Orientation Of Principal Axes Research Articles

Arbitrary controlled re-orientation of a spinning body by evolving its tensor of inertia

Bodies with the nonspherical tensor of inertia (TOI) exhibit a variety of rotational motion patterns, including chaotic motion, stable periodic (quasi-periodic) rotation, unstable rotation around the direction close to the body's second principal axis, featuring a well-known tennis-racket (also known as Garriott-Dzhanibekov [1]) effect – series of seemingly spontaneous 180 degrees flips. These patterns are even more complex if the body's TOI is changing with time. Changing a body's TOI has been discussed recently as a tool to perform controllable Garriott-Dzhanibekov flips and similar maneuvers. In this work, the optimal control of the TOI of the body (spacecraft, or any other device that admits free rotation in three dimensions) is used as a means to perform desirable re-orientations of a body with respect to its angular velocity. Using the spherical TOI as the initial and final point of the maneuver, we optimize the parameters of the maneuver to achieve and stabilize the desired orientation of the body's principal axes with respect to spin angular velocity. It appears that such a procedure allows for finding arbitrarily complex maneuver trajectories of a spinning body. In particular, intermediate axis instability can be used to break the alignment of the body's principal axis and the axis of rotation. Such maneuvers do not require utilization of propellants and could be straightforwardly used for attitude control of a spin-stabilized spacecraft. The capabilities of such a method of angular maneuvering are demonstrated in numerical simulations.

Underwater Directional Acoustic Source Based on Pentamode Material

An underwater directional acoustic emitter is conceived with a highly anisotropic lattice material, whose acoustic characteristics manifest strong dependence on the orientation of the lattice material’s principal axis. Exploiting these features, a cylindrical structure made of such anisotropic lattice material is engineered to possess distinct impedance values in different directions, thereby facilitating wave emission along the principal axis while inducing reflection in other directions. Notably, through numerical simulations, it is demonstrated that the emission direction can be effectively manipulated by adjusting the principal axis orientation, concurrently enhancing the emitted power. In contrast to previous directional acoustic structures, the compact emitter presented in this study can get rid of the size-wavelength constraint, enabling effective control of low-frequency waves.

Seasonal dynamics of water circulation and exchange flows in a shallow lagoon-inlet-coastal ocean system

A wave–current coupled, unstructured-grid, three-dimensional hydrodynamic model was applied to investigate the seasonal dynamics of the Maryland Coastal Bays system. The model's performance was validated successfully against hydrodynamic observations from the spring to fall of 2014, and the driving forces of water circulation and exchange flows were discussed. Results indicate that seasonal dynamics are primarily controlled by tides, modulated by winds, waves, and density variations, and regulated by the inlet orientation and geometry. Seasonal circulation in the surface layer is stronger than that near the bottom. The strong coastal circulation, net outflows via inlets, and the clockwise movements in the southern Isle of Wight Bay are primarily controlled by tides. The directional alignment between winds and the bay's principal axis and inlet orientation are key to the seasonal circulation and exchange flows in Sinepuxent Bay and via inlets. Wave-induced effects are comparable to tides in particular regions (e.g., reaching 30 cm/s in Isle of Wight Bay), and much larger than those caused by density variations overall. Additional numerical experiments indicate that spatial variations in salinity are mainly responsible for the density-induced circulation (e.g., 6 cm/s at the mouth of Newport River in Newport Bay). Further analysis indicates that the net exchange flows vary from the surface to bottom layers (e.g., different magnitudes or transporting directions) both in the lagoon and via the paired inlets. This work is beneficial to coastal communities and numerical modelers in understanding the dynamics of shallow lagoon-inlet-coastal ocean systems at a seasonal timescale.

