Construction of SO(5)⊃SO(3) spherical harmonics and Clebsch-Gordan coefficients

NASA Astrophysics Data System (ADS)

Caprio, M. A.; Rowe, D. J.; Welsh, T. A.

2009-07-01

The SO(5)⊃SO(3) spherical harmonics form a natural basis for expansion of nuclear collective model angular wave functions. They underlie the recently-proposed algebraic method for diagonalization of the nuclear collective model Hamiltonian in an SU(1,1)×SO(5) basis. We present a computer code for explicit construction of the SO(5)⊃SO(3) spherical harmonics and use them to compute the Clebsch-Gordan coefficients needed for collective model calculations in an SO(3)-coupled basis. With these Clebsch-Gordan coefficients it becomes possible to compute the matrix elements of collective model observables by purely algebraic methods. Program summaryProgram title: GammaHarmonic Catalogue identifier: AECY_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECY_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 346 421 No. of bytes in distributed program, including test data, etc.: 16 037 234 Distribution format: tar.gz Programming language: Mathematica 6 Computer: Any which supports Mathematica Operating system: Any which supports Mathematica; tested under Microsoft Windows XP and Linux Classification: 4.2 Nature of problem: Explicit construction of SO(5) ⊃ SO(3) spherical harmonics on S. Evaluation of SO(3)-reduced matrix elements and SO(5) ⊃ SO(3) Clebsch-Gordan coefficients (isoscalar factors). Solution method: Construction of SO(5) ⊃ SO(3) spherical harmonics by orthonormalization, obtained from a generating set of functions, according to the method of Rowe, Turner, and Repka [1]. Matrix elements and Clebsch-Gordan coefficients follow by construction and integration of SO(3) scalar products. Running time: Depends strongly on the maximum SO(5) and SO(3) representation labels involved. A few minutes for the calculation in the Mathematica notebook. References: [1] D.J. Rowe, P.S. Turner, J. Repka, J. Math. Phys. 45 (2004) 2761.

Venus gravity and topography: 60th degree and order model

NASA Technical Reports Server (NTRS)

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.

Spheroidal models of the exterior gravitational field of Asteroids Bennu and Castalia

NASA Astrophysics Data System (ADS)

Sebera, Josef; Bezděk, Aleš; Pešek, Ivan; Henych, Tomáš

2016-07-01

Gravitational field of small bodies can be modeled e.g. with mascons, a polyhedral model or in terms of harmonic functions. If the shape of a body is close to the spheroid, it is advantageous to employ the spheroidal basis functions for expressing the gravitational field. Spheroidal harmonic models, similarly to the spherical ones, may be used in navigation and geophysical tasks. We focus on modeling the exterior gravitational field of oblate-like Asteroid (101955) Bennu and prolate-like Asteroid (4769) Castalia with spheroidal harmonics. Using the Gauss-Legendre quadrature and the spheroidal basis functions, we converted the gravitational potential of a particular polyhedral model of a constant density into the spheroidal harmonics. The results consist of (i) spheroidal harmonic coefficients of the exterior gravitational field for the Asteroids Bennu and Castalia, (ii) spherical harmonic coefficients for Bennu, and (iii) the first and second-order Cartesian derivatives in the local spheroidal South-East-Up frame for both bodies. The spheroidal harmonics offer biaxial flexibility (compared with spherical harmonics) and low computational costs that allow high-degree expansions (compared with ellipsoidal harmonics). The obtained spheroidal models for Bennu and Castalia represent the exterior gravitational field valid on and outside the Brillouin spheroid but they can be used even under this surface. For Bennu, 5 m above the surface the agreement with point-wise integration was 1% or less, while it was about 10% for Castalia due to its more irregular shape. As the shape models may produce very high frequencies, it was crucial to use higher maximum degree to reduce the aliasing. We have used the maximum degree 360 to achieve 9-10 common digits (in RMS) when reconstructing the input (the gravitational potential) from the spheroidal coefficients. The physically meaningful maximum degree may be lower (≪ 360) but its particular value depends on the distance and/or on the application (navigation, exploration, etc.).

Regional TEC dynamic modeling based on Slepian functions

NASA Astrophysics Data System (ADS)

Sharifi, Mohammad Ali; Farzaneh, Saeed

2015-09-01

In this work, the three-dimensional state of the ionosphere has been estimated by integrating the spherical Slepian harmonic function and Kalman filter. The spherical Slepian harmonic functions have been used to establish the observation equations because of their properties in local modeling. Spherical harmonics are poor choices to represent or analyze geophysical processes without perfect global coverage but the Slepian functions afford spatial and spectral selectivity. The Kalman filter has been utilized to perform the parameter estimation due to its suitable properties in processing the GPS measurements in the real-time mode. The proposed model has been applied to the real data obtained from the ground-based GPS observations across some portion of the IGS network in Europe. Results have been compared with the estimated TECs by the CODE, ESA, IGS centers and IRI-2012 model. The results indicated that the proposed model which takes advantage of the Slepian basis and Kalman filter is efficient and allows for the generation of the near-real-time regional TEC map.

Rotationally invariant clustering of diffusion MRI data using spherical harmonics

NASA Astrophysics Data System (ADS)

Liptrot, Matthew; Lauze, François

2016-03-01

We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use 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 coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation. After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion 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 alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.1 The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust 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-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice.

Evaluating Descent and Ascent Trajectories Near Non-Spherical Bodies

NASA Technical Reports Server (NTRS)

Werner, Robert A.

2010-01-01

Spacecraft landing on small bodies pass through regions where conventional gravitation formulations using exterior spherical harmonics are inaccurate. An investigation shows that a formulation using interior solid spherical harmonics might be satisfactory. Interior spherical harmonic expansions are usable inside an imaginary, empty sphere. For this application, such a sphere could be positioned in empty space above the intended landing site and rotating with the body. When the spacecraft is inside this sphere, the interior harmonic expansion would be used instead of the conventional, exterior harmonic expansion. Coefficients can be determined by a least-squares fit to gravitation measurements synthesized from conventional formulations. Due to their unfamiliarity, recurrences for interior, as well as exterior, expansions are derived. Hotine's technique for partial derivatives of exterior spherical harmonics is extended to interior harmonics.

Equivalent source modeling of the core magnetic field using magsat data

NASA Technical Reports Server (NTRS)

Mayhew, M. A.; Estes, R. H.

1983-01-01

Experiments are carried out on fitting the main field using different numbers of equivalent sources arranged in equal area at fixed radii at and inside the core-mantle boundary. In fixing the radius for a given series of runs, the convergence problems that result from the extreme nonlinearity of the problem when dipole positions are allowed to vary are avoided. Results are presented from a comparison between this approach and the standard spherical harmonic approach for modeling the main field in terms of accuracy and computational efficiency. The modeling of the main field with an equivalent dipole representation is found to be comparable to the standard spherical harmonic approach in accuracy. The 32 deg dipole density (42 dipoles) corresponds approximately to an eleventh degree/order spherical harmonic expansion (143 parameters), whereas the 21 dipole density (92 dipoles) corresponds to approximately a seventeenth degree and order expansion (323 parameters). It is pointed out that fixing the dipole positions results in rapid convergence of the dipole solutions for single-epoch models.

The Space-Wise Global Gravity Model from GOCE Nominal Mission Data

NASA Astrophysics Data System (ADS)

Gatti, A.; Migliaccio, F.; Reguzzoni, M.; Sampietro, D.; Sanso, F.

2011-12-01

In the framework of the GOCE data analysis, the space-wise approach implements a multi-step collocation solution for the estimation of a global geopotential model in terms of spherical harmonic coefficients and their error covariance matrix. The main idea is to use the collocation technique to exploit the spatial correlation of the gravity field in the GOCE data reduction. In particular the method consists of an along-track Wiener filter, a collocation gridding at satellite altitude and a spherical harmonic analysis by integration. All these steps are iterated, also to account for the rotation between local orbital and gradiometer reference frame. Error covariances are computed by Montecarlo simulations. The first release of the space-wise approach was presented at the ESA Living Planet Symposium in July 2010. This model was based on only two months of GOCE data and partially contained a priori information coming from other existing gravity models, especially at low degrees and low orders. A second release was distributed after the 4th International GOCE User Workshop in May 2011. In this solution, based on eight months of GOCE data, all the dependencies from external gravity information were removed thus giving rise to a GOCE-only space-wise model. However this model showed an over-regularization at the highest degrees of the spherical harmonic expansion due to the combination technique of intermediate solutions (based on about two months of data). In this work a new space-wise solution is presented. It is based on all nominal mission data from November 2009 to mid April 2011, and its main novelty is that the intermediate solutions are now computed in such a way to avoid over-regularization in the final solution. Beyond the spherical harmonic coefficients of the global model and their error covariance matrix, the space-wise approach is able to deliver as by-products a set of spherical grids of potential and of its second derivatives at mean satellite altitude. These grids have an information content that is very similar to the original along-orbit data, but they are much easier to handle. In addition they are estimated by local least-squares collocation and therefore, although computed by a unique global covariance function, they could yield more information at local level than the spherical harmonic coefficients of the global model. For this reason these grids seem to be useful for local geophysical investigations. The estimated grids with their estimated errors are presented in this work together with proposals on possible future improvements. A test to compare the different information contents of the along-orbit data, the gridded data and the spherical harmonic coefficients is also shown.

Rapid automated superposition of shapes and macromolecular models using spherical harmonics.

PubMed

Konarev, Petr V; Petoukhov, Maxim V; Svergun, Dmitri I

2016-06-01

A rapid algorithm to superimpose macromolecular models in Fourier space is proposed and implemented ( SUPALM ). The method uses a normalized integrated cross-term of the scattering amplitudes as a proximity measure between two three-dimensional objects. The reciprocal-space algorithm allows for direct matching of heterogeneous objects including high- and low-resolution models represented by atomic coordinates, beads or dummy residue chains as well as electron microscopy density maps and inhomogeneous multi-phase models ( e.g. of protein-nucleic acid complexes). Using spherical harmonics for the computation of the amplitudes, the method is up to an order of magnitude faster than the real-space algorithm implemented in SUPCOMB by Kozin & Svergun [ J. Appl. Cryst. (2001 ▸), 34 , 33-41]. The utility of the new method is demonstrated in a number of test cases and compared with the results of SUPCOMB . The spherical harmonics algorithm is best suited for low-resolution shape models, e.g . those provided by solution scattering experiments, but also facilitates a rapid cross-validation against structural models obtained by other methods.

Light propagation in linearly perturbed ΛLTB models

NASA Astrophysics Data System (ADS)

Meyer, Sven; Bartelmann, Matthias

2017-11-01

We apply a generic formalism of light propagation to linearly perturbed spherically symmetric dust models including a cosmological constant. For a comoving observer on the central worldline, we derive the equation of geodesic deviation and perform a suitable spherical harmonic decomposition. This allows to map the abstract gauge-invariant perturbation variables to well-known quantities from weak gravitational lensing like convergence or cosmic shear. The resulting set of differential equations can effectively be solved by a Green's function approach leading to line-of-sight integrals sourced by the perturbation variables on the backward lightcone. The resulting spherical harmonic coefficients of the lensing observables are presented and the shear field is decomposed into its E- and B-modes. Results of this work are an essential tool to add information from linear structure formation to the analysis of spherically symmetric dust models with the purpose of testing the Copernican Principle with multiple cosmological probes.

Learning the spherical harmonic features for 3-D face recognition.

PubMed

Liu, Peijiang; Wang, Yunhong; Huang, Di; Zhang, Zhaoxiang; Chen, Liming

2013-03-01

In this paper, a competitive method for 3-D face recognition (FR) using spherical harmonic features (SHF) is proposed. With this solution, 3-D face models are characterized by the energies contained in spherical harmonics with different frequencies, thereby enabling the capture of both gross shape and fine surface details of a 3-D facial surface. This is in clear contrast to most 3-D FR techniques which are either holistic or feature based, using local features extracted from distinctive points. First, 3-D face models are represented in a canonical representation, namely, spherical depth map, by which SHF can be calculated. Then, considering the predictive contribution of each SHF feature, especially in the presence of facial expression and occlusion, feature selection methods are used to improve the predictive performance and provide faster and more cost-effective predictors. Experiments have been carried out on three public 3-D face datasets, SHREC2007, FRGC v2.0, and Bosphorus, with increasing difficulties in terms of facial expression, pose, and occlusion, and which demonstrate the effectiveness of the proposed method.

Some new methods in geomagnetic field modeling applied to the 1960 - 1980 epoch

NASA Technical Reports Server (NTRS)

Langel, R. A.; Estes, R. H.; Mead, G. H.

1981-01-01

The utilization of satellite and surface data together permitted the incorporation of a solution for the anomaly field at each observatory. The residuals of the observatory measurements to such models is commensurate with the actual measurment accuracy. Incorporation of the anomaly estimation enabled the inclusion of stable time derivatives of the spherical harmonic coefficients up to the third derivative. A spherical harmonic model is derived with degree and order 13 in its constant and first time derivative terms, six in its second derivative terms and four in its third derivative terms.

Mass change from GRACE: a simulated comparison of Level-1B analysis techniques

NASA Astrophysics Data System (ADS)

Andrews, Stuart B.; Moore, Philip; King, Matt. A.

2015-01-01

Spherical harmonic and mascon parameters have both been successfully applied in the recovery of time-varying gravity fields from Gravity Recovery and Climate Experiment (GRACE). However, direct comparison of any mass flux is difficult with solutions generated by different groups using different codes and algorithms. It is therefore opportune to compare these methodologies, within a common software base, to understand potential limitations associated with each technique. Here we use simulations to recover a known monthly surface mass distribution from GRACE KBRR data. The ability of spherical harmonic and mascon parameters to resolve basin-level mass change is quantified with an assessment of how the noise and errors, inherent in GRACE solutions, are handled. Recovery of a noise and error free GLDAS anomaly revealed no quantifiable difference between spherical harmonic and mascon parameters. Expansion of the GLDAS anomaly to degree and order 120 shows that both spherical harmonic and mascon parameters are affected by comparable omission errors. However, the inclusion of realistic KBRR noise and errors in the simulations reveals the advantage of the mascon parameters over spherical harmonics at reducing noise and errors in the higher degree and order harmonics with an rms (cm of EWH) to the GLDAS anomaly of 10.0 for the spherical harmonic solution and 8.8 (8.6) for the 4°(2°) mascon solutions. The introduction of a constraint matrix in the mascon solution based on parameters that share geophysical similarities is shown to further reduce the signal lost at all degrees. The recovery of a simulated Antarctic mass loss signal shows that the mascon methodology is superior to spherical harmonics for this region with an rms (cm of EWH) of 8.7 for the 2° mascon solution compared to 10.0 for the spherical harmonic solution. Investigating the noise and errors for a month when the satellites were in resonance revealed both the spherical harmonic and mascon methodologies are able to recover the GLDAS and Antarctic mass loss signal with either a comparable (spherical harmonic) or improved (mascon) rms compared to non-resonance periods.

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

NASA Astrophysics Data System (ADS)

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.

A problem in representing the core magnetic field of the earth using spherical harmonics

NASA Technical Reports Server (NTRS)

Carle, H. M.; Harrison, C. G. A.

1982-01-01

Although there are computational advantages to the representation of the earth's magnetic field by spherical harmonic coefficients of the magnetic potential, up to the thirteenth degree and order, the following disadvantages emerge: (1) the use of spherical harmonics of up to a certain degree does not remove wavelengths greater than a certain value from the surface fields, and (2) the total field magnitudes represented by spherical harmonics up to a certain degree have minimum wavelengths equal to the circumference of the earth divided by twice the maximum degree of the harmonic used. The implications of the ways in which surface fields are separated into core and crustal components are discussed, and it is concluded that since field signals are generated in the core, the representation of the core field by spherical harmonics of potential does not adequately represent all core field components.

A new description of Earth's wobble modes using Clairaut coordinates: 1. Theory

NASA Astrophysics Data System (ADS)

Rochester, M. G.; Crossley, D. J.; Zhang, Y. L.

2014-09-01

This paper presents a novel mathematical reformulation of the theory of the free wobble/nutation of an axisymmetric reference earth model in hydrostatic equilibrium, using the linear momentum description. The new features of this work consist in the use of (i) Clairaut coordinates (rather than spherical polars), (ii) standard spherical harmonics (rather than generalized spherical surface harmonics), (iii) linear operators (rather than J-square symbols) to represent the effects of rotational and ellipticity coupling between dependent variables of different harmonic degree and (iv) a set of dependent variables all of which are continuous across material boundaries. The resulting infinite system of coupled ordinary differential equations is given explicitly, for an elastic solid mantle and inner core, an inviscid outer core and no magnetic field. The formulation is done to second order in the Earth's ellipticity. To this order it is shown that for wobble modes (in which the lowest harmonic in the displacement field is degree 1 toroidal, with azimuthal order m = ±1), it is sufficient to truncate the chain of coupled displacement fields at the toroidal harmonic of degree 5 in the solid parts of the earth model. In the liquid core, however, the harmonic expansion of displacement can in principle continue to indefinitely high degree at this order of accuracy. The full equations are shown to yield correct results in three simple cases amenable to analytic solution: a general earth model in rigid rotation, the tiltover mode in a homogeneous solid earth model and the tiltover and Chandler periods for an incompressible homogeneous solid earth model. Numerical results, from programmes based on this formulation, are presented in part II of this paper.

Geometrical Method for the Calculation of Spherical Harmonics up to an Arbitrary Degree and Order

NASA Astrophysics Data System (ADS)

Svehla, D.

2009-12-01

We introduce a novel method for the computation and rotation of spherical harmonics, Legendre polynomials and associated Legendre functions without making use of recursive relations. This novel geometrical approach allows calculation of spherical harmonics without any numerical instability up to an arbitrary degree and order, i.e. up to a degree and order 1e6 and beyond. It is shown, that spherical harmonics can be treated as vectors in Hilbert hyperspace leading to the unitary hermitian rotation matrices with geometric properties.

Annual, Seasonal, and Secular Changes in Time-Variable Gravity from GRACE

NASA Astrophysics Data System (ADS)

Lemoine, F. G.; Luthcke, S. B.; Klosko, S. M.; Rowlands, D. D.; Chinn, D. S.; McCarthy, J. J.; Ray, R. D.; Boy, J.

2007-12-01

The NASA/DLR GRACE mission, launched in 2002, has now operated for more than five years, producing monthly and ten-day snapshots of the variations of the gravity field of the Earth. The available solutions, either from spherical harmonics or from mascons, allow us new insights into the variations of surface gravity on the Earth at annual, inter-annual, and secular time scales. Our baseline time series, based on GGM02C, NCEP Atmospheric Gravity with IB, and GOT00 tides now is extended to July 2007, spanning four+ years, and we analyze both mascon and spherical harmonic solutions from this time series with respect to global hydrology variations. Our 4degx4deg mascon solutions are extended to cover all continental regions of the globe. Comparisons with hydrology (land-surface) models can offer insights into how these models might be improved. We compare our baseline time series, with new time series that include an updated Goddard Ocean Tide (GOT) model, ECMWF- 3hr atmosphere de-aliasing data, and the MOG-2D ocean dealiasing product. Finally, we intercompare the spherical harmonic solutions at low degree from GRACE from the various product centers (e.g., GFZ, CSR, GRGS), and look for secular signals in both the GSFC mascon and spherical harmonic solutions, taking care to compare the results for secular gravity field change with independent solutions developed over 25 years of independent tracking to geodetic satellites by Satellite Laser Ranging (SLR) and DORIS.

Computer model for harmonic ultrasound imaging.

PubMed

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.

Computer model for harmonic ultrasound imaging.

PubMed

Li, Y; Zagzebski, J A

2000-01-01

Harmonic ultrasound imaging has received great attention from ultrasound scanner manufacturers and researchers. Here, the authors 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.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2015-07-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees/orders are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the third-order partial derivatives of the magnetic potential field in the local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields and also the third-order partial derivatives of the magnetic potential field at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (GFZ Reference Internal Magnetic Model, version 0.0) with spherical harmonic degrees 16-90. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the magnetic potential field.

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

NASA Astrophysics Data System (ADS)

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.

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

PubMed

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.

An approach for spherical harmonic analysis of non-smooth data

NASA Astrophysics Data System (ADS)

Wang, Hansheng; Wu, Patrick; Wang, Zhiyong

2006-12-01

A method is proposed to evaluate the spherical harmonic coefficients of a global or regional, non-smooth, observable dataset sampled on an equiangular grid. The method is based on an integration strategy using new recursion relations. Because a bilinear function is used to interpolate points within the grid cells, this method is suitable for non-smooth data; the slope of the data may be piecewise continuous, with extreme changes at the boundaries. In order to validate the method, the coefficients of an axisymmetric model are computed, and compared with the derived analytical expressions. Numerical results show that this method is indeed reasonable for non-smooth models, and that the maximum degree for spherical harmonic analysis should be empirically determined by several factors including the model resolution and the degree of non-smoothness in the dataset, and it can be several times larger than the total number of latitudinal grid points. It is also shown that this method is appropriate for the approximate analysis of a smooth dataset. Moreover, this paper provides the program flowchart and an internet address where the FORTRAN code with program specifications are made available.

