Configuration Coordinates Research Articles

On the equations of motion in multibody dynamics

The equations of motion for a multibody system are derived from a continuum mechanical point of view. This will allow for the presence of rigid, as well as deformable, parts in the multibody system. The approach, using the principle of virtual power, leads to the classical Lagrange equations of motion. The generalized forces appearing in the equations are given as expressions involving contact, internal and body forces in the sense of continuum mechanics. A detailed analysis of the interaction between parts and their implication for the equations of motion is presented. Transformation properties, covariance and invariance under changes of configuration coordinates, are elucidated and a power theorem for the multibody system is proved. The equivalence between the standard balance equations for momentum and moment of momentum and the principle of virtual power is demonstrated.

Singularity-free dynamic equations of spacecraft-manipulator systems

In this paper we derive the singularity-free dynamic equations of spacecraft-manipulator systems using a minimal representation. Spacecraft are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange's equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of a spacecraft is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of free-floating and free-flying spacecraft-manipulator systems and we show how to calculate the inertia and Coriolis matrices in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. This paper represents the first detailed study of modeling of spacecraft-manipulator systems with a focus on a singularity free formulation using the proposed framework.

Investigating the luminescence properties as a function of activator concentration in single crystal cerium doped Lu2SiO5: Determination of the configuration coordinate model

The effect of cerium concentration on single crystal lutetium orthosilicate (Lu2SiO5, LSO) was investigated with temperature-dependent steady state and time resolved luminescence spectroscopy. The results were used to determine the thermal quenching activation energies and the phonon energies responsible for the thermal broadening of the luminescence spectra. The measured phonon values were used to calculate configuration coordinate (CC) diagrams of the luminescence centers. The nature of single crystal LSO:Ce concentration quenching was determined to be due to radiative energy transfer by self-absorption. The observed broadening of the excitation spectra and narrowing of the emission spectra with increasing cerium was explained via a CC model. A combination of the CC model and concentration quenching explained the measured thermal quenching activation energies.

Aqua Ions–Graphene Interfacial and Confinement Behavior: Insights from Isobaric–Isothermal Molecular Dynamics

We carry out a systematic microstructural characterization of the solid-fluid interface (SFI) of water and simple metal chloride aqueous solutions in contact with a free-standing plate or with two such plates separated by an interplate distance 0 ≤ h (Å) ≤ 30 at ambient conditions via isothermal-isobaric molecular dynamics. With this characterization, we target the interrogation of the system in search for answers to fundamental questions regarding the structure of the "external" and "internal" (confined) SFIs, the effect of the differential hydration behavior among species, and its link to species expulsion from confinement. For water at ambient conditions, we found that the structure of the "external" SFIs is independent of the interplate distance h in the range 0 ≤ h (Å) ≤ 30, that is, the absence of wall-mediated correlation effects between "external" and "internal" SFIs, and that for h < 9 Å the slit-pores dewet. Moreover, we observed a selective expulsion of ions caused by the differential hydration between the anion and the cations with a consequent charging of the slit-pore. All these observations were interpreted in terms of the axial profiles for precisely defined order parameters, including tetrahedral configuration, hydrogen bonding, and species coordination numbers.

Characterization of protein contributions to cobalt-carbon bond cleavage catalysis in adenosylcobalamin-dependent ethanolamine ammonia-lyase by using photolysis in the ternary complex.

