Three-dimensional Physical Space Research Articles

Real-time haptic-teleoperated robotic system for motor control analysis

A versatile teleoperated robotic system was created as an assessment device for testing upper-extremity motor control adaptation using different control strategies. While many systems display output virtually on a computer monitor, this system was designed to output in three-dimensional physical space. The system accepts haptic force and torque input, and outputs robot end-effector displacements and rotations in three spatial dimensions. Benefits of this system include flexibility to conduct a variety of dissimilar tasks and reality of user feedback in physical space. Two separate experiments validated the teleoperated robotic system. The first experiment tested unimanual human motor control and the second tested bimanual motor control. This teleoperated robotic system can be used as an assessment device to study neuromuscular adaptability via a variety of control strategies providing a new and functional approach to human motor control analysis.

A crumpled surface having transverse attractive interactions as a simplified model with biological significance

Using extensive analogical simulations with square sheets of paper we investigate the influence of short-range transverse attractive interactions on the packing properties of a crumpled surface. These interactions are due to transverse connections or local bridges associated with a given number of binding sites localized on the two-dimensional surface and distributed in several patterns in the three-dimensional physical space. Geometrical relations and critical exponents describing the statistical properties of the crumpled surface are obtained as a function of the strength of the attractive interactions. Our model suggests how the presence of short-range interactions as, e.g. van der Waals forces can be important for the geometric plasticity of biological molecules, which in turn is important for biological function. The relevance of our results to the study of molecular conformation of proteins and membranes is discussed, and a comparison is also made between the behavior of the crumpled surface studied here and other important non-equilibrium fractal structures.

Information flow and interconnections in computing: extensions and applications of Rent's rule

Rent's rule and related concepts of connectivity such as dimensionality, line-length distributions, and separators are discussed. Generalizations for systems for which the Rent exponent is not constant throughout the interconnection hierarchy are provided. The origin of Rent's rule is stressed as resulting from the embedding of a high-dimensional information flow graph to two- or three-dimensional physical space. The applicability of these concepts to free-space optically interconnected systems is discussed. The role of Rent's rule in fundamental studies of different interconnection media, including superconductors and optics, is briefly reviewed.

A Basic Power Decomposition in Lagrangian Mechanics

A Basic Power Decomposition in Lagrangian Mechanics

Energy partitioning for "fuzzy" atoms.

The total energy of a molecule is presented as a sum of one- and two-atomic energy components in terms of "fuzzy" atoms, i.e., such divisions of the three-dimensional physical space into atomic regions in which the regions assigned to the individual atoms have no sharp boundaries but exhibit a continuous transition from one to another. By proper definitions the energy components are on the chemical energy scale. The method is realized by using Becke's integration scheme and weight function permitting very effective numerical integrations.

Overlap populations, bond orders and valences for ‘fuzzy’ atoms

Proper definitions are proposed to calculate interatomic overlap populations, bond order (multiplicity) indices and actual atomic valences from the results of ab initio quantum chemical calculations, in terms of ‘fuzzy’ atoms, i.e., such divisions of the three-dimensional physical space into atomic regions in which the regions assigned to the individual atoms have no sharp boundaries but exhibit a continuous transition from one to another. The results of test calculations are in agreement with the classical chemical notions, exhibit unexpectedly small basis sensitivity and do not depend too much on the selection of the weight function defining the actual division of the space into ‘fuzzy’ atomic regions. The scheme is applicable on both SCF and correlated levels of theory. A free program is available.

The generalized-kinetics-based equilibrium distribution function for composite particles

This work is devoted to the equilibrium distribution function for a fluid of mutually non-interacting identical composite point particles in three-dimensional physical space. The distribution function is derived within the generalized-kinetics (GK) vision from the proposed probabilistic model based on quantum-mechanical bosons and fermions. The first GK advantage is that the derivation does not involve any assumption on the interpolation between bosons and fermions whereas the resulting function provides this interpolation. The second GK advantage is that composons, the particles described with the GK-based distribution function, are considerably less schematic and more consistent physically than quons. Composons correspond to a specific case of Isakov's general q-commutation relation involving an infinite number of the q-coefficients. Connection of the composon concept to previous results in the literature is pointed out. A few directions for future research on the topic are formulated. The results of the work can be used in the composite-particle fluid problems where the Maxwell–Boltzmann description is not valid, for instance, in dense populations of not too massive point-like particles of a complex, composite nature at not too high temperatures. To cite this article: N. Bellomo et al., C. R. Mecanique 331 (2003).

Accurate quantum calculations on three-body collisions in recombination and collision-induced dissociation. I. Converged probabilities for the H+Ne2 system

The exact quantum theory of atomic recombination and collision-induced dissociation (CID) is presented using hyperspherical coordinates. Delves’ coordinates are emphasized, methods for doing numerically exact calculations are discussed and implemented, and fully converged dissociation probabilities (J=0) are presented for a model H+Ne2⇌H+Ne+Ne system. These are the first accurate CID calculations reported for any atomic system in the full three-dimensional physical space.

