Arbitrary Axis Research Articles

Energy of low angle grain boundaries based on continuum dislocation structure

In this paper, we present a continuum model to compute the energy of low angle grain boundaries for any given degrees of freedom (arbitrary rotation axis, rotation angle and boundary plane orientation) based on a continuum dislocation structure. In our continuum model, we minimize the grain boundary energy associated with the dislocation structure subject to the constraint of Frank's formula for dislocations with all possible Burgers vectors. This constrained minimization problem is solved by the penalty method by which it is turned into an unconstrained minimization problem. The grain boundary dislocation structure is approximated by a network of straight dislocations that predicts the energy and dislocation densities of the grain boundaries. The grain boundary energy based on the calculated dislocation structure is able to incorporate its anisotropic nature. We use our continuum model to systematically study the energy of <111> low angle grain boundaries in fcc Al with any boundary plane orientation and all six possible Burgers vectors. Comparisons with atomistic simulation results show that our continuum model is able to give excellent predictions of the energy and dislocation densities of low angle grain boundaries. We also study the energy of low angle grain boundaries in fcc Al with varying rotation axis while the remaining degrees of freedom are fixed. With modifications, our model can also apply to dislocation structures and energy of heterogeneous interfaces.

Twist of generalized skyrmions and spin vortices in a polariton superfluid

We study the spin vortices and skyrmions coherently imprinted into an exciton-polariton condensate on a planar semiconductor microcavity. We demonstrate that the presence of a polarization anisotropy can induce a complex dynamics of these structured topologies, leading to the twist of their circuitation on the Poincaré sphere of polarizations. The theoretical description of the results carries the concept of generalized quantum vortices in two-component superfluids, which are conformal with polarization loops around an arbitrary axis in the pseudospin space.

Rigorous coupled-wave analysis equivalent-index-slab method for analyzing 3D angular misalignment in interlayer grating couplers.

The interlayer waveguide grating coupling efficiencies under angular (rotational) misalignments are simulated using the 3D rigorous coupled-wave analysis (3D-RCWA) together with the RCWA equivalent-index-slab (RCWA-EIS) method. As examples of conical diffraction, rotations about the two coordinate axes, x and z, defined by the vectors [1 0 0] and [0 0 1], respectively, as well as an arbitrary axis, defined by the vector [2 2 1], are simulated for binary rectangular-groove gratings. The interlayer grating coupling efficiency is approximated by the product of the top- and bottom-grating diffraction efficiencies (DEs). It is found that the bottom-grating DEs decrease about 25% when the bottom grating is rotated ±0.1 rad (5.73°) about the z-axis. DEs slightly increase (5% to 10% depending on the grating structures) when the bottom grating is rotated ±0.1 rad about the x-axis. This is consistent with the diffraction behavior of an over-modulated grating. When the bottom grating is rotated about the vector [2 2 1], the change in DEs is asymmetric with a 100% decrease at a rotation angle -0.1 rad and a 67% decrease at a rotation angle +0.1 rad. The method is shown to be computationally efficient and numerically stable for grating structures with optimized parameters, and the resulting bottom-grating diffraction efficiencies demonstrate similar trends as those calculated by the 3D finite-difference time-domain simulations. The procedure presented can be directly used in the analysis and design of interlayer waveguide grating coupling for optical interconnects in high-density integrated electronics.

Dynamic optimum design of a 3UPS-PRU parallel robot

This article deals with the methodology of the dynamic optimum design of the one translational and three rotational degrees of freedom parallel robots while considering the rigid-body dynamic property. The dynamic optimum design of the 3UPS-PRU (underlined P denotes an active prismatic joint driven by a servomotor) parallel robot is presented while considering the constraints on the installation dimension, joint rotation angle, and the interference. The maximum driving torque and the maximum driving power of the actuating joints are taken as the objective functions in the dynamic optimum design, respectively. The physical meanings of the objective functions are the maximum driving torque and the maximum driving power of the actuating joints when the moving platform translates along the z-axis in the maximum linear acceleration amax, rotates about an arbitrary axis in the maximum angular acceleration αmax, translates along the z-axis in the maximum linear velocity vmax, and rotates about an arbitrary axis in the maximum angular velocity ωmax at the same time. The object of the dynamic optimum design is to minimize the maximum driving torque or the maximum driving power by employing worst case criterion. In the predefined design task, the results of the dynamic optimum design of the 3UPS-PRU parallel robot are the same when taking the maximum driving torque and the maximum driving power as the objective functions. The phenomenon can be verified by the fact that the distributions of the maximum driving torque and the maximum driving power are very similar to each other. The robot dimension has also been taken into account in the dynamic optimum design of the 3UPS-PRU parallel robot due to the consideration of the building cost and the miniaturization. The example of the dynamic optimum design of the 3UPS-PRU parallel robot is presented in the simulation. The conclusions are provided at the end of the article.

