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Spherical Symmetry (spherical + symmetry)
Selected AbstractsMagnetic susceptibility: Further insights into macroscopic and microscopic fields and the sphere of LorentzCONCEPTS IN MAGNETIC RESONANCE, Issue 1 2003C.J. Durrant Abstract To make certain quantitative interpretations of spectra from NMR experiments carried out on heterogeneous samples, such as cells and tissues, we must be able to estimate the magnetic and electric fields experienced by the resonant nuclei of atoms in the sample. Here, we analyze the relationships between these fields and the fields obtained by solving the Maxwell equations that describe the bulk properties of the materials present. This analysis separates the contribution to these fields of the molecule in which the atom in question is bonded, the "host" fields, from the contribution of all the other molecules in the system, the "external" fields. We discuss the circumstances under which the latter can be found by determining the macroscopic fields in the sample and then removing the averaged contribution of the host molecule. We demonstrate that the results produced by the, so-called, "sphere of Lorentz" construction are of general validity in both static and time-varying cases. This analytic construct, however, is not "mystical" and its justification rests not on any sphericity in the system but on the local uniformity and isotropy, i.e., spherical symmetry, of the medium when averaged over random microscopic configurations. This local averaging is precisely that which defines the equations that describe the macroscopic fields. Hence, the external microscopic fields, in a suitably averaged sense, can be estimated from the macroscopic fields. We then discuss the calculation of the external fields and that of the resonant nucleus in NMR experiments. © 2003 Wiley Periodicals, Inc. Concepts Magn Reson Part A 18A: 72,95, 2003 [source] A numerical scheme for strong blast wave driven by explosionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006Kaori Kato Abstract After the detonation of a solid high explosive, the material has extremely high pressure keeping the solid density and expands rapidly driving strong shock wave. In order to simulate this blast wave, a stable and accurate numerical scheme is required due to large density and pressure changes in time and space. The compressible fluid equations are solved by a fractional step procedure which consists of the advection phase and non-advection phase. The former employs the Rational function CIP scheme in order to preserve monotone signals, and the latter is solved by interpolated differential operator scheme for achieving the accurate calculation. The procedure is categorized into the fractionally stepped semi-Lagrangian. The accuracy of our scheme is confirmed by checking the one-dimensional plane shock tube problem with 103 times initial density and pressure jump in comparison with the analytic solution. The Sedov,Taylor blast wave problem is also examined in the two-dimensional cylindrical coordinate in order to check the spherical symmetry and the convergence rates. Two- and three-dimensional simulations for the blast waves from the explosion in the underground magazine are carried out. It is found that the numerical results show quantitatively good agreement with the experimental data. Copyright © 2006 John Wiley & Sons, Ltd. [source] Synthesis and crystallization behavior of acetal copolymer/silica nanocomposite by in situ cationic ring-opening copolymerization of trioxane and 1,3-dioxolaneJOURNAL OF APPLIED POLYMER SCIENCE, Issue 3 2008Lanhui Sun Abstract The acetal copolymer/silica nanocomposite was prepared by in situ bulk cationic copolymerization of trioxane and 1,3-dioxolane in the presence of nanosilica. The crystallization behavior of acetal copolymer/silica nanocomposite was studied by AFM, DSC, XRD, and CPOM, and the macromolecular structure of acetal copolymer/silica nanocomposite was characterized by FTIR and 1H-NMR. The 1H-NMR results showed that the macromolecular chain of acetal copolymer had more than two consecutive 1,3-dioxolane units in an oxymethylene main chain, while that of acetal copolymer/silica nanocomposite had only one 1,3-dioxolane unit in an oxymethylene main chain. There existed interaction between the macromolecular chains and nanoparticles (such as hydrogen bonds and coordination). On one hand, nanoparticles acted as nucleation center, which accelerated the crystallization rate but reduced the crystallinity. The spherulite sizes also decreased with addition of nanoparticles attributed to the nucleation effect. On the other hand, the presence of nanoparticles interrupted the spherical symmetry of the crystallite. In conclusion, the high surface energy and small scale of nanoparticles have a prominent impact on the polymerization mechanism and crystallization behavior of nanocomposite. © 2007 Wiley Periodicals, Inc. J Appl Polym Sci, 2008 [source] Hiding cusps in cores: kinematics of disc galaxies in triaxial dark matter haloesMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 3 2006Eric Hayashi ABSTRACT We study the kinematics of gaseous discs in triaxial dark matter haloes using the closed-loop orbit solutions in non-axisymmetric potentials. The orbits are in general