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Spherical Geometry (spherical + geometry)

Distribution by Scientific Domains

Physics and Astronomy	11%
Engineering	11%

Selected Abstracts

Continuation of travelling-wave solutions of the Navier,Stokes equations

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2006
Isabel Mercader
Abstract An efficient way of obtaining travelling waves in a periodic fluid system is described and tested. We search for steady states in a reference frame travelling at the wave phase velocity using a first-order pseudospectral semi-implicit time scheme adapted to carry out the Newton's iterations. The method is compared to a standard Newton,Raphson solver and is shown to be highly efficient in performing this task, even when high-resolution grids are used. This method is well suited to three-dimensional calculations in cylindrical or spherical geometries. Copyright © 2006 John Wiley & Sons, Ltd. [source]

On splitting-based mass and total energy conserving arbitrary order shallow-water schemes

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 3 2007
Yuri N. Skiba
Abstract A new method for numerical solution to the shallow-water equations is suggested. The method allows constructing a family of finite difference schemes of different approximation order that conserve the mass and the total energy. Our approach is based on the method of splitting, and unlike others it permits to derive conservative numerical schemes after discretizing all the partial derivatives, both spatial and temporal. The schemes thus appear to be fully discrete, both in time and in space. Besides, due to a simple structure of the matrices appeared therewith, the method provides essential benefits in the computational cost of solution and is easy-to-implement in the Cartesian and spherical geometries. Numerical results confirm functionality and efficiency of the developed method. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]

Fast direct solver for Poisson equation in a 2D elliptical domain

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2004
Ming-Chih Lai
Abstract In this article, we extend our previous work M.-C. Lai and W.-C. Wang, Numer Methods Partial Differential Eq 18:56,68, 2002 for developing some fast Poisson solvers on 2D polar and spherical geometries to an elliptical domain. Instead of solving the equation in an irregular Cartesian geometry, we formulate the equation in elliptical coordinates. The solver relies on representing the solution as a truncated Fourier series, then solving the differential equations of Fourier coefficients by finite difference discretizations. Using a grid by shifting half mesh away from the pole and incorporating the derived numerical boundary value, the difficulty of coordinate singularity can be elevated easily. Unlike the case of 2D disk domain, the present difference equation for each Fourier mode is coupled with its conjugate mode through the numerical boundary value near the pole; thus, those two modes are solved simultaneously. Both second- and fourth-order accurate schemes for Dirichlet and Neumann problems are presented. In particular, the fourth-order accuracy can be achieved by a three-point compact stencil which is in contrast to a five-point long stencil for the disk case. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 72,81, 2004 [source]

Fast direct solvers for Poisson equation on 2D polar and spherical geometries

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2002
Ming-Chih Lai
Abstract A simple and efficient class of FFT-based fast direct solvers for Poisson equation on 2D polar and spherical geometries is presented. These solvers rely on the truncated Fourier series expansion, where the differential equations of the Fourier coefficients are solved by the second- and fourth-order finite difference discretizations. Using a grid by shifting half mesh away from the origin/poles, and incorporating with the symmetry constraint of Fourier coefficients, the coordinate singularities can be easily handled without pole condition. By manipulating the radial mesh width, three different boundary conditions for polar geometry including Dirichlet, Neumann, and Robin conditions can be treated equally well. The new method only needs O(MN log2N) arithmetic operations for M × N grid points. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 56,68, 2002 [source]

A monotonic and positive,definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 611 2005
Mohamed Zerroukat
Abstract A new monotonic and positive,definite filter is incorporated into an existing Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme for transport problems in both Cartesian and spherical geometry. The SLICE scheme is based on a control-volume approach that uses multiple sweeps of a one-dimensional O (,x4) conservation remapping algorithm along predetermined cascade directions. The new filter combines a selective detection algorithm, to pinpoint regions of non-monotonic behaviour, with a hierarchical reduction of the degree of the piecewise reconstruction in such regions, to re-establish monotonicity. The enhanced, monotonic and positive,definite, SLICE scheme is tested in one dimension, and then applied to standard two-dimensional test problems in both Cartesian and spherical geometries. Comparisons with published results of other conservative semi-Lagrangian schemes show that it performs well. © Crown copyright, 2005. [source]

Spreadsheet for cyclone and hydrocyclone design considering nonspherical particle geometry