Venus - Global gravity and topography

NASA Technical Reports Server (NTRS)

Mcnamee, J. B.; Borderies, N. J.; Sjogren, W. L.

1993-01-01

A new gravity field determination that has been produced combines both the Pioneer Venus Orbiter (PVO) and the Magellan Doppler radio data. Comparisonsbetween this estimate, a spherical harmonic model of degree and order 21, and previous models show that significant improvements have been made. Results are displayed as gravity contours overlaying a topographic map. We also calculate a new spherical harmonic model of topography based on Magellan altimetry, with PVO altimetry included where gaps exist in the Magellan data. This model is also of degree and order 21, so in conjunction with the gravity model, Bouguer and isostatic anomaly maps can be produced. These results are very consistent with previous results, but reveal more spatial resolution in the higher latitudes.

Sampling functions for geophysics

NASA Technical Reports Server (NTRS)

Giacaglia, G. E. O.; Lunquist, C. A.

1972-01-01

A set of spherical sampling functions is defined such that they are related to spherical-harmonic functions in the same way that the sampling functions of information theory are related to sine and cosine functions. An orderly distribution of (N + 1) squared sampling points on a sphere is given, for which the (N + 1) squared spherical sampling functions span the same linear manifold as do the spherical-harmonic functions through degree N. The transformations between the spherical sampling functions and the spherical-harmonic functions are given by recurrence relations. The spherical sampling functions of two arguments are extended to three arguments and to nonspherical reference surfaces. Typical applications of this formalism to geophysical topics are sketched.

Harmonic growth of spherical Rayleigh-Taylor instability in weakly nonlinear regime

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Wanhai; LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190; Chen, Yulian

Harmonic growth in classical Rayleigh-Taylor instability (RTI) on a spherical interface is analytically investigated using the method of the parameter expansion up to the third order. Our results show that the amplitudes of the first four harmonics will recover those in planar RTI as the interface radius tends to infinity compared against the initial perturbation wavelength. The initial radius dramatically influences the harmonic development. The appearance of the second-order feedback to the initial unperturbed interface (i.e., the zeroth harmonic) makes the interface move towards the spherical center. For these four harmonics, the smaller the initial radius is, the faster theymore » grow.« less

Venus spherical harmonic gravity model to degree and order 60

NASA Technical Reports Server (NTRS)

Konopliv, Alex S.; Sjogren, William L.

1994-01-01

The Magellan and Pioneer Venus Orbiter radiometric tracking data sets have been combined to produce a 60th degree and order spherical harmonic gravity field. The Magellan data include the high-precision X-band gravity tracking from September 1992 to May 1993 and post-aerobraking data up to January 5, 1994. Gravity models are presented from the application of Kaula's power rule for Venus and an alternative a priori method using surface accelerations. Results are given as vertical gravity acceleration at the reference surface, geoid, vertical Bouguer, and vertical isostatic maps with errors for the vertical gravity and geoid maps included. Correlation of the gravity with topography for the different models is also discussed.

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

PubMed

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.

Gravity fields of the solar system

NASA Technical Reports Server (NTRS)

Zendell, A.; Brown, R. D.; Vincent, S.

1975-01-01

The most frequently used formulations of the gravitational field are discussed and a standard set of models for the gravity fields of the earth, moon, sun, and other massive bodies in the solar system are defined. The formulas are presented in standard forms, some with instructions for conversion. A point-source or inverse-square model, which represents the external potential of a spherically symmetrical mass distribution by a mathematical point mass without physical dimensions, is considered. An oblate spheroid model is presented, accompanied by an introduction to zonal harmonics. This spheroid model is generalized and forms the basis for a number of the spherical harmonic models which were developed for the earth and moon. The triaxial ellipsoid model is also presented. These models and their application to space missions are discussed.

Light propagation from fluorescent probes in biological tissues by coupled time-dependent parabolic simplified spherical harmonics equations

PubMed Central

Domínguez, Jorge Bouza; Bérubé-Lauzière, Yves

2011-01-01

We introduce a system of coupled time-dependent parabolic simplified spherical harmonic equations to model the propagation of both excitation and fluorescence light in biological tissues. We resort to a finite element approach to obtain the time-dependent profile of the excitation and the fluorescence light fields in the medium. We present results for cases involving two geometries in three-dimensions: a homogeneous cylinder with an embedded fluorescent inclusion and a realistically-shaped rodent with an embedded inclusion alike an organ filled with a fluorescent probe. For the cylindrical geometry, we show the differences in the time-dependent fluorescence response for a point-like, a spherical, and a spherically Gaussian distributed fluorescent inclusion. From our results, we conclude that the model is able to describe the time-dependent excitation and fluorescent light transfer in small geometries with high absorption coefficients and in nondiffusive domains, as may be found in small animal diffuse optical tomography (DOT) and fluorescence DOT imaging. PMID:21483606

Lateral density anomalies and the earth's gravitational field

NASA Technical Reports Server (NTRS)

Lowrey, B. E.

1978-01-01

The interpretation of gravity is valuable for understanding lithospheric plate motion and mantle convection. Postulated models of anomalous mass distributions in the earth and the observed geopotential as expressed in the spherical harmonic expansion are compared. In particular, models of the anomalous density as a function of radius are found which can closely match the average magnitude of the spherical harmonic coefficients of a degree. These models include: (1) a two-component model consisting of an anomalous layer at 200 km depth (below the earth's surface) and at 1500 km depth (2) a two-component model where the upper component is distributed in the region between 1000 and 2800 km depth, and(3) a model with density anomalies which continuously increase with depth more than an order of magnitude.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens. It was shown that the analytical form for normalization coefficients is available primarily forl ≤ 4. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7.more » In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle–Coppens method in the Wolfram Mathematicasoftware to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.« less

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

NASA Astrophysics Data System (ADS)

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.

High-frequency analysis of Earth gravity field models based on terrestrial gravity and GPS/levelling data: a case study in Greece

NASA Astrophysics Data System (ADS)

Papanikolaou, T. D.; Papadopoulos, N.

2015-06-01

The present study aims at the validation of global gravity field models through numerical investigation in gravity field functionals based on spherical harmonic synthesis of the geopotential models and the analysis of terrestrial data. We examine gravity models produced according to the latest approaches for gravity field recovery based on the principles of the Gravity field and steadystate Ocean Circulation Explorer (GOCE) and Gravity Recovery And Climate Experiment (GRACE) satellite missions. Furthermore, we evaluate the overall spectrum of the ultra-high degree combined gravity models EGM2008 and EIGEN-6C3stat. The terrestrial data consist of gravity and collocated GPS/levelling data in the overall Hellenic region. The software presented here implements the algorithm of spherical harmonic synthesis in a degree-wise cumulative sense. This approach may quantify the bandlimited performance of the individual models by monitoring the degree-wise computed functionals against the terrestrial data. The degree-wise analysis performed yields insight in the short-wavelengths of the Earth gravity field as these are expressed by the high degree harmonics.

The 1995 revision of the joint US/UK geomagnetic field models. II: Main field

USGS Publications Warehouse

Quinn, J.M.; Coleman, R.J.; Macmillan, S.; Barraclough, D.R.

1997-01-01

This paper presents the 1995 main-field revision of the World Magnetic Model (WMM-95). It is based on Project MAGNET high-level (??? 15,000 ft.) vector aeromagnetic survey data collected between 1988 and 1994 and on scalar total intensity data collected by the Polar Orbiting Geomagnetic Survey (POGS) satellite during the period 1991 through 1993. The spherical harmonic model produced from these data describes that portion of the Earth's magnetic field generated internal to the Earth's surface at the 1995.0 Epoch. When combined with the spherical harmonic model of the Earth's secular variation described in paper I, the Earth's main magnetic field is fully characterized between the years 1995 and 2000. Regional magnetic field models for the conterminous United States, Alaska and, Hawaii were generated as by-products of the global modeling process.

Acoustic source localization in mixed field using spherical microphone arrays

NASA Astrophysics Data System (ADS)

Huang, Qinghua; Wang, Tong

2014-12-01

Spherical microphone arrays have been used for source localization in three-dimensional space recently. In this paper, a two-stage algorithm is developed to localize mixed far-field and near-field acoustic sources in free-field environment. In the first stage, an array signal model is constructed in the spherical harmonics domain. The recurrent relation of spherical harmonics is independent of far-field and near-field mode strengths. Therefore, it is used to develop spherical estimating signal parameter via rotational invariance technique (ESPRIT)-like approach to estimate directions of arrival (DOAs) for both far-field and near-field sources. In the second stage, based on the estimated DOAs, simple one-dimensional MUSIC spectrum is exploited to distinguish far-field and near-field sources and estimate the ranges of near-field sources. The proposed algorithm can avoid multidimensional search and parameter pairing. Simulation results demonstrate the good performance for localizing far-field sources, or near-field ones, or mixed field sources.

Dynamic ocean-tide effects on Earth's rotation

NASA Technical Reports Server (NTRS)

Dickman, S. R.

1993-01-01

This article develops 'broad-band' Liouville equations which are capable of determining the effects on the rotation of the Earth of a periodic excitation even at frequencies as high as semi-diurnal; these equations are then used to predict the rotational effects of altimetric, numerical and 32-constituent spherical harmonic ocean-tide models. The rotational model includes a frequency-dependent decoupled core, the effects of which are especially marked near retrograde diurnal frequencies; and a fully dynamic oceanic response, whose effects appear to be minor despite significant frequency dependence. The model also includes solid-earth effects which are frequency dependent as the result of both anelasticity at long periods and the fluid-core resonance at nearly diurnal periods. The effects of both tidal inertia and relative angular momentum on Earth rotation (polar motion, length of day, 'nutation' and Universal Time) are presented for 32 long- and short-period ocean tides determined as solutions to the author's spherical harmonic tide theory. The lengthening of the Chandler wobble period by the pole tide is also re-computed using the author's full theory. Additionally, using the spherical harmonic theory, tidal currents and their effects on rotation are determined for available numerical and altimetric tide height models. For all models, we find that the effects of tidal currents are at least as important as those of tide height for diurnal and semi-diurnal constituents.

Spherical harmonic representation of the main geomagnetic field for world charting and investigations of some fundamental problems of physics and geophysics

NASA Technical Reports Server (NTRS)

Barraclough, D. R.; Hide, R.; Leaton, B. R.; Lowes, F. J.; Malin, S. R. C.; Wilson, R. L. (Principal Investigator)

1981-01-01

The data processing of MAGSAT investigator B test tapes and data tapes, and tapes of selected data on 15 magnetically quiet days is reported. The 1980 World Chart spherical model was compared with the MAGSAT (3/80) and MAGSAT vector data were used in the models. An article on modelling the geomagnetic field using satellite data is included.

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

NASA Technical Reports Server (NTRS)

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.

Assessment of the suitability of GOCE-based geoid models for the unification of the North American vertical datums

NASA Astrophysics Data System (ADS)

Amjadiparvar, Babak; Sideris, Michael

2015-04-01

Precise gravimetric geoid heights are required when the unification of vertical datums is performed using the Geodetic Boundary Value Problem (GBVP) approach. Five generations of Global Geopotential Models (GGMs) derived from Gravity field and steady-state Ocean Circulation Explorer (GOCE) observations have been computed and released so far (available via IAG's International Centre for Global Earth Models, ICGEM, http://icgem.gfz-potsdam.de/ICGEM/). The performance of many of these models with respect to geoid determination has been studied in order to select the best performing model to be used in height datum unification in North America. More specifically, Release-3, 4 and 5 of the GOCE-based global geopotential models have been evaluated using GNSS-levelling data as independent control values. Comparisons against EGM2008 show that each successive release improves upon the previous one, with Release-5 models showing an improvement over EGM2008 in Canada and CONUS between spherical harmonic degrees 100 and 210. In Alaska and Mexico, a considerable improvement over EGM2008 was brought by the Release-5 models when used up to spherical harmonic degrees of 250 and 280, respectively. The positive impact of the Release-5 models was also felt when a gravimetric geoid was computed using the GOCE-based GGMs together with gravity and topography data in Canada. This geoid model, with appropriately modified Stokes kernel between spherical harmonic degrees 190 and 260, performed better than the official Canadian gravimetric geoid model CGG2013, thus illustrating the advantages of using the latest release GOCE-based models for vertical datum unification in North America.

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

NASA Astrophysics Data System (ADS)

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.

Data use investigation for the magnetic field satellite (MAGSAT) mission: Geomagnetic field forecasting and fluid dynamics of the core

NASA Technical Reports Server (NTRS)

Benton, E. R. (Principal Investigator)

1982-01-01

MAGSAT data were used to construct a variety of spherical harmonic models of the main geomagnetic field emanating from Earth's liquid core at poch 1980. These models were used to: (1) accurately determine the radius of Earth's core by a magnetic method, (2) calculate estimates, of the long-term ange of variation of geomagnetic Gauss coefficients; (3) establish a preferred truncation level for current spherical harmonic models of the main geomagnetic field from the core; (4) evaluate a method for taking account of electrical conduction in the mantle when the magnetic field is downward continued to the core-mantle boundary; and (5) establish that upwelling and downwelling of fluid motion at the top of the core is probably detectable, observationally. A fluid dynamics forecast model was not produced because of insufficient data.

Spherical Harmonics Functions Modelling of Meteorological Parameters in PWV Estimation

NASA Astrophysics Data System (ADS)

Deniz, Ilke; Mekik, Cetin; Gurbuz, Gokhan

2016-08-01

Aim of this study is to derive temperature, pressure and humidity observations using spherical harmonics modelling and to interpolate for the derivation of precipitable water vapor (PWV) of TUSAGA-Active stations in the test area encompassing 38.0°-42.0° northern latitudes and 28.0°-34.0° eastern longitudes of Turkey. In conclusion, the meteorological parameters computed by using GNSS observations for the study area have been modelled with a precision of ±1.74 K in temperature, ±0.95 hPa in pressure and ±14.88 % in humidity. Considering studies on the interpolation of meteorological parameters, the precision of temperature and pressure models provide adequate solutions. This study funded by the Scientific and Technological Research Council of Turkey (TUBITAK) (The Estimation of Atmospheric Water Vapour with GPS Project, Project No: 112Y350).

Spherical harmonics coefficients for ligand-based virtual screening of cyclooxygenase inhibitors.

PubMed

Wang, Quan; Birod, Kerstin; Angioni, Carlo; Grösch, Sabine; Geppert, Tim; Schneider, Petra; Rupp, Matthias; Schneider, Gisbert

2011-01-01

Molecular descriptors are essential for many applications in computational chemistry, such as ligand-based similarity searching. Spherical harmonics have previously been suggested as comprehensive descriptors of molecular structure and properties. We investigate a spherical harmonics descriptor for shape-based virtual screening. We introduce and validate a partially rotation-invariant three-dimensional molecular shape descriptor based on the norm of spherical harmonics expansion coefficients. Using this molecular representation, we parameterize molecular surfaces, i.e., isosurfaces of spatial molecular property distributions. We validate the shape descriptor in a comprehensive retrospective virtual screening experiment. In a prospective study, we virtually screen a large compound library for cyclooxygenase inhibitors, using a self-organizing map as a pre-filter and the shape descriptor for candidate prioritization. 12 compounds were tested in vitro for direct enzyme inhibition and in a whole blood assay. Active compounds containing a triazole scaffold were identified as direct cyclooxygenase-1 inhibitors. This outcome corroborates the usefulness of spherical harmonics for representation of molecular shape in virtual screening of large compound collections. The combination of pharmacophore and shape-based filtering of screening candidates proved to be a straightforward approach to finding novel bioactive chemotypes with minimal experimental effort.

A new method for gravity field recovery based on frequency analysis of spherical harmonics

NASA Astrophysics Data System (ADS)

Cai, Lin; Zhou, Zebing

2017-04-01

All existing methods for gravity field recovery are mostly based on the space-wise and time-wise approach, whose core processes are constructing the observation equations and solving them by the least square method. It's should be pointed that the least square method means the approximation. On the other hand, we can directly and precisely obtain the coefficients of harmonics by computing the Fast Fourier Transform (FFT) when we do 1-D data (time series) analysis. So the question whether we directly and precisely obtain the coefficients of spherical harmonic by computing 2-D FFT of measurements of satellite gravity mission is of great significance, since this may guide us to a new understanding of the signal components of gravity field and make us determine it quickly by taking advantage of FFT. Like the 1-D data analysis, the 2-D FFT of measurements of satellite can be computed rapidly. If we can determine the relationship between spherical harmonics and 2-D Fourier frequencies and the transfer function from measurements to spherical coefficients, the question mentioned above can be solved. So the objective of this research project is to establish a new method based on frequency analysis of spherical harmonic, which directly compute the confidents of spherical harmonic of gravity field, which is differ from recovery by least squares. There is a one to one correspondence between frequency spectrum and the time series in 1-D FFT. The 2-D FFT has a similar relationship to 1-D FFT. Owing to the fact that any degree or order (higher than one) of spherical function has multi frequencies and these frequencies may be aliased. Fortunately, the elements and ratio of these frequencies of spherical function can be determined, and we can compute the coefficients of spherical function from 2-D FFT. This relationship can be written as equations and equivalent to a matrix, which is solid and can be derived in advance. Until now the relationship has be determined. Some preliminary results, which only compute lower degree spherical harmonics, indicates that the difference between the input (EGM2008) and output (coefficients from recovery) is smaller than 5E-17, while the minimal precision of computer software (Matlab) is 2.2204E-16.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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 transformation of ICGEM geopotential models from ellipsoidal to spherical approximation. The transformation is applied to generate a spherical transform of EGM2008 (sphEGM2008) that can meaningfully be correlated degree-wise with the topographic potential. We exploit this new technique and compare a number of models of topographic potential constituents (e.g., potential implied by land topography, ocean water masses) based on the Earth2014 global relief model and a mass-layer forward modelling technique with sphEGM2008. Different to previous findings, our results show very significant short-scale correlation between Earth's gravitational potential and the potential generated by Earth's land topography (correlation +0.92, and 60% of EGM2008 signals are delivered through the forward modelling). Our tests reveal that the potential generated by Earth's oceans water masses is largely unrelated to the geopotential at short scales, suggesting that altimetry-derived gravity and/or bathymetric data sets are significantly underpowered at 5 arc-min scales. We further decompose the topographic potential into the Bouguer shell and terrain correction and show that they are responsible for about 20 and 25% of EGM2008 short-scale signals, respectively. As a general conclusion, the paper shows the importance of using compatible models in topographic/gravitational potential comparisons and recommends the use of SHCs together with spherical approximation or EHCs with ellipsoidal approximation in order to avoid biases in the correlation measures.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

Makarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism.We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) = (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) = (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star...

Backus Effect on a Perpendicular Errors in Harmonic Models of Real vs. Synthetic Data

NASA Technical Reports Server (NTRS)

Voorhies, C. V.; Santana, J.; Sabaka, T.

1999-01-01

Measurements of geomagnetic scalar intensity on a thin spherical shell alone are not enough to separate internal from external source fields; moreover, such scalar data are not enough for accurate modeling of the vector field from internal sources because of unmodeled fields and small data errors. Spherical harmonic models of the geomagnetic potential fitted to scalar data alone therefore suffer from well-understood Backus effect and perpendicular errors. Curiously, errors in some models of simulated 'data' are very much less than those in models of real data. We analyze select Magsat vector and scalar measurements separately to illustrate Backus effect and perpendicular errors in models of real scalar data. By using a model to synthesize 'data' at the observation points, and by adding various types of 'noise', we illustrate such errors in models of synthetic 'data'. Perpendicular errors prove quite sensitive to the maximum degree in the spherical harmonic expansion of the potential field model fitted to the scalar data. Small errors in models of synthetic 'data' are found to be an artifact of matched truncation levels. For example, consider scalar synthetic 'data' computed from a degree 14 model. A degree 14 model fitted to such synthetic 'data' yields negligible error, but amplifies 4 nT (rmss) added noise into a 60 nT error (rmss); however, a degree 12 model fitted to the noisy 'data' suffers a 492 nT error (rmms through degree 12). Geomagnetic measurements remain unaware of model truncation, so the small errors indicated by some simulations cannot be realized in practice. Errors in models fitted to scalar data alone approach 1000 nT (rmss) and several thousand nT (maximum).

Euler potentials of current-free fields expressed in spherical harmonics

NASA Technical Reports Server (NTRS)

Stern, David P.

1994-01-01

Given a magnetic field B = -del(vector differential operator)(sub gamma) with gamma expanded in spherical harmonics, it is shown that analytic Euler potentials may be derived for B if gamma is asymmetrical but contains only the contribution of a single index n. This work generalizes a result for sectorial harmonics with n = m, derived by Willis and Gardiner (1988).

Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution and terrain correction: An attempt of global numerical computations

NASA Technical Reports Server (NTRS)

Wang, Y. M.

1989-01-01

The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere-at least to the ellipsoid. The goal is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g sub 1 term). The terrain correction was also computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. The fast Fourier transformation was applied to the computations.

Spherical disharmonics in the Earth sciences and the spatial solution: Ridges, hotspots, slabs, geochemistry and tomography correlations

NASA Technical Reports Server (NTRS)

Ray, Terrill W.; Anderson, Don L.

