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Selected AbstractsModelling of small-angle X-ray scattering data using Hermite polynomialsJOURNAL OF APPLIED CRYSTALLOGRAPHY, Issue 4 2001A. K. Swain A new algorithm, called the term-selection algorithm (TSA), is derived to treat small-angle X-ray scattering (SAXS) data by fitting models to the scattering intensity using weighted Hermite polynomials. This algorithm exploits the orthogonal property of the Hermite polynomials and introduces an error-reduction ratio test to select the correct model terms or to determine which polynomials are to be included in the model and to estimate the associated unknown coefficients. With no a priori information about particle sizes, it is possible to evaluate the real-space distribution function as well as three- and one-dimensional correlation functions directly from the models fitted to raw experimental data. The success of this algorithm depends on the choice of a scale factor and the accuracy of orthogonality of the Hermite polynomials over a finite range of SAXS data. An algorithm to select a weighted orthogonal term is therefore derived to overcome the disadvantages of the TSA. This algorithm combines the properties and advantages of both weighted and orthogonal least-squares algorithms and is numerically more robust for the estimation of the parameters of the Hermite polynomial models. The weighting feature of the algorithm provides an additional degree of freedom to control the effects of noise and the orthogonal feature enables the reorthogonalization of the Hermite polynomials with respect to the weighting matrix. This considerably reduces the error in orthogonality of the Hermite polynomials. The performance of the algorithm has been demonstrated considering both simulated data and experimental data from SAXS measurements of dewaxed cotton fibre at different temperatures. [source] MOND plus classical neutrinos are not enough for cluster lensingMONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008Priyamvada Natarajan ABSTRACT Clusters of galaxies offer a robust test bed for probing the nature of dark matter that is insensitive to the assumption of the gravity theories. Both Modified Newtonian Dynamics (MOND) and General Relativity (GR) would require similar amounts of non-baryonic matter in clusters as MOND boosts the gravity only mildly on cluster scales. Gravitational lensing allows us to estimate the enclosed mass in clusters on small (,20,50 kpc) and large (,several 100 kpc) scales independent of the assumptions of equilibrium. Here, we show for the first time that a combination of strong and weak gravitational lensing effects can set interesting limits on the phase-space density of dark matter in the centres of clusters. The phase-space densities derived from lensing observations are inconsistent with neutrino masses ranging from 2,7 eV, and hence do not support the 2 eV-range particles required by MOND. To survive, the most plausible modification for MOND may be an additional degree of dynamical freedom in a covariant incarnation. [source] Semiconducting half-Heusler and LiGaGe structure type compoundsPHYSICA STATUS SOLIDI (A) APPLICATIONS AND MATERIALS SCIENCE, Issue 5 2009Frederick Casper Abstract Compounds with LiAlSi (half-Heusler) and LiGaGe structure types have been investigated by means of band structure calculations. The LiAlSi structure type is known as the half-Heusler structure type, whereas LiGaGe is a closely related hexagonal variant. A remarkable feature of some XYZ half-Heusler compounds with 8 and 18 valence electrons is, that despite being composed of only metallic elements, they are semiconductors. More than 100 semiconducting compounds within these structure types are known. LiGaGe compounds have an additional degree of freedom, namely the degree of puckering of the layers. These compounds can become semiconducting at a certain degree of puckering. Half-metallic behavior is rarely found in this structure type. (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Prevention of Stick-Slip Vibrations by Passive Normal Force ControlPROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2003Martin Rudolph The classical stick-slip oscillator is extended by an additional degree of freedom which couples the slipping motion to the normal force. Using this, the effective friction force can be altered without changing the friction-velocity characteristic. The paper deals with the optimization problem of finding parameters of the additional system that prevent stick-slip motion or minimize the amplitude of the residual limit cycle. Another goal is to increase the decay rate of vibration. Results were achieved by numerical integration based on analytical investigations. [source] Characterization of the pressure-induced second-order phase transition in the mixed-valence vanadate BaV6O11ACTA CRYSTALLOGRAPHICA SECTION B, Issue 3 2009Karen Friese The pressure dependence of the structure of the mixed-valence vanadate BaV6O11 was studied with single-crystal X-ray diffraction in a diamond,anvil cell. The compressibility data could be fitted with a Murnaghan equation of state with the zero-pressure bulk modulus B0 = 161,(7),GPa and the unit-cell volume at ambient pressure = 387.1,(3),Ĺ (B, = 4.00). A phase transition involving a symmetry reduction from P63/mmc to P63mc can be reliably detected in the high-pressure data. The estimated transition pressure lies in the range 1.18,<,Pc,<,3.09,GPa. The transition leads to a breaking of the regular Kagomé net formed by part of the V ions. While in the ambient pressure structure all V,V distances in the Kagomé net are equal, they split into inter-trimer and intra-trimer distances in the high-pressure phase. In general, these changes are comparable to those observed in the corresponding low-temperature transition. However, the pressure-induced transition takes place at a lower unit-cell volume compared with the temperature-induced transition. Furthermore, overall trends for inter-trimer and intra-trimer V,V distances as a function of the unit-cell volume are clearly different for datapoints obtained by variation of pressure and temperature. The behavior of BaV6O11 is compared with that of NaV6O11. While in the latter compound the transition can be explained as a pure volume effect, in BaV6O11 an additional degree of freedom related to the valence distribution among the symmetrically independent vanadium sites has to be taken into account. [source] Use of the tangent derivative boundary integral equations for the efficient computation of stresses and error indicatorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2002K. H. Muci-Küchler Abstract In this work, a new global reanalysis technique for the efficient computation of stresses and error indicators in two-dimensional elastostatic problems is presented. In the context of the boundary element method, the global reanalysis technique can be viewed as a post-processing activity that is carried out once an analysis using Lagrangian elements has been performed. To do the reanalysis, the functional representation for the displacements is changed from Lagrangian to Hermite, introducing the nodal values of the tangential derivatives of those quantities as additional degrees of freedom. Next, assuming that the nodal values of the displacements and the tractions remain practically unchanged from the ones obtained in the analysis using Lagrangian elements, the tangent derivative boundary integral equations are collocated at each functional node in order to determine the additional degrees of freedom that were introduced. Under this scheme, a second system of equations is generated and, once it is solved, the nodal values of the tangential derivatives of the displacements are obtained. This approach gives more accurate results for the stresses at the nodes since it avoids the need to differentiate the shape functions in order to obtain the normal strain in the tangential direction. When compared with the use of Hermite elements, the global reanalysis technique has the attraction that the user does not have to give as input data the additional information required by this type of elements. Another important feature of the proposed approach is that an efficient error indicator for the values of the stresses can also be obtained comparing the values for the stresses obtained through the use of Lagrangian elements and the global reanalysis technique. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||||||||