Volume-elements of integration: A geometric algebra approach

In this work, geometric algebra is applied to obtain the volume-element of integration for the 3 Cartesian coordinates of the center-of-mass, 3 Euler angles, and 3N−6 shape coordinates needed to describe the position, orientation, and shape of an N-atomic molecule. The volume-element is obtained as a product of N volume-elements, each associated with a set of three coordinates. The method presented has several advantages. For example, one does not need to expand any determinants, and all calculations are performed in the three-dimensional physical space (not in some 3N-dimensional abstract configuration space). Several examples and applications are given.

Structural characteristics of vacancy-ordered τ-phases

The vacancy-ordered τ-phases (VOPs) in Al-transition-metal (TM) alloys can be classified into three distinct categories in the commensurate limit. These are: (a) τ3 and its τ3 inflated phases possessing inversion centres on Al and V layers, (b) τ5 and its τ3 related phases displaying centres on Al and TM layers and (c) τ8 and those generated after τ3 inflation having centres on TM and V layers. The six-dimensional model proposed by us earlier generates all of them in three-dimensional physical space with the above structural characteristics. The consequence of taking a physical space cut from a six-dimensional anti-phase domain leads to an anti-phase domain for τ3 and τ∞, but it will be shown that such a cut leads to the generation of translational twins for other phases.

Technical advances toward interactive image-guided laparoscopic surgery.

Laparoscopic surgery uses real-time video to display the operative field. Interactive image-guided surgery (IIGS) is the real-time display of surgical instrument location on corresponding computed tomography (CT) scans or magnetic resonance images (MRI). We hypothesize that laparoscopic IIGS technologies can be combined to offer guidance for general surgery and, in particular, hepatic procedures. Tumor information determined from CT imaging can be overlayed onto laparoscopic video imaging to allow more precise resection or ablation. We mapped three-dimensional (3D) physical space to 2D laparoscopic video space using a common mathematical formula. Inherent distortions present in the video images were quantified and then corrected to determine their effect on this 3D to 2D mapping. Errors in mapping 3D physical space to 2D video image space ranged from 0.65 to 2.75 mm. Laparoscopic IIGS allows accurate (<3.0 mm) confirmation of 3D physical space points on video images. This in combination with accurately tracked instruments and an appropriate display may facilitate enhanced image guidance during laparoscopy.

Synchrotron radiation and symmetries

The total power of radiation emitted by a monoenergetic electron in circular orbit is derived by calculating the instantaneous energy flux of the electron field across the surfaces of spheres and tori that enclose the orbit. These surfaces are such that the positions of the electron at different times are indistinguishable with respect to them, which in turn permits the choice of special spheres and tori that greatly simplify the calculations. The total power of radiation of an electron is usually derived in textbooks with the help of the relativistic formalism. But for the particular motion in a synchrotron, the total power of radiation is obtained here working in the ordinary three-dimensional physical space, where the calculations are conceptually easier to follow than in Minskowski space, especially for students who are taking a first course of electrodynamics.

Atomic Modulation Functions, Periodic Nodal Surfaces and the three-dimensional incommensurately modulated (1 − x)Bi2O3 · xNb2O5, 0.06 &lt; x &lt; 0.23, solid solution

Abstract Superspace group symmetry is used to parameterize the compositional and displacive degrees of freedom associated with the complex, three-dimensional incommensurately modulated (1 − x)Bi2O3 · xNb2O5, 0.06 &lt; x &lt; 0.23, type II solid solution. The metal and oxygen ion Atomic Modulation Functions are shown to be closely related to the so-called D Periodic Nodal Surface. The structural consequences of this shape for real three-dimensional physical space are spelt out and used to test the structural plausibility of previously proposed structural models.

Incommensurate Modulated Structure of &amp;ldquo;Pb&amp;rdquo;-1223 Determined by Combining High Resolution Electron Microscopy and Electron Diffraction

The one-dimensional incommensurate modulated structure of (Pb0.5Sr0.3Cu0.2)Sr-2(Ca0.6Sr0.4)(2)Cu3Oy has been determined. The low-resolution average structure was derived by image deconvolution. The image resolution was enhanced by phase extension based on a set of corrected electron diffraction intensities. Multi-dimensional direct methods were then used to solve the four-dimensional (4D) structure. The incommensurate modulated structure was finally obtained by cutting the 4D structure with the three-dimensional physical space. Occupation and/or displacement modulation has been observed for all atoms.

Technical accuracy of a neuronavigation system measured with a high-precision mechanical micromanipulator.