1994-01-01

There is increasing use of statistical correlations between geophysical fields and between geochemical and geophysical fields in attempts to understand how the Earth works. Typically, such correlations have been based on spherical harmonic expansions. The expression of functions on the sphere as spherical harmonic series has many pitfalls, especially if the data are nonuniformly and/or sparsely sampled. Many of the difficulties involved in the use of spherical harmonic expansion techniques can be avoided through the use of spatial domain correlations, but this introduces other complications, such as the choice of a sampling lattice. Additionally, many geophysical and geochemical fields fail to satisfy the assumptions of standard statistical significance tests. This is especially problematic when the data values to be correlated with a geophysical field were collected at sample locations which themselves correlate with that field. This paper examines many correlations which have been claimed in the past between geochemistry and mantle tomography and between hotspot, ridge, and slab locations and tomography using both spherical harmonic coefficient correlations and spatial domain correlations. No conclusively significant correlations are found between isotopic geochemistry and mantle tomography. The Crough and Jurdy (short) hotspot location list shows statistically significant correlation with lowermost mantle tomography for degree 2 of the spherical harmonic expansion, but there are no statistically significant correlations in the spatial case. The Vogt (long) hotspot location list does not correlate with tomography anywhere in the mantle using either technique. Both hotspot lists show a strong correlation between hotspot locations and geoid highs when spatially correlated, but no correlations are revealed by spherical harmonic techniques. Ridge locations do not show any statistically significant correlations with tomography, slab locations, or the geoid; the strongest correlation is with lowermost mantle tomography, which is probably spurious. The most striking correlations are between mantle tomography and post-Pangean subducted slabs. The integrated locations of slabs correlate strongly with fast areas near the transition zone and the core-mantle boundary and with slow regions from 1022-1248 km depth. This seems to be consistent with the 'avalanching' downwellings which have been indicated by models of the mantle which include an endothermic phase transition at the 670-km discontinuity, although this is not a unique interpretation. Taken as a whole, these results suggest that slabs and associated cold downwellings are the dominant feature of mantle convection. Hotspot locations are no better correlated with lower mantle tomography than are ridge locations.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

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

PubMed

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.

The latitude dependence of the variance of zonally averaged quantities. [in polar meteorology with attention to geometrical effects of earth

NASA Technical Reports Server (NTRS)

North, G. R.; Bell, T. L.; Cahalan, R. F.; Moeng, F. J.

1982-01-01

Geometric characteristics of the spherical earth are shown to be responsible for the increase of variance with latitude of zonally averaged meteorological statistics. An analytic model is constructed to display the effect of a spherical geometry on zonal averages, employing a sphere labeled with radial unit vectors in a real, stochastic field expanded in complex spherical harmonics. The variance of a zonally averaged field is found to be expressible in terms of the spectrum of the vector field of the spherical harmonics. A maximum variance is then located at the poles, and the ratio of the variance to the zonally averaged grid-point variance, weighted by the cosine of the latitude, yields the zonal correlation typical of the latitude. An example is provided for the 500 mb level in the Northern Hemisphere compared to 15 years of data. Variance is determined to increase north of 60 deg latitude.

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

NASA Astrophysics Data System (ADS)

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.

A high resolution gravity model for Venus - GVM-1

NASA Technical Reports Server (NTRS)

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.

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

NASA Astrophysics Data System (ADS)

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 storm time IT state estimates for future studies. In particular, the ability to provide data assimilated estimation of the drivers of the IT system from high to low latitudes is a critical step toward forecasting the influence of geomagnetic storms on the near Earth space environment.

Venus Gravity: 180th Degree and Order Model

NASA Technical Reports Server (NTRS)

Konopliv, A. S.; Banerdt, W. B.; Sjogren, W. L.

1998-01-01

The Megallan Doppler radiometric tracking data provides unprecedented precision for spacecraft based gravity measurements with the maximum resolution approaching spherical harmonic degree and order 180 in selected equatorial regions.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

Markarov, V. V.; Murphy, D. W.

2007-01-01

We analyze the local field of stellar tangential velocities for a sample of 42,339 nonbinary Hipparcos stars with accurate parallaxes, using a vector spherical harmonic formalism. We derive simple relations between the parameters of the classical linear model (Ogorodnikov-Milne) of the local systemic field and low-degree terms of the general vector harmonic decomposition. Taking advantage of these relationships, we determine the solar velocity with respect to the local stars of (V(sub X), V(sub Y), V(sub Z)) (10.5, 18.5, 7.3) +/- 0.1 km s(exp -1) not corrected for the asymmetric drift with respect to the local standard of rest. If only stars more distant than 100 pc are considered, the peculiar solar motion is (V(sub X), V(sub Y), V(sub Z)) (9.9, 15.6, 6.9) +/- 0.2 km s(exp -1). The adverse effects of harmonic leakage, which occurs between the reflex solar motion represented by the three electric vector harmonics in the velocity space and higher degree harmonics in the proper-motion space, are eliminated in our analysis by direct subtraction of the reflex solar velocity in its tangential components for each star. The Oort parameters determined by a straightforward least-squares adjustment in vector spherical harmonics are A=14.0 +/- 1.4, B=13.1 +/- 1.2, K=1.1 +/- 1.8, and C=2.9 +/- 1.4 km s(exp -1) kpc(exp -1). The physical meaning and the implications of these parameters are discussed in the framework of a general linear model of the velocity field. We find a few statistically significant higher degree harmonic terms that do not correspond to any parameters in the classical linear model. One of them, a third-degree electric harmonic, is tentatively explained as the response to a negative linear gradient of rotation velocity with distance from the Galactic plane, which we estimate at approximately -20 km s(exp -1) kpc(exp -1). A similar vertical gradient of rotation velocity has been detected for more distant stars representing the thick disk (z greater than 1 kpc), but here we surmise its existence in the thin disk at z less than 200 pc. The most unexpected and unexplained term within the Ogorodnikov-Milne model is the first-degree magnetic harmonic, representing a rigid rotation of the stellar field about the axis -Y pointing opposite to the direction of rotation. This harmonic comes out with a statistically robust coefficient of 6.2 +/- 0.9 km s(exp -1) kpc(exp -1) and is also present in the velocity field of more distant stars. The ensuing upward vertical motion of stars in the general direction of the Galactic center and the downward motion in the anticenter direction are opposite to the vector field expected from the stationary Galactic warp model.

Density- and wavefunction-normalized Cartesian spherical harmonics for l ≤ 20.

PubMed

Michael, J Robert; Volkov, Anatoliy

2015-03-01

The widely used pseudoatom formalism [Stewart (1976). Acta Cryst. A32, 565-574; Hansen & Coppens (1978). Acta Cryst. A34, 909-921] in experimental X-ray charge-density studies makes use of real spherical harmonics when describing the angular component of aspherical deformations of the atomic electron density in molecules and crystals. The analytical form of the density-normalized Cartesian spherical harmonic functions for up to l ≤ 7 and the corresponding normalization coefficients were reported previously by Paturle & Coppens [Acta Cryst. (1988), A44, 6-7]. It was shown that the analytical form for normalization coefficients is available primarily for l ≤ 4 [Hansen & Coppens, 1978; Paturle & Coppens, 1988; Coppens (1992). International Tables for Crystallography, Vol. B, Reciprocal space, 1st ed., edited by U. Shmueli, ch. 1.2. Dordrecht: Kluwer Academic Publishers; Coppens (1997). X-ray Charge Densities and Chemical Bonding. New York: Oxford University Press]. Only in very special cases it is possible to derive an analytical representation of the normalization coefficients for 4 < l ≤ 7 (Paturle & Coppens, 1988). In most cases for l > 4 the density normalization coefficients were calculated numerically to within seven significant figures. In this study we review the literature on the density-normalized spherical harmonics, clarify the existing notations, use the Paturle-Coppens (Paturle & Coppens, 1988) method in the Wolfram Mathematica software to derive the Cartesian spherical harmonics for l ≤ 20 and determine the density normalization coefficients to 35 significant figures, and computer-generate a Fortran90 code. The article primarily targets researchers who work in the field of experimental X-ray electron density, but may be of some use to all who are interested in Cartesian spherical harmonics.

Zonal harmonic model of Saturn's magnetic field from Voyager 1 and 2 observations

NASA Technical Reports Server (NTRS)

Connerney, J. E. P.; Ness, N. F.; Acuna, M. H.

1982-01-01

An analysis of the magnetic field of Saturn is presented which takes into account both the Voyager 1 and 2 vector magnetic field observations. The analysis is based on the traditional spherical harmonic expansion of a scale potential to derive the magnetic field within 8 Saturn radii. A third-order zonal harmonic model fitted to Voyager 1 and 2 observations is found to be capable of predicting the magnetic field characteristics at one encounter based on those observed at another, unlike models including dipole and quadrupole terms only. The third-order model is noted to lead to significantly enhanced polar surface field intensities with respect to dipole models, and probably represents the axisymmetric part of a complex dynamo field.

Spherical harmonic results for the 3D Kobayashi Benchmark suite

DOE Office of Scientific and Technical Information (OSTI.GOV)

Brown, P N; Chang, B; Hanebutte, U R

1999-03-02

Spherical harmonic solutions are presented for the Kobayashi benchmark suite. The results were obtained with Ardra, a scalable, parallel neutron transport code developed at Lawrence Livermore National Laboratory (LLNL). The calculations were performed on the IBM ASCI Blue-Pacific computer at LLNL.

Spherical harmonic expansion of the Levitus Sea surface topography

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

Prior information for the stationary sea surface topography (SST) may be needed in altimetric solutions that intend to simultaneously improve the gravity field and determine the SST. For this purpose the oceanographically derived SST estimates are represented by a spherical harmonic expansion. The spherical harmonic coefficients are computed from a least squares adjustment of the data covering the majority of the oceanic regions of the world. Several tests are made to determine the optimum maximum degree of solution and the best configuration of the geometry of the data in order to obtain a solution that fits the data and also provides a good spectral representation of the SST.

Implications of two Holocene time-dependent geomagnetic models for cosmogenic nuclide production rate scaling

NASA Astrophysics Data System (ADS)

Lifton, Nathaniel

2016-01-01

The geomagnetic field is a major influence on in situ cosmogenic nuclide production rates at a given location (in addition to atmospheric pressure and, to a lesser extent, solar modulation effects). A better understanding of how past fluctuations in these influences affected production rates should allow more accurate application of cosmogenic nuclides. As such, this work explores the cosmogenic nuclide production rate scaling implications of two recent time-dependent spherical harmonic geomagnetic models spanning the Holocene. Korte and Constable (2011, Phys. Earth Planet. Inter.188, 247-259) and Korte et al. (2011, Earth Planet. Sci. Lett. 312, 497-505) recently updated earlier spherical harmonic paleomagnetic models with new paleomagnetic data from sediment cores in addition to new archeomagnetic and volcanic data. These updated models offer improved resolution and accuracy over the previous versions, in part due to increased temporal and spatial data coverage. In addition, Pavón-Carrasco et al. (2014, Earth Planet. Sci. Lett. 388, 98-109) developed another time-dependent spherical harmonic model of the Holocene geomagnetic field, based solely on archeomagnetic and volcanic paleomagnetic data from the same underlying paleomagnetic database as the Korte et al. models, but extending to 14 ka. With the new models as input, trajectory-traced estimates of effective vertical cutoff rigidity (RC - the standard method for ordering cosmic ray data) yield significantly different time-integrated scaling predictions when compared to each other and to results using the earlier models. In addition, predictions of each new model using RC are tested empirically using recently published production rate calibration data for both 10Be and 3He, and compared to predictions using corresponding time-varying geocentric dipolar RC formulations and a static geocentric axial dipole (GAD) model. Results for the few calibration sites from geomagnetically sensitive regions suggest that the Pavón-Carrasco et al. (2014) time-varying dipolar model tends to predict sea level, high latitude production rates more in line with those from calibration sites not affected by geomagnetic variations. This suggests that uncertainties arising from hemispheric and temporal sampling biases in the Holocene spherical harmonic models considered here, combined with the currently limited spatial and temporal distribution of production rate calibration sites as empirical tests, limit the robustness of the non-dipole aspects of these models for production rate scaling. These analyses should be revisited as such models improve and additional calibration sites become available.

Spherical Tensor Calculus for Local Adaptive Filtering

NASA Astrophysics Data System (ADS)

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.

Parameterization of deformed nuclei for Glauber modeling in relativistic heavy ion collisions

DOE PAGES

Sorensen, P.; Tang, A. H.; Videbaek, F.; ...

2015-08-04

In this study, the density distributions of large nuclei are typically modeled with a Woods–Saxon distribution characterized by a radius R 0 and skin depth a. Deformation parameters β are then introduced to describe non-spherical nuclei using an expansion in spherical harmonics R 0(1+β 2Y 2 0+β 4Y 4 0). But when a nucleus is non-spherical, the R 0 and a inferred from electron scattering experiments that integrate over all nuclear orientations cannot be used directly as the parameters in the Woods–Saxon distribution. In addition, the β 2 values typically derived from the reduced electric quadrupole transition probability B(E2)↑ aremore » not directly related to the β 2 values used in the spherical harmonic expansion. B(E2)↑ is more accurately related to the intrinsic quadrupole moment Q 0 than to β 2. One can however calculate Q 0 for a given β 2 and then derive B(E2)↑ from Q 0. In this paper we calculate and tabulate the R 0, a , and β 2 values that when used in a Woods–Saxon distribution, will give results consistent with electron scattering data. We then present calculations of the second and third harmonic participant eccentricity (ε 2 and ε 3) with the new and old parameters. We demonstrate that ε 3 is particularly sensitive to a and argue that using the incorrect value of a has important implications for the extraction of viscosity to entropy ratio (η/s) from the QGP created in Heavy Ion collisions.« less

A complete set of two-dimensional harmonic vortices on a spherical surface

NASA Astrophysics Data System (ADS)

Esparza, Christian; Rendón, Pablo Luis; Ley Koo, Eugenio

2018-03-01

The solutions of the Euler equations on a spherical surface are constructed, starting from a vector velocity potential A in the radial direction and with a two-dimensional spherical harmonic variation of order m and well-defined parity under \\varphi \\mapsto -\\varphi . The solutions are well-behaved on the entire surface and continuous at the position of a parallel circle θ ={θ }0, where the vorticity is shown to be harmonically distributed. The velocity field is evaluated as the curl of the vector potential: it is shown that the velocity is divergenceless and distributed on the spherical surface. Its polar components at the parallel circle are shown to be continuous, confirming its divergenceless nature, while its azimuthal components are discontinuous at the circle, and their discontinuity is a measure of the vorticity in the radial direction. A closed form for the velocity field lines is also obtained in terms of fixed values of the scalar harmonic function associated with the vector potential. Additionally, the connections of the solutions on a spherical surface with their circular, elliptic and bipolar counterparts on the equatorial plane are implemented via stereographic projections.

Remote listening and passive acoustic detection in a 3-D environment

NASA Astrophysics Data System (ADS)

Barnhill, Colin

Teleconferencing environments are a necessity in business, education and personal communication. They allow for the communication of information to remote locations without the need for travel and the necessary time and expense required for that travel. Visual information can be communicated using cameras and monitors. The advantage of visual communication is that an image can capture multiple objects and convey them, using a monitor, to a large group of people regardless of the receiver's location. This is not the case for audio. Currently, most experimental teleconferencing systems' audio is based on stereo recording and reproduction techniques. The problem with this solution is that it is only effective for one or two receivers. To accurately capture a sound environment consisting of multiple sources and to recreate that for a group of people is an unsolved problem. This work will focus on new methods of multiple source 3-D environment sound capture and applications using these captured environments. Using spherical microphone arrays, it is now possible to capture a true 3-D environment A spherical harmonic transform on the array's surface allows us to determine the basis functions (spherical harmonics) for all spherical wave solutions (up to a fixed order). This spherical harmonic decomposition (SHD) allows us to not only look at the time and frequency characteristics of an audio signal but also the spatial characteristics of an audio signal. In this way, a spherical harmonic transform is analogous to a Fourier transform in that a Fourier transform transforms a signal into the frequency domain and a spherical harmonic transform transforms a signal into the spatial domain. The SHD also decouples the input signals from the microphone locations. Using the SHD of a soundfield, new algorithms are available for remote listening, acoustic detection, and signal enhancement The new algorithms presented in this paper show distinct advantages over previous detection and listening algorithms especially for multiple speech sources and room environments. The algorithms use high order (spherical harmonic) beamforming and power signal characteristics for source localization and signal enhancement These methods are applied to remote listening, surveillance, and teleconferencing.

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

NASA Astrophysics Data System (ADS)

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.

Seasonal and Static Gravity Field of Mars from MGS, Mars Odyssey and MRO Radio Science

NASA Technical Reports Server (NTRS)

Genova, Antonio; Goossens, Sander; Lemoine, Frank G.; Mazarico, Erwan; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.

2016-01-01

We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k 2 Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k 2 solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k 2 of 0.1697 +/-0.0027 (3- sigma). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C 30 and, for the first time, C 50 . Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C 30 for approx.1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics ( l = 60–80) than previous solutions.

Seasonal and static Gravity Field of Mars from MGS, Mars Odyssey and MRO Radio Science

NASA Technical Reports Server (NTRS)

Genova, Antonio; Goossens, Sander; Lemoine, Frank G.; Mazarico, Erwan; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.

2016-01-01

We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k(sub 2) Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k(sub 2) solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k(sub 2) of 0.1697 +/- 0.0027 (3- sigma). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C(sub 30) and, for the first time, C 50. Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C(sub 30) for approximately 1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics ( l = 60-80) than previous solutions.

Orthogonality of spherical harmonic coefficients

NASA Astrophysics Data System (ADS)

McLeod, M. G.

1980-08-01

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

The magnetic field at the core-mantle boundary

NASA Technical Reports Server (NTRS)

Bloxham, J.; Gubbins, D.

1985-01-01

Models of the geomagnetic field are, in general, produced from a least-squares fit of the coefficients in a truncated spherical harmonic expansion to the available data. Downward continuation of such models to the core-mantle boundary (CMB) is an unstable process: the results are found to be critically dependent on the choice of truncation level. Modern techniques allow this fundamental difficulty to be circumvented. The method of stochastic inversion is applied to modeling the geomagnetic field. Prior information is introduced by requiring that the spectrum of spherical harmonic coefficients to fall-off in a particular manner which is consistent with the Ohmic heating in the core having a finite lower bound. This results in models with finite errors in the radial field at the CMB. Curves of zero radial field can then be determined and integrals of the radial field over patches on the CMB bounded by these null-flux curves calculated. With the assumption of negligible magnetic diffusion in the core; frozen-flux hypothesis, these integrals are time-invariant.

Combined study of the solar neighbourhood kinematics - Spherical harmonics and Taylor expansions

NASA Astrophysics Data System (ADS)

Hernandez-Pajares, M.; Nunez, J.

1990-08-01

This paper relates two methods of analyzing the kinematic parameters of the local macroscopic motions of the Galaxy: (1) the Ogorodnikov-Milne model (OM) that consists in the three-dimensional Taylor expansion of the mean velocity field, and (2) the two-dimensional spherical harmonic development of the velocity components (SH). The theoretical relations between the SH coefficients and the second-order OM ones for the radial velocity v(r), and the galactic heliocentric components of the velocity U, V, W are presented. Only the hypothesis of separability of the stellar density function of the sample into angular and radial parts is needed. They are applied to 4732 A-M stars included in the Figueras (1986) sample.

GMD Coupling to Power Systems and Disturbance Mitigation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rivera, Michael Kelly; Bent, Russell Whitford

Presentation includes slides on Geomagnetic Disturbance: Ground Fields; Geomagnetic Disturbance: Coupling to Bulk Electric System; Geomagnetic Disturbance: Transformers; GMD Assessment Workflow (TPL-007-1); FERC order 830; Goals; SuperMag (1 min data) Nov. 20-21, 2003 Storm (DST = -422); Spherical Harmonics; Spherical Harmonics Nov. 20-21, 2003 Storm (DST = -422); DST vs HN0,0; Fluctuations vs. DST; Fluctuations; Conclusions and Next Steps; GMD Assessment Workflow (TPL-007-1); EMP E3 Coupling to Texas 2000 Bus Model; E3 Coupling Comparison (total GIC) Varying Ground Zero; E3 Coupling Comparison (total MVAR) Varying Ground Zero; E3 Coupling Comparison (GIC) at Peak Ground Zero; E3 Coupling Comparison (GIC) atmore » Peak Ground Zero; and Conclusion.« less

Toward a Global Horizontal and Vertical Elastic Load Deformation Model Derived from GRACE and GNSS Station Position Time Series

NASA Astrophysics Data System (ADS)

Chanard, Kristel; Fleitout, Luce; Calais, Eric; Rebischung, Paul; Avouac, Jean-Philippe

2018-04-01

We model surface displacements induced by variations in continental water, atmospheric pressure, and nontidal oceanic loading, derived from the Gravity Recovery and Climate Experiment (GRACE) for spherical harmonic degrees two and higher. As they are not observable by GRACE, we use at first the degree-1 spherical harmonic coefficients from Swenson et al. (2008, https://doi.org/10.1029/2007JB005338). We compare the predicted displacements with the position time series of 689 globally distributed continuous Global Navigation Satellite System (GNSS) stations. While GNSS vertical displacements are well explained by the model at a global scale, horizontal displacements are systematically underpredicted and out of phase with GNSS station position time series. We then reestimate the degree 1 deformation field from a comparison between our GRACE-derived model, with no a priori degree 1 loads, and the GNSS observations. We show that this approach reconciles GRACE-derived loading displacements and GNSS station position time series at a global scale, particularly in the horizontal components. Assuming that they reflect surface loading deformation only, our degree-1 estimates can be translated into geocenter motion time series. We also address and assess the impact of systematic errors in GNSS station position time series at the Global Positioning System (GPS) draconitic period and its harmonics on the comparison between GNSS and GRACE-derived annual displacements. Our results confirm that surface mass redistributions observed by GRACE, combined with an elastic spherical and layered Earth model, can be used to provide first-order corrections for loading deformation observed in both horizontal and vertical components of GNSS station position time series.

