Natural Coordinates Research Articles

Comparing Measures of Association in 2×2 Probability Tables

Measures of association play a role in selecting 2×2 tables exhibiting strong dependence in high-dimensional binary data. Several measures are in use differing on specific tables and in their dependence on the margins. We study a 2-dimensional group of margin transformations on the 3-dimensional manifold of all 2×2 probability tables. The margin transformations allow introducing natural coordinates that identify with the real 3-space such that thex-axis corresponds to and margins vary on planesx=const. We use these coordinates to visualise and compare measures of association with respect to their dependence on the margins given the odds-ratio, their limit behaviour when cells approach zero and their weighting properties. We propose a novel measure of association in which tables with single small entries are up-weighted but those with skewed margins are down-weighted according to the relative entropy among the tables of the same odds-ratio.

Two-particle atomic coalescences: Boundary conditions for the Fock coefficient components

The exact values of the presently determined components of the angular Fock coefficients at the two-particle coalescences were obtained and systematized. The Green's-function approach was successfully applied to simplify the most complicated calculations. The boundary conditions for the Fock coefficient components in hyperspherical angular coordinates, which follow from the Kato cusp conditions for the two-electron wave function in the natural interparticle coordinates, were derived. The validity of the obtained boundary conditions was verified with examples of all the presently determined components. The additional boundary conditions not arising from the Kato cusp conditions were obtained as well. Wolfram's Mathematica was used extensively to obtain these results.

Magnesium complexes in diverse coordination patterns supported by tetradentate aminophenolate ligands: Synthesis, characterization and application in the stereocontrolled ring-opening polymerization of rac-LA

A series of magnesium silylamido complexes supported by tetradentate aminophenolate ligands, LMgN(SiMe3)2 (L={(2-R1)Ar-CH2N[(CH2)2R2]CH2-(4-R4-6-R3)C6H2O−}, R1=NMe2, R2=NiPr2, R3=R4=Cl (1), R3=R4=cumyl (2); R1=NMe2, R2=NEt2, R3=R4=cumyl (3), R3=CPh3, R4=Me (4); R1=NEt2, R2=NEt2, R3=CPh3, R4=Me (5); R1=NMe2, R2=(S)-1-butylpyrrolidine-2-yl, R3=R4=cumyl (6), R3=CPh3, R4=Me (7)), were synthesized and fully characterized, and their catalytic behaviors for the ring-opening polymerization (ROP) of rac-lactide (rac-LA) were explored. The monomeric nature and versatile coordination modes of these complexes in the solid state were further confirmed by X-ray diffraction studies on complexes 1, 3 and 7. In complex 1, the N,N-diisopropylamino group on the alkylamino side arm does not coordinate to the metal centre, whilst the remaining three donors of the aminophenolate ligand and the silylamido group bond with the magnesium centre. By contrast, in complexes 3 and 7, the arylamino moiety does not coordinate to the metal centre, while the alkylamino side arm coordinates. It is worth noting that the introduction of the N,N-dimethyl amino group to the pendant benzyl group realises the diastereoselective synthesis of multichiral aminophenolate magnesium complexes, which has not been achieved by the corresponding tridentate aminophenolate ligand. It was found that most of these magnesium complexes serve as highly active initiators for the ROP of rac-LA. The coordination pattern of the aminophenolate ligand exerted a considerable influence on the activity and stereoselectivity of the corresponding complex toward the polymerization of rac-LA, leading to the production of moderate to high heterotactic biased PLAs. The enantiopure complex 7 showed the highest heteroselectivity among these magnesium complexes (Pr=0.80 in toluene, Pr=0.82 in THF).

Spectroscopic and theoretical evaluation of the metal-olefin interaction in di-μ-chlorobis (1,5-cyclooctadiene) complexes of Ir and Rh

The complexes of di-μ-chlorobis(1,5-cyclooctadiene) of rhodium(I); [Rh(μ-Cl)(COD)]2 and iridium(I); [Ir(μ-Cl)(COD)]2 have shown prominent activities in a number of catalytic reactions. In the solid packing form these two complexes were shown to adopt D2h and C2v symmetries for iridium and rhodium, respectively. In this work vibrational spectroscopic techniques assisted with density functional theory (DFT) calculations have been employed to assess the metal-olefin interaction and to provide thorough assignments of the infrared and Raman spectra for both complexes. The wavenumber shifts associated with the CH2 bending modes have been established as a potential tool to access the σ and π components in the metal-olefin interaction for the two complexes. Examination of the catalytic activity based on calculated reactivity parameters, natural bond orbital (NBO) analysis and coordination energy was also carried out.

