Rigid Rotation Model Research Articles

Present-day movement trends of the major tectonic faults in the Sichuan-Yunnan region based on the constraint of GPS velocity fields

Based on the known fault distribution in Sichuan-Yunnan region (SYR), a rigid Euler rotation model is constructed by using GPS velocities (1998 ~ 2016) after excluding the stations near the fault boundaries and simultaneously a translation-rotation-strain model is constructed by using almost all GPS velocities to calculate three periods strain rate fields (2008.6 ~ 2010.4, 2010.5 ~ 2013.4 and 2013.5 ~ 2016.12) after Wenchuan earthquake. The results show that: (1) the strike-slip activity is the most common trends for the regional faults. The Xianshuihe-Xiaojiang fault, the Lancangjiang-Weixi-Weishan-Wuliangshan fault and the Longmenshan fault are the most active in the whole SYR, and the dislocation rate is more than 15 mm/a, and the trend of activity gradually decreases from the northwest to the southeast. (2) The different activity rates of the faults in the study area indicate that some of the eastward extrusion of the Tibet Plateau is absorbed and adjusted by the inside faults, and it is not a few large strike-slip faults. (3) Through the analysis of three periods’ grid velocity fields, we found that the movement rates of the Bitu section of Lanchangjiang fault, the Northwestern section of Weixi-Weishan fault and the Nujiang fault after Wenchuan earthquake are larger than that after Yushu and Ya’an earthquake, and the difference is about 8 mm/a. Besides, the activity rate of Northwestern section of Longmenshan fault after the Wenchuan earthquake is larger than that after the Ya’an earthquake, although the two epicentres distances are relatively close. (4) The strain rate fields and surface expansion rates show that the high value area is mainly distributed at or around the intersection among some fault zones and its surroundings, and the maximum area is mainly located at some long and deep fault zones such as the Longriba fault, the Longmenshan fault zone, the Ganzi-Yushu fault and the Xianshuihe, and the magnitude is about 35 ~ 50 nanstrain/a. The research should provide fundamental material for the study of crustal stress variation and earthquake prediction in Sichuan-Yunnan region.

Solution Behavior in the Vicinity of Characteristic Envelopes for the Double Slip and Rotation Model

The boundary conditions significantly affect solution behavior near rough interfaces. This paper presents general asymptotic analysis of solutions for the rigid plastic double slip and rotation model in the vicinity of an envelope of characteristics under plane strain and axially symmetric conditions. This model is used in the mechanics of granular materials. The analysis has important implications for solving boundary value problems because the envelope of characteristics is a natural boundary of the analytic solution. Moreover, an envelope of characteristics often coincides with frictional interfaces. In this case, the regime of sticking is not possible independently of the friction law chosen. It is shown that the solution is singular in the vicinity of envelopes. In particular, the profile of the velocity component tangential to the envelope is described by the sum of the constant and square root functions of the normal distance to the envelope in its vicinity. As a result, some components of the strain rate tensor approach infinity. This finding might help to develop an efficient numerical method for solving boundary value problems and provide the basis for the interpretation of some experimental results.

Effect of stirring rate on grain morphology of Mg-Al alloy semi-solid structure by phase field lattice Boltzmann simulation

In order to investigate the effects of stirring rate on semi-solid structure of Mg-Al alloy, a PF-LBM model (Phase Field Lattice Boltzmann model) coupled with a rigid body rotation model were adopted in this work. Grain morphology, grain growth rate and grain rotation at different stirring rates were systematically studied. The results indicated that by driving force of melt flow velocity difference around the grain, the grain rotated during the stirring process, and then solute concentration would present to the low flow areas around the grain, which was caused by the forced convection. The solutes are uniformly distributed around the grain as the grain rotates. As a result, the fine and spherical grain can be obtained owing to the inhibition of grain growth.

Acceleration Response Analysis of the SCR rigid body swing under wave and x-direction motion

Under the action of waves or current, the rigid body oscillation from the suspension point to touch down point(TDP) is a real problem of steel catenary riser(SCR). The influence of the phenomenon on the acceleration in cross flow of riser is not to be ignored. On the basis of the slightness beam with large deformation model coupling the wave force model and the rigid body rotation model, the impact of rigid body swing on the cross flow of structure’s acceleration is researched under the wave action and x direction motion. Numerical calculation manifests that the maximum impact of rigid body swing on structure acceleration is approximately 20%. Rigid body rotation is differ from the wave action and the top motion reducing with the depth of the water. Rigid body rotation increases with the radius vector S. The relative reduction calculation shows that between 10th and 140th, the structural response decreased by about 30%, and between 140th-seabed, by about 15%. The normalized calculation results from each node show that between 10th and 140th, the structural response decreases with the increase of the x-direction load frequency or the decrease of amplitude. Between the 140th-seabed, the structural response is increasing. It is expected that some rational and pragmatic suggestions can be provided for the computation of transverse flow of SCR. With the help from the team, the work of the article can be carried out. It is desired that, this article will help the team.

