A spherical harmonics intensity model for 3D segmentation and 3D shape analysis of heterochromatin foci.

Science.gov (United States)

Eck, Simon; Wörz, Stefan; Müller-Ott, Katharina; Hahn, Matthias; Biesdorf, Andreas; Schotta, Gunnar; Rippe, Karsten; Rohr, Karl

2016-08-01

The genome is partitioned into regions of euchromatin and heterochromatin. The organization of heterochromatin is important for the regulation of cellular processes such as chromosome segregation and gene silencing, and their misregulation is linked to cancer and other diseases. We present a model-based approach for automatic 3D segmentation and 3D shape analysis of heterochromatin foci from 3D confocal light microscopy images. Our approach employs a novel 3D intensity model based on spherical harmonics, which analytically describes the shape and intensities of the foci. The model parameters are determined by fitting the model to the image intensities using least-squares minimization. To characterize the 3D shape of the foci, we exploit the computed spherical harmonics coefficients and determine a shape descriptor. We applied our approach to 3D synthetic image data as well as real 3D static and real 3D time-lapse microscopy images, and compared the performance with that of previous approaches. It turned out that our approach yields accurate 3D segmentation results and performs better than previous approaches. We also show that our approach can be used for quantifying 3D shape differences of heterochromatin foci. Copyright © 2016 Elsevier B.V. All rights reserved.

Rotationally invariant clustering of diffusion MRI data using spherical harmonics

DEFF Research Database (Denmark)

Liptrot, Matthew George; Lauze, Francois Bernard

2016-01-01

simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic...... data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing...... classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre...

Spherical harmonic expansion of short-range screened Coulomb interactions

Energy Technology Data Exchange (ETDEWEB)

Angyan, Janos G [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Gerber, Iann [Laboratoire de Cristallographie et de Modelisation des Materiaux Mineraux et Biologiques, UMR 7036, CNRS-Universite Henri Poincare, BP 239, F-54506 Vandoeuvre-les-Nancy (France); Marsman, Martijn [Institut fuer Materialphysik and Center for Computational Materials Science, Universitaet Wien, Sensengasse 8, A-1090, Vienna (Austria)

2006-07-07

Spherical harmonic expansions of the screened Coulomb interaction kernel involving the complementary error function are required in various problems in atomic, molecular and solid state physics, like for the evaluation of Ewald-type lattice sums or for range-separated hybrid density functionals. A general analytical expression is derived for the kernel, which is non-separable in the radial variables. With the help of series expansions a separable approximate form is proposed, which is in close analogy with the conventional multipole expansion of the Coulomb kernel in spherical harmonics. The convergence behaviour of these expansions is studied and illustrated by the electrostatic potential of an elementary charge distribution formed by products of Slater-type atomic orbitals.

On the spherical harmonic expansion of the neutron angular distribution function

Energy Technology Data Exchange (ETDEWEB)

Depken, Sven

1959-03-15

The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases.

On the spherical harmonic expansion of the neutron angular distribution function

International Nuclear Information System (INIS)

Depken, Sven

1959-03-01

The neutron (one-velocity) angular distribution function is expanded in terms of spherical harmonic tensors. The solution to the equations of the moments is given explicitly and the result is applied to the plane, spherical and cylinder symmetrical cases

Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues

International Nuclear Information System (INIS)

Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Liang, Jimin; Zhang, Qian

2015-01-01

Aiming at the limitations of the simplified spherical harmonics approximation (SP N ) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SP N are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SP N and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SP N model as well as a much better accuracy compared with the DE one. (paper)

Hybrid simplified spherical harmonics with diffusion equation for light propagation in tissues.

Science.gov (United States)

Chen, Xueli; Sun, Fangfang; Yang, Defu; Ren, Shenghan; Zhang, Qian; Liang, Jimin

2015-08-21

Aiming at the limitations of the simplified spherical harmonics approximation (SPN) and diffusion equation (DE) in describing the light propagation in tissues, a hybrid simplified spherical harmonics with diffusion equation (HSDE) based diffuse light transport model is proposed. In the HSDE model, the living body is first segmented into several major organs, and then the organs are divided into high scattering tissues and other tissues. DE and SPN are employed to describe the light propagation in these two kinds of tissues respectively, which are finally coupled using the established boundary coupling condition. The HSDE model makes full use of the advantages of SPN and DE, and abandons their disadvantages, so that it can provide a perfect balance between accuracy and computation time. Using the finite element method, the HSDE is solved for light flux density map on body surface. The accuracy and efficiency of the HSDE are validated with both regular geometries and digital mouse model based simulations. Corresponding results reveal that a comparable accuracy and much less computation time are achieved compared with the SPN model as well as a much better accuracy compared with the DE one.

Computer model for harmonic ultrasound imaging.

Science.gov (United States)

Li, Y; Zagzebski, J A

2000-01-01

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. In this paper, we present a computer model that can generate realistic harmonic images. In this model, the incident ultrasound is modeled after the "KZK" equation, and the echo signal is modeled using linear propagation theory because the echo signal is much weaker than the incident pulse. Both time domain and frequency domain numerical solutions to the "KZK" equation were studied. Realistic harmonic images of spherical lesion phantoms were generated for scans by a circular transducer. This model can be a very useful tool for studying the harmonic buildup and dissipation processes in a nonlinear medium, and it can be used to investigate a wide variety of topics related to B-mode harmonic imaging.

The Spherical Deformation Model

DEFF Research Database (Denmark)

Hobolth, Asgar

2003-01-01

Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...

Application of Vector Spherical Harmonics and Kernel Regression to the Computations of OMM Parameters

Science.gov (United States)

Marco, F. J.; Martínez, M. J.; López, J. A.

2015-04-01

The high quality of Hipparcos data in position, proper motion, and parallax has allowed for studies about stellar kinematics with the aim of achieving a better physical understanding of our galaxy, based on accurate calculus of the Ogorodnikov-Milne model (OMM) parameters. The use of discrete least squares is the most common adjustment method, but it may lead to errors mainly because of the inhomogeneous spatial distribution of the data. We present an example of the instability of this method using the case of a function given by a linear combination of Legendre polynomials. These polynomials are basic in the use of vector spherical harmonics, which have been used to compute the OMM parameters by several authors, such as Makarov & Murphy, Mignard & Klioner, and Vityazev & Tsvetkov. To overcome the former problem, we propose the use of a mixed method (see Marco et al.) that includes the extension of the functions of residuals to any point on the celestial sphere. The goal is to be able to work with continuous variables in the calculation of the coefficients of the vector spherical harmonic developments with stability and efficiency. We apply this mixed procedure to the study of the kinematics of the stars in our Galaxy, employing the Hipparcos velocity field data to obtain the OMM parameters. Previously, we tested the method by perturbing the Vectorial Spherical Harmonics model as well as the velocity vector field.

Cone-beam and fan-beam image reconstruction algorithms based on spherical and circular harmonics

International Nuclear Information System (INIS)

Zeng, Gengsheng L; Gullberg, Grant T

2004-01-01

A cone-beam image reconstruction algorithm using spherical harmonic expansions is proposed. The reconstruction algorithm is in the form of a summation of inner products of two discrete arrays of spherical harmonic expansion coefficients at each cone-beam point of acquisition. This form is different from the common filtered backprojection algorithm and the direct Fourier reconstruction algorithm. There is no re-sampling of the data, and spherical harmonic expansions are used instead of Fourier expansions. As a special case, a new fan-beam image reconstruction algorithm is also derived in terms of a circular harmonic expansion. Computer simulation results for both cone-beam and fan-beam algorithms are presented for circular planar orbit acquisitions. The algorithms give accurate reconstructions; however, the implementation of the cone-beam reconstruction algorithm is computationally intensive. A relatively efficient algorithm is proposed for reconstructing the central slice of the image when a circular scanning orbit is used

Cubic Invariant Spherical Surface Harmonics in Conjunction With Diffraction Strain Pole-Figures

NARCIS (Netherlands)

Brakman, C.M.

1986-01-01

Four kinds of cubic invariant spherical surface harmonics are introduced. It has been shown previously that these harmonics occur in the equations relating measured diffraction (line-shift) elastic strain and macro-stresses generating these strains for the case of textured cubic materials. As a

Sparse Representation of Deformable 3D Organs with Spherical Harmonics and Structured Dictionary

Directory of Open Access Journals (Sweden)

Dan Wang

2011-01-01

Full Text Available This paper proposed a novel algorithm to sparsely represent a deformable surface (SRDS with low dimensionality based on spherical harmonic decomposition (SHD and orthogonal subspace pursuit (OSP. The key idea in SRDS method is to identify the subspaces from a training data set in the transformed spherical harmonic domain and then cluster each deformation into the best-fit subspace for fast and accurate representation. This algorithm is also generalized into applications of organs with both interior and exterior surfaces. To test the feasibility, we first use the computer models to demonstrate that the proposed approach matches the accuracy of complex mathematical modeling techniques and then both ex vivo and in vivo experiments are conducted using 3D magnetic resonance imaging (MRI scans for verification in practical settings. All results demonstrated that the proposed algorithm features sparse representation of deformable surfaces with low dimensionality and high accuracy. Specifically, the precision evaluated as maximum error distance between the reconstructed surface and the MRI ground truth is better than 3 mm in real MRI experiments.

Error and symmetry analysis of Misner's algorithm for spherical harmonic decomposition on a cubic grid

International Nuclear Information System (INIS)

Fiske, David R

2006-01-01

Computing spherical harmonic decompositions is a ubiquitous technique that arises in a wide variety of disciplines and a large number of scientific codes. Because spherical harmonics are defined by integrals over spheres, however, one must perform some sort of interpolation in order to compute them when data are stored on a cubic lattice. Misner (2004 Class. Quantum Grav. 21 S243) presented a novel algorithm for computing the spherical harmonic components of data represented on a cubic grid, which has been found in real applications to be both efficient and robust to the presence of mesh refinement boundaries. At the same time, however, practical applications of the algorithm require knowledge of how the truncation errors of the algorithm depend on the various parameters in the algorithm. Based on analytic arguments and experience using the algorithm in real numerical simulations, I explore these dependences and provide a rule of thumb for choosing the parameters based on the truncation errors of the underlying data. I also demonstrate that symmetries in the spherical harmonics themselves allow for an even more efficient implementation of the algorithm than was suggested by Misner in his original paper

Using Tikhonov Regularization for Spatial Projections from CSR Regularized Spherical Harmonic GRACE Solutions

Science.gov (United States)

Save, H.; Bettadpur, S. V.

2013-12-01

It has been demonstrated before that using Tikhonov regularization produces spherical harmonic solutions from GRACE that have very little residual stripes while capturing all the signal observed by GRACE within the noise level. This paper demonstrates a two-step process and uses Tikhonov regularization to remove the residual stripes in the CSR regularized spherical harmonic coefficients when computing the spatial projections. We discuss methods to produce mass anomaly grids that have no stripe features while satisfying the necessary condition of capturing all observed signal within the GRACE noise level.

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x–y geometry

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2012-01-01

Highlights: ► This paper describes the solution of time-dependent neutron transport equation. ► We use a novel method based on cellular neural networks (CNNs) coupled with the spherical harmonics method. ► We apply the CNN model to simulate step and ramp perturbation transients in a core. ► The accuracy and capabilities of the CNN model are examined for x–y geometry. - Abstract: In an earlier paper we utilized a novel method using cellular neural networks (CNNs) coupled with spherical harmonics method to solve the steady state neutron transport equation in x–y geometry. Here, the previous work is extended to the study of time-dependent neutron transport equation. To achieve this goal, an equivalent electrical circuit based on a second-order form of time-dependent neutron transport equation and one equivalent group of neutron precursor density is obtained by the CNN method. The CNN model is used to simulate step and ramp perturbation transients in a typical 2D core.

Cellular neural network to the spherical harmonics approximation of neutron transport equation in x-y geometry. Part I: Modeling and verification for time-independent solution

International Nuclear Information System (INIS)

Pirouzmand, Ahmad; Hadad, Kamal

2011-01-01

Highlights: → This paper describes the solution of time-independent neutron transport equation. → Using a novel method based on cellular neural networks (CNNs) coupled with P N method. → Utilize the CNN model to simulate spatial scalar flux distribution in steady state. → The accuracy, stability, and capabilities of CNN model are examined in x-y geometry. - Abstract: This paper describes a novel method based on using cellular neural networks (CNN) coupled with spherical harmonics method (P N ) to solve the time-independent neutron transport equation in x-y geometry. To achieve this, an equivalent electrical circuit based on second-order form of neutron transport equation and relevant boundary conditions is obtained using CNN method. We use the CNN model to simulate spatial response of scalar flux distribution in the steady state condition for different order of spherical harmonics approximations. The accuracy, stability, and capabilities of CNN model are examined in 2D Cartesian geometry for fixed source and criticality problems.

On the equivalence between the discrete ordinates and the spherical harmonics methods in radiative transfer

International Nuclear Information System (INIS)

Barichello, L.B.; Siewert, C.E.

1998-01-01

In this work concerning steady-state radiative-transfer calculations in plane-parallel media, the equivalence between the discrete ordinates method and the spherical harmonics method is proved. More specifically, it is shown that for standard radiative-transfer problems without the imposed restriction of azimuthal symmetry the two methods yield identical results for the radiation intensity when the quadrature scheme for the discrete ordinates method is defined by the zeros of the associated Legendre functions and when generalized Mark boundary conditions are used to define the spherical harmonics solution. It is also shown that, with these choices for a quadrature scheme and for the boundary conditions, the two methods can be formulated so as to require the same computational effort. Finally a justification for using the generalized Mark boundary conditions in the spherical harmonics solution is given

Spherical Harmonics Treatment of Epithermal Neutron Spectra in Reactor lattices

International Nuclear Information System (INIS)

Matausek, M.V.

1972-04-01

A procedure has been developed to solve the slowing down transport equation for neutrons in a cylindrized reactor lattice cell. Treating the anisotropy of the epithermal neutron flux by the spherical harmonics formalism, which reduces the space-angle-lethargy-dependent transport equation to the matrix integrodifferential equation in space and lethargy, and replacing the lethargy transfer integrals by finite-difference forms, a set of matrix ordinary differential equations, with lethargy and space dependent coefficients, is obtained. In the resonance region this set takes a lower block triangular form and can be directly solved by forward block substitution; in the lethargy range, where the fast fission effects have to be considered, the iterative procedure is introduced. A simple and efficient approximation is then proposed, making possible the analytical solution for the spatial dependence of the spherical harmonics flux moments. The proposed procedure has been numerically examined and approved. Some typical results are presented and discussed. (author)

General solution of the multigroup spherical harmonics equations in R-Z geometry

International Nuclear Information System (INIS)

Matausek, M.

1983-01-01

In the present paper the generalization is performed of the procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed foe one-dimensional systems in cylindrical or spherical geometry, and later extended for special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r and z directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. The analysis is performed of the possibilities to satisfy the boundary conditions in the case when the system considered represents an elementary reactor lattice cell and in the case when the system represents a reactor as a whole. The computational effort is estimated for system of a given configuration. (author)

Transformation between surface spherical harmonic expansion of arbitrary high degree and order and double Fourier series on sphere

Science.gov (United States)

Fukushima, Toshio

2018-02-01

In order to accelerate the spherical harmonic synthesis and/or analysis of arbitrary function on the unit sphere, we developed a pair of procedures to transform between a truncated spherical harmonic expansion and the corresponding two-dimensional Fourier series. First, we obtained an analytic expression of the sine/cosine series coefficient of the 4 π fully normalized associated Legendre function in terms of the rectangle values of the Wigner d function. Then, we elaborated the existing method to transform the coefficients of the surface spherical harmonic expansion to those of the double Fourier series so as to be capable with arbitrary high degree and order. Next, we created a new method to transform inversely a given double Fourier series to the corresponding surface spherical harmonic expansion. The key of the new method is a couple of new recurrence formulas to compute the inverse transformation coefficients: a decreasing-order, fixed-degree, and fixed-wavenumber three-term formula for general terms, and an increasing-degree-and-order and fixed-wavenumber two-term formula for diagonal terms. Meanwhile, the two seed values are analytically prepared. Both of the forward and inverse transformation procedures are confirmed to be sufficiently accurate and applicable to an extremely high degree/order/wavenumber as 2^{30} {≈ } 10^9. The developed procedures will be useful not only in the synthesis and analysis of the spherical harmonic expansion of arbitrary high degree and order, but also in the evaluation of the derivatives and integrals of the spherical harmonic expansion.

Acoustic reciprocity: An extension to spherical harmonics domain.

Science.gov (United States)

Samarasinghe, Prasanga; Abhayapala, Thushara D; Kellermann, Walter

2017-10-01

Acoustic reciprocity is a fundamental property of acoustic wavefields that is commonly used to simplify the measurement process of many practical applications. Traditionally, the reciprocity theorem is defined between a monopole point source and a point receiver. Intuitively, it must apply to more complex transducers than monopoles. In this paper, the authors formulate the acoustic reciprocity theory in the spherical harmonics domain for directional sources and directional receivers with higher order directivity patterns.

Application of the spherical harmonic gravity model in high precision inertial navigation systems

International Nuclear Information System (INIS)

Wang, Jing; Yang, Gongliu; Zhou, Xiao; Li, Xiangyun

2016-01-01

The spherical harmonic gravity model (SHM) may, in general, be considered as a suitable alternative to the normal gravity model (NGM), because it represents the Earth’s gravitational field more accurately. However, the high-resolution SHM has never been used in current inertial navigation systems (INSs) due to its extremely complex expression. In this paper, the feasibility and accuracy of a truncated SHM are discussed for application in a real-time free-INS with a precision demand better than 0.8 nm h −1 . In particular, the time and space complexity are analyzed mathematically to verify the feasibility of the SHM. Also, a test on a typical navigation computer shows a storable range of cut-off degrees. To further evaluate the appropriate degree and accuracy of the truncated SHM, analyses of covariance and truncation error are proposed. Finally, a SHM of degree 12 is demonstrated to be the appropriate model for routine INSs in the precision range of 0.4–0.75 nm h −1 . Flight simulations and road tests show its outstanding performance over the traditional NGM. (paper)

Spherical harmonics analysis of Fermi gamma-ray data and the Galactic dark matter halo

International Nuclear Information System (INIS)

Malyshev, Dmitry; Bovy, Jo; Cholis, Ilias

2011-01-01

We argue that the decomposition of gamma-ray maps in spherical harmonics is a sensitive tool to study dark matter (DM) annihilation or decay in the main Galactic halo of the Milky Way. Using the spherical harmonic decomposition in a window excluding the Galactic plane, we show for 1 yr of Fermi data that adding a spherical template (such as a line-of-sight DM annihilation profile) to an astrophysical background significantly reduces χ 2 of the fit to the data. In some energy bins the significance of this DM fraction is above three sigma. This can be viewed as a hint of a DM annihilation signal, although astrophysical sources cannot be ruled out at this moment. We use the derived DM fraction as a conservative upper limit on the DM annihilation signal. In the case of bb annihilation channel the limits are about a factor of 2 less constraining than the limits from dwarf galaxies. The uncertainty of our method is dominated by systematics related to modeling the astrophysical background. We show that with 1 yr of Fermi data the statistical sensitivity would be sufficient to detect DM annihilation with thermal freeze-out cross section for masses below 100 GeV.

The Spherical Deformation Model

DEFF Research Database (Denmark)

Hobolth, Asgar

2003-01-01

Miller et al. (1994) describe a model for representing spatial objects with no obvious landmarks. Each object is represented by a global translation and a normal deformation of a sphere. The normal deformation is defined via the orthonormal spherical-harmonic basis. In this paper we analyse the s...... a single central section of the object. We use maximum-likelihood-based inference for this purpose and demonstrate the suggested methods on real data....

Radiation transport benchmarks for simple geometries with void regions using the spherical harmonics method

International Nuclear Information System (INIS)

Kobayashi, K.

2009-01-01

In 2001, an international cooperation on the 3D radiation transport benchmarks for simple geometries with void region was performed under the leadership of E. Sartori of OECD/NEA. There were contributions from eight institutions, where 6 contributions were by the discrete ordinate method and only two were by the spherical harmonics method. The 3D spherical harmonics program FFT3 by the finite Fourier transformation method has been improved for this presentation, and benchmark solutions for the 2D and 3D simple geometries with void region by the FFT2 and FFT3 are given showing fairly good accuracy. (authors)

3-D spherical harmonics code FFT3 by the finite Fourier transformation method

International Nuclear Information System (INIS)

Kobayashi, K.

1997-01-01

In the odd order spherical harmonics method, the rigorous boundary condition at the material interfaces is that the even moments of the angular flux and the normal components of the even order moments of current vectors must be continuous. However, it is difficult to derive spatial discretized equations by the finite difference or finite element methods, which satisfy this material interface condition. It is shown that using the finite Fourier transformation method, space discretized equations which satisfy this interface condition can be easily derived. The discrepancies of the flux distribution near void region between spherical harmonics method codes may be due to the difference of application of the material interface condition. (author)

The spherical harmonics method, 1 (general development of the theory)

International Nuclear Information System (INIS)

Mark, C.

1957-02-01

A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle Ψ(→/r, →/Ω) in spherical harmonic tensors formed from →/Ω the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density Ψ (o) (r). This equation has the form where the numbers ν i depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of Ψ(→/r, →/Ω) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of Ψ(→/r, →/Ω) which we retain be continuous; and this determines the constants in the solution for Ψ (o) (→/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)

On the second spherical harmonics of the cosmics ray angular distribution

International Nuclear Information System (INIS)

Kota, J.

1974-12-01

In order to describe the semi-diurnal variation of the cosmic ray intensity the convection-diffusion theory has been extended by considering the second moments of cosmic ray angular distribution and those of the statistical Boltzmann equation. The quadrupole moment of the directional distribution has been represented by a symmetric traceloss tensor whose elements correspond to the five independent spherical harmonics of second order. The results are basically in agreement with the earlier published ones. However, by contrast with these earlier results, in the present model a different particle flux is predicted from the directions along the magnetic field and normal to the ecliptic plane, respectively, and the interplanetary magnetic field lines are being bent and diverging. The second harmonics of the anisotropy depend on the global feature of the mean free path between the sun and the earth. Arguments are also brought forward that a sunward stream along the interplanetary magnetic field lines gives rise to a distribution of the pitch angle type. (Sz.Z.)

Scalar and Vector Spherical Harmonics for Assimilation of Global Datasets in the Ionosphere and Thermosphere

Science.gov (United States)

Miladinovich, D.; Datta-Barua, S.; Bust, G. S.; Ramirez, U.

2017-12-01

Understanding physical processes during storm time in the ionosphere-thermosphere (IT) system is limited, in part, due to the inability to obtain accurate estimates of IT states on a global scale. One reason for this inability is the sparsity of spatially distributed high quality data sets. Data assimilation is showing promise toward enabling global estimates by blending high quality observational data sets with established climate models. We are continuing development of an algorithm called Estimating Model Parameters for Ionospheric Reverse Engineering (EMPIRE) to enable assimilation of global datasets for storm time estimates of IT drivers. EMPIRE is a data assimilation algorithm that uses a Kalman filtering routine to ingest model and observational data. The EMPIRE algorithm is based on spherical harmonics which provide a spherically symmetric, smooth, continuous, and orthonormal set of basis functions suitable for a spherical domain such as Earth's IT region (200-600 km altitude). Once the basis function coefficients are determined, the newly fitted function represents the disagreement between observational measurements and models. We apply spherical harmonics to study the March 17, 2015 storm. Data sources include Fabry-Perot interferometer neutral wind measurements and global Ionospheric Data Assimilation 4 Dimensional (IDA4D) assimilated total electron content (TEC). Models include Weimer 2000 electric potential, International Geomagnetic Reference Field (IGRF) magnetic field, and Horizontal Wind Model 2014 (HWM14) neutral winds. We present the EMPIRE assimilation results of Earth's electric potential and thermospheric winds. We also compare EMPIRE storm time E cross B ion drift estimates to measured drifts produced from the Super Dual Auroral Radar Network (SuperDARN) and Active Magnetosphere and Planetary Electrodynamics Response Experiment (AMPERE) measurement datasets. The analysis from these results will enable the generation of globally assimilated

Combined analytical-numerical procedure to solve multigroup spherical harmonics equations in two-dimensional r-z geometry

International Nuclear Information System (INIS)

Matausek, M.V.; Milosevic, M.

1986-01-01

In the present paper a generalization is performed of a procedure to solve multigroup spherical harmonics equations, which has originally been proposed and developed for one-dimensional systems in cylindrical or spherical geometry, and later extended for a special case of a two-dimensional system in r-z geometry. The expressions are derived for the axial and the radial dependence of the group values of the neutron flux moments, in the P-3 approximation of the spherical harmonics method, in a cylindrically symmetrical system with an arbitrary number of material regions in both r- and z-directions. In the special case of an axially homogeneous system, these expressions reduce to the relations derived previously. (author)

Efficient molecular density functional theory using generalized spherical harmonics expansions.

Science.gov (United States)

Ding, Lu; Levesque, Maximilien; Borgis, Daniel; Belloni, Luc

2017-09-07

We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r≡(x,y,z) and of the three Euler angles Ω≡(θ,ϕ,ψ) describing the solvent orientation. The standard density functional, equivalent to the hypernetted-chain closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We finally illustrate the formalism by tackling the solvation of molecules of various complexities in water.

The spherical harmonics method, 1 (general development of the theory)

Energy Technology Data Exchange (ETDEWEB)

Mark, C

1957-02-15

A method of obtaining approximate solutions of the transport equation is presented in a form applicable in principle to any geometry. The approximation will give good results in cases where the angular distribution is not very anisotropic. The basis of the approximation is to expand the density per unit solid angle {Psi}({yields}/r, {yields}/{Omega}) in spherical harmonic tensors formed from {yields}/{Omega} the unit vector in the direction of velocity, and to break off the expansion. A differential equation whose degree increases with the order of the approximation is obtained for the total density {Psi}{sup (o)}(r). This equation has the form where the numbers {nu}{sub i} depend on the order of the approximation and on the value of the parameter a of the medium, but not at all on the geometry. When the equation for the total density is an ordinary equation, we simulate the physical condition of continuity of {Psi}({yields}/r, {yields}/{Omega}) at a boundary in a multi-medium problem by requiring that the spherical harmonic moments of {Psi}({yields}/r, {yields}/{Omega}) which we retain be continuous; and this determines the constants in the solution for {Psi}{sup (o)}({yields}/r. The form of the solution for the total density and the necessary moments in an approximation of general order is given explicitly for plane and spherical symmetry; and for cylindrical symmetry the solution is given for two low-order approximations. In a later report (CRT-338, Revised) the application of the method to several problems involving plane and spherical symmetry will be discussed in detail and the results of a number of examples already worked will also be given. (author)

Resonance energy transfer: The unified theory via vector spherical harmonics

Energy Technology Data Exchange (ETDEWEB)

Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk [School of Chemistry, University of East Anglia, Norwich NR4 7TJ (United Kingdom)

2016-08-21

In this work, we derive the well-established expression for the quantum amplitude associated with the resonance energy transfer (RET) process between a pair of molecules that are beyond wavefunction overlap. The novelty of this work is that the field of the mediating photon is described in terms of a spherical wave rather than a plane wave. The angular components of the field are constructed in terms of vector spherical harmonics while Hankel functions are used to define the radial component. This approach alleviates the problem of having to select physically correct solution from non-physical solutions, which seems to be inherent in plane wave derivations. The spherical coordinate system allows one to easily decompose the photon’s fields into longitudinal and transverse components and offers a natural way to analyse near-, intermediate-, and far-zone RET within the context of the relative orientation of the transition dipole moments for the two molecules.

Flyby Characterization of Lower-Degree Spherical Harmonics Around Small Bodies

Science.gov (United States)

Takahashi, Yu; Broschart, Stephen; Lantoine, Gregory

2014-01-01

Interest in studying small bodies has grown significantly in the last two decades, and there are a number of past, present, and future missions. These small body missions challenge navigators with significantly different kinds of problems than the planets and moons do. The small bodies' shape is often irregular and their gravitational field significantly weak, which make the designing of a stable orbit a complex dynamical problem. In the initial phase of spacecraft rendezvous with a small body, the determination of the gravitational parameter and lower-degree spherical harmonics are of crucial importance for safe navigation purposes. This motivates studying how well one can determine the total mass and lower-degree spherical harmonics in a relatively short time in the initial phase of the spacecraft rendezvous via flybys. A quick turnaround for the gravity data is of high value since it will facilitate the subsequent mission design of the main scientific observation campaign. We will present how one can approach the problem to determine a desirable flyby geometry for a general small body. We will work in the non-dimensional formulation since it will generalize our results across different size/mass bodies and the rotation rate for a specific combination of gravitational coefficients.

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

Energy Technology Data Exchange (ETDEWEB)

Radice, David, E-mail: david.radice@aei.mpg.de [Max Planck Institute für Gravitationsphysik, Albert Einstein Institute, Potsdam (Germany); Abdikamalov, Ernazar [TAPIR, California Institute of Technology, Pasadena, CA (United States); Rezzolla, Luciano [Max Planck Institute für Gravitationsphysik, Albert Einstein Institute, Potsdam (Germany); Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA (United States); Ott, Christian D. [TAPIR, California Institute of Technology, Pasadena, CA (United States)

2013-06-01

Recent work by McClarren and Hauck (2010) [31] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations.

A new spherical harmonics scheme for multi-dimensional radiation transport I. Static matter configurations

International Nuclear Information System (INIS)

Radice, David; Abdikamalov, Ernazar; Rezzolla, Luciano; Ott, Christian D.

2013-01-01

Recent work by McClarren and Hauck (2010) [31] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the three-dimensional (3D) case and find that all of the advantages of the filtering approach identified in 2D are present also in the 3D case. We reformulate the filter operation in a way that is independent of the timestep and of the spatial discretization. We also explore different second- and fourth-order filters and find that the second-order ones yield significantly better results. Overall, our findings suggest that the filtered spherical harmonics approach represents a very promising method for 3D radiation transport calculations

An improved filtered spherical harmonic method for transport calculations

International Nuclear Information System (INIS)

Ahrens, C.; Merton, S.

2013-01-01

Motivated by the work of R. G. McClarren, C. D. Hauck, and R. B. Lowrie on a filtered spherical harmonic method, we present a new filter for such numerical approximations to the multi-dimensional transport equation. In several test problems, we demonstrate that the new filter produces results with significantly less Gibbs phenomena than the filter used by McClarren, Hauck and Lowrie. This reduction in Gibbs phenomena translates into propagation speeds that more closely match the correct propagation speed and solutions that have fewer regions where the scalar flux is negative. (authors)

A non-conforming 3D spherical harmonic transport solver

Energy Technology Data Exchange (ETDEWEB)

Van Criekingen, S. [Commissariat a l' Energie Atomique CEA-Saclay, DEN/DM2S/SERMA/LENR Bat 470, 91191 Gif-sur-Yvette, Cedex (France)

2006-07-01

A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)

A non-conforming 3D spherical harmonic transport solver

International Nuclear Information System (INIS)

Van Criekingen, S.

2006-01-01

A new 3D transport solver for the time-independent Boltzmann transport equation has been developed. This solver is based on the second-order even-parity form of the transport equation. The angular discretization is performed through the expansion of the angular neutron flux in spherical harmonics (PN method). The novelty of this solver is the use of non-conforming finite elements for the spatial discretization. Such elements lead to a discontinuous flux approximation. This interface continuity requirement relaxation property is shared with mixed-dual formulations such as the ones based on Raviart-Thomas finite elements. Encouraging numerical results are presented. (authors)

Exactly complete solutions of the Schroedinger equation with a spherically harmonic oscillatory ring-shaped potential

International Nuclear Information System (INIS)

Zhang Mincang; Sun Guohua; Dong Shihai

2010-01-01

A spherically harmonic oscillatory ring-shaped potential is proposed and its exactly complete solutions are presented by the Nikiforov-Uvarov method. The effect of the angle-dependent part on the radial solutions is discussed.

Mapping the total electron content over Malaysia using Spherical Cap Harmonic Analysis

Science.gov (United States)

Bahari, S.; Abdullah, M.; Bouya, Z.; Musa, T. A.

2017-12-01

The ionosphere over Malaysia is unique because of her location which is in close proximity to the geomagnetic equator and is in the equatorial regions. In this region, the magnetic field is horizontally oriented from south to north and field aligned direction is in the meridional plane (ExB) which becomes the source of equatorial ionospheric anomaly occurrence such as plasma bubble, fountain effects and others. Until today, there is no model that has been developed over Malaysia to study the ionosphere. Due to that, the main objective of this paper is to develop a new technique for mapping the total electron content (TEC) from GPS measurements. Data by myRTKnet network of GPS receiver over Malaysia were used in this study. A new methodology, based on modified spherical cap harmonic analysis (SCHA), was developed to estimate diurnal vertical TEC over the region using GPS observations. The SCHA model is based on longitudinal expansion in Fourier series and fractional Legendre co-latitudinal functions over a spherical cap-like region. The TEC map with spatial resolution of 0.15 ° x 0.15 ° in latitude and longitude with the time resolution of 30 seconds are derived. TEC maps from the SCHA model were compared with the global ionospheric map and other regional models. Result shows that during low solar activity, SCHA model had a better mapping with the accuracy of less than 1 TECU compared to other regional models.

Spherical cap modelling of Orsted magnetic field vectors over southern Africa

CSIR Research Space (South Africa)

Kotze, PB

2001-01-01

Full Text Available Vector magnetic field observations by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000, have been employed to derive a spherical cap harmonic model (Haines, 1985) over the southern African region between 10 degrees...

Measurement of The Magnetic Field in a Spherical Torus Plasma via Electron Bernstein Wave Emission Harmonic Overlap

International Nuclear Information System (INIS)

Jones, B.; Taylor, G.; Efthimion, P.C.; Munsat, T.

2004-01-01

Measurement of the magnetic field in a spherical torus by observation of harmonic overlap frequencies in the electron Bernstein wave (EBW) spectrum has been previously suggested [V.F. Shevchenko, Plasma Phys. Reports 26 (2000) 1000]. EBW mode conversion to X-mode radiation has been studied in the Current Drive Experiment-Upgrade spherical torus, [T. Jones, Ph.D. thesis, Princeton University, 1995] with emission measured at blackbody levels [B. Jones et al., Phys. Rev. Lett. 90 (2003) article no. 165001]. Sharp transitions in the thermally emitted EBW spectrum have been observed for the first two harmonic overlaps. These transition frequencies are determined by the magnetic field and electron density at the mode conversion layer in accordance with hot-plasma wave theory. Prospects of extending this measurement to higher harmonics, necessary in order to determine the magnetic field profile, and high beta equilibria are discussed for this proposed magnetic field diagnostic

ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction

Science.gov (United States)

Aganj, Iman; Lenglet, Christophe; Sapiro, Guillermo

2015-01-01

By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data. PMID:20879302

Improved streaming analysis technique: spherical harmonics expansion of albedo data

International Nuclear Information System (INIS)

Albert, T.E.; Simmons, G.L.

1979-01-01

An improved albedo scattering technique was implemented with a three-dimensional Monte Carlo transport code for use in analyzing radiation streaming problems. The improvement was based on a shifted spherical Harmonics expansion of the doubly differential albedo data base. The result of the improvement was a factor of 3 to 10 reduction in data storage requirements and approximately a factor of 3 to 6 increase in computational speed. Comparisons of results obtained using the technique with measurements are shown for neutron streaming in one- and two-legged square concrete ducts

Spherical harmonics analysis of surface density fluctuations of spherical ionic SDS and nonionic C12E8 micelles: A molecular dynamics study.

Science.gov (United States)

Yoshii, Noriyuki; Nimura, Yuki; Fujimoto, Kazushi; Okazaki, Susumu

2017-07-21

The surface structure and its fluctuation of spherical micelles were investigated using a series of density correlation functions newly defined by spherical harmonics and Legendre polynomials based on the molecular dynamics calculations. To investigate the influence of head-group charges on the micelle surface structure, ionic sodium dodecyl sulfate and nonionic octaethyleneglycol monododecylether (C 12 E 8 ) micelles were investigated as model systems. Large-scale density fluctuations were observed for both micelles in the calculated surface static structure factor. The area compressibility of the micelle surface evaluated by the surface static structure factor was tens-of-times larger than a typical value of a lipid membrane surface. The structural relaxation time, which was evaluated from the surface intermediate scattering function, indicates that the relaxation mechanism of the long-range surface structure can be well described by the hydrostatic approximation. The density fluctuation on the two-dimensional micelle surface has similar characteristics to that of three-dimensional fluids near the critical point.

Spherical Harmonics Reveal Standing EEG Waves and Long-Range Neural Synchronization during Non-REM Sleep.

Science.gov (United States)

Sivakumar, Siddharth S; Namath, Amalia G; Galán, Roberto F

2016-01-01

Previous work from our lab has demonstrated how the connectivity of brain circuits constrains the repertoire of activity patterns that those circuits can display. Specifically, we have shown that the principal components of spontaneous neural activity are uniquely determined by the underlying circuit connections, and that although the principal components do not uniquely resolve the circuit structure, they do reveal important features about it. Expanding upon this framework on a larger scale of neural dynamics, we have analyzed EEG data recorded with the standard 10-20 electrode system from 41 neurologically normal children and adolescents during stage 2, non-REM sleep. We show that the principal components of EEG spindles, or sigma waves (10-16 Hz), reveal non-propagating, standing waves in the form of spherical harmonics. We mathematically demonstrate that standing EEG waves exist when the spatial covariance and the Laplacian operator on the head's surface commute. This in turn implies that the covariance between two EEG channels decreases as the inverse of their relative distance; a relationship that we corroborate with empirical data. Using volume conduction theory, we then demonstrate that superficial current sources are more synchronized at larger distances, and determine the characteristic length of large-scale neural synchronization as 1.31 times the head radius, on average. Moreover, consistent with the hypothesis that EEG spindles are driven by thalamo-cortical rather than cortico-cortical loops, we also show that 8 additional patients with hypoplasia or complete agenesis of the corpus callosum, i.e., with deficient or no connectivity between cortical hemispheres, similarly exhibit standing EEG waves in the form of spherical harmonics. We conclude that spherical harmonics are a hallmark of spontaneous, large-scale synchronization of neural activity in the brain, which are associated with unconscious, light sleep. The analogy with spherical harmonics in

A review of recent advances in the spherical harmonics expansion method for semiconductor device simulation.

Science.gov (United States)

Rupp, K; Jungemann, C; Hong, S-M; Bina, M; Grasser, T; Jüngel, A

The Boltzmann transport equation is commonly considered to be the best semi-classical description of carrier transport in semiconductors, providing precise information about the distribution of carriers with respect to time (one dimension), location (three dimensions), and momentum (three dimensions). However, numerical solutions for the seven-dimensional carrier distribution functions are very demanding. The most common solution approach is the stochastic Monte Carlo method, because the gigabytes of memory requirements of deterministic direct solution approaches has not been available until recently. As a remedy, the higher accuracy provided by solutions of the Boltzmann transport equation is often exchanged for lower computational expense by using simpler models based on macroscopic quantities such as carrier density and mean carrier velocity. Recent developments for the deterministic spherical harmonics expansion method have reduced the computational cost for solving the Boltzmann transport equation, enabling the computation of carrier distribution functions even for spatially three-dimensional device simulations within minutes to hours. We summarize recent progress for the spherical harmonics expansion method and show that small currents, reasonable execution times, and rare events such as low-frequency noise, which are all hard or even impossible to simulate with the established Monte Carlo method, can be handled in a straight-forward manner. The applicability of the method for important practical applications is demonstrated for noise simulation, small-signal analysis, hot-carrier degradation, and avalanche breakdown.

Extended Finite Element Method with Simplified Spherical Harmonics Approximation for the Forward Model of Optical Molecular Imaging

Directory of Open Access Journals (Sweden)

Wei Li

2012-01-01

Full Text Available An extended finite element method (XFEM for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SPN. In XFEM scheme of SPN equations, the signed distance function is employed to accurately represent the internal tissue boundary, and then it is used to construct the enriched basis function of the finite element scheme. Therefore, the finite element calculation can be carried out without the time-consuming internal boundary mesh generation. Moreover, the required overly fine mesh conforming to the complex tissue boundary which leads to excess time cost can be avoided. XFEM conveniences its application to tissues with complex internal structure and improves the computational efficiency. Phantom and digital mouse experiments were carried out to validate the efficiency of the proposed method. Compared with standard finite element method and classical Monte Carlo (MC method, the validation results show the merits and potential of the XFEM for optical imaging.

Adaptive tree multigrids and simplified spherical harmonics approximation in deterministic neutral and charged particle transport

International Nuclear Information System (INIS)

Kotiluoto, P.

2007-05-01

A new deterministic three-dimensional neutral and charged particle transport code, MultiTrans, has been developed. In the novel approach, the adaptive tree multigrid technique is used in conjunction with simplified spherical harmonics approximation of the Boltzmann transport equation. The development of the new radiation transport code started in the framework of the Finnish boron neutron capture therapy (BNCT) project. Since the application of the MultiTrans code to BNCT dose planning problems, the testing and development of the MultiTrans code has continued in conventional radiotherapy and reactor physics applications. In this thesis, an overview of different numerical radiation transport methods is first given. Special features of the simplified spherical harmonics method and the adaptive tree multigrid technique are then reviewed. The usefulness of the new MultiTrans code has been indicated by verifying and validating the code performance for different types of neutral and charged particle transport problems, reported in separate publications. (orig.)

On spherical harmonic representation of transient waves in dispersive media

International Nuclear Information System (INIS)

Borisov, Victor V

2003-01-01

Axisymmetric transient solutions to the inhomogeneous telegraph equation are constructed in terms of spherical harmonics. Explicit solutions of the initial-value problem are derived in the spacetime domain by means of the Smirnov method of incomplete separation of variables and the Riemann formula. The corresponding Riemann function is constructed with the help of the Olevsky theorem. Solutions for some source distributions on a sphere expanding with a velocity greater than the wavefront velocity are obtained. This allows an analogous solution in the case of a circle belonging to a sphere expanding with the wavefront velocity to be written at once. Application of the scalar solution to a description of electromagnetic waves is also discussed

Data Assimilation and Adjusted Spherical Harmonic Model of VTEC Map over Thailand

Science.gov (United States)

Klinngam, Somjai; Maruyama, Takashi; Tsugawa, Takuya; Ishii, Mamoru; Supnithi, Pornchai; Chiablaem, Athiwat

2016-07-01

The global navigation satellite system (GNSS) and high frequency (HF) communication are vulnerable to the ionospheric irregularities, especially when the signal travels through the low-latitude region and around the magnetic equator known as equatorial ionization anomaly (EIA) region. In order to study the ionospheric effects to the communications performance in this region, the regional map of the observed total electron content (TEC) can show the characteristic and irregularities of the ionosphere. In this work, we develop the two-dimensional (2D) map of vertical TEC (VTEC) over Thailand using the adjusted spherical harmonic model (ASHM) and the data assimilation technique. We calculate the VTEC from the receiver independent exchange (RINEX) files recorded by the dual-frequency global positioning system (GPS) receivers on July 8th, 2012 (quiet day) at 12 stations around Thailand: 0° to 25°E and 95°N to 110°N. These stations are managed by Department of Public Works and Town & Country Planning (DPT), Thailand, and the South East Asia Low-latitude ionospheric Network (SEALION) project operated by National Institute of Information and Communications Technology (NICT), Japan, and King Mongkut's Institute of Technology Ladkrabang (KMITL). We compute the median observed VTEC (OBS-VTEC) in the grids with the spatial resolution of 2.5°x5° in latitude and longitude and time resolution of 2 hours. We assimilate the OBS-VTEC with the estimated VTEC from the International Reference Ionosphere model (IRI-VTEC) as well as the ionosphere map exchange (IONEX) files provided by the International GNSS Service (IGS-VTEC). The results show that the estimation of the 15-degree ASHM can be improved when both of IRI-VTEC and IGS-VTEC are weighted by the latitude-dependent factors before assimilating with the OBS-VTEC. However, the IRI-VTEC assimilation can improve the ASHM estimation more than the IGS-VTEC assimilation. Acknowledgment: This work is partially funded by the

The DANTE Boltzmann transport solver: An unstructured mesh, 3-D, spherical harmonics algorithm compatible with parallel computer architectures

International Nuclear Information System (INIS)

McGhee, J.M.; Roberts, R.M.; Morel, J.E.

