Frame Transformation Research Articles

Competing ionization and dissociation in the H$$_{2}$$ gerade system

A numerically solvable two-dimensional (2D) model, employed by the authors to study the dissociative recombination of H$_2^+$ in the ungerade symmetry [Phys. Rev. A $\mathbf{98}$, 062706 (2018)], is extended to describe the collision process in the gerade symmetry of H$_2$. In this symmetry the ionization and dissociation processes are driven primarily by the direct, curve-crossing mechanism. The model is represented by a set of three coupled electronic channels in 2D, in the space of $s,p,d$ partial waves of the colliding electron. We demonstrate that the Born-Oppenheimer properties of the H$_2$ molecule in the relevant range of internuclear distances can be described by such a model. The molecular rotational degrees of freedom are accounted for by the rotational frame transformation. The numerical solution of the model is discussed and the resulting rovibrationally inelastic and dissociative recombination cross sections are compared with the available data.

Harmonic Vibration Control of MSCMG Based on Multisynchronous Rotating Frame Transformation

Magnetically suspended control moment gyro (MSCMG) is used in high-performance satellite platforms such as ultraquiet and ultrastable satellite. However, due to the unbalanced mass and sensor runout, the harmonic vibrations of synchronous and multifrequency will be generated, which will affect satellite performance. Aiming at the problem of harmonic vibration suppression of MSCMG, this article proposes a control algorithm based on multisynchronous rotating frame transformation. The electromagnetic force of the active magnetic bearing in MSCMG is directly used as the input signal of the control algorithm to achieve zero magnetic force control. This algorithm uses the orthogonal characteristics of the output signals of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">X</i> -direction and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Y</i> -direction displacement sensors. The vibration force in both directions can be suppressed by one controller simultaneously, saving the computing resources and having a faster response speed. The stability of the proposed method and the robustness to frequency fluctuations are analyzed. By changing the phase compensation angle in different frequency ranges, the stability of the system in the whole frequency band is ensured. Finally, experimental results are given to verify that the proposed method can achieve high precision and fast response suppression of harmonic vibration.

Multiple sawtooth-shape current reversals of traveling wave system

In this paper, we investigate current reversal (CR) of overdamped traveling wave system subjected to an symmetric periodic driving. Numerical results shown that current takes the form of sawtooth-shape, and its direction can reverse more than ten times with traveling wave velocity, called multiple sawtooth-shape CR here. In virtue of transformation of reference frame, we reveal that occurrence of the sawtooth-shape CR comes from step amplitudes induced by the periodic driving in the new reference frame, and reversal time of current depends on the driving and the spatial potential. Moreover, direction of the current changes with the increment of noise intensity in the rocking system, i.e., noise-induced CR, which has not been reported in previous works on stochastic traveling system, and the intrinsic physical mechanisms responsible for the CR is analyzed in detail.

Understanding Chinese Christian Far-Right Narrative in the COVID-19 Context: A Cross-Disciplinary Perspective

AbstractThis article introduces the controversy over the naming of COVID-19 as the “Chinese Virus” and the related hate crimes in the US. It focuses on a group of Chinese Christians in North America who devote themselves to defending and legitimising the concept of the “Chinese Virus” within various social media. This research analyses the content of the related texts and videos and defines the Christian far-right narrative and reviews the relationship between the Christian far-right narrative, Christian fundamentalism, and Christian nationalism. It explores the frame alignment process of American Christian nationalism and evaluates the frame bridging, amplification, extension, and transformation dynamics of the Chinese Christian far-right narrative. It discusses the similarity between Chinese Christian far-right and religious nationalism in different countries and evaluates the cultural and structural factors that contributed to Christian nationalism with Chinese characteristics. The Chinese Christian far-right narrative tends to adopt a friend/foe binary interpretation of political issues, moralise the goal of nation-building, downplay the democratic process and legal systems, and put religious communitarian values over the secular state’s responsibility to protect human rights. The Christian far-right narrative reflects a religious nationalist sentiment to exclude political, religious, and cultural others, which is fundamentalist theologically, opposing to system politically, anti-secular humanism culturally, and anti-progressive morally.

