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Rotational Symmetry (rotational + symmetry)
Selected AbstractsImproved Plasma Spray Torch Stability Through Multi-Electrode DesignCONTRIBUTIONS TO PLASMA PHYSICS, Issue 7 2007J. Schein Abstract Coating production by thermal plasma spray is dependent on the residence time of particles in the plasma jet produced by the gas flow inside a plasma torch. To ensure a high fraction of well-molten particles to be accelerated towards the substrate a long reproducible residence time is needed. This can be achieved by a long plasma jet with little or no temporal variation in length and temperature. While single electrode plasma torches need an unstable attachment of the anodic arc root in order to avoid excess erosion, which also causes an unstable plasma jet, multi-electrode torches allow operation with fixed anode attachments by subdividing the anode current by the number of electrodes used, and thereby thus reducing the power input for each separated arc root. Once the steady anode attachment has been obtained the produced plasma jet exhibits a steady characteristic, but also looses rotational symmetry. The separation can be achieved by using either multi anode or multi cathode geometry with appropriate electrical control. Both version have been produced with 3 electrodes each resulting in two systems known as the Delta Gun (3 anodes) and Triplex (3 cathodes). (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Dependence of s -waves on continuous dimension: The quantum oscillator and free systemsFORTSCHRITTE DER PHYSIK/PROGRESS OF PHYSICS, Issue 12 2006K.B. Wolf Abstract Wavefunctions with rotational symmetry (i.e., zero angular momentum) in D dimensions, are called s -waves. In quantum quadratic systems (free particle, harmonic and repulsive oscillators), their radial parts obey Schrödinger equations with a fictitious centrifugal (for integer D , 4) or centripetal (for D = 2) potential. These Hamiltonians close into the three-dimensional Lorentz algebra so(2,1), whose exceptional interval corresponds to the critical range of continuous dimensions 0 < D < 4, where they exhibit a one-parameter family of self-adjoint extensions in ,2(,+). We study the characterization of these extensions in the harmonic oscillator through their spectra which , except for the Friedrichs extension , are not equally spaced, and we build their time evolution Green function. The oscillator is then contracted to the free particle in continuous- D dimensions, where the extension structure is mantained in the limit of continuous spectra. Finally, we compute the free time evolution of the expectation values of the Hamiltonian, dilatation generator, and square radius between three distinct sets of ,heat'-diffused localized eigenstates. This provides a simple group-theoretic description of the purported contraction/expansion of Gaussian-ring s -waves in D > 0 dimensions. [source] Out-of-plane geometrical spreading in anisotropic mediaGEOPHYSICAL PROSPECTING, Issue 4 2002Norman Ettrich Two-dimensional seismic processing is successful in media with little structural and velocity variation in the direction perpendicular to the plane defined by the acquisition direction and the vertical axis. If the subsurface is anisotropic, an additional limitation is that this plane is a plane of symmetry. Kinematic ray propagation can be considered as a two-dimensional process in this type of medium. However, two-dimensional processing in a true-amplitude sense requires out-of-plane amplitude corrections in addition to compensation for in-plane amplitude variation. We provide formulae for the out-of-plane geometrical spreading for P- and S-waves in transversely isotropic and orthorhombic media. These are extensions of well-known isotropic formulae. For isotropic and transversely isotropic media, the ray propagation is independent of the azimuthal angle. The azimuthal direction is defined with respect to a possibly tilted axis of symmetry. The out-of-plane spreading correction can then be calculated by integrating quantities which describe in-plane kinematics along in-plane rays. If, in addition, the medium varies only along the vertical direction and has a vertical axis of symmetry, no ray tracing need be carried out. All quantities affecting the out-of-plane geometrical spreading can be derived from traveltime information available at the observation surface. Orthorhombic media possess no rotational symmetry and the out-of-plane geometrical spreading includes parameters which, even in principle, are not invertible from in-plane experiments. The exact and approximate formulae derived for P- and S-waves