Dynamics Modeling and Analysis of Spacecraft with Large Deployable Hoop-Truss Antenna

Large deployable hoop-truss antennas are widely used in satellite communication systems for their high antenna gain and small packed volume. Knowledge of the deployment dynamics of the large deployable hoop-truss antenna and its coupling with spacecraft attitude motion are essential for the design of deployment mechanisms and attitude control systems. In this paper, a spacecraft with two flexible solar panels, which are reduced by Craig–Bampton component modal synthesis, is modeled by natural coordinate formulation. A large deployable hoop-truss antenna is modeled with the absolute nodal coordinate formulation. Both lead to a constant-mass matrix without the centrifugal and Coriolis forces. The whole dynamics model is used to solve the attitude and the reaction moment during the deployment process. Nonsynchronous deployment phenomena due to the structural flexibility and the decay of the driving force are investigated, and results show that these phenomena can increase the stresses suffered by the hoop truss, which should be considered in the design of a large deployable hoop-truss antenna.

Quasi-Classical Trajectory Study of Atom-Diatomic Molecule Collisions in Symmetric Hyperspherical Coordinates: The F + HCl Reaction as a Test Case.

We investigate the reactive dynamics of the triatomic system F + HCl → HF + Cl for total angular momentum equal zero and for different low-lying rovibrational states of the diatomic molecule. For each of the initial vibrational quantum numbers, the time evolution of the atom-diatom collision process is investigated for a wide range of impact angles and collision energies. To this purpose, the Quasi-Classical Trajectories (QCT) method was implemented in a hyperspherical configuration space. The Hamilton equations of motion are solved numerically in an intermediate effective Cartesian space to exploit the relative simplicity of this intermediate representation. Interatomic interactions are described by a London-Eyring-Polanyi-Sato potential energy surface, specifically developed for the title reaction, and the results of the QCT simulations are discussed in terms of the time-evolution of the hyperangles. The analysis of the collision dynamics using symmetric hyperspherical coordinates provides, in addition to the description in terms of a natural reaction coordinate (the hyperradius), a more striking representation of the exchange dynamics, in terms of the time-dependent probability distribution along the kinematic rotation hyperangle, and a precise distinction between direct and indirect mechanisms of the reaction.

Identification, design and kinematic analysis of an earthmoving mechanism

Earthmoving mechanisms in motor graders are critical components for earthwork, compaction and re-handling, and yet they have not received much attention by mechanical engineering research in recent times. In this paper, a comprehensive analysis, from mechanism identification and innovative design to kinematic analysis, is presented. First, the mechanism analysis and synthesis method based on multibody system dynamics is carried out through the analysis of the system topology and connectivity. We conclude that the earthmoving multibody system is a spatial hybrid mechanism, which consists of a spatial parallel mechanism and a spatial serial mechanism. Second, a number of new spatial parallel mechanisms, which are advantageous with respect to the original one under certain conditions, are generated. The kinematic characteristics of the parallel mechanism family are investigated in terms of constraint equations formulated in natural coordinates. Third and last, kinematic simulations and optimization processes are carried out to evaluate the advantages of the presented spatial parallel mechanisms. Simulation results show that these mechanisms can provide better kinematic performance.

Two-dimensional shape retrieval using the distribution of extrema of Laplacian eigenfunctions

We propose a new method using the distribution of extrema of Laplacian eigenfunctions for two-dimensional (2D) shape description and matching. We construct a weighted directed graph, which we call signed natural neighbor graph, to represent a Laplacian eigenfunction of a shape. The nodes of this sparse graph are the extrema of the corresponding eigenfunction, and the edge weights are defined by signed natural neighbor coordinates derived from the local spatial arrangement of extrema. We construct the signed natural neighbor graphs defined by a small number of low-frequency Laplacian eigenfunctions of a shape to describe it. This shape descriptor is invariant under rigid transformations and uniform scaling, and is also insensitive to minor boundary deformations. When using our shape descriptor for matching two shapes, we determine their similarity by comparing the graphs induced by corresponding Laplacian eigenfunctions of the two shapes. Our experimental shape-matching results demonstrate that our method is effective for 2D shape retrieval.