Development of flanking structures in layered gneissic rock: Insights from numerical modelling

Flanking structures defined by dragged planar fabrics alongside of quartzo-feldspathic veins in gneissic rocks are very common. Varieties of mesoscale flanking structures were observed in parts of the Chhotonagpur Granite Gneissic Complex (CGGC), Eastern India. Alternate thin layering of quartzo-feldspathic and mafic minerals in gneissic rock causes mechanical anisotropy in rock during deformation. This study aims to explore specially the influence of mechanical anisotropy on the development of flanking structures. With the help of two –dimensional Finite Element modelling, we attempt to understand the effect of initial orientation of cross-cutting element (θ), kinematic vorticity number (Wk) and the anisotropy factor (δ) on the development of flanking structures. Deformed shape of cross-cutting element (RN), amount (LN) and nature (antithetic or synthetic) of offset of layers and pattern of drag (reverse or normal) are considered as important parameters for their nomenclature. As the final geometry of flanking structure does not only depend on the instantaneous deformational condition, we analyze the progressive development of flanking structures by varying the above parameters. Study reveals that mechanical anisotropy has strong influence on the geometry of flanking structures in layered gneissic rock, which depends on the initial orientation of long axis of cross-cutting element and its final position with respect to the orientation of principal stress axes and pole of anisotropy. The study also reveals that the flanking structures can be used as important tool for estimating the mechanical anisotropy in layered rock. Shape of cross-cutting element, amount of offset and the shifting of the object-tip points are the most important parameters for determining the anisotropy factor.

Numerical Simulation of Hole Cleaning of a Horizontal Wellbore Model with Breakout Enlargement Section

Horizontal wells are more likely than vertical wells to have enlarged wellbore sections due to borehole instability. However, there is scarce research on borehole cleaning of horizontal wells with enlarged wellbore sections. In this paper, we establish a horizontal wellbore model with a breakout enlargement section using field borehole diameter data. We used the three-dimensional computational fluid dynamics (CFD) method and the Realizable k-ε turbulence model with the Euler–Euler approach to simulate the effects of the drilling fluid circulation return speed and the spinning speed of the drill pipe on the cutting movement of conventional horizontal wells and horizontal wells with a breakout enlargement section. The simulation results demonstrate that increasing the drilling fluid circulation return speed and the spinning speed of the drill pipe does not significantly improve the hole cleaning impact for horizontal wells with a breakout enlargement section. We analyzed the effects of the enlargement ratio, ellipticity, and principal axis orientation on the borehole cleaning effect of horizontal wells with a breakout enlargement section. The results show that the cleaning impact is better when the enlargement ratio is lower; moreover, the ellipticity is larger and the principal axis orientation is perpendicular to the gravity direction. This paper fills a gap in the existing theory of hole cleaning in horizontal wells and provides a theoretical basis for improving the hole cleaning effect in actual drilling processes.

Universal Method for Determining the Principal Optical Indicatrix Axes in Triclinic Crystals

Determining the orientations of principal optical indicatrix axes is a key prerequisite for the applications of optical crystals, which is still an intriguing challenge for triclinic optical crystals due to the lowest symmetry. The prism method is one of the important ways to determine these directions, but no actual examples are available owing to the complexity and scarcity of the triclinic crystals so far. To solve this remaining problem among seven crystal systems, we proposed a universal method, the so-called “multiple prisms method,” to determine the orientations of principal optical indicatrix axes X, Y, and Z as well as the principal refractive index values nx, ny, and nz in triclinic crystals based on four prisms and demonstrated this method by employing triclinic Nd3+-doped La2CaB8O16 crystals, which is of great significance to the studies and applications of triclinic optical crystals in the future.

DEM study on the dynamic responses of a ballasted track under moving loading

This paper presents the discrete element modeling of the dynamic response of a ballasted track under moving loads. The DEM model, consisting of sleepers, ballast, and sub-ballast, has been calibrated using field and laboratory data. This model was further used to examine the dynamic responses of the ballasted track subjected to a series of moving traffic loading representing various train axle loads and speeds. The results show that the permanent settlement of the sleeper, the breakage of ballast, and the dynamic stresses in the track substructure increase with an increase in train axle load and speed. As the train moves, the magnitudes of dynamic stresses and the orientations of principal stress axes in the track change continuously, and a more pronounced principal stress rotation is observed at sleeper edges than those underneath sleepers. The capping layer is found to play a critical role in reducing train-induced stress and further alleviating the disturbance from the trains to the subgrade. The interparticle contacts and the vibration of ballast during the movement of the train including the influences of train axle load and speed on the dynamic responses of ballasted railway tracks are captured and analyzed from a micromechanical perspective.