Scanning anisotropy parameters in horizontal transversely isotropic media

ABSTRACTThe horizontal transversely isotropic model, with arbitrary symmetry axis orientation, is the simplest effective representative that explains the azimuthal behaviour of seismic data. Estimating the anisotropy parameters of this model is important in reservoir characterisation, specifically in terms of fracture delineation. We propose a travel‐time‐based approach to estimate the anellipticity parameter η and the symmetry axis azimuth ϕ of a horizontal transversely isotropic medium, given an inhomogeneous elliptic background model (which might be obtained from velocity analysis and well velocities). This is accomplished through a Taylor's series expansion of the travel‐time solution (of the eikonal equation) as a function of parameter η and azimuth angle ϕ. The accuracy of the travel time expansion is enhanced by the use of Shanks transform. This results in an accurate approximation of the solution of the non‐linear eikonal equation and provides a mechanism to scan simultaneously for the best fitting effective parameters η and ϕ, without the need for repetitive modelling of travel times. The analysis of the travel time sensitivity to parameters η and ϕ reveals that travel times are more sensitive to η than to the symmetry axis azimuth ϕ. Thus, η is better constrained from travel times than the azimuth. Moreover, the two‐parameter scan in the homogeneous case shows that errors in the background model affect the estimation of η and ϕ differently. While a gradual increase in errors in the background model leads to increasing errors in η, inaccuracies in ϕ, on the other hand, depend on the background model errors. We also propose a layer‐stripping method valid for a stack of arbitrary oriented symmetry axis horizontal transversely isotropic layers to convert the effective parameters to the interval layer values.

Dynamic performance evaluation for a 3UPS-PRU parallel robot

This article deals with the methodology of the kinematic and rigid-body dynamic performance evaluation of the 3UPS-PRU (the underlined P denotes an actuating prismatic joint) parallel robot. The maximum input velocity index, the maximum driving torque index, and the maximum driving power index are formulated based on kinematic and rigid-body dynamic model, the theory of matrix norm and inequality. The physical meanings of the indices are the maximum input velocity, the maximum driving torque, and the maximum driving power, respectively, when the moving platform translates along the z-axis in the maximum linear acceleration amax, rotates about an arbitrary axis in the maximum angular acceleration αmax, translates along the z-axis in the maximum linear velocity vmax, and rotates about an arbitrary axis in the maximum angular velocity [Formula: see text]. Employing the worst-case criterion, the example of the kinematic and rigid-body dynamic performance evaluation of the 3UPS-PRU parallel robot is carried out using the presented indices. It is shown that the distribution trends of the maximum driving torque and the maximum driving power are roughly the same for the 3UPS-PRU parallel robot. The conclusions are provided at the end of the article.

Optimizing qubit phase estimation

The theory of quantum state estimation is exploited here to investigate the most efficient strategies for this task, especially targeting a complete picture identifying optimal conditions in terms of Fisher information, quantum measurement, and associated estimator. The approach is specified to estimation of the phase of a qubit in a rotation around an arbitrary given axis, equivalent to estimating the phase of an arbitrary single-qubit quantum gate, both in noise-free and then in noisy conditions. In noise-free conditions, we establish the possibility of defining an optimal quantum probe, optimal quantum measurement, and optimal estimator together capable of achieving the ultimate best performance uniformly for any unknown phase. With arbitrary quantum noise, we show that in general the optimal solutions are phase dependent and require adaptive techniques for practical implementation. However, for the important case of the depolarizing noise, we again establish the possibility of a quantum probe, quantum measurement, and estimator uniformly optimal for any unknown phase. In this way, for qubit phase estimation, without and then with quantum noise, we characterize the phase-independent optimal solutions when they generally exist, and also identify the complementary conditions where the optimal solutions are phase dependent and only adaptively implementable.