Protein contributions to the substrate-triggered cleavage of the cobalt-carbon (Co-C) bond and formation of the cob(II)alamin-5'-deoxyadenosyl radical pair in the adenosylcobalamin (AdoCbl)-dependent ethanolamine ammonia-lyase (EAL) from Salmonella typhimurium have been studied by using pulsed-laser photolysis of AdoCbl in the EAL-AdoCbl-substrate ternary complex, and time-resolved probing of the photoproduct dynamics by using ultraviolet-visible absorption spectroscopy on the 10(-7)-10(-1) s time scale. Experiments were performed in a fluid dimethylsulfoxide/water cryosolvent system at 240 K, under conditions of kinetic competence for thermal cleavage of the Co-C bond in the ternary complex. The static ultraviolet-visible absorption spectra of holo-EAL and ternary complex are comparable, indicating that the binding of substrate does not labilize the cofactor cobalt-carbon (Co-C) bond by significantly distorting the equilibrium AdoCbl structure. Photolysis of AdoCbl in EAL at 240 K leads to cob(II)alamin-5'-deoxyadenosyl radical pair quantum yields of <0.01 at 10(-6) s in both holo-EAL and ternary complex. Three photoproduct states are populated following a saturating laser pulse, and labeled, P(f), P(s), and P(c). The relative amplitudes and first-order recombination rate constants of P(f) (0.4-0.6; 40-50 s(-1)), P(s) (0.3-0.4; 4 s(-1)), and P(c) (0.1-0.2; 0) are comparable in holo-EAL and in the ternary complex. Time-resolved, full-spectrum electron paramagnetic resonance (EPR) spectroscopy shows that visible irradiation alters neither the kinetics of thermal cob(II)alamin-substrate radical pair formation, nor the equilibrium between ternary complex and cob(II)alamin-substrate radical pair, at 246 K. The results indicate that substrate binding to holo-EAL does not "switch" the protein to a new structural state, which promptly stabilizes the cob(II)alamin-5'-deoxyadenosyl radical pair photoproduct, either through an increased barrier to recombination, a decreased barrier to further radical pair separation, or lowering of the radical pair state free energy, or a combination of these effects. Therefore, we conclude that such a change in protein structure, which is independent of changes in the AdoCbl structure, and specifically the Co-C bond length, is not a basis of Co-C bond cleavage catalysis. The results suggest that, following the substrate trigger, the protein interacts with the cofactor to contiguously guide the cleavage of the Co-C bond, at every step along the cleavage coordinate, starting from the equilibrium configuration of the ternary complex. The cleavage is thus represented by a diagonal trajectory across a free energy surface, that is defined by chemical (Co-C separation) and protein configuration coordinates.

Morfometría geométrica y filogenia en Rhodniini (Hemiptera, Reduviidae) de Venezuela

La tribu Rhodniini incluye los géneros Rhodnius Stål y Psammolestes Bergroth. Evidencias enzimática y molecular sugieren la monofilia de la tribu. La mayoría de las especies son selváticas encontrándose en palmas y en nidos de aves. Tradicionalmente ambos géneros fueron considerados grupos relacionados; no obstante, estudios moleculares cuestionan la monofilia de Rhodnius. El objetivo fue analizar filogenéticamente la variación morfométrica en la arquitectura alar, como apoyo a la taxonomía y sistemática en Rhodniini. Se fotografiaron 524 alas de cinco representantes de Rhodniini: Psammolestes arthuri (Pinto) (n = 89), Rhodnius pictipes Stål, (n = 21), R. robustus Larrousse (n = 24), R. prolixus Stål, (n = 16) y R. neivai Lent (n = 22). Como grupos externos se estudiaron cuatro representantes de Triatomini: Eratyrus mucronatus Stål (n = 15), Panstrongylus rufotuberculatus (Champion) (n = 45), P. geniculatus (Latreille) (n = 183) y Triatoma maculata (Erichson) (n = 109). Se registraron configuraciones de coordenadas (x, y) y se alinearon mediante Análisis Generalizado de Procrustes. Se efectuaronAnálisis de Covarianza con proporción de grupos re-clasificados y MANOVA. Luego, las variables de la forma alar (intervalos de confianza de las deformaciones relativas) y el tamaño del centroide se analizaron cladísticamente. Los análisis estadísticos de varianza no encontraron diferencias significativas (Kruskal-Wallis) en el tamaño isométrico del ala en las especies P. arthuri – R. neivai – R. pictipes; R. robustus – R. prolixus – T. maculata y entre P. rufotuberculatus – P. geniculatus. La reclasificación a posteriori fue perfecta para E. mucrunatus 100% y R. pictipes, seguidas de T. maculata con 96%, R. neivai 95%, P arthuri 93.2%; R. prolixus 87.5%, P. geniculatus 87.4%, P. rufotuberculatus 84.4%, y R. robustus 76%. Los análisis cladísticos con parsimonia seleccionaron dos árboles de mínima longitud (L = 4.461 IC = 0.973 e IR = 0.979). El consenso estricto muestra la monofilia de Panstrongylus (rufotuberculatus + geniculatus) y Triatoma + Rhodniini (Rhodinus + Psammolestes), pero internamente la parafilia de Rhodnius respecto a Psammolestes. Estos resultados son congruentes con análisis molecu-lares previos en Rhodniini, lo cual revela la información filogenética de caracteres morfométricos como apoyo a los estudios sistemáticos, permitiendo combinar por primera vez en este grupo los análisis de morfometría geométrica y métodos filogenéticos.