1997-01-01

A spherical harmonics research code (DANTE) has been developed which is compatible with parallel computer architectures. DANTE provides 3-D, multi-material, deterministic, transport capabilities using an arbitrary finite element mesh. The linearized Boltzmann transport equation is solved in a second order self-adjoint form utilizing a Galerkin finite element spatial differencing scheme. The core solver utilizes a preconditioned conjugate gradient algorithm. Other distinguishing features of the code include options for discrete-ordinates and simplified spherical harmonics angular differencing, an exact Marshak boundary treatment for arbitrarily oriented boundary faces, in-line matrix construction techniques to minimize memory consumption, and an effective diffusion based preconditioner for scattering dominated problems. Algorithm efficiency is demonstrated for a massively parallel SIMD architecture (CM-5), and compatibility with MPP multiprocessor platforms or workstation clusters is anticipated

Convergence and divergence in spherical harmonic series of the gravitational field generated by high-resolution planetary topography—A case study for the Moon

Science.gov (United States)

Hirt, Christian; Kuhn, Michael

2017-08-01

Theoretically, spherical harmonic (SH) series expansions of the external gravitational potential are guaranteed to converge outside the Brillouin sphere enclosing all field-generating masses. Inside that sphere, the series may be convergent or may be divergent. The series convergence behavior is a highly unstable quantity that is little studied for high-resolution mass distributions. Here we shed light on the behavior of SH series expansions of the gravitational potential of the Moon. We present a set of systematic numerical experiments where the gravity field generated by the topographic masses is forward-modeled in spherical harmonics and with numerical integration techniques at various heights and different levels of resolution, increasing from harmonic degree 90 to 2160 ( 61 to 2.5 km scales). The numerical integration is free from any divergence issues and therefore suitable to reliably assess convergence versus divergence of the SH series. Our experiments provide unprecedented detailed insights into the divergence issue. We show that the SH gravity field of degree-180 topography is convergent anywhere in free space. When the resolution of the topographic mass model is increased to degree 360, divergence starts to affect very high degree gravity signals over regions deep inside the Brillouin sphere. For degree 2160 topography/gravity models, severe divergence (with several 1000 mGal amplitudes) prohibits accurate gravity modeling over most of the topography. As a key result, we formulate a new hypothesis to predict divergence: if the potential degree variances show a minimum, then the SH series expansions diverge somewhere inside the Brillouin sphere and modeling of the internal potential becomes relevant.

Solution of multigroup transport equation in x-y-z geometry by the spherical harmonics method using finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Kikuchi, Hirohiko; Tsutsuguchi, Ken

1993-01-01

A neutron multigroup transport equation in x-y-z geometry is solved by the spherical harmonics method using finite Fourier transformation. Using the first term of the Fourier series for the space variables of spherical harmonics moments, three-point finite difference like equations are derived for x-, y- and z-axis directions, which are more consistent and accurate than those derived using the usual finite difference approximation, and these equations are solved by the iteration method in each axis direction alternatively. A method to find an optimum acceleration factor for this inner iteration is described. It is shown in the numerical examples that the present method gives higher accuracy with less mesh points that the usual finite difference method. (author)

The use of the asymptotic expansion to speed up the computation of a series of spherical harmonics

NARCIS (Netherlands)

de Munck, J.C.; de Munck, J.C.; Hämäläinen, M.S.; Peters, M.J.

1991-01-01

When a function is expressed as an infinite series of spherical harmonics the convergence can be accelerated by subtracting its asymptotic expansion and adding it in analytically closed form. In the present article this technique is applied to two biophysical cases: to the potential distribution in

The solution of the multigroup neutron transport equation using spherical harmonics

International Nuclear Information System (INIS)

Fletcher, K.

1981-01-01

A solution of the multi-group neutron transport equation in up to three space dimensions is presented. The flux is expanded in a series of unnormalised spherical harmonics. Using the various recurrence formulae a linked set of first order differential equations is obtained for the moments psisup(g)sub(lm)(r), γsup(g)sub(lm)(r). Terms with odd l are eliminated resulting in a second order system which is solved by two methods. The first is a finite difference formulation using an iterative procedure, secondly, in XYZ and XY geometry a finite element solution is given. Results for a test problem using both methods are exhibited and compared. (orig./RW) [de

Frequency-domain optical tomographic image reconstruction algorithm with the simplified spherical harmonics (SP3) light propagation model.

Science.gov (United States)

Kim, Hyun Keol; Montejo, Ludguier D; Jia, Jingfei; Hielscher, Andreas H

2017-06-01

We introduce here the finite volume formulation of the frequency-domain simplified spherical harmonics model with n -th order absorption coefficients (FD-SP N ) that approximates the frequency-domain equation of radiative transfer (FD-ERT). We then present the FD-SP N based reconstruction algorithm that recovers absorption and scattering coefficients in biological tissue. The FD-SP N model with 3 rd order absorption coefficient (i.e., FD-SP 3 ) is used as a forward model to solve the inverse problem. The FD-SP 3 is discretized with a node-centered finite volume scheme and solved with a restarted generalized minimum residual (GMRES) algorithm. The absorption and scattering coefficients are retrieved using a limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm. Finally, the forward and inverse algorithms are evaluated using numerical phantoms with optical properties and size that mimic small-volume tissue such as finger joints and small animals. The forward results show that the FD-SP 3 model approximates the FD-ERT (S 12 ) solution within relatively high accuracy; the average error in the phase (<3.7%) and the amplitude (<7.1%) of the partial current at the boundary are reported. From the inverse results we find that the absorption and scattering coefficient maps are more accurately reconstructed with the SP 3 model than those with the SP 1 model. Therefore, this work shows that the FD-SP 3 is an efficient model for optical tomographic imaging of small-volume media with non-diffuse properties both in terms of computational time and accuracy as it requires significantly lower CPU time than the FD-ERT (S 12 ) and also it is more accurate than the FD-SP 1 .

Spherical Dunkl-monogenics and a factorization of the Dunkl-Laplacian

International Nuclear Information System (INIS)

Fei Minggang; Cerejeiras, Paula; Kaehler, Uwe

2010-01-01

In this paper, we consider and study a factorization of the Dunkl-Laplacian in terms of spherical coordinates. This allows for the construction of a direct sum decomposition of spherical Dunkl-harmonics. By explicit representation in spherical coordinates of Dunkl-harmonics, one obtains explicit projection operators from Dunkl-harmonics to inner (resp. outer) Dunkl-monogenics. Concrete examples of spherical Dunkl-monogenics will be given at the end.

A theory of frequency domain invariants: spherical harmonic identities for BRDF/lighting transfer and image consistency.

Science.gov (United States)

Mahajan, Dhruv; Ramamoorthi, Ravi; Curless, Brian

2008-02-01

This paper develops a theory of frequency domain invariants in computer vision. We derive novel identities using spherical harmonics, which are the angular frequency domain analog to common spatial domain invariants such as reflectance ratios. These invariants are derived from the spherical harmonic convolution framework for reflection from a curved surface. Our identities apply in a number of canonical cases, including single and multiple images of objects under the same and different lighting conditions. One important case we consider is two different glossy objects in two different lighting environments. For this case, we derive a novel identity, independent of the specific lighting configurations or BRDFs, that allows us to directly estimate the fourth image if the other three are available. The identity can also be used as an invariant to detecttampering in the images. While this paper is primarily theoretical, it has the potential to lay the mathematical foundations for two important practical applications. First, we can develop more general algorithms for inverse rendering problems, which can directly relight and change material properties by transferring the BRDF or lighting from another object or illumination. Second, we can check the consistency of an image, to detect tampering or image splicing.

Tensor-based cortical surface morphometry via weighted spherical harmonic representation.

Science.gov (United States)

Chung, Moo K; Dalton, Kim M; Davidson, Richard J

2008-08-01

We present a new tensor-based morphometric framework that quantifies cortical shape variations using a local area element. The local area element is computed from the Riemannian metric tensors, which are obtained from the smooth functional parametrization of a cortical mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation, which generalizes the traditional SPHARM as a special case. For a specific choice of weights, the weighted-SPHARM is shown to be the least squares approximation to the solution of an isotropic heat diffusion on a unit sphere. The main aims of this paper are to present the weighted-SPHARM and to show how it can be used in the tensor-based morphometry. As an illustration, the methodology has been applied in the problem of detecting abnormal cortical regions in the group of high functioning autistic subjects.

Variable order spherical harmonic expansion scheme for the radiative transport equation using finite elements

International Nuclear Information System (INIS)

Surya Mohan, P.; Tarvainen, Tanja; Schweiger, Martin; Pulkkinen, Aki; Arridge, Simon R.

2011-01-01

Highlights: → We developed a variable order global basis scheme to solve light transport in 3D. → Based on finite elements, the method can be applied to a wide class of geometries. → It is computationally cheap when compared to the fixed order scheme. → Comparisons with local basis method and other models demonstrate its accuracy. → Addresses problems encountered n modeling of light transport in human brain. - Abstract: We propose the P N approximation based on a finite element framework for solving the radiative transport equation with optical tomography as the primary application area. The key idea is to employ a variable order spherical harmonic expansion for angular discretization based on the proximity to the source and the local scattering coefficient. The proposed scheme is shown to be computationally efficient compared to employing homogeneously high orders of expansion everywhere in the domain. In addition the numerical method is shown to accurately describe the void regions encountered in the forward modeling of real-life specimens such as infant brains. The accuracy of the method is demonstrated over three model problems where the P N approximation is compared against Monte Carlo simulations and other state-of-the-art methods.

Fundamentals of spherical array processing

CERN Document Server

Rafaely, Boaz

2015-01-01

This book provides a comprehensive introduction to the theory and practice of spherical microphone arrays. It is written for graduate students, researchers and engineers who work with spherical microphone arrays in a wide range of applications.   The first two chapters provide the reader with the necessary mathematical and physical background, including an introduction to the spherical Fourier transform and the formulation of plane-wave sound fields in the spherical harmonic domain. The third chapter covers the theory of spatial sampling, employed when selecting the positions of microphones to sample sound pressure functions in space. Subsequent chapters present various spherical array configurations, including the popular rigid-sphere-based configuration. Beamforming (spatial filtering) in the spherical harmonics domain, including axis-symmetric beamforming, and the performance measures of directivity index and white noise gain are introduced, and a range of optimal beamformers for spherical arrays, includi...

The relationship between mean anomaly block sizes and spherical harmonic representations. [of earth gravity

Science.gov (United States)

Rapp, R. H.

1977-01-01

The frequently used rule specifying the relationship between a mean gravity anomaly in a block whose side length is theta degrees and a spherical harmonic representation of these data to degree l-bar is examined in light of the smoothing parameter used by Pellinen (1966). It is found that if the smoothing parameter is not considered, mean anomalies computed from potential coefficients can be in error by about 30% of the rms anomaly value. It is suggested that the above mentioned rule should be considered only a crude approximation.

Solutions of transport equation in (X-Y-Z) three-dimensional geometry by finite element method and spherical harmonic expansion

International Nuclear Information System (INIS)

Fernandes, A.; Maiorino, J.R.

1989-01-01

This work presents a method to solve the neutron transport equation in thre space dimensions. The angular flux is aproximated by spherical harmonics and the finite element method is applied to the space component. The program originated by the analytical development is being tested and some results are presented. (author) [pt

All-Sky Interferometry with Spherical Harmonic Transit Telescopes

Energy Technology Data Exchange (ETDEWEB)

Shaw, J.Richard [Canadian Inst. Theor. Astrophys.; Sigurdson, Kris [British Columbia U.; Pen, Ue-Li [Canadian Inst. Theor. Astrophys.; Stebbins, Albert [Fermilab; Sitwell, Michael [British Columbia U.

2013-02-01

In this paper we describe the spherical harmonic transit telescope, a novel formalism for the analysis of transit radio telescopes. This all-sky approach bypasses the curved sky complications of traditional interferometry and so is particularly well suited to the analysis of wide-field radio interferometers. It enables compact and computationally efficient representations of the data and its statistics that allow new ways of approaching important problems like map-making and foreground removal. In particular, we show how it enables the use of the Karhunen-Loeve transform as a highly effective foreground filter, suppressing realistic foreground residuals for our fiducial example by at least a factor twenty below the 21cm signal even in highly contaminated regions of the sky. This is despite the presence of the angle-frequency mode mixing inherent in real-world instruments with frequency-dependent beams. We show, using Fisher forecasting, that foreground cleaning has little effect on power spectrum constraints compared to hypothetical foreground-free measurements. Beyond providing a natural real-world data analysis framework for 21cm telescopes now under construction and future experiments, this formalism allows accurate power spectrum forecasts to be made that include the interplay of design constraints and realistic experimental systematics with twenty-first century 21cm science.

Comparison of Large eddy dynamo simulation using dynamic sub-grid scale (SGS) model with a fully resolved direct simulation in a rotating spherical shell

Science.gov (United States)

Matsui, H.; Buffett, B. A.

2017-12-01

The flow in the Earth's outer core is expected to have vast length scale from the geometry of the outer core to the thickness of the boundary layer. Because of the limitation of the spatial resolution in the numerical simulations, sub-grid scale (SGS) modeling is required to model the effects of the unresolved field on the large-scale fields. We model the effects of sub-grid scale flow and magnetic field using a dynamic scale similarity model. Four terms are introduced for the momentum flux, heat flux, Lorentz force and magnetic induction. The model was previously used in the convection-driven dynamo in a rotating plane layer and spherical shell using the Finite Element Methods. In the present study, we perform large eddy simulations (LES) using the dynamic scale similarity model. The scale similarity model is implement in Calypso, which is a numerical dynamo model using spherical harmonics expansion. To obtain the SGS terms, the spatial filtering in the horizontal directions is done by taking the convolution of a Gaussian filter expressed in terms of a spherical harmonic expansion, following Jekeli (1981). A Gaussian field is also applied in the radial direction. To verify the present model, we perform a fully resolved direct numerical simulation (DNS) with the truncation of the spherical harmonics L = 255 as a reference. And, we perform unresolved DNS and LES with SGS model on coarser resolution (L= 127, 84, and 63) using the same control parameter as the resolved DNS. We will discuss the verification results by comparison among these simulations and role of small scale fields to large scale fields through the role of the SGS terms in LES.

Spherical harmonics solutions of multi-dimensional neutron transport equation by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke

1977-01-01

A method of solution of a monoenergetic neutron transport equation in P sub(L) approximation is presented for x-y and x-y-z geometries using the finite Fourier transformation. A reactor system is assumed to consist of multiregions in each of which the nuclear cross sections are spatially constant. Since the unknown functions of this method are the spherical harmonics components of the neutron angular flux at the material boundaries alone, the three- and two-dimensional equations are reduced to two- and one-dimensional equations, respectively. The present approach therefore gives fewer unknowns than in the usual series expansion method or in the finite difference method. Some numerical examples are shown for the criticality problem. (auth.)

Interpreting angular momentum transfer between electromagnetic multipoles using vector spherical harmonics.

Science.gov (United States)

Grinter, Roger; Jones, Garth A

2018-02-01

The transfer of angular momentum between a quadrupole emitter and a dipole acceptor is investigated theoretically. Vector spherical harmonics are used to describe the angular part of the field of the mediating photon. Analytical results are presented for predicting angular momentum transfer between the emitter and absorber within a quantum electrodynamical framework. We interpret the allowability of such a process, which appears to violate conservation of angular momentum, in terms of the breakdown of the isotropy of space at the point of photon absorption (detection). That is, collapse of the wavefunction results in loss of all angular momentum information. This is consistent with Noether's Theorem and demystifies some common misconceptions about the nature of the photon. The results have implications for interpreting the detection of photons from multipole sources and offers insight into limits on information that can be extracted from quantum measurements in photonic systems.

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Compressible convection in a rotating spherical shell. II. A linear anelastic model

International Nuclear Information System (INIS)

Glatzmaier, G.A.; Gilman, P.A.

1981-01-01

We study the onset of convection for a compressible fluid in a rotating spherical shell via linear anelastic fluid equations for a depth of 40% of the radius, constant kinematic viscosity and thermometric diffusivity, Taylor numbers up to 10 5 , and density stratifications up to seven e-folds across the zone. The perturbations are expanded in spherical harmonics, and the radially dependent equations are solved with a Newton-Raphson relaxation method

Spherical harmonics and energy polynomial solution of the Boltzmann equation for neutrons, 1

International Nuclear Information System (INIS)

Toledo, P.S. de

1974-01-01

The approximate solution of the source-free energy-dependent Boltzmann transport equation for neutrons in plane geometry and isotropic scattering case was given by Leonard and Ferziger using a truncated development in a series of energy-polynomials for the energy dependent neutron flux and solving exactly for the angular dependence. The presence in the general solution of eigenfunctions belonging to a continuous spectrum gives rise to difficult analytical problems in the application of their method even to simple problems. To avoid such difficulties, the angular dependence is treated by a spherical harmonics method and a general solution of the energy-dependent transport equation in plane geometry and isotropic scattering is obtained, in spite of the appearance of matrices as argument of the angular polynomials [pt

Exploration of high harmonic fast wave heating on the National Spherical Torus Experiment

International Nuclear Information System (INIS)

Wilson, J.R.; Bell, R.E.; Bernabei, S.; Bitter, M.; Gates, D.; Hosea, J.; Le Blanc, B.; Medley, S.; Menard, J.; Mueller, D.; Ono, M.; Phillips, C.K.; Rosenberg, A.; Bonoli, P.; Mau, T.K.; Pinsker, R.I.; Raman, R.; Ryan, P.; Swain, D.; Wilgen, J.

2003-01-01

High harmonic fast wave (HHFW) heating has been proposed as a particularly attractive means for plasma heating and current drive in the high beta plasmas that are achievable in spherical torus (ST) devices. The National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, S. Neumeyer et al., in Proceedings of the 18th IEEE/NPSS Symposium on Fusion Engineering, Albuquerque, 1999 (IEEE, Piscataway, NJ, 1999), p. 53] is such a device. An rf heating system has been installed on the NSTX to explore the physics of HHFW heating, current drive via rf waves and for use as a tool to demonstrate the attractiveness of the ST concept as a fusion device. To date, experiments have demonstrated many of the theoretical predictions for HHFW. In particular, strong wave absorption on electrons over a wide range of plasma parameters and wave parallel phase velocities, wave acceleration of energetic ions, and indications of current drive for directed wave spectra have been observed. In addition HHFW heating has been used to explore the energy transport properties of NSTX plasmas, to create H-mode discharges with a large fraction of bootstrap current and to control the plasma current profile during the early stages of the discharge

Exploration of High Harmonic Fast Wave Heating on the National Spherical Torus Experiment

International Nuclear Information System (INIS)

Wilson, J.R.; Bell, R.E.; Bernabei, S.; Bitter, M.; Bonoli, P.; Gates, D.; Hosea, J.; LeBlanc, B.; Mau, T.K.; Medley, S.; Menard, J.; Mueller, D.; Ono, M.; Phillips, C.K.; Pinsker, R.I.; Raman, R.; Rosenberg, A.; Ryan, P.; Sabbagh, S.; Stutman, D.; Swain, D.; Takase, Y.; Wilgen, J.

2003-01-01

High Harmonic Fast Wave (HHFW) heating has been proposed as a particularly attractive means for plasma heating and current drive in the high-beta plasmas that are achievable in spherical torus (ST) devices. The National Spherical Torus Experiment (NSTX) [Ono, M., Kaye, S.M., Neumeyer, S., et al., Proceedings, 18th IEEE/NPSS Symposium on Fusion Engineering, Albuquerque, 1999, (IEEE, Piscataway, NJ (1999), p. 53.)] is such a device. An radio-frequency (rf) heating system has been installed on NSTX to explore the physics of HHFW heating, current drive via rf waves and for use as a tool to demonstrate the attractiveness of the ST concept as a fusion device. To date, experiments have demonstrated many of the theoretical predictions for HHFW. In particular, strong wave absorption on electrons over a wide range of plasma parameters and wave parallel phase velocities, wave acceleration of energetic ions, and indications of current drive for directed wave spectra have been observed. In addition HHFW heating has been used to explore the energy transport properties of NSTX plasmas, to create H-mode (high-confinement mode) discharges with a large fraction of bootstrap current and to control the plasma current profile during the early stages of the discharge

The third post-Newtonian gravitational wave polarizations and associated spherical harmonic modes for inspiralling compact binaries in quasi-circular orbits

International Nuclear Information System (INIS)

Blanchet, Luc; Faye, Guillaume; Iyer, Bala R; Sinha, Siddhartha

2008-01-01

The gravitational waveform (GWF) generated by inspiralling compact binaries moving in quasi-circular orbits is computed at the third post-Newtonian (3PN) approximation to general relativity. Our motivation is two-fold: (i) to provide accurate templates for the data analysis of gravitational wave inspiral signals in laser interferometric detectors; (ii) to provide the associated spin-weighted spherical harmonic decomposition to facilitate comparison and match of the high post-Newtonian prediction for the inspiral waveform to the numerically-generated waveforms for the merger and ringdown. This extension of the GWF by half a PN order (with respect to previous work at 2.5PN order) is based on the algorithm of the multipolar post-Minkowskian formalism, and mandates the computation of the relations between the radiative, canonical and source multipole moments for general sources at 3PN order. We also obtain the 3PN extension of the source multipole moments in the case of compact binaries, and compute the contributions of hereditary terms (tails, tails-of-tails and memory integrals) up to 3PN order. The end results are given for both the complete plus and cross polarizations and the separate spin-weighted spherical harmonic modes

Efficient Compression of Far Field Matrices in Multipole Algorithms based on Spherical Harmonics and Radiating Modes

Directory of Open Access Journals (Sweden)

A. Schroeder

2012-09-01

Full Text Available This paper proposes a compression of far field matrices in the fast multipole method and its multilevel extension for electromagnetic problems. The compression is based on a spherical harmonic representation of radiation patterns in conjunction with a radiating mode expression of the surface current. The method is applied to study near field effects and the far field of an antenna placed on a ship surface. Furthermore, the electromagnetic scattering of an electrically large plate is investigated. It is demonstrated, that the proposed technique leads to a significant memory saving, making multipole algorithms even more efficient without compromising the accuracy.

Periphony-Lattice Mixed-Order Ambisonic Scheme for Spherical Microphone Arrays

DEFF Research Database (Denmark)

Chang, Jiho; Marschall, Marton

2018-01-01

to performance that is independent of the incident direction of the sound waves. On the other hand, mixed-order ambisonic (MOA) schemes that select an appropriate subset of spherical harmonics can improve the performance for horizontal directions at the expense of other directions. This paper proposes an MOA......Most methods for sound field reconstruction and spherical beamforming with spherical microphone arrays are mathematically based on the spherical harmonics expansion. In many cases, this expansion is truncated at a certain order as in higher order ambisonics (HOA). This truncation leads...

Light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities based on hybrid simplified spherical harmonics with radiosity model.

Science.gov (United States)

Yang, Defu; Chen, Xueli; Peng, Zhen; Wang, Xiaorui; Ripoll, Jorge; Wang, Jing; Liang, Jimin

2013-01-01

Modeling light propagation in the whole body is essential and necessary for optical imaging. However, non-scattering, low-scattering and high absorption regions commonly exist in biological tissues, which lead to inaccuracy of the existing light transport models. In this paper, a novel hybrid light transport model that couples the simplified spherical harmonics approximation (SPN) with the radiosity theory (HSRM) was presented, to accurately describe light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities. In the model, the radiosity theory was used to characterize the light transport in non-scattering regions and the SPN was employed to handle the scattering problems, including subsets of low-scattering and high absorption. A Neumann source constructed by the light transport in the non-scattering region and formed at the interface between the non-scattering and scattering regions was superposed into the original light source, to couple the SPN with the radiosity theory. The accuracy and effectiveness of the HSRM was first verified with both regular and digital mouse model based simulations and a physical phantom based experiment. The feasibility and applicability of the HSRM was then investigated by a broad range of optical properties. Lastly, the influence of depth of the light source on the model was also discussed. Primary results showed that the proposed model provided high performance for light transport in turbid media with non-scattering, low-scattering and high absorption heterogeneities.

Meridional-Flow Measurements from 15 Years of GONG Spherical-Harmonic Time Series

International Nuclear Information System (INIS)

Kholikov, S; Hernandez, I Gonzalez; Hill, F; Leibacher, J

2011-01-01

We present results of meridional-flow measurements for 1995-2009, using travel-time differences from velocity images reconstructed using GONG spherical harmonic (SH) coefficients after applying phase-velocity and low-m filters. This filtering technique increases the signal-to-noise ratio and thus extends travel-time measurements to relatively high latitudes and deep into the convection zone. Preliminary analyses shows a strong one-year periodicity presumably due to solar pole misalignment and B 0 -angle artifacts, which makes it difficult to see underlying temporal variations. Removing a simple one-year-period sine wave fit reveals long-term temporal variations of the flow on top of this yearly periodicity. High-latitude measurements are affected more stronger by foreshortening and B 0 -angle artifacts. We analyze different B 0 -angle intervals separately, so in each hemisphere better high-latitude visibility comes six months apart. This approach suggests why at high latitudes travel-time measurements of meridional flow shows a tendency to change sign instead of continuing towards the poles.

An elementary treatise on Fourier's series and spherical, cylindrical, and ellipsoidal harmonics, with applications to problems in mathematical

CERN Document Server

Byerly, William Elwood

2003-01-01

Originally published over a century ago, this work remains among the most useful and practical expositions of Fourier's series, and spherical, cylindrical, and ellipsoidal harmonics. The subsequent growth of science into a diverse range of specialties has enhanced the value of this classic, whose thorough, basic treatment presents material that is assumed in many other studies but seldom available in such concise form. The development of functions, series, and their differential equations receives detailed explanations, and throughout the text, theory is applied to practical problems, with the

A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging

International Nuclear Information System (INIS)

Lu Yujie; Zhu Banghe; Rasmussen, John C; Sevick-Muraca, Eva M; Shen Haiou; Wang Ge

2010-01-01

Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N ) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.

Probabilistic Harmonic Modeling of Wind Power Plants

DEFF Research Database (Denmark)

Guest, Emerson; Jensen, Kim H.; Rasmussen, Tonny Wederberg

2017-01-01

A probabilistic sequence domain (SD) harmonic model of a grid-connected voltage-source converter is used to estimate harmonic emissions in a wind power plant (WPP) comprised of Type-IV wind turbines. The SD representation naturally partitioned converter generated voltage harmonics into those...... with deterministic phase and those with probabilistic phase. A case study performed on a string of ten 3MW, Type-IV wind turbines implemented in PSCAD was used to verify the probabilistic SD harmonic model. The probabilistic SD harmonic model can be employed in the planning phase of WPP projects to assess harmonic...

Numerical evolutions of fields on the 2-sphere using a spectral method based on spin-weighted spherical harmonics

International Nuclear Information System (INIS)

Beyer, Florian; Daszuta, Boris; Frauendiener, Jörg; Whale, Ben

2014-01-01

Many applications in science call for the numerical simulation of systems on manifolds with spherical topology. Through the use of integer spin-weighted spherical harmonics, we present a method which allows for the implementation of arbitrary tensorial evolution equations. Our method combines two numerical techniques that were originally developed with different applications in mind. The first is Huffenberger and Wandelt’s spectral decomposition algorithm to perform the mapping from physical to spectral space. The second is the application of Luscombe and Luban’s method, to convert numerically divergent linear recursions into stable nonlinear recursions, to the calculation of reduced Wigner d-functions. We give a detailed discussion of the theory and numerical implementation of our algorithm. The properties of our method are investigated by solving the scalar and vectorial advection equation on the sphere, as well as the 2 + 1 Maxwell equations on a deformed sphere. (paper)

Harmonic Interaction Analysis in Grid Connected Converter using Harmonic State Space (HSS) Modeling

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

-model, are introduced to analyze these problems. However, it is found that Linear Time Invariant (LTI) base model analysis makes it difficult to analyze these phenomenon because of time varying system operation trajectories, varying output impedance seen by grid connected systems and neglected switching component......An increasing number of power electronics based Distributed Generation (DG) systems and loads generate coupled harmonic as well as non-characteristic harmonic with each other. Several methods like impedance based analysis, which is derived from conventional small signal- and average...... during the modeling process. This paper investigates grid connected converter by means of Harmonic State Space (HSS) small signal model, which is modeled from Linear Time varying Periodically (LTP) system. Further, a grid connected converter harmonic matrix is investigated to analyze the harmonic...

Coarse-mesh rebalance methods compatible with the spherical harmonic fictitious source in neutron transport calculations

International Nuclear Information System (INIS)

Miller, W.F. Jr.

1975-10-01

The coarse-mesh rebalance method, based on neutron conservation, is used in discrete ordinates neutron transport codes to accelerate convergence of the within-group scattering source. Though very powerful for this application, the method is ineffective in accelerating the iteration on the discrete-ordinates-to-spherical-harmonics fictitious sources used for ray-effect elimination. This is largely because this source makes a minimum contribution to the neutron balance equation. The traditional rebalance approach is derived in a variational framework and compared with new rebalance approaches tailored to be compatible with the fictitious source. The new approaches are compared numerically to determine their relative advantages. It is concluded that there is little incentive to use the new methods. (3 tables, 5 figures)

Potential for protein surface shape analysis using spherical harmonics and 3D Zernike descriptors.

Science.gov (United States)

Venkatraman, Vishwesh; Sael, Lee; Kihara, Daisuke

2009-01-01

With structure databases expanding at a rapid rate, the task at hand is to provide reliable clues to their molecular function and to be able to do so on a large scale. This, however, requires suitable encodings of the molecular structure which are amenable to fast screening. To this end, moment-based representations provide a compact and nonredundant description of molecular shape and other associated properties. In this article, we present an overview of some commonly used representations with specific focus on two schemes namely spherical harmonics and their extension, the 3D Zernike descriptors. Key features and differences of the two are reviewed and selected applications are highlighted. We further discuss recent advances covering aspects of shape and property-based comparison at both global and local levels and demonstrate their applicability through some of our studies.

The spherical-harmonics representation for the interaction between diatomic molecules: The general case and applications to COsbnd CO and COsbnd HF

Science.gov (United States)

Barreto, Patricia R. P.; Cruz, Ana Claudia P. S.; Barreto, Rodrigo L. P.; Palazzetti, Federico; Albernaz, Alessandra F.; Lombardi, Andrea; Maciel, Glauciete S.; Aquilanti, Vincenzo

2017-07-01

The spherical-harmonics expansion is a mathematically rigorous procedure and a powerful tool for the representation of potential energy surfaces of interacting molecular systems, determining their spectroscopic and dynamical properties, specifically in van der Waals clusters, with applications also to classical and quantum molecular dynamics simulations. The technique consists in the construction (by ab initio or semiempirical methods) of the expanded potential interaction up to terms that provide the generation of a number of leading configurations sufficient to account for faithful geometrical representations. This paper reports the full general description of the method of the spherical-harmonics expansion as applied to diatomic-molecule - diatomic-molecule systems of increasing complexity: the presentation of the mathematical background is given for providing both the application to the prototypical cases considered previously (O2sbnd O2, N2sbnd N2, and N2sbnd O2 systems) and the generalization to: (i) the COsbnd CO system, where a characteristic feature is the lower symmetry order with respect to the cases studied before, requiring a larger number of expansion terms necessary to adequately represent the potential energy surface; and (ii) the COsbnd HF system, which exhibits the lowest order of symmetry among this class of aggregates and therefore the highest number of leading configurations.

O1, P1, N2 models of the global ocean tide on an elastic earth plus surface potential and spherical harmonic decompositions for M2, S2, and K1

Science.gov (United States)

Parke, M. E.

1982-01-01

The models of M2, S2, and K1 presented in Parke and Hendershott (1980) are supplemented with models of O1, P1, and N2. The models satisfy specified elevation boundary conditions and are generated by fighting a small number of test functions to island data. Maps are presented of the geocentric tide, the induced free space potential, the induced vertical component of the solid earth tide, and the induced vertical component of the gravitational field for each new component. Maps of the tidal potential seen by an observer fixed to the surface of the solid earth are also presented for all six constituents. Spherical harmonic coefficients up to order four and the rms magnitude of the coefficients to order fifteen are presented for each constituent. The rms magnitudes of the P1 and K1 coefficients normalized by their respective equilibrium amplitudes are compared to determine the effect of the diurnal core resonance.

Harmonic modeling of induction motors

Energy Technology Data Exchange (ETDEWEB)

Pedra, J.; Sainz, L.; Corcoles, F. [Department of Electrical Engineering, ETSEIB-UPC, Av. Diagonal 647, 08028 Barcelona (Spain)

2006-07-15

The paper proposes an induction motor model for the study of harmonic load flow in balanced and unbalanced conditions. The parameters of this model are obtained from motor manufacturer data and the positive- and negative-sequence equivalent circuits of the single- and double-cage models. An approximate harmonic model based on motor manufacturer data only is also proposed. In addition, the paper includes manufacturer data and the calculated parameters of 36 induction motors of different rated powers. This database is used to analyze the proposed models. (author)

A simplified spherical harmonic method for coupled electron-photon transport calculations

International Nuclear Information System (INIS)

Josef, J.A.

1996-12-01

In this thesis we have developed a simplified spherical harmonic method (SP N method) and associated efficient solution techniques for 2-D multigroup electron-photon transport calculations. The SP N method has never before been applied to charged-particle transport. We have performed a first time Fourier analysis of the source iteration scheme and the P 1 diffusion synthetic acceleration (DSA) scheme applied to the 2-D SP N equations. Our theoretical analyses indicate that the source iteration and P 1 DSA schemes are as effective for the 2-D SP N equations as for the 1-D S N equations. Previous analyses have indicated that the P 1 DSA scheme is unstable (with sufficiently forward-peaked scattering and sufficiently small absorption) for the 2-D S N equations, yet is very effective for the 1-D S N equations. In addition, we have applied an angular multigrid acceleration scheme, and computationally demonstrated that it performs as well for the 2-D SP N equations as for the 1-D S N equations. It has previously been shown for 1-D S N calculations that this scheme is much more effective than the DSA scheme when scattering is highly forward-peaked. We have investigated the applicability of the SP N approximation to two different physical classes of problems: satellite electronics shielding from geomagnetically trapped electrons, and electron beam problems. In the space shielding study, the SP N method produced solutions that are accurate within 10% of the benchmark Monte Carlo solutions, and often orders of magnitude faster than Monte Carlo. We have successfully modeled quasi-void problems and have obtained excellent agreement with Monte Carlo. We have observed that the SP N method appears to be too diffusive an approximation for beam problems. This result, however, is in agreement with theoretical expectations

Using Spherical-Harmonics Expansions for Optics Surface Reconstruction from Gradients.

Science.gov (United States)

Solano-Altamirano, Juan Manuel; Vázquez-Otero, Alejandro; Khikhlukha, Danila; Dormido, Raquel; Duro, Natividad

2017-11-30

In this paper, we propose a new algorithm to reconstruct optics surfaces (aka wavefronts) from gradients, defined on a circular domain, by means of the Spherical Harmonics. The experimental results indicate that this algorithm renders the same accuracy, compared to the reconstruction based on classical Zernike polynomials, using a smaller number of polynomial terms, which potentially speeds up the wavefront reconstruction. Additionally, we provide an open-source C++ library, released under the terms of the GNU General Public License version 2 (GPLv2), wherein several polynomial sets are coded. Therefore, this library constitutes a robust software alternative for wavefront reconstruction in a high energy laser field, optical surface reconstruction, and, more generally, in surface reconstruction from gradients. The library is a candidate for being integrated in control systems for optical devices, or similarly to be used in ad hoc simulations. Moreover, it has been developed with flexibility in mind, and, as such, the implementation includes the following features: (i) a mock-up generator of various incident wavefronts, intended to simulate the wavefronts commonly encountered in the field of high-energy lasers production; (ii) runtime selection of the library in charge of performing the algebraic computations; (iii) a profiling mechanism to measure and compare the performance of different steps of the algorithms and/or third-party linear algebra libraries. Finally, the library can be easily extended to include additional dependencies, such as porting the algebraic operations to specific architectures, in order to exploit hardware acceleration features.

Analysis on h-harmonics and Dunkl transforms

CERN Document Server

2015-01-01

As a unique case in this Advanced Courses book series, the authors have jointly written this introduction to h-harmonics and Dunkl transforms. These are extensions of the ordinary spherical harmonics and Fourier transforms, in which the usual Lebesgue measure is replaced by a reflection-invariant weighted measure. The theory, originally introduced by C. Dunkl, has been expanded on by many authors over the last 20 years. These notes provide an overview of what has been developed so far. The first chapter gives a brief recount of the basics of ordinary spherical harmonics and the Fourier transform. The Dunkl operators, the intertwining operators between partial derivatives and the Dunkl operators are introduced and discussed in the second chapter. The next three chapters are devoted to analysis on the sphere, and the final two chapters to the Dunkl transform. The authors’ focus is on the analysis side of both h-harmonics and Dunkl transforms. The need for background knowledge on reflection groups is kept to a...

Spherical Slepian as a new method for ionospheric modeling in arctic region

Science.gov (United States)

Etemadfard, Hossein; Hossainali, Masoud Mashhadi

2016-03-01

From the perspective of the physical, chemical and biological balance in the world, the Arctic has gradually turned into an important region opening ways for new researchers and scientific expeditions. In other words, various researches have been funded in order to study this frozen frontier in details. The current study can be seen in the same milieu where researchers intend to propose a set of new base functions for modeling ionospheric in the Arctic. As such, to optimize the Spherical Harmonic (SH) functions, the spatio-spectral concentration is applied here using the Slepian theory that was developed by Simons. For modeling the ionosphere, six International GNSS Service (IGS) stations located in the northern polar region were taken into account. Two other stations were left out for assessing the accuracy of the proposed model. The adopted GPS data starts at DOY 69 (Day of Year) and ends at DOY 83 (totally 15 successive days) in 2013. Three Spherical Slepian models respectively with the maximal degrees of K=15, 20 & 25 were used. Based on the results, K=15 is the optimum degree for the proposed model. The accuracy and precision of the Slepian model are about 0.1 and 0.05 TECU, respectively (TEC Unit=1016 electron/m2). To understand the advantage of this model, it is compared with polynomial and trigonometric series which are developed using the same set of measurements. The accuracy and precision of trigonometric and polynomial models are at least 4 times worse than the Slepian one.

Harmonic Interaction Analysis in Grid-connected Converter using Harmonic State Space (HSS) Modeling

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede

2017-01-01

research about the harmonic interaction. However, it is found that the Linear Time Invariant (LTI) based model analysis makes it difficult to analyze these phenomena because of the time-varying properties of the power electronic based systems. This paper investigates grid-connected converter by using......An increasing number of power electronic based Distributed Generation (DG) systems and loads generate not only characteristic harmonics but also unexpected harmonics. Several methods like impedance based analysis, which are derived from the conventional average model, are introduced to perform...

Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition

Science.gov (United States)

Volegov, P. L.; Danly, C. R.; Fittinghoff, D.; Geppert-Kleinrath, V.; Grim, G.; Merrill, F. E.; Wilde, C. H.

2017-11-01

Neutron, gamma-ray, and x-ray imaging are important diagnostic tools at the National Ignition Facility (NIF) for measuring the two-dimensional (2D) size and shape of the neutron producing region, for probing the remaining ablator and measuring the extent of the DT plasmas during the stagnation phase of Inertial Confinement Fusion implosions. Due to the difficulty and expense of building these imagers, at most only a few two-dimensional projections images will be available to reconstruct the three-dimensional (3D) sources. In this paper, we present a technique that has been developed for the 3D reconstruction of neutron, gamma-ray, and x-ray sources from a minimal number of 2D projections using spherical harmonics decomposition. We present the detailed algorithms used for this characterization and the results of reconstructed sources from experimental neutron and x-ray data collected at OMEGA and NIF.

Software development and its description for Geoid determination based on Spherical-Cap-Harmonics Modelling using digital-zenith camera and gravimetric measurements hybrid data

Science.gov (United States)

Morozova, K.; Jaeger, R.; Balodis, J.; Kaminskis, J.

2017-10-01

Over several years the Institute of Geodesy and Geoinformatics (GGI) was engaged in the design and development of a digital zenith camera. At the moment the camera developments are finished and tests by field measurements are done. In order to check these data and to use them for geoid model determination DFHRS (Digital Finite element Height reference surface (HRS)) v4.3. software is used. It is based on parametric modelling of the HRS as a continous polynomial surface. The HRS, providing the local Geoid height N, is a necessary geodetic infrastructure for a GNSS-based determination of physcial heights H from ellipsoidal GNSS heights h, by H=h-N. The research and this publication is dealing with the inclusion of the data of observed vertical deflections from digital zenith camera into the mathematical model of the DFHRS approach and software v4.3. A first target was to test out and validate the mathematical model and software, using additionally real data of the above mentioned zenith camera observations of deflections of the vertical. A second concern of the research was to analyze the results and the improvement of the Latvian quasi-geoid computation compared to the previous version HRS computed without zenith camera based deflections of the vertical. The further development of the mathematical model and software concerns the use of spherical-cap-harmonics as the designed carrier function for the DFHRS v.5. It enables - in the sense of the strict integrated geodesy approach, holding also for geodetic network adjustment - both a full gravity field and a geoid and quasi-geoid determination. In addition, it allows the inclusion of gravimetric measurements, together with deflections of the vertical from digital-zenith cameras, and all other types of observations. The theoretical description of the updated version of DFHRS software and methods are discussed in this publication.

Phase coherence of parametric-decay modes during high-harmonic fast-wave heating in the National Spherical Torus Experiment

Energy Technology Data Exchange (ETDEWEB)

Carlsson, J. A., E-mail: carlsson@pppl.gov [Crow Radio and Plasma Science, Princeton, New Jersey 08540 (United States); Wilson, J. R.; Hosea, J. C.; Greenough, N. L.; Perkins, R. J. [Princeton Plasma Physics Laboratory, P.O. Box 451, Princeton, New Jersey 08543-0451 (United States)

2016-06-15

Third-order spectral analysis, in particular, the auto bicoherence, was applied to probe signals from high-harmonic fast-wave heating experiments in the National Spherical Torus Experiment. Strong evidence was found for parametric decay of the 30 MHz radio-frequency (RF) pump wave, with a low-frequency daughter wave at 2.7 MHz, the local majority-ion cyclotron frequency. The primary decay modes have auto bicoherence values around 0.85, very close to the theoretical value of one, which corresponds to total phase coherence with the pump wave. The threshold RF pump power for onset of parametric decay was found to be between 200 kW and 400 kW.

A method for solving the spherical harmonics equations applied for space-energy transport of fast and resonance neutrons

International Nuclear Information System (INIS)

Matausek, M.

1972-01-01

A new proposed method for solving the space-energy dependent spherical harmonics equations represents a methodological contribution to neutron transport theory. The proposed method was applied for solving the problem of spec-energy transport of fast and resonance neutrons in multi-zone, cylindrical y symmetric infinite reactor cell and is related to previously developed procedure for treating the thermal energy region. The advantages of this method are as follows: a unique algorithm was obtained for detailed determination of spatial and energy distribution of neutrons (from thermal to fast) in the reactor cell; these detailed distributions enable more precise calculations of criticality conditions, obtaining adequate multigroup data and better interpretation of experimental data; computing time is rather short

Using Spherical-Harmonics Expansions for Optics Surface Reconstruction from Gradients

Directory of Open Access Journals (Sweden)

Juan Manuel Solano-Altamirano

2017-11-01

Full Text Available In this paper, we propose a new algorithm to reconstruct optics surfaces (aka wavefronts from gradients, defined on a circular domain, by means of the Spherical Harmonics. The experimental results indicate that this algorithm renders the same accuracy, compared to the reconstruction based on classical Zernike polynomials, using a smaller number of polynomial terms, which potentially speeds up the wavefront reconstruction. Additionally, we provide an open-source C++ library, released under the terms of the GNU General Public License version 2 (GPLv2, wherein several polynomial sets are coded. Therefore, this library constitutes a robust software alternative for wavefront reconstruction in a high energy laser field, optical surface reconstruction, and, more generally, in surface reconstruction from gradients. The library is a candidate for being integrated in control systems for optical devices, or similarly to be used in ad hoc simulations. Moreover, it has been developed with flexibility in mind, and, as such, the implementation includes the following features: (i a mock-up generator of various incident wavefronts, intended to simulate the wavefronts commonly encountered in the field of high-energy lasers production; (ii runtime selection of the library in charge of performing the algebraic computations; (iii a profiling mechanism to measure and compare the performance of different steps of the algorithms and/or third-party linear algebra libraries. Finally, the library can be easily extended to include additional dependencies, such as porting the algebraic operations to specific architectures, in order to exploit hardware acceleration features.

Verification of the coupled space-angle adaptivity algorithm for the finite element-spherical harmonics method via the method of manufactured solutions

International Nuclear Information System (INIS)

Park, H.; De Oliveira, C. R. E.

2007-01-01

This paper describes the verification of the recently developed space-angle self-adaptive algorithm for the finite element-spherical harmonics method via the Method of Manufactured Solutions. This method provides a simple, yet robust way for verifying the theoretical properties of the adaptive algorithm and interfaces very well with the underlying second-order, even-parity transport formulation. Simple analytic solutions in both spatial and angular variables are manufactured to assess the theoretical performance of the a posteriori error estimates. The numerical results confirm reliability of the developed space-angle error indicators. (authors)

Spherical Cancer Models in Tumor Biology

Directory of Open Access Journals (Sweden)

Louis-Bastien Weiswald

2015-01-01

Full Text Available Three-dimensional (3D in vitro models have been used in cancer research as an intermediate model between in vitro cancer cell line cultures and in vivo tumor. Spherical cancer models represent major 3D in vitro models that have been described over the past 4 decades. These models have gained popularity in cancer stem cell research using tumorospheres. Thus, it is crucial to define and clarify the different spherical cancer models thus far described. Here, we focus on in vitro multicellular spheres used in cancer research. All these spherelike structures are characterized by their well-rounded shape, the presence of cancer cells, and their capacity to be maintained as free-floating cultures. We propose a rational classification of the four most commonly used spherical cancer models in cancer research based on culture methods for obtaining them and on subsequent differences in sphere biology: the multicellular tumor spheroid model, first described in the early 70s and obtained by culture of cancer cell lines under nonadherent conditions; tumorospheres, a model of cancer stem cell expansion established in a serum-free medium supplemented with growth factors; tissue-derived tumor spheres and organotypic multicellular spheroids, obtained by tumor tissue mechanical dissociation and cutting. In addition, we describe their applications to and interest in cancer research; in particular, we describe their contribution to chemoresistance, radioresistance, tumorigenicity, and invasion and migration studies. Although these models share a common 3D conformation, each displays its own intrinsic properties. Therefore, the most relevant spherical cancer model must be carefully selected, as a function of the study aim and cancer type.

