Two-dimensional Rotation Research Articles

A hydrodynamic approach to reproduce multiple spinning vortices in horizontally rotating three-dimensional liquid helium-4

This paper reports a three-dimensional (3D) simulation of a rotating liquid helium-4, using a two-fluid model with spin-angular momentum conservation. Our model was derived from the particle approximation of an inviscid fluid with residual viscosity. Despite the fully classical mechanical picture, the resulting system equations were consistent with those of the conventional two-fluid model. We consider bulk liquid helium-4 to be an inviscid fluid, assuming that the viscous fluid component remains at finite temperatures. As the temperature decreased, the amount of the viscous fluid component decreased, ultimately becoming a fully inviscid fluid at absolute zero. Weak compressibility is assumed to express the volume change because some helium atoms do not render fluid owing to Bose–Einstein condensations or change states because of local thermal excitation. One can solve the governing equations for an incompressible fluid using explicit smoothed-particle hydrodynamics, simultaneously reproducing density fluctuations and describing the fluid in a many-particle system. We assume the following fluid–particle duality: a hydrodynamic interfacial tension between the inviscid and viscous components or a local interaction force between two types of fluid particles. The former can be induced in the horizontal direction when non-negligible non-uniformity of the particles occurs during forced two-dimensional rotation, and the latter is non-negligible when the former is negligible. We performed a large-scale simulation of 3D liquid helium forced to rotate horizontally using 32 graphics processing units. Compared with the low-resolution calculation using 2.4 × 106 particles, the high-resolution calculation using 19.6 × 106 particles showed spinning vortices close to those of the theoretical solution. We obtained a promising venue to establish a practical simulation method for bulk liquid helium-4.

Determination of in-plane surface directions in scanning probe microscopy images.

We describe an approach to determine the in-plane crystallographic surface directions in scanning probe microscopy (SPM) images. This method is based on a one-time characterization of the SPM instrument with an appropriate test sample and is exemplified by the analysis of non-contact atomic force microscopy (NC-AFM) images on surfaces whose natural cleavage occurs along {111} planes. We introduce a two-dimensional rotation matrix relating the crystallographic surface directions known from an analysis of the macroscopic crystal to the directions in the NC-AFM images. The procedure takes into account rotations and mirror axes resulting from sample mounting, the SPM scanner rotation, the choice of scan direction, as well as data processing, storage, and display. We demonstrate the practicability of the approach by determining the [112̄] direction in topographic images of a CeO2(111) film grown on a Si(111) wafer and atomic resolution images of CaF2(111) with an instrument based on the beetle-type scanner.

Two-Dimensional Pointing Mirror Rotation Correction and Stitching Method

Two-Dimensional Pointing Mirror Rotation Correction and Stitching Method

Experimental System and Software: Two-dimensional Return of the Platform to the Sound Source

We created a system, debugged it, and conducted experimental studies of the two-dimensional rotation of the supporting platform (with a camera, and a light source.) on the source of sound waves. The system was assembled based on two SYNCO Mic-M3 cardioid condenser microphones and an Alesis IO-4 sound card. We wrote original software for analyzing and transmitting the result of processing harmonic acoustic signals for the response of the Arduino Uno control board. The rotation of the 2D platform is caused by two MG995 servos controlled by this microcontroller. We used a model of a serial COM port, which allows to send data received from the platform in the form of packets for processing by a portable personal computer. Based on the results of the experimental test and the basis of the literature data, a model of control of the two-dimensional platform of returning to the source of sound has been offered.

The closed-loop control method based on dual-port adaptive internal model control for fine image stabilization of space telescopes.