Tsunami–tide interaction in 1964 Prince William Sound tsunami

We conduct a comprehensive modeling study of the impact of the 1964 Prince William Sound tsunami on the US Pacific Northwest coast. A 3D unstructured grid model, SELFE, is applied in its 2D spherical coordinate configuration. Simulations are conducted with and without dynamic tides to elucidate their influence. We compare numerical results with tide gauge records, maximum wave heights, runups, and inundation extents at several locations in the region. Detailed inundation patterns at Coos Bay and Cannon Beach, Oregon are compared to field estimates. The model results are shown to be in very good agreement with field observations. The results demonstrate that while negligible at the open coast, the tide–tsunami interaction is solely responsible for inundation around some estuaries and rivers.

On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition

This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in mesh-based discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encountered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schrödinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker–Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, etc. This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations.

Dielectric Permeability of Nanocylinder

In the nanocylinder, a cut-off from the molecular crystal, dielectric permeability tensor is investigated. Excitons in the nanocylinder arise due to the exciting of the electron subsystem of the molecule. In evaluation of dielectric permeability Dzhyaloshinskii–Pitaevskii approach is used, connected with retarded and advanced exciton Green’s functions and correct use of Paulion Green’s function. It turned out that refraction and absorption indices depend on configuration coordinates, having maximal values at boundary cross-sections and minimal value at central cross-section of the nanocylinder broken symmetry structure. Although it was expected that boundary conditions make higher refractive and absorptive characteristics of the nanocylinder, this appeared not to be possible because Paulion Green’s function is not proportional to the exciton concentration.

Singularity-free dynamic equations of vehicle–manipulator systems

In this paper we derive the singularity-free dynamic equations of vehicle–manipulator systems using a minimal representation. These systems are normally modeled using Euler angles, which leads to singularities, or Euler parameters, which is not a minimal representation and thus not suited for Lagrange’s equations. We circumvent these issues by introducing quasi-coordinates which allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of the vehicle in general is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the dynamic properties of vehicle–manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. We also show how to calculate the inertia and Coriolis matrices and present these for several different vehicle–manipulator systems in such a way that this can be implemented for simulation and control purposes without extensive knowledge of the mathematical background. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and should reach a wider audience, including engineers and programmers.

Singularity-Free Dynamic Equations of AUV-Manipulator Systems

In this paper we derive the singularity-free dynamic equations of AUV-manipulator systems using a minimal representation. Autonomous underwater vehicles (AUVs) are normally modeled using the singularity-prone Euler angles, but introducing quasi-coordinates allows us to derive the dynamics using minimal and globally valid non-Euclidean configuration coordinates. This is a great advantage as the configuration space of an AUV is non-Euclidean. We thus obtain a computationally efficient and singularity-free formulation of the dynamic equations with the same complexity as the conventional Lagrangian approach. The closed form formulation makes the proposed approach well suited for system analysis and model-based control. This paper focuses on the kinematic and dynamic properties of AUV-manipulator systems and we present the explicit matrices needed for implementation together with several mathematical relations that can be used to speed up the algorithms. The hydrodynamic and damping forces are also included in the equations. By presenting the explicit equations needed for implementation, the approach presented becomes more accessible and engineers and programmers can implement the results without extensive knowledge of the mathematical background.

A DENSITY FUNCTIONAL STUDY OF SMALL NIOBIUM CLUSTERS

Geometrical structures of Nb n clusters up to n = 7 are calculated at the B3LYP/LanL2DZ level. The average binding energy, along the local magnetic moments, is calculated, together with the HOMO–LUMO gap and the mean bond length. The ground-state structures of niobium clusters favor higher-dimensional configuration and higher coordination number. The average binding energy increases with the number of atoms and the magnetic order into the clusters depends on the cluster size, all the clusters present a HOMO–LUMO gap larger than 1 eV.