Lamellar and bundled domain rotations in barium titanate

Cross-correlation of electron backscatter diffraction patterns has been used to generate rotation maps of single crystals of tetragonal barium titanate (BaTiO3) containing multiple lamellae and bundles of ≈ 90° domains. Rotation measurement angular resolutions of 0.1 mrad (0.006°) and spatial resolutions of 30 nm are demonstrated on structures with approximately 1 μm domains extending over 10s of μm. The material orientations demonstrated considerable microstructural dependence: c domains, with polarization perpendicular to a free surface, exhibited little within-domain rotation variation while a-domains, with polarization parallel to the surface, exhibited considerable within-domain variation, particularly in the larger lamellar domain structure. In both lamellar and bundled structures, the maximum a–c between-domain rotation was approximately equal to the value θr ≈ 0.63° (11 mrad) predicted by a rigid rotation of tetragonal BaTiO3 unit cells across the domain boundary. However, in both structures there was gradual variation in rotation throughout, especially adjacent to domain boundaries, suggesting that a rigid rotation model predicts too abrupt a unit cell and polarization rotation. A new BaTiO3 compound defect was deduced through identification of a double integral surface rotation 2θr. The double rotation is indicative of a low-angle grain boundary terminating at a surface by a confined 90° domain.

Response analysis with cable3D of the SCR rigid rotation model under the wave action and y direction motion in the oil production and transportation

The steel catenary riser(SCR) is an important equipment for offshore oil production. Its research is very important for the safety of oil exploitation. The SCR has a rigid rotation axis from the hanging point to the touch down point(TDP). The influence of rigid body rotation on the response of the cross flow is not negligible. This paper considers the bending vibration model, the rigid body model, and the wave forces mode. The effects of rigid body rotation on the structure acted on wave action and y direction motion is studied. The calculation shows that the response of the structure is the largest in the top area and the structure response value no longer changed greatly after a certain depth. The higher the amplitude in the top region, the faster the response goes down. After coupling top y-direction motion, the phenomenon of decreasing with response of water depth is still present, and the effect of rigid body swing on the structure is not more than that of the wave load. It is expected that the above research can be helpful for the design of steel suspension chain riser.

Singular solutions for the rigid plastic double slip and rotation model under plane strain

In the mechanics of granular and other materials the system of equations comprising the rigid plastic double slip and rotation model together with the stress equilibrium equations under plane strain conditions forms a hyperbolic system. Boundary value problems for this system of equations can involve a frictional interface. An envelope of characteristics may coincide with this interface. In this case, the solution is singular. In particular, some components of the strain rate tensor approach infinity in the vicinity of the frictional interface. Such behavior of solutions is in qualitative agreement with experimental data that show that a narrow layer of localized plastic deformation is often generated near frictional interfaces. The present paper deals with asymptotic analysis of the aforementioned system of equations in the vicinity of an envelope of characteristics. It is shown that the shear strain rate and the spin component in a local coordinate system connected to the envelope follow an inverse square root rule in its vicinity.

Photoassociation spectra of ultracold 85Rb2 molecule in long range state near the 5S1/2 + 5P1/2 asymptote**Project supported by the National Natural Science Foundation of China (Grant Nos. 61675120, 11434007, and 61378015), the National Natural Science Foundation of China for Excellent Research Team (Grant No. 61121064), the Shanxi Scholarship Council of China, and the PCSIRT (Grant No. IRT 13076).

We investigate the high resolution photoassociation spectra of Rb molecules in long range state below the (5S + 5P) asymptote. The Rb atomic samples are trapped in a dark magneto–optical trap (MOT) and prepared in the dark state. With the help of trap loss technique, we obtain considerable photoassociation spectroscopy with rovibrational resolution, some of which have never been observed before. The observed spectrum is fitted by a rigid rotation model, and the rotational constants of ultracold Rb molecule in long range are obtained for different vibrational states. By applying the LeRoy–Bernstein method, we assign the vibrational quantum numbers and derive coefficient, which is used to obtain the potential energy curve.