Space Vector Pulse-Width Modulation Control Strategy for Four-Leg Inverters Under Single Line-to-Ground Faults in Islanded Microgrids

In this paper, we propose a novel switching modulation scheme for three-phase four-leg inverters that enables the separation of the fault points occurring in AC distribution networks. The proposed method is aimed at continuously supplying normal voltage to the remaining healthy phases while applying zero voltage to any faulty phase when a single line-to-ground (SLG) fault occurs in the distribution network. This modulation scheme allows isolation without physically blocking the point of failure. This can prevent unnecessary continuous outages in the AC distribution network. To this end, we propose a novel coordinate transformation method to extract accurate values for the magnitude of unbalanced three-phase voltages. A novel space vector pulse-width modulation (SVPWM) method for switching schemes that are used under fault conditions is also presented. The proposed coordinate transformation considers a plane lying in a three-dimensional (3-D) space that describes the rotation of a three-phase voltage vector. This transformation converts a physical quantity that rotates in 3-D space into a value that moves in two-dimensional (2-D) space. Subsequently, the use of synchronous reference frame (SRF) transformation enables the detection and control of the voltage magnitude in case of an SLG fault. Additionally, switching vectors are selected to apply zero voltage to the faulty phase by analyzing the switching vector diagram of a four-leg inverter. Mathematical analyses conducted for the entire process are detailed herein. Further, the experimental results of four-leg inverters designed for the 10 kW class verify the proposed strategies.

Vibration Mechanism and Compensation Strategy of Magnetic Suspension Rotor System Under Unbalanced Magnetic Pull

The existing imbalance compensation strategies for magnetic suspension motors mainly focus on the mass unbalance force, ignoring the effects of the unbalanced magnet pull (UMP). This paper studied the vibration mechanism and compensation strategy of magnetic suspended permanent magnet synchronous motor (PMSM) under the influence of UMP. Firstly, an analytical model of the flux density was established based on equivalent magnetic circuit method, then the analytical expressions of UMP was deduced by Maxwell stress tensor method. Furthermore, an unbalanced compensation method based on hypothetical reference frame (HRF) transformation was proposed. The stability of the closed-loop system with compensation was analyzed based on the complex-coefficients theory. The proposed model and compensation strategy were verified by the simulations and experiments. The results indicate that the proposed compensation strategy can achieve effective suppression of the magnetic rotor vibration.

Secular crustal deformation characteristics prior to the 2011 Tohoku-Oki earthquake detected from GNSS array, 2003–2011

In order to reveal the secular deformation evolution and strain accumulation progress along subduction zone, we focus on high-precision Global Navigation Satellite System (GNSS) data processing, GNSS time series analysis and regional spatiotemporal filtering. The GNSS position time series is modeled as a combination of the long-term plate movements, short-term noise and the frequency-dependent variations and tectonic deformation information. Common Mode Errors (CME) is removed and the deformation signals is then extracted from the residual time series by Principal Component Analysis (PCA). Combing the filtered displacement array and the dynamic regional strain array derived from GNSS baseline, a spatiotemporal tectonic evolution map is exhibited obviously. We process the data recorded by GEONET over the 2003–2011 period in middle Japan island and reveal the dynamic evolution of crustal deformation along subduction zone. The results show that the regional reference frame transformation by constraining one site location and one stable GNSS baseline direction can further improve the Signal-to-Noise Ratio (SNR) of GNSS observations. A integrated analysis combining the baseline length with azimuth change can show the crustal motion feature more comprehensively. The observed behaviors agree well with the simulation experiment results of the rock rupture in the laboratory. We divide the pre-seismic deformation into four stages, the stable linear strain accumulation stage, the formation stage of the local locked area, local decoupling stage, and strain release stage. We also give an appropriate dynamical model for the interplate coupling to explain the observed deformation characteristics. Research result provides some of the observational new evidence for inter-seismic deformation anomaly detection and the medium- to longer-term seismic hazard assessments.