In view of the complex working environment of space astronomical telescopes, the influence of various disturbance sources on the imaging quality cannot be ignored. This paper focuses on compensating for the space telescope line-of-sight (LOS) deviation and suppressing the low-frequency disturbance problem in astronomical observation. A closed-loop control method based on dual-port adaptive internal model control (AIMC) for the fine image stabilization system (FISS) was proposed. To be specific, the fine guidance sensor (FGS) as the high-precision detection unit of the FISS calculates the telescope LOS deviation and sends it to the controller unit in real time. The controller unit drives the large-aperture fast steering mirror (FSM), which performs high-precision two-dimensional rotation to compensate for the telescope LOS deviation, according to the dual-port AIMC control algorithm. Moreover, the dual-port AIMC control method adds an AIMC loop on the basis of the feedback loop and adjusts the filter parameters adaptively according to the target angular velocity of the FSM, achieving higher disturbance suppression capability. The experimental results verify that the control method proposed can effectively compensate for the LOS deviation and suppress the composite frequency disturbance. In the 0-8Hz frequency band, the power spectral density integral values of the star centroid deviation in the X and Y directions of the FGS are, respectively, suppressed by 97.38% and 98.38%.

Decomposition and the Gross–Taylor string theory

It was recently argued by Nguyen, Tanizaki and Ünsal that two-dimensional pure Yang–Mills theory is equivalent to (decomposes into) a disjoint union of (invertible) quantum field theories, known as universes. In this paper, we compare this decomposition to the Gross–Taylor expansion of two-dimensional pure [Formula: see text] Yang–Mills theory in the large-[Formula: see text] limit as the string field theory of a sigma model. Specifically, we study the Gross–Taylor expansion of individual Nguyen–Tanizaki–Ünsal universes. These differ from the Gross–Taylor expansion of the full Yang–Mills theory in two ways: a restriction to single instanton degrees, and some additional contributions not present in the expansion of the full Yang–Mills theory. We propose to interpret the restriction to single instanton degrees as implying a constraint, namely that the Gross–Taylor string has a global (higher-form) symmetry with Noether current related to the worldsheet instanton number. We compare two-dimensional pure Maxwell theory as a prototype obeying such a constraint, and also discuss in that case an analogue of the Witten effect arising under two-dimensional theta angle rotation. We also propose a geometric interpretation of the additional terms, in the special case of Yang–Mills theories on 2-spheres. In addition, also for the case of theories on 2-spheres, we propose a reinterpretation of the terms in the Gross–Taylor expansion of the Nguyen–Tanizaki–Ünsal universes, replacing sigma models on branched covers by counting disjoint unions of stacky copies of the target Riemann surface, that makes the Nguyen–Tanizaki–Ünsal decomposition into invertible field theories more nearly manifest. As the Gross–Taylor string is a sigma model coupled to worldsheet gravity, we also briefly outline the tangentially related topic of decomposition in two-dimensional theories coupled to gravity.

Development of a Public-Domain Measure of Two-Dimensional Rotation Ability and Preliminary Evidence for Discriminant Validity among Occupations.

Despite their known influence in science, technology, engineering, and mathematics (STEM) fields, spatial abilities remain an underassessed aspect of cognition, particularly in educational settings. One explanation could be a lack of affordable, valid instruments for measuring various aspects of spatial ability. We evaluate the validity of a set of public-domain, algorithmically generated two-dimensional rotation items using a sample from the Synthetic Aperture Personality Assessment (SAPA) Project (N = 1,020,195). We examine the psychometric properties of the items and their relationship with various other cognitive abilities and personality traits. In addition, we identify the highest performing college majors and occupations on the 2D rotation items and on a set of 3D rotation items. Findings suggest strong unidimensionality for the 2D rotation items and the presence of lower-order factors which reflect differences across items in mental rotation demands. The highest scoring majors and occupations were similar-but not identical-across the 2D and 3D rotation measures and point to potentially meaningful differences across areas of expertise.