non-circular and, for a given triaxiality, their ellipticity depends on the ratio of escape to circular velocities, V2esc/V2c. This ratio increases steeply towards the centre for cold dark matter (CDM) halo density profiles, implying that even minor deviations from spherical symmetry may induce large deviations from circular orbits in the velocity field of a gaseous disc, especially near the centre. This result suggests that caution should be exercised when interpreting constraints on the presence of density cusps in the dark halo derived from the innermost velocity profile. Simulated long-slit rotation curves vary greatly in shape, depending primarily on the viewing angle of the disc and on its orientation relative to the principal axes of the potential. ,Solid-body' rotation curves , typically interpreted as a signature of a constant density core in the dark matter distribution , are often obtained when the slit samples velocities near the major axis of the closed-loop orbits. Triaxial potentials imprint specific symmetries in 2D velocity fields, generally inducing ,twists' in the isovelocity contours and antisymmetric patterns in opposite quadrants. We suggest that triaxial haloes may be responsible for the variety of shapes of long-slit rotation curves of low surface brightness (LSB) galaxies, as well as for the complex central kinematics of LSBs, which are sometimes ascribed to the presence of ,radial motions' in the gas. We argue that LSB rotation curves might be reconciled with the structure of CDM haloes once the effects of halo triaxiality on the dynamics of gaseous discs are properly taken into account. [source] An improved model for contraction of dark matter haloes in response to condensation of baryonsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 4 2006Marios Kampakoglou ABSTRACT The cooling of gas in the centres of dark matter haloes is expected to lead to a more concentrated dark matter distribution. The response of dark matter to the condensation of baryons is usually calculated using the model of adiabatic contraction, which assumes spherical symmetry and circular orbits. Following Gnedin et al., we improve this model by modifying the assumed invariant from M(r)r to , where r and are the current and orbit-averaged particle positions. We explore the effect of the bulge in the inner regions of the halo for different values of the bulge-to-disc mass ratio. We find that the bulge makes the velocity curve rise faster in the inner regions of the halo. We present an analytical fitting curve that describes the velocity curve of the halo after dissipation. The results should be useful for dark matter detection studies. [source] The origin and formation of cuspy density profiles through violent relaxation of stellar systemsMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2000S. Hozumi It is shown that the cuspy density distributions observed in the cores of elliptical galaxies can be realized by dissipationless gravitational collapse. The initial models consist of power-law density spheres such as ,,r,1 with anisotropic velocity dispersions. Collapse simulations are carried out by integrating the collisionless Boltzmann equation directly, on the assumption of spherical symmetry. From the results obtained, the extent of constant density cores, formed through violent relaxation, decreases as the velocity anisotropy increases radially, and practically disappears for extremely radially anisotropic models. As a result, the relaxed density distributions become more cuspy with increasing radial velocity anisotropy. It is thus concluded that the velocity anisotropy could be a key ingredient for the formation of density cusps in a dissipationless collapse picture. The velocity dispersions increase with radius in the cores according to the nearly power-law density distributions. The power-law index, n, of the density profiles, defined as ,,r,n, changes from n,2.1 at intermediate radii to a shallower power than n,2.1 toward the centre. This density bend can be explained from our postulated local phase-space constraint that the phase-space density accessible to the relaxed state is determined at each radius by the maximum phase-space density of the initial state. [source] Change in the magnetic properties of [FeII(phen)3](PF6)2 in the solid state by combining grinding and annealingPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 4 2004T. Ohshita Abstract By grinding crystalline [FeII(phen)3](PF6)2, the effective magnetic moment, or ,MT, increased with simultaneous amorphization. Subsequent annealing further increased ,MT, despite the restoration of the crystallinity. This was explained by the recovery of the counterion, PF6,, from its strained state in the intact crystal to a less strained state towards higher spherical symmetry. The effects of annealing preceded by grinding suggest a novel method to control the magnetic states of coordination compounds without regard to their crystalline states. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Use of GPS/MET refraction angles in three-dimensional variational analysisTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 570 2000X. Zou Abstract The Spectral Statistical Interpolation (SSI) analysis system of the National Centers for Environmental Prediction (NCEP) is modified to include GPS/MET data (meteorological data from the Global Positioning Satellite system) using a GPS ray-tracing operator. The new system is tested by incorporating 30 actual GPS/MET observations of refraction angles obtained during the GPS/MET experiment. This is the first time that real radio occupation refraction angles and refractivities have been incorporated into a three-dimensional variational analysis system. We examine the magnitude and the vertical distribution of the analysis adjustments that result from using refraction-angle observations in the NCEP SSI analysis system. The average magnitudes of the adjustments in the temperature and specific-humidity fields are approximately 0.4 degC and 0.6 g kg,1, respectively. Individual changes can be as large as 4 degC and 4g kg,1, respectively. The greatest adjustments to the temperature occur in the middle and upper troposphere and stratosphere, while the major changes in specific humidity occur in the lower troposphere. An assessment of the impact of the GPS/MET observations on the analysis, verified by conventional (mostly radiosonde) data, is difficult because of the small number of GPS/MET data used. Nevertheless, it is found that, even over data-rich regions (regions containing many radiosonde observations), and even when the verification data were the radiosonde data themselves, the use of GPS/MET refraction angles makes a slight improvement, overall, to the analysed temperatures and winds. The impact on the water-vapour analyses, again as measured against radiosonde data, is mixed, with improvements shown in some layers and degradation in others. Compared with the background field, the use of refraction angles from one occultation results in an analysis whose simulated refraction angles are much closer to the withheld GPS/MET refraction angles at the two nearby occultation locations, and whose temperature and moisture profiles are also closer to those resulting from the direct assimilation of the two withheld occultations. Although the forward model used in this study, with the ray tracing being carried out in a two-dimensional plane, is much cheaper than a more accurate three-dimensional forward model, it is still quite expensive. In order to further reduce the computational requirement for the assimilation of GPS/MET data, we test a scheme in which the GPS/MET-retrieved refractivities (instead of refraction angles) are used above a selected height for each occupation. These heights are determined objectively based on the departures from spherical symmetry of the model field. It is shown that the mixed use of GPS/MET refraction angles and refractivities produces an analysis result similar to the one using refraction angles alone, while the computational cost is reduced by more than 30%. [source] Electronic structure and transport properties of quantum dotsANNALEN DER PHYSIK, Issue 5 2004M. Tews Abstract The subject of this paper are electronic properties of isolated quantum dots as well as transport properties of quantum dots coupled to two electronic reservoirs. Thereby special focus is put on the effects of Coulomb interaction and possible correlations in the quantum dot states. First, the regime of sequential tunneling to the reservoirs is investigated. It is shown that in case degenerate states participate in transport, the resonance positions in the differential conductance generally depend on temperature and the degree of degeneracy. This effect can be used to directly probe degeneracies in a quantum dot spectrum. A further effect, characteristic for sequential tunneling events, is the complete blocking of individual channels for transport. A generalisation of the well known spin blockade is found for correlated dot states transitions through which are not directly spin-forbidden. In the second part, the electronic structure of spherical quantum dots is calculated. In order to account for correlation effects, the few-particle Schrödinger equation is solved by an exact diagonalization procedure. The calculated electronic structure compares to experimental findings obtained on colloidal semiconductor nanocrystals by Scanning Tunneling Spectroscopy. It is found that the electric field induced by the tunneling tip is gives rise to a Stark effect which can break the spherical symmetry of the electronic ground state density which is in agreement with wave-function mapping experiments. The symmetry breaking depends on the competition between exchange energy and the Stark energy. Moreover, a systematic dependence on particle number is found for the excitation energies of optical transitions which explains recent experimental findings on self-organized quantum dots. In the last part, co-tunneling in the Coulomb blockade regime is studied. For this end the tunneling current is calculated up to the forth order perturbation theory in the tunnel coupling by a real-time Green's function approach for the non-equilibrium case. The differential conductance calculated for a quantum dot containing up to two interacting electrons shows complex signatures of the excitation spectrum which are explained by a combination of co-tunneling and sequential tunneling processes. Thereby the calculations show a peak structure within the Coulomb blockade regime which has also been observed in experiment. [source] | ||||||||||