COMPUTER APPLICATIONS IN ENGINEERING EDUCATION, Issue 2 2007
Marcelo K. Lenzi
Abstract Cyclones and hydrocyclones are widely used for gas,solid and liquid,solid particle separations, respectively. The key feature is the presence of a centrifugal field. Equilibrium zone concept is one of the most used approaches for equipment design. This work revisits the design equations for nonspherical particles and compares design results considering nonspherical geometry to results considering spherical geometry and correcting the values to the non-spherical particle geometry. A didactic spreadsheet was prepared for analysis and instruction, and depending on the particle shape and on the particle orientation, errors up to 38% may be obtained in the cut diameter and 10% in the global collection efficiency. © 2007 Wiley Periodicals, Inc. Comput Appl Eng Educ. 15: 134,142, 2007; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.20102 [source]

DTI-DROID: Diffusion tensor imaging-deformable registration using orientation and intensity descriptors

INTERNATIONAL JOURNAL OF IMAGING SYSTEMS AND TECHNOLOGY, Issue 2 2010
Madhura Ingalhalikar
Abstract This article presents a method (DROID) for deformable registration of diffusion tensor (DT) images that utilizes the full tensor information by integrating the intensity and orientation features into a hierarchical matching framework. The intensity features are derived from eigen value based measures that characterize the tensor in terms of its different shape properties, such as, prolateness, oblateness, and sphericity of the tensor. Local spatial distributions of the prolate, oblate, and spherical geometry are used to create an attribute vector called the geometric/intensity feature for matching. The orientation features are the orientation histograms computed from the eigenvectors. These intensity and orientation features are incorporated into a hierarchical deformable registration framework to develop a deformable registration algorithm for DT images. Using orientation features improves the matching of the white matter fiber tracts by taking into account the underlying fiber orientation information. Extensive experiments on simulated and real brain DT data show promising results that makes DROID potentially useful for subsequent group-based analysis of DT images to identify disease-induced and developmental changes in a population. © 2010 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 20, 99,107, 2010 [source]

Effect of Interparticle Potential on Forming Solid, Spherical Agglomerates during Drying

JOURNAL OF THE AMERICAN CERAMIC SOCIETY, Issue 1 2004
Geoff E. Fair
The effect of the interparticle potential on the shapes of the agglomerates obtained by drying slurry droplets has been investigated using aqueous alumina slurries formulated in the dispersed and weakly attractive (dispersed + added salt) states. For the dispersed slurry, the droplets dried to irregular shapes with hollow centers. When just the right amount of salt was added to produce an attractive, but nontouching, particle network, the droplets dried as solid spheres. These results are discussed by relating both the nature of the particle network (repulsive or weakly attractive), the slurry rheology, and the consolidation mechanics of the networks to the requirements for maintaining a spherical geometry and uniform density during droplet drying. [source]

The cluster environments of radio-loud quasars at 0.6 < z < 1.1

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2003
J. M. Barr
ABSTRACT We have carried out multicolour imaging of a complete sample of radio-loud quasars at 0.6 < z < 1.1 and find groups or clusters of galaxies in the fields of at least eight and possibly 13 of the 21 sources. There is no evidence for an evolution in the richness of the environments of radio-loud quasars from other low-redshift studies to z, 0.9. The quasars associated with groups and clusters in our sample do not necessarily reside in the centre of the galaxy distribution, which rarely displays a spherical geometry. Clustering is preferentially associated with small or asymmetric steep-spectrum radio sources. The quasars with the largest projected angular size are, in nearly all cases, found in non-clustered environments. Radio-based selection (including source size) of high-redshift groups and clusters can be a very efficient method of detecting rich environments at these redshifts. We find that in optical searches for galaxy overdensities above z, 0.6, multiple filters must be used. If the single-filter counting statistics used by groups at lower redshift are applied to our data, uncertainties are too large to make accurate quantifications of cluster richness. This means that genuine clustering of galaxies about quasars will be missed and, in ,10 per cent of cases, putative clusters turn out to be false detections. The statistics are further diluted by the fact that galaxy overdensities are generally not centred on the quasar. [source]

Stability of some exact solutions of the shallow-water equations for testing numerical models in spherical geometry

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 632 2008
A. Staniforth
Abstract Five families of exact axisymmetric solutions of the nonlinear shallow-water equations in spherical geometry have recently been proposed as an aid to the development and testing of global numerical models. Sufficient conditions for the stability of these solutions are here derived to guide the choice of values for the family parameters. Thus it can be ensured that any significant time evolution occurring in a numerical model initialised with one of these exact solutions is of numerical origin, and does not reflect an inherent physical instability. With the caveat that only sufficient conditions for stability are examined, it appears that planetary rotation stabilises the solutions (as would be so if the flow were governed by barotropic vorticity dynamics), and that low Rossby and Froude numbers favour their stability. © Crown Copyright 2008. Reproduced with the permission of the Controller of HMSO. Published by John Wiley & Sons, Ltd [source]