Two-point resistance of an m × n resistor network with an arbitrary boundary and its application in RLC network**Project supported by the Prophase Preparatory Project of Natural Science Foundation of Nantong University, China (Grant No. 15ZY16).

A rectangular m × n resistor network with an arbitrary boundary is investigated, and a general resistance formula between two nodes on an arbitrary axis is derived by the Recursion-Transform (RT) method, a problem that has never been resolved before, for the Green’s function technique and the Laplacian matrix approach are inapplicable to it. To have the exact solution of resistance is important but it is difficult to obtain under the condition of arbitrary boundary. Our result is directly expressed in a single summation and mainly composed of characteristic roots, which contain both finite and infinite cases. Further, the current distribution is given explicitly as a byproduct of the method. Our framework can be effectively applied to RLC networks. As an application to the LC network, we find that our formulation leads to the occurrence of resonances at h1 = 1 − cos ϕi − sin ϕi cot nϕi. This somewhat curious result suggests the possibility of practical applications of our formulae to resonant circuits.

TYPES OF 3D SURFACE OF ROTATIONS EMBEDDED IN 4D MINKOWSKI SPACE

The geometry of surfaces of rotation in three dimensional Euclidean spaces has been studied widely. The rotational surfaces in three dimensional Euclidean spaces are generated byrotating an arbitrary curve about an arbitrary axis. Which should be using a type of matrices called matrices of rotation. But they are should be created by one parameter group of isometry. On the other hand, the Minkowski spaces have shorter history. In 1908 Minkowski [1864-1909] gave his talk on four dimensional real vector space, with a symmetric form of signature (+,+,+,-). In this space there are different types of vectors/ axes (space-liketime- like and null) as well as different types of curves (space-like- time-like and null). The relationship between Euclidean and Minkowskian geometry has many intriguing aspects, one of which is the manner in which formal similarity can co-exist with significantgeometric disparity. There has been considerable interest in the comparison of these twogeometries, as can be seen in the lecture notes of L’opez. In this manuscript we produce different types of surfaces of rotation in four dimensionalMinkowski spaces. And then we will provide a brief description of surfaces of rotation of 4D Minkowski spaces. Firstly consider the beginning by creating different type of matrices of rotation corresponding to the appropriate subgroup of the Lorentz group, and then generate all types of surfaces of rotation. The new work here is the spherical symmetric case which is nonabeliansubalgebra isomorphic to lie algebra. This case is known by expectation.

The Effect of Hinge Axis Position on Mandibular Movements

The objective of this study was to evaluate the effect of an arbitrary and true hinge axis on the Bennett shift and the horizontal condylar path inclination. Ten completely edentulous subjects were selected for this study. For each subject, true and arbitrary hinge axis positions were located. Whip Mix Quick Set Recorder was used to measure the Bennett shift and the horizontal condylar path inclination. The Bennett shift and condylar path inclinations were recorded two times, first using the arbitrary and secondary using the kinematic hinge axis as the starting point for recording. The resultof this study showed that there were no statistical differences between the two measures of the Bennett shift and horizontal condylar path inclination.

Marching-on-in-Degree Solution of the Transient Scattering From Multiple Bodies of Revolution

An efficient marching-on-in-degree (MOD) scheme is proposed to analyze the transient EM scattering from multiple conducting bodies of revolution (MBoRs) with arbitrary axis using the equivalence principle algorithm (EPA). The self-acting of each BoR is calculated by taking advantage of the rotationally symmetrical property in its local BoR coordinate system. The interaction between any two BoRs is replaced by the one between their equivalence spheres which enclose corresponding BoR with EPA. In this way, the transient scattering properties of the randomly distributed MBoRs can be obtained with high efficiency by the use of the BOR basis functions and the weighted Laguerre polynomial. Numerical results are presented to demonstrate the accuracy and efficiency of proposed algorithm.