This study was designed to determine and evaluate the different system-inherent sources of erroneous target localization of a light-emitting diode (LED)-based neuronavigation system (StealthStation, Stealth Technologies, Boulder, CO). The localization accuracy was estimated by applying a high-precision mechanical micromanipulator to move and exactly locate (+/- 0.1 micron) the pointer at multiple positions in the physical three-dimensional space. The localization error was evaluated by calculating the spatial distance between the (known) LED positions and the LED coordinates measured by the neuronavigator. The results are based on a study of approximately 280,000 independent coordinate measurements. The maximum localization error detected was 0.55 +/- 0.29 mm, with the z direction (distance to the camera array) being the most erroneous coordinate. Minimum localization error was found at a distance of 1400 mm from the central camera (optimal measurement position). Additional error due to 1) mechanical vibrations of the camera tripod (+/- 0.15 mm) and the reference frame (+/- 0.08 mm) and 2) extrapolation of the pointer tip position from the LED coordinates of at least +/- 0.12 mm were detected, leading to a total technical error of 0.55 +/- 0.64 mm. Based on this technical accuracy analysis, a set of handling recommendations is proposed, leading to an improved localization accuracy. The localization error could be reduced by 0.3 +/- 0.15 mm by correct camera positioning (1400 mm distance) plus 0.15 mm by vibration-eliminating fixation of the camera. Correct handling of the probe during the operation may improve the accuracy by up to 0.1 mm.

Study of plastically deformed icosahedral Al[sbnd]Pd[sbnd]Mn single quasicrystals by transmission electron microscopy

Abstract Al[sbnd]Pd[sbnd]Mn single-quasicrystals have been plastically deformed at temperatures between 730 and 800°C up to different strain values and analysed in the transmission electron microscope. Dislocations were created during deformation. The dislocation density ranged between 1·7 × 107 cm−2 in undeformed samples and 7·8 × 108cm−2in material deformed at 732°C. Six-dimensional dislocation Burgers vectors were determined employing the convergent-beam electron diffraction technique. 87% of these Burgers vectors were oriented parallel to twofold directions in three-dimensional physical space. Their moduli were 0·113, 0·183 and 0·296nm. The ratio of the phason to the phonon component of the Burgers vectors was found to increase with increasing strain. A variety of slip systems was observed. In most cases the respective slip plane normals were parallel to fivefold and threefold directions.

A detailed three-dimensional quantum study of the Li+FH reaction

Accurate quantum reactive scattering calculations in the full three-dimensional physical space have been carried out for the Li+FH reaction at zero total angular momentum using the adiabatically adjusting principal axis of inertia hyperspherical coordinate formalism. The procedures for fitting the potential energy surface, calculating the surface functions, and propagating the solutions in a coupled channel treatment are given and discussed. Features of the resulting reactive probability plots are analyzed, and simple explanations of a number of the quantum resonance and oscillatory features are found.

Kinematics of vorticity: Vorticity-strain conjugation in incompressible fluid flows.

An exact kinematic analysis is made of the three-dimensional incompressible Euler flows. It is found that the vorticity and rate-of-strain tensors are connected with each other through an identical singular integral transform. Some formal properties of this transform are derived. In particular, there exist harmonic functions in (3+1)-dimensional space so that the boundary values (toward our three-dimensional physical space) of a pair of conjugates are simply the vorticity and rate-of-strain tensors. The generalized Cauchy-Riemann equations are explicitly written. As an application, three of Siggia's invariants are related by some integrals.

Matrix tensor notation part I. Rectilinear orthogonal coordinates

A notation for vectors (first order tensors) and tensors (second order tensors) in physical three-dimensional space is proposed that satisfies a number of requirements which are missing in the customary vector, matrix and tensor notations. It is designed particularly to distinguish between vectors and tensors and their representation as vectors and matrices in different coordinate systems. This is achieved by the introduction of the base as a tensor quantity in the fundamental equation for the relation between a tensor and its representation as a matrix. The main purpose of the new notation is that it can be used in the teaching situation, therefore, it conveys all the information explicitly in the symbols, and it can be used in handwriting. All different numerical quantities have different symbols so that in numerical and symbolic computer applications the symbols can be copied directly to similar computer names which provides for well chosen names of variables in a computer program. It is also shown that the same notation is equally useful for vectors in abstract higher dimensional space and transformations and transforms in function space. Part I discusses the notation for orthogonal coordinates, including Cartesian coordinates for which the notation is very simple. Part II discusses how the same notation is equally efficient for skew and curved coordinates, and how it is integrated with tensor notation for higher than second order tensors.

Burgers vector of dislocations in an icosahedral Al62Cu25.5Fe12.5 quasicrystal determined by means of convergent-beam electron diffraction.

Dislocations in an Al62Cu25.5Fe12.5 face-centered icosahedral quasicrystal were studied by means of the contrast experiment and defocus convergent-beam electron diffraction technique. The indices of the six-dimensional Burgers vector of the dislocations were determined to be 1/2[1-11-100]. The projection b(parallel-to) of this six-dimensional Burgers vector in the three-dimensional physical space is exactly parallel to a twofold axis of the icosahedron. The magnitude \b(parallel-to) = 0.291 nm was calculated when a = 0.896 nm is taken for the lattice constant of the face-centered icosahedral phase.