Conservative constraint for a quasi-uniform overset grid on the sphere

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 616 2006
Xindong Peng
Abstract A conservative constraint is presented for a new quasi-uniform overset (Yin-Yang) grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry created by matching two notched latitude,longitude grids which are normal to each other. Global and local conservation is achieved with an interpolation algorithm that exactly guarantees that the fluxes on boundaries of the two grid components are identical. Several numerical experiments are shown to confirm the conservation in passive transport situations and shallow-water dynamical equations. Copyright © 2006 Royal Meteorological Society. [source]

A monotonic and positive,definite filter for a Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme

SLICE-S: A Semi-Lagrangian Inherently Conserving and Efficient scheme for transport problems on the Sphere

THE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 602 2004
Mohamed Zerroukat
Abstract The Semi-Lagrangian Inherently Conserving and Efficient (SLICE) scheme developed for Cartesian geometry is generalized to spherical geometry. The spherical version, SLICE-S, is similarly based on a Control Volume approach and multiple sweeps of a one-dimensional O(,s4) (where s is the spherical distance) conservative remapping algorithm along Eulerian latitudes, then along Lagrangian longitudes. The resulting conservative scheme requires no restriction on either the polar meridional or zonal Courant numbers. SLICE-S is applied to the standard problems of solid-body rotation and deformational flow, and results are compared with those of a standard non-conservative and other published conservative semi-Lagrangian schemes. In addition to mass conservation, and consistent with the performance of SLICE, the present scheme is competitive in terms of accuracy and efficiency. © Crown copyright, 2004. Royal Meteorological Society [source]

Differential rotation and meridional circulation in global models of solar convection

ASTRONOMISCHE NACHRICHTEN, Issue 10 2007
M.S. MieschArticle first published online: 27 DEC 200
Abstract In the outer envelope of the Sun and in other stars, differential rotation and meridional circulation are maintained via the redistribution of momentum and energy by convective motions. In order to properly capture such processes in a numerical model, the correct spherical geometry is essential. In this paper I review recent insights into the maintenance of mean flows in the solar interior obtained from high-resolution simulations of solar convection in rotating spherical shells. The Coriolis force induces a Reynolds stress which transports angular momentum equatorward and also yields latitudinal variations in the convective heat flux. Meridional circulations induced by baroclinicity and rotational shear further redistribute angular momentum and alter the mean stratification. This gives rise to a complex nonlinear interplay between turbulent convection, differential rotation, meridional circulation, and the mean specific entropy profile. I will describe how this drama plays out in our simulations as well as in solar and stellar convection zones. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Physicochemical studies on the biopolymer inulin: A critical evaluation of its self-aggregation, aggregate-morphology, interaction with water, and thermal stability

BIOPOLYMERS, Issue 9 2009
Abhijit Dan
Abstract Physicochemical properties viz., aggregation, molar mass, shape, and size of chicory inulin in solution were determined by fluorimetry, DLS, SLS, TEM, and viscometry methods. The thermal stability of the biopolymer was examined by TGA, DTA, and DSC measurements. The water vapor adsorption of desiccated inulin was also studied by the isopiestic method, and the data were analyzed in the light of the BET equation. On the basis of the obstruction to ion conductance by the inulin aggregates in solution and analysis of the data, the extent of hydration of inulin in solution was estimated. The result was coupled with the intrinsic viscosity, [,], of inulin to ascertain the shape of the biopolymer aggregates in aqueous solution. The critical aggregation concentration (cac) of inulin in aqueous as well as in salt solution was assessed by fluorimetry. The weight average molar mass, , of inulin monomer and its aggregate was found to be 4468 and 1.03 × 106 g/mol, respectively, in aqueous solution. This aggregated mass was 2.4 × 106 g/mol in 0.5M NH4SCN solution. The [,] values of the soft supramolecular aggregates in solution (without and with salt) were small and comparable with globular proteins evidencing spherical geometry of the biopolymer aggregates as supported by the TEM results. In DMSO, rod-like aggregates of inulin was found by the TEM study. The [,] of the biopolymer in the DMSO medium was therefore, higher than that in the aqueous medium. Unlike aqueous medium, the aggregation in DMSO was not associated with a cac. © 2009 Wiley Periodicals, Inc. Biopolymers 91: 687,699, 2009. This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com [source]