RESULTS OF THE TECTONOPHYSICAL STUDY IN THE DZHANKHOT THRUST ZONE (NORTHWESTERN CAUCASUS)

The paper presents the results of detailed structural analysis of the Dzhankhot thrust zone which is a part of the system of overthrust nappe structures in the southern slope of the Northwestern Caucasus. The relevance of the research topic is found on the reason that despite the obvious importance of these overthrust nappes in the structure of the Greater Caucasus there is still lack of in-situ observational data on the detailed structure of thrust zones and on tectonic stress distribution pattern therein.As a result of the structural and geological studies of small disjunctive and plicative forms in the Upper Cretaceous and Paleocene sediment contact along the Dzhankhot thrust, there were identified the major structural and tectonic deformation patterns and the areal distribution of tectonic deformations depending on the distance to the thrust. There was determined the major type of stress in different parts of the thrust zone. There was shown the difference in the development of geological indicators of faults for different elements of the folded structures. In some cases, there was determined the sequence of deformations, from synsedimentary structures (clastic dikes in particular) to post-sedimentary brittle structures.The orientation of principal stress axes determined from the reconstruction data by method of cataclastic analysis of faults confirms a thrust-type deformation within the studied area near the Dzhankhot thrust. Local stress-tensor determinations are in good agreement with the location of observation points in the regional tectonic structure. Trajectories of the maximum compression axes, most of which are submeridionally and NNW-trending, change orientation to the northwest in the immediate vicinity of the Dzhankhot thrust fault zone. The identified features of tectonic structure and stressed-strained state of the Dzhankhot thrust zone allow considering this area as a natural structural and tectonophysical testing ground for both tectonic-stress-reconstruction-improvement methodologies and a study on natural deformation structures of the Greater Caucasus.

A model-free method for attitude estimation and inertial parameter identification of a noncooperative target

Determining the attitude and inertial parameters of a noncooperative target is essential in an on-orbit servicing mission. Various methods based on machine vision have been proposed, but most of them require the 3D model of the target. This paper proposes a model-free method through sequentially registering point clouds captured by a depth camera. Our main contributions are the avoidance of the ambiguity in registration, and the combination of the multiplicative extended Kalman filter and the pose graph optimization to reduce the effect of measurement noise and drift error. A hardware experiment was performed to generate the sequence of point clouds of a three-axis free-floating target and validate our method. The result shows that the proposed method outperforms existing methods and effectively identifies the inertial parameters, including the normalized principal moments of inertia and the orientation of principal axes.

A model problem for the evolution of strain structure at the crossing of a flame front

The local thermal effect of a flame front is simulated by a model for a mass density front by specifying a likely expansion rate. This model problem includes two independent parameters, namely the heat release parameter and a parameter akin to a Karlovitz number. The analysis is focused on the influence of the Karlovitz number on the evolution of strain properties at the crossing of the front. The latter are derived from an equation system for the velocity gradient tensor and the pressure Hessian tensor undergoing the forcing of the expansion rate. Strain eigenvalues, orientation of strain principal axes, and stretching in the direction of forcing are especially scrutinized. Furthermore, the model shows that, when approaching a flame front, the special alignments of strain are mostly caused by anisotropy of pressure Hessian resulting from forcing by expansion.

Raman tensor determination of transparent uniaxial crystals and their thin films—a-plane GaN as exemplary case

The classical Raman tensor approach does not work for optically anisotropic materials in general. For the transparency regime, this can be circumvented by using an effective Raman tensor that considers the material's birefringence. In the specific case of an uniaxial crystal with in-plane orientation of principal axis, this effective Raman tensor is similar to the classical one, except for an additional phase factor for each tensor element. This phase is dependent on the sample thickness, which is demonstrated here experimentally via polarization resolved Raman scattering of a-plane GaN thin films. The experimental observations coincide very well with our model predictions.

