Angular Degrees Of Freedom Research Articles

Geometrical product specifications: A structure of linear dimensions tolerances

The paper reveals the relationship of linear dimensions tolerances with other geometrical specifications: coordinates, deviations of position and deviations of surface configuration of component geometric features. The dependence of the precision structure of the linear dimensions on the functional purpose of features. The basic concept of the paper is informativeness of the feature, which represents the total number of linear and angular degrees of freedom, constrained by the feature in the component at operation. The very informativeness of the feature determines the two-dimensional linear-angular composition of the structure of the linear size, its tolerance and standard grade. This paper discusses only the linear dimensions of the features involved in couplings and forming fits.

New X-Ray Tomography Method Based on the 3D Radon Transform Compatible with Anisotropic Sources.

In this work, we propose a novel computed tomography (CT) approach for three-dimensional (3D) object reconstruction, based on a generalized tomographic geometry with two-dimensional angular sampling (two angular degrees of freedom). The reconstruction is based on the 3D Radon transform and is compatible with anisotropic beam conditions. This allows isotropic 3D imaging with a source, which can be extended along one direction for increased flux, while high resolution is achieved by a small source size only in the orthogonal direction. This novel scheme for analytical CT is demonstrated by numerical simulations and proof-of-concept experiments. In this way high resolution and coherence along a single direction determines the reconstruction quality of the entire 3D data set, opening up, for example, new opportunities to achieve nanoscale resolution and/or phase contrast with low brilliance sources such as laboratory x-ray or neutron sources.

Superintegrability of generalized Calogero models with oscillator or Coulomb potential

We deform N-dimensional (Euclidean, spherical and hyperbolic) oscillator and Coulomb systems, replacing their angular degrees of freedom by those of a generalized rational Calogero model. Using the action-angle description, it is established that maximal superintegrability is retained. For the rational Calogero model with Coulomb potential, we present all constants of motion via matrix model reduction. In particular, we construct the analog of the Runge-Lenz vector.

Multidimensional optical trapping of a mirror

Alignment control in gravitational-wave detectors has consistently proven to be a difficult problem due to the stringent noise contamination requirement for the gravitational wave readout and the radiation-pressure-induced angular instability in Fabry-Perot cavities (Sidles-Sigg instability). We present the analysis of a dual-carrier control scheme that uses radiation pressure to control a suspended mirror, trapping it in the longitudinal degree of freedom and one angular degree of freedom. We show that this scheme can control the Sidles-Sigg angular instability. Its limiting fundamental noise source is the quantum radiation pressure noise, providing an advantage compared to the conventional angular control schemes. In the Appendix we also derive an exact expression for the optical spring constant used in the control scheme.

Calculation of state-to-state cross sections for triatomic reaction by the multi-configuration time-dependent Hartree method.

A framework for quantum state-to-state integral and differential cross sections of triatomic reactive scattering using the Multi-Configuration Time-Dependent Hartree (MCTDH) method is introduced, where a modified version of the Heidelberg MCTDH package is applied. Parity of the system is adopted using only non-negative helicity quantum numbers, which reduces the basis set size of the single particle functions in angular degree of freedom almost by half. The initial wave packet is constructed in the space-fixed frame, which can accurately account for the centrifugal potential. By using the reactant-coordinate-based method, the product state-resolved information can be accurately extracted. Test calculations are presented for the H + H2 reactive scattering. This work demonstrates the capability of the MCTDH method for extracting accurate state-to-state integral and differential cross sections. As an efficient scheme for high-dimensional problems, the MCTDH method may be promising for the study of product state-resolved cross sections for polyatomic reactive systems.

Total Ankle Arthroplasty Accuracy and Reproducibility Using Preoperative CT Scan-Derived, Patient-Specific Guides