Spectral analysis of the gravity and topography of Mars

NASA Technical Reports Server (NTRS)

Bills, Bruce G.; Frey, Herbert V.; Kiefer, Walter S.; Nerem, R. Steven; Zuber, Maria T.

1993-01-01

New spherical harmonic models of the gravity and topography of Mars place important constraints on the structure and dynamics of the interior. The gravity and topography models are significantly phase coherent for harmonic degrees n less than 30 (wavelengths greater than 700 km). Loss of coherence below that wavelength is presumably due to inadequacies of the models, rather than a change in behavior of the planet. The gravity/topography admittance reveals two very different spectral domains: for n greater than 4, a simple Airy compensation model, with mean depth of 100 km, faithfully represents the observed pattern; for degrees 2 and 3, the effective compensation depths are 1400 and 550 km, respectively, strongly arguing for dynamic compensation at those wavelengths. The gravity model has been derived from a reanalysis of the tracking data for Mariner 9 and the Viking Orbiters, The topography model was derived by harmonic analysis of the USGS digital elevation model of Mars. Before comparing gravity and topography for internal structure inferences, we must ensure that both are consistently referenced to a hydrostatic datum. For the gravity, this involves removal of hydrostatic components of the even degree zonal coefficients. For the topography, it involves adding the degree 4 equipotential reference surface, to get spherically referenced values, and then subtracting the full degree 50 equipotential. Variance spectra and phase coherence of orthometric heights and gravity anomalies are addressed.

Non-singular spherical harmonic expressions of geomagnetic vector and gradient tensor fields in the local north-oriented reference frame

NASA Astrophysics Data System (ADS)

Du, J.; Chen, C.; Lesur, V.; Wang, L.

2014-12-01

General expressions of magnetic vector (MV) and magnetic gradient tensor (MGT) in terms of the first- and second-order derivatives of spherical harmonics at different degrees and orders, are relatively complicated and singular at the poles. In this paper, we derived alternative non-singular expressions for the MV, the MGT and also the higher-order partial derivatives of the magnetic field in local north-oriented reference frame. Using our newly derived formulae, the magnetic potential, vector and gradient tensor fields at an altitude of 300 km are calculated based on a global lithospheric magnetic field model GRIMM_L120 (version 0.0) and the main magnetic field model of IGRF11. The corresponding results at the poles are discussed and the validity of the derived formulas is verified using the Laplace equation of the potential field.

Investigation on plasmonic responses in multilayered nanospheres including asymmetry and spatial nonlocal effects

NASA Astrophysics Data System (ADS)

Dong, Tianyu; Shi, Yi; Liu, Hui; Chen, Feng; Ma, Xikui; Mittra, Raj

2017-12-01

In this work, we present a rigorous approach for analyzing the optical response of multilayered spherical nano-particles comprised of either plasmonic metal or dielectric, when there is no longer radial symmetry and when nonlocality is included. The Lorenz-Mie theory is applied, and a linearized hydrodynamic Drude model as well as the general nonlocal optical response model for the metals are employed. Additional boundary conditions, viz., the continuity of normal components of polarization current density and the continuity of first-order pressure of free electron density, respectively, are incorporated when handling interfaces involving metals. The application of spherical addition theorems, enables us to express a spherical harmonic about one origin to spherical harmonics about a different origin, and leads to a linear system of equations for the inward- and outward-field modal coefficients for all the layers in the nanoparticle. Scattering matrices at interfaces are obtained and cascaded to obtain the expansion coefficients, to yield the final solution. Through extensive modelling of stratified concentric and eccentric metal-involved spherical nanoshells illuminating by a plane wave, we show that, within a nonlocal description, significant modifications of plasmonic response appear, e.g. a blue-shift in the extinction / scattering spectrum and a broadening spectrum of the resonance. In addition, it has been demonstrated that core-shell nanostructures provide an option for tunable Fano-resonance generators. The proposed method shows its capability and flexibility to analyze the nonlocal response of eccentric hybrid metal-dielectric multilayer structures as well as adjoined metal-involved nanoparticles, even when the number of layers is large.

A novel approach for quantitative harmonization in PET.

PubMed

Namías, M; Bradshaw, T; Menezes, V O; Machado, M A D; Jeraj, R

2018-05-04

Positron emission tomography (PET) imaging allows for measurement of activity concentrations of a given radiotracer in vivo. The quantitative capabilities of PET imaging are particularly important in the context of monitoring response to treatment, where quantitative changes in tracer uptake could be used as a biomarker of treatment response. Reconstruction algorithms and settings have a significant impact on PET quantification. In this work we introduce a novel harmonization methodology requiring only a simple cylindrical phantom and show that it can match the performance of more complex harmonization approaches based on phantoms with spherical inserts. Resolution and noise measurements from cylindrical phantoms are used to simulate the spherical inserts from NEMA image quality phantoms. An optimization algorithm was used to find the optimal smoothing filters for the simulated NEMA phantom images to identify those that best harmonized the PET scanners. Our methodology was tested on seven different PET models from two manufacturers installed at five institutions. Our methodology is able to predict contrast recovery coefficients (CRCs) from NEMA phantoms with errors within  ±5.2% for CRCmax and  ±3.7% for CRCmean (limits of agreement  =  95%). After applying the proposed harmonization protocol, all the CRC values were within the tolerances from EANM. Quantitative harmonization in compliance with the EARL FDG-PET/CT accreditation program is achieved in a simpler way, without the need of NEMA phantoms. This may lead to simplified scanner harmonization workflows more accessible to smaller institutions.

An Improved 360 Degree and Order Model of Venus Topography

NASA Technical Reports Server (NTRS)

Rappaport, Nicole J.; Konopliv, Alex S.; Kucinskas, Algis B.; Ford, Peter G.

1999-01-01

We present an improved 360 degree and order spherical harmonic solution for Venus' topography. The new model uses the most recent set of Venus altimetry data with spacecraft positions derived from a recent high resolution gravity model. Geometric analysis indicates that the offset between the center of mass and center of figure of Venus is about 10 times smaller than that for the Earth, the Moon, or Mars. Statistical analyses confirm that the RMS topography follows a power law over the central part of the spectrum. Compared to the previous topography model, the new model is more highly correlated with Venus' harmonic gravity field.

Normalization and Implementation of Three Gravitational Acceleration Models

NASA Technical Reports Server (NTRS)

Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.; Gottlieb, Robert G.

2016-01-01

Unlike the uniform density spherical shell approximations of Newton, the consequence of spaceflight in the real universe is that gravitational fields are sensitive to the asphericity of their generating central bodies. The gravitational potential of an aspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities that must be removed to generalize the method and solve for any possible orbit, including polar orbits. Samuel Pines, Bill Lear, and Robert Gottlieb developed three unique algorithms to eliminate these singularities. This paper documents the methodical normalization of two of the three known formulations for singularity-free gravitational acceleration (namely, the Lear and Gottlieb algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre polynomials and Associated Legendre Functions (ALFs) for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Anisotropic Developments for Homogeneous Shear Flows

NASA Technical Reports Server (NTRS)

Cambon, Claude; Rubinstein, Robert

2006-01-01

The general decomposition of the spectral correlation tensor R(sub ij)(k) by Cambon et al. (J. Fluid Mech., 202, 295; J. Fluid Mech., 337, 303) into directional and polarization components is applied to the representation of R(sub ij)(k) by spherically averaged quantities. The decomposition splits the deviatoric part H(sub ij)(k) of the spherical average of R(sub ij)(k) into directional and polarization components H(sub ij)(sup e)(k) and H(sub ij)(sup z)(k). A self-consistent representation of the spectral tensor in the limit of weak anisotropy is constructed in terms of these spherically averaged quantities. The directional polarization components must be treated independently: models that attempt the same representation of the spectral tensor using the spherical average H(sub ij)(k) alone prove to be inconsistent with Navier-Stokes dynamics. In particular, a spectral tensor consistent with a prescribed Reynolds stress is not unique. The degree of anisotropy permitted by this theory is restricted by realizability requirements. Since these requirements will be less severe in a more accurate theory, a preliminary account is given of how to generalize the formalism of spherical averages to higher expansion of the spectral tensor. Directionality is described by a conventional expansion in spherical harmonics, but polarization requires an expansion in tensorial spherical harmonics generated by irreducible representations of the spatial rotation group SO(exp 3). These expansions are considered in more detail in the special case of axial symmetry.

New GRACE-Derived Storage Change Estimates Using Empirical Mode Extraction

NASA Astrophysics Data System (ADS)

Aierken, A.; Lee, H.; Yu, H.; Ate, P.; Hossain, F.; Basnayake, S. B.; Jayasinghe, S.; Saah, D. S.; Shum, C. K.

2017-12-01

Estimated mass change from GRACE spherical harmonic solutions have north/south stripes and east/west banded errors due to random noise and modeling errors. Low pass filters like decorrelation and Gaussian smoothing are typically applied to reduce noise and errors. However, these filters introduce leakage errors that need to be addressed. GRACE mascon estimates (JPL and CSR mascon solutions) do not need decorrelation or Gaussian smoothing and offer larger signal magnitudes compared to the GRACE spherical harmonics (SH) filtered results. However, a recent study [Chen et al., JGR, 2017] demonstrated that both JPL and CSR mascon solutions also have leakage errors. We developed a new postprocessing method based on empirical mode decomposition to estimate mass change from GRACE SH solutions without decorrelation and Gaussian smoothing, the two main sources of leakage errors. We found that, without any post processing, the noise and errors in spherical harmonic solutions introduced very clear high frequency components in the spatial domain. By removing these high frequency components and reserve the overall pattern of the signal, we obtained better mass estimates with minimum leakage errors. The new global mass change estimates captured all the signals observed by GRACE without the stripe errors. Results were compared with traditional methods over the Tonle Sap Basin in Cambodia, Northwestern India, Central Valley in California, and the Caspian Sea. Our results provide larger signal magnitudes which are in good agreement with the leakage corrected (forward modeled) SH results.

Spherical nanoindentation stress-strain analysis, Version 1

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weaver, Jordan S.; Turner, David; Miller, Calvin

Nanoindentation is a tool that allows the mechanical response of a variety of materials at the nano to micron length scale to be measured. Recent advances in spherical nanoindentation techniques have allowed for a more reliable and meaningful characterization of the mechanical response from nanoindentation experiments in the form on an indentation stress-strain curve. This code base, Spin, is written in MATLAB (The Mathworks, Inc.) and based on the analysis protocols developed by S.R. Kalidindi and S. Pathak [1, 2]. The inputs include the displacement, load, harmonic contact stiffness, harmonic displacement, and harmonic load from spherical nanoindentation tests in themore » form of an Excel (Microsoft) spreadsheet. The outputs include indentation stress-strain curves and indentation properties as well their variance due to the uncertainty of the zero-point correction in the form of MATLAB data (.mat) and figures (.png). [1] S. Pathak, S.R. Kalidindi. Spherical nanoindentation stress–strain curves, Mater. Sci. Eng R-Rep 91 (2015). [2] S.R. Kalidindi, S. Pathak. Determination of the effective zero-point and the extraction of spherical nanoindentation stress-strain curves, Acta Materialia 56 (2008) 3523-3532.« less

Geomagnetic temporal change: 1903-1982 - A spline representation

NASA Technical Reports Server (NTRS)

Langel, R. A.; Kerridge, D. J.; Barraclough, D. R.; Malin, S. R. C.

1986-01-01

The secular variation of the earth's magnetic field is itself subject to temporal variations. These are investigated with the aid of the coefficients of a series of spherical harmonic models of secular variation deduced from data for the interval 1903-1982 from the worldwide network of magnetic observatories. For some studies it is convenient to approximate the time variation of the spherical harmonic coefficients with a smooth, continuous, function; for this a spline fitting is used. The phenomena that are investigated include periodicities, discontinuities, and correlation with the length of day. The numerical data presented will be of use for further investigations and for the synthesis of secular variation at any place and at any time within the interval of the data - they are not appropriate for temporal extrapolations.

Are Superplumes a Myth?

NASA Astrophysics Data System (ADS)

Steinberger, Bernhard; Conrad, Clinton

2017-04-01

Two large seismically slow lower mantle regions beneath the Pacific and Africa are sometimes referred to as "superplumes". This names evokes associations of large-scale active upwellings, however it is not clear whether these are real, or rather just regular mantle plumes occur more frequently in these regions. Here we study the implications of new results on dynamic topography, which would be associated with active upwellings, on this question. Recently, Hoggard et al. (2016) developed a detailed model of marine residual topography, after subtracting isostatic crustal topography. Combining this with results from continents, a global model can be expanded in spherical harmonics. Comparison with dynamic topography derived from mantle flow models inferred from seismic tomography (Steinberger, 2016) yields overall good agreement and similar power spectra, except at spherical harmonic degree two where mantle flow models predict about six times as much power as is inferred from observations: Mantle flow models feature two large-scale antipodal upwellings at the seismically slow regions, whereas the actual topography gives only little indication of these. We will discuss here what this discrepancy could possibly mean and how it could be resolved.

Calculation of the Transition Matrix for the Scattering of Acoustic Waves from a Thin Elastic Spherical Shell Using the ATILA Finite Element Code

DTIC Science & Technology

1994-03-01

products of radial Hankel functions and spherical harmonics. The chosen driving frequency was 474 Hz, corresponding to a value of ka 1, where k is the...spherical harmonics. The chosen driving frequency was 474 Hz, corresponding to a value of ka = 1, where k is the wavenumber of sound in water and a is...wife Adriana for her support, understanding, and for her help in typing this thesis. vi I. INTRODUCTION The utilization of sonar systems in

High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data.

PubMed

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

2014-05-28

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 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. 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. We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models.

High-resolution local gravity model of the south pole of the Moon from GRAIL extended mission data

PubMed Central

Goossens, Sander; 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 1/6° by 1/6° (equivalent to that of a degree and order 1080 model in spherical harmonics), covering a cap over the south pole with a radius of 40°. 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. Key Points We present a high-resolution gravity model of the south pole of the Moon Improved correlations with topography to higher degrees than global models Improved fits to the data and reduced striping that is present in global models PMID:26074637

The point spread function of the human head and its implications for transcranial current stimulation

NASA Astrophysics Data System (ADS)

Dmochowski, Jacek P.; Bikson, Marom; Parra, Lucas C.

2012-10-01

Rational development of transcranial current stimulation (tCS) requires solving the ‘forward problem’: the computation of the electric field distribution in the head resulting from the application of scalp currents. Derivation of forward models has represented a major effort in brain stimulation research, with model complexity ranging from spherical shells to individualized head models based on magnetic resonance imagery. Despite such effort, an easily accessible benchmark head model is greatly needed when individualized modeling is either undesired (to observe general population trends as opposed to individual differences) or unfeasible. Here, we derive a closed-form linear system which relates the applied current to the induced electric potential. It is shown that in the spherical harmonic (Fourier) domain, a simple scalar multiplication relates the current density on the scalp to the electric potential in the brain. Equivalently, the current density in the head follows as the spherical convolution between the scalp current distribution and the point spread function of the head, which we derive. Thus, if one knows the spherical harmonic representation of the scalp current (i.e. the electrode locations and current intensity to be employed), one can easily compute the resulting electric field at any point inside the head. Conversely, one may also readily determine the scalp current distribution required to generate an arbitrary electric field in the brain (the ‘backward problem’ in tCS). We demonstrate the simplicity and utility of the model with a series of characteristic curves which sweep across a variety of stimulation parameters: electrode size, depth of stimulation, head size and anode-cathode separation. Finally, theoretically optimal montages for targeting an infinitesimal point in the brain are shown.

A global estimate of the Earth's magnetic crustal thickness

NASA Astrophysics Data System (ADS)

Vervelidou, Foteini; Thébault, Erwan

2014-05-01

The Earth's lithosphere is considered to be magnetic only down to the Curie isotherm. Therefore the Curie isotherm can, in principle, be estimated by analysis of magnetic data. Here, we propose such an analysis in the spectral domain by means of a newly introduced regional spatial power spectrum. This spectrum is based on the Revised Spherical Cap Harmonic Analysis (R-SCHA) formalism (Thébault et al., 2006). We briefly discuss its properties and its relationship with the Spherical Harmonic spatial power spectrum. This relationship allows us to adapt any theoretical expression of the lithospheric field power spectrum expressed in Spherical Harmonic degrees to the regional formulation. We compared previously published statistical expressions (Jackson, 1994 ; Voorhies et al., 2002) to the recent lithospheric field models derived from the CHAMP and airborne measurements and we finally developed a new statistical form for the power spectrum of the Earth's magnetic lithosphere that we think provides more consistent results. This expression depends on the mean magnetization, the mean crustal thickness and a power law value that describes the amount of spatial correlation of the sources. In this study, we make a combine use of the R-SCHA surface power spectrum and this statistical form. We conduct a series of regional spectral analyses for the entire Earth. For each region, we estimate the R-SCHA surface power spectrum of the NGDC-720 Spherical Harmonic model (Maus, 2010). We then fit each of these observational spectra to the statistical expression of the power spectrum of the Earth's lithosphere. By doing so, we estimate the large wavelengths of the magnetic crustal thickness on a global scale that are not accessible directly from the magnetic measurements due to the masking core field. We then discuss these results and compare them to the results we obtained by conducting a similar spectral analysis, but this time in the cartesian coordinates, by means of a published statistical expression (Maus et al., 1997). We also compare our results to crustal thickness global maps derived by means of additional geophysical data (Purucker et al., 2002).

Orbital Disturbance Analysis due to the Lunar Gravitational Potential and Deviation Minimization through the Trajectory Control in Closed Loop

NASA Astrophysics Data System (ADS)

Gonçalves, L. D.; Rocco, E. M.; de Moraes, R. V.

2013-10-01

A study evaluating the influence due to the lunar gravitational potential, modeled by spherical harmonics, on the gravity acceleration is accomplished according to the model presented in Konopliv (2001). This model provides the components x, y and z for the gravity acceleration at each moment of time along the artificial satellite orbit and it enables to consider the spherical harmonic degree and order up to100. Through a comparison between the gravity acceleration from a central field and the gravity acceleration provided by Konopliv's model, it is obtained the disturbing velocity increment applied to the vehicle. Then, through the inverse problem, the Keplerian elements of perturbed orbit of the satellite are calculated allowing the orbital motion analysis. Transfer maneuvers and orbital correction of lunar satellites are simulated considering the disturbance due to non-uniform gravitational potential of the Moon, utilizing continuous thrust and trajectory control in closed loop. The simulations are performed using the Spacecraft Trajectory Simulator-STRS, Rocco (2008), which evaluate the behavior of the orbital elements, fuel consumption and thrust applied to the satellite over the time.

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

NASA Technical Reports Server (NTRS)

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.

Global evaluation of new GRACE mascon products for hydrologic applications

NASA Astrophysics Data System (ADS)

Scanlon, Bridget R.; Zhang, Zizhan; Save, Himanshu; Wiese, David N.; Landerer, Felix W.; Long, Di; Longuevergne, Laurent; Chen, Jianli

2016-12-01

Recent developments in mascon (mass concentration) solutions for GRACE (Gravity Recovery and Climate Experiment) satellite data have significantly increased the spatial localization and amplitude of recovered terrestrial Total Water Storage anomalies (TWSA); however, land hydrology applications have been limited. Here we compare TWSA from April 2002 through March 2015 from (1) newly released GRACE mascons from the Center for Space Research (CSR-M) with (2) NASA JPL mascons (JPL-M), and with (3) CSR Tellus gridded spherical harmonics rescaled (sf) (CSRT-GSH.sf) in 176 river basins, ˜60% of the global land area. Time series in TWSA mascons (CSR-M and JPL-M) and spherical harmonics are highly correlated (rank correlation coefficients mostly >0.9). The signal from long-term trends (up to ±20 mm/yr) is much less than that from seasonal amplitudes (up to 250 mm). Net long-term trends, summed over all 176 basins, are similar for CSR and JPL mascons (66-69 km3/yr) but are lower for spherical harmonics (˜14 km3/yr). Long-term TWSA declines are found mostly in irrigated basins (-41 to -69 km3/yr). Seasonal amplitudes agree among GRACE solutions, increasing confidence in GRACE-based seasonal fluctuations. Rescaling spherical harmonics significantly increases agreement with mascons for seasonal fluctuations, but less for long-term trends. Mascons provide advantages relative to spherical harmonics, including (1) reduced leakage from land to ocean increasing signal amplitude, and (2) application of geophysical data constraints during processing with little empirical postprocessing requirements, making it easier for nongeodetic users. Results of this product intercomparison should allow hydrologists to better select suitable GRACE solutions for hydrologic applications.