are nevertheless useful for modelling purposes. [source] Axial symmetric elasticity analysis in non-homogeneous bodies under gravitational load by triple-reciprocity boundary element methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 7 2009Yoshihiro Ochiai Abstract In general, internal cells are required to solve elasticity problems by involving a gravitational load in non-homogeneous bodies with variable mass density when using a conventional boundary element method (BEM). Then, the effect of mesh reduction is not achieved and one of the main merits of the BEM, which is the simplicity of data preparation, is lost. In this study, it is shown that the domain cells can be avoided by using the triple-reciprocity BEM formulation, where the density of domain integral is expressed in terms of other fields that are represented by boundary densities and/or source densities at isolated interior points. Utilizing the rotational symmetry, the triple-reciprocity BEM formulation is developed for axially symmetric elasticity problems in non-homogeneous bodies under gravitational force. A new computer program was developed and applied to solve several test problems. Copyright © 2008 John Wiley & Sons, Ltd. [source] Modelling of diffraction from fibre texture gradients in thin polycrystalline filmsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2007M. Birkholz Crystallographic textures in thin polycrystalline films typically exhibit a rotational symmetry, i.e. they occur as a fibre texture with the texture pole being orientated in the direction of the substrate normal. As a further characteristic of thin-film textures, it was often observed that the degree of preferred orientation increases with increasing thickness. It is shown in this work how a fibre texture gradient may be modelled in kinematical X-ray diffraction and which effects it has on the intensity mapping of the IHKL reflection, when the HKL pole is the fibre axis. A general expression for IHKL is derived for a depth-dependent fibre texture that is based on the finite Laplace transform of the texture distribution. The concept is outlined for the cosn, function to model the tilt-angle dependence of intensity, with the parameter n denoting the degree of texture. It is found that the measured intensity distribution sensitively depends on the ratio of texture gradient over X-ray attenuation coefficient. For particular cases, it is found that the maximum intensity may occur for non-zero tilt angles and thus arise at a different tilt angle from the pole of the fibre texture. [source] Evaluation of equatorial orientation distributionsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 6 2006W. Ruland Two conflicting methods reported in the literature [Kratky (1933). Kolloid Z.64, 213,222; Leadbetter & Norris (1979). Mol. Phys.38, 669,686] for the relationship between axial orientation distributions and equatorial intensity profiles are analyzed. Both methods are in common use by their respective proponents for the evaluation of scattering patterns with preferred orientation under rotational symmetry. The correctness of these methods is assessed, and the consequences of the findings are discussed. [source] Spin densities in two-component relativistic density functional calculations: Noncollinear versus collinear approachJOURNAL OF COMPUTATIONAL CHEMISTRY, Issue 8 2002Christoph Van WüllenArticle first published online: 3 APR 200 Abstract With present day exchange-correlation functionals, accurate results in nonrelativistic open shell density functional calculations can only be obtained if one uses functionals that do not only depend on the electron density but also on the spin density. We consider the common case where such functionals are applied in relativistic density functional calculations. In scalar-relativistic calculations, the spin density can be defined conventionally, but if spin-orbit coupling is taken into account, spin is no longer a good quantum number and it is not clear what the "spin density" is. In many applications, a fixed quantization axis is used to define the spin density ("collinear approach"), but one can also use the length of the local spin magnetization vector without any reference to an external axis ("noncollinear approach"). These two possibilities are compared in this work both by formal analysis and numerical experiments. It is shown that the (nonrelativistic) exchange-correlation functional should be invariant with respect to rotations in spin space, and this only holds for the noncollinear approach. Total energies of open shell species are higher in the collinear approach because less exchange energy is assigned to a