Small Relative Rotation Research Articles

Dual-Branch Deep Point Cloud Registration Framework for Unconstrained Rotation

Learning-based rigid point cloud registration (RPCR) studies have made great progress recently but most existing methods have a small convergence region and can only be used to solve the registration problem with a small rotation angle, which is usually constrained within <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[0, 45^\circ ]$</tex-math></inline-formula> . However, the relative rotation between point clouds is usually unconstrained in practice. To address this challenging problem, we propose a new RPCR network and integrate it into a new dual-branch registration framework for unconstrained rotation point cloud registration. The dual-branch framework consists of a large-rotation branch and a small-rotation branch, which are used to accurately register point clouds with large and small relative rotations, respectively. In addition, we propose a multi-view Intersection over Union module (MVIOU) to select a better registration result from the output of the two branches. Extensive experiments on both ModelNet40 and MVP-RG datasets demonstrate that our proposed method outperforms existing state-of-the-art techniques by a large margin. The code and pre-trained models will be available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/fukexue/Point-DR</uri> .

A non-linear direct peridynamics plate theory

In this paper a direct non-local peridynamics theory for thin plates is developed. Peridynamic points are assumed to behave like rigid bodies with independent translation and finite rotation degrees of freedom. The non-local mechanical interaction between points is characterized by force and moment vectors. The balance equations including the linear momentum, the angular momentum and the energy are presented. Peridynamic deformation states of the plate are introduced including the actual bond vector (relative translation of two points within the bond) and the relative finite rotation tensor (actual relative orientation of two points in the bond). The corresponding power-conjugate bond force and bond moment states are derived. The framework to develop constitutive equations for the plate peridynamic states is addressed. Special cases of the theory including plates with zero drilling moments, membranes, soft interlayers as well as stiff plate layers with small relative rotations are considered.

Gauge-phonon dominated resistivity in twisted bilayer graphene near magic angle

Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime because although they couple to current, they do not induce charge and are therefore unscreened by the large density of states close to magic angle. We show that the resistivity has a strong monotonically decreasing carrier density dependence at low temperature due to charged impurity scattering, and weak density dependence at high temperature due to gauge phonons. Away from charge neutrality, the resistivity increases with temperature, while it does the opposite close to the Dirac point. A non-monotonic temperature dependence observed only at low temperature and carrier density is a signature of our theory that can be tested in experimentally available samples.

Theory of optical absorption by interlayer excitons in transition metal dichalcogenide heterobilayers

We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moir\'e pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moir\'e Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the exciton moir\'e potential energy restores circular optical selection rules by coupling excitons with different center of mass momenta. A variety of interlayer excitons with both senses of circular optical activity, and energies that are tunable by twist angle, are present at each valley. The lowest energy exciton states are generally localized near the exciton potential energy minima. We discuss the possibility of using the moir\'e pattern to achieve scalable two-dimensional arrays of nearly identical quantum dots.

Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices

In this paper, we derive a continuum variational model for a two-dimensional deformable lattice of atoms interacting with a two-dimensional rigid lattice. The starting point is a discrete atomistic model for the two lattices which are assumed to have slightly different lattice parameters and, possibly, a small relative rotation. This is a prototypical example of a three-dimensional system consisting of a graphene sheet suspended over a substrate. We use a discrete-to-continuum procedure to obtain the continuum model which recovers both qualitatively and quantitatively the behaviour observed in the corresponding discrete model. The continuum model predicts that the deformable lattice develops a network of domain walls characterized by large shearing, stretching and bending deformation that accommodates the misalignment and/or mismatch between the deformable and rigid lattices. Two integer-valued parameters, which can be identified with the components of a Burgers vector, describe the mismatch between the lattices and determine the geometry and the details of the deformation associated with the domain walls.

On a class of Gibbs potential-based nonlinear elastic models with small strains

The aim of this paper is to show that it is possible to develop a fully internally consistent model for an isotropic elastic body that has nonlinear response relations but with small strains, if one chooses to begin from a Gibbs potential (or complementary energy) rather than the classical Helmholtz potential (or strain energy). We demonstrate the practical applicability of such a model and also compare the results of exact solutions (internal pressurization of a circular cylinder and the bending of a rectangular block) for incompressible materials undergoing finite deformations with corresponding exact solutions based on small deformations. Surprisingly, the results show quite remarkable agreement up to maximum strains of nearly 20–30 %. Given that most applications of nonlinear elastic materials are in this range, the results have broad implications for the ability to consistently use small deformation nonlinear theories for a wide class of applications than hitherto considered. We also show that the nonlinear compatibility equations play a key role in determining the applicability of this approach. In particular, we show that for 3-D bodies whose dimensions are of comparable orders of magnitude (i.e., excluding rod-like or shell-like bodies), the finite deformation compatibility condition ensures that small strains and strain gradients imply small relative rotations and hence small deformations. For thin bodies (rods, plates and shells), it is well-known result that small strains do not lead to small deformations due to the possibility of large rotation gradients thus leading to other possible approximations.