Harmonic current prediction by impedance modeling of grid-tied inverters

DEFF Research Database (Denmark)

Pereira, Heverton A.; Freijedo, Francisco D.; Silva, M. M.

2017-01-01

and harmonic voltage profiles. Results reinforce that impedance models can represent with relatively accuracy the harmonic current emitted by the PV plants at the point of common coupling (PCC). Lastly, a stress test is performed to show how a variation in the harmonic voltage phase angle impacts the PV plant...... impedance models when used in harmonic integration studies. It is aimed to estimate the harmonic current contribution as a function of the background harmonic voltages components. Time domain simulations based on detailed and average models are compared with the impedance model developed in frequency domain....... In grids with harmonic voltages, impedance models can predict the current distortion for all active power injection scenarios. Furthermore, measurements in a 1.4 MW PV plant connected in a distributed grid are used to validate the simulation based on impedance models during different power injections...

Spherical Harmonics Analysis of the ECMWF Global Wind Fields at the 10-Meter Height Level During 1985: A Collection of Figures Illustrating Results

Science.gov (United States)

Sanchez, Braulio V.; Nishihama, Masahiro

1997-01-01

Half-daily global wind speeds in the east-west (u) and north-south (v) directions at the 10-meter height level were obtained from the European Centre for Medium Range Weather Forecasts (ECMWF) data set of global analyses. The data set covered the period 1985 January to 1995 January. A spherical harmonic expansion to degree and order 50 was used to perform harmonic analysis of the east-west (u) and north-south (v) velocity field components. The resulting wind field is displayed, as well as the residual of the fit, at a particular time. The contribution of particular coefficients is shown. The time variability of the coefficients up to degree and order 3 is presented. Corresponding power spectrum plots are given. Time series analyses were applied also to the power associated with degrees 0-10; the results are included.

Spherical convolutions and their application in molecular modelling

DEFF Research Database (Denmark)

Boomsma, Wouter; Frellsen, Jes

2017-01-01

Convolutional neural networks are increasingly used outside the domain of image analysis, in particular in various areas of the natural sciences concerned with spatial data. Such networks often work out-of-the box, and in some cases entire model architectures from image analysis can be carried over...... to other problem domains almost unaltered. Unfortunately, this convenience does not trivially extend to data in non-euclidean spaces, such as spherical data. In this paper, we introduce two strategies for conducting convolutions on the sphere, using either a spherical-polar grid or a grid based...... of spherical convolutions in the context of molecular modelling, by considering structural environments within proteins. We show that the models are capable of learning non-trivial functions in these molecular environments, and that our spherical convolutions generally outperform standard 3D convolutions...

Input Harmonic Analysis on the Slim DC-Link Drive Using Harmonic State Space Model

DEFF Research Database (Denmark)

Yang, Feng; Kwon, Jun Bum; Wang, Xiongfei

2017-01-01

The harmonic performance of the slim dc-link adjustable speed drives has shown good performance in some studies but poor in some others. The contradiction indicates that a feasible theoretical analysis is still lacking to characterize the harmonic distortion for the slim dc-link drive. Considerin...... results of the slim dc-link drive, loaded up to 2.0 kW, are presented to validate the theoretical analysis....... variation according to the switching instant, the harmonics at the steady-state condition, as well as the coupling between the multiple harmonic impedances. By using this model, the impaction on the harmonics performance by the film capacitor and the grid inductance is derived. Simulation and experimental...

Worldwide complete spherical Bouguer and isostatic anomaly maps

Science.gov (United States)

Bonvalot, S.; Balmino, G.; Briais, A.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2011-12-01

We present here a set of digital maps of the Earth's gravity anomalies (surface "free air", Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW). The free air and Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, submitted). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial Intelligence Agency (NGA) (Pavlis

A pseudospectral matrix method for time-dependent tensor fields on a spherical shell

International Nuclear Information System (INIS)

Brügmann, Bernd

2013-01-01

We construct a pseudospectral method for the solution of time-dependent, non-linear partial differential equations on a three-dimensional spherical shell. The problem we address is the treatment of tensor fields on the sphere. As a test case we consider the evolution of a single black hole in numerical general relativity. A natural strategy would be the expansion in tensor spherical harmonics in spherical coordinates. Instead, we consider the simpler and potentially more efficient possibility of a double Fourier expansion on the sphere for tensors in Cartesian coordinates. As usual for the double Fourier method, we employ a filter to address time-step limitations and certain stability issues. We find that a tensor filter based on spin-weighted spherical harmonics is successful, while two simplified, non-spin-weighted filters do not lead to stable evolutions. The derivatives and the filter are implemented by matrix multiplication for efficiency. A key technical point is the construction of a matrix multiplication method for the spin-weighted spherical harmonic filter. As example for the efficient parallelization of the double Fourier, spin-weighted filter method we discuss an implementation on a GPU, which achieves a speed-up of up to a factor of 20 compared to a single core CPU implementation

Model-free and analytical EAP reconstruction via spherical polar Fourier diffusion MRI.

Science.gov (United States)

Cheng, Jian; Ghosh, Aurobrata; Jiang, Tianzi; Deriche, Rachid

2010-01-01

How to estimate the diffusion Ensemble Average Propagator (EAP) from the DWI signals in q-space is an open problem in diffusion MRI field. Many methods were proposed to estimate the Orientation Distribution Function (ODF) that is used to describe the fiber direction. However, ODF is just one of the features of the EAP. Compared with ODF, EAP has the full information about the diffusion process which reflects the complex tissue micro-structure. Diffusion Orientation Transform (DOT) and Diffusion Spectrum Imaging (DSI) are two important methods to estimate the EAP from the signal. However, DOT is based on mono-exponential assumption and DSI needs a lot of samplings and very large b values. In this paper, we propose Spherical Polar Fourier Imaging (SPFI), a novel model-free fast robust analytical EAP reconstruction method, which almost does not need any assumption of data and does not need too many samplings. SPFI naturally combines the DWI signals with different b-values. It is an analytical linear transformation from the q-space signal to the EAP profile represented by Spherical Harmonics (SH). We validated the proposed methods in synthetic data, phantom data and real data. It works well in all experiments, especially for the data with low SNR, low anisotropy, and non-exponential decay.

Characterization of the diversity in bat biosonar beampatterns with spherical harmonics power spectra.

Science.gov (United States)

Motamedi, Mohammad; Müller, Rolf

2014-06-01

The biosonar beampatterns found across different bat species are highly diverse in terms of global and local shape properties such as overall beamwidth or the presence, location, and shape of multiple lobes. It may be hypothesized that some of this variability reflects evolutionary adaptation. To investigate this hypothesis, the present work has searched for patterns in the variability across a set of 283 numerical predictions of emission and reception beampatterns from 88 bat species belonging to four major families (Rhinolophidae, Hipposideridae, Phyllostomidae, Vespertilionidae). This was done using a lossy compression of the beampatterns that utilized real spherical harmonics as basis functions. The resulting vector representations showed differences between the families as well as between emission and reception. These differences existed in the means of the power spectra as well as in their distribution. The distributions were characterized in a low dimensional space found through principal component analysis. The distinctiveness of the beampatterns across the groups was corroborated by pairwise classification experiments that yielded correct classification rates between ~85 and ~98%. Beamwidth was a major factor but not the sole distinguishing feature in these classification experiments. These differences could be seen as an indication of adaptive trends at the beampattern level.

Harmonic Instability Analysis of Single-Phase Grid Connected Converter using Harmonic State Space (HSS) modeling method

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

The increasing number of renewable energy sources at the distribution grid is becoming a major issue for utility companies, since the grid connected converters are operating at different operating points due to the probabilistic characteristics of renewable energy. Besides, typically, the harmonics...... proposes a new model of a single phase grid connected renewable energy source using the Harmonic State Space modeling approach, which is able to identify such problems and the model can be extended to be applied in the multiple connected converter analysis. The modeling results show the different harmonic...... and impedance from other renewable energy sources are not taken carefully into account in the installation and design. However, this may bring an unknown harmonic instability into the multiple power sourced system and also make the analysis difficult due to the complexity of the grid network. This paper...

The spherical limit of the n-vector model and correlation inequaljties

International Nuclear Information System (INIS)

Angelescu, N.; Bundaru, M.; Costache, G.

1978-08-01

The asymptotics of the state of the n-vector model with a finite number of spins in the spherical limit is studied. Besides rederiving the limit free energy, corresponding to a generalized spherical model (with ''spherical constraint'' at every site), we obtain also the limit of the correlation functions, which allow a precise definition of the state of the latter model. Correlation inequalities are proved for ferromagnetic interactions in the asymptotic regime. In particular, it is shown that the generalized spherical model fulfills the expected Griffiths' type inequalities, differing in this respect from the spherical model with overall constraint. (author)

Sequence Domain Harmonic Modeling of Type-IV Wind Turbines

DEFF Research Database (Denmark)

Guest, Emerson; Jensen, Kim Høj; Rasmussen, Tonny Wederberg

2017-01-01

-sampled pulsewidth modulation and an analysis of converter generated voltage harmonics due to compensated dead-time. The decoupling capabilities of the proposed the SD harmonic model are verified through a power quality (PQ) assessment of a 3MW Type-IV wind turbine. The assessment shows that the magnitude and phase...... of low-order odd converter generated voltage harmonics are dependent on the converter operating point and the phase of the fundamental component of converter current respectively. The SD harmonic model can be used to make PQ assessments of Type-IV wind turbines or incorporated into harmonic load flows...... for computation of PQ in wind power plants....

Modeling mantle convection in the spherical annulus

Science.gov (United States)

Hernlund, John W.; Tackley, Paul J.

2008-12-01

Most methods for modeling mantle convection in a two-dimensional (2D) circular annular domain suffer from innate shortcomings in their ability to capture several characteristics of the spherical shell geometry of planetary mantles. While methods such as rescaling the inner and outer radius to reduce anomalous effects in a 2D polar cylindrical coordinate system have been introduced and widely implemented, such fixes may have other drawbacks that adversely affect the outcome of some kinds of mantle convection studies. Here we propose a new approach that we term the "spherical annulus," which is a 2D slice that bisects the spherical shell and is quantitatively formulated at the equator of a spherical polar coordinate system after neglecting terms in the governing equations related to variations in latitude. Spherical scaling is retained in this approximation since the Jacobian function remains proportional to the square of the radius. We present example calculations to show that the behavior of convection in the spherical annulus compares favorably against calculations performed in other 2D annular domains when measured relative to those in a fully three-dimensional (3D) spherical shell.

High-order perturbations of a spherical collapsing star

International Nuclear Information System (INIS)

Brizuela, David; Martin-Garcia, Jose M.; Sperhake, Ulrich; Kokkotas, Kostas D.

2010-01-01

A formalism to deal with high-order perturbations of a general spherical background was developed in earlier work [D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 74, 044039 (2006); D. Brizuela, J. M. Martin-Garcia, and G. A. Mena Marugan, Phys. Rev. D 76, 024004 (2007)]. In this paper, we apply it to the particular case of a perfect fluid background. We have expressed the perturbations of the energy-momentum tensor at any order in terms of the perturbed fluid's pressure, density, and velocity. In general, these expressions are not linear and have sources depending on lower-order perturbations. For the second-order case we make the explicit decomposition of these sources in tensor spherical harmonics. Then, a general procedure is given to evolve the perturbative equations of motions of the perfect fluid for any value of the harmonic label. Finally, with the problem of a spherical collapsing star in mind, we discuss the high-order perturbative matching conditions across a timelike surface, in particular, the surface separating the perfect fluid interior from the exterior vacuum.

Towards Quantitative Optical Cross Sections in Entomological Laser Radar - Potential of Temporal and Spherical Parameterizations for Identifying Atmospheric Fauna.

Directory of Open Access Journals (Sweden)

Mikkel Brydegaard

Full Text Available In recent years, the field of remote sensing of birds and insects in the atmosphere (the aerial fauna has advanced considerably, and modern electro-optic methods now allow the assessment of the abundance and fluxes of pests and beneficials on a landscape scale. These techniques have the potential to significantly increase our understanding of, and ability to quantify and manage, the ecological environment. This paper presents a concept whereby laser radar observations of atmospheric fauna can be parameterized and table values for absolute cross sections can be catalogued to allow for the study of focal species such as disease vectors and pests. Wing-beat oscillations are parameterized with a discrete set of harmonics and the spherical scatter function is parameterized by a reduced set of symmetrical spherical harmonics. A first order spherical model for insect scatter is presented and supported experimentally, showing angular dependence of wing beat harmonic content. The presented method promises to give insights into the flight heading directions of species in the atmosphere and has the potential to shed light onto the km-range spread of pests and disease vectors.

Profiles of fast ions that are accelerated by high harmonic fast waves in the National Spherical Torus Experiment

International Nuclear Information System (INIS)

Liu, D; Heidbrink, W W; Podesta, M; Ruskov, E; Bell, R E; Fredrickson, E D; Medley, S S; Harvey, R W

2010-01-01

Combined neutral beam injection and high-harmonic fast-wave (HHFW) heating accelerate deuterium fast ions in the National Spherical Torus Experiment (NSTX). With 1.1 MW of HHFW power, the neutron emission rate is about three times larger than in the comparison discharge without HHFW heating. Acceleration of fast ions above the beam injection energy is evident on an E||B type neutral particle analyzer (NPA), a 4-chord solid state neutral particle analyzer (SSNPA) array and a 16-channel fast-ion D-alpha (FIDA) diagnostic. The accelerated fast ions observed by the NPA and SSNPA diagnostics mainly come from passive charge exchange reactions at the edge due to the NPA/SSNPA localization in phase space. The spatial profile of accelerated fast ions that is measured by the FIDA diagnostic is much broader than in conventional tokamaks because of the multiple resonance layers and large orbits in NSTX. The fast-ion distribution function calculated by the CQL3D Fokker-Planck code differs from the measured spatial profile, presumably because the current version of CQL3D uses a zero-banana-width model. In addition, compressional Alfven eigenmode activity is stronger during the HHFW heating and it may affect the fast-ion spatial profile.

Intelligent harmonic load model based on neural networks

Science.gov (United States)

Ji, Pyeong-Shik; Lee, Dae-Jong; Lee, Jong-Pil; Park, Jae-Won; Lim, Jae-Yoon

2007-12-01

In this study, we developed a RBFNs(Radial Basis Function Networks) based load modeling method with harmonic components. The developed method implemented by using harmonic information as well as fundamental frequency and voltage which are essential input factors in conventional method. Thus, the proposed method makes it possible to effectively estimate load characteristics in power lines with harmonics. The RBFNs have certain advantage such as simple structure and rapid computation ability compared with multilayer perceptron which is extensively applied for load modeling. To show the effectiveness, the proposed method has been intensively tested with various dataset acquired under the different frequency and voltage and compared it with conventional methods such as polynominal 2nd equation method, MLP and RBF without considering harmonic components.

Homogeneous collapsing star: Tensor and vector harmonics for matter and field asymmetries

International Nuclear Information System (INIS)

Gerlach, U.H.; Sengupta, U.K.

1978-01-01

For the space-time of the interior of a homogeneous collapsing star complete sets of orthogonal vector and tensor harmonics are presented. Their relationship to the set of vector and tensor harmonics for a generic spherically symmetric space-time is exhibited

Virial theorem and hypervirial theorem in a spherical geometry

International Nuclear Information System (INIS)

Li Yan; Chen Jingling; Zhang Fulin

2011-01-01

The virial theorem in the one- and two-dimensional spherical geometry are presented in both classical and quantum mechanics. Choosing a special class of hypervirial operators, the quantum hypervirial relations in the spherical spaces are obtained. With the aid of the Hellmann-Feynman theorem, these relations can be used to formulate a perturbation theorem without wavefunctions, corresponding to the hypervirial-Hellmann-Feynman theorem perturbation theorem of Euclidean geometry. The one-dimensional harmonic oscillator and two-dimensional Coulomb system in the spherical spaces are given as two sample examples to illustrate the perturbation method. (paper)

Spherical model for superfluidity in a restricted geometry

International Nuclear Information System (INIS)

Fishman, S.; Ziman, T.A.L.

1982-01-01

The spherical model is solved on a hypercubic lattice in d dimensions, each bond of which is decorated with l spins. The thermodynamic functions and the helicity modulus, analogous to a superfluid density, are calculated. We find that at least two spherical fields are required for the model to exhibit low-temperature properties that can approximate reasonably those of O(n) models. The heuristic prediction that the critical temperature behaves as T/sub c/(l)approx.(l+1) -1 is checked for the model and found to hold quite accurately even for small l(> or approx. =2). The helicity modulus and magnetization of the two-constraint spherical model are found to scale approximately with the critical temperature, but the relation between them is more complex than in the undecorated model. This relation is used to check heuristic arguments concerning the helicity modulus at low temperatures. We comment on the relevance to physical systems, in particular, the problem of boson condensation in a restricted geometry

Exact solutions of the spherically symmetric multidimensional ...

African Journals Online (AJOL)

The complete orthonormalised energy eigenfunctions and the energy eigenvalues of the spherically symmetric isotropic harmonic oscillator in N dimensions, are obtained through the methods of separation of variables. Also, the degeneracy of the energy levels are examined. KEY WORDS: - Schrödinger Equation, Isotropic ...

Confluent hypergeometric orthogonal polynomials related to the rational quantum Calogero system with harmonic confinement

International Nuclear Information System (INIS)

van Diejen, J.F.

1997-01-01

Two families (type A and type B) of confluent hypergeometric polynomials in several variables are studied. We describe the orthogonality properties, differential equations, and Pieri-type recurrence formulas for these families. In the one-variable case, the polynomials in question reduce to the Hermite polynomials (type A) and the Laguerre polynomials (type B), respectively. The multivariable confluent hypergeometric families considered here may be used to diagonalize the rational quantum Calogero models with harmonic confinement (for the classical root systems) and are closely connected to the (symmetric) generalized spherical harmonics investigated by Dunkl. (orig.)

Calculation of spherical harmonics and Wigner d functions by FFT. Applications to fast rotational matching in molecular replacement and implementation into AMoRe.

Science.gov (United States)

Trapani, Stefano; Navaza, Jorge

2006-07-01

The FFT calculation of spherical harmonics, Wigner D matrices and rotation function has been extended to all angular variables in the AMoRe molecular replacement software. The resulting code avoids singularity issues arising from recursive formulas, performs faster and produces results with at least the same accuracy as the original code. The new code aims at permitting accurate and more rapid computations at high angular resolution of the rotation function of large particles. Test calculations on the icosahedral IBDV VP2 subviral particle showed that the new code performs on the average 1.5 times faster than the original code.

The simplified spherical harmonics (SPL) methodology with space and moment decomposition in parallel environments

International Nuclear Information System (INIS)

Gianluca, Longoni; Alireza, Haghighat

2003-01-01

In recent years, the SP L (simplified spherical harmonics) equations have received renewed interest for the simulation of nuclear systems. We have derived the SP L equations starting from the even-parity form of the S N equations. The SP L equations form a system of (L+1)/2 second order partial differential equations that can be solved with standard iterative techniques such as the Conjugate Gradient (CG). We discretized the SP L equations with the finite-volume approach in a 3-D Cartesian space. We developed a new 3-D general code, Pensp L (Parallel Environment Neutral-particle SP L ). Pensp L solves both fixed source and criticality eigenvalue problems. In order to optimize the memory management, we implemented a Compressed Diagonal Storage (CDS) to store the SP L matrices. Pensp L includes parallel algorithms for space and moment domain decomposition. The computational load is distributed on different processors, using a mapping function, which maps the 3-D Cartesian space and moments onto processors. The code is written in Fortran 90 using the Message Passing Interface (MPI) libraries for the parallel implementation of the algorithm. The code has been tested on the Pcpen cluster and the parallel performance has been assessed in terms of speed-up and parallel efficiency. (author)

On computing ellipsoidal harmonics using Jekeli's renormalization

Czech Academy of Sciences Publication Activity Database

Sebera, Josef; Bouman, J.; Bosch, W.

2012-01-01

Roč. 86, č. 9 (2012), s. 713-726 ISSN 0949-7714 Institutional support: RVO:67985815 Keywords : Earth's gravitational field * spherical and ellipsoidal harmonics * hypergeometric function Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 2.808, year: 2012

Spherical harmonics based descriptor for neural network potentials: Structure and dynamics of Au147 nanocluster.

Science.gov (United States)

Jindal, Shweta; Chiriki, Siva; Bulusu, Satya S

2017-05-28

We propose a highly efficient method for fitting the potential energy surface of a nanocluster using a spherical harmonics based descriptor integrated with an artificial neural network. Our method achieves the accuracy of quantum mechanics and speed of empirical potentials. For large sized gold clusters (Au 147 ), the computational time for accurate calculation of energy and forces is about 1.7 s, which is faster by several orders of magnitude compared to density functional theory (DFT). This method is used to perform the global minimum optimizations and molecular dynamics simulations for Au 147 , and it is found that its global minimum is not an icosahedron. The isomer that can be regarded as the global minimum is found to be 4 eV lower in energy than the icosahedron and is confirmed from DFT. The geometry of the obtained global minimum contains 105 atoms on the surface and 42 atoms in the core. A brief study on the fluxionality in Au 147 is performed, and it is concluded that Au 147 has a dynamic surface, thus opening a new window for studying its reaction dynamics.

Overhead distribution line models for harmonics studies

Energy Technology Data Exchange (ETDEWEB)

Nagpal, M.; Xu, W.; Dommel, H.W.

1994-01-01

Carson's formulae and Maxwell's potential coefficients are used for calculating the per unit length series impedances and shunt capacitances of the overhead lines. The per unit length values are then used for building the models, nominal pi-circuit, and equivalent pi-circuit at the harmonic frequencies. This paper studies the accuracy of these models for presenting the overhead distribution lines in steady-state harmonic solutions at frequencies up to 5 kHz. The models are verified with a field test on a 25 kV distribution line and the sensitivity of the models to ground resistivity, skin effect, and multiple grounding is reported.

Validation Techniques of network harmonic models based on switching of a series linear component and measuring resultant harmonic increments

DEFF Research Database (Denmark)

Wiechowski, Wojciech Tomasz; Lykkegaard, Jan; Bak, Claus Leth

2007-01-01

In this paper two methods of validation of transmission network harmonic models are introduced. The methods were developed as a result of the work presented in [1]. The first method allows calculating the transfer harmonic impedance between two nodes of a network. Switching a linear, series network......, as for example a transmission line. Both methods require that harmonic measurements performed at two ends of the disconnected element are precisely synchronized....... are used for calculation of the transfer harmonic impedance between the nodes. The determined transfer harmonic impedance can be used to validate a computer model of the network. The second method is an extension of the fist one. It allows switching a series element that contains a shunt branch...

Harmonic Analyzing of the Double PWM Converter in DFIG Based on Mathematical Model

Directory of Open Access Journals (Sweden)

Jing Liu

2017-12-01

Full Text Available Harmonic pollution of double fed induction generators (DFIGs has become a vital concern for its undesirable effects on power quality issues of wind generation systems and grid-connected system, and the double pulse width modulation (PWMconverter is one of the main harmonic sources in DFIGs. Thus the harmonic analysis of the converter in DFIGs is a necessary step to evaluate their harmonic pollution of DFIGs. This paper proposes a detailed harmonic modeling method to discuss the main harmonic components in a converter. In general the harmonic modeling could be divided into the low-order harmonic part (up to 30th order and the high-order harmonic part (greater than order 30 parts in general. The low-order harmonics are produced by the circuit topology and control algorithm, and the harmonic component will be different if the control strategy changes. The high-order harmonics are produced by the modulation of the switching function to the dc variable. In this paper, the low-order harmonic modeling is established according to the directions of power flow under the vector control (VC, and the high-order harmonic modeling is established by the switching function of space vector PWM and dc currents. Meanwhile, the simulations of harmonic a components in a converter are accomplished in a real time digital simulation system. The results indicate that the proposed modeling could effectively show the harmonics distribution of the converter in DFIGs.

Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

Science.gov (United States)

Burnett, Sarah; Rojas, Ruben; Perevalov, Artur; Lathrop, Daniel; Ide, Kayo; Schaeffer, Nathanael

2017-11-01

The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108 . In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

A non-conforming generalization of Raviart-Thomas elements to the spherical harmonic form of the even-parity neutron transport equation

Energy Technology Data Exchange (ETDEWEB)

Van Criekingen, S. [Commissariat a l' energie atomique (CEA-Saclay), DEN/DM2S/SERMA/LENR (Bat 470), 91191 Gif-sur-Yvette Cedex (France)]. E-mail: serge.van-criekingen@cea.fr

2006-05-15

The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P {sub N}) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements.

A non-conforming generalization of Raviart-Thomas elements to the spherical harmonic form of the even-parity neutron transport equation

International Nuclear Information System (INIS)

Van Criekingen, S.

2006-01-01

The Raviart-Thomas finite elements provide an appropriate spatial discretization of the mixed-dual form of the diffusion equation. This discretization can then be coupled to an efficient solution method. The high performances achieved by such an approach triggered research on its possible generalization to the transport equation using a spherical harmonic (or P N ) angular approximation. In view of the difficulty of developing a straightforward generalization within the mixed-dual framework, we here consider 2D non-conforming (i.e., allowing interface discontinuities) finite elements coupled to the second-order form of the transport equation. This non-conforming approach keeps the mixed-dual property of the relaxation of the flux interface continuity constraint. We investigate different non-conforming elements and compare them to the well-known Lagrangian conforming elements

A New Model of Jupiter's Magnetic Field from Juno's First Nine Orbits

DEFF Research Database (Denmark)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.

2018-01-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter......'s magnetic field with a coarse longitudinal separation of ~45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary (“internal”) field, combined with a simple model of the magnetodisc for the field (“external”) due to distributed magnetospheric...... currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model (“Juno Reference Model through Perijove 9”) of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed...

A New Model of Jupiter's Magnetic Field From Juno's First Nine Orbits

Science.gov (United States)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.; Espley, J. R.; Joergensen, J. L.; Joergensen, P. S.; Merayo, J. M. G.; Herceg, M.; Bloxham, J.; Moore, K. M.; Bolton, S. J.; Levin, S. M.

2018-03-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter's magnetic field with a coarse longitudinal separation of 45° between perijoves. The magnetic field is represented with a degree 20 spherical harmonic model for the planetary ("internal") field, combined with a simple model of the magnetodisc for the field ("external") due to distributed magnetospheric currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model ("Juno Reference Model through Perijove 9") of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed view of a planetary dynamo beyond Earth.

On the advantage of the finite fourier transformation method for the solution of a multigroup transport equation by the spherical harmonics method

International Nuclear Information System (INIS)

Kobayashi, K.

1995-01-01

A simple formulation to derive second order differential equations of the spherical harmonics method is described, and it is shown that there is difficulty in deriving finite difference equations for these differential equations at material interfaces, because the second order differential terms of higher order moments must be expressed by the values in a mesh box. On the other hand, it is shown that there is no such difficulty, if the author uses the finite Fourier transformation method, since the differential equations are transformed into integral equations and the differentiation corresponds simply to a multiplication by the transformation parameter. Solution can be obtained in the form of Fourier series without making use of the inversion integral

Sigma models in (4,4) harmonic superspace

International Nuclear Information System (INIS)

Ivanov, E.; Joint Inst. for Nuclear Research, Dubna; Sutulin, A.

1994-04-01

We define basics of (4,4) 2D harmonic superspace with two independent sets of SU(2) harmonic variables and apply it to construct new superfield actions of (4,4) supersymmetric two-dimensional sigma models with torsion and mutually commuting left and right complex structures, as well as of their massive deformations. We show that the generic off-shell sigma model action is the general action of constrained analytic superfields q (1,1) representing twisted N=4 multiplets in (4,4) harmonic superspace. The massive term of q (1,1) is shown to be unique; it generates a scalar potential the form of which is determined by the metric on the target bosonic manifold. We discuss in detail (4,4) supersymmetric group manifold SU(2)xU(1) WZNW sigma model and its Liouville deformation. A deep analogy of the relevant superconformally invariant analytic superfield action to that of the improved tensor N=2 4D multiplet is found. We define (4,4) duality transformation and find new off-shell dual representations of the previously constructed actions via unconstrained analytic (4,4) superfields. The main peculiarities of the (4,4) duality transformation are: (i) It preserves manifest (4,4) supersymmetry; (ii) dual actions reveal a gauge invariance needed for the onshell equivalence to the original description; (iii) in the actions dual to the massive ones 2D supersymmetry is modified off shell by SU(2) tensor central charges. The dual representation suggests some hints of how to describe (4,4) models with non-commuting complex structures in the harmonic superspace. (orig.)

Exploring harmonization between integrated assessment and capacity expansion models

Science.gov (United States)

Iyer, G.; Brown, M.; Cohen, S.; Macknick, J.; Patel, P.; Wise, M. A.; Horing, J.

2017-12-01

Forward-looking quantitative models of the electric sector are extensively used to provide science-based strategic decision support to national, international and private-sector entities. Given that these models are used to inform a wide-range of stakeholders and influence policy decisions, it is vital to examine how the models' underlying data and structure influence their outcomes. We conduct several experiments harmonizing key model characteristics between ReEDS—an electric sector only model, and GCAM—an integrated assessment model—to understand how different degrees of harmonization impact model outcomes. ReEDS has high spatial, temporal, and process detail but lacks electricity demand elasticity and endogenous representations of other economic sectors, while GCAM has internally consistent representations of energy (including the electric sector), agriculture, and land-use systems but relatively aggregate representations of the factors influencing electric sector investments . We vary the degree of harmonization in electricity demand, fuel prices, technology costs and performance, and variable renewable energy resource characteristics. We then identify the prominent sources of divergence in key outputs (electricity capacity, generation, and price) across the models and study how the convergence between models can be improved with permutations of harmonized characteristics. The remaining inconsistencies help to establish how differences in the models' underlying data, construction, perspective, and methodology play into each model's outcome. There are three broad contributions of this work. First, our study provides a framework to link models with similar scope but different resolutions. Second, our work provides insight into how the harmonization of assumptions contributes to a unified and robust portrayal of the US electricity sector under various potential futures. Finally, our study enhances the understanding of the influence of structural uncertainty

Two dimensional code for modeling of high ione cyclotron harmonic fast wave heating and current drive

International Nuclear Information System (INIS)

Grekov, D.; Kasilov, S.; Kernbichler, W.

2016-01-01

A two dimensional numerical code for computation of the electromagnetic field of a fast magnetosonic wave in a tokamak at high harmonics of the ion cyclotron frequency has been developed. The code computes the finite difference solution of Maxwell equations for separate toroidal harmonics making use of the toroidal symmetry of tokamak plasmas. The proper boundary conditions are prescribed at the realistic tokamak vessel. The currents in the RF antenna are specified externally and then used in Ampere law. The main poloidal tokamak magnetic field and the ''kinetic'' part of the dielectric permeability tensor are treated iteratively. The code has been verified against known analytical solutions and first calculations of current drive in the spherical torus are presented.

Emulating Spherical Wave Channel Models in Multi-probe Anechoic Chamber Setups

DEFF Research Database (Denmark)

Fan, Wei; Carreño, Xavier; Nielsen, Jesper Ødum

2015-01-01

to emulate spherical wave channel models in multi-probe anechoic chamber setups. In this paper, a technique based on the field synthesis principle is proposed to approximate spherical waves emitted from arbitrarily located point sources with arbitrary polarizations. Simulation results show that static......Spherical wave channel modeling has attracted huge research attention for massive multiple-input multiple-output (MIMO) and short-distance MIMO systems. Current research work in multi-probe anechoic chamber systems is limited to reproduce radio channels assuming planar wavefronts. There is a need...... spherical waves can be reproduced with a limited number of probes, and the field synthesis accuracy of spherical wave depends on the location of the source point....

Data harmonization and model performance

Science.gov (United States)

The Joint Committee on Urban Storm Drainage of the International Association for Hydraulic Research (IAHR) and International Association on Water Pollution Research and Control (IAWPRC) was formed in 1982. The current committee members are (no more than two from a country): B. C. Yen, Chairman (USA); P. Harremoes, Vice Chairman (Denmark); R. K. Price, Secretary (UK); P. J. Colyer (UK), M. Desbordes (France), W. C. Huber (USA), K. Krauth (FRG), A. Sjoberg (Sweden), and T. Sueishi (Japan).The IAHR/IAWPRC Joint Committee is forming a Task Group on Data Harmonization and Model Performance. One objective is to promote international urban drainage data harmonization for easy data and information exchange. Another objective is to publicize available models and data internationally. Comments and suggestions concerning the formation and charge of the Task Group are welcome and should be sent to: B. C. Yen, Dept. of Civil Engineering, Univ. of Illinois, 208 N. Romine St., Urbana, IL 61801.

On the moment of inertia of a quantum harmonic oscillator

International Nuclear Information System (INIS)

Khamzin, A. A.; Sitdikov, A. S.; Nikitin, A. S.; Roganov, D. A.

2013-01-01

An original method for calculating the moment of inertia of the collective rotation of a nucleus on the basis of the cranking model with the harmonic-oscillator Hamiltonian at arbitrary frequencies of rotation and finite temperature is proposed. In the adiabatic limit, an oscillating chemical-potential dependence of the moment of inertia is obtained by means of analytic calculations. The oscillations of the moment of inertia become more pronounced as deformations approach the spherical limit and decrease exponentially with increasing temperature.

Semi-Numerical Studies of the Three-Meter Spherical Couette Experiment Utilizing Data Assimilation

Science.gov (United States)

Burnett, S. C.; Rojas, R.; Perevalov, A.; Lathrop, D. P.

2017-12-01

The model of the Earth's magnetic field has been investigated in recent years through experiments and numerical models. At the University of Maryland, experimental studies are implemented in a three-meter spherical Couette device filled with liquid sodium. The inner and outer spheres of this apparatus mimic the planet's inner core and core-mantle boundary, respectively. These experiments incorporate high velocity flows with Reynolds numbers 108. In spherical Couette geometry, the numerical scheme applied to this work features finite difference methods in the radial direction and pseudospectral spherical harmonic transforms elsewhere [Schaeffer, N. G3 (2013)]. Adding to the numerical model, data assimilation integrates the experimental outer-layer magnetic field measurements. This semi-numerical model can then be compared to the experimental results as well as forecasting magnetic field changes. Data assimilation makes it possible to get estimates of internal motions of the three-meter experiment that would otherwise be intrusive or impossible to obtain in experiments or too computationally expensive with a purely numerical code. If we can provide accurate models of the three-meter device, it is possible to attempt to model the geomagnetic field. We gratefully acknowledge the support of NSF Grant No. EAR1417148 & DGE1322106.

Terrestrial Water Storage in African Hydrological Regimes Derived from GRACE Mission Data: Intercomparison of Spherical Harmonics, Mass Concentration, and Scalar Slepian Methods.

Science.gov (United States)

Rateb, Ashraf; Kuo, Chung-Yen; Imani, Moslem; Tseng, Kuo-Hsin; Lan, Wen-Hau; Ching, Kuo-En; Tseng, Tzu-Pang

2017-03-10

Spherical harmonics (SH) and mascon solutions are the two most common types of solutions for Gravity Recovery and Climate Experiment (GRACE) mass flux observations. However, SH signals are degraded by measurement and leakage errors. Mascon solutions (the Jet Propulsion Laboratory (JPL) release, herein) exhibit weakened signals at submascon resolutions. Both solutions require a scale factor examined by the CLM4.0 model to obtain the actual water storage signal. The Slepian localization method can avoid the SH leakage errors when applied to the basin scale. In this study, we estimate SH errors and scale factors for African hydrological regimes. Then, terrestrial water storage (TWS) in Africa is determined based on Slepian localization and compared with JPL-mascon and SH solutions. The three TWS estimates show good agreement for the TWS of large-sized and humid regimes but present discrepancies for the TWS of medium and small-sized regimes. Slepian localization is an effective method for deriving the TWS of arid zones. The TWS behavior in African regimes and its spatiotemporal variations are then examined. The negative TWS trends in the lower Nile and Sahara at -1.08 and -6.92 Gt/year, respectively, are higher than those previously reported.

Linearized vector radiative transfer model MCC++ for a spherical atmosphere

International Nuclear Information System (INIS)

Postylyakov, O.V.

2004-01-01

Application of radiative transfer models has shown that optical remote sensing requires extra characteristics of radiance field in addition to the radiance intensity itself. Simulation of spectral measurements, analysis of retrieval errors and development of retrieval algorithms are in need of derivatives of radiance with respect to atmospheric constituents under investigation. The presented vector spherical radiative transfer model MCC++ was linearized, which allows the calculation of derivatives of all elements of the Stokes vector with respect to the volume absorption coefficient simultaneously with radiance calculation. The model MCC++ employs Monte Carlo algorithm for radiative transfer simulation and takes into account aerosol and molecular scattering, gas and aerosol absorption, and Lambertian surface albedo. The model treats a spherically symmetrical atmosphere. Relation of the estimated derivatives with other forms of radiance derivatives: the weighting functions used in gas retrieval and the air mass factors used in the DOAS retrieval algorithms, is obtained. Validation of the model against other radiative models is overviewed. The computing time of the intensity for the MCC++ model is about that for radiative models treating sphericity of the atmosphere approximately and is significantly shorter than that for the full spherical models used in the comparisons. The simultaneous calculation of all derivatives (i.e. with respect to absorption in all model atmosphere layers) and the intensity is only 1.2-2 times longer than the calculation of the intensity only

Interbasis expansions for isotropic harmonic oscillator

Energy Technology Data Exchange (ETDEWEB)

Dong, Shi-Hai, E-mail: dongsh2@yahoo.com [Departamento de Física, Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, Edificio 9, Unidad Profesional Adolfo López Mateos, Mexico D.F. 07738 (Mexico)

2012-03-12

The exact solutions of the isotropic harmonic oscillator are reviewed in Cartesian, cylindrical polar and spherical coordinates. The problem of interbasis expansions of the eigenfunctions is solved completely. The explicit expansion coefficients of the basis for given coordinates in terms of other two coordinates are presented for lower excited states. Such a property is occurred only for those degenerated states for given principal quantum number n. -- Highlights: ► Exact solutions of harmonic oscillator are reviewed in three coordinates. ► Interbasis expansions of the eigenfunctions is solved completely. ► This is occurred only for those degenerated states for given quantum number n.

Symmetric tensor spherical harmonics on the N-sphere and their application to the de Sitter group SO(N,1)

International Nuclear Information System (INIS)

Higuchi, A.

1987-01-01

The symmetric tensor spherical harmonics (STSH's) on the N-sphere (S/sup N/), which are defined as the totally symmetric, traceless, and divergence-free tensor eigenfunctions of the Laplace--Beltrami (LB) operator on S/sup N/, are studied. Specifically, their construction is shown recursively starting from the lower-dimensional ones. The symmetric traceless tensors induced by STSH's are introduced. These play a crucial role in the recursive construction of STSH's. The normalization factors for STSH's are determined by using their transformation properties under SO(N+1). Then the symmetric, traceless, and divergence-free tensor eigenfunctions of the LB operator in the N-dimensional de Sitter space-time which are obtained by the analytic continuation of the STSH's on S/sup N/ are studied. Specifically, the allowed eigenvalues of the LB operator under the restriction of unitarity are determined. Our analysis gives a group-theoretical explanation of the forbidden mass range observed earlier for the spin-2 field theory in de Sitter space-time

Models for randomly distributed nanoscopic domains on spherical vesicles

Science.gov (United States)

Anghel, Vinicius N. P.; Bolmatov, Dima; Katsaras, John

2018-06-01

The existence of lipid domains in the plasma membrane of biological systems has proven controversial, primarily due to their nanoscopic size—a length scale difficult to interrogate with most commonly used experimental techniques. Scattering techniques have recently proven capable of studying nanoscopic lipid domains populating spherical vesicles. However, the development of analytical methods able of predicting and analyzing domain pair correlations from such experiments has not kept pace. Here, we developed models for the random distribution of monodisperse, circular nanoscopic domains averaged on the surface of a spherical vesicle. Specifically, the models take into account (i) intradomain correlations corresponding to form factors and interdomain correlations corresponding to pair distribution functions, and (ii) the analytical computation of interdomain correlations for cases of two and three domains on a spherical vesicle. In the case of more than three domains, these correlations are treated either by Monte Carlo simulations or by spherical analogs of the Ornstein-Zernike and Percus-Yevick (PY) equations. Importantly, the spherical analog of the PY equation works best in the case of nanoscopic size domains, a length scale that is mostly inaccessible by experimental approaches such as, for example, fluorescent techniques and optical microscopies. The analytical form factors and structure factors of nanoscopic domains populating a spherical vesicle provide a new and important framework for the quantitative analysis of experimental data from commonly studied phase-separated vesicles used in a wide range of biophysical studies.

Integrals of products of spherical functions

International Nuclear Information System (INIS)

Veverka, O.

1975-01-01

Various branches of mathematical physics use integral formulas of the products of spherical functions. In quantum mechanics and in transport theory the integrals ∫sub((4π))dΩ vectorYsub(s)sup(t)(Ω vector)Ysub(l)sup(k)(Ω vector)Ysub(n)sup(m)(Ω vector), ∫sub(-1)sup(1)dμPsub(s)sup(t)(μ)Psub(l)sup(k)(μ)Psub(n)sup(m)(μ), ∫sub(-1)sup(1)dμPsub(s)(μ)Psub(l)(μ)Psub(n)(μ) are generally applied, where Ysub(α)sup(β)(Ω vector) are spherical harmonics, Psub(α)sup(β)(μ) are associated Legendre functions, and Psub(α)(μ) are Legendre polynomials. In the paper, the general procedure of calculating the integrals of the products of any combination of spherical functions is given. The procedure is referred to in a report on the boundary conditions for the cylindrical geometry in neutron transport theory for both the outer and inner cylindrical boundaries. (author)

Preparation of spherical particles by vibrating orifice technique

Science.gov (United States)

Shibata, Shuichi; Tomizawa, Atsushi; Yoshikawa, Hidemi; Yano, Tetsuji; Yamane, Masayuki

2000-05-01

Preparation of micrometer-sized spherical particles containing Rhodamine 6G (R6G) has been investigated for the spherical cavity micro-laser. Using phenyl triethoxy silane (PTES) as a starting material, R6G-doped monodisperse spherical particles were prepared by the vibrating orifice technique. Processing consists of two major processes: (1) Hydrolysis and polymerization of PTES and (2) Droplet formation from PTES oligomers by vibrating orifice technique. A cylindrical liquid jet passing through the orifice of 10 and 20 micrometers in diameter breaks up into equal- sized droplets by mechanical vibration. Alcohol solvent of these droplets was evaporated during flying with carrier gas and subsequently solidified in ammonium water trap. For making smooth surface and god shaped particles, control of molecular weight of PTES oligomer was essential. R6G-doped hybrid spherical particles of 4 to 10 micrometers size of cavity structure were successfully obtained. The spherical particles were pumped by a second harmonic pulse of Q- switched Nd:YAG laser and laser emission peaks were observed at wavelengths which correspond to the resonance modes.

Sphericity in the interacting boson model

International Nuclear Information System (INIS)

Ogata, H.

1977-01-01

The interacting boson model (IBM) of Arima and Iachello is examined. The transition between the rotational and vibrational modes of even-even nuclei is presented as a function of a sphericity parameter, which is determined primarily from yrast band spectra. The backbending feature is reasonably reproduced. (author)

Venus gravity and topography: 60th degree and order model

Science.gov (United States)

Konopliv, A. S.; Borderies, N. J.; Chodas, P. W.; Christensen, E. J.; Sjogren, W. L.; Williams, B. G.; Balmino, G.; Barriot, J. P.

1993-01-01

We have combined the most recent Pioneer Venus Orbiter (PVO) and Magellan (MGN) data with the earlier 1978-1982 PVO data set to obtain a new 60th degree and order spherical harmonic gravity model and a 120th degree and order spherical harmonic topography model. Free-air gravity maps are shown over regions where the most marked improvement has been obtained (Ishtar-Terra, Alpha, Bell and Artemis). Gravity versus topography relationships are presented as correlations per degree and axes orientation.

Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy.

Science.gov (United States)

Morimoto, Satoshi; Remijn, Gerard B; Nakajima, Yoshitaka

2016-01-01

Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects of preceding chords on harmonic expectancy from a computational perspective, using stochastic modeling. We conducted a behavioral experiment, in which participants listened to short chord sequences and evaluated the subjective relatedness of the last chord to the preceding ones. Based on these judgments, we built stochastic models of the computational process underlying harmonic expectancy. Following this, we compared the explanatory power of the models. Our results imply that, even when listening to short chord sequences, internally constructed and updated tonal assumptions determine the expectancy of the upcoming chord.

Spherical collapse model in time varying vacuum cosmologies

International Nuclear Information System (INIS)

Basilakos, Spyros; Plionis, Manolis; Sola, Joan

2010-01-01

We investigate the virialization of cosmic structures in the framework of flat Friedmann-Lemaitre-Robertson-Walker cosmological models, in which the vacuum energy density evolves with time. In particular, our analysis focuses on the study of spherical matter perturbations, as they decouple from the background expansion, 'turn around', and finally collapse. We generalize the spherical collapse model in the case when the vacuum energy is a running function of the Hubble rate, Λ=Λ(H). A particularly well-motivated model of this type is the so-called quantum field vacuum, in which Λ(H) is a quadratic function, Λ(H)=n 0 +n 2 H 2 , with n 0 ≠0. This model was previously studied by our team using the latest high quality cosmological data to constrain its free parameters, as well as the predicted cluster formation rate. It turns out that the corresponding Hubble expansion history resembles that of the traditional ΛCDM cosmology. We use this Λ(t)CDM framework to illustrate the fact that the properties of the spherical collapse model (virial density, collapse factor, etc.) depend on the choice of the considered vacuum energy (homogeneous or clustered). In particular, if the distribution of the vacuum energy is clustered, then, under specific conditions, we can produce more concentrated structures with respect to the homogeneous vacuum energy case.