given Kohn-Sham reference function. More importantly, the collinear approach breaks rotational symmetry, that is, in molecular calculations one may find different energies for different orientations of the molecule. Data for the first ionization potentials of Tl, Pb, element 113, and element 114, and for the orientation dependence of the total energy of I and PbF indicate that the error introduced by the collinear approximation is ,0.1 eV for valence ionization potentials, but can be much larger if highly ionized open shell states are considered. Rotational invariance is broken by the same amount. This clearly indicates that the collinear approach should not be used, as the full treatment is easily implemented and does not introduce much more computational effort. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 779,785, 2002 [source] A method for quantifying rotational symmetryNEW PHYTOLOGIST, Issue 4 2007Frank M. Frey Summary ,,Here, a new approach for quantifying rotational symmetry based on vector analysis was described and compared with information obtained from a geometric morphometric analysis and a technique based on distance alone. ,,A new method was developed that generates a polygon from the length and angle data of a structure and then quantifies the minimum change necessary to convert that polygon into a regular polygon. This technique yielded an asymmetry score (s) that can range from 0 (perfect symmetry) to 1 (complete asymmetry). Using digital images of Geranium robertianum flowers, this new method was compared with a technique based on lengths alone and with established geometric morphometric methods used to quantify shape variation. ,,Asymmetry scores (s) more clearly described variation in symmetry and were more consistent with a visual assessment of the images than either comparative technique. ,,This procedure is the first to quantify the asymmetry of radial structures accurately, uses easily obtainable measures to calculate the asymmetry score and allows comparisons among individuals and species, even when the comparisons involve structures with different patterns of symmetry. This technique enables the rigorous analysis of polysymmetric structures and provides a foundation for a better understanding of symmetry in nature. [source] Single-wall carbon nanotubes: spintronics in the Luttinger liquid phasePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 11-12 2009Balázs Dóra Abstract We study the electron spin resonance (ESR) intensity in the Luttinger liquid phase of carbon nanotubes. The ESR measurables such as the signal intensity and the line-width are calculated in the framework of Luttinger liquid theory with broken spin rotational symmetry as a function of magnetic field and temperature. The linewidth is broadened significantly at high temperatures, and the intensity is well describes by Lorentzians. At very low temperatures, however, the ESR lineshape becomes asymmetric around the resonance, and is characterized by threshold behavior. These observables are of special importance for the spintronics applications of carbon nanotubes. [source] RDC-assisted modeling of symmetric protein homo-oligomersPROTEIN SCIENCE, Issue 5 2008Xu Wang Abstract Protein oligomerization serves an important function in biological processes, yet solving structures of protein oligomers has always been a challenge. For solution NMR, the challenge arises both from the increased size of these systems and, in the case of homo-oligomers, from ambiguities in assignment of intra- as opposed to intersubunit NOEs. In this study, we present a residual dipolar coupling (RDC)-assisted method for constructing models of homo-oligomers with purely rotational symmetry. Utilizing the fact that one of the principal axes of the tensor describing the alignment needed for RDC measurement is always parallel to the oligomer symmetry axis, it is possible to greatly restrict possible models for the oligomer. Here, it is shown that, if the monomer structure is known, all allowed dimer models can be constructed using a grid search algorithm and evaluated based on RDC simulations and the quality of the interface between the subunits. Using the Bacillus subtilis protein YkuJ as an example, it is shown that the evaluation criteria based on just two sets of NH RDCs are very selective and can unambiguously produce a model in good agreement with an existing X-ray structure of YkuJ. [source] Ring conformations and intermolecular interactions in two fused dibenzoazocinesACTA CRYSTALLOGRAPHICA SECTION C, Issue 6 2010Andrés F. Yepes 5-Acetyl-2-chloro-8,11-dimethyl-5,6,11,12-tetrahydrodibenzo[b,f]azocine, C19H20ClNO, (I), crystallizes