A Novel Stratified Self-calibration Method of Camera Based on Rotation Movement

This paper proposes a novel stratified self- calibration method of camera based on rotation movement. The proposed method firstly captures more than three images of the same scene in the case of constant internal parameters by panning and rotating the camera with small relative rotation angles among the captured images. After feature extraction and matching of captured images, the pixel coordinates of feature point are normalized. Then the stratified self-calibration is performed, following projective, affine and metric calibration. Projective calibration determines the camera projective matrix of every image in the projective reconstruct space. Affine calibration calculates the parameters of infinity reference plane in this space and the homography according to approximately equal relationship among the main diagonal elements of homography, which is inferred by virtue of small relative rotation angles among the captured images and the property of internal reference matrix corresponding to normalized pixel coordinates. Lastly metric calibration acquires internal reference matrix from the calculated homography. The proposed method can be online applied to simply, fast, accurately obtain internal parameters of camera without using the calibration reference with known 3D information. Real data has been used to test the proposed approach, and very good results have been achieved.

Magnetic Field Dependent Damping of Magnetic Particle Filled Polypropylene

The behavior of internal friction Q-1 and dynamic shear modulus has been studied in polypropylene charged with either different volume fraction or size of magnetite (Fe3O4) particles, as a function of the applied magnetic field at 318 K. An increase of the alternating (AC) magnetic field oscillating with 50 Hz, leads to an increase of the internal friction. In addition, during the subsequently decreasing alternating magnetic field, the internal friction decreases, but a hysteretic behavior appeared. In fact, the internal friction of the decreasing part of magnetic field amplitude is found to be smaller than during the previously increasing amplitude part of the treatment with the alternating magnetic field. Subsequent magnetic treatment cycles, lead to successively decreasing internal friction. In contrast, during the increase of a direct (DC) magnetic field, the internal friction decreases and the elastic modulus increases. The behavior of the internal friction and the elastic modulus during the application of an oscillating magnetic field (AC) is discussed on the basis of the development of both, a new zone with different rheological characteristics than the matrix but of the same material (self-inclusion), and/or a deteriorated or damaged zone (chain’s cuts) of the polymer matrix in the neighborhood of the magnetite inclusion. These effects are promoted by the movement or small relative rotation of the magnetite particles related to the surrounding matrix controlled by the oscillating field. The behavior of the internal friction and elastic modulus during the application of a direct (DC) magnetic field is discussed on the basis of the increase of the internal stresses into the polymer matrix due to the promotion of the magnetomechanical stresses.

Theoretical Studies of the XY-FP Seismic Isolation Bearing for Bridges

The XY-friction pendulum (XY-FP) bearing is a modified friction pendulum that consists of two perpendicular steel rails with opposing concave surfaces and a connector. The connector resists tensile forces, allows independent sliding in the two orthogonal directions and enables small relative rotation of the rails about a vertical axis. Theoretical analyses were undertaken to study applications of XY-FP bearings to bridges. Two of the key features of the XY-FP bearing for the seismic isolation of bridges are: (1) resistance to tensile axial loads and (2) opportunity to provide a different period of isolation in each principal direction of the isolated structure. Numerical analyses on an XY-FP isolated bridge with different isolation periods in the principal directions subjected to near-field ground motions demonstrated the effectiveness of XY-FP bearings. Furthermore, numerical analyses that investigated the sensitivity of XY-FP isolation system response to differences in the coefficients of friction of the bearings demonstrated that bounding analysis using upper and lower estimates of the coefficients of friction will generally provide conservative estimates of displacements and shear forces for isolation systems with nonuniform isolator properties.

Image-guided radiosurgery for spinal tumors: methods, accuracy and patient intrafraction motion

Image-guided frameless extracranial radiosurgery has become an established treatment option; however, without a frame to restrict patient movements, intrafraction field mispositioning becomes more probable. The primary aim of this study is to determine the intrafraction motion of spinal radiosurgery patients. This aim was approached in two steps. First, a phantom study demonstrated that the system can detect movements accurately within 0.1 mm and rotational changes within 0.2°. Second, patient positioning and monitoring were carried out for a group of 15 patients with 20 treatment sites. For the patient pool in the study, vertebral anatomy movement was observed to vary as much as 3 mm between sequential measurements and could occur in as little as 5 min. These results suggest a need for intrafraction patient monitoring and correctional shifts, even for patients whose overall treatment times are expected to be relatively short. Small relative rotations with standard deviations of less than 1.5° were observed. The small relative rotational movements observed do not, alone, justify patient monitoring using the image-guidance system during the treatments of generally small radiosurgical targets.

Evaluation of the implantable force transducer for chronic tendon-force recordings

In vivo force measurements from tendons and ligaments have become an important technique to determine internal forces, joint loading, and mechanisms of neuromotor control. The most frequently used transducers for such force recordings were placed external to the target tissue. Because of space restrictions and the associated impingement artifacts, these external transducers cannot be used for force measurements in all tendons and ligaments. In these situations, transducers placed inside the target tissue have been used recently; however, the suitability and performance characteristics of these internal transducers have not been assessed systematically. The purpose of this study was to assess the suitability and performance characteristics of an internally placed force transducer which has been used previously. The results indicated that small angular displacements of the transducer within the target tissue, as well as small relative rotations of the corresponding bones, resulted in substantially changed transducer output for given externally applied loads. Also, the transducer output was found to depend on the rate of load application. It was concluded that, although the internal force transducer gave reliable signals within a given experiment, and thus, could be used to assess relative changes in tissue forces pre- and post-interventions, it would be difficult to use the transducer for the accurate determination of the actual tissue forees during unrestrained animal locomotion.