Application of Spectral Method for Vibration-Induced High-Cycle Fatigue Evaluation of an High-Pressure Turbine Blade

Abstract A method of fluid–structure interaction coupling is implemented for a forced-response, vibration-induced fatigue life estimation of a high-pressure turbine blade. Two simulations approaches; a two-way (fully coupled) and one-way (uncoupled) methods are implemented to investigate the influence of fluid–solid coupling on a turbine blade structural response. The fatigue analysis is performed using the frequency domain spectral moments estimated from the response power spectral density (PSD) of the two simulation cases. The method is demonstrated in relation to the time-domain method of the rainflow cycle counting method with mean stress correction. Correspondingly, the mean stress and multi-axiality effects are also accounted for in the frequency domain spectral approach. In this case, a multiplication coefficient is derived based on the Morrow equation, while the case of multi-axiality is based on a criterion which reduces the triaxial stress state to an equivalent uniaxial stress using the critical plane assumption. The analyses show that while the vibration-induced stress histories of both simulation approaches are stationary, they violate the assumption of normality of the frequency domain approaches. The stress history profile of both processes can be described as platykurtic with the distributions having less mass near its mean and in the tail region, as compared to a Gaussian distribution with an equal standard deviation. The fully coupled method is right leaning with positive skewness while the uncoupled approach is left leaning with negative skewness. The directional orientation of the principal axes was also analyzed based on the Euler angle estimation. Although noticeable differences were found in the peak distribution of the normal stresses for both methods, the predicted Euler angle orientations were consistent in both cases, depicting a similar orientation of the critical plane during a crack initiation and propagation process. Finally, the fatigue life estimation was shown to be conservative in the fully coupled solution approach.

Modelling of Elastic Stress Field of the Earth’s Crust in Central Asia Based on the Orientations of Principal Stress Axes

Modelling of Elastic Stress Field of the Earth’s Crust in Central Asia Based on the Orientations of Principal Stress Axes

Anatomical and principal axes are not aligned in the torso: Considerations for users of geometric modelling methods

The accuracy and accessibility of methods to calculate body segment inertial parameters are a key concern for many researchers. It has recently been demonstrated that the magnitude and orientation of principal moments of inertia are crucial for accurate dynamic models. This is important to consider given that the orientation of principal axes is fixed for the majority of geometric and regression body models. This paper quantifies the effect of subject specific geometry on the magnitude and orientation of second moments of volume in the trunk segment. The torsos of 40 male participants were scanned using a 3D imaging system and the magnitude and orientation of principal moments of volume were calculated from the resulting geometry. Principal axes are not aligned with the segment co-ordinate system in the torso segment, with mean Euler angles of 11.7, 1.9 and 10.3 in the ZXY convention. Researchers using anatomical modelling techniques should try and account for subject specific geometry and the mis-alignment of principal axes. This will help to reduce errors in simulation by mitigating the effect of errors in magnitude of principal moments.

Measurements of anisotropic g-factors for electrons in InSb nanowire quantum dots

We have measured the Zeeman splitting of quantum levels in few-electron quantum dots (QDs) formed in narrow bandgap InSb nanowires via the Schottky barriers at the contacts under application of different spatially orientated magnetic fields. The effective g-factor tensor extracted from the measurements is strongly anisotropic and level-dependent, which can be attributed to the presence of strong spin–orbit interaction (SOI) and asymmetric quantum confinement potentials in the QDs. We have demonstrated a successful determination of the principal values and the principal axis orientations of the g-factor tensors in an InSb nanowire QD by the measurements under rotations of a magnetic field in the three orthogonal planes. We also examine the magnetic field evolution of the excitation spectra in an InSb nanowire QD and extract a SOI strength of ∼ 180 μeV from an avoided level crossing between a ground state and its neighboring first excited state in the QD.