Spraying layer-by-layer assembly film based on the coordination bond of bioinspired polydopamine–FeIII

Spraying layer-by-layer (LbL) assembly technique has been developed for rapid and efficient fabrication of functional films. The spraying method generally requires relatively fast formation of stable interactions among the building components. In this study, inspired by nature, the fast and strong coordination bond between catechol groups (polydopamine, PDA) and metal ions (Fe3+) was employed to fabricate (poly(ethylenimine)/PDA-coated carbon nanotubes) (PEI/CNTs@PDA) multilayer film. The coordination bond significantly enhanced the films' crosslinking during the spraying LbL procedures. Ellipsometry results confirmed the successful assembly of the [PEI/(CNTs@PDA+Fe3+)] multilayer film. The hierarchical micro/nano-structures were observed on the multilayer surface. As a potential functionalization, the multilayer film was then coated with a low surface energy silane compound via thermal chemical vapor deposition method, leading to a superhydrophobic surface. By taking advantages of the specific rapid coordination bond of PDA and Fe3+, this study provides an efficient and fast strategy to fabricate functional surfaces through spraying LbL assembly.

Dynamics of a Space Manipulator: Relative vs. Natural Coordinates

Dynamics of a Space Manipulator: Relative vs. Natural Coordinates

Four-parameter functionally graded cracked plates of arbitrary shape: A GDQFEM solution for free vibrations

ABSTRACTThe dynamic behavior of moderately thick FGM plates with geometric discontinuities and arbitrarily curved boundaries is investigated. The Generalized Differential Quadrature Finite Element Method (GDQFEM) is proposed as a numerical approach. The irregular physical domain in Cartesian coordinates is transformed into a regular domain in natural coordinates. Several types of cracked FGM plates are investigated. It appears that GDQFEM is analogous to the well-known Finite Element Method (FEM). With reference to the proposed technique the governing FSDT equations are solved in their strong form and the connections between the elements are imposed with the inter-element compatibility conditions. The results show excellent agreement with other numerical solutions obtained by FEM.

Origin of structure in the universe: quantum cosmology reconsidered

Based on a more careful canonical analysis, we motivate a reduced quantization—in the sense of superspace quantization—of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in the vacuum case. This is attained through consideration of configuration space geometries at various levels of reduction. Some of these have the good fortunate of being flat. Geometrically natural coordinates for these are interpreted in terms of the original redundant formulation’s well-known mode expansion coefficients.

A Dual Space Approach for Force/Motion Transmissibility Analysis of Lower Mobility Parallel Manipulators

By drawing on the duality of twist space and wrench space, this paper presents a general and systematic approach for force/motion transmissibility analysis of lower mobility nonredundant and nonoverconstrained parallel manipulators. This leads to the formulation of a complete and justifiable model that enables the force/motion transmissibility analysis to be integrated into a unified framework under the umbrella of a homogenous and decoupled linear transformation that maps the coordinates of the platform wrench/twist in the joint space to its natural coordinates in the operation space. Utilizing the penalty method to avoid the indeterminate form “0/0” when the local maximum of a virtual coefficient approaches zero, a set of dimensionally homogeneous transmission indices is proposed which can be employed for precisely representing the closeness to different types of singularities defined in twist space as well as for dimensional optimization. An example is given to illustrate the effectiveness of this approach.

Optimization of a crossbar parallel machine tool based on workspace and dexterity

Increasing workspace and improving dexterity are important tasks for the design of parallel machine tools. The workspace of a crossbar parallel machine tool with constraints is obtained by using a 3D search method based on inverse kinematics. The new Jacobian matrix of the machine is also derived by using the natural coordinate method. Dexterity distribution of the machine tool is obtained on the basis of the workspace and the new Jacobian matrix. Influences of the structural parameters on the workspace volume index (WVI) and global dexterity index (GDI) are analyzed. Structural optimization is conducted by treating the WVI and GDI as the global optimization goals. Unlike the initial data, the optimized results increased by 0.43 and 0.34 times.

Effects of Coordinate Rotation on Turbulent Flux Measurements during Wintertime Haze Pollution in Beijing, China

AbstractEddy-covariance observations from the Beijing 325-m meteorological tower are used to evaluate the effects of coordinate rotation on the turbulent exchange of momentum and scalars during wintertime haze pollution (January–February 2013). Two techniques are used in the present evaluation; namely, the natural wind coordinate (NWC) and the planar fit coordinate (PFC), with the latter being applied by means of two methods for linear regression (i.e., overall and sector-wise). The different techniques show a general agreement in both turbulent fluxes and transport efficiencies, especially evident at the lower, 140-m level above the ground (compared to the higher, 280-m level), perhaps implying that the selection of a technique for coordinate rotation (NWC or PFC) is less of a concern for a sufficiently low level, despite the complexities of urban terrain. Additionally, sector-wise regression is a recommended approach for practical application of the PFC in a complex urban environment subjected to partic...

Stereoselective Polymerization of rac-Lactide Catalyzed by Zinc Complexes with Tetradentate Aminophenolate Ligands in Different Coordination Patterns: Kinetics and Mechanism.

