Rotation Sequence Research Articles

Canonical description of T-duality for fundamental string and D1-brane and double Wick rotation

We study T-duality transformations in canonical formalism for Nambu–Goto action. Then we investigate the relation between worldsheet double Wick rotation and sequence of target space T-dualities and Wick rotation in case of fundamental string and D1-brane.

Instantaneous progression reference frame for calculating pelvis rotations: Reliable and anatomically-meaningful results independent of the direction of movement

In motion analysis, pelvis angles are conventionally calculated as the rotations between the pelvis and laboratory reference frame. This approach assumes that the participant's motion is along the anterior–posterior laboratory reference frame axis. When this assumption is violated interpretation of pelvis angels become problematic. In this paper a new approach for calculating pelvis angles based on the rotations between the pelvis and an instantaneous progression reference frame was introduced. At every time-point, the tangent to the trajectory of the midpoint of the pelvis projected into the horizontal plane of the laboratory reference frame was used to define the anterior–posterior axis of the instantaneous progression reference frame. This new approach combined with the rotation–obliquity–tilt rotation sequence was compared to the conventional approach using the rotation–obliquity–tilt and tilt–obliquity–rotation sequences. Four different movement tasks performed by eight healthy adults were analysed. The instantaneous progression reference frame approach was the only approach that showed reliable and anatomically meaningful results for all analysed movement tasks (mean root-mean-square-differences below 5°, differences in pelvis angles at pre-defined gait events below 10°). Both rotation sequences combined with the conventional approach led to unreliable results as soon as the participant's motion was not along the anterior–posterior laboratory axis (mean root-mean-square-differences up to 30°, differences in pelvis angles at pre-defined gait events up to 45°). The instantaneous progression reference frame approach enables the gait analysis community to analysis pelvis angles for movements that do not follow the anterior–posterior axis of the laboratory reference frame.

A minimal subsystem of the Kari–Culik tilings

The Kari–Culik tilings are formed from a set of 13 Wang tiles that tile the plane only aperiodically. They are the smallest known set of Wang tiles to do so and are not as well understood as other examples of aperiodic Wang tiles. We show that the $\mathbb{Z}^{2}$ action by translation on a certain subset of the Kari–Culik tilings, namely those whose rows can be interpreted as Sturmian sequences (rotation sequences), is minimal. We give a characterization of this space as a skew product as well as explicit bounds on the waiting time between occurrences of $m\times n$ configurations.

A model for developing job rotation schedules that eliminate sequential high workloads and minimize between-worker variability in cumulative daily workloads: Application to automotive assembly lines

The aim of study is to suggest a job rotation schedule by developing a mathematical model in order to reduce cumulative workload from the successive use of the same body region. Workload assessment using rapid entire body assessment (REBA) was performed for the model in three automotive assembly lines of chassis, trim, and finishing to identify which body part exposed to relatively high workloads at workstations. The workloads were incorporated to the model to develop a job rotation schedule. The proposed schedules prevent the exposure to high workloads successively on the same body region and minimized between-worker variance in cumulative daily workload. Whereas some of workers were successively assigned to high workload workstation under no job rotation and serial job rotation. This model would help to reduce the potential for work-related musculoskeletal disorders (WMSDs) without additional cost for engineering work, although it may need more computational time and relative complex job rotation sequences.

Sex-based differences in lifting technique under increasing load conditions: A principal component analysis

The objective of the present study was to determine if there is a sex-based difference in lifting technique across increasing-load conditions. Eleven male and 14 female participants (n = 25) with no previous history of low back disorder participated in the study. Participants completed freestyle, symmetric lifts of a box with handles from the floor to a table positioned at 50% of their height for five trials under three load conditions (10%, 20%, and 30% of their individual maximum isometric back strength). Joint kinematic data for the ankle, knee, hip, and lumbar and thoracic spine were collected using a two-camera Optotrak motion capture system. Joint angles were calculated using a three-dimensional Euler rotation sequence. Principal component analysis (PCA) and single component reconstruction were applied to assess differences in lifting technique across the entire waveforms. Thirty-two PCs were retained from the five joints and three axes in accordance with the 90% trace criterion. Repeated-measures ANOVA with a mixed design revealed no significant effect of sex for any of the PCs. This is contrary to previous research that used discrete points on the lifting curve to analyze sex-based differences, but agrees with more recent research using more complex analysis techniques. There was a significant effect of load on lifting technique for five PCs of the lower limb (PC1 of ankle flexion, knee flexion, and knee adduction, as well as PC2 and PC3 of hip flexion) (p < 0.005). However, there was no significant effect of load on the thoracic and lumbar spine. It was concluded that when load is standardized to individual back strength characteristics, males and females adopted a similar lifting technique. In addition, as load increased male and female participants changed their lifting technique in a similar manner.