A modulation model for mode splitting of magnetic perturbations in the Mega Ampere Spherical Tokamak

International Nuclear Information System (INIS)

Hole, M J; Appel, L C

2009-01-01

Recent observations of magnetic fluctuation activity in the Mega Ampere Spherical Tokamak (MAST) reveal the presence of plasmas with bands of both low and high frequency magnetic fluctuations. Such plasmas exhibit a spectrum of low frequency modes with adjacent toroidal mode numbers, for which the measured frequency is near the Doppler shifted rotation frequency of the plasma. These are thought to be tearing modes. Also present are a spectrum of high frequency modes (e.g. Alfven, fishbone and/or ICE). The frequency and mode number of the tearing mode and its harmonics is identical to the frequency and mode number splitting of the high frequency MHD activity, strongly suggesting that the high frequency splitting is produced by modulation of the high and low frequency modes. We describe a strong modulation model, in which the nonlinear terms are fitted to produce the amplitude envelope profile of the tearing mode. A bispectral analysis proves that the low frequency modes are indeed in phase with the fundamental, while Fourier-SVD mode analysis confirms the mode numbers are toroidal harmonics. Employing this model, the sideband amplitude profile of the high frequency modes is predicted, and found to be in good agreement with experimental observations. Also, toroidal mode number splitting of the high frequency activity matches the mode number of the tearing mode. Weak evidence is found to indicate the Alfvenic sidebands are in phase with the Alfven eigenmode fundamental. The findings support predictions of a strong modulation model, and suggest a need to further develop nonlinear MHD theory to predict the amplitude of coupled sidebands, and so corroborate the observed nonlinear plasma response.

Classical properties and semiclassical quantization of a spherical nuclear potential

International Nuclear Information System (INIS)

Carbonell, J.; Brut, F.; Arvieu, R.; Touchard, J.

1984-03-01

The geometrical properties of the classical energy-action surface are studied for a nuclear Woods-Saxon-like spherical potential, in connection with the E.B.K. semiclassical method of quantization. Comparisons are made with other well known cases: the spherical harmonic oscillator and the spherical billiard. The shift of single particle energies from A = 208 to A = 16 is calculated by a simple method inspired by the Erhenfest adiabatic invariants. Semiclassical results are then compared with exact Schroedinger energies. It is seen that the most significant features of the single particle spectrum are explained by local properties of the energy action surface (curvature, slope) and by their evolution with the particle number

Computational science and re-discovery: open-source implementation of ellipsoidal harmonics for problems in potential theory

International Nuclear Information System (INIS)

Bardhan, Jaydeep P; Knepley, Matthew G

2012-01-01

We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are used surprisingly infrequently, considering their substantial value for problems ranging in scale from molecules to the entire solar system. In this paper, we suggest two possible reasons for the paucity relative to spherical harmonics. The first is essentially historical—ellipsoidal harmonics developed during the late 19th century and early 20th, when it was found that only the lowest-order harmonics are expressible in closed form. Each higher-order term requires the solution of an eigenvalue problem, and tedious manual computation seems to have discouraged applications and theoretical studies. The second explanation is practical: even with modern computers and accurate eigenvalue algorithms, expansions in ellipsoidal harmonics are significantly more challenging to compute than those in Cartesian or spherical coordinates. The present implementations reduce the 'barrier to entry' by providing an easy and free way for the community to begin using ellipsoidal harmonics in actual research. We demonstrate our implementation using the specific and physiologically crucial problem of how charged proteins interact with their environment, and ask: what other analytical tools await re-discovery in an era of inexpensive computation?

Method of solution of the neutron transport equation in multidimensional cartesian geometries using spherical harmonics and spatially orthogonal polynomials

International Nuclear Information System (INIS)

Fenstermacher, T.E.

1981-01-01

The solution of the neutron transport equation has long been a subject of intense interest to nuclear engineers. Present computer codes for the solution of this equation, however, are expensive to run for large, multidimensional problems, and also suffer from computational problems such as the ray effect. A method has been developed which eliminates many of these problems. It consists of transforming the transport equation into a set of linear partial differential equations by the use of spherical harmonics. The problem volume is divided into mesh boxes, and the flux components are approximated within each mesh box by spatially orthogonal quadratic polynomials, which need not be continuous at mesh box interfaces. A variational principle is developed, and used to solve for the unknown coefficients of these polynomials. Both one dimensional and two dimensional computer codes using this method have been written. The codes have each been tested on several test cases, and the solutions checked against solutions obtained by other methods. While the codes have some difficulty in modeling sharp transients, they produce excellent results on problems where the characteristic lengths are many mean free paths. On one test case, the two dimensional code, SHOP/2D, required only one-fourth the computer time required by the finite difference, discrete ordinates code TWOTRAN to produce a solution. In addition, SHOP/2D converged much better than TWOTRAN and produced more physical-appearing results

Simple spherical ablative-implosion model

International Nuclear Information System (INIS)

Mayer, F.J.; Steele, J.T.; Larsen, J.T.

1980-01-01

A simple model of the ablative implosion of a high-aspect-ratio (shell radius to shell thickness ratio) spherical shell is described. The model is similar in spirit to Rosenbluth's snowplow model. The scaling of the implosion time was determined in terms of the ablation pressure and the shell parameters such as diameter, wall thickness, and shell density, and compared these to complete hydrodynamic code calculations. The energy transfer efficiency from ablation pressure to shell implosion kinetic energy was examined and found to be very efficient. It may be possible to attach a simple heat-transport calculation to our implosion model to describe the laser-driven ablation-implosion process. The model may be useful for determining other energy driven (e.g., ion beam) implosion scaling

Design and evaluation of a higher-order spherical microphone/ambisonic sound reproduction system for the acoustical assessment of concert halls

Science.gov (United States)

Clapp, Samuel W.

Previous studies of the perception of concert hall acoustics have generally employed two methods for soliciting listeners' judgments. One method is to have listeners rate the sound in a hall while physically present in that hall. The other method is to make recordings of different halls and seat positions, and then recreate the environment for listeners in a laboratory setting via loudspeakers or headphones. In situ evaluations offer a completely faithful rendering of all aspects of the concert hall experience. However, many variables cannot be controlled and the short duration of auditory memory precludes an objective comparison of different spaces. Simulation studies allow for more control over various aspects of the evaluations, as well as A/B comparisons of different halls and seat positions. The drawback is that all simulation methods suffer from limitations in the accuracy of reproduction. If the accuracy of the simulation system is improved, then the advantages of the simulation method can be retained, while mitigating its disadvantages. Spherical microphone array technology has received growing interest in the acoustics community in recent years for many applications including beamforming, source localization, and other forms of three-dimensional sound field analysis. These arrays can decompose a measured sound field into its spherical harmonic components, the spherical harmonics being a set of spatial basis functions on the sphere that are derived from solving the wave equation in spherical coordinates. Ambisonics is a system for two- and three-dimensional spatialized sound that is based on recreating a sound field from its spherical harmonic components. Because of these shared mathematical underpinnings, ambisonics provides a natural way to present fully spatialized renderings of recordings made with a spherical microphone array. Many of the previously studied applications of spherical microphone arrays have used a narrow frequency range where the array

Modelling and Analysis of DFIG Wind Turbine Harmonics Generated in Grids

OpenAIRE

A.Chilambuchelvan; B.BabyPriya,

2010-01-01

In this paper an analytic technique for modelling harmonics is proposed for a DFIG wind turbine connected to the grid. An algorithm based on Hilbert transform for the analysis of harmonics in power systems isdeveloped. The simulation results prove the effectiveness of the Hilbert Transform (HT) for power harmonic analysis in DFIG wind turbine connected to a grid.

A New Model of Jupiter's Magnetic Field from Juno's First Nine Orbits

DEFF Research Database (Denmark)

Connerney, J. E. P.; Kotsiaros, S.; Oliversen, R. J.

2018-01-01

A spherical harmonic model of the magnetic field of Jupiter is obtained from vector magnetic field observations acquired by the Juno spacecraft during its first nine polar orbits about the planet. Observations acquired during eight of these orbits provide the first truly global coverage of Jupiter...... currents. Partial solution of the underdetermined inverse problem using generalized inverse techniques yields a model (“Juno Reference Model through Perijove 9”) of the planetary magnetic field with spherical harmonic coefficients well determined through degree and order 10, providing the first detailed...

Rotating field current drive in spherical plasmas

International Nuclear Information System (INIS)

Brotherton-Ratcliffe, D.; Storer, R.G.

1988-01-01

The technique of driving a steady Hall current in plasmas using a rotating magnetic field is studied both numerically and analytically in the approximation of negligible ion flow. A spherical plasma bounded by an insulating wall and immersed in a uniform magnetic field which has both a rotating component (for current drive) and a constant ''vertical'' component (for MHD equilibrium) is considered. The problem is formulated in terms of an expansion of field quantities in vector spherical harmonics. The numerical code SPHERE solves the resulting pseudo-harmonic equations by a multiple shooting technique. The results presented, in addition to being relevant to non-inductive current drive generally, have a direct relevance to the rotamak experiments. For the case of no applied vertical field the steady state toroidal current driven by the rotating field per unit volume of plasma is several times less than in the long cylinder limit for a plasma of the same density, resistivity and radius. The application of a vertical field, which for certain parameter regimes gives rise to a compact torus configuration, improves the current drive dramatically and in many cases gives ''better'' current drive than the long cylinder limit. This result is also predicted by a second order perturbation analysis of the pseudo-harmonic equations. A steady state toroidal field is observed which appears consistent with experimental observations in rotamaks regarding magnitude and spatial dependence. This is an advance over previous analytical theory which predicted an oppositely directed toroidal field of undefined magnitude. (author)

Terrestrial Water Storage in African Hydrological Regimes Derived from GRACE Mission Data: Intercomparison of Spherical Harmonics, Mass Concentration, and Scalar Slepian Methods

Directory of Open Access Journals (Sweden)

Ashraf Rateb

2017-03-01

Full Text Available Spherical harmonics (SH and mascon solutions are the two most common types of solutions for Gravity Recovery and Climate Experiment (GRACE mass flux observations. However, SH signals are degraded by measurement and leakage errors. Mascon solutions (the Jet Propulsion Laboratory (JPL release, herein exhibit weakened signals at submascon resolutions. Both solutions require a scale factor examined by the CLM4.0 model to obtain the actual water storage signal. The Slepian localization method can avoid the SH leakage errors when applied to the basin scale. In this study, we estimate SH errors and scale factors for African hydrological regimes. Then, terrestrial water storage (TWS in Africa is determined based on Slepian localization and compared with JPL-mascon and SH solutions. The three TWS estimates show good agreement for the TWS of large-sized and humid regimes but present discrepancies for the TWS of medium and small-sized regimes. Slepian localization is an effective method for deriving the TWS of arid zones. The TWS behavior in African regimes and its spatiotemporal variations are then examined. The negative TWS trends in the lower Nile and Sahara at −1.08 and −6.92 Gt/year, respectively, are higher than those previously reported.

Turbulence Scattering of High Harmonic Fast Waves

International Nuclear Information System (INIS)

M. Ono; J. Hosea; B. LeBlanc; J. Menard; C.K. Phillips; R. Wilson; P. Ryan; D. Swain; J. Wilgen; S. Kubota; and T.K. Mau

2001-01-01

Effect of scattering of high-harmonic fast-magnetosonic waves (HHFW) by low-frequency plasma turbulence is investigated. Due to the similarity of the wavelength of HHFW to that of the expected low-frequency turbulence in the plasma edge region, the scattering of HHFW can become significant under some conditions. The scattering probability increases with the launched wave parallel-phase-velocity as the location of the wave cut-off layer shifts toward the lower density edge. The scattering probability can be reduced significantly with higher edge plasma temperature, steeper edge density gradient, and magnetic field. The theoretical model could explain some of the HHFW heating observations on the National Spherical Torus Experiment (NSTX)

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood's classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson-Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online.

Models of light nuclei

International Nuclear Information System (INIS)

Harvey, M.; Khanna, F.C.

1975-01-01

The general problem of what constitutes a physical model and what is known about the free nucleon-nucleon interaction are considered. A time independent formulation of the basic equations is chosen. Construction of the average field in which particles move in a general independent particle model is developed, concentrating on problems of defining the average spherical single particle field for any given nucleus, and methods for construction of effective residual interactions and other physical operators. Deformed shell models and both spherical and deformed harmonic oscillator models are discussed in detail, and connections between spherical and deformed shell models are analyzed. A section on cluster models is included. 11 tables, 21 figures

Infinite dimensional spherical analysis and harmonic analysis for groups acting on homogeneous trees

DEFF Research Database (Denmark)

Axelgaard, Emil

In this thesis, we study groups of automorphisms for homogeneous trees of countable degree by using an inductive limit approach. The main focus is the thourough discussion of two Olshanski spherical pairs consisting of automorphism groups for a homogeneous tree and a homogeneous rooted tree, resp...... finite. Finally, we discuss conditionally positive definite functions on the groups and use the generalized Bochner-Godement theorem for Olshanski spherical pairs to prove Levy-Khinchine formulas for both of the considered pairs....

A comparative study of spherical and flat-Earth geopotential modeling at satellite elevations

Science.gov (United States)

Parrott, M. H.; Hinze, W. J.; Braile, L. W.; Vonfrese, R. R. B.

1985-01-01

Flat-Earth modeling is a desirable alternative to the complex spherical-Earth modeling process. These methods were compared using 2 1/2 dimensional flat-earth and spherical modeling to compute gravity and scalar magnetic anomalies along profiles perpendicular to the strike of variably dimensioned rectangular prisms at altitudes of 150, 300, and 450 km. Comparison was achieved with percent error computations (spherical-flat/spherical) at critical anomaly points. At the peak gravity anomaly value, errors are less than + or - 5% for all prisms. At 1/2 and 1/10 of the peak, errors are generally less than 10% and 40% respectively, increasing to these values with longer and wider prisms at higher altitudes. For magnetics, the errors at critical anomaly points are less than -10% for all prisms, attaining these magnitudes with longer and wider prisms at higher altitudes. In general, in both gravity and magnetic modeling, errors increase greatly for prisms wider than 500 km, although gravity modeling is more sensitive than magnetic modeling to spherical-Earth effects. Preliminary modeling of both satellite gravity and magnetic anomalies using flat-Earth assumptions is justified considering the errors caused by uncertainties in isolating anomalies.

Precise Model Analysis for 3-phase High Power Converter using the Harmonic State Space Modeling

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede

2015-01-01

This paper presents about the generalized multi-frequency modeling and analysis methodology, which can be used in control loop design and stability analysis. In terms of the switching frequency of high power converter, there can be harmonics interruption if the voltage source converter has a low...... switching frequency ratio or multi-sampling frequency. The range of the control bandwidth can include the switching component. Thus, the systems become unstable. This paper applies the Harmonic State Space (HSS) Modeling method in order to find out the transfer function for each harmonics terms...

Harmonicity in supermanifolds and sigma models

International Nuclear Information System (INIS)

Munoz-Masque, Jaime; Vallejo, Jose A.

2009-01-01

We show that given an odd metric G on a supermanifold (M, A) and its associated Laplacian Δ, it is possible to interpret harmonic superfunctions (i.e., those f is an element of A such that Δf = 0) as solutions to a variational problem describing a supersymmetric sigma model.

The Two-Capacitor Problem Revisited: A Mechanical Harmonic Oscillator Model Approach

Science.gov (United States)

Lee, Keeyung

2009-01-01

The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that "exactly half" the work done by a constant applied…

Towards Spherical Mesh Gravity and Magnetic Modelling in an HPC Environment

Science.gov (United States)

Lane, R. J.; Brodie, R. C.; de Hoog, M.; Navin, J.; Chen, C.; Du, J.; Liang, Q.; Wang, H.; Li, Y.

2013-12-01

) to develop software for spherical mesh modelling of gravity and magnetic data, 2) to ensure that we had access to the source code for any modelling software so that we could customize and compile it for the HPC environment of our choosing, 3) to learn about the different types of HPC environments, 4) to investigate which type of HPC environment would have the optimum mix of availability to us, compute resources, and architecture, and 5) to promote the in-house development a virtual globe application that is built on an open-source Eclipse Rich Client Platform (RCP) called ';EarthSci' that in turn makes use of the NASA World Wind Software Development Kit (SDK) as the globe rendering engine. We hope to have an initial test capability in place in the early part of 2014. With a region-of-interest enclosing 40-180 degrees E, 0-90 degrees S, the first application will be very coarse compared to our final aspirations. This work will be based on the following; a) the global CRUST1.0 litho-model, b) the GOCO03S spherical harmonic satellite gravity model, and c) the EMAG2 global grid of the anomaly of the magnetic intensity. These development activities will enable us to understand the geology of the Australian region and to use this knowledge in a range of applications, including mineral and energy exploration, natural hazard mitigation, and groundwater management.

FDTD verification of deep-set brain tumor hyperthermia using a spherical microwave source distribution

Energy Technology Data Exchange (ETDEWEB)

Dunn, D. [20th Intelligence Squadron, Offutt AFB, NE (United States); Rappaport, C.M. [Northeastern Univ., Boston, MA (United States). Center for Electromagnetics Research; Terzuoli, A.J. Jr. [Air Force Inst. of Tech., Dayton, OH (United States). Graduate School of Engineering

1996-10-01

Although use of noninvasive microwave hyperthermia to treat cancer is problematic in many human body structures, careful selection of the source electric field distribution around the entire surface of the head can generate a tightly focused global power density maximum at the deepest point within the brain. An analytic prediction of the optimum volume field distribution in a layered concentric head model based on summing spherical harmonic modes is derived and presented. This ideal distribution is then verified using a three-dimensional finite difference time domain (TDTD) simulation with a discretized, MRI-based head model excited by the spherical source. The numerical computation gives a very similar dissipated power pattern as the analytic prediction. This study demonstrates that microwave hyperthermia can theoretically be a feasible cancer treatment modality for tumors in the head, providing a well-resolved hot-spot at depth without overheating any other healthy tissue.

The Tax harmonization in open regionalism ; The European model

Directory of Open Access Journals (Sweden)

Mouloud MELIKAOUI

2014-06-01

Full Text Available This research examines the subject of alternative regionalism or open regionalism and reality within the multilateral trading system, based on growing liberalization of trade, and the problem of compatibility between them, as well as the limits of economic policy harmonization in the framework of Open regionalism, special tax harmonization, in the light of economic and tax disparities of the Member States, with an overview of the European tax harmonization and limits. The Study concluded the importance of tax harmonization as a tool by activation of the concept of open regionalism, through facilitating capitals flows and investments between member states and reduction of the négatives phenomena of tax. It recommended the need to emphasizing on the importance of gradually harmonization for tax policy, and expand the rule of tax treaties and exchange of tax information and experiences between countries, This is in light a holistic approach to other economic policies as a the exchange rate policy and monetary policy, just as is the case in the European model.

The simplified spherical harmonics (SP{sub L}) methodology with space and moment decomposition in parallel environments

Energy Technology Data Exchange (ETDEWEB)

Gianluca, Longoni; Alireza, Haghighat [Florida University, Nuclear and Radiological Engineering Department, Gainesville, FL (United States)

2003-07-01

In recent years, the SP{sub L} (simplified spherical harmonics) equations have received renewed interest for the simulation of nuclear systems. We have derived the SP{sub L} equations starting from the even-parity form of the S{sub N} equations. The SP{sub L} equations form a system of (L+1)/2 second order partial differential equations that can be solved with standard iterative techniques such as the Conjugate Gradient (CG). We discretized the SP{sub L} equations with the finite-volume approach in a 3-D Cartesian space. We developed a new 3-D general code, Pensp{sub L} (Parallel Environment Neutral-particle SP{sub L}). Pensp{sub L} solves both fixed source and criticality eigenvalue problems. In order to optimize the memory management, we implemented a Compressed Diagonal Storage (CDS) to store the SP{sub L} matrices. Pensp{sub L} includes parallel algorithms for space and moment domain decomposition. The computational load is distributed on different processors, using a mapping function, which maps the 3-D Cartesian space and moments onto processors. The code is written in Fortran 90 using the Message Passing Interface (MPI) libraries for the parallel implementation of the algorithm. The code has been tested on the Pcpen cluster and the parallel performance has been assessed in terms of speed-up and parallel efficiency. (author)

Modeling the Interaction of Mineral Dust with Solar Radiation: Spherical versus Non-spherical Particles

Science.gov (United States)

Hoshyaripour, A.; Vogel, B.; Vogel, H.

2017-12-01

Mineral dust, emitted from arid and semi-arid regions, is the most dominant atmospheric aerosol by mass. Beside detrimental effect on air quality, airborne dust also influences the atmospheric radiation by absorbing and scattering solar and terrestrial radiation. As a result, while the long-term radiative impacts of dust are important for climate, the short-term effects are significant for the photovoltaic energy production. Therefore, it is a vital requirement to accurately forecast the effects of dust on energy budget of the atmosphere and surface. To this end, a major issue is the fact that dust particles are non-spherical. Thus, the optical properties of such particles cannot be calculated precisely using the conventional methods like Mie theory that are often used in climate and numerical weather forecast models. In this study, T-Matrix method is employed, which is able to treat the non-sphericity of particles. Dust particles are assumed to be prolate spheroids with aspect ratio of 1.5 distributed in three lognormal modes. The wavelength-dependent refractive indices of dust are used in T-Matrix algorithm to calculate the extinction coefficient, single scattering albedo, asymmetry parameter and backscattering ratio at different wavelengths. These parameters are then implemented in ICON-ART model (ICOsahedral Nonhydrostatic model with Aerosols and Reactive Trace gases) to conduct a global simulation with 80 km horizontal resolution and 90 vertical levels. April 2014 is selected as the simulation period during which North African dust plumes reached central Europe and Germany. Results show that treatment of non-sphericity reduces the dust AOD in the range of 10 to 30%/. The impacts on diffuse and direct radiation at global, regional and local scales show strong dependency on the size distribution of the airborne dust. The implications for modeling and remote sensing the dust impacts on solar energy are also discussed.

Quantification of intraventricular hemorrhage with electrical impedance tomography using a spherical model

International Nuclear Information System (INIS)

Tang, T; Sadleir, R J

2011-01-01

We have developed a robust EEG-based current pattern which shows promise for the detection of intraventricular hemorrhage (IVH) in neonates. Our reconstructions to date are based on a layered spherical head model. In this study, the current pattern was used to gather data from three realistic-shaped neonatal head models and a physical phantom based on one of these models. We found that a sensitivity matrix calculated from a spherical model gave us satisfactory reconstructions in terms of both image quality and quantification. Incorporating correct geometry information into the forward model improved image quality. However, it did not improve quantification accuracy. The results indicate that using a spherical matrix may be a more practical choice for monitoring IVH volumes in neonates for whom patient-specific models are not available

Digital model for harmonic interactions in AC/DC/AC systems

Energy Technology Data Exchange (ETDEWEB)

Guarini, A P; Rangel, R D; Pilotto, L A.S.; Pinto, R J; Passos, Junior, R [Centro de Pesquisas de Energia Eletrica (CEPEL), Rio de Janeiro, RJ (Brazil)

1994-12-31

The main purpose of this paper is to present a model for calculation of HVdc converter harmonics taking into account the influence of the harmonic interactions between the ac systems in dc link transmissions. The ideas and methodologies used in the model development take into account the dc current ripple and ac voltage distortion in the ac systems. The theory of switching functions is applied to contemplate for the frequency conversions between the ac and dc sides, in an iterative process. It is possible then to obtain, even in balanced situations, non-characteristic harmonics that are produced by frequencies originated in the other terminal, which can be significant in a strongly coupled system, such as back-to-back configuration. (author) 9 refs., 3 figs.

Numerical modeling of Harmonic Imaging and Pulse Inversion fields

Science.gov (United States)

Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis

2003-10-01

Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.

The Combination of Spherical Photogrammetry and UAV for 3D Modeling

Science.gov (United States)

Ihsanudin, T.; Affriani, A. R.

2017-12-01

The complete of 3D models required the object that was recorded from both side and top. If the object recorded from above, then the object from the side can not be covered, and if the objects recorded from the side, it can not be covered from the top. Recording of objects from the side using spherical photogrammetry method and from the top using UAV method. The merge of both models using a conform transformation, by bringing the spherical photogrammetry coordinates system to the UAV model. The object of this research is Ratu Boko temple, Sleman, Yogyakarta. The spherical photogrammetry recording was performed by rotating the camera in 360° angle on the entire area of the temple. The area consists of 12 stations. The UAV method uses a drone with flight attitude of 20 meters. The merge of the both models produced the completeness of the temple model from the top and side.

Global and Regional Gravity Field Determination from GOCE Kinematic Orbit by Means of Spherical Radial Basis Functions

Czech Academy of Sciences Publication Activity Database

Bucha, B.; Bezděk, Aleš; Sebera, Josef; Janak, J.

2015-01-01

Roč. 36, č. 6 (2015), s. 773-801 ISSN 0169-3298 R&D Projects: GA ČR GA13-36843S Grant - others:SAV(SK) VEGA 1/0954/15 Institutional support: RVO:67985815 Keywords : spherical radial basis functions * spherical harmonics * geopotential Subject RIV: BN - Astronomy, Celestial Mechanics, Astrophysics Impact factor: 3.622, year: 2015

Spherical conformal models for compact stars

Energy Technology Data Exchange (ETDEWEB)

Takisa, P.M.; Maharaj, S.D.; Manjonjo, A.M.; Moopanar, S. [University of KwaZulu-Natal, Astrophysics and Cosmology Research Unit, School of Mathematics, Statistics and Computer Science, Durban (South Africa)

2017-10-15

We consider spherical exact models for compact stars with anisotropic pressures and a conformal symmetry. The conformal symmetry condition generates an integral relationship between the gravitational potentials. We solve this condition to find a new anisotropic solution to the Einstein field equations. We demonstrate that the exact solution produces a relativistic model of a compact star. The model generates stellar radii and masses consistent with PSR J1614-2230, Vela X1, PSR J1903+327 and Cen X-3. A detailed physical examination shows that the model is regular, well behaved and stable. The mass-radius limit and the surface red shift are consistent with observational constraints. (orig.)

Building Mathematical Models of Simple Harmonic and Damped Motion.

Science.gov (United States)

Edwards, Thomas

1995-01-01

By developing a sequence of mathematical models of harmonic motion, shows that mathematical models are not right or wrong, but instead are better or poorer representations of the problem situation. (MKR)

Analytical solutions of electric potential and impedance for a multilayered spherical volume conductor excited by time-harmonic electric current source: application in brain EIT

International Nuclear Information System (INIS)

Xiao Chunyan; Lei Yinzhao

2005-01-01

A model of a multilayered spherical volume conductor with four electrodes is built. In this model, a time-harmonic electric current is injected into the sphere through a pair of drive electrodes, and electric potential is measured by the other pair of measurement electrodes. By solving the boundary value problem of the electromagnetic field, the analytical solutions of electric potential and impedance in the whole conduction region are derived. The theoretical values of electric potential on the surface of the sphere are in good accordance with the experimental results. The analytical solutions are then applied to the simulation of the forward problem of brain electrical impedance tomography (EIT). The results show that, for a real human head, the imaginary part of the electric potential is not small enough to be ignored at above 20 kHz, and there exists an approximate linear relationship between the real and imaginary parts of the electric potential when the electromagnetic parameters of the innermost layer keep unchanged. Increase in the conductivity of the innermost layer leads to a decrease of the magnitude of both real and imaginary parts of the electric potential on the scalp. However, the increase of permittivity makes the magnitude of the imaginary part of the electric potential increase while that of the real part decreases, and vice versa

Faddeev wave function decomposition using bipolar harmonics

International Nuclear Information System (INIS)

Friar, J.L.; Tomusiak, E.L.; Gibson, B.F.; Payne, G.L.

1981-01-01

The standard partial wave (channel) representation for the Faddeev solution to the Schroedinger equation for the ground state of 3 nucleons is written in terms of functions which couple the interacting pair and spectator angular momenta to give S, P, and D waves. For each such coupling there are three terms, one for each of the three cyclic permutations of the nucleon coordinates. A series of spherical harmonic identities is developed which allows writing the Faddeev solution in terms of a basis set of 5 bipolar harmonics: 1 for S waves; 1 for P waves; and 3 for D waves. The choice of a D-wave basis is largely arbitrary, and specific choices correspond to the decomposition schemes of Derrick and Blatt, Sachs, Gibson and Schiff, and Bolsterli and Jezak. The bipolar harmonic form greatly simplifies applications which utilize the wave function, and we specifically discuss the isoscalar charge (or mass) density and the 3 He Coulomb energy

Policy harmonized approach for the EU agricultural sector modelling

Directory of Open Access Journals (Sweden)

G. SALPUTRA

2008-12-01

Full Text Available Policy harmonized (PH approach allows for the quantitative assessment of the impact of various elements of EU CAP direct support schemes, where the production effects of direct payments are accounted through reaction prices formed by producer price and policy price add-ons. Using the AGMEMOD model the impacts of two possible EU agricultural policy scenarios upon beef production have been analysed – full decoupling with a switch from historical to regional Single Payment scheme or alternatively with re-distribution of country direct payment envelopes via introduction of EU-wide flat area payment. The PH approach, by systematizing and harmonizing the management and use of policy data, ensures that projected differential policy impacts arising from changes in common EU policies reflect the likely actual differential impact as opposed to differences in how “common” policies are implemented within analytical models. In the second section of the paper the AGMEMOD model’s structure is explained. The policy harmonized evaluation method is presented in the third section. Results from an application of the PH approach are presented and discussed in the paper’s penultimate section, while section 5 concludes.;

Quantization of a 3D Nonstationary Harmonic plus an Inverse Harmonic Potential System

Directory of Open Access Journals (Sweden)

Salim Medjber

2016-01-01

Full Text Available The Schrödinger solutions for a three-dimensional central potential system whose Hamiltonian is composed of a time-dependent harmonic plus an inverse harmonic potential are investigated. Because of the time-dependence of parameters, we cannot solve the Schrödinger solutions relying only on the conventional method of separation of variables. To overcome this difficulty, special mathematical methods, which are the invariant operator method, the unitary transformation method, and the Nikiforov-Uvarov method, are used when we derive solutions of the Schrödinger equation for the system. In particular, the Nikiforov-Uvarov method with an appropriate coordinate transformation enabled us to reduce the eigenvalue equation of the invariant operator, which is a second-order differential equation, to a hypergeometric-type equation that is convenient to treat. Through this procedure, we derived exact Schrödinger solutions (wave functions of the system. It is confirmed that the wave functions are represented in terms of time-dependent radial functions, spherical harmonics, and general time-varying global phases. Such wave functions are useful for studying various quantum properties of the system. As an example, the uncertainty relations for position and momentum are derived by taking advantage of the wave functions.

Person Appearance Modeling and Orientation Estimation using Spherical Harmonics

NARCIS (Netherlands)

Liem, M.C.; Gavrila, D.M.

2013-01-01

We present a novel approach for the joint estimation of a person's overall body orientation, 3D shape and texture, from overlapping cameras. Overall body orientation (i.e. rotation around torso major axis) is estimated by minimizing the difference between a learned texture model in a canonical

Nonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators

Science.gov (United States)

Bardhan, Jaydeep P.; Knepley, Matthew G.; Brune, Peter

2015-01-01

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical harmonics. To introduce this uncommon approach for calculations in separable geometries, we first re-derive Kirkwood’s classic results for a protein surrounded concentrically by a pure-water ion-exclusion (Stern) layer and then a dilute electrolyte, which is modeled with the linearized Poisson–Boltzmann equation. The eigenfunction-expansion approach provides a computationally efficient way to test some implications of nonlocal models, including estimating the reasonable range of the nonlocal length-scale parameter λ. Our results suggest that nonlocal solvent response may help to reduce the need for very high dielectric constants in calculating pH-dependent protein behavior, though more sophisticated nonlocal models are needed to resolve this question in full. An open-source MATLAB implementation of our approach is freely available online. PMID:26273581

Modelling the harmonized tertiary Institutions Salary Structure ...

African Journals Online (AJOL)

This paper analyses the Harmonized Tertiary Institution Salary Structure (HATISS IV) used in Nigeria. The irregularities in the structure are highlighted. A model that assumes a polynomial trend for the zero step salary, and exponential trend for the incremental rates, is suggested for the regularization of the structure.

Quantitative modeling of the third harmonic emission spectrum of plasmonic nanoantennas.

Science.gov (United States)

Hentschel, Mario; Utikal, Tobias; Giessen, Harald; Lippitz, Markus

2012-07-11

Plasmonic dimer nanoantennas are characterized by a strong enhancement of the optical field, leading to large nonlinear effects. The third harmonic emission spectrum thus depends strongly on the antenna shape and size as well as on its gap size. Despite the complex shape of the nanostructure, we find that for a large range of different geometries the nonlinear spectral properties are fully determined by the linear response of the antenna. We find excellent agreement between the measured spectra and predictions from a simple nonlinear oscillator model. We extract the oscillator parameters from the linear spectrum and use the amplitude of the nonlinear perturbation only as scaling parameter of the third harmonic spectra. Deviations from the model only occur for gap sizes below 20 nm, indicating that only for these small distances the antenna hot spot contributes noticeable to the third harmonic generation. Because of its simplicity and intuitiveness, our model allows for the rational design of efficient plasmonic nonlinear light sources and is thus crucial for the design of future plasmonic devices that give substantial enhancement of nonlinear processes such as higher harmonics generation as well as difference frequency mixing for plasmonically enhanced terahertz generation.

A Comprehensive and Harmonized Digital Forensic Investigation Process Model.

Science.gov (United States)

Valjarevic, Aleksandar; Venter, Hein S

2015-11-01

Performing a digital forensic investigation (DFI) requires a standardized and formalized process. There is currently neither an international standard nor does a global, harmonized DFI process (DFIP) exist. The authors studied existing state-of-the-art DFIP models and concluded that there are significant disparities pertaining to the number of processes, the scope, the hierarchical levels, and concepts applied. This paper proposes a comprehensive model that harmonizes existing models. An effort was made to incorporate all types of processes proposed by the existing models, including those aimed at achieving digital forensic readiness. The authors introduce a novel class of processes called concurrent processes. This is a novel contribution that should, together with the rest of the model, enable more efficient and effective DFI, while ensuring admissibility of digital evidence. Ultimately, the proposed model is intended to be used for different types of DFI and should lead to standardization. © 2015 American Academy of Forensic Sciences.

Vibrational collective model for spheric even-even nuclei

International Nuclear Information System (INIS)

Cruz, M.T.F. da.

1985-01-01

A review is made on the evidences of collective motions in spherical even-even nuclei. The several multipole transitions occuring in such a nuclei are discussed. Some hypothesis which are necessary in order to build-up the model are presented. (L.C.) [pt

The prospects for electron Bernstein wave heating of spherical tokamaks

International Nuclear Information System (INIS)

Cairns, R.A.; Lashmore-Davies, C.N.

2000-02-01

Electron Bernstein waves are analysed as possible candidates for heating spherical tokamaks. An inhomogeneous plane slab model of the plasma with a sheared magnetic field is used to calculate the linear conversion of the ordinary mode (O-mode) to the extraordinary mode (X-mode). A formula for the fraction of the incident O-mode energy which is converted to the X-mode at the O-mode cut-off is derived. This fraction is then able to propagate to the upper hybrid resonance where it is converted to the electron Bernstein mode. The damping of electron Bernstein waves at the fourth harmonic resonance, corresponding to a 60GHz source on the Mega Amp Spherical Tokamak MAST [A C Darke et al Proc 16th Symposium on Fusion Energy, Champaign- Urbana, Illinois USA IEEE, 2 p1456 (1995)], is computed. This is shown to be so strongly absorbing that the electron Bernstein wave would be totally absorbed in the outer regions of the resonance. This feature implies that electron Bernstein wave current drive (on- or off-axis) could be very efficient. (author)

A Method for Harmonic Sources Detection based on Harmonic Distortion Power Rate

Science.gov (United States)

Lin, Ruixing; Xu, Lin; Zheng, Xian

2018-03-01

Harmonic sources detection at the point of common coupling is an essential step for harmonic contribution determination and harmonic mitigation. The harmonic distortion power rate index is proposed for harmonic source location based on IEEE Std 1459-2010 in the paper. The method only based on harmonic distortion power is not suitable when the background harmonic is large. To solve this problem, a threshold is determined by the prior information, when the harmonic distortion power is larger than the threshold, the customer side is considered as the main harmonic source, otherwise, the utility side is. A simple model of public power system was built in MATLAB/Simulink and field test results of typical harmonic loads verified the effectiveness of proposed method.

The generalized spherical model of ferromagnetic films

International Nuclear Information System (INIS)

Costache, G.

1977-12-01

The D→ infinity of the D-vectorial model of a ferromagnetic film with free surfaces is exactly solved. The mathematical mechanism responsible for the onset of a phase transition in the system is a generalized sticking phenomenon. It is shown that the temperature at which the sticking appears, the transition temperature of the model is monotonously increasing with increasing the number of layers of the film, contrary to what happens in the spherical model with overall constraint. Certain correlation inequalities of Griffiths type are shown to hold. (author)

Vector model for polarized second-harmonic generation microscopy under high numerical aperture

International Nuclear Information System (INIS)

Wang, Xiang-Hui; Chang, Sheng-Jiang; Lin, Lie; Wang, Lin-Rui; Huo, Bing-Zhong; Hao, Shu-Jian

2010-01-01

Based on the vector diffraction theory and the generalized Jones matrix formalism, a vector model for polarized second-harmonic generation (SHG) microscopy is developed, which includes the roles of the axial component P z , the weight factor and the cross-effect between the lateral components. The numerical results show that as the relative magnitude of P z increases, the polarization response of the second-harmonic signal will vary from linear polarization to elliptical polarization and the polarization orientation of the second-harmonic signal is different from that under the paraxial approximation. In addition, it is interesting that the polarization response of the detected second-harmonic signal can change with the value of the collimator lens NA. Therefore, it is more advantageous to adopt the vector model to investigate the property of polarized SHG microscopy for a variety of cases

Effect of Rolling Resistance in Dem Models With Spherical Bodies

Directory of Open Access Journals (Sweden)

Dubina Radek

2016-12-01

Full Text Available The rolling resistance is an artificial moment arising on the contact of two discrete elements which mimics resistance of two grains of complex shape in contact rolling relatively to each other. The paper investigates the influence of rolling resistance on behaviour of an assembly of spherical discrete elements. Besides the resistance to rolling, the contacts between spherical particles obey the Hertzian law in normal straining and Coulomb model of friction in shear.

Equivalence of the spherical and deformed shell-model approach to intruder states

International Nuclear Information System (INIS)

Heyde, K.; Coster, C. de; Ryckebusch, J.; Waroquier, M.

1989-01-01

We point out that the description of intruder states, incorporating particle-hole (p-h) excitation across a closed shell in the spherical shell model or a description starting from the Nilsson model are equivalent. We furthermore indicate that the major part of the nucleon-nucleon interaction, responsible for the low excitation energy of intruder states comes as a two-body proton-neutron quadrupole interaction in the spherical shell model. In the deformed shell model, quadrupole binding energy is gained mainly through the one-body part of the potential. (orig.)

Spherical and hyperspherical harmonics representation of van der Waals aggregates

Science.gov (United States)

Lombardi, Andrea; Palazzetti, Federico; Aquilanti, Vincenzo; Grossi, Gaia; Albernaz, Alessandra F.; Barreto, Patricia R. P.; Cruz, Ana Claudia P. S.

2016-12-01

The representation of the potential energy surfaces of atom-molecule or molecular dimers interactions should account faithfully for the symmetry properties of the systems, preserving at the same time a compact analytical form. To this aim, the choice of a proper set of coordinates is a necessary precondition. Here we illustrate a description in terms of hyperspherical coordinates and the expansion of the intermolecular interaction energy in terms of hypersherical harmonics, as a general method for building potential energy surfaces suitable for molecular dynamics simulations of van der Waals aggregates. Examples for the prototypical case diatomic-molecule-diatomic-molecule interactions are shown.

Methodologies for Wind Turbine and STATCOM Integration in Wind Power Plant Models for Harmonic Resonances Assessment

DEFF Research Database (Denmark)

Freijedo Fernandez, Francisco Daniel; Chaudhary, Sanjay Kumar; Guerrero, Josep M.

2015-01-01

-domain. As an alternative, a power based averaged modelling is also proposed. Type IV wind turbine harmonic signature and STATCOM active harmonic mitigation are considered for the simulation case studies. Simulation results provide a good insight of the features and limitations of the proposed methodologies.......This paper approaches modelling methodologies for integration of wind turbines and STATCOM in harmonic resonance studies. Firstly, an admittance equivalent model representing the harmonic signature of grid connected voltage source converters is provided. A simplified type IV wind turbine modelling...... is then straightforward. This linear modelling is suitable to represent the wind turbine in the range of frequencies at which harmonic interactions are likely. Even the admittance method is suitable both for frequency and time domain studies, some limitations arise in practice when implementing it in the time...

Spherical CNNs

OpenAIRE

Cohen, Taco S.; Geiger, Mario; Koehler, Jonas; Welling, Max

2018-01-01

Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have created a demand for models that can analyze spherical images. Examples include omnidirectional vision for drones, robots, and autonomous cars, molecular regression problems, and global weather and climate modelling. A naive application of convolutional networks to a planar projection of the spherical signal is destined t...

Time-dependent Hartree approximation and time-dependent harmonic oscillator model

International Nuclear Information System (INIS)

Blaizot, J.P.

1982-01-01

We present an analytically soluble model for studying nuclear collective motion within the framework of the time-dependent Hartree (TDH) approximation. The model reduces the TDH equations to the Schroedinger equation of a time-dependent harmonic oscillator. Using canonical transformations and coherent states we derive a few properties of the time-dependent harmonic oscillator which are relevant for applications. We analyse the role of the normal modes in the time evolution of a system governed by TDH equations. We show how these modes couple together due to the anharmonic terms generated by the non-linearity of the theory. (orig.)

Towards Relaxing the Spherical Solar Radiation Pressure Model for Accurate Orbit Predictions

Science.gov (United States)

Lachut, M.; Bennett, J.

2016-09-01

The well-known cannonball model has been used ubiquitously to capture the effects of atmospheric drag and solar radiation pressure on satellites and/or space debris for decades. While it lends itself naturally to spherical objects, its validity in the case of non-spherical objects has been debated heavily for years throughout the space situational awareness community. One of the leading motivations to improve orbit predictions by relaxing the spherical assumption, is the ongoing demand for more robust and reliable conjunction assessments. In this study, we explore the orbit propagation of a flat plate in a near-GEO orbit under the influence of solar radiation pressure, using a Lambertian BRDF model. Consequently, this approach will account for the spin rate and orientation of the object, which is typically determined in practice using a light curve analysis. Here, simulations will be performed which systematically reduces the spin rate to demonstrate the point at which the spherical model no longer describes the orbital elements of the spinning plate. Further understanding of this threshold would provide insight into when a higher fidelity model should be used, thus resulting in improved orbit propagations. Therefore, the work presented here is of particular interest to organizations and researchers that maintain their own catalog, and/or perform conjunction analyses.

A simple mechanical model for the isotropic harmonic oscillator

International Nuclear Information System (INIS)

Nita, Gelu M

2010-01-01

A constrained elastic pendulum is proposed as a simple mechanical model for the isotropic harmonic oscillator. The conceptual and mathematical simplicity of this model recommends it as an effective pedagogical tool in teaching basic physics concepts at advanced high school and introductory undergraduate course levels.

Numerical Modeling of a Spherical Array of Monopoles Using FDTD Method

DEFF Research Database (Denmark)

Franek, Ondrej; Pedersen, Gert Frølund; Andersen, Jørgen Bach

2006-01-01

In this paper, the spherical-coordinate finite-difference time-domain method is applied to numerical analysis of phased array of monopoles distributed over a sphere. Outer boundary of the given problem is modeled by accurate spherical-coordinate anisotropic perfectly matched layer. The problem...... of increased cell aspect ratio near the sphere poles causing degradation of results is solved by dispersion optimization through artificial anisotropy. The accuracy of the approach is verified by comparing a model case with an exact solution. Finally, radiation patterns obtained by frequency-domain near-to-far-field...

National Spherical Torus Experiment (NSTX)

International Nuclear Information System (INIS)

Masayuki Ono

2000-01-01

The main aim of National Spherical Torus Experiment (NSTX) is to establish the fusion physics principles of the innovative spherical torus (ST) concept. Physics outcome of the NSTX research program is relevant to near-term applications such as the Volume Neutron Source (VNS) and burning plasmas, and future applications such as the pilot and power plants. The NSTX device began plasma operations in February 1999 and the plasma current was successfully ramped up to the design value of 1 million amperes (MA) on December 14, 1999. The CHI (Coaxial Helicity Injection) and HHFW (High Harmonic Fast Wave) experiments have also started. Stable CHI discharges of up to 133 kA and 130-msec duration have been produced using 20 kA of injected current. Using eight antennas connected to two transmitters, up to 2 MW of HHFW power was successfully coupled to the plasma. The Neutral-beam Injection (NBI) heating system and associated NBI-based diagnostics such as the Charge-exchange Recombination Spectrometer (CHERS) will be operational in October 2000

On the shell-model-connection of the cluster model

International Nuclear Information System (INIS)

Cseh, J.