General flat crack arbitrarily located in the transversely-isotropic body

The author published an article (Fabrikant, 2011), where the problem of a general flat crack located in the plane, perpendicular to the plane of isotropy, namely, x=0 was solved. The case of arbitrary normal or tangential loading was considered. A more complicated case of a flat crack, related to arbitrary axes (x1,x2,x3) was solved in (Fabrikant, 2015). The crack is still located in the plane x1=0 perpendicular to the planes of isotropy, but the other two axes (x2,x3) are rotated by angle φ from the major axes (y,z). We consider here a more complicated case of transversely isotropic body, related to the system of axes (x1,x2,x3), weakened in the plane x3=0 by a flat crack of arbitrary shape. We derive the governing integral equation for such general case. As illustrations, we consider the cases of elliptical crack subjected to normal and tangential tractions. We present complete solution for the fields of displacements and stresses as single contour integrals of elementary integrands. We compute stress intensity factors as well.

Binary neutron stars with arbitrary spins in numerical relativity

We present a code to construct initial data for binary neutron star systems in which the stars are rotating. Our code, based on a formalism developed by Tichy, allows for arbitrary rotation axes of the neutron stars and is able to achieve rotation rates near rotational breakup. We compute the neutron star angular momentum through quasi-local angular momentum integrals. When constructing irrotational binary neutron stars, we find a very small residual dimensionless spin of $\sim 2\times 10^{-4}$. Evolutions of rotating neutron star binaries show that the magnitude of the stars' angular momentum is conserved, and that the spin- and orbit-precession of the stars is well described by post-Newtonian approximation. We demonstrate that orbital eccentricity of the binary neutron stars can be controlled to $\sim 0.1\%$. The neutron stars show quasi-normal mode oscillations at an amplitude which increases with the rotation rate of the stars.

Probabilistic constraints on structural lineament best fit plane precision obtained through numerical analysis

Understanding the orientation distribution of structural discontinuities using the limited information afforded by their trace in outcrop has considerable application, with such analysis often providing the basis for geological modelling. However, eigen analysis of 3D structural lineaments mapped at decimetre to regional scales indicates that discontinuity best fit plane estimates from such datasets tend to be unreliable. Here, the relationship between digitised lineament vertex geometry (coplanarity/collinearity) and the reliability of their estimated best fitting plane is investigated using Monte Carlo experiments. Lineaments are modelled as the intersection curve between two orthonormally oriented fractional Brownian surfaces representing the outcrop and discontinuity plane. Commensurate to increasing lineament vertex collinearity (K), systematic decay in estimated pole vector precision is observed from these experiments. Pole vector distributions are circumferentially constrained around the axis of rotation set by the end nodes of the synthetic lineaments, reducing the rotational degrees of freedom of the vertex set from three to one. Vectors on the unit circle formed perpendicular to this arbitrary axis of rotation conform to von Mises (circular normal) distributions tending towards uniform at extreme values of K. This latter observation suggests that whilst intrinsically unreliable, confidence limits can be placed upon orientation estimates from 3D structural lineaments digitised from remotely sensed data. A probabilistic framework is introduced which draws upon the statistical constraints obtained from our experiments to provide robust best fit plane estimates from digitised 3D structural lineaments.

On-chip plasmonic waveguide optical waveplate.

Polarization manipulation is essential in almost every photonic system ranging from telecommunications to bio-sensing to quantum information. This is traditionally achieved using bulk waveplates. With the developing trend of photonic systems towards integration and miniaturization, the need for an on-chip waveguide type waveplate becomes extremely urgent. However, this is very challenging using conventional dielectric waveguides, which usually require complex 3D geometries to alter the waveguide symmetry and are also difficult to create an arbitrary optical axis. Recently, a waveguide waveplate was realized using femtosecond laser writing, but the device length is in millimeter range. Here, for the first time we propose and experimentally demonstrate an ultracompact, on-chip waveplate using an asymmetric hybrid plasmonic waveguide to create an arbitrary optical axis. The device is only in several microns length and produced in a flexible integratable IC compatible format, thus opening up the potential for integration into a broad range of systems.

High-fidelity resonant gating of a silicon-based quantum dot hybrid qubit

AbstractWe implement resonant single qubit operations on a semiconductor hybrid qubit hosted in a three-electron Si/SiGe double quantum dot structure. By resonantly modulating the double dot energy detuning and employing electron tunnelling-based readout, we achieve fast (&gt;100 MHz) Rabi oscillations and purely electrical manipulations of the three-electron spin states. We demonstrate universal single qubit gates using a Ramsey pulse sequence as well as microwave phase control, the latter of which shows control of an arbitrary rotation axis on the X–Y plane of the Bloch sphere. Quantum process tomography yields π rotation gate fidelities higher than 93 (96)% around the X (Z) axis of the Bloch sphere. We further show that the implementation of dynamic decoupling sequences on the hybrid qubit enables coherence times longer than 150 ns.