The Foldability of Cylindrical Foldable Structures Based on Rigid Origami

Foldable structures, a new kind of space structures developed in recent decades, can be deployed gradually to a working configuration and also can be folded for transportation, thus have potentially broad application prospects in the fields of human life, military, aerospace, building structures, and so on. Combined with the technology of origami folding, foldable structures derive more diversified models, and the foldable structures in cylindrical shape are mainly studied in this paper. Some researchers use the theory of quaternion representing spatial fixed-point rotation and construct the rotating vector model to obtain the quaternion rotation sequence method (QRS method) analyzing origami, but the method is very limited and not suitable for the cylindrical foldable structures. In order to solve the problem, a new method is developed, which combines the QRS method and the dual quaternion method. After analyzing the folding angle via the QRS method for multivertex crease system and calculating the coordinates of all vertices via the dual quaternion, the rigid foldability can be checked. Finally, two examples are carried out to confirm validity and versatility of the method.

Growth and Agronomic Performance of Cotton When Grown in Rotation with Soybean

Mid-South United States (US) cotton producers are now rotating cotton (Gossypium hirsutum L.) with other crops such as corn (Zea mays L.) or soybean [Glycine max (L.) Merr.] , in response to economic conditions, rather than growing cotton continuously as was the tradition. This research investigated cotton growth and development, lint yield, and fiber quality when cotton was grown following soybean compared to following cotton. Cotton and soybean were grown in six rotational sequences (CCCC, SSSS, CSCS, CSSC, SCSC, and SCCS) during 2012-2015 at Stoneville, MS. These rotations were imposed in production systems utilizing either transgenic or conventional cultivars, with or without glyphosate in the herbicide regime. Dry matter partitioning, leaf chlorophyll (Chl) concentration, lint yield, and fiber quality data were collected. Years when cotton was grown following soybean, produced cotton plants that were on average 13% taller, intercepted on average 6% more sunlight, and contained 13% greater leaf Chl concentrations compared to plants in continuous cotton. Cotton grown following soybean produced increased yields one of the two years. Fiber quality was not impacted by the different rotation sequences. Cotton grown in a conventional production system was competitive with that grown in a transgenic production system. The yield increase observed when growing cotton in rotation with soybean is possibly due to increased soil N via N-fixation from the prior soybean crop and/or due to altered soil microbial populations favorable to the subsequent cotton crop.

The attitude adjustment algorithm in drilling end-effector for aviation

To ensure the perpendicularity of drilling holes in aircraft manufacturing, the attitude of spindle axis must be adjusted to coincide with the normal vector of drilling point before drilling. The double eccentric discs-spherical pair structure was used as attitude adjustment mechanism in drilling end-effector. Therefore, the attitude adjustment algorithm of spindle axis is proposed in this article. There were two attitudes for current and target position, respectively, and the rotation sequence of each eccentric disc would affect the attitude adjustment efficiency. This article presents the path planning and optimal solution choosing from multiple solutions. Finally, the effectiveness and accuracy of the algorithm are verified in simulation and drilling experiment, resulting in a normality tolerance of ±0.5° and precision of H9.

Sugar beet rotation effects on soil organic matter and calculated humus balance in Central Germany

