Three-dimensional Reference Frame Research Articles

Transient Deformation in California From Two Decades of GPS Displacements: Implications for a Three-Dimensional Kinematic Reference Frame.

Our understanding of plate boundary deformation has been enhanced by transient signals observed against the backdrop of time‐independent secular motions. We make use of a new analysis of displacement time series from about 1,000 continuous Global Positioning System (GPS) stations in California from 1999 to 2018 to distinguish tectonic and nontectonic transients from secular motion. A primary objective is to define a high‐resolution three‐dimensional reference frame (datum) for California that can be rapidly maintained with geodetic data to accommodate both secular and time‐dependent motions. To this end, we compare the displacements to those predicted by a horizontal secular fault slip model for the region and construct displacement and strain rate fields. Over the past 19 years, California has experienced 19 geodetically detectable earthquakes and widespread postseismic deformation. We observe postseismic strain rate variations as large as 1,000 nstrain/year with moment releases equivalent up to an Mw6.8 earthquake. We find significant secular differences up to 10 mm/year with the fault slip model, from the Mendocino Triple Junction to the southern Cascadia subduction zone, the northern Basin and Range, and the Santa Barbara channel. Secular vertical uplift is observed across the Transverse Ranges, Coastal Ranges, Sierra Nevada, as well as large‐scale postseismic uplift after the 1999 Mw7.1 Hector Mine and 2010 Mw7.2 El Mayor‐Cucapah earthquakes. We also identify areas of vertical land motions due to anthropogenic, natural, and magmatic processes. Finally, we demonstrate the utility of the kinematic datum by improving the accuracy of high‐spatial‐resolution 12‐day repeat‐cycle Sentinel‐1 Interferometric Synthetic Aperture Radar displacement and velocity maps.

Three-dimensional analysis for changes in dentigerous cyst-associated maxillary canines after marsupialization in adolescents

To observe three-dimensional changes of dentigerous cyst-associated maxillary canines (DCAMC) in adolescents after marsupialization by using cone beam computed tomography (CBCT). Methods: A total of 34 DCAMC patients with dentigerous cyst aged 10-14 were divided into central type and lateral type, while canines on the non-cyst side served as a control. A three-dimensional reference frame was set up to analyze the position, angle changes and influential factors for DCAMC by using CBCT before operation and in 3-6 month after operation. Results: 1) Compared with pre-operation, there was significant vertical movement in DCAMC after marsupialization. Tip of tooth moved labially while tooth axis inclined mesiodistally; 2) Horizontal, vertical movement and mesiodistal inclination of DCAMC were significantly greater than those in the health side; 3) Compared with the lateral type DCAMC, the central type DCAMC showed a significant changes in labial inclination; 4) Horizontal movement, mesiodistal and labial inclination of lateral type DCAMC were all evidently greater than those of the central type DCAMC; 5) Vertical movement and inclination of DCAMC after marsupialization were significantly correlated to the time interval (r=0.354, 0.374, both P<0.05), while vertical movement of cuspid in health side was significantly negative correlated with the patients' age and the level of root formation (r=-0.506, -0.721, both P<0.01). Conclusion: DCAMC in adolescents can obtain obvious changes in position and angles after marsupialization regardless of the level of root formation, which is beneficial for further orthodontic treatment.

Transfer of spatial reference frame using singlet states and classical communication

A simple protocol is described for transferring spatial orientation from Alice to Bob (two spatially separated observers). The two observers are assumed to share quantum singlet states and classical communication. The protocol assumes that Alice and Bob have complete free will (measurement independence) and is based on maximizing the Shannon mutual information between Alice and Bob’s measurement outcomes. Repeated use of this protocol for each spatial axis of Alice allows transfer of a complete three-dimensional reference frame, up to inversion of each of the axes. The technological complexity of this protocol is similar to that needed for BB84 quantum key distribution and hence is much simpler to implement than recently proposed schemes for transmission of reference frames. A second protocol based on a Bayesian formalism is also discussed.

The impact of the scale factor on the horizontal geodetic coordinates obtained by a three-dimensional similarity transformation

In surveying the three-dimensional similarity transformation is commonly used for transforming horizontal geodetic coordinates between a three-dimensional reference frame and a two-dimensional horizontal geodetic datum. A problem that arises when the seven transformation parameters are given in beforehand is to implement the parameters with the correct values and signs. Assigning a wrong sign to the translations or the rotations will probably reveal itself, as the resulting errors in the transformed coordinates normally go up to several tens of metres. However, applying the scale correction with an erroneous sign will not always be discovered easily. In this paper, estimates are given of the errors in the transformed horizontal coordinates caused by an erroneous scale correction. Furthermore, it is demonstrated that an erroneous scale factor will have minor influence on the scale of the transformed horizontal coordinates. Finally an alternative transformation model is suggested which eliminates the need of a scale correction.