2000-01-01

Complete text of publication follows. The interrelation of basic nuclear structure models is a longstanding problem. The connection between the spherical shell model and the quadrupole collective model has been studied extensively, and symmetry considerations proved to be especially useful in this respect. A collective band was interpreted in the shell model language long ago [1] as a set of states (of the valence nucleons) with a specific SU(3) symmetry. Furthermore, the energies of these rotational states are obtained to a good approximation as eigenvalues of an SU(3) dynamically symmetric shell model Hamiltonian. On the other hand the relation of the shell model and cluster model is less well explored. The connection of the harmonic oscillator (i.e. SU(3)) bases of the two approaches is known [2] but it was established only for the unrealistic harmonic oscillator interactions. Here we investigate the question: Can an SU(3) dynamically symmetric interaction provide a similar connection between the spherical shell model and the cluster model, like the one between the shell and collective models? In other words: whether or not the energy of the states of the cluster bands, defined by a specific SU(3) symmetries, can be obtained from a shell model Hamiltonian (with SU(3) dynamical symmetry). We carried out calculations within the framework of the semimicroscopic algebraic cluster model [3,4] in order to find an answer to this question, which seems to be affirmative. In particular, the energies obtained from such a Hamiltonian for several bands of the ( 12 C, 14 C, 16 O, 20 Ne, 40 Ca) + α systems turn out to be in good agreement with the experimental values. The present results show that the simple and transparent SU(3) connection between the spherical shell model and the cluster model is valid not only for the harmonic oscillator interactions, but for much more general (SU(3) dynamically symmetric) Hamiltonians as well, which result in realistic energy spectra. Via

Mathematical analysis of the boundary-integral based electrostatics estimation approximation for molecular solvation: exact results for spherical inclusions.

Science.gov (United States)

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GBε theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. © 2011 American Institute of Physics

Improved dq-axes Model of PMSM Considering Airgap Flux Harmonics and Saturation

DEFF Research Database (Denmark)

Fasil, Muhammed; Antaloae, Ciprian; Mijatovic, Nenad

-saturation on constant torque curves of PMSM. Two interior permanent magnet motor with two different rotor topologies and different specifications are designed to evaluate the effect of saturation on synchronous and harmonic inductances, and operating points of the machines.......The classical dq-axes model of permanent magnet synchronous machines (PMSM) uses linear approximation. This was not an issue in earlier versions of PMSM drives because they mostly used surface magnet motors. With the arrival of interior permanent magnet (IPM) machines, which use reluctance torque...... along with magnet torque, the accuracy of linear models are found to be insufficient. In this work, the effect of air gap flux harmonics is included in the classical model of PMSM using d and q-axes harmonic inductances. Further, a method has been presented to assess the effect of saturation and cross...

On the implementation of the spherical collapse model for dark energy models

Energy Technology Data Exchange (ETDEWEB)

Pace, Francesco [Jodrell Bank Centre for Astrophysics, School of Physics and Astronomy, The University of Manchester, Manchester, M13 9PL (United Kingdom); Meyer, Sven; Bartelmann, Matthias, E-mail: francesco.pace@manchester.ac.uk, E-mail: sven.meyer@uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de [Zentrum für Astronomie der Universität Heidelberg, Institut für theoretische Astrophysik, Philosophenweg 12, D-69120, Heidelberg (Germany)

2017-10-01

In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δ{sub c}, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δ{sub c} for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.

On the implementation of the spherical collapse model for dark energy models

Science.gov (United States)

Pace, Francesco; Meyer, Sven; Bartelmann, Matthias

2017-10-01

In this work we review the theory of the spherical collapse model and critically analyse the aspects of the numerical implementation of its fundamental equations. By extending a recent work by [1], we show how different aspects, such as the initial integration time, the definition of constant infinity and the criterion for the extrapolation method (how close the inverse of the overdensity has to be to zero at the collapse time) can lead to an erroneous estimation (a few per mill error which translates to a few percent in the mass function) of the key quantity in the spherical collapse model: the linear critical overdensity δc, which plays a crucial role for the mass function of halos. We provide a better recipe to adopt in designing a code suitable to a generic smooth dark energy model and we compare our numerical results with analytic predictions for the EdS and the ΛCDM models. We further discuss the evolution of δc for selected classes of dark energy models as a general test of the robustness of our implementation. We finally outline which modifications need to be taken into account to extend the code to more general classes of models, such as clustering dark energy models and non-minimally coupled models.

World Gravity Map: a set of global complete spherical Bouguer and isostatic anomaly maps and grids

Science.gov (United States)

Bonvalot, S.; Balmino, G.; Briais, A.; Kuhn, M.; Peyrefitte, A.; Vales, N.; Biancale, R.; Gabalda, G.; Reinquin, F.

2012-04-01

We present here a set of digital maps of the Earth's gravity anomalies (surface free air, Bouguer and isostatic), computed at Bureau Gravimetric International (BGI) as a contribution to the Global Geodetic Observing Systems (GGOS) and to the global geophysical maps published by the Commission for the Geological Map of the World (CGMW) with support of UNESCO and other institutions. The Bouguer anomaly concept is extensively used in geophysical interpretation to investigate the density distributions in the Earth's interior. Complete Bouguer anomalies (including terrain effects) are usually computed at regional scales by integrating the gravity attraction of topography elements over and beyond a given area (under planar or spherical approximations). Here, we developed and applied a worldwide spherical approach aimed to provide a set of homogeneous and high resolution gravity anomaly maps and grids computed at the Earth's surface, taking into account a realistic Earth model and reconciling geophysical and geodetic definitions of gravity anomalies. This first version (1.0) has been computed by spherical harmonics analysis / synthesis of the Earth's topography-bathymetry up to degree 10800. The detailed theory of the spherical harmonics approach is given in Balmino et al., (Journal of Geodesy, 2011). The Bouguer and terrain corrections have thus been computed in spherical geometry at 1'x1' resolution using the ETOPO1 topography/bathymetry, ice surface and bedrock models from the NOAA (National Oceanic and Atmospheric Administration) and taking into account precise characteristics (boundaries and densities) of major lakes, inner seas, polar caps and of land areas below sea level. Isostatic corrections have been computed according to the Airy-Heiskanen model in spherical geometry for a constant depth of compensation of 30km. The gravity information given here is provided by the Earth Geopotential Model (EGM2008), developed at degree 2160 by the National Geospatial

Direct-phase-variable model of a synchronous reluctance motor including all slot and winding harmonics

International Nuclear Information System (INIS)

Obe, Emeka S.; Binder, A.

2011-01-01

A detailed model in direct-phase variables of a synchronous reluctance motor operating at mains voltage and frequency is presented. The model includes the stator and rotor slot openings, the actual winding layout and the reluctance rotor geometry. Hence, all mmf and permeance harmonics are taken into account. It is seen that non-negligible harmonics introduced by slots are present in the inductances computed by the winding function procedure. These harmonics are usually ignored in d-q models. The machine performance is simulated in the stator reference frame to depict the difference between this new direct-phase model including all harmonics and the conventional rotor reference frame d-q model. Saturation is included by using a polynomial fitting the variation of d-axis inductance with stator current obtained by finite-element software FEMAG DC (registered) . The detailed phase-variable model can yield torque pulsations comparable to those obtained from finite elements while the d-q model cannot.

The Modeling and Harmonic Coupling Analysis of Multiple-Parallel Connected Inverter Using Harmonic State Space (HSS)

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

As the number of power electronics based systems are increasing, studies about overall stability and harmonic problems are rising. In order to analyze harmonics and stability, most research is using an analysis method, which is based on the Linear Time Invariant (LTI) approach. However, this can...... be difficult in terms of complex multi-parallel connected systems, especially in the case of renewable energy, where possibilities for intermittent operation due to the weather conditions exist. Hence, it can bring many different operating points to the power converter, and the impedance characteristics can...... can demonstrate other phenomenon, which can not be found in the conventional LTI approach. The theoretical modeling and analysis are verified by means of simulations and experiments....

harmonic load modeling: a case study of 33 kv abuja steel mill feeder

African Journals Online (AJOL)

HOD

An in-depth study of the harmonic orders inherent in a power system network is required ... This paper studied the harmonic orders of the 33 kV Abuja Steel Feeder .... models for various industrial and household electrical ..... Malaysia, 2013.

Measurement-based harmonic current modeling of mobile storage for power quality study in the distribution system

Directory of Open Access Journals (Sweden)

Wenge Christoph

2017-12-01

Full Text Available Electric vehicles (EVs can be utilized as mobile storages in a power system. The use of battery chargers can cause current harmonics in the supplied AC system. In order to analyze the impact of different EVs with regardto their number and their emission of current harmonics, a generic harmonic current model of EV types was built and implemented in the power system simulation tool PSS®NETOMAC. Based on the measurement data for different types of EVs three standardized harmonic EV models were developed and parametrized. Further, the identified harmonic models are used by the computation of load flow in a modeled, German power distribution system. As a benchmark, a case scenario was studied regarding a high market penetration of EVs in the year 2030 for Germany. The impact of the EV charging on the power distribution system was analyzed and evaluated with valid power quality standards.

Harmonic Instability Assessment Using State-Space Modeling and Participation Analysis in Inverter-Fed Power Systems

DEFF Research Database (Denmark)

Wang, Yanbo; Wang, Xiongfei; Blaabjerg, Frede

2017-01-01

parameters on the harmonic instability of the power system. Moreover, the harmonic-frequency oscillation modes are identified, where participation analysis is presented to evaluate the contributions of different states to these modes and to further reveal how the system gives rise to harmonic instability......This paper presents a harmonic instability analysis method using state-space modeling and participation analysis in the inverter-fed ac power systems. A full-order state-space model for the droop-controlled Distributed Generation (DG) inverter is built first, including the time delay of the digital...... control system, inner current and voltage control loops, and outer droop-based power control loop. Based on the DG inverter model, an overall state-space model of a two-inverter-fed system is established. The eigenvalue-based stability analysis is then presented to assess the influence of controller...

Creation and annihilation operators, symmetry and supersymmetry of the 3D isotropic harmonic oscillator

International Nuclear Information System (INIS)

Mota, R D; Granados, V D; Queijeiro, A; Garcia, J; Guzman, L

2003-01-01

We show that the supersymmetric radial ladder operators of the three-dimensional isotropic harmonic oscillator are contained in the spherical components of the creation and annihilation operators of the system. Also, we show that the constants of motion of the problem, written in terms of these spherical components, lead us to second-order radial operators. Further, we show that these operators change the orbital angular momentum quantum number by two units and are equal to those obtained by the Infeld-Hull factorization method

An aggregated approach to harmonic modelling of loads in power distribution networks

Energy Technology Data Exchange (ETDEWEB)

Moellerstedt, E.

1998-06-01

The use of power electronics have given possibilities for more sophisticated control of power networks. This creates new demands on power network modelling. The models must not only allow for efficient and accurate simulation, but also be suitable for analysis and control design. The Harmonic Norton Equivalent presented in this thesis addresses two problems that are central in control theory, namely model reduction and system identification. It is essential to have simple representations of large systems, and there must be a way to obtain these simple models experimentally, as detailed modelling most often is too complicated. The Harmonic Norton Equivalent has its roots in the method of harmonic balance. It is a frequency domain description of loads in electric networks and describes a linear relation between the current spectrum and the voltage spectrum. The linearization implies that aggregation of loads for model reduction is a straightforward, non-iterative procedure. The models can be obtained through analytical calculations, measurements or time domain simulations. A procedure for experimental estimation of model parameters is presented. The procedure is used to estimate the parameters of a dimmer model from measurements on a real dimmer. The obtained model shows a very good agreement with validation data 24 refs, 24 figs

Sparse tensor spherical harmonics approximation in radiative transfer

International Nuclear Information System (INIS)

Grella, K.; Schwab, Ch.

2011-01-01

The stationary monochromatic radiative transfer equation is a partial differential transport equation stated on a five-dimensional phase space. To obtain a well-posed problem, boundary conditions have to be prescribed on the inflow part of the domain boundary. We solve the equation with a multi-level Galerkin FEM in physical space and a spectral discretization with harmonics in solid angle and show that the benefits of the concept of sparse tensor products, known from the context of sparse grids, can also be leveraged in combination with a spectral discretization. Our method allows us to include high spectral orders without incurring the 'curse of dimension' of a five-dimensional computational domain. Neglecting boundary conditions, we find analytically that for smooth solutions, the convergence rate of the full tensor product method is retained in our method up to a logarithmic factor, while the number of degrees of freedom grows essentially only as fast as for the purely spatial problem. For the case with boundary conditions, we propose a splitting of the physical function space and a conforming tensorization. Numerical experiments in two physical and one angular dimension show evidence for the theoretical convergence rates to hold in the latter case as well.

A theoretical-electron-density databank using a model of real and virtual spherical atoms.

Science.gov (United States)

Nassour, Ayoub; Domagala, Slawomir; Guillot, Benoit; Leduc, Theo; Lecomte, Claude; Jelsch, Christian

2017-08-01

A database describing the electron density of common chemical groups using combinations of real and virtual spherical atoms is proposed, as an alternative to the multipolar atom modelling of the molecular charge density. Theoretical structure factors were computed from periodic density functional theory calculations on 38 crystal structures of small molecules and the charge density was subsequently refined using a density model based on real spherical atoms and additional dummy charges on the covalent bonds and on electron lone-pair sites. The electron-density parameters of real and dummy atoms present in a similar chemical environment were averaged on all the molecules studied to build a database of transferable spherical atoms. Compared with the now-popular databases of transferable multipolar parameters, the spherical charge modelling needs fewer parameters to describe the molecular electron density and can be more easily incorporated in molecular modelling software for the computation of electrostatic properties. The construction method of the database is described. In order to analyse to what extent this modelling method can be used to derive meaningful molecular properties, it has been applied to the urea molecule and to biotin/streptavidin, a protein/ligand complex.

An accelerated life test model for harmonic drives under a segmental stress history and its parameter optimization

Directory of Open Access Journals (Sweden)

Zhang Chao

2015-12-01

Full Text Available Harmonic drives have various distinctive advantages and are widely used in space drive mechanisms. Accelerated life test (ALT is commonly conducted to shorten test time and reduce associated costs. An appropriate ALT model is needed to predict the lifetime of harmonic drives with ALT data. However, harmonic drives which are used in space usually work under a segmental stress history, and traditional ALT models can hardly be used in this situation. This paper proposes a dedicated ALT model for harmonic drives applied in space systems. A comprehensive ALT model is established and genetic algorithm (GA is adopted to obtain optimal parameters in the model using the Manson fatigue damage rule to describe the fatigue failure process and a cumulative damage method to calculate and accumulate the damage caused by each segment in the stress history. An ALT of harmonic drives was carried out and experimental results show that this model is acceptable and effective.

FRW cosmological model inside an isolated Schwarzschild black hole

OpenAIRE

Ortiz, C.; Rosales, J. J.; Socorro, J.; Tkach, V. I.

2004-01-01

Using the canonical quantum theory of spherically symmetric pure gravitational systems, we present a direct correspondence between the Friedmann-Robertson-Walker (FRW) cosmological model in the interior of a Schwarzschild black hole and the nth energy eigenstate of a linear harmonic oscillator. Such type of universe has a quantized mass of the order of the Planck mass and harmonic oscillator wave functions

Design of six pulse bridge multiplication converter model for current harmonic elimination of three phase ac-dc converter

International Nuclear Information System (INIS)

Soomro, M.A.; Helepoto, I.A.

2014-01-01

The recent development of semiconductor technology and wide spread use of power electronic devices in power system have open the era of the power system harmonics due to increasing penetration of non-linear loads. Harmonics are widely admitted as most important issues of power quality which must be eliminated to maintain power system reliability. The tolerable THD (Total Harmonic Distortion) values must be bounded in well-defined limits recognized by IEEE-519 standard. In this work, in order to eliminate the current harmonics produced by non-linear loads, six pulse multiplication converter technique in conjunction with STSSHPE (Single Tuned Shunt Harmonic Passive Filter) is proposed. The proposed model has the capacity of harmonic cancellation of the dominant 3rd order harmonics. Besides that, the 5th and 7th order harmonics are also reduced to a diminishing level. The hardware model has been experimentally tested by PQA (Power Quality Analyzer) and simulation model is designed using MATLAB software. The acquired results have been measured by considering THD values in terms of current and voltage. Furthermore, they have been compared against IEEE-519 performance standards. The prosed model, successfully bounds the total harmonic distortion under defined limits by IEEE-519 standard. (author)

Assessing harmonic current source modelling and power definitions in balanced and unbalanced networks

Energy Technology Data Exchange (ETDEWEB)

Atkinson-Hope, Gary; Stemmet, W.C. [Cape Peninsula University of Technology, Cape Town Campus, Cape Town (South Africa)

2006-07-01

The purpose of this paper is to assess the DlgSILENT PowerFactory software power definitions (indices) in terms of phase and sequence components for balanced and unbalanced networks when harmonic distortion is present and to compare its results to hand calculations done, following recommendation made by the IEEE Working Group on this topic. This paper also includes the development of a flowchart for calculating power indices in balanced and unbalanced three-phase networks when non-sinusoidal voltages and currents are present. A further purpose is to determine how two industrial grade harmonic analysis software packages (DlgSILENT and ERACS) model three-phase harmonic sources used for current penetration studies and to compare their results when applied to a network. From the investigations, another objective was to develop a methodology for modelling harmonic current sources based on a spectrum obtained from measurements. Three case studies were conducted and the assessment and developed methodologies were shown to be effective. (Author)

Effects of snow grain non-sphericity on climate simulations: Sensitivity tests with the NorESM model

Science.gov (United States)

Räisänen, Petri; Makkonen, Risto; Kirkevåg, Alf

2017-04-01

Snow grains are non-spherical and generally irregular in shape. Still, in radiative transfer calculations, they are often treated as spheres. This also applies to the computation of snow albedo in the Snow, Ice, and Aerosol Radiation (SNICAR) model and in the Los Alamos sea ice model, version 4 (CICE4), both of which are employed in the Community Earth System Model and in the Norwegian Earth System Model (NorESM). In this work, we evaluate the effect of snow grain shape on climate simulated by NorESM in a slab ocean configuration of the model. An experiment with spherical snow grains (SPH) is compared with another (NONSPH) in which the snow shortwave single-scattering properties are based on a combination of non-spherical snow grain shapes optimized using measurements of angular scattering by blowing snow. The key difference between these treatments is that the asymmetry parameter is smaller in the non-spherical case (≈ 0.78 in the visible region) than in the spherical case (≈ 0.89). Therefore, for a given snow grain size, the use of non-spherical snow grains yields a higher snow broadband albedo, typically by ≈0.03. Consequently, considering the spherical case as the baseline, the use of non-spherical snow grains results in a negative radiative forcing (RF), with a global-mean top-of-the-model value of ≈ -0.22 W m-2. Although this global-mean RF is modest, it has a rather substantial impact on the climate simulated by NoRESM. In particular, the global annual-mean 2-m air temperature in NONSPH is 1.17 K lower than in SPH, with substantially larger differences at high latitudes. The climatic response is amplified by strong snow and sea ice feedbacks. It is further found that the difference between NONSPH and SPH could be largely "tuned away" by adjusting the snow grain size in the NONSPH experiment by ≈ 70%. The impact of snow grain shape on the radiative effect (RE) of absorbing aerosols in snow (black carbon and mineral dust) is also discussed. For an

Small-angle scattering of polychromatic X-rays: effects of bandwidth, spectral shape and high harmonics

Energy Technology Data Exchange (ETDEWEB)

Chen, Sen; Luo, Sheng-Nian

2018-02-16

Polychromatic X-ray sources can be useful for photon-starved small-angle X-ray scattering given their high spectral fluxes. Their bandwidths, however, are 10–100 times larger than those using monochromators. To explore the feasibility, ideal scattering curves of homogeneous spherical particles for polychromatic X-rays are calculated and analyzed using the Guinier approach, maximum entropy and regularization methods. Monodisperse and polydisperse systems are explored. The influence of bandwidth and asymmetric spectra shape are exploredviaGaussian and half-Gaussian spectra. Synchrotron undulator spectra represented by two undulator sources of the Advanced Photon Source are examined as an example, as regards the influence of asymmetric harmonic shape, fundamental harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.

Small-angle scattering of polychromatic X-rays: effects of bandwidth, spectral shape and high harmonics.

Science.gov (United States)

Chen, Sen; Luo, Sheng Nian

2018-03-01

Polychromatic X-ray sources can be useful for photon-starved small-angle X-ray scattering given their high spectral fluxes. Their bandwidths, however, are 10-100 times larger than those using monochromators. To explore the feasibility, ideal scattering curves of homogeneous spherical particles for polychromatic X-rays are calculated and analyzed using the Guinier approach, maximum entropy and regularization methods. Monodisperse and polydisperse systems are explored. The influence of bandwidth and asymmetric spectra shape are explored via Gaussian and half-Gaussian spectra. Synchrotron undulator spectra represented by two undulator sources of the Advanced Photon Source are examined as an example, as regards the influence of asymmetric harmonic shape, fundamental harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.

A high resolution gravity model for Venus - GVM-1

Science.gov (United States)

Nerem, R. S.; Bills, B. G.; Mcnamee, J. B.

1993-01-01

A spherical harmonic model of the gravitational field of Venus complete to degree and order 50 has been developed using the S-band Doppler tracking data of the Pioneer Venus Orbiter (PVO) collected between 1979 and 1982. The short wavelengths of this model could only be resolved near the PVO periapse location (about 14 deg N latitude), therefore a priori constraints were applied to the model to bias poorly observed coefficients towards zero. The resulting model has a half-wavelength resolution of 400 km near the PVO periapse location, but the resolution degrades to greater than 1000 km near the poles. This gravity model correlates well with a degree 50 spherical harmonic expansion of the Venus topography derived from a combination of Magellan and PVO data. New tracking data from Magellan's gravity mission should provide some improvement to this model, although a complete model of the Venusian gravity field will depend on tracking of Magellan after the circularization of its orbit using aerobraking.

Improved dq-Axes Model of PMSM Considering Airgap Flux Harmonics and Saturation

DEFF Research Database (Denmark)

Fasil, Muhammed; Antaloae, Ciprian; Mijatovic, Nenad

2016-01-01

In this work, the classical linear model of a permanent magnet synchronous motor (PMSM) is modified by adding d and q-axes harmonic inductances so that the modified model can consider non-linearities present in an interior permanent magnet (IPM) motor. Further, a method has been presented to assess...... the effect of saturation and cross-saturation on constant torque curves of PMSM. Two IPM motors with two different rotor topologies and different specifications are designed to evaluate the effect of saturation on synchronous and harmonic inductances, and on operating points of the machines...

Deconvolving the wedge: maximum-likelihood power spectra via spherical-wave visibility modelling

Science.gov (United States)

Ghosh, A.; Mertens, F. G.; Koopmans, L. V. E.

2018-03-01

Direct detection of the Epoch of Reionization (EoR) via the red-shifted 21-cm line will have unprecedented implications on the study of structure formation in the infant Universe. To fulfil this promise, current and future 21-cm experiments need to detect this weak EoR signal in the presence of foregrounds that are several orders of magnitude larger. This requires extreme noise control and improved wide-field high dynamic-range imaging techniques. We propose a new imaging method based on a maximum likelihood framework which solves for the interferometric equation directly on the sphere, or equivalently in the uvw-domain. The method uses the one-to-one relation between spherical waves and spherical harmonics (SpH). It consistently handles signals from the entire sky, and does not require a w-term correction. The SpH coefficients represent the sky-brightness distribution and the visibilities in the uvw-domain, and provide a direct estimate of the spatial power spectrum. Using these spectrally smooth SpH coefficients, bright foregrounds can be removed from the signal, including their side-lobe noise, which is one of the limiting factors in high dynamics-range wide-field imaging. Chromatic effects causing the so-called `wedge' are effectively eliminated (i.e. deconvolved) in the cylindrical (k⊥, k∥) power spectrum, compared to a power spectrum computed directly from the images of the foreground visibilities where the wedge is clearly present. We illustrate our method using simulated Low-Frequency Array observations, finding an excellent reconstruction of the input EoR signal with minimal bias.

Analysis of Harmonic Coupling and Stability in Back-to-Back Converter Systems for Wind Turbines using Harmonic State Space (HSS)

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Bak, Claus Leth

2015-01-01

Understanding about harmonic propagation in wind turbine converter is fundamental to research the influence of these on a large network harmonic distortion. Therefore, the analysis of wind turbine converter harmonic spectrum as well as the influence of converter operating point into the network i...... connected into the large wind farm model to analyze the overall steady-state harmonic as well as harmonic stability. All theoretical modeling and analysis is verified by means of simulation and experimental results.......Understanding about harmonic propagation in wind turbine converter is fundamental to research the influence of these on a large network harmonic distortion. Therefore, the analysis of wind turbine converter harmonic spectrum as well as the influence of converter operating point into the network...... is urgently important issues in harmonic studies on wind farm. However, the conventional modeling procedure and simplified model for controller design are not enough to analyze such complicated systems. Besides, they have many limitations in terms of including a non-linear component, different operating...

Non-conformal contact mechanical characteristic analysis on spherical components

Energy Technology Data Exchange (ETDEWEB)

Zhen-zhi, G.; Bin, H.; Zheng-ming, G.; Feng-mei, Y.; Jin, Q [The 2. Artillery Engineering Univ., Xi' an (China)

2017-03-15

Non-conformal spherical-contact mechanical problems is a three-dimensional coordination or similar to the coordination spherical contact. Due to the complexity of the problem of spherical-contact and difficulties of solving higher-order partial differential equations, problems of three-dimensional coordination or similar to the coordination spherical-contact is still no exact analytical method for solving. It is based on three-dimensional taper model is proposed a model based on the contour surface of the spherical contact and concluded of the formula of the contact pressure and constructed of finite element model by contact pressure distribution under the non-conformal spherical. The results shows spherical contact model can reflect non-conformal spherical-contacting mechanical problems more than taper-contacting model, and apply for the actual project.

Three-Dimensional Visualization of Wave Functions for Rotating Molecule: Plot of Spherical Harmonics

Science.gov (United States)

Nagaoka, Shin-ichi; Teramae, Hiroyuki; Nagashima, Umpei

2013-01-01

At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

Development of Spherical Near Field Model for Geological Radioactive Waste Repository

International Nuclear Information System (INIS)

Kim, S. Y.; Lee, K. J.; Chang, S. H.; Lee, K. J.; Chang, S. H.

2012-01-01

Modeling for geological radioactive waste repository can be divided into 3 parts. They are near field modeling related to engineered barrier, far field modeling related to natural barrier and biosphere modeling. In order to make the general application for safety assessment of geological waste repository, spherical geometry near field model has been developed. This model can be used quite extensively when users calculate equivalent spherical geometry for specific engineered barrier like equivalent waste radius, equivalent barrier radius and etc. Only diffusion was considered for general purpose but advection part can be updated. Goldsim and Goldsim Radionuclide Transport (RT) module were chosen and used as developing tool for the flexible modeling. Developer can freely make their own model with developer friendly graphic interface by using Goldsim. Furthermore, model with user friendly graphic interface can be developed by using Goldsim Dashboard Authoring module. The model has been validated by comparing the result with that of another model, inserting similar inputs and conditions. The model has been proved to be reasonably operating from the comparison result by validation process. Cylindrical model can be developed as a further work based on the knowledge and experience from this research

Development of Spherical Near Field Model for Geological Radioactive Waste Repository

Energy Technology Data Exchange (ETDEWEB)

Kim, S. Y.; Lee, K. J.; Chang, S. H. [Korea Advanced Institute of Science and Technology, Daejeon (Korea, Republic of); Lee, K. J.; Chang, S. H. [Khalifa Univ. of Science/Technology and Research, Abu Dhabi (United Arab Emirates)

2012-03-15

Modeling for geological radioactive waste repository can be divided into 3 parts. They are near field modeling related to engineered barrier, far field modeling related to natural barrier and biosphere modeling. In order to make the general application for safety assessment of geological waste repository, spherical geometry near field model has been developed. This model can be used quite extensively when users calculate equivalent spherical geometry for specific engineered barrier like equivalent waste radius, equivalent barrier radius and etc. Only diffusion was considered for general purpose but advection part can be updated. Goldsim and Goldsim Radionuclide Transport (RT) module were chosen and used as developing tool for the flexible modeling. Developer can freely make their own model with developer friendly graphic interface by using Goldsim. Furthermore, model with user friendly graphic interface can be developed by using Goldsim Dashboard Authoring module. The model has been validated by comparing the result with that of another model, inserting similar inputs and conditions. The model has been proved to be reasonably operating from the comparison result by validation process. Cylindrical model can be developed as a further work based on the knowledge and experience from this research.

Spherical collapse in quintessence models with zero speed of sound

International Nuclear Information System (INIS)

Creminelli, Paolo; D'Amico, Guido; Noreña, Jorge; Senatore, Leonardo; Vernizzi, Filippo

2010-01-01

We study the spherical collapse model in the presence of quintessence with negligible speed of sound. This case is particularly motivated for w Q /Ω m . This gives a distinctive modification of the total mass function at low redshift

ESA' s novel gravitational modeling of irregular planetary bodies

Science.gov (United States)

Ortega, Guillermo

A detailed understanding and modeling of the gravitational modeling is required for realistic investigation of the dynamics of orbits close to irregularly shaped bodies. Gravity field modelling up to a certain maximum spherical harmonic degree N involves N2 unkown spherical harmonic coefficients or complex harmonics. The corresponding number of matrix entries reaches till N4 . For missions like CHAMP, GRACE or GOCE, the maximum degree of resolution is 75, 150 and 300 respectively. Therefore, the number of unknowns for a satellite like GOCE will be around 100.000. Since these missions usually fly for a period of time of several years, the number of observations is huge. Hence, gravity field recovery from these missions is a high demanding task. The classical approaches like spherical expansion of the potential lead generally to a high number of coefficients, which reduce the software computational efficiency of the orbit propagation and which have mostly a limited physical meaning. One of the main targets of the activity is the modelling of asteroids, small moons, and cometary bodies. All celestial bodies are irregular by definition. However, the scope of the activity is broad enough as to be able to use the models and the software in quasy-regular bodies as well. Therefore the models and tools could be used for bodies such as the Moon, Mars, Venus, Deimos, Europa, Eros, Mathilda, and Churyumov-Gerasimenko, etc., being these applications relevant for scientific (Rosetta, Bepi Colombo), exploration (Exo-Mars), NEO mitigation (Don Quijote) and Earth observation (GOCE) missions of ESA.

The spherical sector of the Calogero model as a reduced matrix model

Energy Technology Data Exchange (ETDEWEB)

Hakobyan, Tigran, E-mail: hakob@yerphi.am [Yerevan State University, 1 Alex Manoogian, 0025 Yerevan (Armenia); Yerevan Physics Institute, 2 Alikhanyan Br., 0036 Yerevan (Armenia); Lechtenfeld, Olaf, E-mail: lechtenf@itp.uni-hannover.de [Leibniz Universitaet Hannover, Institut fuer Theoretische Physik, Appelstr. 2, D-30167 Hannover (Germany); Nersessian, Armen, E-mail: arnerses@ysu.am [Yerevan State University, 1 Alex Manoogian, 0025 Yerevan (Armenia)

2012-05-11

We investigate the matrix-model origin of the spherical sector of the rational Calogero model and its constants of motion. We develop a diagrammatic technique which allows us to find explicit expressions of the constants of motion and calculate their Poisson brackets. In this way we obtain all functionally independent constants of motion to any given order in the momenta. Our technique is related to the valence-bond basis for singlet states.

A Harmonized Process Model for Digital Forensic Investigation Readiness

OpenAIRE

Valjarevic , Aleksandar; Venter , Hein

2013-01-01

Part 2: FORENSIC MODELS; International audience; Digital forensic readiness enables an organization to prepare itself to perform digital forensic investigations in an efficient and effective manner. The benefits include enhancing the admissibility of digital evidence, better utilization of resources and greater incident awareness. However, a harmonized process model for digital forensic readiness does not currently exist and, thus, there is a lack of effective and standardized implementations...

Acoustic manipulation of active spherical carriers: Generation of negative radiation force

Energy Technology Data Exchange (ETDEWEB)

Rajabi, Majid, E-mail: majid_rajabi@iust.ac.ir; Mojahed, Alireza

2016-09-15

This paper examines theoretically a novel mechanism of generating negative (pulling) radiation force for acoustic manipulation of spherical carriers equipped with piezoelectric actuators in its inner surface. In this mechanism, the spherical particle is handled by common plane progressive monochromatic acoustic waves instead of zero-/higher- order Bessel beams or standing waves field. The handling strategy is based on applying a spatially uniform harmonic electrical voltage at the piezoelectric actuator with the same frequency of handling acoustic waves, in order to change the radiation force effect from repulsive (away from source) to attractive (toward source). This study may be considered as a start point for development of contact-free precise handling and entrapment technology of active carriers which are essential in many engineering and medicine applications.

One-degree-of-freedom spherical model for the passive motion of the human ankle joint.

Science.gov (United States)

Sancisi, Nicola; Baldisserri, Benedetta; Parenti-Castelli, Vincenzo; Belvedere, Claudio; Leardini, Alberto

2014-04-01

Mathematical modelling of mobility at the human ankle joint is essential for prosthetics and orthotic design. The scope of this study is to show that the ankle joint passive motion can be represented by a one-degree-of-freedom spherical motion. Moreover, this motion is modelled by a one-degree-of-freedom spherical parallel mechanism model, and the optimal pivot-point position is determined. Passive motion and anatomical data were taken from in vitro experiments in nine lower limb specimens. For each of these, a spherical mechanism, including the tibiofibular and talocalcaneal segments connected by a spherical pair and by the calcaneofibular and tibiocalcaneal ligament links, was defined from the corresponding experimental kinematics and geometry. An iterative procedure was used to optimize the geometry of the model, able to predict original experimental motion. The results of the simulations showed a good replication of the original natural motion, despite the numerous model assumptions and simplifications, with mean differences between experiments and predictions smaller than 1.3 mm (average 0.33 mm) for the three joint position components and smaller than 0.7° (average 0.32°) for the two out-of-sagittal plane rotations, once plotted versus the full flexion arc. The relevant pivot-point position after model optimization was found within the tibial mortise, but not exactly in a central location. The present combined experimental and modelling analysis of passive motion at the human ankle joint shows that a one degree-of-freedom spherical mechanism predicts well what is observed in real joints, although its computational complexity is comparable to the standard hinge joint model.

Spherical Collapse in Chameleon Models

CERN Document Server

Brax, Ph; Steer, D A

2010-01-01

We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse depends on the initial comoving size of the inhomogeneity.

Spherical collapse in chameleon models

Energy Technology Data Exchange (ETDEWEB)

Brax, Ph. [Institut de Physique Théorique, CEA, IPhT, CNRS, URA 2306, F-91191Gif/Yvette Cedex (France); Rosenfeld, R. [Instituto de Física Teórica, Universidade Estadual Paulista, Rua Dr. Bento T. Ferraz, 271, 01140-070, São Paulo (Brazil); Steer, D.A., E-mail: brax@spht.saclay.cea.fr, E-mail: rosenfel@ift.unesp.br, E-mail: daniele.steer@apc.univ-paris7.fr [APC, UMR 7164, CNRS, Université Paris 7, 10 rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13 (France)

2010-08-01

We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity.

Spherical collapse in chameleon models

International Nuclear Information System (INIS)

Brax, Ph.; Rosenfeld, R.; Steer, D.A.

2010-01-01

We study the gravitational collapse of an overdensity of nonrelativistic matter under the action of gravity and a chameleon scalar field. We show that the spherical collapse model is modified by the presence of a chameleon field. In particular, we find that even though the chameleon effects can be potentially large at small scales, for a large enough initial size of the inhomogeneity the collapsing region possesses a thin shell that shields the modification of gravity induced by the chameleon field, recovering the standard gravity results. We analyse the behaviour of a collapsing shell in a cosmological setting in the presence of a thin shell and find that, in contrast to the usual case, the critical density for collapse in principle depends on the initial comoving size of the inhomogeneity

Method to determine the optimal constitutive model from spherical indentation tests

Directory of Open Access Journals (Sweden)

Tairui Zhang

2018-03-01

Full Text Available The limitation of current indentation theories was investigated and a method to determine the optimal constitutive model through spherical indentation tests was proposed. Two constitutive models, the Power-law and the Linear-law, were used in Finite Element (FE calculations, and then a set of indentation governing equations was established for each model. The load-depth data from the normal indentation depth was used to fit the best parameters in each constitutive model while the data from the further loading part was compared with those from FE calculations, and the model that better predicted the further deformation was considered the optimal one. Moreover, a Yang’s modulus calculation model which took the previous plastic deformation and the phenomenon of pile-up (or sink-in into consideration was also proposed to revise the original Sneddon-Pharr-Oliver model. The indentation results on six materials, 304, 321, SA508, SA533, 15CrMoR, and Fv520B, were compared with tensile ones, which validated the reliability of the revised E calculation model and the optimal constitutive model determination method in this study. Keywords: Optimal constitutive model, Spherical indentation test, Finite Element calculations, Yang’s modulus

Spherical and cylindrical cavity expansion models based prediction of penetration depths of concrete targets.

Directory of Open Access Journals (Sweden)

Xiaochao Jin

Full Text Available The cavity expansion theory is most widely used to predict the depth of penetration of concrete targets. The main purpose of this work is to clarify the differences between the spherical and cylindrical cavity expansion models and their scope of application in predicting the penetration depths of concrete targets. The factors that influence the dynamic cavity expansion process of concrete materials were first examined. Based on numerical results, the relationship between expansion pressure and velocity was established. Then the parameters in the Forrestal's formula were fitted to have a convenient and effective prediction of the penetration depth. Results showed that both the spherical and cylindrical cavity expansion models can accurately predict the depth of penetration when the initial velocity is lower than 800 m/s. However, the prediction accuracy decreases with the increasing of the initial velocity and diameters of the projectiles. Based on our results, it can be concluded that when the initial velocity is higher than the critical velocity, the cylindrical cavity expansion model performs better than the spherical cavity expansion model in predicting the penetration depth, while when the initial velocity is lower than the critical velocity the conclusion is quite the contrary. This work provides a basic principle for selecting the spherical or cylindrical cavity expansion model to predict the penetration depth of concrete targets.

Frictional-faulting model for harmonic tremor before Redoubt Volcano eruptions

Science.gov (United States)

Dmitrieva, Ksenia; Hotovec-Ellis, Alicia J.; Prejean, Stephanie G.; Dunham, Eric M.

2013-01-01

Seismic unrest, indicative of subsurface magma transport and pressure changes within fluid-filled cracks and conduits, often precedes volcanic eruptions. An intriguing form of volcano seismicity is harmonic tremor, that is, sustained vibrations in the range of 0.5–5 Hz. Many source processes can generate harmonic tremor. Harmonic tremor in the 2009 eruption of Redoubt Volcano, Alaska, has been linked to repeating earthquakes of magnitudes around 0.5–1.5 that occur a few kilometres beneath the vent. Before many explosions in that eruption, these small earthquakes occurred in such rapid succession—up to 30 events per second—that distinct seismic wave arrivals blurred into continuous, high-frequency tremor. Tremor abruptly ceased about 30 s before the explosions. Here we introduce a frictional-faulting model to evaluate the credibility and implications of this tremor mechanism. We find that the fault stressing rates rise to values ten orders of magnitude higher than in typical tectonic settings. At that point, inertial effects stabilize fault sliding and the earthquakes cease. Our model of the Redoubt Volcano observations implies that the onset of volcanic explosions is preceded by active deformation and extreme stressing within a localized region of the volcano conduit, at a depth of several kilometres.

Morphology of the Iceland Basin Excursion from a spherical harmonics analysis and an iterative Bayesian inversion procedure of sedimentary records

Science.gov (United States)

Lanci, Luca; Kissel, Catherine; Leonhardt, Roman; Laj, Carlo

2008-08-01

Based on 5 published marine high-resolution sedimentary records of the Iceland Basin Excursion [IBE; Channell, J.E.T., Hodell, D.A., Lehman, B., 1997. Relative geomagnetic paleointensity and ∂ 18O at ODP Site 983/Gardar Drift, North Atlantic since 350 ka. Earth Planet. Sci. Lett. 153, 103-118; Laj, C., Kissel, C., Roberts, A., 2006. Geomagnetic field behavior during the Iceland Basin and Laschamp geomagnetic excursions: a simple transitional field geometry? Geochem. Geophys. Geosystems. 7, Q03004, doi:10.1029/2005GC001122] dated around 186-190 kyr, we present models of the excursional geomagnetic field at the Earth's surface using two different approaches. First a spherical harmonics analysis is performed after synchronization of the records using their paleointensity profiles. Second, we have used an iterative Bayesian inversion procedure, calibrated using the single volcanic data available so far. Both modeling approaches suffer from imperfections of the paleomagnetic signals and mostly from the still poor geographical distribution of detailed records, presently available only from the North Atlantic and the West Pacific. For these reasons, our modeling results should only be regarded as preliminary models of the geomagnetic field during the IBE, susceptible to improvements when including results from future paleomagnetic studies. Nevertheless, both approaches show distinct similarities and are stable against moderate variations of modeling parameters. The general picture is that of a dipole field undergoing a strong reduction, but remaining higher than the non-dipole field all through the excursional process, except for a very short interval of time corresponding to the dipole minimum at the center of the excursion. On the other hand, some differences exist between the results of the two models with each other and with the real data when the virtual geomagnetic pole (VGP) paths are considered. The non-dipole field does not appear to undergo very significant

Spherical Detector Device Mathematical Modelling with Taking into Account Detector Module Symmetry

International Nuclear Information System (INIS)

Batyj, V.G.; Fedorchenko, D.V.; Prokopets, S.I.; Prokopets, I.M.; Kazhmuradov, M.A.

2005-01-01

Mathematical Model for spherical detector device accounting to symmetry properties is considered. Exact algorithm for simulation of measurement procedure with multiple radiation sources is developed. Modelling results are shown to have perfect agreement with calibration measurements

Frequency Domain Modeling and Simulation of DC Power Electronic Systems Using Harmonic State Space Method

DEFF Research Database (Denmark)

Kwon, Jun Bum; Wang, Xiongfei; Blaabjerg, Frede

2017-01-01

For the efficiency and simplicity of electric systems, the dc power electronic systems are widely used in a variety of applications such as electric vehicles, ships, aircraft and also in homes. In these systems, there could be a number of dynamic interactions and frequency coupling between network...... with different switching frequency or harmonics from ac-dc converters makes that harmonics and frequency coupling are both problems of ac system and challenges of dc system. This paper presents a modeling and simulation method for a large dc power electronic system by using Harmonic State Space (HSS) modeling...

Subduction to the lower mantle – a comparison between geodynamic and tomographic models

Directory of Open Access Journals (Sweden)

T. W. Becker

2012-11-01

Full Text Available It is generally believed that subduction of lithospheric slabs is a major contribution to thermal heterogeneity in Earth's entire mantle and provides a main driving force for mantle flow. Mantle structure can, on the one hand, be inferred from plate tectonic models of subduction history and geodynamic models of mantle flow. On the other hand, seismic tomography models provide important information on mantle heterogeneity. Yet, the two kinds of models are only similar on the largest (1000 s of km scales and are quite different in their detailed structure. Here, we provide a quantitative assessment how good a fit can be currently achieved with a simple viscous flow geodynamic model. The discrepancy between geodynamic and tomography models can indicate where further model refinement could possibly yield an improved fit. Our geodynamical model is based on 300 Myr of subduction history inferred from a global plate reconstruction. Density anomalies are inserted into the upper mantle beneath subduction zones, and flow and advection of these anomalies is calculated with a spherical harmonic code for a radial viscosity structure constrained by mineral physics and surface observations. Model viscosities in the upper mantle beneath the lithosphere are ~1020 Pas, and viscosity increases to ~1023 Pas in the lower mantle above D". Comparison with tomography models is assessed in terms of correlation, both overall and as a function of depth and spherical harmonic degree. We find that, compared to previous geodynamic and tomography models, correlation is improved, presumably because of advances in both plate reconstructions and mantle flow computations. However, high correlation is still limited to lowest spherical harmonic degrees. An important ingredient to achieve high correlation – in particular at spherical harmonic degree two – is a basal chemical layer. Subduction shapes this layer into two rather stable hot but chemically dense "piles

SPHERICAL HARMONIC ANALYSES OF INTENSITY MAPPING POWER SPECTRA

Energy Technology Data Exchange (ETDEWEB)

Liu, Adrian; Zhang, Yunfan; Parsons, Aaron R., E-mail: acliu@berkeley.edu [Department of Astronomy and Radio Astronomy Laboratory, University of California Berkeley, Berkeley, CA 94720 (United States)

2016-12-20

Intensity mapping is a promising technique for surveying the large-scale structure of our universe from z  = 0 to z  ∼ 150, using the brightness temperature field of spectral lines to directly observe previously unexplored portions of our cosmic timeline. Examples of targeted lines include the 21 cm hyperfine transition of neutral hydrogen, rotational lines of carbon monoxide, and fine-structure lines of singly ionized carbon. Recent efforts have focused on detections of the power spectrum of spatial fluctuations, but have been hindered by systematics such as foreground contamination. This has motivated the decomposition of data into Fourier modes perpendicular and parallel to the line of sight, which has been shown to be a particularly powerful way to diagnose systematics. However, such a method is well-defined only in the limit of a narrow-field, flat-sky approximation. This limits the sensitivity of intensity mapping experiments, as it means that wide surveys must be separately analyzed as a patchwork of smaller fields. In this paper, we develop a framework for analyzing intensity mapping data in a spherical Fourier–Bessel basis, which incorporates curved sky effects without difficulty. We use our framework to generalize a number of techniques in intensity mapping data analysis from the flat sky to the curved sky. These include visibility-based estimators for the power spectrum, treatments of interloper lines, and the “foreground wedge” signature of spectrally smooth foregrounds.