Characteristics of cosmic ray pole-equator anisotropy derived from spherical harmonic analysis of neutron monitor data

NASA Technical Reports Server (NTRS)

Takahashi, H.; Yahagi, N.

1985-01-01

The spherical harmonic analysis of cosmic ray neutron data from the worldwide network neutron monitor stations during the years, 1966 to 1969 was carried out. The second zonal harmonic component obtained from the analysis corresponds to the Pole-Equator anisotropy of the cosmic ray neutron intensity. Such an anisotropy makes a semiannual variation. In addition to this, it is shown that the Pole-Equator anisotropy makes a variation depending on the interplanetary magnetic field (IMF) sector polarities around the passages of the IMF sector boundary. A mechanism to interpret these results is also discussed.

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

NASA Astrophysics Data System (ADS)

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.

Is the Non-Dipole Magnetic Field Random?

NASA Technical Reports Server (NTRS)

Walker, Andrew D.; Backus, George E.

1996-01-01

Statistical modelling of the Earth's magnetic field B has a long history. In particular, the spherical harmonic coefficients of scalar fields derived from B can be treated as Gaussian random variables. In this paper, we give examples of highly organized fields whose spherical harmonic coefficients pass tests for independent Gaussian random variables. The fact that coefficients at some depth may be usefully summarized as independent samples from a normal distribution need not imply that there really is some physical, random process at that depth. In fact, the field can be extremely structured and still be regarded for some purposes as random. In this paper, we examined the radial magnetic field B(sub r) produced by the core, but the results apply to any scalar field on the core-mantle boundary (CMB) which determines B outside the CMB.

A spherical harmonics method for asteroid pole determination

NASA Technical Reports Server (NTRS)

Lumme, K.; Karttunen, H.; Bowell, E.

1990-01-01

A new and general method is presented for determining pole orientations of unresolved solar system bodies that exhibit brightness variation with rotation. The accuracy of the method is limited only by the number of available apparitions, which imposes the degree where the Legendre expansion must be truncated. It is shown that power spectra of lightcurves provide enough information to extract pole coordinates from the data, independent of body shape and albedo variegation. The method has been tested using several computer-generated synthetic light-curves, and the accuracy is found to be about 5 deg in both the longitude and latitude of the pole, which is considerably better than that obtained from the standard triaxial ellipsoid model. Finally, the new spherical harmonics method has been applied to six well-observed asteroids: 16 Psyche, 22 Kalliope, 39 Laetitia, 44 Nysa, 45 Eugenia, and 349 Dembowska.

Refinements in the Combined Adjustment of Satellite Altimetry and Gravity Anomaly Data

DTIC Science & Technology

1977-07-12

observations. - 151 UM Uj&liiäUäBä&immeä*,*^^ ^«^V^.^.v.rf ffM ’* ^.,/-=:jfcfe^te:^*ä*di 9.2 Spherical Harmonic Resolution The number of spherical harmonic...depend on the point mass parameters, 185 —--■ ^* p^^!?8!^ Bpp ^pg(p|SP!|p|g| we can write dr 1 dN 1 and use (9.44a). The presence of the state

A computationally tractable version of the collective model

NASA Astrophysics Data System (ADS)

Rowe, D. J.

2004-05-01

A computationally tractable version of the Bohr-Mottelson collective model is presented which makes it possible to diagonalize realistic collective models and obtain convergent results in relatively small appropriately chosen subspaces of the collective model Hilbert space. Special features of the proposed model are that it makes use of the beta wave functions given analytically by the softened-beta version of the Wilets-Jean model, proposed by Elliott et al., and a simple algorithm for computing SO(5)⊃SO(3) spherical harmonics. The latter has much in common with the methods of Chacon, Moshinsky, and Sharp but is conceptually and computationally simpler. Results are presented for collective models ranging from the spherical vibrator to the Wilets-Jean and axially symmetric rotor-vibrator models.

Comment on “Error made in reports of main field decay”

NASA Astrophysics Data System (ADS)

IAGA Working Group V-MOD on Geomagnetic Field Modeling,; Maus, Stefan; Macmillan, Susan

2004-09-01

As the International Association of Geomagnetism and Aeronomy (IAGA) Working Group on Geomagnetic Field Modeling (http://www.ngdc.noaa.gov/IAGA/vmod/), responsible for the International Geomagnetic Reference Field (IGRF) [Macmillan et al., 2003], we would like to comment on the Forum article by Wallace H.Campbell (Eos,85(16),20 April 2004). Campbell claims that reports of dipole decay at a special session held at the AGU 2003 Fall Meeting were misleading due to an incorrect choice of the coordinate system for the spherical harmonic analysis (SHA) of the geomagnetic field used for the IGRF the model on which the decay calculation was based.Campbell alleges that the dipole moment of a spherical harmonic expansion depends on the choice of the origin of the coordinate system. In his textbook on geomagnetism, Campbell goes one step further in asserting that, without changing the origin, the process of “tilting the analysis axis to align with the geomagnetic axis…would enhance the dipole term at the expense of the higher multipoles” [Campbell, 2003].

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

PubMed Central

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

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. PMID:23227108

Extended finite element method with simplified spherical harmonics approximation for the forward model of optical molecular imaging.

PubMed

Li, Wei; Yi, Huangjian; Zhang, Qitan; Chen, Duofang; Liang, Jimin

2012-01-01

An extended finite element method (XFEM) for the forward model of 3D optical molecular imaging is developed with simplified spherical harmonics approximation (SP(N)). In XFEM scheme of SP(N) 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.

Comparing Time-Dependent Geomagnetic and Atmospheric Effects on Cosmogenic Nuclide Production Rate Scaling

NASA Astrophysics Data System (ADS)

Lifton, N. A.

2014-12-01

A recently published cosmogenic nuclide production rate scaling model based on analytical fits to Monte Carlo simulations of atmospheric cosmic ray flux spectra (both of which agree well with measured spectra) (Lifton et al., 2014, Earth Planet. Sci. Lett. 386, 149-160: termed the LSD model) provides two main advantages over previous scaling models: identification and quantification of potential sources of bias in the earlier models, and the ability to generate nuclide-specific scaling factors easily for a wide range of input parameters. The new model also provides a flexible framework for exploring the implications of advances in model inputs. In this work, the scaling implications of two recent time-dependent spherical harmonic geomagnetic models spanning the Holocene will be explored. Korte and Constable (2011, Phys. Earth Planet. Int. 188, 247-259) and Korte et al. (2011, Earth Planet. Sci. Lett. 312, 497-505) recently updated earlier spherical harmonic paleomagnetic models used by Lifton et al. (2014) with paleomagnetic measurements from sediment cores in addition to archeomagnetic and volcanic data. These updated models offer improved accuracy over the previous versions, in part to due to increased temporal and spatial data coverage. With the new models as input, trajectory-traced estimates of effective vertical cutoff rigidity (RC- the standard method for ordering cosmic ray data) yield significantly different time-integrated scaling predictions when compared to the earlier models. These results will be compared to scaling predictions using another recent time-dependent spherical harmonic model of the Holocene geomagnetic field by Pavón-Carrasco et al. (2014, Earth Planet. Sci. Lett. 388, 98-109), based solely on archeomagnetic and volcanic paleomagnetic data, but extending to 14 ka. In addition, the potential effects of time-dependent atmospheric models on LSD scaling predictions will be presented. Given the typical dominance of altitudinal over latitudinal scaling effects on cosmogenic nuclide production, incorporating transient global simulations of atmospheric structure (e.g., Liu et al., 2009, Science 325, 310-314) into scaling frameworks may contribute to improved understanding of long-term production rate variations.

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

PubMed

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.

Normalization of Gravitational Acceleration Models

NASA Technical Reports Server (NTRS)

Eckman, Randy A.; Brown, Aaron J.; Adamo, Daniel R.

2011-01-01

Unlike the uniform density spherical shell approximations of Newton, the con- sequence of spaceflight in the real universe is that gravitational fields are sensitive to the nonsphericity of their generating central bodies. The gravitational potential of a nonspherical central body is typically resolved using spherical harmonic approximations. However, attempting to directly calculate the spherical harmonic approximations results in at least two singularities which must be removed in order to generalize the method and solve for any possible orbit, including polar orbits. Three unique algorithms have been developed to eliminate these singularities by Samuel Pines [1], Bill Lear [2], and Robert Gottlieb [3]. This paper documents the methodical normalization of two1 of the three known formulations for singularity-free gravitational acceleration (namely, the Lear [2] and Gottlieb [3] algorithms) and formulates a general method for defining normalization parameters used to generate normalized Legendre Polynomials and ALFs for any algorithm. A treatment of the conventional formulation of the gravitational potential and acceleration is also provided, in addition to a brief overview of the philosophical differences between the three known singularity-free algorithms.

Normal modes of the shallow water system on the cubed sphere

NASA Astrophysics Data System (ADS)

Kang, H. G.; Cheong, H. B.; Lee, C. H.

2017-12-01

Spherical harmonics expressed as the Rossby-Haurwitz waves are the normal modes of non-divergent barotropic model. Among the normal modes in the numerical models, the most unstable mode will contaminate the numerical results, and therefore the investigation of normal mode for a given grid system and a discretiztaion method is important. The cubed-sphere grid which consists of six identical faces has been widely adopted in many atmospheric models. This grid system is non-orthogonal grid so that calculation of the normal mode is quiet challenge problem. In the present study, the normal modes of the shallow water system on the cubed sphere discretized by the spectral element method employing the Gauss-Lobatto Lagrange interpolating polynomials as orthogonal basis functions is investigated. The algebraic equations for the shallow water equation on the cubed sphere are derived, and the huge global matrix is constructed. The linear system representing the eigenvalue-eigenvector relations is solved by numerical libraries. The normal mode calculated for the several horizontal resolution and lamb parameters will be discussed and compared to the normal mode from the spherical harmonics spectral method.

Lunar gravitational field estimation and the effects of mismodeling upon lunar satellite orbit prediction. M.S. Thesis

NASA Technical Reports Server (NTRS)

Davis, John H.

1993-01-01

Lunar spherical harmonic gravity coefficients are estimated from simulated observations of a near-circular low altitude polar orbiter disturbed by lunar mascons. Lunar gravity sensing missions using earth-based nearside observations with and without satellite-based far-side observations are simulated and least squares maximum likelihood estimates are developed for spherical harmonic expansion fit models. Simulations and parameter estimations are performed by a modified version of the Smithsonian Astrophysical Observatory's Planetary Ephemeris Program. Two different lunar spacecraft mission phases are simulated to evaluate the estimated fit models. Results for predicting state covariances one orbit ahead are presented along with the state errors resulting from the mismodeled gravity field. The position errors from planning a lunar landing maneuver with a mismodeled gravity field are also presented. These simulations clearly demonstrate the need to include observations of satellite motion over the far side in estimating the lunar gravity field. The simulations also illustrate that the eighth degree and order expansions used in the simulated fits were unable to adequately model lunar mascons.

Investigations of medium wavelength magnetic anomalies in the Eastern Pacific using MAGSAT data

NASA Technical Reports Server (NTRS)

Harrison, C. G. A. (Principal Investigator)

1982-01-01

A paper which discusses a problem in representing the core magnetic field of the Earth using spherical harmonics was revised and accepted for publications. Page proofs of a second paper concerning off center dipole modelling of the Earth's magnetic field are presented.

Rayleigh-Taylor instability at spherical interfaces between viscous fluids: Fluid/vacuum interface

DOE PAGES

Terrones, Guillermo; Carrara, Mark D.

2015-05-01

For a spherical interface of radius R separating two different homogeneous regions of incompressible viscous fluids under the action of a radially directed acceleration, we perform a linear stability analysis in terms of spherical surface harmonics Y n to derive the dispersion relation. The instability behavior is investigated by computing the growth rates and the most-unstable modes as a function of the spherical harmonic degree n. This general methodology is applicable to the entire parameter space spanned by the Atwood number, the viscosity ratio, and the dimensionless number B = (α RΡ² 2/μ² ²)¹ /³ R (where α R, Ρmore » 2 and μ 2 are the local radial acceleration at the interface, and the density and viscosity of the denser overlying fluid, respectively). While the mathematical formulation here is general, this paper focuses on instability that arises at a spherical viscous fluid/vacuum interface as there is a great deal to be learned from the effects of one-fluid viscosity and sphericity alone. To quantify and understand the effect that curvature and radial accelerationhave on the Rayleigh-Taylor instability, a comparison of the growth rates, under homologous driving conditions, between the planar and spherical interfaces is performed. The derived dispersion relation for the planar interface accounts for an underlying finite fluid region of thickness L and normal acceleration α R. Under certain conditions, the development of the most-unstable modes at a spherical interface can take place via the superposition of two adjacent spherical harmonics Y n and Y n+1. This bimodality in the evolution of disturbances in the linear regime does not have a counterpart in the planar configuration where the most-unstable modes are associated with a unique wave number.« less

Acoustic reciprocity: An extension to spherical harmonics domain.

PubMed

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.

Spherical harmonics and rigged Hilbert spaces

NASA Astrophysics Data System (ADS)

Celeghini, E.; Gadella, M.; del Olmo, M. A.

2018-05-01

This paper is devoted to study discrete and continuous bases for spaces supporting representations of SO(3) and SO(3, 2) where the spherical harmonics are involved. We show how discrete and continuous bases coexist on appropriate choices of rigged Hilbert spaces. We prove the continuity of relevant operators and the operators in the algebras spanned by them using appropriate topologies on our spaces. Finally, we discuss the properties of the functionals that form the continuous basis.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

1997-06-01

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 formore » 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.« less

A Spherical Harmonic Analysis of the Ooty Wide Field Array (OWFA) Visibility Signal

NASA Astrophysics Data System (ADS)

Chatterjee, Suman; Bharadwaj, Somnath

2018-04-01

Considering redshifted 21-cm intensity mapping with the upcoming OWFA whose field of view subtends ˜57° in the N-S direction, we present a formalism which relates the measured visibilities to the spherical harmonic coefficients of the sky signal. We use this to calculate window functions which relate the two-visibility correlations i.e. the correlation between the visibilities measured at two baselines and two frequencies, to different multipoles of the multi-frequency angular power spectrum Cℓ(ν1, ν2). The formalism here is validated using simulations. We also present approximate closed form analytical expressions which can be used to calculate the window functions. Comparing the widely adopted flat sky approximation, we find that its predictions match those of our spherical harmonic formalism to within 16% across the entire OWFA baseline range. The match improves at large baselines where we have <5% deviations.

Gravitational potential energy of the earth: A spherical harmonic approach

NASA Technical Reports Server (NTRS)

Rubincam, D. P.

1977-01-01

A spherical harmonic equation for the gravitational potential energy of the earth is derived for an arbitrary density distribution by conceptually bringing in mass-elements from infinity and building up the earth shell upon spherical shell. The zeroth degree term in the spherical harmonic equation agrees with the usual expression for the energy of a radial density distribution. The second degree terms give a maximum nonhydrostatic energy in the mantle and crust of -2.77 x 10 to the twenty-ninth power ergs, an order of magnitude. If the earth is assumed to be a homogeneous viscous oblate spheroid relaxing to an equilibrium shape, then a lower limit to the mantle viscosity of 1.3 x 10 to the twentieth power poises is found by assuming the total geothermal flux is due to viscous dissipation. If the nonequilibrium figure is dynamically maintained by the earth acting as a heat engine at one per cent efficiency, then the viscosity is ten to the twenty second power poises, a number preferred by some as the viscosity of the mantle.

Oceanic lithospheric magnetisation: Forward modelling and analysis using vector spherical harmonics (Invited)

NASA Astrophysics Data System (ADS)

Masterton, S. M.; Gubbins, D.; Müller, D.; Williams, S.

2013-12-01

The lithospheric contribution to the geomagnetic field arises from magnetised rocks that are cooler than the Curie temperature of their constituent minerals. Inversion of the magnetic field for this magnetisation is subject to inherent non-uniqueness, as many magnetisation distributions yield no potential field outside of the lithosphere. Such distributions are termed annihilators. We use a complete set of orthogonal vector spherical harmonics that separate the part of the magnetisation responsible for the magnetic field observed above the Earth's surface from the annihilators. A similar set of vector harmonics has been developed in Cartesian geometry suitable for small scale, industrial applications. In an attempt to quantify the significance of the annihilators, we first construct a global model of vertically integrated magnetisation (VIM) by combining a model of remanent magnetisation for the oceans with a previous model of induced magnetisation for the whole Earth. Remanence is computed by assigning magnetisations to the oceanic lithosphere acquired at the location and time of formation. The magnetising field is assumed to be an axial dipole that switches polarity with the reversal time scale. The magnetisation evolves with time by decay of thermal remanence and acquisition of chemical remanence. Remanence directions are calculated by implementing finite rotations of the original geomagnetic field direction with respect to an absolute reference frame. We then represent our estimated VIM in terms of vector spherical harmonics, to allow us to evaluate its relative contributions to a potential field that is observable outside of the lithosphere and to fields (both potential and non-potential) that are not observable. This analysis shows that our model of magnetisation is dominated by a part of the magnetisation that produces a potential field restricted to Earth's sub-lithospheric interior; it therefore contributes significantly to the huge null space in the inversion of lithospheric magnetic anomaly data for VIM. We calculate the observable potential field that arises from our magnetisation estimates and compare it with a model that is based upon satellite data (MF7); this allows us to evaluate our magnetisation estimates and suggest likely sources of error in areas with high misfit between our predictions and the observed magnetic field. For example, under-prediction of the observed magnetic field may be indicative of poorly-known magnetisation deep in the crust or upper mantle, locally underplated continental lithosphere or anomalous oceanic crust.

The CHAOS-4 geomagnetic field model

NASA Astrophysics Data System (ADS)

Olsen, Nils; Lühr, Hermann; Finlay, Christopher C.; Sabaka, Terence J.; Michaelis, Ingo; Rauberg, Jan; Tøffner-Clausen, Lars

2014-05-01

We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly determined. More than 14 yr of data from the satellites Ørsted, CHAMP and SAC-C, augmented with magnetic observatory monthly mean values have been used for this model. Maximum spherical harmonic degree of the static (lithospheric) field is n = 100. The core field is expressed by spherical harmonic expansion coefficients up to n = 20; its time-evolution is described by order six splines, with 6-month knot spacing, spanning the time interval 1997.0-2013.5. The third time derivative of the squared radial magnetic field component is regularized at the core-mantle boundary. No spatial regularization is applied to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its high-degree lithospheric field part is solely determined from low-altitude CHAMP satellite observations taken during the last 2 yr (2008 September-2010 September) of the mission. We obtain a good agreement with other recent lithospheric field models like MF7 for degrees up to n = 85, confirming that lithospheric field structures down to a horizontal wavelength of 500 km are currently robustly determined.

Shallow Water Quasi-Geostrophic Theory on the Sphere

NASA Astrophysics Data System (ADS)

Schubert, Wayne H.; Taft, Richard K.; Silvers, Levi G.

2009-02-01

Quasi-geostrophic theory forms the basis for much of our understanding of mid-latitude atmospheric dynamics. The theory is typically presented in either its f-plane form or its β-plane form. However, for many applications, including diagnostic use in global climate modeling, a fully spherical version would be most useful. Such a global theory does in fact exist and has for many years, but few in the scientific community seem to have ever been aware of it. In the context of shallow water dynamics, it is shown that the spherical version of quasigeostrophic theory is easily derived (re-derived) based on a partitioning of the flow between nondivergent and irrotational components, as opposed to a partitioning between geostrophic and ageostrophic components. In this way, the invertibility principle is expressed as a relation between the streamfunction and the potential vorticity, rather than between the geopotential and the potential vorticity. This global theory is then extended by showing that the invertibility principle can be solved analytically using spheroidal harmonic transforms, an advancement that greatly improves the usefulness of this "forgotten" theory. When the governing equation for the time evolution of the potential vorticity is linearized about a state of rest, a simple Rossby-Haurwitz wave dispersion relation is derived and examined. These waves have a horizontal structure described by spheroidal harmonics, and the Rossby-Haurwitz wave frequencies are given in terms of the eigenvalues of the spheroidal harmonic operator. Except for sectoral harmonics with low zonal wavenumber, the quasi-geostrophic Rossby-Haurwitz frequencies agree very well with those calculated from the primitive equations. One of the many possible applications of spherical quasi-geostrophic theory is to the study of quasi-geostrophic turbulence on the sphere. In this context, the theory is used to derive an anisotropic Rhines barrier in three-dimensional wavenumber space.

Statistics of the geomagnetic secular variation for the past 5Ma

NASA Technical Reports Server (NTRS)

Constable, C. G.; Parker, R. L.