Detecting Lateral Motion using Light's Orbital Angular Momentum.

Interrogating an object with a light beam and analyzing the scattered light can reveal kinematic information about the object, which is vital for applications ranging from autonomous vehicles to gesture recognition and virtual reality. We show that by analyzing the change in the orbital angular momentum (OAM) of a tilted light beam eclipsed by a moving object, lateral motion of the object can be detected in an arbitrary direction using a single light beam and without object image reconstruction. We observe OAM spectral asymmetry that corresponds to the lateral motion direction along an arbitrary axis perpendicular to the plane containing the light beam and OAM measurement axes. These findings extend OAM-based remote sensing to detection of non-rotational qualities of objects and may also have extensions to other electromagnetic wave regimes, including radio and sound.

Optimized parallel transmit and receive radiofrequency coil for ultrahigh-field MRI of monkeys

Monkeys are a valuable model for investigating the structure and function of the brain. To attain the requisite resolution to resolve fine anatomical detail and map localized brain activation requires radiofrequency (RF) coils that produce high signal-to-noise ratios (SNRs) both spatially (image SNR) and temporally. Increasing the strength of the static magnetic field is an effective method to improve SNR, yet this comes with commensurate challenges in RF coil design. First, at ultrahigh field strengths, the magnetic field produced by a surface coil in a dielectric medium is asymmetric. In neuroimaging of rhesus macaques, this complex field pattern is compounded by the heterogeneous structure of the head. The confluence of these effects results in a non-uniform flip angle, but more markedly, a suboptimal circularly polarized mode with reduced transmit efficiency. Secondly, susceptibility-induced geometric distortions are exacerbated when performing echo-planar imaging (EPI), which is a standard technique in functional studies. This requires receive coils capable of parallel imaging with low noise amplification during image reconstruction. To address these challenges at 7T, this study presents a parallel (8-channel) transmit coil developed for monkey imaging, along with a highly parallel (24-channel) receive coil. RF shimming with the parallel-transmit coil produced significant advantages—the transmit field was 38% more uniform than a traditional circularly polarized mode and 54% more power-efficient, demonstrating that parallel-transmit coils should be used for monkey imaging at ultrahigh field strengths. The receive coil had the ability to accelerate along an arbitrary axis with at least a three-fold reduction factor, thereby reducing geometric distortions in whole-brain EPI.

On Rotation About Lightlike Axis in Three-Dimensional Minkowski Space

We obtain matrix of the rotation about arbitrary lightlike axis in three-dimensional Minkowski space by deriving the Rodrigues’ rotation formula and using the corresponding Cayley map. We prove that a unit timelike split quaternion q with a lightlike vector part determines rotation R q about lightlike axis and show that a split quaternion product of two unit timelike split quaternions with null vector parts determines the rotation about a spacelike, a timelike or a lightlike axis. Finally, we give some examples.

Closed-loop magnetic bearing and angular velocity control of a reaction sphere actuator

This article presents the first closed-loop magnetic bearing and angular velocity experimental results of a reaction sphere actuator for satellite attitude control. The proposed reaction sphere is a permanent magnet spherical actuator whose rotor is supported by magnetic bearing and can be torqued electronically about any desired axis. The spherical actuator is composed of an 8-pole permanent magnet spherical rotor and of a 20-pole stator with electromagnets. The electromechanical model of the reaction sphere is summarized together with procedures to estimate the rotor magnetic state, the back-EMF voltage, and the rotor angular velocity, which are all fundamental ingredients for controller design. Dynamic controllers are developed to levitate the rotor inside the stator (magnetic bearing) and to control the rotor angular velocity. The magnetic bearing is based on a state-space controller with reduced-order displacement velocity estimator whereas the angular velocity controller is a simple proportional controller with a dedicated angular velocity estimator. The developed control algorithms are experimentally validated using the developed laboratory prototype showing the ability of simultaneously levitating the rotor while rotating it about a given arbitrary axis.