A rare tetrahydroimidazopyridine from the marine-derived fungus Paraconiothyrium sp. YK-03

A new tetrahydroimidazopyridine named butyl (5R,6R,7S,8S)-5,6,7,8-tetrahydro-6,7,8-trihydroxy-5-(hydroxymethyl)imidazo[1,2-a]pyridine-2-carboxylate(1), together with eight known compounds (2–9), were isolated from the fermentation broth of a marine-derived fungus Paraconiothyrium sp. YK-03. Their chemical structures were elucidated by extensive analysis of one-dimensional and two-dimensional NMR spectroscopy, HR-ESIMS and optical rotation. Among these compounds, compound 1 represented a rare tetrahydroimidazopyridine, and compounds 2–7 were isolated from the Paraconiothyrium species for the first time. A plausible biosynthetic pathway for compound 1 was proposed.

Whether Informing Participants with High Self-Relevance of Gender Stereotype Alleviates Stereotype Activation Threat

Females, as a minority group, experience social inequalities relative to males in most societies. Part of the inequalities originates from gender-stereotypical thoughts, which impose threats and anxiety on females, worsening their performances. The study aimed to investigate the relationship between the self-relevance level of the stereotypical traits and the performance improvement under the informing women about stereotype threat. Female participants finished a gender role orientation inventory and were exposed to gender stereotype threats before the two-dimensional mental orientation task. The performance of the task was measured by reaction time and the number of correct answers. The participants in the teaching-intervention condition were additionally informed that gender stereotype threat could interfere with their spatial performance. Results showed that women with female gender role orientation performed worse than those without. However, no relation between gender role orientation and teaching-intervention was found. The results suggest a potential problem under the two-dimensional mental rotation tasks and provide future studies with further suggestions.

Vehicle Directional Cosine Calculation Method

Teaching kinematic rotations is a daunting task for even some of the most advanced mathematical minds. However, changing the paradigm can highly simplify envisioning and explaining the three-dimensional rotations. This paradigm change allows a high school student with an understanding of geometry to develop the matrix and explain the rotations at a collegiate level. The proposed method includes the assumption of a point (P) within the initial three-dimensional frame with axes (x^i, y^i, z^i). The method then utilizes a two-dimensional rotation view (2DRV) to measure how the coordinates of point P translate after a rotation around the initial axis. The equations are used in matrix notation to develop a rotation matrix for follow-on direction cosine matrixes. The method removes the requirement to use Euler’s formula, ultimately, providing a high school student with an elementary and repeatable process to compose and explain kinematic rotations, which are critical to attitude direction control systems commonly found in vehicles.

Habitual Subjective Sleep Continuity is Not Associated With Fluid Intelligence: An Exploratory Study

The link between sleep and cognition is well-established, but the link between subjective sleep and fluid intelligence is poorly understood. The aim of this exploratory study was to examine the relationship between habitual subjective sleep continuity and fluid intelligence. In this study, a total of 56 healthy sleepers (M<sub>age</sub> = 30.91 years; SD<sub>age</sub> = 12.93 years) completed two fluid intelligence (abstract reasoning and two-dimensional mental rotation) tasks after completing seven consecutive days of sleep diaries. Relationships between subjective sleep continuity (total sleep time [TST]; sleep efficiency [SE%]); wake after sleep onset (WASO) and sleep onset latency (SOL), and task accuracy and speed were assessed using Pearson correlations. Overall, there were no associations between subjective sleep continuity (TST, SE%, WASO, SOL) and either task accuracy or speed (adjusted p-values > 0.0125). Overall, habitual subjective sleep continuity and fluid intelligence may not be associated. These results should be replicated in larger samples.