Plate Convergence and Block Motions in Mindanao Island, Philippine as Derived from Campaign GPS Observations

We conducted yearlyGlobal Positioning System(GPS) campaigns in the eastern part of Mindanao from March 2010 to March 2014. The obtained station velocities with respect to the Sunda plate (SU) show that WNW motions are dominant due to the convergence of the Philippine Sea plate (PHS). However, it was found that elastic deformations caused by a full coupling of the plate interface down to 80 km could explain a maximum of only 29% of the observed station velocities. In order to interpret the displacement pattern, we applied a rigid block rotation model and determined the Euler vector. As a result, we determined that Mindanao Island could be divided into at least three blocks and that the Philippine fault is one of the block boundaries. Although it was not possible to determine the coupling ratio at the Philippine trench, the dislocation pattern of the Philippine fault showed along-strike variation in Mindanao Island.

A hybrid rigid body rotation model for predicting a response of a temporary soil-filled wall subjected to blast loading

This study is aimed to provide an efficient analytical model to calculate a time history of response for a free-standing soil-filled HESCO Bastion concertainer ® wall subjected to air blast loading. The model is formulated based on the observations of the wall response to air blast loading in the experiments and on the deformation of a finite element model. This hybrid rigid body rotation model combines both a reverse Winkler foundation to model the distribution of pressure at the base of the wall and perfectly plastic shear resistance to model the shear deformation at the corner. The time histories of horizontal and vertical displacements calculated from the proposed analytical model are validated with displacements from both full-scale blast testing of free-standing simple straight walls and calculations using a finite element model.

Crack Size Evaluation Using Unloading Compliance in Single-Specimen Single-Edge-Notched Tension Fracture Toughness Testing

Abstract Crack-mouth-opening displacement (CMOD) unloading compliances of single-edge-notched tension (SE(T)) specimens, both pin-loaded and clamped, have been evaluated by finite element analysis (FEA), including evaluation of the effect of rotation during testing on compliance. For pin-loaded specimens, FEA results are compared with compliance correction equations based on a rigid-body rotation model recommended by Joyce and Link. The results agree reasonably well when the load line is far from the midsection of the ligament. However, the discrepancy increases when the load line approaches the midsection of the ligament where the bending load becomes small or negligible compared with the tension component and the rigid-rotation model breaks down. For clamped SE(T) specimens, factors affecting specimen rotation, such as the ratio H/W of span between load points H to width of the specimen W, normalized crack size, a/W, and material strain hardening coefficient, N, were investigated. This work was performed for specific application to surface circumferential cracks in pipes, for which the best constraint matching has been found to occur for clamped specimens with H/W = 10. For this geometry, an equation is proposed to correct compliance for rotation and to estimate crack size from rotation-corrected CMOD compliance. Crack sizes evaluated using this equation are compared with measurements on broken specimens. Excellent agreement has been achieved for initial and final crack sizes of both plain-sided and side-grooved SE(T) specimens.

An asteroseismic study of the Cephei star Ophiuchi: constraints on global stellar parameters and core overshooting

We present a seismic study of the β Cephei star θ Ophiuchi. Our analysis is based on the observation of one radial mode, one rotationally split ℓ= 1 triplet and three components of a rotationally split ℓ= 2 quintuplet for which the m values were well identified by spectroscopy. We identify the radial mode as fundamental, the triplet as p1 and the quintuplet as g1. Our non‐local thermodynamic equilibrium abundance analysis results in a metallicity and CNO abundances in full agreement with the most recent updated solar values. With X∈[0.71, 0.7211] and Z∈[0.009, 0.015], and using the Asplund et al. mixture but with a Ne abundance about 0.3 dex larger, the matching of the three independent modes enables us to deduce constrained ranges for the mass (M= 8.2 ± 0.3 M⊙) and central hydrogen abundance (Xc= 0.38 ± 0.02) of θ Oph and to prove the occurrence of core overshooting (αov= 0.44 ± 0.07). We also derive an equatorial rotation velocity of 29 ± 7 km s−1. Moreover, we show that the observed non‐equidistance of the ℓ= 1 triplet can be reproduced by the second‐order effects of rotation. Finally, we show that the observed rotational splitting of two modes cannot rule out a rigid rotation model.