An Equivalent Source Method for Modelling the Global Lithospheric Magnetic Field

DEFF Research Database (Denmark)

Kother, Livia Kathleen; Hammer, Magnus Danel; Finlay, Chris

2014-01-01

We present a new technique for modelling the global lithospheric magnetic field at Earth's surface based on the estimation of equivalent potential field sources. As a demonstration we show an application to magnetic field measurements made by the CHAMP satellite during the period 2009-2010 when...... are also employed to minimize the influence of the ionospheric field. The model for the remaining lithospheric magnetic field consists of magnetic point sources (monopoles) arranged in an icosahedron grid. The corresponding source values are estimated using an iteratively reweighted least squares algorithm...... in the CHAOS-4 and MF7 models using more conventional spherical harmonic based approaches. Advantages of the equivalent source method include its local nature, allowing e.g. for regional grid refinement, and the ease of transforming to spherical harmonics when needed. Future applications will make use of Swarm...

Spherical Model Integrating Academic Competence with Social Adjustment and Psychopathology.

Science.gov (United States)

Schaefer, Earl S.; And Others

This study replicates and elaborates a three-dimensional, spherical model that integrates research findings concerning social and emotional behavior, psychopathology, and academic competence. Kindergarten teachers completed an extensive set of rating scales on 100 children, including the Classroom Behavior Inventory and the Child Adaptive Behavior…

Fuel cell/back-up battery hybrid energy conversion systems: Dynamic modeling and harmonic considerations

International Nuclear Information System (INIS)

Fathabadi, Hassan

2015-01-01

Highlights: • Novel technique to completely eliminate the harmful harmonics of fuel cell system. • Presenting a novel high accurate detailed electrochemical dynamic model of fuel cells. • Back-up battery system to compensate the slow dynamic response of fuel cell system. • Exact analysis of real electrochemical reactions occurring inside fuel cells. - Abstract: In this study, a novel dynamic model of fuel cells is presented. High accurate static and dynamic responses of the proposed model are experimentally validated by comparing simulated results with real experimental data. The obtained model together with theoretical results shows that a fuel cell or a fuel cell stack has very slow dynamic response, so that, it cannot adapt itself to the fast variations in load demand. It is shown that for adapting well a fuel cell stack to the load demand, the stack should be equipped with a proposed back-up battery system which compensates the slow dynamic response of the stack by providing a bidirectional path to transmit/absorb the extra instant power. It is proved that the conventional switching waveforms used in the converters of the stacks and back-up systems produce an enormous amount of harmful harmonics. Then, a novel technique is proposed to completely eliminate main harmful harmonics. It is worthwhile to note that all the other techniques only reduce the harmful harmonics. Simulated results verify that the back-up battery system together with applying the proposed technique provide a fast dynamic response for the fuel cell/back-up battery system, and also completely eliminate the main harmful harmonics

Electron Bernstein Wave Emission Based Diagnostic on National Spherical Torus Experiment

International Nuclear Information System (INIS)

Diem, S.; Taylor, G.; Caughman, John B.; Efthimion, P.C.; Kugel, H.; LeBlanc, B.; Preinhaelter, J.; Sabbagh, S.A.; Urban, J.; Wilgen, John B.

2008-01-01

National Spherical Torus Experiment (NSTX) is a spherical tokamak (ST) that operates with n(e) up to 10(20) m(-3) and B(T) less than 0.6 T, cutting off low harmonic electron cyclotron (EC) emission widely used for T(e) measurements on conventional aspect ratio tokamaks. The electron Bernstein wave (EBW) can propagate in ST plasmas and is emitted at EC harmonics. These properties suggest thermal EBW emission (EBE) may be used for local T(e) measurements in the ST. Practically, a robust T(e)(R,t) EBE diagnostic requires EBW transmission efficiencies of >90% for a wide range of plasma conditions. EBW emission and coupling physics were studied on NSTX with an obliquely viewing EBW to O-mode (B-X-O) diagnostic with two remotely steered antennas, coupled to absolutely calibrated radiometers. While T(e)(R,t) measurements with EBW emission on NSTX were possible, they were challenged by several issues. Rapid fluctuations in edge n(e) scale length resulted in >20% changes in the low harmonic B-X-O transmission efficiency. Also, B-X-O transmission efficiency during H modes was observed to decay by a factor of 5-10 to less than a few percent. The B-X-O transmission behavior during H modes was reproduced by EBE simulations that predict that EBW collisional damping can significantly reduce emission when T(e)< 30 eV inside the B-X-O mode conversion (MC) layer. Initial edge lithium conditioning experiments during H modes have shown that evaporated lithium can increase T(e) inside the B-X-O MC layer, significantly increasing B-X-O transmission.

The prediction of spherical aberration with schematic eyes.

Science.gov (United States)

Liou, H L; Brennan, N A

1996-07-01

Many model eyes have been proposed; they differ in optical characteristics and therefore have different aberrations and image quality. In predicting the visual performance of the eye, we are most concerned with the central foveal vision. Spherical aberration is the only on-axis monochromatic aberration and can be used as a criterion to assess the degree of resemblance of eye models to the human eye. We reviewed and compiled experimental values of the spherical aberration of the eye, calculated the spherical aberration of several different categories of model eyes and compared the calculated results to the experimental data. Results show an over-estimation of spherical aberration by all models, the finite schematic eyes predicting values of spherical aberration closest to the experimental data. Current model eyes do not predict the average experimental values of the spherical aberration of the eye. A new model eye satisfying this assessment criterion is required for investigations of the visual performance of the eye.

Harmonic supergraphs

International Nuclear Information System (INIS)

Galperin, A.; Ivanov, E.; Ogievetsky, V.; Sokatchev, E.

1985-01-01

This paper completes a descrption of the quantization procedure in the harmonic superspace approach. The Feynman rules for N=2 matter and Yang-Mills theories are derived and the various examples of harmonic supergraph calculations are given. Calculations appear to be not more difficult than those in the N=1 case. The integration over harmonic variables does not lead to any troubles, a non-locality in these disappears on-shell. The important property is that the quantum corrections are always writen as integrals over the full harmonic superspace even though the initial action is an integral over the analytic subspace. As a by-product our results imply a very simple proof of finiteness of a wide class of the N=4, d=2 non-linear Σ-models. The most general self-couplings of hypermultiplets including those with broken SU(2) are considered.The duality relations among the N=2 linear multiplet and both kinds of hypermultiplet are established

Proton-neutron sdg boson model and spherical-deformed phase transition

Science.gov (United States)

Otsuka, Takaharu; Sugita, Michiaki

1988-12-01

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing+quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.

Proton-neutron sdg boson model and spherical-deformed phase transition

Energy Technology Data Exchange (ETDEWEB)

Otsuka, Takaharu; Sugita, Michiaki

1988-12-15

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing + quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects.

Magnetic saturation in semi-analytical harmonic modeling for electric machine analysis

NARCIS (Netherlands)

Sprangers, R.L.J.; Paulides, J.J.H.; Gysen, B.L.J.; Lomonova, E.

2016-01-01

A semi-analytical method based on the harmonic modeling (HM) technique is presented for the analysis of the magneto-static field distribution in the slotted structure of rotating electric machines. In contrast to the existing literature, the proposed model does not require the assumption of infinite

Pion-cloud corrections to the relativistic S + V harmonic potential model

International Nuclear Information System (INIS)

Palladino, B.E.; Ferreira, P.L.

1988-01-01

Pionic corrections to the mass spectrum of low-lying s-wave baryons are incorporated in a relativistic independent quark model with equally mixed Lorentz scalar and vector harmonic potentials. (M.W.O.) [pt

Proton-neutron sdg boson model and spherical-deformed phase transition

International Nuclear Information System (INIS)

Otsuka, Takaharu; Sugita, Michiaki

1988-01-01

The spherical-deformed phase transition in nuclei is described in terms of the proton-neutron sdg interacting boson model. The sdg hamiltonian is introduced to model the pairing + quadrupole interaction. The phase transition is reproduced in this framework as a function of the boson number in the Sm isotopes, while all parameters in the hamiltonian are kept constant at values reasonable from the shell-model point of view. The sd IBM is derived from this model through the renormalization of g-boson effects. (orig.)

Fast calculation of low altitude disturbing gravity for ballistics

Science.gov (United States)

Wang, Jianqiang; Wang, Fanghao; Tian, Shasha

2018-03-01

Fast calculation of disturbing gravity is a key technology in ballistics while spherical cap harmonic(SCH) theory can be used to solve this problem. By using adjusted spherical cap harmonic(ASCH) methods, the spherical cap coordinates are projected into a global coordinates, then the non-integer associated Legendre functions(ALF) of SCH are replaced by integer ALF of spherical harmonics(SH). This new method is called virtual spherical harmonics(VSH) and some numerical experiment were done to test the effect of VSH. The results of earth's gravity model were set as the theoretical observation, and the model of regional gravity field was constructed by the new method. Simulation results show that the approximated errors are less than 5mGal in the low altitude range of the central region. In addition, numerical experiments were conducted to compare the calculation speed of SH model, SCH model and VSH model, and the results show that the calculation speed of the VSH model is raised one order magnitude in a small scope.

Integrating Work and Basic Values into the Spherical Model of Interests

Science.gov (United States)

Sodano, Sandro M.

2011-01-01

Two prominent models of values, one in work and the other in life, were examined as they each related to the dimensions underlying the Spherical Model of Interests (Tracey & Rounds, 1996) as measured by the Personal Globe Inventory (PGI; Tracey, 2002). The technique of external property vector fitting was utilized to plot the value constructs onto…

Exploration of spherical torus physics in the NSTX device

Science.gov (United States)

Ono, M.; Kaye, S. M.; Peng, Y.-K. M.; Barnes, G.; Blanchard, W.; Carter, M. D.; Chrzanowski, J.; Dudek, L.; Ewig, R.; Gates, D.; Hatcher, R. E.; Jarboe, T.; Jardin, S. C.; Johnson, D.; Kaita, R.; Kalish, M.; Kessel, C. E.; Kugel, H. W.; Maingi, R.; Majeski, R.; Manickam, J.; McCormack, B.; Menard, J.; Mueller, D.; Nelson, B. A.; Nelson, B. E.; Neumeyer, C.; Oliaro, G.; Paoletti, F.; Parsells, R.; Perry, E.; Pomphrey, N.; Ramakrishnan, S.; Raman, R.; Rewoldt, G.; Robinson, J.; Roquemore, A. L.; Ryan, P.; Sabbagh, S.; Swain, D.; Synakowski, E. J.; Viola, M.; Williams, M.; Wilson, J. R.; NSTX Team

2000-03-01

The National Spherical Torus Experiment (NSTX) is being built at Princeton Plasma Physics Laboratory to test the fusion physics principles for the spherical torus concept at the MA level. The NSTX nominal plasma parameters are R0 = 85 cm, a = 67 cm, R/a >= 1.26, Bt = 3 kG, Ip = 1 MA, q95 = 14, elongation κ The plasma heating/current drive tools are high harmonic fast wave (6 MW, 5 s), neutral beam injection (5 MW, 80 keV, 5 s) and coaxial helicity injection. Theoretical calculations predict that NSTX should provide exciting possibilities for exploring a number of important new physics regimes, including very high plasma β, naturally high plasma elongation, high bootstrap current fraction, absolute magnetic well and high pressure driven sheared flow. In addition, the NSTX programme plans to explore fully non-inductive plasma startup as well as a dispersive scrape-off layer for heat and particle flux handling.

On the shell model connection of the cluster model

International Nuclear Information System (INIS)

Cseh, J.; Levai, G.; Kato, K.

2000-01-01

Complete text of publication follows. The interrelation of basic nuclear structure models is a longstanding problem. The connection between the spherical shell model and the quadrupole collective model has been studied extensively, and symmetry considerations proved to be especially useful in this respect. A collective band was interpreted in the shell model language long ago as a set of states (of the valence nucleons) with a specific SU(3) symmetry. Furthermore, the energies of these rotational states are obtained to a good approximation as eigenvalues of an SU(3) dynamically symmetric shell model Hamiltonian. On the other hand the relation of the shell model and cluster model is less well explored. The connection of the harmonic oscillator (i.e. SU(3)) bases of the two approaches is known, but it was established only for the unrealistic harmonic oscillator interactions. Here we investigate the question: Can an SU(3) dynamically symmetric interaction provide a similar connection between the spherical shell model and the cluster model, like the one between the shell and collective models? In other words: whether or not the energy of the states of the cluster bands, defined by a specific SU(3) symmetries, can be obtained from a shell model Hamiltonian (with SU(3) dynamical symmetry). We carried out calculations within the framework of the semimicroscopic algebraic cluster model, in which not only the cluster model space is obtained from the full shell model space by an SU(3) symmetry-dictated truncation, but SU(3) dynamically symmetric interactions are also applied. Actually, Hamiltonians of this kind proved to be successful in describing the gross features of cluster states in a wide energy range. The novel feature of the present work is that we apply exclusively shell model interactions. The energies obtained from such a Hamiltonian for several bands of the ( 12 C, 14 C, 16 O, 20 Ne, 40 Ca) + α systems turn out to be in good agreement with the experimental

Particle Trapping and Dropouts in Magnetic Turbulence in a Spherical Geometry

Science.gov (United States)

Tooprakai, P.; Ruffolo, D.; Matthaeus, W. H.; Chuychai, P.

2006-12-01

The observed dropouts of solar energetic particles from impulsive solar events (i.e., the inhomogeneity and sharp gradients in particle density) indicate the partial filamentation of magnetic connection from small regions of the corona to Earth orbit. This can be understood in terms of persistent trapping of field lines due to small- scale topological structures in the solar wind. We further explore how this turbulence structure should be manifest in particle observations, by evaluating particle trajectories obtained from the Newton-Lorentz equations. By adapting a two-component model of turbulence to spherical geometry, we include the adiabatic focusing of particles. The 2D magnetic field is generated by either 1) a 2D fast Fourier transform, a valid approximation over a small angular region, or 2) a spherical harmonic series with ℓ up to 2000. Dropout features at 1 AU are clearly indicated for low-energy particles, but these features are washed out for E >~ 100 MeV. Different time-intensity profiles are found at locations at 1 AU that are distinct with regard to the small-scale topology. Partially supported by the Thailand Research Fund, the Rachadapisek Sompoj Fund of Chulalongkorn University, and NASA Grant NNG05GG83G.

Detailed Equivalent VSC-HVDC Modelling for Time Domain Harmonic Stability Studies in Wind Power Plants

DEFF Research Database (Denmark)

Glasdam, Jakob Bærholm; Bak, Claus Leth; Kocewiak, Lukasz Hubert

2018-01-01

system with 201 voltage levels, without loss of accuracy compared to conventional modelling of the converter. Harmonic stability is a core concern for both existing and future offshore wind power plants (OWPPs). A harmonic stability study will be undertaken with focus on the number of wind turbine...

Electron Bernstein wave emission based diagnostic on National Spherical Torus Experiment (invited)

International Nuclear Information System (INIS)

Diem, S.; Taylor, G.; Caughman, John B.; Efthimion, P.C.; Kugel, H.; LeBlanc, B.; Preinhaelter, J.; Sabbagh, S.A.; Urban, J.

2008-01-01

National Spherical Torus Experiment (NSTX) is a spherical tokamak (ST) that operates with n(e) up to 10(20) m(-3) and B-T less than 0.6 T, cutting off low harmonic electron cyclotron (EC) emission widely used for T-e measurements on conventional aspect ratio tokamaks. The electron Bernstein wave (EBW) can propagate in ST plasmas and is emitted at EC harmonics. These properties suggest thermal EBW emission (EBE) may be used for local T-e measurements in the ST. Practically, a robust T-e(R,t) EBE diagnostic requires EBW transmission efficiencies of >90% for a wide range of plasma conditions. EBW emission and coupling physics were studied on NSTX with an obliquely viewing EBW to O-mode (B-X-O) diagnostic with two remotely steered antennas, coupled to absolutely calibrated radiometers. While T-e(R,t) measurements with EBW emission on NSTX were possible, they were challenged by several issues. Rapid fluctuations in edge n(e) scale length resulted in >20% changes in the low harmonic B-X-O transmission efficiency. Also, B-X-O transmission efficiency during H modes was observed to decay by a factor of 5-10 to less than a few percent. The B-X-O transmission behavior during H modes was reproduced by EBE simulations that predict that EBW collisional damping can significantly reduce emission when T-e < 30 eV inside the B-X-O mode conversion (MC) layer. Initial edge lithium conditioning experiments during H modes have shown that evaporated lithium can increase T-e inside the B-X-O MC layer, significantly increasing B-X-O transmission.

The two-capacitor problem revisited: a mechanical harmonic oscillator model approach

International Nuclear Information System (INIS)

Lee, Keeyung

2009-01-01

The well-known two-capacitor problem, in which exactly half the stored energy disappears when a charged capacitor is connected to an identical capacitor, is discussed based on the mechanical harmonic oscillator model approach. In the mechanical harmonic oscillator model, it is shown first that exactly half the work done by a constant applied force is dissipated irrespective of the form of dissipation mechanism when the system comes to a new equilibrium after a constant force is abruptly applied. This model is then applied to the energy loss mechanism in the capacitor charging problem or the two-capacitor problem. This approach allows a simple explanation of the energy dissipation mechanism in these problems and shows that the dissipated energy should always be exactly half the supplied energy whether that is caused by the Joule heat or by the radiation. This paper, which provides a simple treatment of the energy dissipation mechanism in the two-capacitor problem, is suitable for all undergraduate levels

Initial results from the TST-2 spherical tokamak

International Nuclear Information System (INIS)

Takase, Y.; Ejiri, A.; Kasuya, N.

2001-01-01

A new spherical tokamak TST-2 was constructed at the University of Tokyo and started operation in September 1999. Reliable plasma initiation is achieved with typically 1 kW of ECH power at 2.45 GHz. Plasma currents of up to 90 kA and toroidal fields of up to 0.2 T have been achieved during the initial experimental campaign. The ion temperature is typically 100 eV. Internal reconnection events (IREs) are often observed. The internal magnetic field measured at r/a=2/3 indicated growth of fluctuations up to the 4 th harmonic, suggesting the existence of modes with several different mode numbers. In the presence of a toroidal field and a vertically oriented mirror field, noninductively driven currents of order 1 kA were observed with 1 kW of ECH power. The driven current increased with decreasing filling pressure, down to 3x10 -6 torr. A study of high harmonic fast wave (HHFW) excitation and propagation has begun. Initial results indicate highly efficient wave launching. (author)

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

Science.gov (United States)

López-Ruiz, F. F.; Guerrero, J.; Aldaya, V.; Cossío, F.

2012-08-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

The Quantum Arnold Transformation for the damped harmonic oscillator: from the Caldirola-Kanai model toward the Bateman model

International Nuclear Information System (INIS)

López-Ruiz, F F; Guerrero, J; Aldaya, V; Cossío, F

2012-01-01

Using a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations (LSODE), including systems with friction linear in velocity such as the damped harmonic oscillator, can be related to the quantum free-particle dynamical system. This implies that symmetries and simple computations in the free particle can be exported to the LSODE-system. The quantum Arnold transformation is given explicitly for the damped harmonic oscillator, and an algebraic connection between the Caldirola-Kanai model for the damped harmonic oscillator and the Bateman system will be sketched out.

A semi-local quasi-harmonic model to compute the thermodynamic and mechanical properties of silicon nanostructures

International Nuclear Information System (INIS)

Zhao, H; Aluru, N R

2007-01-01

This paper presents a semi-local quasi-harmonic model with local phonon density of states (LPDOS) to compute the thermodynamic and mechanical properties of silicon nanostructures at finite temperature. In contrast to an earlier approach (Tang and Aluru 2006 Phys. Rev. B 74 235441), where a quasi-harmonic model with LPDOS computed by a Green's function technique (QHMG) was developed considering many layers of atoms, the semi-local approach considers only two layers of atoms to compute the LPDOS. We show that the semi-local approach combines the accuracy of the QHMG approach and the computational efficiency of the local quasi-harmonic model. We present results for several silicon nanostructures to address the accuracy and efficiency of the semi-local approach

Perfect fluid models in noncomoving observational spherical coordinates

International Nuclear Information System (INIS)

Ishak, Mustapha

2004-01-01

We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a noncomoving frame of reference. In this frame, we find that the velocity field has shear, acceleration, and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a noncomoving frame. We use the dust models in a noncomoving frame to outline a fitting procedure

High-resolution Local Gravity Model of the South Pole of the Moon from GRAIL Extended Mission Data

Science.gov (United States)

Goossens, Sander Johannes; Sabaka, Terence J.; Nicholas, Joseph B.; Lemoine, Frank G.; Rowlands, David D.; Mazarico, Erwan; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.

2014-01-01

We estimated a high-resolution local gravity field model over the south pole of the Moon using data from the Gravity Recovery and Interior Laboratory's extended mission. Our solution consists of adjustments with respect to a global model expressed in spherical harmonics. The adjustments are expressed as gridded gravity anomalies with a resolution of 1/6deg by 1/6deg (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40deg. The gravity anomalies have been estimated from a short-arc analysis using only Ka-band range-rate (KBRR) data over the area of interest. We apply a neighbor-smoothing constraint to our solution. Our local model removes striping present in the global model; it reduces the misfit to the KBRR data and improves correlations with topography to higher degrees than current global models.

Spherically symmetric Einstein-aether perfect fluid models

Energy Technology Data Exchange (ETDEWEB)

Coley, Alan A.; Latta, Joey [Department of Mathematics and Statistics, Dalhousie University, Halifax, Nova Scotia, B3H 3J5 (Canada); Leon, Genly [Instituto de Física, Pontificia Universidad Católica de Valparaíso, Casilla 4950, Valparaíso (Chile); Sandin, Patrik, E-mail: aac@mathstat.dal.ca, E-mail: genly.leon@ucv.cl, E-mail: patrik.sandin@aei.mpg.de, E-mail: lattaj@mathstat.dal.ca [Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, D-14476 Potsdam (Germany)

2015-12-01

We investigate spherically symmetric cosmological models in Einstein-aether theory with a tilted (non-comoving) perfect fluid source. We use a 1+3 frame formalism and adopt the comoving aether gauge to derive the evolution equations, which form a well-posed system of first order partial differential equations in two variables. We then introduce normalized variables. The formalism is particularly well-suited for numerical computations and the study of the qualitative properties of the models, which are also solutions of Horava gravity. We study the local stability of the equilibrium points of the resulting dynamical system corresponding to physically realistic inhomogeneous cosmological models and astrophysical objects with values for the parameters which are consistent with current constraints. In particular, we consider dust models in (β−) normalized variables and derive a reduced (closed) evolution system and we obtain the general evolution equations for the spatially homogeneous Kantowski-Sachs models using appropriate bounded normalized variables. We then analyse these models, with special emphasis on the future asymptotic behaviour for different values of the parameters. Finally, we investigate static models for a mixture of a (necessarily non-tilted) perfect fluid with a barotropic equations of state and a scalar field.

Linear analysis on the growth of non-spherical perturbations in supersonic accretion flows

Energy Technology Data Exchange (ETDEWEB)

Takahashi, Kazuya; Yamada, Shoichi, E-mail: ktakahashi@heap.phys.waseda.ac.jp [Advanced Research Institute for Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku 169-8555 (Japan)

2014-10-20

We analyzed the growth of non-spherical perturbations in supersonic accretion flows. We have in mind an application to the post-bounce phase of core-collapse supernovae (CCSNe). Such non-spherical perturbations have been suggested by a series of papers by Arnett, who has numerically investigated violent convections in the outer layers of pre-collapse stars. Moreover, Couch and Ott demonstrated in their numerical simulations that such perturbations may lead to a successful supernova even for a progenitor that fails to explode without fluctuations. This study investigated the linear growth of perturbations during the infall onto a stalled shock wave. The linearized equations are solved as an initial and boundary value problem with the use of a Laplace transform. The background is a Bondi accretion flow whose parameters are chosen to mimic the 15 M {sub ☉} progenitor model by Woosley and Heger, which is supposed to be a typical progenitor of CCSNe. We found that the perturbations that are given at a large radius grow as they flow down to the shock radius; the density perturbations can be amplified by a factor of 30, for example. We analytically show that the growth rate is proportional to l, the index of the spherical harmonics. We also found that the perturbations oscillate in time with frequencies that are similar to those of the standing accretion shock instability. This may have an implication for shock revival in CCSNe, which will be investigated in our forthcoming paper in more detail.

Continuous energy Monte Carlo calculations for randomly distributed spherical fuels based on statistical geometry model

Energy Technology Data Exchange (ETDEWEB)

Murata, Isao [Osaka Univ., Suita (Japan); Mori, Takamasa; Nakagawa, Masayuki; Itakura, Hirofumi

1996-03-01

The method to calculate neutronics parameters of a core composed of randomly distributed spherical fuels has been developed based on a statistical geometry model with a continuous energy Monte Carlo method. This method was implemented in a general purpose Monte Carlo code MCNP, and a new code MCNP-CFP had been developed. This paper describes the model and method how to use it and the validation results. In the Monte Carlo calculation, the location of a spherical fuel is sampled probabilistically along the particle flight path from the spatial probability distribution of spherical fuels, called nearest neighbor distribution (NND). This sampling method was validated through the following two comparisons: (1) Calculations of inventory of coated fuel particles (CFPs) in a fuel compact by both track length estimator and direct evaluation method, and (2) Criticality calculations for ordered packed geometries. This method was also confined by applying to an analysis of the critical assembly experiment at VHTRC. The method established in the present study is quite unique so as to a probabilistic model of the geometry with a great number of spherical fuels distributed randomly. Realizing the speed-up by vector or parallel computations in future, it is expected to be widely used in calculation of a nuclear reactor core, especially HTGR cores. (author).

Inertial waves in a spherical shell induced by librations of the inner sphere: experimental and numerical results

Energy Technology Data Exchange (ETDEWEB)

Koch, S; Harlander, U; Egbers, C [Department of Aerodynamics and Fluid Mechanics, Brandenburg University of Technology Cottbus, Siemens-Halske-Ring 14, D-03046 Cottbus (Germany); Hollerbach, R, E-mail: uwe.harlander@tu-cottbus.de [Institute of Geophysics, ETH Zuerich, Sonneggstrasse 5, CH-8092 Zurich (Switzerland)

2013-06-15

We begin with an experimental investigation of the flow induced in a rotating spherical shell. The shell globally rotates with angular velocity {Omega}. A further periodic oscillation with angular velocity 0 Less-Than-Or-Slanted-Equal-To {omega} Less-Than-Or-Slanted-Equal-To 2{Omega}, a so-called longitudinal libration, is added on the inner sphere's rotation. The primary response is inertial waves spawned at the critical latitudes on the inner sphere, and propagating throughout the shell along inclined characteristics. For sufficiently large libration amplitudes, the higher harmonics also become important. Those harmonics whose frequencies are still less than 2{Omega} behave as inertial waves themselves, propagating along their own characteristics. The steady component of the flow consists of a prograde zonal jet on the cylinder tangent to the inner sphere and parallel to the axis of rotation, and increases with decreasing Ekman number. The jet becomes unstable for larger forcing amplitudes as can be deduced from the preliminary particle image velocimetry observations. Finally, a wave attractor is experimentally detected in the spherical shell as the pattern of largest variance. These findings are reproduced in a two-dimensional numerical investigation of the flow, and certain aspects can be studied numerically in greater detail. One aspect is the scaling of the width of the inertial shear layers and the width of the steady jet. Another is the partitioning of the kinetic energy between the forced wave, its harmonics and the mean flow. Finally, the numerical simulations allow for an investigation of instabilities, too local to be found experimentally. For strong libration amplitudes, the boundary layer on the inner sphere becomes unstable, triggering localized Goertler vortices during the prograde phase of the forcing. This instability is important for the transition to turbulence of the spherical shell flow. (paper)

Interacting Multiple Model (IMM Fifth-Degree Spherical Simplex-Radial Cubature Kalman Filter for Maneuvering Target Tracking

Directory of Open Access Journals (Sweden)

Hua Liu

2017-06-01

Full Text Available For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM filter and the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF. The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with the interacting multiple model unscented Kalman filter (IMMUKF, the interacting multiple model cubature Kalman filter (IMMCKF and the interacting multiple model fifth-degree cubature Kalman filter (IMM5thCKF.

Interacting Multiple Model (IMM) Fifth-Degree Spherical Simplex-Radial Cubature Kalman Filter for Maneuvering Target Tracking.

Science.gov (United States)

Liu, Hua; Wu, Wen

2017-06-13

For improving the tracking accuracy and model switching speed of maneuvering target tracking in nonlinear systems, a new algorithm named the interacting multiple model fifth-degree spherical simplex-radial cubature Kalman filter (IMM5thSSRCKF) is proposed in this paper. The new algorithm is a combination of the interacting multiple model (IMM) filter and the fifth-degree spherical simplex-radial cubature Kalman filter (5thSSRCKF). The proposed algorithm makes use of Markov process to describe the switching probability among the models, and uses 5thSSRCKF to deal with the state estimation of each model. The 5thSSRCKF is an improved filter algorithm, which utilizes the fifth-degree spherical simplex-radial rule to improve the filtering accuracy. Finally, the tracking performance of the IMM5thSSRCKF is evaluated by simulation in a typical maneuvering target tracking scenario. Simulation results show that the proposed algorithm has better tracking performance and quicker model switching speed when disposing maneuver models compared with the interacting multiple model unscented Kalman filter (IMMUKF), the interacting multiple model cubature Kalman filter (IMMCKF) and the interacting multiple model fifth-degree cubature Kalman filter (IMM5thCKF).

Structure of Vocational Interests in Serbia: Evaluation of the Spherical Model

Science.gov (United States)

Hedrih, Vladimir

2008-01-01

To explore the structure of vocational interests in Serbia, 1063 participants of various age, education and gender completed the Serbian version of the Personal Globe Inventory [PGI, Tracey, T. (2002). "Personal Globe Inventory: Measurement of the spherical model of interests and competence beliefs." "Journal of Vocational…

Evaluation of Harmonics Impact on Digital Relays

Directory of Open Access Journals (Sweden)

Kinan Wannous

2018-04-01

Full Text Available This paper presents the concept of the impact of harmonic distortion on a digital protection relay. The aim is to verify and determine the reasons of a mal-trip or failure to trip the protection relays; the suggested solution of the harmonic distortion is explained by a mathematical model in the Matlab Simulink programming environment. The digital relays have been tested under harmonic distortions in order to verify the function of the relays algorithm under abnormal conditions. The comparison between the protection relay algorithm under abnormal conditions and a mathematical model in the Matlab Simulink programming environment based on injected harmonics of high values is provided. The test is separated into different levels; the first level is based on the harmonic effect of an individual harmonic and mixed harmonics. The test includes the effect of the harmonics in the location of the fault point into distance protection zones. This paper is a new proposal in the signal processing of power quality disturbances using Matlab Simulink and the power quality impact on the measurements of the power system quantities; the test simulates the function of protection in power systems in terms of calculating the current and voltage values of short circuits and their faults. The paper includes several tests: frequency variations and decomposition of voltage waveforms with Fourier transforms (model and commercial relay, the effect of the power factor on the location of fault points, the relation between the tripping time and the total harmonic distortion (THD levels in a commercial relay, and a comparison of the THD capture between the commercial relay and the model.

Modeling and Identification of Harmonic Instability Problems In Wind Farms

DEFF Research Database (Denmark)

Ebrahimzadeh, Esmaeil; Blaabjerg, Frede; Wang, Xiongfei

2016-01-01

In power electronics based power systems like wind farms, the interactions between the inner control systems of the power converters and the passive components may lead to high frequency oscillations, which can be called harmonic instability. In this paper, a simple methodology is presented...... to identify harmonic instability problems in wind farms, where many wind turbines, cables, transformers, capacitor banks, shunt reactors, etc, typically are located. This methodology introduces the wind farm as a Multi-Input Multi-Outpur (MIMO) control system, where the linearized models of fast inner control....../EMTDC software environment for a 400-MW wind farm. The proposed analytical analysis method and time-domain simulation results show that both dynamics of the power electronic converter and the parameters of the passive component can effect on the wind farm stability....

An Inquiry-Based Approach to Teaching the Spherical Earth Model to Preservice Teachers Using the Global Positioning System

Science.gov (United States)

Song, Youngjin; Schwenz, Richard

2013-01-01

This article describes an inquiry-based lesson to deepen preservice teachers' understanding of the spherical Earth model using the Global Positioning System. The lesson was designed with four learning goals: (1) to increase preservice teachers' conceptual knowledge of the spherical Earth model; (2) to develop preservice teachers'…

Second harmonic inversion for ultrasound contrast harmonic imaging

Energy Technology Data Exchange (ETDEWEB)

Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico [THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam (Netherlands); Cachard, Christian; Basset, Olivier, E-mail: mirza.pasovic@creatis.insa-lyon.fr [CREATIS-LRMN, Universite de Lyon, INSA-Lyon, Universite Lyon 1, Inserm U630, CNRS UMR 5220 (France)

2011-06-07

Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f{sub 0} and the same amplitude P{sub 0} to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.

Second harmonic inversion for ultrasound contrast harmonic imaging

International Nuclear Information System (INIS)

Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico; Cachard, Christian; Basset, Olivier

2011-01-01

Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f 0 and the same amplitude P 0 to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.

Modeling and analysis of periodic orbits around a contact binary asteroid

Science.gov (United States)

Feng, Jinglang; Noomen, Ron; Visser, Pieter N. A. M.; Yuan, Jianping

2015-06-01

The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is represented by a combination of an ellipsoid and a sphere. The gravitational field of this configuration is for the first time expanded into a spherical harmonics model up to degree and order 8. Compared with the exact potential, the truncation at degree and order 4 is found to introduce an error of less than 10 % at the circumscribing sphere and less than 1 % at a distance of the double of the reference radius. The Hamiltonian taking into account harmonics up to degree and order 4 is developed. After double averaging of this Hamiltonian, the model is reduced to include zonal harmonics only and frozen orbits are obtained. The tesseral terms are found to introduce significant variations on the frozen orbits and distort the frozen situation. Applying the method of Poincaré sections, phase space structures of the single-averaged model are generated for different energy levels and rotation rates of the asteroid, from which the dynamics driven by the 4×4 harmonics model is identified and POs are found. It is found that the disturbing effect of the highly irregular gravitational field on orbital motion is weakened around the polar region, and also for an asteroid with a fast rotation rate. Starting with initial conditions from this averaged model, families of exact POs in the original non-averaged system are obtained employing a numerical search method and a continuation technique. Some of these POs are stable and are candidates for future missions.

Ergodic model for the expansion of spherical nanoplasmas.

Science.gov (United States)

Peano, F; Coppa, G; Peinetti, F; Mulas, R; Silva, L O

2007-06-01

Recently, the collisionless expansion of spherical nanoplasmas has been analyzed with a new ergodic model, clarifying the transition from hydrodynamiclike to Coulomb-explosion regimes, and providing accurate laws for the relevant features of the phenomenon. A complete derivation of the model is presented here. The important issue of the self-consistent initial conditions is addressed by analyzing the initial charging transient due to the electron expansion, in the approximation of immobile ions. A comparison among different kinetic models for the expansion is presented, showing that the ergodic model provides a simplified description, which retains the essential information on the electron distribution, in particular, the energy spectrum. Results are presented for a wide range of initial conditions (determined from a single dimensionless parameter), in excellent agreement with calculations from the exact Vlasov-Poisson theory, thus providing a complete and detailed characterization of all the stages of the expansion.

Turbulence Modulation by Non-Spherical Particles

DEFF Research Database (Denmark)

Mandø, Matthias

This study deals with the interaction between turbulence and non-spherical particles and represents an extension of the modeling framework for particleladen flows. The effect of turbulence on particles is commonly referred to as turbulent dispersion while the effect of particles on the carrier....... This study encompass an outlook on existing work, an experimental study, development of a numerical model and a case study advancing the modeling techniques for pulverized coal combustion to deal with larger non-spherical biomass particles. Firstly, existing knowledge concerning the motion of non......-spherical particles and turbulence modulation are outlined. A complete description of the motion of non-spherical particles is still lacking. However, evidence suggests that the equation of motion for a sphere only represent an asymptotical value for a more general, but yet unformulated, description of the motion...

Simulation model of harmonics reduction technique using shunt active filter by cascade multilevel inverter method

Science.gov (United States)

Andreh, Angga Muhamad; Subiyanto, Sunardiyo, Said

2017-01-01

Development of non-linear loading in the application of industry and distribution system and also harmonic compensation becomes important. Harmonic pollution is an urgent problem in increasing power quality. The main contribution of the study is the modeling approach used to design a shunt active filter and the application of the cascade multilevel inverter topology to improve the power quality of electrical energy. In this study, shunt active filter was aimed to eliminate dominant harmonic component by injecting opposite currents with the harmonic component system. The active filter was designed by shunt configuration with cascaded multilevel inverter method controlled by PID controller and SPWM. With this shunt active filter, the harmonic current can be reduced so that the current wave pattern of the source is approximately sinusoidal. Design and simulation were conducted by using Power Simulator (PSIM) software. Shunt active filter performance experiment was conducted on the IEEE four bus test system. The result of shunt active filter installation on the system (IEEE four bus) could reduce THD current from 28.68% to 3.09%. With this result, the active filter can be applied as an effective method to reduce harmonics.

Analytical method for analysis of electromagnetic scattering from inhomogeneous spherical structures using duality principles

Science.gov (United States)

Kiani, M.; Abdolali, A.; Safari, M.

2018-03-01

In this article, an analytical approach is presented for the analysis of electromagnetic (EM) scattering from radially inhomogeneous spherical structures (RISSs) based on the duality principle. According to the spherical symmetry, similar angular dependencies in all the regions are considered using spherical harmonics. To extract the radial dependency, the system of differential equations of wave propagation toward the inhomogeneity direction is equated with the dual planar ones. A general duality between electromagnetic fields and parameters and scattering parameters of the two structures is introduced. The validity of the proposed approach is verified through a comprehensive example. The presented approach substitutes a complicated problem in spherical coordinate to an easy, well posed, and previously solved problem in planar geometry. This approach is valid for all continuously varying inhomogeneity profiles. One of the major advantages of the proposed method is the capability of studying two general and applicable types of RISSs. As an interesting application, a class of lens antenna based on the physical concept of the gradient refractive index material is introduced. The approach is used to analyze the EM scattering from the structure and validate strong performance of the lens.

Mean spherical model for hard ions and dipoles: Thermodynamics and correlation functions

International Nuclear Information System (INIS)

Vericat, F.; Blum, L.

1980-01-01

The solution of the mean spherical model of a mixture of equal-size hard ions and dipoles is reinvestigated. Simple expressions for the coefficients of the Laplace transform of the pair correlation function and the other thermodynamic properties are given

Harmonic wave model of a permanent magnet synchronous machine for modeling partial demagnetization under short circuit conditions

NARCIS (Netherlands)

Kral, C.; Haumer, A.; Bogomolov, M.D.; Lomonova, E.

2012-01-01

This paper proposes a multi domain physical model of permanent magnet synchronous machines, considering electrical, magnetic, thermal and mechanical effects. For each component of the model, the main wave as well as lower and higher harmonic wave components of the magnetic flux and the magnetic

Investigations of Low and Moderate Harmonic Fast Wave Physics on CDX-U

International Nuclear Information System (INIS)

Spaleta, J.; Majeski, R.; Phillips, C.K.; Dumont, R.J.; Kaita, R.; Soukhanovskii, V.; Zakharov, L.

2003-01-01

Third harmonic hydrogen cyclotron fast wave heating studies are planned in the near term on CDX-U to investigate the potential for bulk ion heating. In preparation for these studies, the available radio-frequency power in CDX-U has been increased to 0.5 MW. The operating frequency of the CDX-U radio-frequency transmitter was lowered to operate in the range of 8-10 MHz, providing access to the ion harmonic range 2* ∼ 4* in hydrogen. A similar regime is accessible for the 30 MHz radio-frequency system on the National Spherical Torus Experiment (NSTX), at 0.6 Tesla in hydrogen. Preliminary computational studies over the plasma regimes of interest for NSTX and CDX-U indicate the possibility of strong localized absorption on bulk ion species

Surface multifragmentation investigated with a finite temperature spherical TDHF model

International Nuclear Information System (INIS)

Ngo, H.; Ighezou, F.Z.; Paula, L. De

1992-01-01

A model for multifragmentation caused by heavy ion collision is developed. The initial state is a hot and compressed spherical nucleus in thermal equilibrium. The dynamical evolution of this nucleus is studied. The nuclear density of the system is calculated with mean field approximation. It is shown that, in some cases, the surface of the nucleus breaks up before its volume. (K.A.) 8 refs.; 1 fig

Analysis of two colliding fractionally damped spherical shells in modelling blunt human head impacts

Science.gov (United States)

Rossikhin, Yury A.; Shitikova, Marina V.

2013-06-01

The collision of two elastic or viscoelastic spherical shells is investigated as a model for the dynamic response of a human head impacted by another head or by some spherical object. Determination of the impact force that is actually being transmitted to bone will require the model for the shock interaction of the impactor and human head. This model is indended to be used in simulating crash scenarios in frontal impacts, and provide an effective tool to estimate the severity of effect on the human head and to estimate brain injury risks. The model developed here suggests that after the moment of impact quasi-longitudinal and quasi-transverse shock waves are generated, which then propagate along the spherical shells. The solution behind the wave fronts is constructed with the help of the theory of discontinuities. It is assumed that the viscoelastic features of the shells are exhibited only in the contact domain, while the remaining parts retain their elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shells are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. It is shown that the fractional parameter of the fractional derivative model plays very important role, since its variation allows one to take into account the age-related changes in the mechanical properties of bone.

Modeling and analysis of periodic orbits around a contact binary asteroid

NARCIS (Netherlands)

Feng, J.; Noomen, R.; Visser, P.N.A.M.; Yuan, J.

2015-01-01

The existence and characteristics of periodic orbits (POs) in the vicinity of a contact binary asteroid are investigated with an averaged spherical harmonics model. A contact binary asteroid consists of two components connected to each other, resulting in a highly bifurcated shape. Here, it is

Modeling of VSC-Based Power Systems in The Extended Harmonic Domain

DEFF Research Database (Denmark)

Esparza, Miguel; Segundo-Ramirez, Juan; Kwon, Jun Bum

2017-01-01

Averaged modeling is a commonly used approach used to obtain mathematical representations of VSC-based systems. However, essential characteristics mainly related to the modulation process and the harmonic distortion of the signals are not able to be accurately captured and analyzed. The extended ...... on simulations and experimental case studies. The obtained results show that the resulting EHD models are accurate and reliable, while the memory and computation time are improved with the proposed model order reductions....

The mass spectrum of double heavy baryons in new potential quark models

Directory of Open Access Journals (Sweden)

Kovalenko Vladimir

2017-01-01

Full Text Available A new approach to study the mass spectrum of double heavy baryons (QQ′q containing strange and charmed quarks is proposed. It is based on the separation of variables in the Schrodinger equation in the prolate spheroidal coordinates. Two nonrelativistic potential models are considered. In the first model, the interaction potential of the quarks is the sum of the Coulomb and non-spherically symmetrical linear confinement potential. In the second model it is assumed that the quark confinement provided by a spherically symmetric harmonic oscillator potential. In both models the mass spectrum is calculated, and a comparison with previous results from other models is performed.

Novel Harmonic Regularization Approach for Variable Selection in Cox’s Proportional Hazards Model

Directory of Open Access Journals (Sweden)

Ge-Jin Chu

2014-01-01

Full Text Available Variable selection is an important issue in regression and a number of variable selection methods have been proposed involving nonconvex penalty functions. In this paper, we investigate a novel harmonic regularization method, which can approximate nonconvex Lq  (1/2model using microarray gene expression data. The harmonic regularization method can be efficiently solved using our proposed direct path seeking approach, which can produce solutions that closely approximate those for the convex loss function and the nonconvex regularization. Simulation results based on the artificial datasets and four real microarray gene expression datasets, such as real diffuse large B-cell lymphoma (DCBCL, the lung cancer, and the AML datasets, show that the harmonic regularization method can be more accurate for variable selection than existing Lasso series methods.