Accurate prediction of higher-level electronic structure energies for large databases using neural networks, Hartree–Fock energies, and small subsets of the database

A novel method is presented that significantly reduces the computational bottleneck of executing high-level, electronic structure calculations of the energies and their gradients for a large database that adequately samples the configuration space of importance for systems containing more than four atoms that are undergoing multiple, simultaneous reactions in several energetically open channels. The basis of the method is the high-degree of correlation that generally exists between the Hartree-Fock (HF) and higher-level electronic structure energies. It is shown that if the input vector to a neural network (NN) includes both the configuration coordinates and the HF energies of a small subset of the database, MP4(SDQ) energies with the same basis set can be predicted for the entire database using only the HF and MP4(SDQ) energies for the small subset and the HF energies for the remainder of the database. The predictive error is shown to be less than or equal to the NN fitting error if a NN is fitted to the entire database of higher-level electronic structure energies. The general method is applied to the computation of MP4(SDQ) energies of 68,308 configurations that comprise the database for the simultaneous, unimolecular decomposition of vinyl bromide into six different reaction channels. The predictive accuracy of the method is investigated by employing successively smaller subsets of the database to train the NN to predict the MP4(SDQ) energies of the remaining configurations of the database. The results indicate that for this system, the subset can be as small as 8% of the total number of configurations in the database without loss of accuracy beyond that expected if a NN is employed to fit the higher-level energies for the entire database. The utilization of this procedure is shown to save about 78% of the total computational time required for the execution of the MP4(SDQ) calculations. The sampling error involved with selection of the subset is shown to be about 10% of the predictive error for the higher-level energies. A practical procedure for utilization of the method is outlined. It is suggested that the method will be equally applicable to the prediction of electronic structure energies computed using even higher-level methods than MP4(SDQ).

Mechanism of Defect Reactions in Semiconductors

AbstractProposed mechanisms so far on defect reactions in semiconductors are reexamined. Structural instability of point defects is explained in terms of the Jahn-Teller effect. It is found that the tetrahedral coordinated bonds, which do not have inversion symmetry, are not so rigid as we consider, especially for hole localization. Second topic is the phonon-kick mechanism for defect reactions under carrier injection. In order to discuss this mechanism in detail, we recall the configuration coordinate (c-c) diagram, which is often misunderstood in the literature. The proper relation is explained among the lattice distortion, the position of the electronic level in the band gap (thermal and optical depths), the total energy the multiphonon (e and h) carrier capture processes and the following induced lattice relaxation. A numerical simulation has been performed on phonon kick mechanism. It is found that a rapid increase of the transient lattice vibration around the defect is possible and the probability critically depends on the carrier concentrations and the phonon frequency distribution.

Hard X-ray photon-in photon-out spectroscopy

Spectroscopic techniques to study the electron configuration and local coordination of a central atom by detecting inner-shell radiative decays following photoexcitation using hard X-rays are presented. The experimental setup requires an X-ray spectrometer based on perfect crystal Bragg optics. The possibilities arising from non-resonant and resonant X-ray emission spectroscopy are discussed when the instrumental energy broadenings of the primary (beamline) monochromator and the crystal spectrometer for X-ray emission detection are on the order of the core hole lifetimes of the intermediate and final electronic states. The small energy bandwidth in the emission detection yields line-sharpened absorption features. In transition metal compounds, electron–electron interactions as well as orbital splittings and fractional population can be revealed. Combination with EXAFS spectroscopy enables to extend the k-range beyond unwanted absorption edges in dilute samples that limit the EXAFS range in conventional absorption spectroscopy.

Singularity-Free Dynamic Equations of Open-Chain Mechanisms With General Holonomic and Nonholonomic Joints

Standard methods to model multibody systems are aimed at systems with configuration spaces isomorphic to Ropfn. This limitation leads to singularities and other artifacts in case the configuration space has a different topology, for example, in the case of ball joints or a free-floating mechanism. This paper discusses an extension of classical methods that allows for a more general class of joints, including all joints with a Lie group structure as well as nonholonomic joints. The model equations are derived using the Boltzmann-Hamel equations and have very similar structure and complexity as obtained using classical methods. However, singularities are avoided through the use of global non-Euclidean configuration coordinates, together with mappings describing a local Euclidean structure around each configuration. The resulting equations are explicit (unconstrained) differential equations, both for holonomic and nonholonomic joints, which do not require a coordinate atlas and can be directly implemented in simulation software.