Onomastic codes of the “Poem Without A Hero” by A. A. Akhmatova as hidden intertextual addressing

The subject of this research is the principles of correlation of onomastic code of the &amp;ldquo;Poem Without A Hero&amp;rdquo; with the text frame of its various editions, viewed from the communicative-pragmatic perspective. The object of this research is nine editions of the &amp;ldquo;Poem Without a Hero&amp;rdquo; and intertextual references marked within the text frame. The author dwells on such aspects as the interrelation between the literary onomastics and hidden meanings of the poem, transformations of the text frame, methods of &amp;ldquo;instilling&amp;rdquo; the authorial meanings to intertextual sources (the works of Byron, Pushkin, and Gumilyov). Special attention is given to projection of the personal myth of Anna Akhmatova, which is traced through the poem, on Western European and Russian literature and the evolution of the text frame. It is demonstrated that the ensemble of epigraphs, which represents an implicit dedication to the poet fallen in disfavor, dissolves leaving imprints in the form of mentioning of Byron and Don Juan in the text of the poem. The main conclusion lies in the establishment of a number of semantic correspondences between the text frame and the historical-cultural halo of names, which on the one hand are associated with the imagery-motif level of a particular poem, while on the other &amp;ndash; with personal mythology of the poet. The author&amp;rsquo;s special contribution to this research lies in outlining the strategies aimed at preservation of special intertextual memory in the names. The novelty consists in determination of the semantic halo of the name, which specifies a range of implicit meanings of the poem. It is revealed that these meanings are &amp;ldquo;supported&amp;rdquo; by the corresponding references. Such reminiscences, interweaving into a complex ornamental pattern, on the one side are conceptually programmed by the very structure of the &amp;ldquo;Poem Without A Hero&amp;rdquo;, and on the other side, determined biographically.

Visual Analysis of Ancient Egyptian Mythology Character in Marvel Comic

The goal of this research is to find the transformation in the perception framing of the ancient Egyptian Goddess in marvel’s comic book. This research studied the visual aspects of the character design of Sekhmet, one of marvel’s super-villain characters that were adapted from ancient Egyptian mythology. Marvel comic is one of the most popular American comic books that tell stories of its original superheroes and super-villain characters. The focus of this research is Sekhmet’s character that was designed based on an ancient Egyptian Goddess with the same name, Hathor-Sekhmet. This study used a qualitative research method to describe the character of Sekhmet based on its original narration in Egyptian mythology and marvel’s comic book version. Then using the manga matrix method, the character design’s form, costume, and personality matrix were studied and analysed. This method helped to find the relation and similarities among the theories and the perception elements. This method helped to find the relation and similarities among the theories and the perception elements. This study proved that Sekhmet’s character design contained imagery framing that formed a new perception of the lion goddess image, where in the costume matrix there has been an addition of leather, metals and gold attributes and accessories and in the personality area, Sekhmet personality shifted from its neutral character to an evil villain character. This imagery framing transformation affects the way Sekhmet is being perceived by readers

Transformation of spin in quantum reference frames

In physical experiments, reference frames are standardly modeled through a specific choice of coordinates used to describe the physical systems, but they themselves are not considered as such. However, any reference frame is a physical system that ultimately behaves according to quantum mechanics. We develop a framework for rotational (i.e., spin) quantum reference frames, with respect to which quantum systems with spin degrees of freedom are described. We give an explicit model for such frames as systems composed of three spin coherent states of angular momentum $j$ and introduce the transformations between them by upgrading the Euler angles occurring in classical $\text{SO}(3)$ spin transformations to quantum mechanical operators acting on the states of the reference frames. To ensure that an arbitrary rotation can be applied on the spin we take the limit of infinitely large $j$, in which case the angle operator possesses a continuous spectrum. We prove that rotationally invariant Hamiltonians (such as that of the Heisenberg model) are invariant under a larger group of quantum reference frame transformations. Our result is a development of the quantum reference frame formalism for a non-Abelian group.

Quantum mechanical rotation of a photon polarization by Earth\u2019s gravitational field

We describe the quantum mechanical rotation of a photon state, the Wigner rotation—a quantum effect that couples a transformation of a reference frame to a particle’s spin, to investigate geometric phases induced by Earth’s gravitational field for observers in various orbits. We find a potentially measurable quantum phase of the Wigner rotation angle in addition to the rotation of standard fame, the latter of which is computed and agrees well with the geodetic rotation. When an observer is in either a circular or a spiraling orbit containing non-zero angular momentum, the additional quantum phase contributes 10−6 degree to 10−4 degree respectively, depending on the altitude of the Earth orbit. In the former case, the additional quantum phase is dominant over the near-zero classical geodetic rotation. Our results show that the Wigner rotation represents a non-trivial semi-classical effect of quantum field theory on a background classical gravitational field.

Homography-based Visual Servoing with Remote Center of Motion for Semi-autonomous Robotic Endoscope Manipulation.