1986-01-01

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.

Statistics of the geomagnetic secular variation for the past 5 m.y

NASA Technical Reports Server (NTRS)

Constable, C. G.; Parker, R. L.

1988-01-01

A new statistical model is proposed for the geomagnetic secular variation over the past 5Ma. Unlike previous models, the model makes use of statistical characteristics of the present day geomagnetic field. The spatial power spectrum of the non-dipole field is consistent with a white source near the core-mantle boundary with Gaussian distribution. After a suitable scaling, the spherical harmonic coefficients may be regarded as statistical samples from a single giant Gaussian process; this is the model of the non-dipole field. The model can be combined with an arbitrary statistical description of the dipole and probability density functions and cumulative distribution functions can be computed for declination and inclination that would be observed at any site on Earth's surface. Global paleomagnetic data spanning the past 5Ma are used to constrain the statistics of the dipole part of the field. A simple model is found to be consistent with the available data. An advantage of specifying the model in terms of the spherical harmonic coefficients is that it is a complete statistical description of the geomagnetic field, enabling us to test specific properties for a general description. Both intensity and directional data distributions may be tested to see if they satisfy the expected model distributions.

Comparison of parametric methods for modeling corneal surfaces

NASA Astrophysics Data System (ADS)

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.

Assessing mass change trends in GRACE models

NASA Astrophysics Data System (ADS)

Siemes, C.; Liu, X.; Ditmar, P.; Revtova, E.; Slobbe, C.; Klees, R.; Zhao, Q.

2009-04-01

The DEOS Mass Transport model, release 1 (DMT-1), has been recently presented to the scientific community. The model is based on GRACE data and consists of sets of spherical harmonic coefficients to degree 120, which are estimated once per month. Currently, the DMT-1 model covers the time span from Feb. 2003 to Dec. 2006. The high spatial resolution of the model could be achieved by applying a statistically optimal Wiener-type filter, which is superior to standard filtering techniques. The optimal Wiener-type filter is a regularization-type filter which makes full use of the variance/covariance matrices of the sets of spherical harmonic coefficients. It can be shown that applying this filter is equivalent to introducing an additional set of observations: Each set of spherical harmonic coefficients is assumed to be zero. The variance/covariance matrix of this information is chosen according to the signal contained within the sets of spherical harmonic coefficients, expressed in terms of equivalent water layer thickness in the spatial domain, with respect to its variations in time. It will be demonstrated that DMT-1 provides a much better localization and more realistic amplitudes than alternative filtered models. In particular, we will consider a lower maximum degree of the spherical harmonic expansion (e.g. 70), as well as standard filters like an isotropic Gaussian filter. For the sake of a fair comparison, we will use the same GRACE observations as well as the same method for the inversion of the observations to obtain the alternative filtered models. For the inversion method, we will choose the three-point range combination approach. Thus, we will compare four different models: (1) GRACE solution with maximum degree 120, filtered by optimal Wiener-type filter (the DMT-1 model) (2) GRACE solution with maximum degree 120, filtered by standard filter (3) GRACE solution with maximum degree 70, filtered by optimal Wiener-type filter (4) GRACE solution with maximum degree 70, filtered by standard filter Within the comparison, we will focus on the amplitude of long-term mass change signals with respect to spatial resolution. The challenge for the recovery of such signals from GRACE based solutions results from the fact that the solutions must be filtered and that filtering of always smoothes not only noise, but also to some extend signal. Since the observation density is much higher near the poles than at the equator, which is due to the orbits of the GRACE satellites, we expect that the magnitude of estimated mass change signals in polar areas is less underestimated than in equatorial areas. For this reason will investigate trends at locations in equatorial areas as well as trends at locations in polar areas. In particular, we will investigate Lake Victoria, Lake Malawi and Lake Tanganyika, which are all located in Eastern Africa, near to the equator. Furthermore, we will show trends of two locations at the South-East coast of Greenland, Abbot Ice-Shelf and Marie-Byrd-Land in Antarctica For validation, we use water level variations in Lake Victoria (69000 km2), Lake Malawi (29000 km2) and Lake Tanganyika (33000 km2) as ground truth. The water level, which is measured by satellite radar altimetry, decreases at a rate of approximately 47 cm in Lake Victoria, 42 cm in Lake Malawi and 30 cm in Lake Tanganyika over the period from Feb. 2003 to Dec. 2006. Because all three lakes are located in tropical and subtropical clime, the mass change signal will consist of large seasonal variations in addition to the trend component we are interested in. However, also the amplitude of estimated seasonal variations can be used as an indicator of the quality of the models within the comparison. Since the lakes' areas are at the edge of the spatial resolution GRACE data can provide, they are a good example of the advantages of high-resolution mass change models like DMT-1.

Extended Applicability of the Spherical-Harmonic and Point-Mass Modeling of the Gravity Field,

DTIC Science & Technology

1980-02-01

the metric in spherical coordinates {X,F, rl reads ds2 = r2cos 2j dX2 + r 2d 2 + dr2 yielding the metric tensor and the associated metric tensor: {grs...leading to (3.52) would have required considerably more space if the tensor approach to this problem had been avoided, whether for pedagogical or other...useful, especially from the pedagogical point of view, since it addresses itself to large audiences and exposes the treated subject in great depth. On

Critical insights into nuclear collectivity from complementary nuclear spectroscopic methods

NASA Astrophysics Data System (ADS)

Garrett, P. E.; Wood, J. L.; Yates, S. W.

2018-06-01

Low-energy collectivity of nuclei has been, and is being, characterized in a critical manner using data from a variety of spectroscopic methods, including Coulomb excitation, β decay, inelastic scattering of charged and uncharged particles, transfer reactions, etc. In addition to level energies and spins, transition multipolarities and intensities, lifetimes, and nuclear moments are available. The totality of information from these probes must be considered in achieving an accurate vision of the excitations in nuclei and determining the applicability of nuclear models. From these data, major changes in our view of low-energy collectivity in nuclei have emerged; most notable is the demise of the long-held view of low-energy quadrupole collectivity near closed shells as due to vibrations about a spherical equilibrium shape. In this contribution, we focus on the basic predictions of the spherical harmonic vibrator limit of the Bohr Hamiltonian. Properties such as B(E2) values, quadrupole moments, E0 strengths, etc are outlined. Using the predicted properties as a guide, evidence is cited for and against the existence of vibrational states, and especially multi-phonon states, in nuclei that are, or historically were considered to be, spherical or have a nearly spherical shape in their ground state. It is found that very few of the nuclei that were identified in the last major survey seeking nearly spherical harmonic vibrators satisfy the more stringent guidelines presented herein. Details of these fundamental shifts in our view of low-energy collectivity in nuclei are presented.

Optimal secondary source position in exterior spherical acoustical holophony

NASA Astrophysics Data System (ADS)

Pasqual, A. M.; Martin, V.

2012-02-01

Exterior spherical acoustical holophony is a branch of spatial audio reproduction that deals with the rendering of a given free-field radiation pattern (the primary field) by using a compact spherical loudspeaker array (the secondary source). More precisely, the primary field is known on a spherical surface surrounding the primary and secondary sources and, since the acoustic fields are described in spherical coordinates, they are naturally subjected to spherical harmonic analysis. Besides, the inverse problem of deriving optimal driving signals from a known primary field is ill-posed because the secondary source cannot radiate high-order spherical harmonics efficiently, especially in the low-frequency range. As a consequence, a standard least-squares solution will overload the transducers if the primary field contains such harmonics. Here, this is avoided by discarding the strongly decaying spherical waves, which are identified through inspection of the radiation efficiency curves of the secondary source. However, such an unavoidable regularization procedure increases the least-squares error, which also depends on the position of the secondary source. This paper deals with the above-mentioned questions in the context of far-field directivity reproduction at low and medium frequencies. In particular, an optimal secondary source position is sought, which leads to the lowest reproduction error in the least-squares sense without overloading the transducers. In order to address this issue, a regularization quality factor is introduced to evaluate the amount of regularization required. It is shown that the optimal position improves significantly the holophonic reconstruction and maximizes the regularization quality factor (minimizes the amount of regularization), which is the main general contribution of this paper. Therefore, this factor can also be used as a cost function to obtain the optimal secondary source position.

High-resolution regional gravity field modelling in a mountainous area from terrestrial gravity data

NASA Astrophysics Data System (ADS)

Bucha, Blažej; Janák, Juraj; Papčo, Juraj; Bezděk, Aleš

2016-11-01

We develop a high-resolution regional gravity field model by a combination of spherical harmonics, band-limited spherical radial basis functions (SRBFs) and the residual terrain model (RTM) technique. As the main input data set, we employ a dense terrestrial gravity database (3-6 stations km-2), which enables gravity field modelling up to very short spatial scales. The approach is based on the remove-compute-restore methodology in which all the parts of the signal that can be modelled are removed prior to the least-squares adjustment in order to smooth the input gravity data. To this end, we utilize degree-2159 spherical harmonic models and the RTM technique using topographic models at 2 arcsec resolution. The residual short-scale gravity signal is modelled via the band-limited Shannon SRBF expanded up to degree 21 600, which corresponds to a spatial resolution of 30 arcsec. The combined model is validated against GNSS/levelling-based height anomalies, independent surface gravity data, deflections of the vertical and terrestrial vertical gravity gradients achieving an accuracy of 2.7 cm, 0.53 mGal, 0.39 arcsec and 279 E in terms of the RMS error, respectively. A key aspect of the combined approach, especially in mountainous areas, is the quality of the RTM. We therefore compare the performance of two RTM techniques within the innermost zone, the tesseroids and the polyhedron. It is shown that the polyhedron-based approach should be preferred in rugged terrain if a high-quality RTM is required. In addition, we deal with the RTM computations at points located below the reference surface of the residual terrain which is known to be a rather delicate issue.

Fully non-inductive second harmonic electron cyclotron plasma ramp-up in the QUEST spherical tokamak

NASA Astrophysics Data System (ADS)

Idei, H.; Kariya, T.; Imai, T.; Mishra, K.; Onchi, T.; Watanabe, O.; Zushi, H.; Hanada, K.; Qian, J.; Ejiri, A.; Alam, M. M.; Nakamura, K.; Fujisawa, A.; Nagashima, Y.; Hasegawa, M.; Matsuoka, K.; Fukuyama, A.; Kubo, S.; Shimozuma, T.; Yoshikawa, M.; Sakamoto, M.; Kawasaki, S.; Nakashima, H.; Higashijima, A.; Ide, S.; Maekawa, T.; Takase, Y.; Toi, K.

2017-12-01

Fully non-inductive second (2nd) harmonic electron cyclotron (EC) plasma current ramp-up was demonstrated with a newlly developed 28 GHz system in the QUEST spherical tokamak. A high plasma current of 54 kA was non-inductively ramped up and sustained stably for 0.9 s with a 270 kW 28 GHz wave. A higher plasma current of 66 kA was also non-inductively achieved with a slow ramp-up of the vertical field. We have achieved a significantly higher plasma current than those achieved previously with the 2nd harmonic EC waves. This fully non-inductive 2nd harmonic EC plasma ramp-up method might be useful for future burning plasma devices and fusion reactors, in particular for operations at half magnetic field with the same EC heating equipment.

Analytical Solution of Coupled Perturbation of Tesseral Harmonic Terms of Mars's Non-Spherical Gravitational Potential

NASA Astrophysics Data System (ADS)

Zhou, Chui-hong; Yu, Sheng-xian; Liu, Lin

2012-10-01

The non-spherical gravitational potential of the planet Mars is sig- nificantly different from that of the Earth. The magnitudes of Mars' tesseral harmonic coefficients are basically ten times larger than the corresponding val- ues of the Earth. Especially, the magnitude of its second degree and order tesseral harmonic coefficient J2,2 is nearly 40 times that of the Earth, and approaches to the one tenth of its second zonal harmonic coefficient J2. For a low-orbit Mars probe, if the required accuracy of orbit prediction of 1-day arc length is within 500 m (equivalent to the order of magnitude of 10-4 standard unit), then the coupled terms of J2 with the tesseral harmonics, and even those of the tesseral harmonics themselves, which are negligible for the Earth satellites, should be considered when the analytical perturbation solution of its orbit is built. In this paper, the analytical solutions of the coupled terms are presented. The anal- ysis and numerical verification indicate that the effect of the above-mentioned coupled perturbation on the orbit may exceed 10-4 in the along-track direc- tion. The conclusion is that the solutions of Earth satellites cannot be simply used without any modification when dealing with the analytical perturbation solutions of Mars-orbiting satellites, and that the effect of the coupled terms of Mars's non-spherical gravitational potential discussed in this paper should be taken into consideration.

Model for the dynamics of two interacting axisymmetric spherical bubbles undergoing small shape oscillations

PubMed Central

Kurihara, Eru; Hay, Todd A.; Ilinskii, Yurii A.; Zabolotskaya, Evgenia A.; Hamilton, Mark F.

2011-01-01

Interaction between acoustically driven or laser-generated bubbles causes the bubble surfaces to deform. Dynamical equations describing the motion of two translating, nominally spherical bubbles undergoing small shape oscillations in a viscous liquid are derived using Lagrangian mechanics. Deformation of the bubble surfaces is taken into account by including quadrupole and octupole perturbations in the spherical-harmonic expansion of the boundary conditions on the bubbles. Quadratic terms in the quadrupole and octupole amplitudes are retained, and surface tension and shear viscosity are included in a consistent manner. A set of eight coupled second-order ordinary differential equations is obtained. Simulation results, obtained by numerical integration of the model equations, exhibit qualitative agreement with experimental observations by predicting the formation of liquid jets. Simulations also suggest that bubble-bubble interactions act to enhance surface mode instability. PMID:22088009

High-resolution combined global gravity field modelling: Solving large kite systems using distributed computational algorithms

NASA Astrophysics Data System (ADS)

Zingerle, Philipp; Fecher, Thomas; Pail, Roland; Gruber, Thomas

2016-04-01

One of the major obstacles in modern global gravity field modelling is the seamless combination of lower degree inhomogeneous gravity field observations (e.g. data from satellite missions) with (very) high degree homogeneous information (e.g. gridded and reduced gravity anomalies, beyond d/o 1000). Actual approaches mostly combine such data only on the basis of the coefficients, meaning that previously for both observation classes (resp. models) a spherical harmonic analysis is done independently, solving dense normal equations (NEQ) for the inhomogeneous model and block-diagonal NEQs for the homogeneous. Obviously those methods are unable to identify or eliminate effects as spectral leakage due to band limitations of the models and non-orthogonality of the spherical harmonic base functions. To antagonize such problems a combination of both models on NEQ-basis is desirable. Theoretically this can be achieved using NEQ-stacking. Because of the higher maximum degree of the homogeneous model a reordering of the coefficient is needed which leads inevitably to the destruction of the block diagonal structure of the appropriate NEQ-matrix and therefore also to the destruction of simple sparsity. Hence, a special coefficient ordering is needed to create some new favorable sparsity pattern leading to a later efficient computational solving method. Such pattern can be found in the so called kite-structure (Bosch, 1993), achieving when applying the kite-ordering to the stacked NEQ-matrix. In a first step it is shown what is needed to attain the kite-(NEQ)system, how to solve it efficiently and also how to calculate the appropriate variance information from it. Further, because of the massive computational workload when operating on large kite-systems (theoretically possible up to about max. d/o 100.000), the main emphasis is put on to the presentation of special distributed algorithms which may solve those systems parallel on an indeterminate number of processes and are therefore suitable for the application on supercomputers (such as SuperMUC). Finally, (if time or space) some in-detail problems are shown that occur when dealing with high degree spherical harmonic base functions (mostly due to instabilities of Legendre polynomials), introducing also an appropriate solution for each.

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

NASA Astrophysics Data System (ADS)

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.

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

NASA Astrophysics Data System (ADS)

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.

Sound Source Localization Using Non-Conformal Surface Sound Field Transformation Based on Spherical Harmonic Wave Decomposition

PubMed Central

Zhang, Lanyue; Ding, Dandan; Yang, Desen; Wang, Jia; Shi, Jie

2017-01-01

Spherical microphone arrays have been paid increasing attention for their ability to locate a sound source with arbitrary incident angle in three-dimensional space. Low-frequency sound sources are usually located by using spherical near-field acoustic holography. The reconstruction surface and holography surface are conformal surfaces in the conventional sound field transformation based on generalized Fourier transform. When the sound source is on the cylindrical surface, it is difficult to locate by using spherical surface conformal transform. The non-conformal sound field transformation by making a transfer matrix based on spherical harmonic wave decomposition is proposed in this paper, which can achieve the transformation of a spherical surface into a cylindrical surface by using spherical array data. The theoretical expressions of the proposed method are deduced, and the performance of the method is simulated. Moreover, the experiment of sound source localization by using a spherical array with randomly and uniformly distributed elements is carried out. Results show that the non-conformal surface sound field transformation from a spherical surface to a cylindrical surface is realized by using the proposed method. The localization deviation is around 0.01 m, and the resolution is around 0.3 m. The application of the spherical array is extended, and the localization ability of the spherical array is improved. PMID:28489065

Error and Symmetry Analysis of Misner's Algorithm for Spherical Harmonic Decomposition on a Cubic Grid

NASA Technical Reports Server (NTRS)

Fiske, David R.

2004-01-01

In an earlier paper, Misner (2004, Class. Quant. Grav., 21, S243) presented a novel algorithm for computing the spherical harmonic components of data represented on a cubic grid. I extend Misner s original analysis by making detailed error estimates of the numerical errors accrued by the algorithm, by using symmetry arguments to suggest a more efficient implementation scheme, and by explaining how the algorithm can be applied efficiently on data with explicit reflection symmetries.

Deconvolution and analysis of wide-angle longwave radiation data from Nimbus 6 Earth radiation budget experiment for the first year

NASA Technical Reports Server (NTRS)

Bess, T. D.; Green, R. N.; Smith, G. L.

1980-01-01

One year of longwave radiation data from July 1975 through June 1976 from the Nimbus 6 satellite Earth radiation budget experiment is analyzed by representing the radiation field by a spherical harmonic expansion. The data are from the wide field of view instrument. Contour maps of the longwave radiation field and spherical harmonic coefficients to degree 12 and order 12 are presented for a 12 month data period.

Scalar and tensor spherical harmonics expansion of the velocity correlation in homogeneous anisotropic turbulence

DOE PAGES

Rubinstein, Robert; Kurien, Susan; Cambon, Claude

2015-06-22

The representation theory of the rotation group is applied to construct a series expansion of the correlation tensor in homogeneous anisotropic turbulence. The resolution of angular dependence is the main analytical difficulty posed by anisotropic turbulence; representation theory parametrises this dependence by a tensor analogue of the standard spherical harmonics expansion of a scalar. As a result, the series expansion is formulated in terms of explicitly constructed tensor bases with scalar coefficients determined by angular moments of the correlation tensor.

Spherical Harmonic Decomposition of Gravitational Waves Across Mesh Refinement Boundaries

NASA Technical Reports Server (NTRS)

Fiske, David R.; Baker, John; vanMeter, James R.; Centrella, Joan M.

2005-01-01

We evolve a linearized (Teukolsky) solution of the Einstein equations with a non-linear Einstein solver. Using this testbed, we are able to show that such gravitational waves, defined by the Weyl scalars in the Newman-Penrose formalism, propagate faithfully across mesh refinement boundaries, and use, for the first time to our knowledge, a novel algorithm due to Misner to compute spherical harmonic components of our waveforms. We show that the algorithm performs extremely well, even when the extraction sphere intersects refinement boundaries.

A discrete spherical harmonics method for radiative transfer analysis in inhomogeneous polarized planar atmosphere

NASA Astrophysics Data System (ADS)

Tapimo, Romuald; Tagne Kamdem, Hervé Thierry; Yemele, David

2018-03-01

A discrete spherical harmonics method is developed for the radiative transfer problem in inhomogeneous polarized planar atmosphere illuminated at the top by a collimated sunlight while the bottom reflects the radiation. The method expands both the Stokes vector and the phase matrix in a finite series of generalized spherical functions and the resulting vector radiative transfer equation is expressed in a set of polar directions. Hence, the polarized characteristics of the radiance within the atmosphere at any polar direction and azimuthal angle can be determined without linearization and/or interpolations. The spatial dependent of the problem is solved using the spectral Chebyshev method. The emergent and transmitted radiative intensity and the degree of polarization are predicted for both Rayleigh and Mie scattering. The discrete spherical harmonics method predictions for optical thin atmosphere using 36 streams are found in good agreement with benchmark literature results. The maximum deviation between the proposed method and literature results and for polar directions \\vert μ \\vert ≥0.1 is less than 0.5% and 0.9% for the Rayleigh and Mie scattering, respectively. These deviations for directions close to zero are about 3% and 10% for Rayleigh and Mie scattering, respectively.