Abstract In order to quantify the influence of land use systems on the level of soil organic matter (SOM) to develop recommendations, long-term field studies are essential. Based on a crop rotation experiment which commenced in 1970, this paper investigated the impact of crop rotations involving increased proportions of sugar beet on SOM content. To this end, soil samples were taken in 2010 and 2012 from the following crop rotation sequences: sugar beet–sugar beet–winter wheat–winter wheat (SB–SB–WW–WW = 50%), sugar beet–sugar beet–sugar beet–winter wheat (SB–SB–SB–WW = 75%), sugar beet–grain maize (SB–GM = 50%) and sugar beet-monoculture (SB = 100%); these were analysed in terms of total organic carbon (TOC) and microbial biomass carbon (MBC) content, MBC/TOC ratio and the TOC stocks per hectare. In addition, humus balances were created (using the software REPRO, reference period 12 years) in order to calculate how well the soil was supplied with organic matter. In the field experiment, harvest by-products (WW and GM straw as well as SB leaves) were removed. After 41 years, no statistically significant differences were measured between the crop rotations for the parameters TOC, MBC, MBC/TOC ratio and the TOC stock per hectare. However, the calculated humus balance was significantly affected by the crop rotation. The calculated humus balance became increasingly negative in the order SB–SB–WW–WW, SB–SB–SB–WW, SB monoculture and SB–GM, and correlated with the soil parameters. The calculated humus balances for the reference period did not reflect the actual demand for organic matter by the crop rotations, but instead overestimated it.

PAPR reduction for FBMC-OQAM systems using P-PTS scheme

Filter bank multi-carrier (FBMC) with offset quadrature amplitude modulation (OQAM) has been regarded as one of the candidates for next generation broadband wireless communication systems. Being a multi-carrier technique, FBMC suffers from the inherent drawback of high peak-to-average power ratio (PAPR). And it has been turned out that conventional PAPR reduction schemes for orthogonal frequency division multiplexing (OFDM) systems are ineffective for FBMC-OQAM systems, due to the overlapping structure of FBMC-OQAM signals. In this paper, we propose an efficient PAPR reduction scheme based on a two-step optimization structure, named pretreated partial transmit sequence (P-PTS). The first step uses a multiple overlapping symbols joint optimization scheme that the phase rotation sequences for current symbol is determined and optimized according to previous overlapped symbols. And in the second step, it employs a novel segment PAPR reduction scheme based on PTS technique. Simulation results indicate that the proposed P-PTS scheme can achieve better PAPR reduction performance than conventional methods with lower computational complexity and the complexity can be traded off more flexibly with PAPR reduction performance.

Multi-Scale Jacobi Method for Anderson Localization

A new KAM-style proof of Anderson localization is obtained. A sequence of local rotations is defined, such that off-diagonal matrix elements of the Hamiltonian are driven rapidly to zero. This leads to the first proof via multi-scale analysis of exponential decay of the eigenfunction correlator (this implies strong dynamical localization). The method has been used in recent work on many-body localization [arXiv:1403.7837].

Optimal forest rotation age under efficient climate change mitigation

This paper considers the optimal rotation of forests when the carbon flows from forest growth and harvest are priced with an increasing price. Such evolution of carbon price is generally associated with economically efficient climate change mitigation, and would provide incentives for the land-owner for enhanced carbon sequestration. For an infinitely long sequence of even-aged forest rotations, the optimal harvest age changes with subsequent rotations due to the changing carbon price. The first-order optimality conditions therefore also involve an infinite chain of lengths for consecutive forest rotations, and allow the approximation of the infinite-time problem with a truncated series of forest rotations.Illustrative numerical calculations show that when starting from bare land, the initial carbon price and its growth rate both primarily increase the length of the first rotation. With some combinations of the carbon pricing parameters, the optimal harvest age can be several hundred years if the forest carbon is released to the atmosphere upon harvest. In the near term, however, a higher growth rate of carbon price can lead to shorter rotations for forests that are already near their optimal rotation age, indicating that the effect of carbon price dynamics on optimal rotation is not entirely monotonous. The introduction of carbon pricing can also have a significant impact on bare land value, and in some considered parametrizations the land value was based solely on its potential to capture and store atmospheric carbon.

Shooting motion in high school, collegiate, and professional men’s lacrosse players

The purposes of this research were to quantify the kinematics of the lacrosse shot, based on arm dominance and player experience level. Male players (N = 39; 14–30 years; high school [n = 24], collegiate [n = 9], professional [n = 6]), performed overhead shots using dominant and non-dominant sides. Motion was captured using a high-speed, 12-camera optical system and high-speed filming. Body segment rotational velocities and joint angles were determined at key points in the shot cycle from foot contact (0% of shot) to ball release (100% of shot). All players shot with less anterior trunk lean, less transverse shoulder rotation, and slower trunk-shoulder rotational velocities with the non-dominant side than the dominant side (all p < 0.05). Professional players produced crosse angular velocities 21% faster than high school or collegiate players (p < 0.05). Transverse shoulder rotation range of motion on both dominant and non-dominant and trunk rotation sides was highest in the professional players (p < 0.05). These kinematic features enable professional players to produce faster ball speeds than younger players (138 ± 7 km/h vs. 112 ± 15 km/h, respectively; p < 0.05). Less anterior lean or suboptimal rotation sequence could increase proximal shoulder forces that could contribute to injury as in other throwing sports.