Low degree Earth's gravity coefficients determined from different space geodetic observations and climate models

Science.gov (United States)

Wińska, Małgorzata; Nastula, Jolanta

2017-04-01

Large scale mass redistribution and its transport within the Earth system causes changes in the Earth's rotation in space, gravity field and Earth's ellipsoid shape. These changes are observed in the ΔC21, ΔS21, and ΔC20 spherical harmonics gravity coefficients, which are proportional to the mass load-induced Earth rotational excitations. In this study, linear trend, decadal, inter-annual, and seasonal variations of low degree spherical harmonics coefficients of Earth's gravity field, determined from different space geodetic techniques, Gravity Recovery and Climate Experiment (GRACE), satellite laser ranging (SLR), Global Navigation Satellite System (GNSS), Earth rotation, and climate models, are examined. In this way, the contribution of each measurement technique to interpreting the low degree surface mass density of the Earth is shown. Especially, we evaluate an usefulness of several climate models from the Coupled Model Intercomparison Project phase 5 (CMIP5) to determine the low degree Earth's gravity coefficients using GRACE satellite observations. To do that, Terrestrial Water Storage (TWS) changes from several CMIP5 climate models are determined and then these simulated data are compared with the GRACE observations. Spherical harmonics ΔC21, ΔS21, and ΔC20 changes are calculated as the sum of atmosphere and ocean mass effect (GAC values) taken from GRACE and a land surface hydrological estimate from the selected CMIP5 climate models. Low degree Stokes coefficients of the surface mass density determined from GRACE, SLR, GNSS, Earth rotation measurements and climate models are compared to each other in order to assess their consistency. The comparison is done by using different types of statistical and signal processing methods.

An Angular Leakage Correction for Modeling a Hemisphere, Using One-Dimensional Spherical Coordinates

International Nuclear Information System (INIS)

Schwinkendorf, K.N.; Eberle, C.S.

2003-01-01

A radially dependent, angular leakage correction was applied to a one-dimensional, multigroup neutron diffusion theory computer code to accurately model hemispherical geometry. This method allows the analyst to model hemispherical geometry, important in nuclear criticality safety analyses, with one-dimensional computer codes, which execute very quickly. Rapid turnaround times for scoping studies thus may be realized. This method uses an approach analogous to an axial leakage correction in a one-dimensional cylinder calculation. The two-dimensional Laplace operator was preserved in spherical geometry using a leakage correction proportional to 1/r 2 , which was folded into the one-dimensional spherical calculation on a mesh-by-mesh basis. Hemispherical geometry is of interest to criticality safety because of its similarity to piles of spilled fissile material and accumulations of fissile material in process containers. A hemisphere also provides a more realistic calculational model for spilled fissile material than does a sphere

Modeling of large aperture third harmonic frequency conversion of high power Nd:glass laser systems

International Nuclear Information System (INIS)

Henesian, M.A.; Wegner, P.J.; Speck, D.R.; Bibeau, C.; Ehrlich, R.B.; Laumann, C.W.; Lawson, J.K.; Weiland, T.L.

1991-01-01

To provide high-energy, high-power beams at short wavelengths for inertial-confinement-fusion experiments, we routinely convert the 1.053-μm output of the Nova, Nd:phosphate-glass, laser system to its third-harmonic wavelength. We describe performance and conversion efficiency modeling of the 3 x 3 arrays potassium-dihydrogen-phosphate crystal plates used for type II/type II phase-matched harmonic conversion of Nova 0.74-m diameter beams, and an alternate type I/type II phase-matching configuration that improves the third-harmonic conversion efficiency. These arrays provide energy conversion of up to 65% and intensity conversion to 70%. 19 refs., 11 figs

Spherical collapse in quintessence models with zero speed of sound

CERN Document Server

Creminelli, Paolo; Noreña, Jorge; Senatore, Leonardo; Vernizzi, Filippo

2010-01-01

We study the spherical collapse model in the presence of quintessence with zero speed of sound. This case is particularly motivated for w<-1 as it is required by stability. As pressure gradients are negligible, quintessence follows dark matter during the collapse. The spherical overdensity behaves as a separate closed FLRW universe, so that its evolution can be studied exactly. We derive the critical overdensity for collapse and we use the extended Press-Schechter theory to study how the clustering of quintessence affects the dark matter mass function. The effect is dominated by the modification of the linear dark matter growth function. A larger effect occurs on the total mass function, which includes the quintessence overdensities. Indeed, here quintessence constitutes a third component of virialized objects, together with baryons and dark matter, and contributes to the total halo mass by a fraction ~ (1+w) Omega_Q / Omega_m. This gives a distinctive modification of the total mass function at low redshif...

Modeling of higher harmonics formation in medical ultrasound systems

DEFF Research Database (Denmark)

Taylor, Louise Kold; Schlaikjer, Malene; Jensen, Jørgen Arendt

2002-01-01

a valuable tool for simulating ultrasound harmonic imaging. An extended version of Field II is obtained by means of operator splitting. The pressure eld is calculated by propagation of the eld from the transducer through a number of planes. Every plane serves as a virtual aperture for the next plane...... of the approach is demonstrated by comparing results from simulations and measurements from a convex array transducer. The new simulation tool is capable of simulating the formation of higher harmonics in water on the acoustical axis. The generation of nonlinear higher harmonic components can be predicted...

Third-harmonic generation for photoionization studies

International Nuclear Information System (INIS)

Compton, R.N.; Miller, J.C.

1982-01-01

Our group at Oak Ridge National Laboratory (ORNL) has studied resonantly enhanced multiphoton ionization (MPI) of alkali atoms, rare gases, and small molecules using tightly focused dye laser beams (power densities of 10 9 to 10 11 W/cm 2 ). In the case of alkali atoms, some ionization signals appear as a result of gas density effects (dimers or quasi-collisions) as previously discovered by Collins and his collaborators. These have been termed hybrid-resonances. By contrast, in the case of the rare gases, certain resonance ionization signals disappear with increasing gas density. The disappearance of the ionization signals in the rare gases is due to the interference of excitation of the third-harmonic and fundamental laser beam. At low pressure (10 -7 to 10 -5 torr) we have studied (1) mass spectra, (2) kinetic energy released in ionic fragmentation, and (3) photoelectron kinetic energy spectra using time-of-flight mass analysis and a 160 0 spherical sector electrostatic energy analyzer. These experiments, combined with two-color dye laser experiments, can often offer an unambiguous and detailed description of the MPI and subsequent fragmentation events. The major part of this talk will be devoted to the production and the use of vacuum ultraviolet (VUV) light from third-harmonic generation (THG) in the rare gases

Status of National Spherical Torus Experiment (NSTX)*

Science.gov (United States)

Ono, Masayuki

2001-10-01

The main aim of National Spherical Torus Experiment (NSTX) is to establish the fusion physics principles of the innovative spherical torus (ST) concept. The NSTX experimental facility has been operating reliably and its capabilities steadily improving. Due to relatively efficient ohmic current drive and benign halo current behavior, the plasma current was increased to 1.4 MA, which is well above the design value of 1 MA. The plasmas at 1 MA are now routinely heated by NBI to the average toroidal beta value of 20 percent range at 3 kG with electrons and ions in the 1-2 keV range. Even with the “L-mode” edge, the energy confinement time can well exceed the so-called L-mode (and even H-mode) scaling values. As a part of ST tool development, High Harmonic Fast Wave (HHFW) heating has demonstrated efficient electron heating with the central electron temperatures reaching 3.7 keV. HHFW induced H-modes have been also observed. For CHI (Coaxial Helicity Injection) non-inductive start-up, CHI discharges of up to 300 kA of toroidal current and 300 msec duration have been produced from zero current using = 25 kA of injected current. The poster presentation will also include the near term NSTX facility upgrade plan.

Towards an Open Modelling Interface (OpenMI the HarmonIT project

Directory of Open Access Journals (Sweden)

M. Blind

2005-01-01

Full Text Available The Water Framework Directive (WFD poses an immense challenge to water management in Europe. Aiming at a "good ecological status" of surface waters in 2015, integrated river basin management plans need to be in place by 2009, and broadly supported by stakeholders. Information & Communication Technology (ICT tools, such as computational models, are very helpful in designing river basin management plans (rbmp-s. However, many scientists believe that a single integrated modelling system to support the WFD cannot be developed, and integrated systems need to be quite tailored to the local situation and evolve during a collaborative planning process. As a consequence there is an urgent need to increase the flexibility of modelling systems, such that dedicated model systems can be developed from available building blocks. In the recent past a number of initiatives have been started to develop an IT framework for modelling to meet the required flexibility. In Europe the international project HarmonIT, which is sponsored by the European Commission, is developing and implementing a standard interface for modelling components and other relevant tools: The Open Modelling Interface (OpenMI. This paper describes the HarmonIT project and objectives in general. The current progress is described. It describes the roles for different types of stakeholders in modelling, varying from software coders to non-specialized users of decision support systems. It will provide insight in the requirements imposed when using the OpenMI.

Internal-Model-Principle-Based Specific Harmonics Repetitive Controller for Grid-Connected PWM Inverters

Directory of Open Access Journals (Sweden)

Wenzhou Lu

2016-01-01

Full Text Available This paper analyzes the general properties of IMP-based controller and presents an internal-model-principle-based (IMP-based specific harmonics repetitive control (SHRC scheme. The proposed SHRC is effective for specific nk±m order harmonics, with n>m≥0 and k=0,1,2,…. Using the properties of exponential function, SHRC can also be rewritten into the format of multiple resonant controllers in parallel, where the control gain of SHRC is n/2 multiple of that of conventional RC (CRC. Therefore, including SHRC in a stable closed-loop feedback control system, asymptotic disturbance eliminating, or reference tracking for any periodic signal only including these specific harmonic components at n/2 times faster error convergence rate compared with CRC can be achieved. Application examples of SHRC controlled three-phase/single-phase grid-connected PWM inverters demonstrate the effectiveness and advantages of the proposed SHRC scheme.

An Analysis of Spherical Particles Distribution Randomly Packed in a Medium for the Monte Carlo Implicit Modeling

Energy Technology Data Exchange (ETDEWEB)

Lee, Jae Yong; Kim, Song Hyun; Shin, Chang Ho; Kim, Jong Kyung [Hanyang Univ., Seoul (Korea, Republic of)

2014-05-15

In this study, as a preliminary study to develop an implicit method having high accuracy, the distribution characteristics of spherical particles were evaluated by using explicit modeling techniques in various volume packing fractions. This study was performed to evaluate implicitly simulated distribution of randomly packed spheres in a medium. At first, an explicit modeling method to simulate random packed spheres in a hexahedron medium was proposed. The distributed characteristics of l{sub p} and r{sub p}, which are used in the particle position sampling, was estimated. It is analyzed that the use of the direct exponential distribution, which is generally used in the implicit modeling, can cause the distribution bias of the spheres. It is expected that the findings in this study can be utilized for improving the accuracy in using the implicit method. Spherical particles, which are randomly distributed in medium, are utilized for the radiation shields, fusion reactor blanket, fuels of VHTR reactors. Due to the difficulty on the simulation of the stochastic distribution, Monte Carlo (MC) method has been mainly considered as the tool for the analysis of the particle transport. For the MC modeling of the spherical particles, three methods are known; repeated structure, explicit modeling, and implicit modeling. Implicit method (called as the track length sampling method) is a modeling method that is the sampling based modeling technique of each spherical geometry (or track length of the sphere) during the MC simulation. Implicit modeling method has advantages in high computational efficiency and user convenience. However, it is noted that the implicit method has lower modeling accuracy in various finite mediums.

Harmonic Distortion of Rectifier Topologies for Adjustable Speed Drives

DEFF Research Database (Denmark)

Hansen, Steffan

This thesis deals with the harmonic distortion of the diode rectifier and a number of alternative rectifier topologies for adjustable speed drives. The main intention of this thesis is to provide models and tools that allow easy prediction of the harmonic distortion of ASD’s in a given system...... rectifier are presented. The first level is an ideal model where the diode rectifier basically is treated as an independent (harmonic) current source. The second level is an empirical model, where simulated (or measured) values of the harmonic currents of the diode rectifier for different parameters......-angle of the individual harmonic currents of different diode rectifier types is analyzed. Four selected rectifier topologies with a high input power factor are presented. It is shown that using ac- or dc-coils is a very simple and efficient method to reduce the harmonic currents compared to the basic diode rectifier...

Harmonic Analysis of Offshore Wind Farms with Full Converter Wind Turbines

DEFF Research Database (Denmark)

Kocewiak, Lukasz Hubert; Hjerrild, Jesper; Bak, Claus Leth

2009-01-01

to a shore with a long HV cable. The way of propagation and effects of harmonics are presented for different study cases. Modeling strategies of harmonic sources for harmonic analysis are described and compared. Different results dependent on applied harmonic models are shown and discussed in this paper...

Ørsted Initial Field Model

DEFF Research Database (Denmark)

Olsen, Nils; Holme, R.; Hulot, G.

2000-01-01

Magnetic measurements taken by the Orsted satellite during geomagnetic quiet conditions around January 1, 2000 have been used to derive a spherical harmonic model of the Earth's magnetic field for epoch 2000.0. The maximum degree and order of the model is 19 for internal, and 2 for external, source...... fields; however, coefficients above degree 14 may not be robust. Such a detailed model exists for only one previous epoch, 1980. Achieved rms misfit is ... to the Orsted mission, this model supercedes IGRF 2000....

Modeling stock return distributions with a quantum harmonic oscillator

Science.gov (United States)

Ahn, K.; Choi, M. Y.; Dai, B.; Sohn, S.; Yang, B.

2017-11-01

We propose a quantum harmonic oscillator as a model for the market force which draws a stock return from short-run fluctuations to the long-run equilibrium. The stochastic equation governing our model is transformed into a Schrödinger equation, the solution of which features “quantized” eigenfunctions. Consequently, stock returns follow a mixed χ distribution, which describes Gaussian and non-Gaussian features. Analyzing the Financial Times Stock Exchange (FTSE) All Share Index, we demonstrate that our model outperforms traditional stochastic process models, e.g., the geometric Brownian motion and the Heston model, with smaller fitting errors and better goodness-of-fit statistics. In addition, making use of analogy, we provide an economic rationale of the physics concepts such as the eigenstate, eigenenergy, and angular frequency, which sheds light on the relationship between finance and econophysics literature.

Math Model and Calculation Analysis of Inter-harmonic of Double PWM Speed Control System in Distribution Network

Directory of Open Access Journals (Sweden)

Yang Wen-Huan

2014-11-01

Full Text Available Aiming at the problem that the distribution network voltage will fluctuate because of the inter-harmonic currents injected into the network by double PWM speed control system when regulating the speed of the asynchronous motor, we established the inter-harmonic current math model of double PWM speed control system according to switching function based on a real bridge crane. The distribution law of the inter-harmonic is got by calculating the grid-side currents and their spectrum while letting the motor run at different quadrants and frequencies. The result which is verified by simulation and experiment shows that the content of the inter harmonic currents is more than that of harmonic currents in double PWM speed control system, the frequency of the inter harmonics of the grid-side current mainly focus on the scope lower than the fundamental frequency, and when the motor runs at low frequencies, the THD of the grid-side current is high. The result has verified the reason why the voltage of a bridge crane distribution system of a deepwater port in Shanghai flickers.

Heterogeneous nucleation on convex spherical substrate surfaces: A rigorous thermodynamic formulation of Fletcher's classical model and the new perspectives derived.

Science.gov (United States)

Qian, Ma; Ma, Jie

2009-06-07

Fletcher's spherical substrate model [J. Chem. Phys. 29, 572 (1958)] is a basic model for understanding the heterogeneous nucleation phenomena in nature. However, a rigorous thermodynamic formulation of the model has been missing due to the significant complexities involved. This has not only left the classical model deficient but also likely obscured its other important features, which would otherwise have helped to better understand and control heterogeneous nucleation on spherical substrates. This work presents a rigorous thermodynamic formulation of Fletcher's model using a novel analytical approach and discusses the new perspectives derived. In particular, it is shown that the use of an intermediate variable, a selected geometrical angle or pseudocontact angle between the embryo and spherical substrate, revealed extraordinary similarities between the first derivatives of the free energy change with respect to embryo radius for nucleation on spherical and flat substrates. Enlightened by the discovery, it was found that there exists a local maximum in the difference between the equivalent contact angles for nucleation on spherical and flat substrates due to the existence of a local maximum in the difference between the shape factors for nucleation on spherical and flat substrate surfaces. This helps to understand the complexity of the heterogeneous nucleation phenomena in a practical system. Also, it was found that the unfavorable size effect occurs primarily when R<5r( *) (R: radius of substrate and r( *): critical embryo radius) and diminishes rapidly with increasing value of R/r( *) beyond R/r( *)=5. This finding provides a baseline for controlling the size effects in heterogeneous nucleation.

Spherical Process Models for Global Spatial Statistics

KAUST Repository

Jeong, Jaehong

2017-11-28

Statistical models used in geophysical, environmental, and climate science applications must reflect the curvature of the spatial domain in global data. Over the past few decades, statisticians have developed covariance models that capture the spatial and temporal behavior of these global data sets. Though the geodesic distance is the most natural metric for measuring distance on the surface of a sphere, mathematical limitations have compelled statisticians to use the chordal distance to compute the covariance matrix in many applications instead, which may cause physically unrealistic distortions. Therefore, covariance functions directly defined on a sphere using the geodesic distance are needed. We discuss the issues that arise when dealing with spherical data sets on a global scale and provide references to recent literature. We review the current approaches to building process models on spheres, including the differential operator, the stochastic partial differential equation, the kernel convolution, and the deformation approaches. We illustrate realizations obtained from Gaussian processes with different covariance structures and the use of isotropic and nonstationary covariance models through deformations and geographical indicators for global surface temperature data. To assess the suitability of each method, we compare their log-likelihood values and prediction scores, and we end with a discussion of related research problems.

HARMONIZED EUROPE OR EUROPEAN HARMONY?

Directory of Open Access Journals (Sweden)

Cosmin Marinescu

2007-07-01

Full Text Available Recent evolutions in Europe raise questions on the viability of the present economic and social model that defines the European construction project. In this paper, the author will try to explain the viability of institutional European model that sticks between free market mechanisms and protectionism. The main challenge for the EU is about the possibility to bring together the institutional convergence and the welfare for all Europeans. This is the result of the view, still dominant, of European politics elite, according to which institutional harmonization is the solution of a more dynamic and prosper Europe. But, economic realities convince us that, more and more, a harmonized, standardized Europe is not necessarily identical with a Europe of harmony and social cooperation. If „development through integration” seems to be harmonization through „institutional transplant”, how could then be the European model one sufficiently wide open to market, which creates the prosperity so long waited for by new member countries?

Brane solutions of a spherical sigma model in six dimensions

International Nuclear Information System (INIS)

Lee, Hyun Min; Papazoglou, Antonios

2005-01-01

We explore solutions of six-dimensional gravity coupled to a non-linear sigma model, in the presence of codimension-two branes. We investigate the compactifications induced by a spherical scalar manifold and analyze the conditions under which they are of finite volume and singularity free. We discuss the issue of single-valuedness of the scalar fields and provide some special embedding of the scalar manifold to the internal space which solves this problem. These brane solutions furnish some self-tuning features, however they do not provide a satisfactory explanation of the vanishing of the effective four-dimensional cosmological constant. We discuss the properties of this model in relation with the self-tuning example based on a hyperbolic sigma model

Local lubrication model for spherical particles within incompressible Navier-Stokes flows

Science.gov (United States)

Lambert, B.; Weynans, L.; Bergmann, M.

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

Local lubrication model for spherical particles within incompressible Navier-Stokes flows.

Science.gov (United States)

Lambert, B; Weynans, L; Bergmann, M

2018-03-01

The lubrication forces are short-range hydrodynamic interactions essential to describe suspension of the particles. Usually, they are underestimated in direct numerical simulations of particle-laden flows. In this paper, we propose a lubrication model for a coupled volume penalization method and discrete element method solver that estimates the unresolved hydrodynamic forces and torques in an incompressible Navier-Stokes flow. Corrections are made locally on the surface of the interacting particles without any assumption on the global particle shape. The numerical model has been validated against experimental data and performs as well as existing numerical models that are limited to spherical particles.

About the functions of the Wigner distribution for the q-deformed harmonic oscillator model

International Nuclear Information System (INIS)

Atakishiev, N.M.; Nagiev, S.M.; Djafarov, E.I.; Imanov, R.M.

2005-01-01

Full text : A q-deformed model of the linear harmonic oscillator in the Wigner phase-space is studied. It was derived an explicit expression for the Wigner probability distribution function, as well as the Wigner distribution function of a thermodynamic equilibrium for this model

Multisite EPR oximetry from multiple quadrature harmonics.

Science.gov (United States)

Ahmad, R; Som, S; Johnson, D H; Zweier, J L; Kuppusamy, P; Potter, L C

2012-01-01

Multisite continuous wave (CW) electron paramagnetic resonance (EPR) oximetry using multiple quadrature field modulation harmonics is presented. First, a recently developed digital receiver is used to extract multiple harmonics of field modulated projection data. Second, a forward model is presented that relates the projection data to unknown parameters, including linewidth at each site. Third, a maximum likelihood estimator of unknown parameters is reported using an iterative algorithm capable of jointly processing multiple quadrature harmonics. The data modeling and processing are applicable for parametric lineshapes under nonsaturating conditions. Joint processing of multiple harmonics leads to 2-3-fold acceleration of EPR data acquisition. For demonstration in two spatial dimensions, both simulations and phantom studies on an L-band system are reported. Copyright © 2011 Elsevier Inc. All rights reserved.

Mathematical Modeling and Kinematics Analysis of Double Spherical Shell Rotary Docking Skirt

Directory of Open Access Journals (Sweden)

Gong Haixia

2017-01-01

Full Text Available In order to solve the problem of large trim and heel angles of the wrecked submarine, the double spherical shell rotating docking skirt is studied. According to the working principle of the rotating docking skirt, and the fixed skirt, the directional skirt, the angle skirt are simplified as the connecting rod. Therefore, the posture equation and kinematics model of the docking skirt are deduced, and according to the kinematics model, the angle of rotation of the directional skirt and the angle skirt is obtained when the wrecked submarine is in different trim and heel angles. Through the directional skirt and angle skirt with the matching rotation can make docking skirt interface in the 0°~2γ range within the rotation, to complete the docking skirt and the wrecked submarine docking. The MATLAB software is used to visualize the rotation angle of fixed skirt and directional skirt, which lays a good foundation for the development of the control of the double spherical shell rotating docking skirt in future.

Physics results from the National Spherical Torus Experiment

International Nuclear Information System (INIS)

Kaye, S.; Bell, M.

2000-01-01

The mission of the National Spherical Torus Experiment (NSTX) is to extend the understanding of toroidal physics to low aspect ratio (R/a ∼ 1.25) in low collisionality regimes. NSTX is designed to operate with up to 6 MW of High Harmonic Fast Wave (HHFW) heating and current drive, 5 MW of Neutral Beam Injection (NBI), and Co-Axial Helicity Injection (CHI) for non-inductive startup. Initial experiments focused on establishing conditions that will allow NSTX to achieve its aims of simultaneous high-β t and high-bootstrap current fraction, and to develop methods for non-inductive operation, which will be necessary for Spherical Torus power plants. Ohmic discharges with plasma currents up to 1 MA, stored energies up to 55 kJ, β t ∼ 10%, and a range of shapes and configurations were produced. Density limits in deuterium and helium reached 80% and 120% of the Greenwald limit respectively. Significant electron heating was observed with up to 2.3 MW of HHFW. Up to 270 kA of toroidal current for up to 200 msec was produced noninductively using CHI. Initial NBI experiments were carried out with up to two beam sources (3.2 MW). Plasmas with stored energies of up to 140 kJ and β t =21% were produced

Forward modelling of global gravity fields with 3D density structures and an application to the high-resolution ( 2 km) gravity fields of the Moon

Science.gov (United States)

Šprlák, M.; Han, S.-C.; Featherstone, W. E.

2017-12-01

Rigorous modelling of the spherical gravitational potential spectra from the volumetric density and geometry of an attracting body is discussed. Firstly, we derive mathematical formulas for the spatial analysis of spherical harmonic coefficients. Secondly, we present a numerically efficient algorithm for rigorous forward modelling. We consider the finite-amplitude topographic modelling methods as special cases, with additional postulates on the volumetric density and geometry. Thirdly, we implement our algorithm in the form of computer programs and test their correctness with respect to the finite-amplitude topography routines. For this purpose, synthetic and realistic numerical experiments, applied to the gravitational field and geometry of the Moon, are performed. We also investigate the optimal choice of input parameters for the finite-amplitude modelling methods. Fourth, we exploit the rigorous forward modelling for the determination of the spherical gravitational potential spectra inferred by lunar crustal models with uniform, laterally variable, radially variable, and spatially (3D) variable bulk density. Also, we analyse these four different crustal models in terms of their spectral characteristics and band-limited radial gravitation. We demonstrate applicability of the rigorous forward modelling using currently available computational resources up to degree and order 2519 of the spherical harmonic expansion, which corresponds to a resolution of 2.2 km on the surface of the Moon. Computer codes, a user manual and scripts developed for the purposes of this study are publicly available to potential users.

Fisheye image rectification using spherical and digital distortion models

Science.gov (United States)

Li, Xin; Pi, Yingdong; Jia, Yanling; Yang, Yuhui; Chen, Zhiyong; Hou, Wenguang

2018-02-01

Fisheye cameras have been widely used in many applications including close range visual navigation and observation and cyber city reconstruction because its field of view is much larger than that of a common pinhole camera. This means that a fisheye camera can capture more information than a pinhole camera in the same scenario. However, the fisheye image contains serious distortion, which may cause trouble for human observers in recognizing the objects within. Therefore, in most practical applications, the fisheye image should be rectified to a pinhole perspective projection image to conform to human cognitive habits. The traditional mathematical model-based methods cannot effectively remove the distortion, but the digital distortion model can reduce the image resolution to some extent. Considering these defects, this paper proposes a new method that combines the physical spherical model and the digital distortion model. The distortion of fisheye images can be effectively removed according to the proposed approach. Many experiments validate its feasibility and effectiveness.

Experimental and modeling studies of small molecule chemistry in expanding spherical flames

Science.gov (United States)

Santner, Jeffrey

Accurate models of flame chemistry are required in order to predict emissions and flame properties, such that clean, efficient engines can be designed more easily. There are three primary methods used to improve such combustion chemistry models - theoretical reaction rate calculations, elementary reaction rate experiments, and combustion system experiments. This work contributes to model improvement through the third method - measurements and analysis of the laminar burning velocity at constraining conditions. Modern combustion systems operate at high pressure with strong exhaust gas dilution in order to improve efficiency and reduce emissions. Additionally, flames under these conditions are sensitized to elementary reaction rates such that measurements constrain modeling efforts. Measurement conditions of the present work operate within this intersection between applications and fundamental science. Experiments utilize a new pressure-release, heated spherical combustion chamber with a variety of fuels (high hydrogen content fuels, formaldehyde (via 1,3,5-trioxane), and C2 fuels) at pressures from 0.5--25 atm, often with dilution by water vapor or carbon dioxide to flame temperatures below 2000 K. The constraining ability of these measurements depends on their uncertainty. Thus, the present work includes a novel analytical estimate of the effects of thermal radiative heat loss on burning velocity measurements in spherical flames. For 1,3,5-trioxane experiments, global measurements are sufficiently sensitive to elementary reaction rates that optimization techniques are employed to indirectly measure the reaction rates of HCO consumption. Besides the influence of flame chemistry on propagation, this work also explores the chemistry involved in production of nitric oxide, a harmful pollutant, within flames. We find significant differences among available chemistry models, both in mechanistic structure and quantitative reaction rates. There is a lack of well

Generalized theory of resonance scattering (GTRS) using the translational addition theorem for spherical wave functions.

Science.gov (United States)

Mitri, Farid

2014-11-01

The generalized theory of resonance scattering (GTRS) by an elastic spherical target in acoustics is extended to describe the arbitrary scattering of a finite beam using the addition theorem for the spherical wave functions of the first kind under a translation of the coordinate origin. The advantage of the proposed method over the standard discrete spherical harmonics transform previously used in the GTRS formalism is the computation of the off-axial beam-shape coefficients (BSCs) stemming from a closed-form partial-wave series expansion representing the axial BSCs in spherical coordinates. With this general method, the arbitrary acoustical scattering can be evaluated for any particle shape and size, whether the particle is partially or completely illuminated by the incident beam. Numerical examples for the axial and off-axial resonance scattering from an elastic sphere placed arbitrarily in the field of a finite circular piston transducer with uniform vibration are provided. Moreover, the 3-D resonance directivity patterns illustrate the theory and reveal some properties of the scattering. Numerous applications involving the scattering phenomenon in imaging, particle manipulation, and the characterization of multiphase flows can benefit from the present analysis because all physically realizable beams radiate acoustical waves from finite transducers as opposed to waves of infinite extent.

The Virasoro algebra from harmonic superspace

International Nuclear Information System (INIS)

Saidi, E.H.; Zakkari, M.

1990-08-01

Using harmonic superspace techniques, we construct a new field realization of the Virasoro algebra. The main conformal objects are U(1) Cartan tensors instead of the U(1) Lorentz ones. The new conformal model, which admits moreover a d=2 (4,0) global supersymmetry is constructed out of the infinitely relaxed HST and FS hypermultiplets. The conformal current T 4+ together with the harmonic superspace OPE rules are given. The Virasoro algebra and the harmonic superspace Schwarzian derivative S 4+ are also derived. (author). 14 refs

Standing and travelling waves in a spherical brain model: The Nunez model revisited

Science.gov (United States)

Visser, S.; Nicks, R.; Faugeras, O.; Coombes, S.

2017-06-01

The Nunez model for the generation of electroencephalogram (EEG) signals is naturally described as a neural field model on a sphere with space-dependent delays. For simplicity, dynamical realisations of this model either as a damped wave equation or an integro-differential equation, have typically been studied in idealised one dimensional or planar settings. Here we revisit the original Nunez model to specifically address the role of spherical topology on spatio-temporal pattern generation. We do this using a mixture of Turing instability analysis, symmetric bifurcation theory, centre manifold reduction and direct simulations with a bespoke numerical scheme. In particular we examine standing and travelling wave solutions using normal form computation of primary and secondary bifurcations from a steady state. Interestingly, we observe spatio-temporal patterns which have counterparts seen in the EEG patterns of both epileptic and schizophrenic brain conditions.

Harmonic regression of Landsat time series for modeling attributes from national forest inventory data

Science.gov (United States)

Wilson, Barry T.; Knight, Joseph F.; McRoberts, Ronald E.

2018-03-01

Imagery from the Landsat Program has been used frequently as a source of auxiliary data for modeling land cover, as well as a variety of attributes associated with tree cover. With ready access to all scenes in the archive since 2008 due to the USGS Landsat Data Policy, new approaches to deriving such auxiliary data from dense Landsat time series are required. Several methods have previously been developed for use with finer temporal resolution imagery (e.g. AVHRR and MODIS), including image compositing and harmonic regression using Fourier series. The manuscript presents a study, using Minnesota, USA during the years 2009-2013 as the study area and timeframe. The study examined the relative predictive power of land cover models, in particular those related to tree cover, using predictor variables based solely on composite imagery versus those using estimated harmonic regression coefficients. The study used two common non-parametric modeling approaches (i.e. k-nearest neighbors and random forests) for fitting classification and regression models of multiple attributes measured on USFS Forest Inventory and Analysis plots using all available Landsat imagery for the study area and timeframe. The estimated Fourier coefficients developed by harmonic regression of tasseled cap transformation time series data were shown to be correlated with land cover, including tree cover. Regression models using estimated Fourier coefficients as predictor variables showed a two- to threefold increase in explained variance for a small set of continuous response variables, relative to comparable models using monthly image composites. Similarly, the overall accuracies of classification models using the estimated Fourier coefficients were approximately 10-20 percentage points higher than the models using the image composites, with corresponding individual class accuracies between six and 45 percentage points higher.

Adaptive back-stepping control of the harmonic drive system with LuGre model-based friction compensation

Science.gov (United States)

Liu, Sen; Gang, Tieqiang

2018-03-01

Harmonic drives are widely used in aerospace and industrial robots. Flexibility, friction and parameter uncertainty will result in transmission performance degradation. In this paper, an adaptive back-stepping method with friction compensation is proposed to improve the tracking performance of the harmonic drive system. The nonlinear friction is described by LuGre model and compensated with a friction observer, and the uncertainty of model parameters is resolved by adaptive parameter estimation method. By using Lyapunov stability theory, it is proved that all the errors of the closed-loop system are uniformly ultimately bounded. Simulations illustrate the effectiveness of our friction compensation method.

Harmonic statistics

International Nuclear Information System (INIS)

Eliazar, Iddo

2017-01-01

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

Harmonic statistics

Energy Technology Data Exchange (ETDEWEB)

Eliazar, Iddo, E-mail: eliazar@post.tau.ac.il

2017-05-15

The exponential, the normal, and the Poisson statistical laws are of major importance due to their universality. Harmonic statistics are as universal as the three aforementioned laws, but yet they fall short in their ‘public relations’ for the following reason: the full scope of harmonic statistics cannot be described in terms of a statistical law. In this paper we describe harmonic statistics, in their full scope, via an object termed harmonic Poisson process: a Poisson process, over the positive half-line, with a harmonic intensity. The paper reviews the harmonic Poisson process, investigates its properties, and presents the connections of this object to an assortment of topics: uniform statistics, scale invariance, random multiplicative perturbations, Pareto and inverse-Pareto statistics, exponential growth and exponential decay, power-law renormalization, convergence and domains of attraction, the Langevin equation, diffusions, Benford’s law, and 1/f noise. - Highlights: • Harmonic statistics are described and reviewed in detail. • Connections to various statistical laws are established. • Connections to perturbation, renormalization and dynamics are established.

Probabilistic aspects of harmonic emission of large offshore wind farms

Energy Technology Data Exchange (ETDEWEB)

Jensen, Christian F. [Energinet.dk, Fredericia (Denmark); Bak, Claus L. [Aalborg Univ. (Denmark). Dept. of Energy Technology; Kocewiak, Lukasz; Hjerrild, Jesper [DONG Energy, Skaerbaek (Denmark); Berthelsen, Kasper K. [Aalborg Univ. (Denmark). Dept. of Mathematical Sciences

2011-07-01

In this article, a new probabilistic method of assessment of harmonic emission of large offshore wind farms is presented. Based on measurements from the British wind farm Burbo Banks, probability density functions are estimated for the dominating low order harmonic currents injected by a single turbine. The degree and type of dependence between the harmonic emission and the operating point of a single turbine is established. A model of Burbo Banks, suitable for harmonic load flow studies, is created in DIgSILENT Power Factory along with a DPL-script that deals with the probabilistic issues of the harmonic emission. The simulated harmonic distortion at the PCC is compared to measurement. This reveals some difficulties regarding harmonic load flow studies. The harmonic background distortion in the grid to where the wind farms is connected must be included in the study. Furthermore, a very detailed representation of the frequency dependent short circuit impedance must be used before sufficiently accurate results can be obtained from the model. (orig.)

A Model for Semantic Equivalence Discovery for Harmonizing Master Data

Science.gov (United States)

Piprani, Baba

IT projects often face the challenge of harmonizing metadata and data so as to have a "single" version of the truth. Determining equivalency of multiple data instances against the given type, or set of types, is mandatory in establishing master data legitimacy in a data set that contains multiple incarnations of instances belonging to the same semantic data record . The results of a real-life application define how measuring criteria and equivalence path determination were established via a set of "probes" in conjunction with a score-card approach. There is a need for a suite of supporting models to help determine master data equivalency towards entity resolution—including mapping models, transform models, selection models, match models, an audit and control model, a scorecard model, a rating model. An ORM schema defines the set of supporting models along with their incarnation into an attribute based model as implemented in an RDBMS.

Modelling of Spherical Gas Bubble Oscillations and Sonoluminescence

Science.gov (United States)

Prosperetti, A.; Hao, Y.

1999-01-01

The discovery of single-bubble sonoluminescence has led to a renewed interest in the forced radial oscillations of gas bubbles. Many of the more recent studies devoted to this topic have used several simplifications in the modelling, and in particular in accounting for liquid compressibility and thermal processes in the bubble. In this paper the significance of these simplifications is explored by contrasting the results of Lohse and co-workers with those of a more detailed model. It is found that, even though there may be little apparent difference between the radius-versus time behaviour of the bubble as predicted by the two models, quantities such as the spherical stability boundary and the threshold for rectified diffusion are affected in a quantitatively significant way. These effects are a manifestation of the subtle dependence upon dissipative processes of the phase of radial motion with respect to the driving sound field. The parameter space region, where according to the theory of Lohse and co-workers, sonoluminescence should be observable, is recalculated with the new model and is found to be enlarged with respect to the earlier estimate. The dependence of this parameter region on sound frequency is also illustrated.

Spherical 2+p spin-glass model: An exactly solvable model for glass to spin-glass transition

International Nuclear Information System (INIS)

Crisanti, A.; Leuzzi, L.

2004-01-01

We present the full phase diagram of the spherical 2+p spin-glass model with p≥4. The main outcome is the presence of a phase with both properties of full replica symmetry breaking phases of discrete models, e.g., the Sherrington-Kirkpatrick model, and those of one replica symmetry breaking. This phase has a finite complexity which leads to different dynamic and static properties. The phase diagram is rich enough to allow the study of different kinds of glass to spin glass and spin glass to spin glass phase transitions

Spherical Demons: Fast Surface Registration

Science.gov (United States)

Yeo, B.T. Thomas; Sabuncu, Mert; Vercauteren, Tom; Ayache, Nicholas; Fischl, Bruce; Golland, Polina

2009-01-01

We present the fast Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizers for the modified demons objective function can be efficiently implemented on the sphere using convolution. Based on the one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast – registration of two cortical mesh models with more than 100k nodes takes less than 5 minutes, comparable to the fastest surface registration algorithms. Moreover, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different settings: (1) parcellation in a set of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:18979813

Deflection modeling of permanent magnet spherical chains in the presence of external magnetic fields

Energy Technology Data Exchange (ETDEWEB)

O' Donoghue, Kilian, E-mail: kilianod@rennes.ucc.ie; Cantillon-Murphy, Pádraig, E-mail: padraig@alum.mit.edu

2013-10-15

This work examines the interaction of permanently magnetised spheres in the presence of external magnetic fields at the millimetre scale. Static chain formation and deflection models are described for N spheres in the presence of an external magnetic field. Analytical models are presented for the two sphere case by neglecting the effects of magnetocrystalline anisotropy while details of a numerical approach to solve a chain of N spheres are shown. The model is experimentally validated using chain deflections in 4.5 mm diameter spheres in groups of 2, 3 and 4 magnets in the presence of uniform magnetic fields, neglecting gravitational effects, with good agreement between the theoretical model and experimental results. This spherical chain structure could be used as an end effector for catheters as a deflection mechanism for magnetic guidance. The spherical point contacts result in large deflections for navigation around tight corners in endoluminal minimally invasive clinical applications. - Highlights: • We model the interaction of magnetic spheres with uniform external fields. • Analytical models are presented for two spheres interacting with an external field. • Numerical methods are used to model the interaction of N spheres in chain formations. • These models are tested experimentally. • We report good agreement between experiment and theory.

Deflection modeling of permanent magnet spherical chains in the presence of external magnetic fields

International Nuclear Information System (INIS)

O'Donoghue, Kilian; Cantillon-Murphy, Pádraig

2013-01-01

This work examines the interaction of permanently magnetised spheres in the presence of external magnetic fields at the millimetre scale. Static chain formation and deflection models are described for N spheres in the presence of an external magnetic field. Analytical models are presented for the two sphere case by neglecting the effects of magnetocrystalline anisotropy while details of a numerical approach to solve a chain of N spheres are shown. The model is experimentally validated using chain deflections in 4.5 mm diameter spheres in groups of 2, 3 and 4 magnets in the presence of uniform magnetic fields, neglecting gravitational effects, with good agreement between the theoretical model and experimental results. This spherical chain structure could be used as an end effector for catheters as a deflection mechanism for magnetic guidance. The spherical point contacts result in large deflections for navigation around tight corners in endoluminal minimally invasive clinical applications. - Highlights: • We model the interaction of magnetic spheres with uniform external fields. • Analytical models are presented for two spheres interacting with an external field. • Numerical methods are used to model the interaction of N spheres in chain formations. • These models are tested experimentally. • We report good agreement between experiment and theory

Optical third-harmonic generation using ultrashort laser pulses

International Nuclear Information System (INIS)

Stoker, D.; Keto, J.W.; Becker, M.F.

2005-01-01

To better predict optical third-harmonic generation (THG) in transparent dielectrics, we model a typical ultrashort pulsed Gaussian beam, including both group velocity mismatch and phase mismatch of the fundamental and harmonic fields. We find that competition between the group velocity mismatch and phase mismatch leads to third-harmonic generation that is sensitive only to interfaces. In this case, the spatial resolution is determined by the group velocity walk-off length. THG of modern femtosecond lasers in optical solids is a bulk process, without a surface susceptibility, but bears the signature of a surface enhancement effect in z-scan measurements. We demonstrate the accuracy of the model, by showing the agreement between the predicted spectral intensity and the measured third-harmonic spectrum from a thin sapphire crystal

OWL: A code for the two-center shell model with spherical Woods-Saxon potentials

Science.gov (United States)

Diaz-Torres, Alexis

2018-03-01

A Fortran-90 code for solving the two-center nuclear shell model problem is presented. The model is based on two spherical Woods-Saxon potentials and the potential separable expansion method. It describes the single-particle motion in low-energy nuclear collisions, and is useful for characterizing a broad range of phenomena from fusion to nuclear molecular structures.

[Depth of focus in spherical and aspheric intraocular lenses].

Science.gov (United States)

Nan, Li; Tang, Xin; Liu, Yong-ji

2012-02-01

To investigate depth of focus (DOF) in spherical and aspheric IOL eye models. Computer numerical simulation experiment was used. IOL eye model based on Liou-Brennan eye model was constructed by using ZEMAX optical design software. Different IOL were implanted in this eye model. Monochromatic through focus modulation transfer function (MTF) curves were computed. Pupil and aspheric designs' effect on DOF were analyzed. DOF of eye model increased with pupil shrinkage in 550 nm monochromatic light (FY60AD 1.20 D at 6 mm pupil, 1.35 D at 5 mm pupil, 1.70 D at 4 mm pupil, 2.46 D at 3 mm pupil; YA60BBR 1.24 D at 6 mm pupil, 1.48 D at 5 mm pupil, 1.80 D at 4 mm pupil, 2.50 D at 3 mm pupil). MTF in spherical IOL eye model was higher with minus defocus, this trend was obvious at larger pupil. MTF of aspheric IOL eyes were higher than spherical IOL eyes when well focused at 5 mm pupil, while the DOF was lower in aspheric IOL with negative spherical aberration (Tecnis Z9000 1.31 D, FY60AD 1.35 D, CeeOn911 1.55 D, YA60BBR 1.48 D). DOF decreased less in aspheric IOL with zero spherical aberration (LI61AO 1.42 D). DOF in IOL eye model was higher at smaller pupil. When the pupil was large, well focused aspheric IOL improved optical quality compared with spherical IOL, while DOF and the tolerance to defocus in aspheric IOL were partially lost; this phenomenon was obvious with minus defocus.

Kovacs effect in solvable model glasses

International Nuclear Information System (INIS)

Aquino, Gerardo; Leuzzi, Luca; Nieuwenhuizen, Theo M

2006-01-01

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs and applied on glassy polymers, is implemented in an exactly solvable model with facilitated dynamics. This model is based on interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property and to slow dynamics, the model reproduces the characteristic nonmonotonic evolution known as the 'Kovacs effect', observed in polymers, spin glasses, in granular materials and models of molecular liquids, when similar experimental protocols are implemented

Kovacs effect in solvable model glasses

Science.gov (United States)

Aquino, Gerardo; Leuzzi, Luca; Nieuwenhuizen, Theo M.

2006-05-01

The Kovacs protocol, based on the temperature shift experiment originally conceived by A.J. Kovacs and applied on glassy polymers [1], is implemented in an exactly solvable model with facilitated dynamics. This model is based on interacting fast and slow modes represented respectively by spherical spins and harmonic oscillator variables. Due to this fundamental property and to slow dynamics, the model reproduces the characteristic nonmonotonic evolution known as the ''Kovacs effect'', observed in polymers, spin glasses, in granular materials and models of molecular liquids, when similar experimental protocols are implemented.

Evaluation of the hexagonal and spherical model of vocational interests in the young people in Serbia and Bulgaria

Directory of Open Access Journals (Sweden)

Hedrih Vladimir

2016-01-01

Full Text Available The aim of this study was to validate Holland’s hexagonal and Tracey’s spherical model of vocational interests in young adults in Serbia and Bulgaria. To this end, 1250 participants, 560 from Serbia and 690 from Bulgaria, filled in Serbian and Bulgarian versions of the Personal Globe Inventory (PGI, Tracey, 2002. Hubert and Arabie’s randomization test of hypothetical orders, multidimensional scaling with fixed coordinates, Myors test and exploratory factor analysis were used. The results showed that the hexagonal and spherical models well explained the structure of vocational interests in both samples. The level of fit of the hexagonal model to the data obtained by using the PGI was generally higher than those established in the studies that used other Holland-based instruments. Furthermore, the levels of fit of both hexagonal and spherical model were in the same range like those obtained in previous studies in other countries. The results also pointed out a remarkable similarity in the structure of vocational interests in the Bulgarian and Serbian samples. [Projekat Ministarstva nauke Republike Srbije, br. 179002

Quantization of the damped harmonic oscillator revisited

Energy Technology Data Exchange (ETDEWEB)

Baldiotti, M.C., E-mail: baldiott@fma.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Fresneda, R., E-mail: fresneda@gmail.co [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil); Gitman, D.M., E-mail: gitman@dfn.if.usp.b [Instituto de Fisica, Universidade de Sao Paulo, Caixa Postal 66318-CEP, 05315-970 Sao Paulo, S.P. (Brazil)

2011-04-11

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: We prove the local equivalence of two damped harmonic oscillator models. We find different high energy behaviors between the two models. Based on the local equivalence, we make a simple construction of the coherent states.