Description of Seismic Sources in Underground Mines: Theory

ABSTRACTIn underground mines, episodes of sudden inelastic deformation in the rockmass are often induced by mining and are therefore localized near the excavations. The seismic radiation associated with such deformation can be described by a point seismic source using a volume integral of the stress-free strain (or incremental plastic strain)—expression (1) in the Theory section. This conventional description is valid if seismic waveforms are modeled or inverted using the elastodynamic Green’s function, which takes the presence of nearby excavation(s) into account. If the adopted Green’s function does not model these excavations, then the conventional expressions for a point source need to be adjusted by adding a term that depends on the displacement at the surface of the excavations (equations 2). Alternatively, a Kirchhoff-type representation can be used, in which the parameters of the point source are expressed using increments of displacement and traction over the surface covering both the volume of inelastic deformation and nearby excavation(s) (equations 3). Numerical simulations demonstrate that the suggested expressions provide a very different result to the conventional expressions for the case of inelastic deformation in a volume adjacent to an excavation. The utilization of the suggested expressions results in a change in the type of mechanisms from explosive to implosive and significantly affects other characteristics of the modeled sources (moment magnitude and orientation of principal axes). Typically, seismic waveforms recorded by monitoring systems in underground mines are processed using an elastodynamic Green’s function that does not take medium-sized excavations (e.g., tunnels and stopes) into account. Therefore, the results of such processing need to be interpreted using the suggested expressions: adjusted conventional (equations 2) or Kirchhoff-type (equations 3).

Multi-criteria decision making for a large heating system with heat loss

A large heat supply system, which always has a multi-level hierarchical structure, is considered. There are levels of trunk and distribution heating networks with intermediate levels of regulation. Planning and selection of a mode that provides the required heat loads are associated in such a system with a large number of different factors that complicate the decision-making process. The present study investigates heat transfer in a flat anisotropic insulating plate with uniformly distributed internal heat sinks subjected to heat flows. An analytical solution is obtained that allowed us to study and build temperature distribution fields for various orientations of principal axes of thermal conductivity tensor in an insulating plate. The thermal field localization regime is shown to be possible in the presence of thermal energy sinks/sources inside the plate wherein heat propagation is bound with limiting isotherms.

Computational study of electron paramagnetic resonance spectra for Li and Ga vacancies in LiGaO2

A first-principles computational study of the electron paramagnetic resonance (EPR) parameters of Li and Ga vacancies in LiGaO2 is presented. In the EPR active charge states of the neutral lithium vacancy () and doubly negative ionized gallium vacancy (), the spin is localized on one of the O neighbors of the vacancy. We compare the calculated EPR parameters for spin density localized on different O neighbors. Good agreement with experiment is obtained for both the g-tensor values and principal axes orientations and the superfhyperfine interaction parameters supporting the prior experimental identification of which O the spin is localized on. The g-tensor orientations are found to be close to the bond rather than the crystalline axes. The high energy of formation of compared to also explains why were only observed after high energy irradiation while were found in as grown samples. On the other hand, the transition levels and Fermi level position explain why required ionization from the −1 to 0 charge state to become active while were already found in the q = −2 EPR active state.

Investigation on aggregate particles migration characteristics of porous asphalt concrete (PAC) during vibration compaction process

Porous asphalt concrete (PAC) has been widely used in the pavement for excellent performance in noise reduction and drainage. As a typical mixture with a skeleton-void structure, the performance of PAC is greatly affected by the compaction mechanism and internal structure of asphalt mixtures. This study tries to investigate compaction characteristics and migration trends of aggregate particles in porous asphalt mixtures prepared by a vertical vibration compaction method (VVCM) with different compaction parameters. The principal axis orientation and interlayer distance as evaluation indicators obtained by digital image processing (DIP) and Image-pro plus (IPP) software are used to evaluate the migration characteristics of aggregate particles in asphalt mixtures. The results show that the self-organization and immigration of aggregate particles in PAC are unified and the migration data of particles present statistical regularity. The aggregate particles are gradually deflected toward the horizontal direction to form a stable aggregate skeleton during the vibration compaction. Besides, the compaction degree of asphalt mixture in the middle and upper parts is significantly improved by the increase of the vibration frequency, while prolonging the vibration time is conducive to improve the compaction degree of asphalt mixture in the middle and lower parts.

Effects of Initial Direction and Subsequent Rotation of Principal Stresses on Liquefaction Potential of Loose Sand

AbstractThe effects of the initial orientation of principal stress axes and subsequent rotation of principal stresses on liquefaction susceptibility of sands were investigated. Monotonic and cyclic...