model, opAMS and ipAMS are calculated and it is shown how they can be used to accurately represent the strain anisotropy.

Predicting intragranular misorientation distributions in polycrystalline metals using the viscoplastic self-consistent formulation

In a recent paper, we reported the methodology to calculate intragranular fluctuations in the instantaneous lattice rotation rates in polycrystalline materials within the mean-field viscoplastic self-consistent (VPSC) model. This paper is concerned with the time integration and subsequent use of these fluctuations to predict orientation-dependent misorientation distributions developing inside each grain representing the polycrystalline aggregate. To this end, we propose and assess two approaches to update the intragranular misorientation distribution within the VPSC framework. To illustrate both approaches, we calculate intragranular misorientations in face-centered cubic polycrystals deformed in tension and plane-strain compression. These predictions are tested by comparison with corresponding experiments for polycrystalline copper and aluminum, respectively, and with full-field calculations. It is observed that at sufficiently high strains some grains develop large misorientations that may lead to grain fragmentation and/or act as driving forces for recrystallization. The proposed VPSC-based prediction of intragranular misorientations enables modeling of grain fragmentation, as well as a more accurate modeling of texture using a computationally efficient mean-field approach, as opposed to computationally more expensive full-field approaches.

Microwave Encoders for Chipless RFID and Angular Velocity Sensors Based on S-Shaped Split Ring Resonators

In this paper, it is demonstrated that a chain of S-shaped split ring resonators (S-SRRs) etched on a dielectric substrate can modulate the amplitude of a carrier signal injected to a transmission line (a coplanar waveguide (CPW). To this end, the S-SRR chain must be transversally displaced above the CPW, in close proximity to it. By this means, the transmission coefficient of the line is modulated by the time-varying electromagnetic (inductive) coupling between the line and the S-SRRs of the chain, related to their relative motion. Based on this principle, two different applications can be envisaged: 1) angular velocity sensors and 2) near-field chipless radiofrequency identification (chipless-RFID) tags. In the former application, the S-SRR chain is circularly shaped and the S-SRRs are distributed uniformly along the perimeter of the rotor, at equidistant positions. By this means, the amplitude-modulated signal generated by rotor motion exhibits envelope peaks, whose distance is related to the angular velocity of the rotor. In the use of S-SRRs as microwave encoders for chipless RFID tags, not all the S-SRRs of the chain are present. Their presence or absence at the predefined (equidistant) positions is related to the logic state “1” or “0.” Tag reading is sequential, and it is achieved through tag motion (at constant velocity) above the reader, a CPW transmission line fed by a carrier signal. The ID code is contained in the envelope function of the resulting amplitude modulated signal, which can be obtained by means of an envelope detector. With the proposed approach, a high number of pulses in angular velocity sensors can be achieved (with direct impact on angle resolution and sensitivity to changes in instantaneous rotation speed). Moreover, chipless-RFID tags with unprecedented number of bits can be obtained. The proposed angular velocity sensors can be useful in space environments, whereas the chipless-RFID systems based on the proposed tags are useful in applications where reading range can be sacrificed in favor of high data capacity (large number of bits), e.g., security and authentication.

Condition monitoring of rotating machinery under varying operating conditions based on Cyclo-Non-Stationary Indicators and a multi-order probabilistic approach for Instantaneous Angular Speed tracking

During the last decades, an emerging interest has been reported on modelling rotating machinery signals as cyclostationary. Several tools, such as the Spectral Correlation Density (SCD) and the Cyclic Modulation Spectrum (CMS) have been proposed, assuming constant or almost constant rotating speed. To overcome this limitation, generalizations of SCD and CMS have been proposed that display cyclic Order versus Frequency. On the other hand the estimation of the instantaneous angular speed of the rotating machine is a crucial issue that has to be tackled before any analysis or diagnosis of the machine operating under non-stationary conditions. This operation is generally carried out thanks to a tachometer, or an angle encoder, but in some cases this information can be missing for different reasons. The goal of this paper is to combine a novel approach for the analysis of cyclo-non-stationary signals based on the generalization of the indicators of cyclostationarity in order to cover the speed varying conditions, introducing a new speed-dependent angle averaging operator, with a new speed estimation method, that extracts from a vibration signal the most probable instantaneous rotation frequency without focusing on one specific order based on the a priori knowledge of the kinematics of the machine. The effectiveness of the ensemble method is evaluated on an acceleration signal captured at the wind turbine gearbox operating under speed varying conditions.