High-resolution Neogene and Quaternary estimates of Nubia-Eurasia-North America Plate motion

Reconstructions of the history of convergence between the Nubia and Eurasia plates constitute an important part of a broader framework for understanding deformation in the Mediterranean region and the closing of the Mediterranean Basin. Herein, we combine high-resolution reconstructions of Eurasia-North America and Nubia-North America Plate motions to determine rotations that describe Nubia-Eurasia Plate motion at ∼1 Myr intervals for the past 20 Myr. We apply trans-dimensional hierarchical Bayesian inference to the Eurasia-North America and Nubia-North America rotation sequences in order to reduce noise in the newly estimated Nubia-Eurasia rotations. The noise-reduced rotation sequences for the Eurasia-North America and Nubia-North America Plate pairs describe remarkably similar kinematic histories since 20 Ma, consisting of relatively steady seafloor spreading from 20 to 8 Ma, ∼20 per cent opening-rate slowdowns at 8–6.5 Ma, and steady plate motion from ∼7 Ma to the present. Our newly estimated Nubia-Eurasia rotations predict that convergence across the central Mediterranean Sea slowed by ∼50 per cent and rotated anticlockwise after ∼25 Ma until 13 Ma. Motion since 13 Ma has remained relatively steady. An absence of evidence for a significant change in motion immediately before or during the Messinian Salinity Crisis at 6.3–5.6 Ma argues against a change in plate motion as its causative factor. The detachment of the Arabian Peninsula from Africa at 30–24 Ma may have triggered the convergence rate slowdown before 13 Ma; however, published reconstructions of Nubia-Eurasia motion for times before 20 Ma are too widely spaced to determine with confidence whether the two are correlated. A significant discrepancy between our new estimates of Nubia-Eurasia motion during the past few Myr and geodetic estimates calls for further investigation.

Scaling of oscillation frequencies in rotating stars

AbstractWe have studied oscillation frequencies of two-dimensional uniformly rotating zero-age main sequence stellar models in the delta Scuti mass range. We identified 370 p and g axisymmetric modes for non-rotating models and then traced their evolution as the rotational velocity was increased. For each mass we considered a rotation sequence of ten models, with the largest rotation rate being about 200 km s−1. We constrained the models to have the same surface shape, which can be characterized for uniform rotation by the ratio between the polar and the equatorial radii. We find that scaling relationships exist among the oscillation frequencies calculated for models with the same shape. For p modes, this scaling closely follows the period root-mean-density relation found in spherical stars. The g modes also scale between models of the same shape, with the scaling reflecting the change in properties outside the convective core as the stellar mass increases. These scaling relationships can be particularly useful in finding specific stellar models to match the oscillation frequencies of individual stars.

Atomic Level Distributed Strain within Graphene Divacancies from Bond Rotations

Vacancy defects play an important role in influencing the properties of graphene, and understanding their detailed atomic structure is crucial for developing accurate models to predict their impact. Divacancies (DVs) are one of the most common defects in graphene and can take three different structural forms through various sequences of bond rotations to minimize the energy. Using aberration-corrected transmission electron microscopy with monochromation of the electron source, we resolve the position of C atoms in graphene and measure the C-C bond lengths within the three DVs, enabling a map of bond strain to be generated. We show that bond rotations reduce the maximum single bond strain reached within a DV and help distribute the strain over a larger number of bonds to minimize the peak magnitude.

In-field self-calibration of robotic manipulator using stereo camera: application to Humanitarian Demining Robot

A robotic manipulator using a stereo camera mounted on one of its links requires a precise kinematic transformation calibration between the manipulator and the camera coordinate frames, the so-called hand–eye calibration, to achieve high-accuracy end-effector positioning. This paper introduces a new method that performs simultaneous joint angle and hand–eye calibration, based on a traditional method that uses a sequence of pure rotations of the manipulator links. The new method considers an additional joint angle constraint, which improves the calibration accuracy when the circular arc that can be measured by the stereo camera is very limited. Experimental results using a manipulator developed for humanitarian demining demonstrate that relative errors between the end effector and the external points mapped by the stereo camera are greatly reduced compared to traditional methods.