The dominant visual servoing approaches in Minimally Invasive Surgery (MIS) follow single points or adapt the endoscope's field of view based on the surgical tools' distance. These methods rely on point positions with respect to the camera frame to infer a control policy. Deviating from the dominant methods, we formulate a robotic controller that allows for image-based visual servoing that requires neither explicit tool and camera positions nor any explicit image depth information. The proposed method relies on homography-based image registration, which changes the automation paradigm from point-centric towards surgical-scene-centric approach. It simultaneously respects a programmable Remote Center of Motion (RCM). Our approach allows a surgeon to build a graph of desired views, from which, once built, views can be manually selected and automatically servoed to irrespective of robot-patient frame transformation changes. We evaluate our method on an abdominal phantom and provide an open source ROS Moveit integration for use with any serial manipulator. A video is provided.

A Deep Learning Approach for Foot Trajectory Estimation in Gait Analysis Using Inertial Sensors.

Gait performance is an important marker of motor and cognitive decline in older adults. An instrumented gait analysis resorting to inertial sensors allows the complete evaluation of spatiotemporal gait parameters, offering an alternative to laboratory-based assessments. To estimate gait parameters, foot trajectories are typically obtained by integrating acceleration two times. However, to deal with cumulative integration errors, additional error handling strategies are required. In this study, we propose an alternative approach based on a deep recurrent neural network to estimate heel and toe trajectories. We propose a coordinate frame transformation for stride trajectories that eliminates the dependency from previous strides and external inputs. Predicted trajectories are used to estimate an extensive set of spatiotemporal gait parameters. We evaluate the results in a dataset comprising foot-worn inertial sensor data acquired from a group of young adults, using an optical motion capture system as a reference. Heel and toe trajectories are predicted with low errors, in line with reference trajectories. A good agreement is also achieved between the reference and estimated gait parameters, in particular when turning strides are excluded from the analysis. The performance of the method is shown to be robust to imperfect sensor-foot alignment conditions.

Transformations of Reference Frames and Model Development for Multi-Phase Machines

Transformations of Reference Frames and Model Development for Multi-Phase Machines

Static Gait Scheme for Horizontal Posture Slope Climbing with Quadruped Robot

With a view to expanding serviceability in different applications, the slope climbing ability of a quadruped robot is important. In this paper, a gait scheme i.e. walking algorithm for slope climbing is proposed. It differs from the previous studies in terms of the posture of the robot while climbing. The presented scheme is designed such a way that the body of the robot maintains horizontal posture with positive static stability which can be used for carrying a load and disabled while climbing the slope. For this proposed scheme, different parameters of gait are shown. The algorithm is tested with a multibody simulation and based on the results of transformation of the inertial frame about the world frame; it is proven to be steady.

Inverse optimal damper placement via shear model for elastic–plastic moment-resisting frames under large-amplitude ground motions

A new method of optimal damper design is presented for elastic–plastic planar frame structures under large-amplitude earthquake ground motions. The transformation of a moment frame into the 1st-mode equivalent shear mass system leads to an efficient search of the optimal damper placement along the building height for the elastic–plastic moment frame. In the optimization procedure, a linear elastic bare frame is transformed into the 1st-mode equivalent shear mass system first. Then the optimization of the damper placement is conducted for the elastic shear mass system. After that, the damped shear mass system is inversely transformed into the elastic–plastic moment frame with the added dampers. This inversely transformed damper system in the moment frame is employed as an initial design and the local search-based optimization is conducted for the efficient distribution of dampers not only along the building height, but also among the different bay. The proposed method greatly reduces the computational task in the whole optimization procedure because only a limited number of time-history response analyses is required for elastic–plastic moment frames. It is demonstrated through numerical examples that the proposed method efficiently provides the damper designs with high accuracy. Finally, the importance of using the large-amplitude ground motions for damper optimization is demonstrated through the incremental dynamic analysis (IDA) for the optimally designed models.