Broken Ergodicity in MHD Turbulence in a Spherical Domain

NASA Technical Reports Server (NTRS)

Shebalin, John V.; wang, Yifan

2011-01-01

Broken ergodicity (BE) occurs in Fourier method numerical simulations of ideal, homogeneous, incompressible magnetohydrodynamic (MHD) turbulence. Although naive statistical theory predicts that Fourier coefficients of fluid velocity and magnetic field are zero-mean random variables, numerical simulations clearly show that low-wave-number coefficients have non-zero mean values that can be very large compared to the associated standard deviation. In other words, large-scale coherent structure (i.e., broken ergodicity) in homogeneous MHD turbulence can spontaneously grow out of random initial conditions. Eigenanalysis of the modal covariance matrices in the probability density functions of ideal statistical theory leads to a theoretical explanation of observed BE in homogeneous MHD turbulence. Since dissipation is minimal at the largest scales, BE is also relevant for resistive magnetofluids, as evidenced in numerical simulations. Here, we move beyond model magnetofluids confined by periodic boxes to examine BE in rotating magnetofluids in spherical domains using spherical harmonic expansions along with suitable boundary conditions. We present theoretical results for 3-D and 2-D spherical models and also present computational results from dynamical simulations of 2-D MHD turbulence on a rotating spherical surface. MHD turbulence on a 2-D sphere is affected by Coriolus forces, while MHD turbulence on a 2-D plane is not, so that 2-D spherical models are a useful (and simpler) intermediate stage on the path to understanding the much more complex 3-D spherical case.

On the "Optimal" Choice of Trial Functions for Modelling Potential Fields

NASA Astrophysics Data System (ADS)

Michel, Volker

2015-04-01

There are many trial functions (e.g. on the sphere) available which can be used for the modelling of a potential field. Among them are orthogonal polynomials such as spherical harmonics and radial basis functions such as spline or wavelet basis functions. Their pros and cons have been widely discussed in the last decades. We present an algorithm, the Regularized Functional Matching Pursuit (RFMP), which is able to choose trial functions of different kinds in order to combine them to a stable approximation of a potential field. One main advantage of the RFMP is that the constructed approximation inherits the advantages of the different basis systems. By including spherical harmonics, coarse global structures can be represented in a sparse way. However, the additional use of spline basis functions allows a stable handling of scattered data grids. Furthermore, the inclusion of wavelets and scaling functions yields a multiscale analysis of the potential. In addition, ill-posed inverse problems (like a downward continuation or the inverse gravimetric problem) can be regularized with the algorithm. We show some numerical examples to demonstrate the possibilities which the RFMP provides.

Rectangular rotation of spherical harmonic expansion of arbitrary high degree and order

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2017-08-01

In order to move the polar singularity of arbitrary spherical harmonic expansion to a point on the equator, we rotate the expansion around the y-axis by 90° such that the x-axis becomes a new pole. The expansion coefficients are transformed by multiplying a special value of Wigner D-matrix and a normalization factor. The transformation matrix is unchanged whether the coefficients are 4 π fully normalized or Schmidt quasi-normalized. The matrix is recursively computed by the so-called X-number formulation (Fukushima in J Geodesy 86: 271-285, 2012a). As an example, we obtained 2190× 2190 coefficients of the rectangular rotated spherical harmonic expansion of EGM2008. A proper combination of the original and the rotated expansions will be useful in (i) integrating the polar orbits of artificial satellites precisely and (ii) synthesizing/analyzing the gravitational/geomagnetic potentials and their derivatives accurately in the high latitude regions including the arctic and antarctic area.

Spherical harmonic analysis of the sound radiation from omnidirectional loudspeaker arrays

NASA Astrophysics Data System (ADS)

Pasqual, A. M.

2014-09-01

Omnidirectional sound sources are widely used in room acoustics. These devices are made up of loudspeakers mounted on a spherical or polyhedral cabinet, where the dodecahedral shape prevails. Although such electroacoustic sources have been made readily available to acousticians by many manufacturers, an in-depth investigation of their vibroacoustic behavior has not been provided yet. In order to fulfill this lack, this paper presents a theoretical study of the sound radiation from omnidirectional loudspeaker arrays, which is carried out by using a mathematical model based on the spherical harmonic analysis. Eight different loudspeaker arrangements on the sphere are considered: the well-known five Platonic solid layouts and three extremal system layouts. The latter possess useful properties for spherical loudspeaker arrays used as directivity controlled sound sources, so that these layouts are included here in order to investigate whether or not they could be of interest as omnidirectional sources as well. It is shown through a comparative analysis that the dodecahedral array leads to the lowest error in producing an omnidirectional sound field and to the highest acoustic power, which corroborates the prevalence of such a layout. In addition, if a source with less than 12 loudspeakers is required, it is shown that tetrahedra or hexahedra can be used alternatively, whereas the extremal system layouts are not interesting choices for omnidirectional loudspeaker arrays.

The Gravity field of Comet 67 P/Churyumov-Gerasimenko Expressed in Bispherical Harmonics

NASA Astrophysics Data System (ADS)

Andert, T.; Barriot, J. P.; Paetzold, M.; Sichoix, L.; Tellmann, S.; Häusler, B.

2015-12-01

On 6 August 2014, after a ten years cruise, the ESA-Rosetta spacecraft arrived at comet 67P/Churyumov-Gerasimenko. At that time the spacecraft was commanded to drift along with the comet at distances between 100 km and 50 km, the distance was then successfully lowered to 30 km in September 2014 and to 10 km in November 2014 and bound orbits could be achieved. Based on Doppler tracking data the Rosetta radio science experiment (RSI) was able to determine the mass of the nucleus and its gravity field in spherical harmonics series in order to constrain density and the internal structure of the nucleus. The shape of the comet is complex, a representation of the gravity field as belonging to one single body in either spherical or ellipsoidal harmonics series will give the shape of the body more preference than its internal structure. The observed shape of the nucleus, however, offers the opportunity to interpret it as consisting of two different bodies, namely the "head" and the "feet" sections of 67P/Churyumov-Gerasimenko, both having a nearly ellipsoidal shape. In this new approach, the bispherical harmonics expansion, the comet nucleus has been approximated by two independent lobes, each lobe represented by its own spherical harmonics expansion. As a result of the bispherical harmonics representation, it is anticipated that the gravity field will gain higher accuracy and will be less dominated by the complex shape of the comet. We have derived the analytical expressions of the gravity potential and its derivatives of a body in bispherical coordinates and applied this concept to the comet Churyumov-Gerasimenko. The paper will present the bispherical harmonics representation of the gravity field and first results derived from this new concept.

Ocean Domains and Maximum Degree of Spherical Harmonic and Orthonormal Expansions

NASA Technical Reports Server (NTRS)

Rapp, R.

1999-01-01

Ocean domains used for the orthonormal (ON) systems are studied to determine the maximum degree of spherical harmonic and orthonormal expansions that can be constructed. Although it was shown that one domain was restricted to degree 24, others were shown could be constructed to determine expansions to at least degree 36. Since 1991 the maximum degree expansion used for several Ohio State studies has been 24. In this report it is shown that the maximum degree for the ocean domain used by Wang and Rapp [1994] was 32 and 29 for the domain used by Rapp, Zhang, Yi [1996]. A modification of the former domain was developed (D1e) that enabled a solution to degree 36 to be determined. A modification of the Rapp, Zhang, Yi domain (D7d) enabled a degree 30 solution to be made. Combination coefficients were developed for domain D1e, to degree 36, and to degree 30 for domain D7d. The degree 30 spherical harmonic expansion provided by Pavlis [1998] of the POCM_4B dynamic ocean topography (DOT), and the degree 30 part of the degree 360 expansion [Rapp. 1998] of the POCM_4B model was converted to an ON expansion valid for the D7d domain. The degree 36 part of the degree 360 expansion was converted to the ON expansion for the D1e domain. The square root of the degree variances of the various solutions were compared. The root mean square value of DOT from the Pai,lis expansion, after conversion to the ON system, was + or - 66.52 cm (D7d domain). The value from the degree 30 part of the 360 expansion was + or - 66.65 cm. The value based on the actual POCM-4B data, in the D7d domain, was + or - 66.74 cm showing excellent agreement with the ON results. If the spherical harmonic coefficients had been used the implied root mean square value was + or - 60.76 cm [Pavlis] and + or -59.70 cm [Rapp].

Role of membrane stresses in the support of planetary topography

NASA Technical Reports Server (NTRS)

Turcotte, D. L.; Willemann, R. J.; Haxby, W. F.; Norberry, J.

1981-01-01

The role of membrane stresses and bending stresses in supporting topographic loads on planetary elastic lithospheres is examined. A dimensionless parameter is introduced in order to determine the ability of a spherical shell to support loads through membrane stresses. It is determined that when this parameter is large, membrane stresses can fully support topographic loads with flexure, and when it is small the influence of the membrane stresses can be neglected. Equations governing the behavior of a spherical shell are solved for a topographic load expressed in terms of spherical harmonics, and spherical harmonic expansions of the measured gravity and topography for Mars and the moon are compared with the theory. It is concluded that membrane stresses play an important role in the support of topographic loads on the moon and Mars. The correlation of observed gravitational potential anomalies with the topography on Mars is explained by membrane stresses in the elastic lithosphere.

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

PubMed Central

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

Design Aspects of the Rayleigh Convection Code

NASA Astrophysics Data System (ADS)

Featherstone, N. A.

2017-12-01

Understanding the long-term generation of planetary or stellar magnetic field requires complementary knowledge of the large-scale fluid dynamics pervading large fractions of the object's interior. Such large-scale motions are sensitive to the system's geometry which, in planets and stars, is spherical to a good approximation. As a result, computational models designed to study such systems often solve the MHD equations in spherical geometry, frequently employing a spectral approach involving spherical harmonics. We present computational and user-interface design aspects of one such modeling tool, the Rayleigh convection code, which is suitable for deployment on desktop and petascale-hpc architectures alike. In this poster, we will present an overview of this code's parallel design and its built-in diagnostics-output package. Rayleigh has been developed with NSF support through the Computational Infrastructure for Geodynamics and is expected to be released as open-source software in winter 2017/2018.

Transformation of a Finite-Element Model of a Piezoelectric Spherical Shell Transducer from a Nodal to a Spherical Harmonic Function Representation

DTIC Science & Technology

1990-06-01

J) :(270, )..pTod( 301,j)s(331,j)- pcod (302.j) s(271,j)-prod(303,J)s(332,j ):prod(304,J) s(272,J) prod(305,i) s(333,j) prod(306,j) s(273,jJ.’ptod(307...j).prodf 335,J) sf348, j)-prod( 336.1) 9(288,j)-prod(337,J) of 349, j)- pcod ( 338,J) s(209, j)-prod(339,J) of 350,j)-prod( 340,J) s(290,jJ.. pCod (341,J

Electrostatic similarity of proteins: Application of three dimensional spherical harmonic decomposition

PubMed Central

Długosz, Maciej; Trylska, Joanna

2008-01-01

We present a method for describing and comparing global electrostatic properties of biomolecules based on the spherical harmonic decomposition of electrostatic potential data. Unlike other approaches our method does not require any prior three dimensional structural alignment. The electrostatic potential, given as a volumetric data set from a numerical solution of the Poisson or Poisson–Boltzmann equation, is represented with descriptors that are rotation invariant. The method can be applied to large and structurally diverse sets of biomolecules enabling to cluster them according to their electrostatic features. PMID:18624502

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

NASA Technical Reports Server (NTRS)

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.

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

PubMed

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

A novel surface registration algorithm with biomedical modeling applications.

PubMed

Huang, Heng; Shen, Li; Zhang, Rong; Makedon, Fillia; Saykin, Andrew; Pearlman, Justin

2007-07-01

In this paper, we propose a novel surface matching algorithm for arbitrarily shaped but simply connected 3-D objects. The spherical harmonic (SPHARM) method is used to describe these 3-D objects, and a novel surface registration approach is presented. The proposed technique is applied to various applications of medical image analysis. The results are compared with those using the traditional method, in which the first-order ellipsoid is used for establishing surface correspondence and aligning objects. In these applications, our surface alignment method is demonstrated to be more accurate and flexible than the traditional approach. This is due in large part to the fact that a new surface parameterization is generated by a shortcut that employs a useful rotational property of spherical harmonic basis functions for a fast implementation. In order to achieve a suitable computational speed for practical applications, we propose a fast alignment algorithm that improves computational complexity of the new surface registration method from O(n3) to O(n2).

SPHERE: SPherical Harmonic Elastic REgistration of HARDI Data

PubMed Central

Yap, Pew-Thian; Chen, Yasheng; An, Hongyu; Yang, Yang; Gilmore, John H.; Lin, Weili

2010-01-01

In contrast to the more common Diffusion Tensor Imaging (DTI), High Angular Resolution Diffusion Imaging (HARDI) allows superior delineation of angular microstructures of brain white matter, and makes possible multiple-fiber modeling of each voxel for better characterization of brain connectivity. However, the complex orientation information afforded by HARDI makes registration of HARDI images more complicated than scalar images. In particular, the question of how much orientation information is needed for satisfactory alignment has not been sufficiently addressed. Low order orientation representation is generally more robust than high order representation, although the latter provides more information for correct alignment of fiber pathways. However, high order representation, when naïvely utilized, might not necessarily be conducive to improving registration accuracy since similar structures with significant orientation differences prior to proper alignment might be mistakenly taken as non-matching structures. We present in this paper a HARDI registration algorithm, called SPherical Harmonic Elastic REgistration (SPHERE), which in a principled means hierarchically extracts orientation information from HARDI data for structural alignment. The image volumes are first registered using robust, relatively direction invariant features derived from the Orientation Distribution Function (ODF), and the alignment is then further refined using spherical harmonic (SH) representation with gradually increasing orders. This progression from non-directional, single-directional to multi-directional representation provides a systematic means of extracting directional information given by diffusion-weighted imaging. Coupled with a template-subject-consistent soft-correspondence-matching scheme, this approach allows robust and accurate alignment of HARDI data. Experimental results show marked increase in accuracy over a state-of-the-art DTI registration algorithm. PMID:21147231

Helioseismic Constraints on the Depth Dependence of Large-Scale Solar Convection

NASA Astrophysics Data System (ADS)

Woodard, Martin F.

2017-08-01

A recent helioseismic statistical waveform analysis of subsurface flow based on a 720-day time series of SOHO/MDI Medium-l spherical-harmonic coefficients has been extended to cover a greater range of subphotospheric depths. The latest analysis provides estimates of flow-dependent oscillation-mode coupling-strength coefficients b(s,t;n,l) over the range l = 30 to 150 of mode degree (angular wavenumber) for solar p-modes in the approximate frequency range 2 to 4 mHz. The range of penetration depths of this mode set covers most of the solar convection zone. The most recent analysis measures spherical harmonic (s,t) components of the flow velocity for odd s in the angular wavenumber range 1 to 19 for t not much smaller than s at a given s. The odd-s b(s,t;n,l) coefficients are interpreted as averages over depth of the depth-dependent amplitude of one spherical-harmonic (s,t) component of the toroidal part of the flow velocity field. The depth-dependent weighting function defining the average velocity is the fractional kinetic energy density in radius of modes of the (n,l) multiplet. The b coefficients have been converted to estimates of root velocity power as a function of l0 = nu0*l/nu(n,l), which is a measure of mode penetration depth. (nu(n,l) is mode frequency and nu0 is a reference frequency equal to 3 mHz.) A comparison of the observational results with simple convection models will be presented.

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

PubMed

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 quantum mechanics suggests that the variances (eigenvalues) of the principal components follow a Boltzmann distribution, or equivalently, that standing waves are in a sort of "thermodynamic" equilibrium during non-REM sleep. By extension, we speculate that consciousness emerges as the brain dynamics deviate from such equilibrium.

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

PubMed Central

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 quantum mechanics suggests that the variances (eigenvalues) of the principal components follow a Boltzmann distribution, or equivalently, that standing waves are in a sort of “thermodynamic” equilibrium during non-REM sleep. By extension, we speculate that consciousness emerges as the brain dynamics deviate from such equilibrium. PMID:27445777

Using synchronization in multi-model ensembles to improve prediction

NASA Astrophysics Data System (ADS)

Hiemstra, P.; Selten, F.

2012-04-01

In recent decades, many climate models have been developed to understand and predict the behavior of the Earth's climate system. Although these models are all based on the same basic physical principles, they still show different behavior. This is for example caused by the choice of how to parametrize sub-grid scale processes. One method to combine these imperfect models, is to run a multi-model ensemble. The models are given identical initial conditions and are integrated forward in time. A multi-model estimate can for example be a weighted mean of the ensemble members. We propose to go a step further, and try to obtain synchronization between the imperfect models by connecting the multi-model ensemble, and exchanging information. The combined multi-model ensemble is also known as a supermodel. The supermodel has learned from observations how to optimally exchange information between the ensemble members. In this study we focused on the density and formulation of the onnections within the supermodel. The main question was whether we could obtain syn-chronization between two climate models when connecting only a subset of their state spaces. Limiting the connected subspace has two advantages: 1) it limits the transfer of data (bytes) between the ensemble, which can be a limiting factor in large scale climate models, and 2) learning the optimal connection strategy from observations is easier. To answer the research question, we connected two identical quasi-geostrohic (QG) atmospheric models to each other, where the model have different initial conditions. The QG model is a qualitatively realistic simulation of the winter flow on the Northern hemisphere, has three layers and uses a spectral imple-mentation. We connected the models in the original spherical harmonical state space, and in linear combinations of these spherical harmonics, i.e. Empirical Orthogonal Functions (EOFs). We show that when connecting through spherical harmonics, we only need to connect 28% of the state variables to obtain synchronization. In addition, when connecting through EOFs, we can reduce this percentage even more to 12%. This reduction is caused by the more efficient description of the model state variables when using EOFs. The connected state variables center around the medium scale structures in the model. Small and large scale structures need not be connected in order to obtain synchronization. This could be related to the baroclinic instabilities in the QG model which are located in the medium scale structures of the model. The baroclinic instabilities are the main source of divergence between the two connected models.

Internal and external potential-field estimation from regional vector data at varying satellite altitude

NASA Astrophysics Data System (ADS)

Plattner, Alain; Simons, Frederik J.

2017-10-01

When modelling satellite data to recover a global planetary magnetic or gravitational potential field, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-posed. In those cases, adopting explicitly local methods is to be preferred over adapting global ones (e.g. by regularization). Here, we develop the theory behind a procedure to invert for planetary potential fields from vector observations collected within a spatially bounded region at varying satellite altitude. Our method relies on the construction of spatiospectrally localized bases of functions that mitigate the noise amplification caused by downward continuation (from the satellite altitude to the source) while balancing the conflicting demands for spatial concentration and spectral limitation. The `altitude-cognizant' gradient vector Slepian functions (AC-GVSF) enjoy a noise tolerance under downward continuation that is much improved relative to the `classical' gradient vector Slepian functions (CL-GVSF), which do not factor satellite altitude into their construction. Furthermore, venturing beyond the realm of their first application, published in a preceding paper, in the present article we extend the theory to being able to handle both internal and external potential-field estimation. Solving simultaneously for internal and external fields under the limitation of regional data availability reduces internal-field artefacts introduced by downward-continuing unmodelled external fields, as we show with numerical examples. We explain our solution strategies on the basis of analytic expressions for the behaviour of the estimation bias and variance of models for which signal and noise are uncorrelated, (essentially) space- and band-limited, and spectrally (almost) white. The AC-GVSF are optimal linear combinations of vector spherical harmonics. Their construction is not altogether very computationally demanding when the concentration domains (the regions of spatial concentration) have circular symmetry, for example, on spherical caps or rings—even when the spherical-harmonic bandwidth is large. Data inversion proceeds by solving for the expansion coefficients of truncated function sequences, by least-squares analysis in a reduced-dimensional space. Hence, our method brings high-resolution regional potential-field modelling from incomplete and noisy vector-valued satellite data within reach of contemporary desktop machines.

Exact Solutions of Schrödinger Equation with Improved Ring-Shaped Non-Spherical Harmonic Oscillator and Coulomb Potential

NASA Astrophysics Data System (ADS)

Ndem Ikot, Akpan; Akpan, Ita O.; Abbey, T. M.; Hassanabadi, Hassan

2016-05-01

We propose improved ring shaped like potential of the form, V(r, θ) = V(r) + (ħ2/2Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2 and its exact solutions are presented via the Nikiforov-Uvarov method. The angle dependent part V(θ) = (ħ2 / 2 Mr2)[(β sin2 θ + γ cos2 θ + λ) / sin θ cos θ]2, which is reported for the first time embodied the novel angle dependent (NAD) potential and harmonic novel angle dependent potential (HNAD) as special cases. We discuss in detail the effects of the improved ring shaped like potential on the radial parts of the spherical harmonic and Coulomb potentials.

Mathematical Development and Computational Analysis of Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) Based on Bloch Nuclear Magnetic Resonance (NMR) Diffusion Model for Myocardial Motion.