A series of monomeric zinc silylamido complexes bearing [NNNO]-type tetradentate aminophenolate ligands, LZnN(SiMe3)2 [L = {(2-R(1))ArCH2N[(CH2)2R(2)]CH2(4-R(4)-6-R(3))C6H2O-}, R(1) = NMe2, R(2) = N(i)Pr2, R(3) = R(4) = Cl (1), R(3) = R(4) = cumyl (3); R(1) = NMe2, R(2) = NEt2, R(3) = R(4) = cumyl (2), R(3) = CPh3, R(4) = Me (4); R(1) = NEt2, R(2) = NEt2, R(3) = CPh3, R(4) = Me (5); R(1) = NMe2, R(2) = (S)-1-butylpyrrolidin-2-yl, R(3) = R(4) = cumyl (6), R(3) = CPh3, R(4) = Me (7)], have been synthesized via reactions of Zn[N(SiMe3)2]2 and 1 equiv of the corresponding aminophenols. The monomeric nature and versatile coordination patterns of these complexes in the solid state were further confirmed by X-ray diffraction studies on complexes 2, 3, 5, and 7. In complex 3, the N,N-diisopropylamino group on the pendant side arm does not coordinate to the metal center; only the remaining three donors of the aminophenolate ligand and the silylamido group interact with the zinc center. By contrast, in complexes 2, 5, and 7, the amino group of the aryl moiety does not coordinate to the metal center, while the amino group on the pendant side arm coordinates. At room temperature, the above-mentioned structural features of these complexes are retained in solution, as confirmed by (1)H NMR spectroscopy. Complexes 1-7 proved to be efficient initiators for the ring-opening polymerization of rac-lactide (rac-LA) at ambient temperature, and the polymerizations were better controlled in the presence of 2-propanol. The coordination pattern of the aminophenolate ligand exerted a significant influence on the stereoselectivity of the corresponding complex toward the polymerization of rac-LA, leading to the production of heterotactic biased polylactides (PLAs) by complexes 1 and 3 (Pm = 0.40-0.46) and moderately to highly isotactic PLAs by complexes 2 and 4-7 (Pm = 0.70-0.81). Detailed kinetic investigations revealed a first-order dependence on the monomer concentration for all complexes and different orders in the initiator concentration ranging from 1.78 to 1.81. The nature of the solvent as well as the molar ratio of the zinc complex and 2-propanol also displayed certain influence on the order of rac-LA polymerization in the initiator concentration. Factional orders of 1.80, 1.38, and 1.11 were obtained by using complex 5/(i)PrOH (1:1) in toluene and tetrahydrofuran and complex 5/(i)PrOH (1:2) in toluene, respectively. On the basis of DOSY and (1)H and (13)C NMR studies of zinc alkoxide model complexes "LZn(OCMe2COOMe)" as well as the fractional orders of 1.78-1.81 in the initiator concentration, activation/insertion processes likely involving more than one monomeric active species were then hypothesized.

A natural absolute coordinate formulation for the kinematic and dynamic analysis of rigid multibody systems

The purpose of this paper was to present the key features of a novel coordinate formulation for the analytical description of the motion of rigid multibody systems, namely the natural absolute coordinate formulation (NACF). As it is shown in this work, the kinematic and dynamic analysis of rigid multibody systems can be significantly enhanced employing the NACF. In particular, this formulation combines the main advantages of the natural coordinate formulation (NCF), such as the remarkable property of leading to a constant mass matrix and to zero centrifugal and Coriolis generalized inertia forces, with the generality and the effectiveness of the reference point coordinate formulation (RPCF), which is essentially represented by the possibility to develop and assemble the equations of motion of a multibody system together with the algebraic equations which model the joint constraints in a systematic manner. Moreover, a new computational method hereinafter referred to as the robust generalized coordinate partitioning algorithm is also introduced in this work. The robust generalized coordinate partitioning algorithm can be successfully utilized to numerically solve the index-one form of the multibody system equations of motion formulated by using the proposed NACF as well as the well-known RPCF. In particular, the computational procedure presented in this paper owes its robustness to the combination of the main ideas of the well-established generalized coordinate partitioning method, which is commonly employed to cope with the drift phenomenon of the constraint equations at the position and velocity levels when an index-one formulation of the equations of motion is considered, with the more general and advanced constraint enforcement technique at the acceleration level represented by the fundamental equations of constrained motion. In fact, the fundamental equations of constrained motion represent an effective and efficient method able to calculate analytically the generalized constraint forces relative to a multibody system subjected to a general set of redundant holonomic and/or nonholonomic constraint equations by using the Gauss principle of least constraint, thus avoiding the definition of the Lagrange multipliers. The fundamental equations of constrained motion are remarkably effective when used for modeling the dynamic behavior of rigid multibody systems mathematically represented employing the NACF, as it is shown in this paper. Four simple benchmark multibody systems are also examined in order to exemplify the application of the principal concepts developed in the paper.