Preoperative navigation has provided many potential benefits for total knee arthroplasty, including patient-specific alignment, repeatable implant placement, and decreased operative time. For the first time, this technology was applied to total ankle arthroplasty (TAA). This study evaluated repeatability of tibia and talus patient-specific guide placement and deviation between the preoperative plan and actual implant placement. Routine ankle CT scans were acquired of 15 cadaveric lower extremity limbs, converted into 3D solid models, and imported into a computer-assisted design assembly. Anatomic landmarks defining tibia/talus alignment were established and used to perform a virtual TAA. Commercially available implant components were placed to mimic traditional cases. An operative guide referencing the cadaver-specific anatomy was engineered to define the resection planes necessary to re-create virtual placement of traditional tibia and talus implants in the postoperative position. Board-certified TAA orthopaedic surgeons with no prior preoperative navigation experience placed the operative guides onto the bones based on tactile and visual feedback. Guide placement was repeated 4 times to determine variability. Final implant position was recorded with an infrared probe, confirmed with CT scans, and compared to the preoperative plan. Average deviations between planned and actual guide placement were determined for all rotational and translational degrees of freedom (DOF). In addition, implant component location was measured radiographically. Intraobserver tibia and talus guide variation between all trials was 0.26 ± 0.18 degrees and 0.36 ± 0.25 degrees in flexion/extension, 0.61 ± 0.58 and 0.53 ± 0.53 in varus/valgus, and 0.79 ± 0.38 degrees and 1.15 ± 0.77 degrees in internal/external rotation, respectively. Average variation between preoperative and postoperative implant placement was less than 2 degrees and 1.4 mm in all specimens tested. Preliminary data suggest that preoperative navigation and custom operative guides result in reliable and reproducible placement of TAA implants and patient-specific ankle alignment. Deviation of final implant placement from the preoperative plan was less than 2 degrees in all angular DOF, providing greater accuracy than the ±3 degrees determined in other implant system studies using traditional instrumentation and computer navigation. We have further demonstrated that final implant position is successfully guided by these patient-specific guides, with reproducibility of tibial component placement falling within 2 degrees of the intended target. This level of reproducibility suggests a promise for this technology, and it is hoped this level of accuracy will become the benchmark for the next generation of total ankle arthroplasty.

Momentum and photon energy dependence of the circular dichroic photoemission in the bulk Rashba semiconductorsBiTeX(X=I, Br, Cl)

Bulk Rashba systems BiTeX (X = I, Br, Cl) are emerging as important candidates for developing spintronics devices, because of the coexistence of spin-split bulk and surface states, along with the ambipolar character of the surface charge carriers. The need of studying the spin texture of strongly spin-orbit coupled materials has recently promoted circular dichroic Angular Resolved Photoelectron Spectroscopy (cd-ARPES) as an indirect tool to measure the spin and the angular degrees of freedom. Here we report a detailed photon energy dependent study of the cd-ARPES spectra in BiTeX (X = I, Br and Cl). Our work reveals a large variation of the magnitude and sign of the dichroism. Interestingly, we find that the dichroic signal modulates differently for the three compounds and for the different spin-split states. These findings show a momentum and photon energy dependence for the cd-ARPES signals in the bulk Rashba semiconductor BiTeX (X = I, Br, Cl). Finally, the outcome of our experiment indicates the important relation between the modulation of the dichroism and the phase differences between the wave-functions involved in the photoemission process. This phase difference can be due to initial or final state effects. In the former case the phase difference results in possible interference effects among the photo-electrons emitted from different atomic layers and characterized by entangled spin-orbital polarized bands. In the latter case the phase difference results from the relative phases of the expansion of the final state in different outgoing partial waves.

Control Effectiveness Analysis of the hawkmoth Manduca sexta: a Multibody Dynamics Approach

This paper presents a control effectiveness analysis of the hawkmoth Manduca sexta. A multibody dynamic model of the insect that considers the time-varying inertia of two flapping wings is established, based on measurement data from the real hawkmoth. A six-degree-of-freedom (6-DOF) multibody flight dynamics simulation environment is used to analyze the effectiveness of the control variables defined in a wing kinematics function. The aerodynamics from complex wing flapping motions is estimated by a blade element approach, including translational and rotational force coefficients derived from relevant experimental studies. Control characteristics of flight dynamics with respect to the changes of three angular degrees of freedom (stroke positional, feathering, and deviation angle) of the wing kinematics are investigated. Results show that the symmetric (asymmetric) wing kinematics change of each wing only affects the longitudinal (lateral) flight forces and moments, which implies that the longitudinal and lateral flight controls are decoupled. However, there are coupling effects within each plane of motion. In the longitudinal plane, pitch and forward/backward motion controls are coupled; in the lateral plane, roll and side-translation motion controls are coupled.