Coupled tearing modes in plasmas with differential rotation

The global asymptotic matching equations for multiple coupled resistive modes of arbitrary parity in a cylindrical plasma are derived. Three different variational principles are given for the outer region matching data, while the inner region analysis features a careful treatment of the symmetry-breaking effect of a gradient in the equilibrium current for a zero-β slab model. It is concluded that the usual constant-ψ result remains valid and constrains the matrix matching formalism. The dispersion relation is compared with initial value calculations of a double tearing mode when there are small relative rotation velocities between the rational surfaces. In treating differential rotation within the asymptotic matching formalism, flow is ignored in the outer region and is assumed to affect the inner response solely through a Doppler shift. It is shown that the relative rotation can have a strong stabilizing effect by making all but one rational surface effectively ideal.

Normal and Angular Motions at Rough Planar Contacts During Sliding With Friction

The planar dynamics of a rough block in nominally stationary or sliding contact with a counter-surface is studied in this work. Starting with the Greenwood-Williamson model of a rough surface, the analysis of elastic contact deflections is extended to accommodate angular as well as normal motions. The real area of contact and the normal contact force are obtained in terms of the relative approach and orientation of the surfaces. It is shown that angular and normal motions at frictional contacts are generally coupled. The contact area and normal contact force are shown to be nonlinearly related to the normal and angular motions. However, the contact area remains proportional to the normal load, even in the presence of angular motions. When the friction force is assumed to be proportional to the real area of contact, the coefficient of sliding friction will be unchanged by small relative rotations between the sliding bodies. Based on this contact and friction model, the nonlinear equations of motion that describe the planar contact vibrations of a sliding block can be written directly. Although a detailed analysis of the stability and response characteristics of these nonlinear equations is beyond the scope of the present work, a limited comparison of calculations and measurements taken on both stationary and sliding blocks indicate that the small amplitude contact vibrations are reasonably well captured by the model developed in this work.

Large Deformation Analysis of Orthodontic Appliances

The deformations of orthodontic appliances used for space closure are large so that any mathematical analysis will require a nonlinear approach. Existing incremental finite element and finite difference numerical methods suffer from excessive computational effort when analyzing these problems. An accurate segmental technique is proposed to handle these difficulties in an extremely efficient fashion. The segmental technique starts by assuming that an orthodontic appliance is composed of a number of smaller segments, the ends of which undergo small relative rotation. With an appropriate choice of local coordinate system the equilibrium equations for each segment are linearized and solved in a straightforward manner. The segments are then assembled using geometric and force compatibility relations similar to the transfer matrix method. Consequently, the original nonlinear boundary value problem is solved as a sequence of linear initial value problems which converge to the required boundary conditions. As only one segment need be considered at a time, the computations can be performed accurately and efficiently on a PC type computer. Although an iterative solution is used to match the boundary conditions, the time required to solve a given problem ranges from a few seconds to a couple of minutes depending on the initial geometric complexity. The accuracy of the segmental technique is verified by comparison with an exact solution for an initially curved cantilever beam with an end load. In addition, comparisons are made with existing experimental and numerical results as well as with a new set of experimental data. In all cases the segmental technique is in excellent agreement with the results of these other studies.

Nonlinear Bending of Inextensible Thin Rods Under Distributed and Concentrated Loads

A method is presented for the analysis of thin rods loaded by concentrated and distributed loads. The technique is also applicable to non-uniform rods. The solution of a nonlinear differential equation is avoided by considering the rod as a series of short rod segments. Each segment undergoes only small strains and small relative rotations so that the differential equation governing its shape is linear and easily solvable. The method is illustrated by two problems; the stiffened caternary and the tapered cantilever under distributed and concentrated loads.

Precessional torques as the cause of geomagnetism

The difference in the precessional torques on the core and mantle of the earth can produce a small relative rotation between the two. The magnitude of the relative rotation depends upon the inertial reaction resulting from the figure of the core-mantle boundary and upon the frictional torque caused by the shearing flow. It is concluded in this study that the frictional torque due to a turbulent hydromagnetic Ekman layer is the principal restraint on relative rotation. From the gross geophysical parameters of figure and density and the electrical conductivity of core material, the resulting magnetic fields, fluid velocities, and characteristic periods are found to compare favorably with the available information.

Spiral Cleavage of Mica

We chanced on a slice of mica which was cleaved spirally. The spiral lamella was several hundredths mm thick. Detailed observations on the structure of this specimen including polarization microscopic and X-ray studies are described. A tentative explanation of the origin of this unusually thick growth-layer is proposed assuming that an external force, which was exerted during the formation of the crystal, caused the left and right halves of the crystal to make a small relative rotation around the a -axis.