A quantitative assessment of the eating capability in the elderly individuals

Ageing process implies physiologically weakened muscles, loss of natural teeth and movement coordination, causing difficulties in the eating process. A term “eating capability” has been proposed to measure objectively how capable an elderly individual is in overall food management. Our objectives were to establish feasible methodologies of eating capability assessment, examine correlations between hand and oro-facial muscle strengths and grade elderly subjects into groups based on their eating capabilities. This study was performed with 203 elderly subjects living in the UK (n=103, 7 community centres, 2 sheltered accommodation) and Spain (n=100, 3 nursing homes, 1 community centre). Hand gripping force, finger gripping force, biting force, lip sealing pressure, tongue pressing pressure and touching sensitivity were measured for elderly subjects. Measured parameters were normalised and scored between 1 and 5, with 1 being the weakest. Subjects were then grouped into 4 groups based on their eating capability scores, being participants of cluster 1 the weakest group and 4 the strongest. Perception of oral processing difficulty was assessed by showing food images. Hand gripping force showed a strong linear correlation with tongue pressure (UK: 0.35; Spain: 0.326) and biting force (UK: 0.351; Spain: 0.427). Biting force was strongly dependent on the denture status. Elderly of the first three groups perceived food products with more hardness and/or fibrous structure as difficult to process orally. The objective measurements of various physiological factors enabled quantitative characterisation of the eating capabilities of elderly people. The observed relationship between hand and oro-facial muscle strengths provides possibility of using non-invasive hand gripping force measurement for eating capability assessment.

The Coplane Analysis Technique for Three-Dimensional Wind Retrieval Using the HIWRAP Airborne Doppler Radar

AbstractThe coplane analysis technique for mapping the three-dimensional wind field of precipitating systems is applied to the NASA High-Altitude Wind and Rain Airborne Profiler (HIWRAP). HIWRAP is a dual-frequency Doppler radar system with two downward-pointing and conically scanning beams. The coplane technique interpolates radar measurements onto a natural coordinate frame, directly solves for two wind components, and integrates the mass continuity equation to retrieve the unobserved third wind component. This technique is tested using a model simulation of a hurricane and compared with a global optimization retrieval. The coplane method produced lower errors for the cross-track and vertical wind components, while the global optimization method produced lower errors for the along-track wind component. Cross-track and vertical wind errors were dependent upon the accuracy of the estimated boundary condition winds near the surface and at nadir, which were derived by making certain assumptions about the vertical velocity field. The coplane technique was then applied successfully to HIWRAP observations of Hurricane Ingrid (2013). Unlike the global optimization method, the coplane analysis allows for a transparent connection between the radar observations and specific analysis results. With this ability, small-scale features can be analyzed more adequately and erroneous radar measurements can be identified more easily.

Genetic algorithm optimization of point charges in force field development: challenges and insights.

Evolutionary methods, such as genetic algorithms (GAs), provide powerful tools for optimization of the force field parameters, especially in the case of simultaneous fitting of the force field terms against extensive reference data. However, GA fitting of the nonbonded interaction parameters that includes point charges has not been explored in the literature, likely due to numerous difficulties with even a simpler problem of the least-squares fitting of the atomic point charges against a reference molecular electrostatic potential (MEP), which often demonstrates an unusually high variation of the fitted charges on buried atoms. Here, we examine the performance of the GA approach for the least-squares MEP point charge fitting, and show that the GA optimizations suffer from a magnified version of the classical buried atom effect, producing highly scattered yet correlated solutions. This effect can be understood in terms of the linearly independent, natural coordinates of the MEP fitting problem defined by the eigenvectors of the least-squares sum Hessian matrix, which are also equivalent to the eigenvectors of the covariance matrix evaluated for the scattered GA solutions. GAs quickly converge with respect to the high-curvature coordinates defined by the eigenvectors related to the leading terms of the multipole expansion, but have difficulty converging with respect to the low-curvature coordinates that mostly depend on the buried atom charges. The performance of the evolutionary techniques dramatically improves when the point charge optimization is performed using the Hessian or covariance matrix eigenvectors, an approach with a significant potential for the evolutionary optimization of the fixed-charge biomolecular force fields.