A rigid block rotation model for the GPS derived velocity field along the Ryukyu arc

Using a GPS derived velocity field, we try to estimate the kinematic features of the Ryukyu arc, and discuss its implications to the spreading of the Okinawa trough. The GPS derived strain rate field implies that internal deformation within the Ryukyu arc is not significant, therefore, we adopt a rigid block rotation model for the motion of the Ryukyu arc. The velocity field in the Ryukyu arc is best explained by a model with three blocks rather than one with only one block. The estimated block rotations predict the spreading along the Okinawa trough. The predicted spreading is slow (10 mm per year) in the north and fast (50 mm per year) in the southwest. The direction of the predicted spreading is normal to the Okinawa trough (N170°E–N180°E) in the southwest, while in the north the direction of the spreading is oblique to the Okinawa trough (N150°E–N180°E).

Equilibrium of a non-neutral plasma in a toroidal magnetic shear configuration

The conventional rigid rotation model of thermal equilibrium does not apply to a toroidal non-neutral plasma trap; the nonuniformity of the magnetic field produces an inhomogeneous flow. For sufficiently large ωc/ωp (ωc: cyclotron frequency; ωp: plasma frequency), the flow can be approximated by the E×B drift velocity. The toroidal equilibrium of an electron plasma has been analyzed for a rather complex geometry of magnetic shear configuration.

Ferromagnetic-resonance field shift in an exchange-biased CoO/Ni 80Fe 20 bilayer

The temperature dependence of the ferromagnetic resonance field shift has been investigated in a CoO/Permalloy bilayer between room temperature and 4 K. The field shift is found to consist of two components: a unidirectional exchange-bias field shift and a uniaxial anisotropic field shift. These field shifts are shown to be equal to the conventional exchange bias and anisotropy fields, provided the rigid spin rotation hypothesis is correct. We have also measured the temperature variation of the exchange bias and the magnetic anisotropy fields from hysteresis loops obtained from SQUID-magnetometry, and found incomplete agreement with the parameters obtained from the ferromagnetic resonance spectra. Analogies with spin-glass phenomena indicate that this incomplete agreement results from the breakdown of the rigid rotation model (or equivalently, the surface anisotropy model) results due to the large rotation angles encountered in a magnetic moment reversal. Notwithstanding, we show that the results of rotating the sample by 180° in the plane of the film yields changes in the resonance field shift which are in agreement with hysteresis loop parameters. A connection between results observed in exchange bias materials and those in spin-glass materials is suggested.

Relaxation of the non-polar ( [formula omitted]) surfaces of wurtzite AℓN and ZnS

Using the pseudo-function method and local density theory, we minimize the total energy of the ( 10 10 ) surfaces of AℓN and ZnS, within the context of a Rigid Rotation Model. We predict that the surface anions rotate inward toward the bulk through very small angles (in contrast to the anions of the (110) surface of GaAs, which rotate outward through large angles, ω≅29°). Thus, to an adequate approximation, the ( 10 10 ) surfaces of these relatively ionic wurtzite semiconductors do not relax.

Basic Characteristics of Centrifuges, (IV)

A method of numerically solving the convection-diffusion equation is presented for a binary isotopie gas mixture in the axisymmetric velocity field. A modified Newton's method is employed to perform the numerical integration without the assumptions that the pressure can be estimated from the rigid rotation model and the temperature of gas is uniform. A suitable form of the finite difference equation gives a computationally stable integration with reasonable representation of the molar concentration distribution of isotopie molecules in a rotating cylinder. The method includes a Gaussian elimination procedure which consists of the transformation of the Jacobian matrix to a triangular matrix followed by the backward elimination. Computations are made on UF6 gas in various centrifuges which have the openings for feed, product and waste on the end plates. Discussions are also presented on gas flows and separative efficiencies for the centrifuges which have baffle plates, skirting plates and bellows.

Basic Characteristics of Centrifuges, (III)

A method of numerically solving the convection-diffusion equation is presented for a binary isotopie gas mixture in the axisymmetric velocity field. A modified Newton's method is employed to perform the numerical integration without the assumptions that the pressure can be estimated from the rigid rotation model and the temperature of gas is uniform. A suitable form of the finite difference equation gives a computationally stable integration with reasonable representation of the molar concentration distribution of isotopie molecules in a rotating cylinder. The method includes a Gaussian elimination procedure which consists of the transformation of the Jacobian matrix to a triangular matrix followed by the backward elimination. Computations are made on UF6 gas in various centrifuges which have the openings for feed, product and waste on the end plates. Discussions are also presented on gas flows and separative efficiencies for the centrifuges which have baffle plates, skirting plates and bellows.