Mechanism of competitive growth during directional solidification of a nickel-base superalloy in a three-dimensional reference frame

The microstructure evolution of bicrystal samples during directional solidification was studied, both by simulation and experiment, to explore the mechanism of competitive growth. A new orientation relationship of bicrystal samples, the non-uniplanar case, is proposed, which expands the orientation relationship of bicrystal samples from two dimensions to three dimensions. The results show that, in the non-uniplanar case, the favorably oriented grain overgrows the unfavorably oriented grain by developing new dendrites in the lateral gap where the primary dendrites of the unfavorably oriented grain diverge from the mold wall. During this process, the grain boundary is found to move in two directions, one perpendicular to the grain boundary and the other parallel to the grain boundary. To characterize the state of dendrite growth, a three-dimensional reference frame is constructed. In this reference frame, the mechanism of competitive growth can be categorized as a converging case, a non-uniplanar case and a diverging case. Furthermore, the simulation results are in good agreement with the experimental findings.

Rigorous Estimation of Local Accuracies

This technical note introduces a rigorous calculation of “local accuracies.” The term local accuracies refers to the relative error between two arbitrary points (uncertainty of one point with respect to the other), expressed in a local horizon three-dimensional reference frame ( e,n,u ) , that were connected using any geodetic-surveying methodology [optical procedures, global positioning system (GPS), etc.]. It is calculated as a function of the full global Cartesian variance-covariance matrix of the ( x,y,z ) coordinates of the points defining the spatial network.

Mohr-cyclides, a 3D representation of geological tensors: The examples of stress and flow

Mohr-circles are commonly used to represent second-rank tensors in two dimensions. In geology, this mainly applies to stress, flow, strain and deformation. Three-dimensional second rank tensors have been represented by sets of three Mohr-circles, mainly in the application of stress. This paper demonstrates that three-dimensional second rank tensors can in fact be represented in a three-dimensional reference frame by Mohr surfaces, which are members of the cyclide family. Such Mohr-cyclides can be used to represent any second rank tensor and are exemplified with the stress and flow tensors.

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Three-dimensional changes of maxilla after rapid maxillary expansion

To investigate three-dimensional changes of maxilla after rapid maxillary expansion (RME). Ten patients treated with RME were included in the study. Spiral CT images were used to evaluate three-dimensional changes of the maxilla. A three-dimensional reference frame was set up. (1) ANS, PNS' and PNS displaced downward and forward. ANS-PNS plane rotated clockwise in the mid-sagittal plane. ANS-PNS' plane, which represents the real position of maxilla, was not changed in the mid-sagittal plane. The palatal suture was expanded in taper shape and two halves of the maxilla rotated in the frontal plane. (2) The maxillary suture was opened wider in the middle and narrower at both ends, which was like a spindle. Three-dimensional changes were found after RME treatment. Spiral CT was useful in the three-dimensional evaluation of maxilla.

Fractal characterization of three-dimensional zooplankton swimming trajectories

Several natural processes, such as swimming and flying, occur in a three-dimensional reference frame and thus describe three-dimensional trajectories. Analysing such tracks is no easy task. To this aim, here we propose a new technique, based on the box-counting approach, by which to estimate the three-dimensional fractal dimension ( D 3D) of spatially-evolving routes. This technique has been preliminary tested on two sets of random walks (pure and correlated). Then, our approach has been utilised to characterise the swimming trajectories performed by the freshwater cladoceran Daphnia pulex under two light conditions. Morphologically different tracks attain statistically different D 3D values, smoother paths having lower values than more tortuous ones; therefore, our proposed methodology proves to be fruitful in direct comparisons. Moreover D 3D can highlight bizarre situations, in which differently convoluted tracks are characterised by the same degree of contortion.

Testing the three-dimensional reference frame transformation for express and memory-guided saccades

The geometry of eye rotations necessitates an internal reference frame transformation between retinocentric visual codes and headcentric displacement commands for saccades. Here, we ask if this eye position-dependent transformation is bypassed in “express saccades” or degraded in “memory saccades”, perhaps to favor a more direct visuomotor transformation. The answer to both was no: quantification of the behavioral data against simulated predictions revealed a correct biological transformation common to all saccades. This is discussed in terms of our “conversion-on-demand” model, wherein target representations are stored and updated within an early visual frame, but then transformed into appropriate motor frames for action.

Near-electrode model for 100-standard atmosphere arc discharges

The near-electrode region is important to the design of high-pressure electric arc heaters. An understanding of the detailed physics of the discharge in the immediate region around the attachment to the electrode surfaces, where there is a rapid transition from gaseous to solid-state conduction of electrical current, is key to understanding such issues as electrode erosion and survival. A continuum model for the near-electrode region at high pressure is presented, extending from the flow region all the way into a copper electrode. The gaseous part of the model is treated with a one-dimensional approximation, and the heat conduction in the solid material is analyzed in a three-dimensional reference frame that moves with the arc attachment spot. Experimental data on the near-electrode region of high-pressure arc heaters are very limited, they mainly consist of dimensions of arc tracks and mass-loss measurements. Incorporating a field-emission boundary condition at the cathode spot and a nonequilibrium electron temperature at the anode spot yields results that agree with the data.