Holographic Optimization Method of Acoustic Radiation Force for Continuously Manipulating a Mie Particle through a Fluid

Acoustic holography is widely used in particle manipulation. However, previous methods focus on modulating the amplitude and phase of the target sound field. In general, the amplitude gradient and phase gradient of the sound field correspond to the gradient force and the scattering force, respectively. But the relationship between the force and the aforementioned gradient is nonlinear even for a Rayleigh particle (whose radius is much smaller than the wavelength), not to mention the Mie particle(whose radius is comparable with the wavelength). If we want to control the continuous motion of a Mie particle quantitatively, we need to design force based on the relationship among the force, acceleration, and velocity. Here we propose to design radiation force along the path of a particle directly in holography methods. Compared to the usual modulation of amplitude and phase, the method designing radiation force directly can control the acceleration and orbital limiting velocity of a two-dimensional orbit rotation of a Mie particle with radius $a=0.4\phantom{\rule{0.2em}{0ex}}\mathrm{mm}$ (approximately $2/3$ wavelength) in simulation. The experiment verified its feasibility in controlling the continuous motion of particle quantitatively. This work shows its superiority over the pure acoustic holography methods in quantitative particle manipulation.

Quantum mechanical analysis of the geared rotation of a model molecule

The quantum chemical calculations of a model molecule for the molecular spur gear at the M06-2X/6-31++G(d,p) level of theory have been carried out to obtain the potential energy surface for the two-dimensional internal rotations. The energy levels, the wavefunctions and the time evolution of the wave packets have been calculated to evaluate the performance of the molecule as a gear. It was confirmed that the geared rotation of the two rotors is a hindered rotation, not a free rotation. It has been also revealed that the molecule can undergo the “slippage” of the gear mesh because of the tunneling.

Ferris-wheel-assisted parylene-C dielectric deposition for improving organic thin-film transistor uniformity

Organic thin film transistor is one of the most promising electronic device technologies for flexible and printed electronics, but device uniformity remains a challenge for large-scale integration circuit design. Despite the advances in semiconductor layers, the quality of dielectric layers is equally important. Parylene-C dielectric has good intrasample thickness uniformity, but demonstrates significant variation among samples fabricated at the same time, thus causing device non-uniformity. In this study, we present a two-dimensional (2D) sample rotation method using a Ferris wheel to improve the thickness uniformity of parylene-C dielectrics. The Ferris wheel averages the deposition rate of parylene-C dielectric on different samples over an identical spherical space, rather than over different horizontal planes by the conventional one-dimensional sample rotation with a rack. The dielectrics fabricated on different cabins of the Ferris wheel demonstrate better thickness uniformity than those fabricated on different floors of the rack, and thus better uniformity of transistors. Specifically, using the 2D rotation Ferris wheel, the coefficient of variation of dielectric thickness is lowered to 0.01 from 0.12 (which uses the conventional rack); the coefficients of variation for the on-state drain current, process transconductance parameter, and threshold voltage of the fabricated transistors are improved to 0.15, 0.16 and 0.08, from 0.33, 0.20 and 0.14, respectively. The improved device uniformity has the potential in complicated flexible circuit design for advanced applications such as edge intelligence.

Numerical evaluation of convective heat transfer properties of two-dimensional rotating PCM melt in the unilaterally heated rectangular container

This paper carried out numerical investigations on the flow and heat transfer characteristics of a phase change with two-dimensional rotation of the three-dimensional paraffin (RT -27)-filled rectangular encapsulated container (PCM-REC) in space. A three-dimensional transient numerical heat transfer model was established and the enthalpy method was used to simulate the solid-liquid phase transition process and the flow evolution at the PCM interface. In this paper, the solid-liquid interface distribution, temperature distribution and melting time of PCM in PCM-REC heated at a constant temperature on one side were compared when rotated at different angles (0°, arctan (0.4), 2arctan (0.4) and 90°) along the heating direction and vertical heating direction. Results demonstrated that the peak value of maximum natural convection velocity increased from 0.0072 m/s to 0.0184 m/s with increasing radial height when PCM-REC was rotated in vertical heating direction. When PCM-REC was rotated in two dimensions by the same angle, the melting time was fastest when γ was an obtuse angle, and with the increase of the obtuse angle, the melting time shortened from 17 min to 6 min; when γ was an acute angle, the melting time was slowest, and with the decrease of the acute angle, the melting time lengthened from 49 min to 288 min.