Identifying Kondo orbitals through spatially resolved STS

AbstractWe study the influence of angular degrees of freedom of magnetic adatoms on metallic surfaces onto scanning tunneling spectra. Kondo scattering of electrons off the adatom changes the local density of states near the Fermi level. The spatial dependence of this correction is set by the orbital structure of the local moment localized on the adatom. By considering a multilevel Anderson model with non‐degenerate orbitals of differing orbital structure, we demonstrate that the spatial dependence of the scanning tunneling spectrum contains sufficient information to infer the orbital degrees of freedom of the magnetic adatom.

Grain misorientation and grain-boundary rotation dependent mechanical properties in polycrystalline graphene

In two-dimensional polycrystalline graphene, two angular degrees of freedom (DOF) are needed to define a general grain boundary (GB): the misorientation of two grains and the rotation of the boundary line. Via both molecular dynamics simulations and theoretical analysis, we see that the density of GB defects strongly depends on grain misorientation but is insensitive to GB rotation. And reveal the dependence of mechanical properties on grain misorientation and GB rotation in polycrystalline graphene. We find that the dependence of GB normal strength on grain misorientation and GB rotation in graphene stems from the superposition of the stress field induced by a pentagon–heptagon pair itself to that from the interaction between the other defects and the one under consideration. Based on MD simulations and ab initio calculations, we show that failure starts from the bond shared by hexagon–heptagon rings. We then apply continuum mechanics to explain the dependence of GB normal strength on the two angular DOF in graphene with pentagon–heptagon rings. The investigation showed here supplies valuable guidance to develop multiscale and multiphysics models for graphene.

A 3-degree of freedom binary search pose estimation technique

This paper describes a novel, binary search pose estimation (BSPE) technique for poses constrained to 3 degrees of freedom (DOF). The technique requires three fiduciary marker points and operates by minimising the angular DOF through a binary search driven algorithm. The technique is less computationally intensive than the standard closed form solutions and quickly converges to a solution which can be verified if additional fiduciary points are available. Evaluation for the technique is presented through a comparison to pose from orthography and scaling with iterations (POSIT) using synthetic data and a real-world application, where the technique is used for pose estimation of a mobile robot with respect to a motor vehicle for inspection purposes.

Alignment of chirped-pulse compressor

An original method of alignment of grating compressors for ultrahigh-power CPA laser systems is proposed. The use of this method for adjustment of the grating compressor of a PEARL subpetawattlaser complex made it possible to align the diffraction gratings with a second accuracy in all three angular degrees of freedom, including alignment of the grooves, and to adjust the angles of beam incidence on the grating with a high accuracy. A simple method for measuring the difference in the groove densities of gratings with accuracy better than 0.005 lines mm-1 is proposed and tested.

OPTIMUM USE OF DYNAMIC STANDS CONSTRUCTIVE RESOURCES AT IMITATION OF ACCELERATЕ INFLUENCES ON ANGULAR FREEDOM DEGREES

Formulation and solution of the problem of optimal use of design resources of motion system while force cueing along the angular degrees of freedom which significantly improve the quality of physical modeling on flight simulators is presented.

Angular degrees of freedom in twin-beam parametric down-conversion

We investigate the effect of angular tuning on coherently coupled optical parametric generation (OPG) in two-dimensional purely nonlinear lattices and demonstrate how it allows accessing both shared signal and shared idler regimes, resulting in twin-beam outputs in the mid- and near infrared, respectively. Furthermore, we present the results of a systematic spectral and angular mapping of the twin-beam OPG response in the near-infrared as a function of the pump incidence angle.

Excitation, relaxation, and quantum diffusion of CO on copper

We investigate the effect of intermode coupling and anharmonicity on the excitation and relaxation dynamics of CO on Cu(100). The nonadiabatic coupling of the adsorbate to the surface is treated perturbatively using a position-dependent state-resolved transition rate model. Using the potential energy surface of Marquardt et al. [J. Chem. Phys. 132, 074108 (2010)], which provides an accurate description of intermode interactions, we propose a four-dimensional model that represents simultaneously the diffusion and the desorption of the adsorbate. The system is driven by both rational and optimized infrared laser pulses to favor either selective mode and state excitations or lateral displacement along the diffusion coordinate. The dissipative dynamics is simulated using the reduced density matrix in its Lindblad form. We show that coupling between the degrees of freedom, mediated by the creation and annihilation of electron-hole pairs in the metal substrate, significantly affects the system excitation and relaxation dynamics. In particular, the angular degrees of freedom appear to play an important role in the energy redistribution among the molecule-surface vibrations. We also show that coherent excitation using simple IR pulses can achieve population transfer to a specific target to some extent but does not allow enforcement of the directionality to the diffusion motion.