as a single fully ordered isomer, but 14-acetyl-8,11-dimethyl-7,8,13,14-tetrahydrobenzo[f]naphtho[1,2- b]azocine,14-acetyl-8,9-dimethyl-7,8,13,14-tetrahydrobenzo[f]naphtho[1,2- b]azocine (74/26), C23H23NO, (II), exhibits threefold whole-molecule disorder involving both configurational and structural isomers. In (I) and in the predominant form of (II), the azocine rings adopt very similar conformations, forming boat-shaped rings having approximate twofold rotational symmetry. There are no direction-specific intermolecular interactions in the crystal structure of (I), but the molecules of (II) are weakly linked into chains by an aromatic ,,, stacking interaction. The compounds were made under green conditions using an acid-catalysed cyclization process having very high atom utilization. [source] Di-,-oxido-bis{bis[N,N,-bis(2-pyridylmethyl)ethane-1,2-diamine]manganese(III,IV)} tris(perchlorate) hexahydrate: clarification of an order,disorder phase transitionACTA CRYSTALLOGRAPHICA SECTION C, Issue 11 2009Anne Nielsen The title compound, [Mn2O2(C14H18N4)2](ClO4)3·6H2O, contains a mixed-valent MnIII/MnIV complex. In accordance with a previous report [Collins, Hodgson, Michelsen & Towle (1987). J. Chem. Soc. Chem. Commun. pp. 1659,1660], the structure at 295,K is best described in the space group C2/c, with the complex exhibiting twofold rotational symmetry, and with half site occupancy for one perchlorate anion and several solvent water molecules. At 180,K, the structure is ordered in the subgroup P21/n and is clearly shown to be a hexahydrate, rather than the previously reported trihydrate. The origin of the order,disorder phase transition lies in the thermal motion of the perchlorate anions. [source] Bis(1,3,4-trimethylpyridinium) tetrachloridocuprate(II) and bis(1,3,4-trimethylpyridinium) tetrabromidocuprate(II): an examination of the A2CuX4Fdd2 structure typeACTA CRYSTALLOGRAPHICA SECTION C, Issue 8 2009Marcus R. Bond The title bis(1,3,4-trimethylpyridinium) tetrahalidocuprate(II) structures, (C8H12N)2[CuCl4], (I), and (C8H12N)2[CuBr4], (II), respectively, consist of flattened [CuX4]2, tetrahedral complex anions and planar 1,3,4-trimethylpyridinium cations. Chloride compound (I) is a rare example of an A2CuCl4 structure with an elongated unit cell in the polar space group Fdd2. The [CuCl4]2, anions have twofold rotational symmetry and are arranged in distorted hexagonal close-packed (hcp) layers, which are interleaved with layers of cations, each in a four-layer repeat sequence, to generate the elongated axis. The organic cations stack along [101] or [10] in alternating layers. The methyl groups meta on the cation ring and the larger of the trans Cl,Cu,Cl angles both face the same direction along the polar axis and are the most prominent features determining the polarity of the structure. Bromide compound (II) crystallizes in a centrosymmetric structure with a similar layer structure but with only a two-layer repeat sequence. Here, symmetry-inequivalent cations are segregated into alternating layers with cations, forming hcp layers of inversion-related cation pairs in one layer and parallel stacks of cations in the other. The change in space group when the larger Br, ion is present suggests that the 1,3,4-trimethylpyridinium ion has a minimal size to allow the Fdd2 A2CuX4 structure type. [source] Detection and correction of underassigned rotational symmetry prior to structure depositionACTA CRYSTALLOGRAPHICA SECTION D, Issue 5 2010Billy K. Poon Up to 2% of X-ray structures in the Protein Data Bank (PDB) potentially fit into a higher symmetry space group. Redundant protein chains in these structures can be made compatible with exact crystallographic symmetry with minimal atomic movements that are smaller than the expected range of coordinate uncertainty. The incidence of problem cases is somewhat difficult to define precisely, as there is no clear line between underassigned symmetry, in which the subunit differences are unsupported by the data, and pseudosymmetry, in which the subunit differences rest on small but significant intensity differences in the diffraction pattern. To help catch symmetry-assignment problems in the future, it is useful to add a validation step that operates on the refined coordinates just prior to structure deposition. If redundant symmetry-related chains can be removed at this stage, the resulting model (in a higher symmetry space group) can readily serve as an isomorphous replacement starting point for re-refinement using re-indexed and re-integrated raw data. These ideas are implemented in new software tools available at http://cci.lbl.gov/labelit. [source] | |||||||||||||