Domain-adapted Gaussian mixture models for population-based structural health monitoring

Transfer learning, in the form of domain adaptation, seeks to overcome challenges associated with a lack of available health-state data for a structure, which severely limits the effectiveness of conventional machine learning approaches to structural health monitoring (SHM). These technologies utilise labelled information across a population of structures (and physics-based models), such that inferences are improved, either for the complete population, or for particular target structures — enabling a population-based view of SHM. The aim of these methods is to infer a mapping between each member of the population’s feature space (called a domain) in which a classifier trained on one member of the population will generalise to the remaining structures. This paper introduces the domain-adapted Gaussian mixture model (DA-GMM) for population-based SHM (PBSHM) scenarios. The DA-GMM, infers a linear mapping that transforms target data from one structure onto a Gaussian mixture model that has been inferred from source data (from another structure). The proposed model is solved via an expectation maximisation technique. The method is demonstrated on three case studies: an artificial dataset demonstrating the approach’s effectiveness when the target domain differs by two-dimensional rotations; a population of two numerical shear-building structures; and a heterogeneous population of two bridges, the Z24 and KW51 bridges. In each case study, the method is shown to provide informative results, outperforming other conventional forms of GMM (where no target labelled data are assumed available), and provide mappings that allow the effective exchange of labelled information from source to target datasets.

A rotary vision system for high-precision measurement over large size

This paper introduced a rotary binocular vision measurement system (RBVMS) consisting of two cameras and two theodolites, with the latter employed as a two-dimensional rotation platform. The camera was driven by mounting it on the theodolite to cover different areas, effectively increasing the measuring range. In the camera calibration stage, virtual 3D points were generated by accurately moving the planar calibration board. A two-order radial and two-order tangential distortion model was considered. The experimental results showed that the intrinsic parameters of the camera had high stability, and the mean reprojection error was about 0.035 pixels. A unit quaternion method was applied to calibrate the transformation matrix between the camera and the theodolite. By solving the transformation matrix between the two theodolites, the measurement data of each position was unified under a fixed coordinate system. At 500 mm in front of the camera, the camera's field of view was about 200 mm. Two targets of different sizes were measured to verify the effectiveness and accuracy of the method. The measurement accuracy of 300 mm and 600 mm targets was about 0.014 mm and 0.027 mm, respectively.

Investigating H2 Adsorption in Isostructural Metal-Organic Frameworks M-CUK-1 (M = Co and Mg) through Experimental and Theoretical Studies.

A combined experimental and theoretical study of H2 adsorption was carried out in Co-CUK-1 and Mg-CUK-1, two isostructural metal-organic frameworks (MOFs) that consist of M2+ ions (M = Co and Mg) coordinated to pyridine-2,4-dicarboxylate (pdc2-) and OH- ligands. These MOFs possess saturated metal centers in distorted octahedral environments and narrow pore sizes and display high chemical and thermal stability. Previous experimental studies revealed that Co-CUK-1 exhibits a H2 uptake of 183 cm3 g-1 at 77 K/1.0 atm [ Angew. Chem., Int. Ed. 2007, 46, 272-275, DOI: 10.1002/anie.200601627], while that for Mg-CUK-1 under the same conditions is 240 cm3 g-1 on the basis of the experimental measurements carried out herein. The theoretical H2 adsorption isotherms are in close agreement with the corresponding experimental measurements for simulations using electrostatic and polarizable potentials of the adsorbate. Through simulated annealing calculations, it was found that the primary binding site for H2 in both isostructural analogues is localized proximal to the center of the aromatic rings belonging to the pdc2- linkers. Inelastic neutron scattering (INS) spectroscopic studies of H2 adsorbed in both MOFs revealed a rotational tunnelling transition occurring at around 8 meV in the corresponding spectra; this peak represents H2 adsorbed at the primary binding site. Two-dimensional quantum rotation calculations for H2 localized at the primary and secondary binding sites in both MOFs yielded rotational energy levels that are in agreement with the transitions observed in the INS spectra. Even though both M-CUK-1 analogues possess different metal ions, they exhibit similar electrostatic environments, modeled structures at H2 saturation, and rotational potentials for H2 adsorbed at the most favorable adsorption site. Overall, this study demonstrates how important molecular-level details of the H2 adsorption mechanism inside MOF micropores can be derived from a combination of experimental measurements and theoretical calculations using two stable and isostructural MOFs with saturated metal centers and small pore windows as model systems.