Luminescent Lanthanide Complexes with 1,2-Bis(ethylsulfinyl)ethane: Structural Dependences on Reacting Solvent, Ratio, and Co-Ligand

The present paper reports our sequential efforts to investigate the structures and properties of flexible disulfoxide–lanthanide complexes. Combining our reported results, on the basis of changing synthesis conditions and using a co-ligand, six new complexes, [Ln(meso-L)4](ClO4)3(H2O) n (n = 0.5, Ln = Eu (1), Gd (2); n = 0, Ln = Tb (3)) and [Ln(meso-L)2(phen)2](ClO4)3(CHCl3)2 (Ln = Eu (4), Gd (5), and Tb (6)) (herein, L = 1,2-bis(ethylsulfinyl)ethane, phen = 1,10-phenanthroline) were synthesized, and their structures were characterized by IR spectroscopy, elemental analysis, and X-ray single-crystal diffraction. The dependence of the formation of 1–3 on the solvents used and reaction ratios in the preparation was confirmed. Complexes 1–3 are isomorphous ionic complexes, and the coordination cation is chiral and has a mononuclear structure, in which the LnIII atom is eight-coordinated by four L ligands. Complexes 4–6 are also isomorphous mononuclear ionic complexes, and in each complex cation, the central LnIII atom is eight-coordinated by two L ligands and two phen molecules. In 1–6, all the L ligands exhibit the meso configuration and bis-monodentate chelating coordination mode. Further, the absorption and luminescent spectra of L, phen and complexes 4–6 in solution were investigated at room temperature. The absorption spectra show that only a very slight shift of the absorption band occurred for the ligands L and phen when coordinating to metal ions, being consistent with their origin. The photoluminescence of 4 and 6 exhibits the usual metal-centred emission spectra arising from ligand-to-metal energy transfer and the emission of π → π* transitions from the phen ligand; the latter is also seen in the emission spectrum of 5.

Adiabatic decoupling of the reaction coordinate

AbstractWhen the dynamics is constrained by adiabatic invariance, a reactive process can be described as a one‐dimensional motion along the reaction coordinate in an effective potential. This simplification is often valid for central potentials and for the curved harmonic valley studied in the reaction path Hamiltonian model. For an ion–molecule reaction, the action integral 〈Pθ〉 = (1/2π)∮Pθ dθ is an adiabatic invariant. The Poisson bracket of 〈Pθ〉2 with Hamiltonians corresponding to a great variety of long‐range electrostatic interactions is found to decrease with the separation coordinate r, faster than the corresponding potential. This indicates that the validity of the adiabatic approximation is not directly related to the shape of the potential energy surface. The leading role played by the translational momentum is accounted for by Jacobi's form of the least action principle. However, although the identification of adiabatic regions by this procedure is limited to a specific range of coordinate configurations, equivalent constraints must persist all along the reaction coordinate and must operate during the entire reaction, as a result of entropy conservation. The study of the translational kinetic energy released on the fragments is particularly appropriate to detect restrictions on energy exchange between the reaction coordinate and the bath of internal degrees of freedom. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008

On the reduction of stochastic kinetic theory models of complex fluids

Kinetic theory models involving the Fokker–Planck equation are usually solved in the framework of stochastic approaches, which allows us to circumvent the difficulties related to the multidimensional character of that equation. In fact, the Fokker–Planck equation governs the evolution of the distribution function that defines the molecular configuration at each point of the physical space and at each time. As the molecular conformation is usually defined by several coordinates, the resulting distribution function will depend on the physical and configuration coordinates and the time. Although different numerical strategies have recently been proposed for solving that equation with efficiency and accuracy (Ammar et al 2006 J. Non-Newtonian Fluid Mech. 134 136–47, Ammar et al 2006 J. Non-Newtonian Fluid Mech. 139 153–76) the stochastic approach is today the most common for solving general kinetic theory models. This paper presents some preliminary results that provide evidence for the potential applicability of model reduction techniques based on the Karhunen–Loève decomposition or on separated representations for reducing the computational efforts related to the solution of such models in the Brownian configuration fields framework.

Theoretical study of electronic structures and magnetic properties in iron clusters ( n ⩽ 8)

Geometrical structures of the Fe n clusters up to n = 8 are calculated at the BPW91/LanL2DZ level. The bond length, average binding energy, along with the magnetic moment per atom are calculated, together with vibrational frequency. The ground-state structures of iron clusters favor higher-dimensional configuration and higher coordination number. The average binding energy decreases monotonically with the increase of n, and closer to experimental values than other theoretical results. The magnetic moment per atom shows small oscillatory behavior with cluster size but remains in the vicinity of 3.0 μ B/atom over this size range.