Liquid-liquid extraction intensification by micro-droplet rotation in a hydrocyclone

The previous literature reports that using a hydrocyclone as an extractor intensifies the mass transfer and largely reduces the consumption of extractant from 1800–2000 kg h−1 to 30–90 kg h−1. However, the intensification mechanism has not been clear. This paper presents experimental and numerical methods to study the multi-scale motion of particles in hydrocyclones. In addition to the usually considered translational behavior, the high-speed rotation of dispersed micro-spheres caused by the anisotropic swirling shear flow is determined. The rotation speeds of the tested micro-spheres are above 1000 rad s−1, which are much larger than the instantaneous rotation speed in isotropic turbulence. Due to the conical structure of a hydrocyclone, the rotation speed maintains stability along the axial direction. Numerical results show that the particle Reynolds number of micro-droplets in a hydrocyclone is equal to that in conventional extractors, but the particles have high rotation speeds of up to 10,000 rad s−1 and long mixing lengths of more than 1000 mm. Both the rotation of micro-droplets along the spiral trajectories and the intense eddy diffusion in a hydrocyclone contribute to the extraction intensification.

Analysis of the perturbed Chandler wobble of the Earth pole

Based on the model of a viscoelastic rigid body for the deformable Earth, we investigate the behavior of the main component of the perturbed Earth pole oscillation process, the Chandler wobble. An amplitude- frequency analysis of the perturbed Chandler wobble of the Earth pole due to the precessional motion of the lunar orbit is provided. The parameters of the complex dynamical process that describes the mutual orientation of the Earth’s instantaneous rotation axis, the axis of its figure, and its angular momentum vector are studied qualitatively. Using a numerical-analytical approach, we consider the possibilities for identifying the Chandler wobble parameters and fitting the developed refined theoretical model to the real trajectory measurements of the Earth pole.

Axial Uplift Behavior of Belled Piers in Sloping Ground

Belled piers are frequently utilized for self-supporting transmission line towers, and the uplift loading is normally the controlling design load. However, belled piers placed in sloping ground have less uplift resistance than the same foundations built on flat ground. This study elucidates the uplift behavior of axially uplift-loaded belled piers in sloping ground. Two full-scale belled piers were constructed in a loess slope having an inclination of 20° with the horizontal, and pullout load testing was conducted for each belled pier. Both the site conditions and the load tests were documented comprehensively. The uplift load versus vertical shaft-head displacement curve of the belled piers in sloping ground exhibited an initial linear region, a curvilinear transition, and a final linear region, which is similar to that of a typical uplift or compression load–displacement curve for level ground. However, the shaft-head displacement at the lower sloping side was larger than that at the upper sloping side. Therefore, the shaft head rotated in the uplift loading direction, and the instantaneous rotation angle increased with the applied load. Unlike the level ground case, the uplift failure of the belled piers in sloping ground initiated from the edge of the bell at the lower sloping side and propagated into the slope surface as the soils deformed and pushed laterally toward the lower sloping side. The failure cracks on the ground surface were not symmetric and developed mainly on the lower sloping side. A comparison of the elastic limit load and the interpreted failure load of the two belled piers revealed that additional embedment of the foundation in sloping ground can achieve an increase in uplift resistance to match the level ground uplift capacity.

Determining elliptical polarization of light from rotation of calcite crystals.

This paper demonstrates the non-uniform circular rotation of calcite crystals in an elliptically polarized laser mode. Birefringent calcite crystals respond in predictable ways to polarization. A laser mode with high ellipticity (approaching circular polarization) causes a calcite crystal to rotate at a higher rate than that with a low ellipticity (approaching linear polarization). The polarization orientation of the laser mode also directly affects the instantaneous crystal rotation. We place calcite crystals in a trapping region, and observe their behavior under different polarization modes. Measurements of rotation rates, orientation, and motion of calcite crystals are made by synchronizing information from video images and a quadrant photodiode. These measurements are then compared with predicted values.

Diesel engine torsional vibration control coupling with speed control system

The coupling problems between shafting torsional vibration and speed control system of diesel engine are very common. Neglecting the coupling problems sometimes lead to serious oscillation and vibration during the operation of engines. For example, during the propulsion shafting operation of a diesel engine, the oscillation of engine speed and the severe vibration of gear box occur which cause the engine is unable to operate. To find the cause of the malfunctions, a simulation model coupling the speed control system with the torsional vibration of deformable shafting is proposed and investigated. In the coupling model, the shafting is simplified to be a deformable one which consists of several inertias and shaft sections and with characteristics of torsional vibration. The results of instantaneous rotation speed from this proposed model agree with the test results very well and are successful in reflecting the real oscillation state of the engine operation. Furthermore, using the proposed model, the speed control parameters can be tuned up to predict the diesel engine a stable and safe running. The results from the tests on the diesel engine with a set of tuned control parameters are consistent with the simulation results very well.