SU‐E‐T‐761: TOMOMC, A Monte Carlo‐Based Planning VerificationTool for Helical Tomotherapy

Purpose:Present a new Monte Carlo code (TOMOMC) to calculate 3D dose distributions for patients undergoing helical tomotherapy treatments. TOMOMC performs CT‐based dose calculations using the actual dynamic variables of the machine (couch motion, gantry rotation, and MLC sequences).Methods:TOMOMC is based on the GEPTS (Gama Electron and Positron Transport System) general‐purpose Monte Carlo system (Chibani and Li, Med. Phys. 29, 2002, 835). First, beam models for the Hi‐Art Tomotherpy machine were developed for the different beam widths (1, 2.5 and 5 cm). The beam model accounts for the exact geometry and composition of the different components of the linac head (target, primary collimator, jaws and MLCs). The beams models were benchmarked by comparing calculated Pdds and lateral/transversal dose profiles with ionization chamber measurements in water. See figures 1–3. The MLC model was tuned in such a way that tongue and groove effect, inter‐leaf and intra‐leaf transmission are modeled correctly. See figure 4.Results:By simulating the exact patient anatomy and the actual treatment delivery conditions (couch motion, gantry rotation and MLC sinogram), TOMOMC is able to calculate the 3D patient dose distribution which is in principal more accurate than the one from the treatment planning system (TPS) since it relies on the Monte Carlo method (gold standard). Dose volume parameters based on the Monte Carlo dose distribution can also be compared to those produced by the TPS. Attached figures show isodose lines for a H&amp;N patient calculated by TOMOMC (transverse and sagittal views). Analysis of differences between TOMOMC and TPS is an ongoing work for different anatomic sites.Conclusion:A new Monte Carlo code (TOMOMC) was developed for Tomotherapy patient‐specific QA. The next step in this project is implementing GPU computing to speed up Monte Carlo simulation and make Monte Carlo‐based treatment verification a practical solution.

Measured symmetry of facial 3D shape and perceived facial symmetry and attractiveness before and after orthognathic surgery

One aim of cranio-maxillo-facial surgery is to strive for an esthetical appearance. Do facial symmetry and attractiveness correlate? How are they affected by surgery? Within this study faces of patients with orthognathic surgery were captured and analyzed regarding their symmetry.A total of 25 faces of patients were measured three-dimensionally by an optical sensor using the fringe projection technique before and after orthognathic surgery. Based upon this data an asymmetry index was calculated for each case. In order to gather subjective ratings each face was presented to 100 independent test subjects in a 3D rotation sequence. Those were asked to rate the symmetry and the attractiveness of the faces. It was analyzed to what extend the ratings correlate with the measured asymmetry indices and whether pre- and post-surgical data differ.The measured asymmetry indices correlate significantly with the subjective ratings of both items. The measured symmetry as well as the rated symmetry and attractiveness increased on average after surgery. The increase of the ratings was even statistically significant. A larger enhancement of symmetry is achieved in pre-surgical strongly asymmetric faces than in rather symmetric faces.

In-field fast calibration of FOG-based MWD IMU for horizontal drilling

A fiber optic gyroscope (FOG)-based measuring-while-drilling (MWD) device for horizontal drilling is developed and an in-field fast calibration method of the MWD inertial measurement unit (IMU) is presented. The IMU consists of a FOG triad and a quartz accelerometer triad. An error model for the inertial sensors is established and 12 errors are confirmed as the main error sources for horizontal drilling after an analysis. A five-rotation-in-level-plane (5RILP) in-field fast calibration scheme for the main errors of the MWD IMU is illustrated. The scheme can be conveniently implemented on an almost level plane, such as a table plane, without any special external equipment. To solve the calibrated errors, a systematic approach based on specific force measurement observation is adopted. Observation equations of the IMU errors are derived according to the rotation sequence of the calibration scheme. Simulation results show that the proposed calibration method is effective even if there are 5° errors in level and 10° errors in heading. Calibration experiments using the developed FOG-based MWD equipment on a table plane confirm the validity of the proposed in-field calibration method. Inertial navigation tests show that the actual accuracy of the MWD IMU is greatly improved by 60.6% after in-field calibration.