Polarization-Resolved Study of High Harmonics from Bulk Semiconductors

Science.gov (United States)

Kaneshima, Keisuke; Shinohara, Yasushi; Takeuchi, Kengo; Ishii, Nobuhisa; Imasaka, Kotaro; Kaji, Tomohiro; Ashihara, Satoshi; Ishikawa, Kenichi L.; Itatani, Jiro

2018-06-01

The polarization property of high harmonics from gallium selenide is investigated using linearly polarized midinfrared laser pulses. With a high electric field, the perpendicular polarization component of the odd harmonics emerges, which is not present with a low electric field and cannot be explained by the perturbative nonlinear optics. A two-dimensional single-band model is developed to show that the anisotropic curvature of an energy band of solids, which is pronounced in an outer part of the Brillouin zone, induces the generation of the perpendicular odd harmonics. This model is validated by three-dimensional quantum mechanical simulations, which reproduce the orientation dependence of the odd-order harmonics. The quantum mechanical simulations also reveal that the odd- and even-order harmonics are produced predominantly by the intraband current and interband polarization, respectively. These experimental and theoretical demonstrations clearly show a strong link between the band structure of a solid and the polarization property of the odd-order harmonics.

Improved lumped models for transient combined convective and radiative cooling of a two-layer spherical fuel element

International Nuclear Information System (INIS)

Silva, Alice Cunha da; Su, Jian

2013-01-01

The High Temperature Gas cooled Reactor (HTGR) is a fourth generation thermal nuclear reactor, graphite-moderated and helium cooled. The HTGRs have important characteristics making essential the study of these reactors, as well as its fuel element. Examples of these are: high thermal efficiency,low operating costs and construction, passive safety attributes that allow implication of the respective plants. The Pebble Bed Modular Reactor (PBMR) is a HTGR with spherical fuel elements that named the reactor. This fuel element is composed by a particulate region with spherical inclusions, the fuel UO2 particles, dispersed in a graphite matrix and a convective heat transfer by Helium happens on the outer surface of the fuel element. In this work, the transient heat conduction in a spherical fuel element of a pebble-bed high temperature reactor was studied in a transient situation of combined convective and radiative cooling. Improved lumped parameter model was developed for the transient heat conduction in the two-layer composite sphere subjected to combined convective and radiative cooling. The improved lumped model was obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of the two-layer spherical fuel element was analyzed to illustrate the applicability of the proposed lumped model, with respect to die rent values of the Biot number, the radiation-conduction parameter, the dimensionless thermal contact resistance, the dimensionless inner diameter and coating thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the improved lumped model, with H2,1/H1,1/H0,0 approximation yielded significant improvement of average temperature prediction over the classical lumped model. (author)

Harmonic generation effect in high-Tc films

International Nuclear Information System (INIS)

Khare, Neeraj; Shrivastava, S.K.; Padmanabhan, V.P.N.; Khare, Sangeeta; Gupta, A.K.

1997-01-01

Harmonic generation in thick BPSCCO and thin YBCO films are reported. The application of an ac field (H ac > H c1 ) of frequency f causes the generation of odd harmonics of frequency (2n+1)f. The application of dc field in addition to the ac field causes the appearance of even harmonics also in the BPSCCO film. However, the appearance of even harmonics is not observed in YBCO film with high J c ∼ 1.6x10 6 A/cm 2 and appearance of second harmonic with small magnitude is observed in YBCO film with low J c ∼ 2x10 3 A/cm 2 . The variation of amplitudes of these harmonics are studied as a function of magnitude of ac and dc field and the results are explained in the framework of critical state model. A high-T c film magnetometer based on the measurement of the amplitude of second harmonic has been developed whose field sensitivity is ∼ 1.5x10 -8 T. (author)

A comparison of tripolar concentric ring electrode and spline Laplacians on a four-layer concentric spherical model.

Science.gov (United States)

Liu, Xiang; Makeyev, Oleksandr; Besio, Walter

2011-01-01

We have simulated a four-layer concentric spherical head model. We calculated the spline and tripolar Laplacian estimates and compared them to the analytical Laplacian on the spherical surface. In the simulations we used five different dipole groups and two electrode configurations. The comparison shows that the tripolar Laplacian has higher correlation coefficient to the analytical Laplacian in the electrode configurations tested (19, standard 10/20 locations and 64 electrodes).

Harmonics in large offshore wind farms

DEFF Research Database (Denmark)

Kocewiak, Lukasz Hubert

and nature of various harmonic components. A comprehensive comparison of harmonic voltages and currents based on probability distribution estimation and appropriate statistics calculation (mean, variance, probability density function, etc.) is applied. Such approach gives a better overview and comparison...... and analysis, and ϐinally ending up on modelling and models application. Different aspects of validation in time domain, frequency domain, and by application of statistical methods are mentioned in relation to respective problems. Measurements constitute a core part in industry-oriented research. Due...... that it is of great importance to know the nature of generated harmonics in large offshore wind farms in order to apply the most suitable data processing technique. Time-frequency analysis based on multiresolution wavelet transform is used in order to perform time-frequency domain analysis helpful to distinguish...

High order harmonic generation in rare gases

Energy Technology Data Exchange (ETDEWEB)

Budil, Kimberly Susan [Univ. of California, Davis, CA (United States)

1994-05-01

The process of high order harmonic generation in atomic gases has shown great promise as a method of generating extremely short wavelength radiation, extending far into the extreme ultraviolet (XUV). The process is conceptually simple. A very intense laser pulse (I ~10¹³-10¹⁴ W/cm²) is focused into a dense (~10¹⁷ particles/cm³) atomic medium, causing the atoms to become polarized. These atomic dipoles are then coherently driven by the laser field and begin to radiate at odd harmonics of the laser field. This dissertation is a study of both the physical mechanism of harmonic generation as well as its development as a source of coherent XUV radiation. Recently, a semiclassical theory has been proposed which provides a simple, intuitive description of harmonic generation. In this picture the process is treated in two steps. The atom ionizes via tunneling after which its classical motion in the laser field is studied. Electron trajectories which return to the vicinity of the nucleus may recombine and emit a harmonic photon, while those which do not return will ionize. An experiment was performed to test the validity of this model wherein the trajectory of the electron as it orbits the nucleus or ion core is perturbed by driving the process with elliptically, rather than linearly, polarized laser radiation. The semiclassical theory predicts a rapid turn-off of harmonic production as the ellipticity of the driving field is increased. This decrease in harmonic production is observed experimentally and a simple quantum mechanical theory is used to model the data. The second major focus of this work was on development of the harmonic "source". A series of experiments were performed examining the spatial profiles of the harmonics. The quality of the spatial profile is crucial if the harmonics are to be used as the source for experiments, particularly if they must be refocused.

The relation between degree-2160 spectral models of Earth's gravitational and topographic potential: a guide on global correlation measures and their dependency on approximation effects

Science.gov (United States)

Hirt, Christian; Rexer, Moritz; Claessens, Sten; Rummel, Reiner

2017-10-01

Comparisons between high-degree models of the Earth's topographic and gravitational potential may give insight into the quality and resolution of the source data sets, provide feedback on the modelling techniques and help to better understand the gravity field composition. Degree correlations (cross-correlation coefficients) or reduction rates (quantifying the amount of topographic signal contained in the gravitational potential) are indicators used in a number of contemporary studies. However, depending on the modelling techniques and underlying levels of approximation, the correlation at high degrees may vary significantly, as do the conclusions drawn. The present paper addresses this problem by attempting to provide a guide on global correlation measures with particular emphasis on approximation effects and variants of topographic potential modelling. We investigate and discuss the impact of different effects (e.g., truncation of series expansions of the topographic potential, mass compression, ellipsoidal versus spherical approximation, ellipsoidal harmonic coefficient versus spherical harmonic coefficient (SHC) representation) on correlation measures. Our study demonstrates that the correlation coefficients are realistic only when the model's harmonic coefficients of a given degree are largely independent of the coefficients of other degrees, permitting degree-wise evaluations. This is the case, e.g., when both models are represented in terms of SHCs and spherical approximation (i.e. spherical arrangement of field-generating masses). Alternatively, a representation in ellipsoidal harmonics can be combined with ellipsoidal approximation. The usual ellipsoidal approximation level (i.e. ellipsoidal mass arrangement) is shown to bias correlation coefficients when SHCs are used. Importantly, gravity models from the International Centre for Global Earth Models (ICGEM) are inherently based on this approximation level. A transformation is presented that enables a

Quasiparticle--phonon model of the nucleus. V. Odd spherical nuclei

International Nuclear Information System (INIS)

Vdovin, A.I.; Voronov, V.V.; Solov'ev, V.G.; Stoyanov, C.

1985-01-01

The formalism of the quasiparticle--phonon model of the nucleus for odd spherical nuclei is presented. The exact commutation relations of the quasiparticle and phonon operators together with the anharmonic corrections for the phonon excitations are taken into account in the derivation of equations for the energies and structure coefficients of the wave functions of excited states, which include quasiparticle--phonon and quasiparticle--two-phonon components. The influence of various physical effects and of the dimension of the phonon basis on the fragmentation of the single-quasiparticle and quasiparticle-phonon states is investigated

Kovacs effect in a model for a fragile glass

Science.gov (United States)

Aquino, Gerardo; Leuzzi, Luca; Nieuwenhuizen, Theo M.

2006-03-01

The Kovacs protocol, based on the temperature shift experiment originally conceived by A. J. Kovacs for glassy polymers, is implemented in an exactly solvable dynamical model. This model is characterized by interacting fast and slow modes represented, respectively, by spherical spins and harmonic oscillator variables. Due to this fundamental property, the model reproduces the characteristic nonmonotonic evolution known as the “Kovacs effect,” observed in polymers, spin glasses, granular materials, and molecular liquid models, when similar experimental protocols are implemented.

Modelling of BLDCM with a double 3-phase stator winding and back EMF harmonics

Directory of Open Access Journals (Sweden)

Drozdowski Piotr

2015-03-01

Full Text Available In this paper the mathematical model of the brushless DC motor (BLDCM with a double 3-phase stator winding is analysed. Both the 3-phase windings are mutually displaced by 30 electrical degree. Special care has been sacrificed to influence of higher harmonics of induced electromotive forces (EMF on electromagnetic torque and zero sequence voltages that may be used for sensorless control. The mathematical model has been presented in natural variables and, after transformation to symmetrical components, in a vector form. This allows, from one side, for formulating the equivalent circuit suitable for circuit oriented simulators (e.g.: Spice, SimPowerSystems of Simulink and, from the other point of view, for analysis of higher harmonics influence on control possibilities. These considerations have been illustrated with some results of four quadrant operation obtainded due to simulation at automatic control.

One dimension harmonic oscillator

International Nuclear Information System (INIS)

Cohen-Tannoudji, Claude; Diu, Bernard; Laloe, Franck.

1977-01-01

The importance of harmonic oscillator in classical and quantum physics, eigenvalues and eigenstates of hamiltonian operator are discussed. In complement are presented: study of some physical examples of harmonic oscillators; study of stationnary states in the /x> representation; Hermite polynomials; resolution of eigenvalue equation of harmonic oscillator by polynomial method; isotope harmonic oscillator with three dimensions; charged harmonic oscillator in uniform electric field; quasi classical coherent states of harmonic oscillator; eigenmodes of vibration of two coupled harmonic oscillators; vibration modus of a continuous physical system (application to radiation: photons); vibration modus of indefinite linear chain of coupled harmonic oscillators (phonons); one-dimensional harmonic oscillator in thermodynamic equilibrium at temperature T [fr

Quantization of the damped harmonic oscillator revisited

International Nuclear Information System (INIS)

Baldiotti, M.C.; Fresneda, R.; Gitman, D.M.

2011-01-01

We return to the description of the damped harmonic oscillator with an assessment of previous works, in particular the Bateman-Caldirola-Kanai model and a new model proposed by one of the authors. We argue the latter has better high energy behavior and is connected to existing open-systems approaches. - Highlights: → We prove the local equivalence of two damped harmonic oscillator models. → We find different high energy behaviors between the two models. → Based on the local equivalence, we make a simple construction of the coherent states.

Investigation of Ion Absorption of the High Harmonic Fast Wave in NSTX using HPRT

International Nuclear Information System (INIS)

Rosenberg, A.; Menard, J.E.; LeBlanc, B.P.

2001-01-01

Understanding high harmonic fast wave (HHFW) power absorption by ions in a spherical torus (ST) is of critical importance to assessing the wave's viability as a means of heating and especially driving current. In this work, the HPRT code is used to calculate absorption for helium and deuterium, with and without minority hydrogen in National Spherical Torus Experiment (NSTX) plasmas using experimental EFIT code equilibria and kinetic profiles. HPRT is a two-dimensional ray-tracing code which uses the full hot plasma dielectric to compute the perpendicular wave number along the hot electron and cold ion plasma ray path. Ion and electron absorption dependence on antenna phasing, ion temperature, beta (subscript t), and minority temperature and concentration is analyzed. These results form the basis for comparisons with other codes, such as CURRAY, METS, TORIC, and AORSA

3D Printing Electrically Small Spherical Antennas

DEFF Research Database (Denmark)

Kim, Oleksiy S.

2013-01-01

3D printing is applied for rapid prototyping of an electrically small spherical wire antenna. The model is first printed in plastic and subsequently covered with several layers of conductive paint. Measured results are in good agreement with simulations.......3D printing is applied for rapid prototyping of an electrically small spherical wire antenna. The model is first printed in plastic and subsequently covered with several layers of conductive paint. Measured results are in good agreement with simulations....

Harmonization of future needs for dermal exposure assessment and modeling : a workshop report

NARCIS (Netherlands)

Marquart, H.; Maidment, S.; Mcclaflin, J.L.; Fehrenbacher, M.C.

2001-01-01

Dermal exposure assessment and modeling is still in early phases of development. This article presents the results of a workshop organized to harmonize the future needs in this field. Methods for dermal exposure assessment either assess the mass of contaminant that is transferred to the skin, or the

An object-oriented approach for harmonization of multimedia markup languages

Science.gov (United States)

Chen, Yih-Feng; Kuo, May-Chen; Sun, Xiaoming; Kuo, C.-C. Jay

2003-12-01

An object-oriented methodology is proposed to harmonize several different markup languages in this research. First, we adopt the Unified Modelling Language (UML) as the data model to formalize the concept and the process of the harmonization process between the eXtensible Markup Language (XML) applications. Then, we design the Harmonization eXtensible Markup Language (HXML) based on the data model and formalize the transformation between the Document Type Definitions (DTDs) of the original XML applications and HXML. The transformation between instances is also discussed. We use the harmonization of SMIL and X3D as an example to demonstrate the proposed methodology. This methodology can be generalized to various application domains.

HARMONIC DRIVE SELECTION

Directory of Open Access Journals (Sweden)

Piotr FOLĘGA

2014-03-01

Full Text Available The variety of types and sizes currently in production harmonic drive is a problem in their rational choice. Properly selected harmonic drive must meet certain requirements during operation, and achieve the anticipated service life. The paper discusses the problems associated with the selection of the harmonic drive. It also presents the algorithm correct choice of harmonic drive. The main objective of this study was to develop a computer program that allows the correct choice of harmonic drive by developed algorithm.

Comparison of parametric methods for modeling corneal surfaces

Science.gov (United States)

Bouazizi, Hala; Brunette, Isabelle; Meunier, Jean

2017-02-01

Corneal topography is a medical imaging technique to get the 3D shape of the cornea as a set of 3D points of its anterior and posterior surfaces. From these data, topographic maps can be derived to assist the ophthalmologist in the diagnosis of disorders. In this paper, we compare three different mathematical parametric representations of the corneal surfaces leastsquares fitted to the data provided by corneal topography. The parameters obtained from these models reduce the dimensionality of the data from several thousand 3D points to only a few parameters and could eventually be useful for diagnosis, biometry, implant design etc. The first representation is based on Zernike polynomials that are commonly used in optics. A variant of these polynomials, named Bhatia-Wolf will also be investigated. These two sets of polynomials are defined over a circular domain which is convenient to model the elevation (height) of the corneal surface. The third representation uses Spherical Harmonics that are particularly well suited for nearly-spherical object modeling, which is the case for cornea. We compared the three methods using the following three criteria: the root-mean-square error (RMSE), the number of parameters and the visual accuracy of the reconstructed topographic maps. A large dataset of more than 2000 corneal topographies was used. Our results showed that Spherical Harmonics were superior with a RMSE mean lower than 2.5 microns with 36 coefficients (order 5) for normal corneas and lower than 5 microns for two diseases affecting the corneal shapes: keratoconus and Fuchs' dystrophy.

Calculation of spherical models of lead with a source of 14 MeV-neutrons

International Nuclear Information System (INIS)

Markovskij, D.V.; Borisov, A.A.

1989-01-01

Neutron transport calculations for spherical models of lead have been done with the one-dimensional code BLANK realizing the direct Monte Carlo method in the whole range of neutron energies and they are compared with the experimental results. 6 refs, 10 figs, 3 tabs

The algebraic collective model

International Nuclear Information System (INIS)

Rowe, D.J.; Turner, P.S.

2005-01-01

A recently proposed computationally tractable version of the Bohr collective model is developed to the extent that we are now justified in describing it as an algebraic collective model. The model has an SU(1,1)xSO(5) algebraic structure and a continuous set of exactly solvable limits. Moreover, it provides bases for mixed symmetry collective model calculations. However, unlike the standard realization of SU(1,1), used for computing beta wave functions and their matrix elements in a spherical basis, the algebraic collective model makes use of an SU(1,1) algebra that generates wave functions appropriate for deformed nuclei with intrinsic quadrupole moments ranging from zero to any large value. A previous paper focused on the SO(5) wave functions, as SO(5) (hyper-)spherical harmonics, and computation of their matrix elements. This paper gives analytical expressions for the beta matrix elements needed in applications of the model and illustrative results to show the remarkable gain in efficiency that is achieved by using such a basis in collective model calculations for deformed nuclei

Effects of harmonic roving on pitch discrimination

DEFF Research Database (Denmark)

Santurette, Sébastien; de Kérangal, Mathilde le Gal; Joshi, Suyash Narendra

2015-01-01

Performance in pitch discrimination tasks is limited by variability intrinsic to listeners which may arise from peripheral auditory coding limitations or more central noise sources. The present study aimed at quantifying such “internal noise” by estimating the amount of harmonic roving required...... to impair pitch discrimination performance. Fundamental-frequency difference limens (F0DLs) were obtained in normal-hearing listeners with and without musical training for complex tones filtered between 1.5 and 3.5 kHz with F0s of 300 Hz (resolved harmonics) and 75 Hz (unresolved harmonics). The harmonicity...... that could be used to quantify the internal noise and provide strong constraints for physiologically inspired models of pitch perception....

Static harmonization of dynamically harmonized Fourier transform ion cyclotron resonance cell.

Science.gov (United States)

Zhdanova, Ekaterina; Kostyukevich, Yury; Nikolaev, Eugene

2017-08-01

Static harmonization in the Fourier transform ion cyclotron resonance cell improves the resolving power of the cell and prevents dephasing of the ion cloud in the case of any trajectory of the charged particle, not necessarily axisymmetric cyclotron (as opposed to dynamic harmonization). We reveal that the Fourier transform ion cyclotron resonance cell with dynamic harmonization (paracell) is proved to be statically harmonized. The volume of the statically harmonized potential distribution increases with an increase in the number of trap segments.

Vibration test of spherical shell structure and replacing method into mathematical model

International Nuclear Information System (INIS)

Takayanagi, M.; Suzuki, S.; Okamura, T.; Haas, E.E.; Krutzik, N.J.

1989-01-01

To verify the beam-type and oval-type vibratory characteristics of a spherical shell structure, two test specimens were made and vibration tests were carried out. Results of these tests are compared with results of detailed analyses using 3-D FEM and 2-D axisymmetric FEM models. The analytical results of overall vibratory characteristics are in good agreement with the test results, has been found that the effect of the attached mass should be considered in evaluating local vibration. The replacing method into equivalent beam model is proposed

Spherical neutron generator

Science.gov (United States)

Leung, Ka-Ngo

2006-11-21

A spherical neutron generator is formed with a small spherical target and a spherical shell RF-driven plasma ion source surrounding the target. A deuterium (or deuterium and tritium) ion plasma is produced by RF excitation in the plasma ion source using an RF antenna. The plasma generation region is a spherical shell between an outer chamber and an inner extraction electrode. A spherical neutron generating target is at the center of the chamber and is biased negatively with respect to the extraction electrode which contains many holes. Ions passing through the holes in the extraction electrode are focused onto the target which produces neutrons by D-D or D-T reactions.

The Realistic Versus the Spherical Head Model in EEG Dipole Source Analysis in the Presence of Noise

National Research Council Canada - National Science Library

Vanrumste, Bart

2001-01-01

.... For 27 electrodes, an EEG epoch of one time sample and spatially white Gaussian noise we found that the importance of the realistic head model over the spherical head model reduces by increasing the noise level.

Cosmological observables in the quasi-spherical Szekeres model

Science.gov (United States)

Buckley, Robert G.

2014-10-01

The standard model of cosmology presents a homogeneous universe, and we interpret cosmological data through this framework. However, structure growth creates nonlinear inhomogeneities that may affect observations, and even larger structures may be hidden by our limited vantage point and small number of independent observations. As we determine the universe's parameters with increasing precision, the accuracy is contingent on our understanding of the effects of such structures. For instance, giant void models can explain some observations without dark energy. Because perturbation theory cannot adequately describe nonlinear inhomogeneities, exact solutions to the equations of general relativity are important for these questions. The most general known solution capable of describing inhomogeneous matter distributions is the Szekeres class of models. In this work, we study the quasi-spherical subclass of these models, using numerical simulations to calculate the inhomogeneities' effects on observations. We calculate the large-angle CMB in giant void models and compare with simpler, symmetric void models that have previously been found inadequate to matchobservations. We extend this by considering models with early-time inhomogeneities as well. Then, we study distance observations, including selection effects, in models which are homogeneous on scales around 100 Mpc---consistent with standard cosmology---but inhomogeneous on smaller scales. Finally, we consider photon polarizations, and show that they are not directly affected by inhomogeneities. Overall, we find that while Szekeres models have some advantages over simpler models, they are still seriously limited in their ability to alter our parameter estimation while remaining within the bounds of current observations.

Dynamics of a spherical minority game

International Nuclear Information System (INIS)

Galla, T; Coolen, A C C; Sherrington, D

2003-01-01

We present an exact dynamical solution of a spherical version of the batch minority game (MG) with random external information. The control parameters in this model are the ratio of the number of possible values for the public information over the number of agents, and the radius of the spherical constraint on the microscopic degrees of freedom. We find a phase diagram with three phases: two without anomalous response (an oscillating versus a frozen state) and a further frozen phase with divergent integrated response. In contrast to standard MG versions, we can also calculate the volatility exactly. Our study reveals similarities between the spherical and the conventional MG, but also intriguing differences. Numerical simulations confirm our analytical results

Evaluation of regional ionospheric grid model over China from dense GPS observations

Directory of Open Access Journals (Sweden)

Xin Zhao

2016-09-01

Full Text Available The current global or regional ionospheric models have been established for monitoring the ionospheric variations. However, the spatial and temporal resolutions are not enough to describe total electron content (TEC variations in small scales for China. In this paper, a regional ionospheric grid model (RIGM with high spatial-temporal resolution (0.5° × 0.5° and 10-min interval in China and surrounding areas is established based on spherical harmonics expansion from dense GPS measurements provided by Crustal Movement Observation Network of China (CMONOC and the International GNSS Service (IGS. The correlation coefficient between the estimated TEC from GPS and the ionosonde measurements is 0.97, and the root mean square (RMS with respect to Center for Orbit Determination in Europe (CODE Global Ionosphere Maps (GIMs is 4.87 TECU. In addition, the impact of different spherical harmonics orders and degrees on TEC estimations are evaluated and the degree/order 6 is better. Moreover, effective ionospheric shell heights from 300 km to 700 km are further assessed and the result indicates that 550 km is the most suitable for regional ionospheric modeling in China at solar maximum.

A better understanding of biomass co-firing by developing an advanced non-spherical particle tracking model

DEFF Research Database (Denmark)

Yin, Chungen; Rosendahl, Lasse Aistrup; Kær, Søren Knudsen

2004-01-01

-area-to-volume ratio and thus experiences a totally different motion and reaction as a non-spherical particle. Therefore, an advanced non-spherical particle-tracking model is developed to calculate the motion and reaction of nonspherical biomass particles. The biomass particles are assumed as solid or hollow cylinders......-gradient force. Since the drag and lift forces are both shape factor- and orientation-dependent, coupled particle rotation equations are resolved to update particle orientation. In the reaction of biomass particles, the actual particle surface area available and the average oxygen mass flux at particle surface...

The evolution of applied harmonic analysis models of the real world

CERN Document Server

Prestini, Elena

2016-01-01

A sweeping exploration of the development and far-reaching applications of harmonic analysis such as signal processing, digital music, optics, radio astronomy, crystallography, medical imaging, spectroscopy, and more. Featuring a wealth of illustrations, examples, and material not found in other harmonic analysis books, this unique monograph skillfully blends together historical narrative with scientific exposition to create a comprehensive yet accessible work. While only an understanding of calculus is required to appreciate it, there are more technical sections that will charm even specialists in harmonic analysis. From undergraduates to professional scientists, engineers, and mathematicians, there is something for everyone here. The second edition of The Evolution of Applied Harmonic Analysis contains a new chapter on atmospheric physics and climate change, making it more relevant for today’s audience. Praise for the first edition: "…can be thoroughly recommended to any reader who is curious about the ...

Some properties of the statistical models of the spherical Friedman world

International Nuclear Information System (INIS)

Rumyantseva, E.N.

1981-01-01

Considered are some properties of the statistical model of the spherical Friedman world filled with quantum gas of massless particles the spin of which can be equal to 0, 1/2, 1. Obtained are approximate expressions for a number of particles of Fermi- and Bose-gas and for the radius of the world taking into account mainly the dependence on the spin. The dependence of the number of particles on the radius of the world and temperature of the gas is illustrated [ru

harmonic load modeling: a case study of 33 kv abuja steel mill feeder

African Journals Online (AJOL)

HOD

techniques are adopted. This paper studied the harmonic orders of the 33 kV Abuja Steel Feeder modeled as a ... (ETAP) software package was deployed to perform Discrete Fast Transform (DFT) while the input ... and documented in research and development articles ... network with 33kV Abuja Steel feeder as case study.

Photoionization and third-order susceptibility of a neutral donor in ZnS/InP/ZnSe core/shell spherical quantum dots

International Nuclear Information System (INIS)

Xie, Wenfang

2014-01-01

The optical properties of a neutral donor in a ZnS/InP/ZnSe core/shell spherical quantum dot have been investigated using the variational method and the compact density-matrix approach. Two parametric potential is chosen as a confinement potential for the shell. Considering the band structure of the system it is assumed that electron is localized in InP shell. It is assumed that the impurity is located in the center of quantum dot core (ZnS). The photoionization cross section as well as the third-order nonlinear optical susceptibility of third harmonic generation has been calculated. The results show that the photoionization and the third-order nonlinear optical susceptibility of a donor in a core/shell spherical quantum dot are strongly affected by the shell thickness. We found that small applied shell thickness will lead to a significant blue shift of the peak positions in the optical spectrum. This kind of structure gives an opportunity to tune and control the photoionization and the third-order nonlinear optical susceptibility of third harmonic generation of a donor impurity by changing the shell thickness

Generalized theory of resonance excitation by sound scattering from an elastic spherical shell in a nonviscous fluid.

Science.gov (United States)

Mitri, Farid G

2012-08-01

This work presents the general theory of resonance scattering (GTRS) by an elastic spherical shell immersed in a nonviscous fluid and placed arbitrarily in an acoustic beam. The GTRS formulation is valid for a spherical shell of any size and material regardless of its location relative to the incident beam. It is shown here that the scattering coefficients derived for a spherical shell immersed in water and placed in an arbitrary beam equal those obtained for plane wave incidence. Numerical examples for an elastic shell placed in the field of acoustical Bessel beams of different types, namely, a zero-order Bessel beam and first-order Bessel vortex and trigonometric (nonvortex) beams are provided. The scattered pressure is expressed using a generalized partial-wave series expansion involving the beam-shape coefficients (BSCs), the scattering coefficients of the spherical shell, and the half-cone angle of the beam. The BSCs are evaluated using the numerical discrete spherical harmonics transform (DSHT). The far-field acoustic resonance scattering directivity diagrams are calculated for an albuminoidal shell immersed in water and filled with perfluoropropane gas, by subtracting an appropriate background from the total far-field form function. The properties related to the arbitrary scattering are analyzed and discussed. The results are of particular importance in acoustical scattering applications involving imaging and beam-forming for transducer design. Moreover, the GTRS method can be applied to investigate the scattering of any beam of arbitrary shape that satisfies the source-free Helmholtz equation, and the method can be readily adapted to viscoelastic spherical shells or spheres.

Harmonic excitations in quasicrystals

International Nuclear Information System (INIS)

Luck, J.M.

1986-03-01

The harmonic excitations (phonons) of quasicrystals are studied in a simple one-dimensional model. The spectrum is a Cantor set, which exhibits selfsimilarity properties. The eigenstates are generically ''critical'', i.e. neither extended nor localized

Harmonic Domain Modelling of Transformer Core Nonlinearities Using the DIgSILENT PowerFactory Software

DEFF Research Database (Denmark)

Bak, Claus Leth; Bak-Jensen, Birgitte; Wiechowski, Wojciech

2008-01-01

This paper demonstrates the results of implementation and verification of an already existing algorithm that allows for calculating saturation characteristics of singlephase power transformers. The algorithm was described for the first time in 1993. Now this algorithm has been implemented using...... the DIgSILENT Programming Language (DPL) as an external script in the harmonic domain calculations of a power system analysis tool PowerFactory [10]. The algorithm is verified by harmonic measurements on a single-phase power transformer. A theoretical analysis of the core nonlinearities phenomena...... in single and three-phase transformers is also presented. This analysis leads to the conclusion that the method can be applied for modelling nonlinearities of three-phase autotransformers....

Symmetry-dictated trucation: Solutions of the spherical shell model for heavy nuclei

International Nuclear Information System (INIS)

Guidry, M.W.

1992-01-01

Principles of dynamical symmetry are used to simplify the spherical shell model. The resulting symmetry-dictated truncation leads to dynamical symmetry solutions that are often in quantitative agreement with a variety of observables. Numerical calculations, including terms that break the dynamical symmetries, are shown that correspond to shell model calculations for heavy deformed nuclei. The effective residual interaction is simple, well-behaved, and can be determined from basic observables. With this approach, we intend to apply the shell model in systematic fashion to all nuclei. The implications for nuclear structure far from stability and for nuclear masses and other quantities of interest in astrophysics are discussed

Behaviour modelling of two aluminas in divergent spherical pyrotechnical experiments

International Nuclear Information System (INIS)

Malaise, F.; Tranchet, J.Y.; Collombet, F.

1997-01-01

Two pure aluminas of different characteristics have been subjected to the propagation of a longitudinal divergent spherical shock wave through pyrotechnical experiments. An approach combining a phenomenological analysis and numerical 1D-calculations is proposed to study the behaviour of these aluminas submitted to that type of wave loading. The modelling, proposed in a previous paper, is refined and gives satisfying experimentation-calculation correlations. An analysis of the influence exerted by the various encountered phenomena (plastic activity, pore closure, microcracking) is performed. The significant consequence of the activation of damage with an extension criterion is also underlined. (orig.)

Tunneling ionization and harmonic generation in two-color fields

International Nuclear Information System (INIS)

Kondo, K.; Kobayashi, Y.; Sagisaka, A.; Nabekawa, Y.; Watanabe, S.

1996-01-01

Tunneling ionization and harmonic generation in two-color fields were studied with a fundamental beam (ω) and its harmonics (2ω,3ω), which were generated by a 100-fs Ti:sapphire laser. Ion yields of atoms and molecules were successfully controlled by means of a change in the relative phase between ω and 3ω pulses. Two-color interference was clearly observed in photoelectron spectra and harmonic spectra. In the ω endash 2ω field even-order harmonics were observed in which the intensity was almost equal to that of the odd harmonics because of an asymmetric optical field. These results were compared with the quasi-static model for ionization and with the quantum theory for harmonic generation. copyright 1996 Optical Society of America

Stability of the spherical form of nuclei

International Nuclear Information System (INIS)

Sabry, A.A.

1976-08-01

An extension of the mass formula for a spherical nucleus in the drop model to include a largely deformed nucleus of different forms is investigated. It is found that although the spherical form is stable under small deformations from equilibrium, there exists for heavier nuclei another more favourable stable form, which can be approximated by two, or three touching prolate ellipsoids of revolution

A relativistic gauge model describing N particles bound by harmonic forces

International Nuclear Information System (INIS)

Filippov, A.T.

1987-01-01

Application of the principle of gauging to linear canonical symmetries of simplest/rudimentary/bilinear lagrangians is shown to produce a relativistic version of the Lagrangian describing N particles bound by harmonic forces. For pairwise coupled identical particles the gauge group is T 1 xU 1 , xSU N-1 . A model for the relativistic discrete string (a chain of N particles) is also discussed. All these gauge theoried of particles can be quantized by standard methods

Determining spherical lens correction for astronaut training underwater.

Science.gov (United States)

Porter, Jason; Gibson, C Robert; Strauss, Samuel

2011-09-01

To develop a model that will accurately predict the distance spherical lens correction needed to be worn by National Aeronautics and Space Administration astronauts while training underwater. The replica space suit's helmet contains curved visors that induce refractive power when submersed in water. Anterior surface powers and thicknesses were measured for the helmet's protective and inside visors. The impact of each visor on the helmet's refractive power in water was analyzed using thick lens calculations and Zemax optical design software. Using geometrical optics approximations, a model was developed to determine the optimal distance spherical power needed to be worn underwater based on the helmet's total induced spherical power underwater and the astronaut's manifest spectacle plane correction in air. The validity of the model was tested using data from both eyes of 10 astronauts who trained underwater. The helmet's visors induced a total power of -2.737 D when placed underwater. The required underwater spherical correction (FW) was linearly related to the spectacle plane spherical correction in air (FAir): FW = FAir + 2.356 D. The mean magnitude of the difference between the actual correction worn underwater and the calculated underwater correction was 0.20 ± 0.11 D. The actual and calculated values were highly correlated (r = 0.971) with 70% of eyes having a difference in magnitude of astronauts. The model accurately predicts the actual values worn underwater and can be applied (more generally) to determine a suitable spectacle lens correction to be worn behind other types of masks when submerged underwater.

Global Harmonic Current Rejection of Nonlinear Backstepping Control with Multivariable Adaptive Internal Model Principle for Grid-Connected Inverter under Distorted Grid Voltage

Directory of Open Access Journals (Sweden)

Yang Yu

2013-01-01

Full Text Available Based on a brief review on current harmonics generation mechanism for grid-connected inverter under distorted grid voltage, the harmonic disturbances and uncertain items are immersed into the original state-space differential equation of grid-connected inverter. A new algorithm of global current harmonic rejection based on nonlinear backstepping control with multivariable internal model principle is proposed for grid-connected inverter with exogenous disturbances and uncertainties. A type of multivariable internal model for a class of nonlinear harmonic disturbances is constructed. Based on application of backstepping control law of the nominal system, a multivariable adaptive state feedback controller combined with multivariable internal model and adaptive control law is designed to guarantee the closed-loop system globally uniformly bounded, which is proved by a constructed Lyapunov function. The presented algorithm extends rejection of nonlinear single-input systems to multivariable globally defined normal form, the correctness and effectiveness of which are verified by the simulation results.

Computational-Model-Based Analysis of Context Effects on Harmonic Expectancy

OpenAIRE

Morimoto, Satoshi; Remijn, Gerard B.; Nakajima, Yoshitaka

2016-01-01

Expectancy for an upcoming musical chord, harmonic expectancy, is supposedly based on automatic activation of tonal knowledge. Since previous studies implicitly relied on interpretations based on Western music theory, the underlying computational processes involved in harmonic expectancy and how it relates to tonality need further clarification. In particular, short chord sequences which cannot lead to unique keys are difficult to interpret in music theory. In this study, we examined effects ...

EEG-distributed inverse solutions for a spherical head model

Science.gov (United States)

Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.

1998-08-01

The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.

Stress in Harmonic Serialism

Science.gov (United States)

Pruitt, Kathryn Ringler

2012-01-01

This dissertation proposes a model of word stress in a derivational version of Optimality Theory (OT) called Harmonic Serialism (HS; Prince and Smolensky 1993/2004, McCarthy 2000, 2006, 2010a). In this model, the metrical structure of a word is derived through a series of optimizations in which the "best" metrical foot is chosen…

2017 Updates: Earth Gravitational Model 2020

Science.gov (United States)

Barnes, D. E.; Holmes, S. A.; Ingalls, S.; Beale, J.; Presicci, M. R.; Minter, C.

2017-12-01

The National Geospatial-Intelligence Agency [NGA], in conjunction with its U.S. and international partners, has begun preliminary work on its next Earth Gravitational Model, to replace EGM2008. The new `Earth Gravitational Model 2020' [EGM2020] has an expected public release date of 2020, and will retain the same harmonic basis and resolution as EGM2008. As such, EGM2020 will be essentially an ellipsoidal harmonic model up to degree (n) and order (m) 2159, but will be released as a spherical harmonic model to degree 2190 and order 2159. EGM2020 will benefit from new data sources and procedures. Updated satellite gravity information from the GOCE and GRACE mission, will better support the lower harmonics, globally. Multiple new acquisitions (terrestrial, airborne and shipborne) of gravimetric data over specific geographical areas (Antarctica, Greenland …), will provide improved global coverage and resolution over the land, as well as for coastal and some ocean areas. Ongoing accumulation of satellite altimetry data as well as improvements in the treatment of this data, will better define the marine gravity field, most notably in polar and near-coastal regions. NGA and partners are evaluating different approaches for optimally combining the new GOCE/GRACE satellite gravity models with the terrestrial data. These include the latest methods employing a full covariance adjustment. NGA is also working to assess systematically the quality of its entire gravimetry database, towards correcting biases and other egregious errors. Public release number 15-564

Discrete Model Reference Adaptive Control for Gimbal Servosystem of Control Moment Gyro with Harmonic Drive

Directory of Open Access Journals (Sweden)

Bangcheng Han

2013-01-01

Full Text Available The double-gimbal control moment gyro (DGCMG demands that the gimbal servosystem should have fast response and small overshoot. But due to the low and nonlinear torsional stiffness of harmonic drive, the gimbal servo-system has poor dynamic performance with large overshoot and low bandwidth. In order to improve the dynamic performance of gimbal servo-system, a model reference adaptive control (MRAC law is introduced in this paper. The model of DGCMG gimbal servo-system with harmonic drive is established, and the adaptive control law based on POPOV super stable theory is designed. The MATLAB simulation results are provided to verify the effectiveness of the proposed control algorithm. The experimental results indicate that the MRAC could increase the bandwidth of gimbal servo-system to 3 Hz and improve the dynamic performance with small overshoot.

Nonlinear propagation in ultrasonic fields: measurements, modelling and harmonic imaging.

Science.gov (United States)

Humphrey, V F

2000-03-01

In high amplitude ultrasonic fields, such as those used in medical ultrasound, nonlinear propagation can result in waveform distortion and the generation of harmonics of the initial frequency. In the nearfield of a transducer this process is complicated by diffraction effects associated with the source. The results of a programme to study the nonlinear propagation in the fields of circular, focused and rectangular transducers are described, and comparisons made with numerical predictions obtained using a finite difference solution to the Khokhlov-Zabolotskaya-Kuznetsov (or KZK) equation. These results are extended to consider nonlinear propagation in tissue-like media and the implications for ultrasonic measurements and ultrasonic heating are discussed. The narrower beamwidths and reduced side-lobe levels of the harmonic beams are illustrated and the use of harmonics to form diagnostic images with improved resolution is described.

Mapping quadrupole collectivity in the Cd isotopes: The breakdown of harmonic vibrational motion

Science.gov (United States)

Garrett, P. E.; Green, K. L.; Bangay, J.; Varela, A. Diaz; Sumithrarachchi, C. S.; Austin, R. A. E.; Ball, G. C.; Bandyopadhyay, D. S.; Bianco, L.; Colosimo, S.; Cross, D. S.; Demand, G. A.; Finlay, P.; Garnsworthy, A. B.; Grinyer, G. F.; Hackman, G.; Kulp, W. D.; Leach, K. G.; Morton, A. C.; Orce, J. N.; Pearson, C. J.; Phillips, A. A.; Schumaker, M. A.; Svensson, C. E.; Triambak, S.; Wong, J.; Wood, J. L.; Yates, S. W.

2011-10-01

The stable Cd isotopes have long been used as paradigms for spherical vibrational motion. Extensive investigations with in-beam γ spectroscopy have resulted in very-well-established level schemes, including many lifetimes or lifetime limits. A programme has been initiated to complement these studies with very-high-statistics β decay using the 8π spectrometer at the TRIUMF radioactive beam facility. The decays of 112In and 112Ag have been studied with an emphasis on the observation of, or the placement of stringent limits on, low-energy branches between potential multi-phonon levels. A lack of suitable 0+ or 2+ three-phonon candidates has been revealed. Further, the sum of the B(E2) strength from spin 0+ and 2+ states up to 3 MeV in excitation energy to the assigned two-phonon levels falls far short of the harmonic-vibrational expectations. This lack of strength points to the failing of collective models based on vibrational phonon structures.

The contribution of radio-frequency rectification to field-aligned losses of high-harmonic fast wave power to the divertor in the National Spherical Torus eXperiment

Energy Technology Data Exchange (ETDEWEB)

Perkins, R. J., E-mail: rperkins@pppl.gov; Hosea, J. C.; Jaworski, M. A.; Diallo, A.; Bell, R. E.; Bertelli, N.; Gerhardt, S.; Kramer, G. J.; LeBlanc, B. P.; Phillips, C. K.; Podestà, M.; Roquemore, L.; Taylor, G.; Wilson, J. R. [Princeton Plasma Physics Laboratory, Princeton, New Jersey 08543 (United States); Ahn, J.-W.; Gray, T. K. [Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (United States); McLean, A. [Lawrence Livermore National Laboratory, Livermore, California 94550 (United States); Sabbagh, S. [Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States)

2015-04-15

The National Spherical Torus eXperiment (NSTX) can exhibit a major loss of high-harmonic fast wave (HHFW) power along scrape-off layer (SOL) field lines passing in front of the antenna, resulting in bright and hot spirals on both the upper and lower divertor regions. One possible mechanism for this loss is RF sheaths forming at the divertors. Here, we demonstrate that swept-voltage Langmuir probe characteristics for probes under the spiral are shifted relative to those not under the spiral in a manner consistent with RF rectification. We estimate both the magnitude of the RF voltage across the sheath and the sheath heat flux transmission coefficient in the presence of the RF field. Although precise comparison between the computed heat flux and infrared (IR) thermography cannot yet be made, the computed heat deposition compares favorably with the projections from IR camera measurements. The RF sheath losses are significant and contribute substantially to the total SOL losses of HHFW power to the divertor for the cases studied. This work will guide future experimentation on NSTX-U, where a wide-angle IR camera and a dedicated set of coaxial Langmuir probes for measuring the RF sheath voltage directly will quantify the contribution of RF sheath rectification to the heat deposition from the SOL to the divertor.

Integrated predictive modeling simulations of the Mega-Amp Spherical Tokamak

International Nuclear Information System (INIS)

Nguyen, Canh N.; Bateman, Glenn; Kritz, Arnold H.; Akers, Robert; Byrom, Calum; Sykes, Alan

2002-01-01

Integrated predictive modeling simulations are carried out using the BALDUR transport code [Singer et al., Comput. Phys. Commun. 49, 275 (1982)] for high confinement mode (H-mode) and low confinement mode (L-mode) discharges in the Mega-Amp Spherical Tokamak (MAST) [Sykes et al., Phys. Plasmas 8, 2101 (2001)]. Simulation results, obtained using either the Multi-Mode transport model (MMM95) or, alternatively, the mixed-Bohm/gyro-Bohm transport model, are compared with experimental data. In addition to the anomalous transport, neoclassical transport is included in the simulations and the ion thermal diffusivity in the inner third of the plasma is found to be predominantly neoclassical. The sawtooth oscillations in the simulations radially spread the neutral beam injection heating profiles across a broad sawtooth mixing region. The broad sawtooth oscillations also flatten the central temperature and electron density profiles. Simulation results for the electron temperature and density profiles are compared with experimental data to test the applicability of these models and the BALDUR integrated modeling code in the limit of low aspect ratio toroidal plasmas

Harmonic generation and flux quantization in granular superconductors

International Nuclear Information System (INIS)

Lam, Q.H.; Jeffries, C.D.

1989-01-01

Simple dynamical models of granular superconductors are used to compute the generation of harmonic power in ac and dc magnetic fields. In zero order, the model is a single superconducting loop, with or without a weak link. The sample-average power is predicted by averaging over suitable distribution functions for loop areas and orientations in a dc magnetic field. In a first-order model, inductance and resistance are also included. In all models the power at high harmonics shows strikingly sharp dips periodic in the dc field, revealing flux quantization in the prototype loops

Research on Harmonic Characteristics Influence for Distribution Network with Renewable Energy