Secure information capacity of photons entangled in many dimensions

We quantify precisely the maximum secure information capacity of photons entangled in high dimensions for entanglement in the orbital angular momentum and angular degrees of freedom. Our analysis takes careful account of the influence of experimental imperfections, such as nonunity detection efficiency, on the degree of Einstein-Podolsky-Rosen (EPR) entanglement and hence on the secure information capacity of the photon pairs. We find that there is is an optimal dimension that maximizes the secure information capacity whose value can be predicted analytically from the knowledge of only a few experimental parameters.

Integrable generalizations of oscillator and Coulomb systems via action–angle variables

Oscillator and Coulomb systems on N-dimensional spaces of constant curvature can be generalized by replacing their angular degrees of freedom with a compact integrable (N−1)-dimensional system. We present the action–angle formulation of such models in terms of the radial degree of freedom and the action–angle variables of the angular subsystem. As an example, we construct the spherical and pseudospherical generalization of the two-dimensional superintegrable models introduced by Tremblay, Turbiner and Winternitz and by Post and Winternitz. We demonstrate the superintegrability of these systems and give their hidden constant of motion.

Design of an Instrument Guide for MRI-Guided Percutaneous Interventions

This paper describes the design of an instrument guidance device for percutaneous interventions in closed bore magnetic resonance (MR) imaging systems. The device consists of a curved arm piece that travels around a circular base and an additional needle holder that travels along the curved arm, thus providing two angular degrees of freedom that enable an ablation probe to pivot about a remote center of motion located at the skin entry point. The device is intended to be mounted onto a custom built MR coil that rests on the patient while they are imaged. Exact constraint design principles were used to incorporate translational bearings into the plastic parts. Thumbscrews were used for preload and locking so that the probe guide could be fixed along a specific trajectory. The device was prototyped via stereolithography as a proof of concept and demonstrated that a probe could be angled about a remote pivot point.

Extending The Resolution In Total Internal Reflection Fluorescence (TIRF) Microscopy

Total internal reflection fluorescence (TIRF) microscopy is the method of choice to image structures close to the cell-substrate interface. Illuminating the specimen with evanescent light decaying exponentially in axial direction results in essentially two-dimensional images without interference from regions deeper within the specimen. However, the lateral resolution of TIRF microscopy remains diffraction-limited to about 240 nm for green emission. Lateral resolution can be increased by up to a factor of 2.5 when illuminating the sample with evanescent standing waves [1].Here we report a compact and versatile illumination set-up employing two beam splitters and two piezo-actuated mirrors featuring two angular degrees of freedom. The piezo-actuated mirrors provide full control over the orientation and penetration depth of the evanescent standing wave. In contrast to grating-projection set-ups [1], beam steering via mirrors facilitates simultaneous excitation at multiple wavelengths since the angle of incidence is set by reflection off the mirrors and does not vary for different wavelengths. To obtain a two-dimensional image with extended resolution, the specimen is illuminated with at least two differently oriented standing wave patterns. More directions lead to higher isotropy of the extended optical transfer function (OTF). In practice, however, we found that the cloverleaf-shaped OTF resulting from two illumination directions yields images of comparable morphology as the more isotropic OTF resulting from three illumination directions. Using only two directions increases imaging speed, whereas three illumination directions lead to more spectral overlap within the extended OTF, which facilitates image reconstruction. We further demonstrate the potential of this technique for biological imaging on examples including HeLa cells expressing GFP-actin.[1] Beck, M., Aschwanden, M. & Stemmer, A. (2008) Sub-100-nanometre resolution in total internal reflection fluorescence microscopy. J. Microsc., 232, 99-105.

Fuzzy scalar field theory as a multitrace matrix model

We develop an analytical approach to scalar field theory on the fuzzy sphere based on considering a perturbative expansion of the kinetic term. This expansion allows us to integrate out the angular degrees of freedom in the hermitian matrices encoding the scalar field. The remaining model depends only on the eigenvalues of the matrices and corresponds to a multitrace hermitian matrix model. Such a model can be solved by standard techniques as e.g. the saddle-point approximation. We evaluate the perturbative expansion up to second order and present the one-cut solution of the saddle-point approximation in the large N limit. We apply our approach to a model which has been proposed as an appropriate regularization of scalar field theory on the plane within the framework of fuzzy geometry.