Classification and Assessing Methods of the Complexity of “Group A” Acrobatic Exercises in Artistic Swimming

Article purpose – to classify acrobatic movements of group A “airborne” (jumps) and identify the main components that affect their technical value. According to research, acrobatic movements of group A “airborne” – (in the air) – are not divided into subgroups but differ (classified) by the variety of construction, the direction of the jump, the position of the featured swimmer’s body in the air (posture) and the type and number of rotation demonstrated by the featured-swimmer in the air. The first criteria of difficulty was defined as “Construction” – is a generalized name for collaborated work of all athletes according to their assigned role in the acrobatic movement (base+ support+ featured swimmer), and it is also the name of a “formation” from which the acrobatic moves of group A “airborne” begins. Depending on the complexity and efficiency of the design, was is classified into four levels. The fourth level of construction – a “square” (basket), is defined as the most difficult and highly effective. The main components that affect the technical value of the component “Construction” were defined. The second criterion of difficulty, respectively, and technical value, was the directions of the jumps. Five directions of jumps are classified. The most difficult, and rated at 0,4 points, is the jump “in the opposite direction”. The next evaluation criterion was how the acrobatic movement is performed in the air. All positions are divided into four groups (considering flexibility and additional factors). An important criterion for assessing the technical value of acrobatic exercise is the number of rotations and the plane in which the rotation is performed in the air. Rotations are classified into 4 types: "twists", "somersaults", "side flips" and "two-dimensional rotations". The technical value of rotation depends on each additional 180 degrees rotation and increases with 0,2 for each 360 to prevent disbalance in the general classification. So, the rotation of 180 ° is estimated at 0,1 point, 360 ° – 0,3 points, 540 ° – 0,5 points, 720 ° – 0,7 points, 900 – 0,9 ° points. To get total technical value of the acrobatic movement, all components’ numbers should be summarized. Technical value varies between all acrobatic movements in this group depending on which coach would choose different components of the acrobatic movements. The developed system allows the creation of any combination (“set”) of the components, so it doesn’t ruin the creativity of routine in artistic swimming, which is one of the main ideas of this sport. Based on the developed method of calculating the technical value of acrobatic movements, a single table of technical value of acrobatic exercises “group A” was created – in the air, where acrobatic moves were distributed from easiest to most accessible most difficult according to the calculated technical value.

Kinematic Analysis and Verification of a New 5-DOF Parallel Mechanism

This paper first designs a new 5-DOF parallel mechanism with 5PUS-UPU, and then analyses its DOF by traditional Grubler–Kutzbach and motion spiral theory. It theoretically shows that the mechanism meets the requirement of five dimensions of freedoms including three-dimensional movement and two-dimensional rotation. Based on this, the real mechanism is built, but unfortunately it is found unstable in some positions. Grassmann line geometry method is applied to analyze its unstable problem caused by singular posture, and then an improving method is put forward to solve it. With the improved mechanism, closed loop vector method is employed to establish the inverse position equation of the parallel mechanism, and kinematics analysis is carried out to get the mapping relationships between position, speed, and acceleration of moving and fixed platform. Monte Carlo method is used to analyze the workspace of the mechanism, to explore the influencing factors of workspace, and then to get the better workspace. Finally, an experiment is designed to verify the mechanism working performance.