Fault-Tolerant Control of a Three-Phase Permanent Magnet Synchronous Motor for Lightweight UAV Propellers via Central Point Drive

This paper deals with the development and the performance characterization of a novel Fault-Tolerant Control (FTC) aiming to the diagnosis and accommodation of electrical faults in a three-phase Permanent Magnet Synchronous Motor (PMSM) employed for the propulsion of a modern lightweight fixed-wing UAV. To implement the fault-tolerant capabilities, a four-leg inverter is used to drive the reference PMSM, so that a system reconfiguration can be applied in case of a motor phase fault or an inverter fault, by enabling the control of the central point of the three-phase connection. A crucial design point is to develop Fault-Detection and Isolation (FDI) algorithms capable of minimizing the system failure transients, which are typically characterized by high-amplitude high-frequency torque ripples. The proposed FTC is composed of two sections: in the first, a deterministic model-based FDI algorithm is used, based the evaluation of the current phasor trajectory in the Clarke’s plane; in the second, a novel technique for fault accommodation is implemented by applying a reference frame transformation to post-fault commands. The FTC effectiveness is assessed via detailed nonlinear simulation (including sensors errors, digital signal processing, mechanical transmission compliance, propeller loads and electrical faults model), by characterizing the FDI latency and the post-fault system performances when open circuit faults are injected. Compared with reports in the literature, the proposed FTC demonstrates relevant potentialities: the FDI section of the algorithm provides the smallest ratio between latency and monitoring samples per electrical period, while the accommodation section succeeds in both eliminating post-fault torque ripples and maintaining the mechanical power output with negligible efficiency degradation.

Load Sharing Scheme Incorporating Power Security Margins for Parallel Operation of Voltage Source Inverters

The interconnection of distributed energy resources (DERs) in microgrids (MGs) operating in both islanded and grid-connected modes require coordinated control strategies. DERs are interfaced with voltage source inverters (VSIs) enabling interconnection. This paper proposes a load demand sharing scheme for the parallel operation of VSIs in an islanded voltage source inverter-based microgrid (VSI-MG). The ride-through capability of a heavily loaded VSI-MG, where some of the VSIs are fully loaded due to the occurrence of an event is investigated. In developing analytical equations to model the VSI, the concept of virtual synchronous machines (VSM) is applied to enable the VSI mimic the inertia effect of synchronous machines. A power frame transformation (PFT) that takes the line ratios of the MG network into account is also incorporated to yield satisfactory transient responses of both network frequency and bus voltages in the MG network. A Jacobian-based method is then developed to take into account the operational capacity of each VSI in the VSI-MG. The resulting amendable droop control constrains the VSIs within their power capabilities when an event occurs. Simulation results presented within demonstrate the effectiveness of the proposed procedure which has great potential to facilitate efforts in maintaining system reliability and resiliency.

Cross Sections and Rate Coefficients for Vibrational Excitation of H2O by Electron Impact

Cross-sections and thermally averaged rate coefficients for vibration (de-)excitation of a water molecule by electron impact are computed; one and two quanta excitations are considered for all three normal modes. The calculations use a theoretical approach that combines the normal mode approximation for vibrational states of water, a vibrational frame transformation employed to evaluate the scattering matrix for vibrational transitions and the UK molecular R-matrix code. The interval of applicability of the rate coefficients is from 10 to 10,000 K. A comprehensive set of calculations is performed to assess uncertainty of the obtained data. The results should help in modelling non-LTE spectra of water in various astrophysical environments.

Practical Algorithms on Lunar Reference Frame Transformations for Korea Pathfinder Lunar Orbiter Flight Operation

This technical paper deals the practical transformation algorithms between several lunar reference frames which will be used for Korea pathfinder lunar orbiter (KPLO) flight operation. Despite of various lunar reference frame definitions already exist, use of a common transformation algorithm while establishing lunar reference frame is very important for all members related to KPLO mission. This is because use of slight different parameters during frame transformation may result significant misleading while reprocessing data based on KPLO flight dynamics. Therefore, details of practical transformation algorithms for the KPLO mission specific lunar reference frames is presented with step by step implementation procedures. Examples of transformation results are also presented to support KPLO flight dynamics data user community which is expected to give practical guidelines while post processing the data as their needs. With this technical paper, common understandings of reference frames that will be used throughout not only the KPLO flight operation but also science data reprocessing can be established. It is expected to eliminate, or at least minimize, unnecessary confusion among all of the KPLO mission members including: Korea Aerospace Research Institute (KARI), National Aeronautics and Space Administration (NASA) as well as other organizations participating in KPLO payload development and operation, or further lunar science community world-wide who are interested in KPLO science data post processing.