PubMed

Dada, Michael O; Jayeoba, Babatunde; Awojoyogbe, Bamidele O; Uno, Uno E; Awe, Oluseyi E

2017-09-13

Harmonic Phase-Magnetic Resonance Imaging (HARP-MRI) is a tagged image analysis method that can measure myocardial motion and strain in near real-time and is considered a potential candidate to make magnetic resonance tagging clinically viable. However, analytical expressions of radially tagged transverse magnetization in polar coordinates (which is required to appropriately describe the shape of the heart) have not been explored because the physics required to directly connect myocardial deformation of tagged Nuclear Magnetic Resonance (NMR) transverse magnetization in polar geometry and the appropriate harmonic phase parameters are not yet available. The analytical solution of Bloch NMR diffusion equation in spherical geometry with appropriate spherical wave tagging function is important for proper analysis and monitoring of heart systolic and diastolic deformation with relevant boundary conditions. In this study, we applied Harmonic Phase MRI method to compute the difference between tagged and untagged NMR transverse magnetization based on the Bloch NMR diffusion equation and obtained radial wave tagging function for analysis of myocardial motion. The analytical solution of the Bloch NMR equations and the computational simulation of myocardial motion as developed in this study are intended to significantly improve healthcare for accurate diagnosis, prognosis and treatment of cardiovascular related deceases at the lowest cost because MRI scan is still one of the most expensive anywhere. The analysis is fundamental and significant because all Magnetic Resonance Imaging techniques are based on the Bloch NMR flow equations.

Harmonic analysis of the DTU10 global gravity anomalies

NASA Astrophysics Data System (ADS)

Abrykosov, O.; Förste, Ch.; Gruber, Ch.; Shako, R.; Barthelmes, F.

2012-04-01

We have computed the Earth's gravity models to degree/order 5400 and 10800 (in terms of the ellipsoidal and spherical harmonics) from a rigorous integration of the 2'x2' and 1'x1' global grids of gravity anomalies provided by the Danish Technical University (DTU). The gravity signal recovered from the DTU10 data shows 1) a strong dependency on the truncation of the EGM2008 gravity model which were used to fill-in land areas in the DTU10 grids and 2) an irregular behaviour at frequencies behind the resolution of the EGM2008. We discuss the gravity signal and its accuracy estimation computed from the complete DTU10 grids as well as separately from the data over land and ocean areas.

Tensor spherical harmonics theories on the exact nature of the elastic fields of a spherically anisotropic multi-inhomogeneous inclusion

NASA Astrophysics Data System (ADS)

Shodja, H. M.; Khorshidi, A.

2013-04-01

Eshelby's theories on the nature of the disturbance strains due to polynomial eigenstrains inside an isotropic ellipsoidal inclusion, and the form of homogenizing eigenstrains corresponding to remote polynomial loadings in the equivalent inclusion method (EIM) are not valid for spherically anisotropic inclusions and inhomogeneities. Materials with spherically anisotropic behavior are frequently encountered in nature, for example, some graphite particles or polyethylene spherulites. Moreover, multi-inclusions/inhomogeneities/inhomogeneous inclusions have abundant engineering and scientific applications and their exact theoretical treatment would be of great value. The present work is devoted to the development of a mathematical framework for the exact treatment of a spherical multi-inhomogeneous inclusion with spherically anisotropic constituents embedded in an unbounded isotropic matrix. The formulations herein are based on tensor spherical harmonics having orthogonality and completeness properties. For polynomial eigenstrain field and remote applied loading, several theorems on the exact closed-form expressions of the elastic fields associated with the matrix and all the phases of the inhomogeneous inclusion are stated and proved. Several classes of impotent eigenstrain fields associated to a generally anisotropic inclusion as well as isotropic and spherically anisotropic multi-inclusions are also introduced. The presented theories are useful for obtaining highly accurate solutions of desired accuracy when the constituent phases of the multi-inhomogeneous inclusion are made of functionally graded materials (FGMs).

Weekly Solutions of Time-Variable Gravity from 1993 to 2010

NASA Technical Reports Server (NTRS)

Lemoine, F.; Chinn, D.; Le Bail, K.; Zelensky, N.; Melachroinos, S.; Beall, J.

2011-01-01

The GRACE mission has been highly successful in determining the time-variable gravity field of the Earth, producing monthly or even more frequent solutions (cf. 10-day) solutions using both spherical harmonics and mascons. However the GRACE time series only commences in 2002 - 2003 and a gap of several years may occur in the series before a GRACE follow-on satellite is launched. Satellites tracked by SLR and DORIS have also been used to study time variations in the Earth's gravitational field. These include (most recently) the solutions of Cox and Chao (2002), Cheng et al. (2004, 2007) and Lemoine et al. (2007). In this paper we discuss the development of a new time series of low degree spherical harmonic fields based on the available SLR, DORIS and GPS data. We develop simultaneous solutions for both the geocenter and the low degree harmonics up to 5x5. The solutions integrate data from SLR geodetic satellites (e.g., Lageos1, Lageos2, Starlette, Stella, Ajisai, Larets, Westpac), altimetry satellites (TOPEX/Poseidon, Envisat, Jason-1, Jason-2), and satellites tracked solely by DORIS (e.g. SPOT2-5). We discuss some pertinent aspects of the satellite-specific modeling. We include altimeter crossovers in the weekly solutions where feasible and time permits. The resulting geocenter time series is compared with geophysical model predictions and other independently-derived solutions. Over the GRACE time period the fidelity and consistency with the GRACE solutions are presented.

Worldwide complete spherical Bouguer and isostatic anomaly maps

NASA Astrophysics Data System (ADS)

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 et al., 2008), which represents the best up-to-date global gravity model (including surface gravity measurements from land, marine and airborne surveys as well as gravity and altimetry satellite measurements). The surface gravity anomaly (free air) is computed at the Earth's surface in the context of Molodensky theory and includes corrections from the mass of the atmosphere. The way gravity anomalies are computed on a worldwide basis slightly differs from the classical usage, but meets modern concerns which tend to take the real Earth into account. The resulting anomaly maps and grids will be distributed for scientific and education purposes by the Commission for the Geological Map of the World (CGMW) with support of UNESCO and other institutions. Upgraded versions might be done as soon as new global gravity model is available (including satellite GOCE and new surface measurements: ground, airborne). Visit / contact BGI (http://bgi.omp.obs-mip.fr) and CCMW (http://ccgm.free.fr) for more information.

Evaluation of geopotential and luni-solar perturbations by a recursive algorithm

NASA Technical Reports Server (NTRS)

Giacaglia, G. E. O.

1975-01-01

The disturbing functions due to the geopotential and Luni-solar attractions are linear and bilinear forms in spherical harmonics. Making use of recurrence relations for the solid spherical harmonics and their derivatives, recurrence formulas are obtained for high degree terms as function of lower degree for any term of those disturbing functions and their derivative with respect to any element. The equations obtained are effective when a numerical integration of the equations of motion is appropriate. In analytical theories, they provide a fast way of obtaining high degree terms starting from initial very simple functions.

What Supergranule Flow Models Tell Us About the Sun's Surface Shear Layer and Magnetic Flux Transport

NASA Technical Reports Server (NTRS)

Hathaway, David

2011-01-01

Models of the photospheric flows due to supergranulation are generated using an evolving spectrum of vector spherical harmonics up to spherical harmonic wavenumber l1500. Doppler velocity data generated from these models are compared to direct Doppler observations from SOHO/MDI and SDO/HMI. The models are adjusted to match the observed spatial power spectrum as well as the wavenumber dependence of the cell lifetimes, differential rotation velocities, meridional flow velocities, and relative strength of radial vs. horizontal flows. The equatorial rotation rate as a function of wavelength matches the rotation rate as a function of depth as determined by global helioseismology. This leads to the conclusions that the cellular structures are anchored at depths equal to their widths, that the surface shear layer extends to at least 70 degrees latitude, and that the poleward meridional flow decreases in amplitude and reverses direction at the base of the surface shear layer (approx.35 Mm below the surface). Using the modeled flows to passively transport magnetic flux indicates that the observed differential rotation and meridional flow of the magnetic elements are directly related to the differential rotation and meridional flow of the convective pattern itself. The magnetic elements are transported by the evolving boundaries of the supergranule pattern (where the convective flows converge) and are unaffected by the weaker flows associated with the differential rotation or meridional flow of the photospheric plasma.

Regional inversion of GRACE data for continental water mass time-variations. Comparison with global hydrology models, classical spherical harmonics and "mascons" solutions

NASA Astrophysics Data System (ADS)

Seoane, L.; Ramillien, G.; Frappart, F.; Biancale, R.; Gratton, S.; Bourgogne, S.

2010-12-01

Time series of 2°-by-2° constrained/unconstrained GRACE geoid solutions have been computed with a 10-day resolution by using a new regional method recently implemented at GRGS (Toulouse, France). This approach uses the dynamical orbit analysis of GRACE Level-1 measurements, and specially accurate along-track KBRR residuals to estimate the continental water mass changes over large geographical regions. For validation, our GRACE-derived regional maps are compared to: (1) the global hydrological model outputs (WGHM, LaD, NOAH), (2) the NASA "mascons" solutions based on spherical harmonics and (3) the global solutions produced by GRGS and CSR, GFZ, JPL filtered with different methodologies (Gaussian, destriped and smoothed, ICA). In this study, we focus on the annual time scale of water mass redistributions occuring in drainage basins like Amazon or Congo. Each 2°-averaged surface element is characterized by its seasonal amplitude and phase. Even if the all sources are expected to provide quite comparable results for the continental water cycle, we suspect the residual differences are from smoothing effects of the spatial constraints included in the "mascons" solutions and the underestimating the seasonal amplitudes by global hydrological models.

Resonance energy transfer: The unified theory via vector spherical harmonics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grinter, Roger, E-mail: r.grinter@uea.ac.uk; Jones, Garth A., E-mail: garth.jones@uea.ac.uk

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 inherentmore » 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.« less

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

PubMed Central

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. PMID:24156077

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

PubMed

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.

Precise and efficient evaluation of gravimetric quantities at arbitrarily scattered points in space

NASA Astrophysics Data System (ADS)

Ivanov, Kamen G.; Pavlis, Nikolaos K.; Petrushev, Pencho

2017-12-01

Gravimetric quantities are commonly represented in terms of high degree surface or solid spherical harmonics. After EGM2008, such expansions routinely extend to spherical harmonic degree 2190, which makes the computation of gravimetric quantities at a large number of arbitrarily scattered points in space using harmonic synthesis, a very computationally demanding process. We present here the development of an algorithm and its associated software for the efficient and precise evaluation of gravimetric quantities, represented in high degree solid spherical harmonics, at arbitrarily scattered points in the space exterior to the surface of the Earth. The new algorithm is based on representation of the quantities of interest in solid ellipsoidal harmonics and application of the tensor product trigonometric needlets. A FORTRAN implementation of this algorithm has been developed and extensively tested. The capabilities of the code are demonstrated using as examples the disturbing potential T, height anomaly ζ , gravity anomaly Δ g , gravity disturbance δ g , north-south deflection of the vertical ξ , east-west deflection of the vertical η , and the second radial derivative T_{rr} of the disturbing potential. After a pre-computational step that takes between 1 and 2 h per quantity, the current version of the software is capable of computing on a standard PC each of these quantities in the range from the surface of the Earth up to 544 km above that surface at speeds between 20,000 and 40,000 point evaluations per second, depending on the gravimetric quantity being evaluated, while the relative error does not exceed 10^{-6} and the memory (RAM) use is 9.3 GB.

Mathematics of Computed Tomography

NASA Astrophysics Data System (ADS)

Hawkins, William Grant

A review of the applications of the Radon transform is presented, with emphasis on emission computed tomography and transmission computed tomography. The theory of the 2D and 3D Radon transforms, and the effects of attenuation for emission computed tomography are presented. The algebraic iterative methods, their importance and limitations are reviewed. Analytic solutions of the 2D problem the convolution and frequency filtering methods based on linear shift invariant theory, and the solution of the circular harmonic decomposition by integral transform theory--are reviewed. The relation between the invisible kernels, the inverse circular harmonic transform, and the consistency conditions are demonstrated. The discussion and review are extended to the 3D problem-convolution, frequency filtering, spherical harmonic transform solutions, and consistency conditions. The Cormack algorithm based on reconstruction with Zernike polynomials is reviewed. An analogous algorithm and set of reconstruction polynomials is developed for the spherical harmonic transform. The relations between the consistency conditions, boundary conditions and orthogonal basis functions for the 2D projection harmonics are delineated and extended to the 3D case. The equivalence of the inverse circular harmonic transform, the inverse Radon transform, and the inverse Cormack transform is presented. The use of the number of nodes of a projection harmonic as a filter is discussed. Numerical methods for the efficient implementation of angular harmonic algorithms based on orthogonal functions and stable recursion are presented. The derivation of a lower bound for the signal-to-noise ratio of the Cormack algorithm is derived.

Non-linear three dimensional spectral model of the Venusian thermosphere with super-rotation. I - Formulation and numerical technique. II - Temperature, composition and winds

NASA Technical Reports Server (NTRS)

Stevens-Rayburn, D. R.; Mengel, J. G.; Harris, I.; Mayr, H. G.

1989-01-01

A three-dimensional spectral model for the Venusion thermosphere is presented which uses spherical harmonics to represent the horizontal variations in longitude and latitude and which uses Fourier harmonics to represent the LT variations due to atmospheric rotation. A differencing scheme with tridiagonal block elimination is used to perform the height integration. Quadratic nonlinearities are taken into account. In the second part, numerical results obtained with the model are shown to reproduce the observed broad daytime maxima in CO2 and CO and the significantly larger values at dawn than at dusk. It is found that the diurnal variations in He are most sensitive to thermospheric superrotation, and that, given a globally uniform atmosphere as input, larger heating rates yield a larger temperature contrast between day and night.

A Comprehensive Study of Gridding Methods for GPS Horizontal Velocity Fields

NASA Astrophysics Data System (ADS)

Wu, Yanqiang; Jiang, Zaisen; Liu, Xiaoxia; Wei, Wenxin; Zhu, Shuang; Zhang, Long; Zou, Zhenyu; Xiong, Xiaohui; Wang, Qixin; Du, Jiliang

2017-03-01

Four gridding methods for GPS velocities are compared in terms of their precision, applicability and robustness by analyzing simulated data with uncertainties from 0.0 to ±3.0 mm/a. When the input data are 1° × 1° grid sampled and the uncertainty of the additional error is greater than ±1.0 mm/a, the gridding results show that the least-squares collocation method is highly robust while the robustness of the Kriging method is low. In contrast, the spherical harmonics and the multi-surface function are moderately robust, and the regional singular values for the multi-surface function method and the edge effects for the spherical harmonics method become more significant with increasing uncertainty of the input data. When the input data (with additional errors of ±2.0 mm/a) are decimated by 50% from the 1° × 1° grid data and then erased in three 6° × 12° regions, the gridding results in these three regions indicate that the least-squares collocation and the spherical harmonics methods have good performances, while the multi-surface function and the Kriging methods may lead to singular values. The gridding techniques are also applied to GPS horizontal velocities with an average error of ±0.8 mm/a over the Chinese mainland and the surrounding areas, and the results show that the least-squares collocation method has the best performance, followed by the Kriging and multi-surface function methods. Furthermore, the edge effects of the spherical harmonics method are significantly affected by the sparseness and geometric distribution of the input data. In general, the least-squares collocation method is superior in terms of its robustness, edge effect, error distribution and stability, while the other methods have several positive features.

The ITSG-Grace2014 Gravity Field Model

NASA Astrophysics Data System (ADS)

Kvas, Andreas; Mayer-Gürr, Torsten; Zehenter, Norbert; Klinger, Beate

2015-04-01

The ITSG-Grace2014 GRACE-only gravity field model consists of a high resolution unconstrained static model (up to degree 200) with trend and annual signal, monthly unconstrained solutions with different spatial resolutions as well as daily snapshots derived by using a Kalman smoother. Apart from the estimated spherical harmonic coefficients, full variance-covariance matrices for the monthly solutions and the static gravity field component are provided. Compared to the previous release, multiple improvements in the processing chain are implemented: updated background models, better ionospheric modeling for GPS observations, an improved satellite attitude by combination of star camera and angular accelerations, estimation of K-band antenna center variations within the gravity field recovery process as well as error covariance function determination. Furthermore, daily gravity field variations have been modeled in the adjustment process to reduce errors caused by temporal leakage. This combined estimation of daily gravity variations field variations together with the static gravity field component represents a computational challenge due to the significantly increased parameter count. The modeling of daily variations up to a spherical harmonic degree of 40 for the whole GRACE observation period results in a system of linear equations with over 6 million unknown gravity field parameters. A least squares adjustment of this size is not solvable in a sensible time frame, therefore measures to reduce the problem size have to be taken. The ITSG-Grace2014 release is presented and selected parts of the processing chain and their effect on the estimated gravity field solutions are discussed.

On regional geomagnetic charts

USGS Publications Warehouse

Alldredge, L.R.

1987-01-01

When regional geomagnetic charts for areas roughly the size of the US were compiled by hand, some large local anomalies were displayed in the isomagnetic lines. Since the late 1960s, when the compilation of charts using computers and mathematical models was started, most of the details available in the hand drawn regional charts have been lost. One exception to this is the Canadian magnetic declination chart for 1980. This chart was constructed using a 180 degrees spherical harmonic model. -from Author

The Influence of Atmosphere Parameters on the Signal for Remote Sensing Polarimetric Electro-Optical Systems

NASA Astrophysics Data System (ADS)

Budak, Vladimir P.; Korkin, Sergey V.

2009-03-01

The singularity subtraction on the vectorial modification of spherical harmonics method (VMSH) of the solution of the vectorial radiative transfer equation boundary problem is applied to the problem of influence of atmosphere parameters on the polarimetric system signal. We assume in this model different phase matrices (Mie, Rayleigh, and Henyey-Greenstein), reflecting bottom and particle size distribution. The authors describe the main features of the model and some results of its implementation.

Decoding Mode-mixing in Black-hole Merger Ringdown

NASA Technical Reports Server (NTRS)

Kelly, Bernard J.; Baker, John G.

2013-01-01

Optimal extraction of information from gravitational-wave observations of binary black-hole coalescences requires detailed knowledge of the waveforms. Current approaches for representing waveform information are based on spin-weighted spherical harmonic decomposition. Higher-order harmonic modes carrying a few percent of the total power output near merger can supply information critical to determining intrinsic and extrinsic parameters of the binary. One obstacle to constructing a full multi-mode template of merger waveforms is the apparently complicated behavior of some of these modes; instead of settling down to a simple quasinormal frequency with decaying amplitude, some |m| = modes show periodic bumps characteristic of mode-mixing. We analyze the strongest of these modes the anomalous (3, 2) harmonic mode measured in a set of binary black-hole merger waveform simulations, and show that to leading order, they are due to a mismatch between the spherical harmonic basis used for extraction in 3D numerical relativity simulations, and the spheroidal harmonics adapted to the perturbation theory of Kerr black holes. Other causes of mode-mixing arising from gauge ambiguities and physical properties of the quasinormal ringdown modes are also considered and found to be small for the waveforms studied here.

Spherical beamforming for spherical array with impedance surface

NASA Astrophysics Data System (ADS)

Tontiwattanakul, Khemapat

2018-01-01

Spherical microphone array beamforming has been a popular research topic for recent years. Due to their isotropic beam in three dimensional spaces as well as a certain frequency range, the arrays are widely used in many applications such as sound field recording, acoustic beamforming, and noise source localisation. The body of a spherical array is usually considered perfectly rigid. A sound field captured by the sensors on spherical array can be decomposed into a series of spherical harmonics. In noise source localisation, the amplitude density of sound sources is estimated and illustrated by mean of colour maps. In this work, a rigid spherical array covered by fibrous materials is studied via numerical simulation and the performance of the spherical beamforming is discussed.

Matrix eigenvalue method for free-oscillations modelling of spherical elastic bodies

NASA Astrophysics Data System (ADS)

Zábranová, E.; Hanyk, L.; Matyska, C.

2017-11-01

Deformations and changes of the gravitational potential of pre-stressed self-gravitating elastic bodies caused by free oscillations are described by means of the momentum and Poisson equations and the constitutive relation. For spherically symmetric bodies, the equations and boundary conditions are transformed into ordinary differential equations of the second order by the spherical harmonic decomposition and further discretized by highly accurate pseudospectral difference schemes on Chebyshev grids; we pay special attention to the conditions at the centre of the models. We thus obtain a series of matrix eigenvalue problems for eigenfrequencies and eigenfunctions of the free oscillations. Accuracy of the presented numerical approach is tested by means of the Rayleigh quotients calculated for the eigenfrequencies up to 500 mHz. Both the modal frequencies and eigenfunctions are benchmarked against the output from the Mineos software package based on shooting methods. The presented technique is a promising alternative to widely used methods because it is stable and with a good capability up to high frequencies.

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system.

PubMed

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-21

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer's Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26 cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients.

On the Retrieval of Geocenter Motion from Gravity Data

NASA Astrophysics Data System (ADS)

Rosat, S.; Mémin, A.; Boy, J. P.; Rogister, Y. J. G.

2017-12-01

The center of mass of the whole Earth, the so-called geocenter, is moving with respect to the Center of Mass of the solid Earth because of the loading exerted by the Earth's fluid layers on the solid crust. Space geodetic techniques tying satellites and ground stations (e.g. GNSS, SLR and DORIS) have been widely employed to estimate the geocenter motion. Harmonic degree-1 variations of the gravity field are associated to the geocenter displacement. We show that ground records of time-varying gravity from Superconducting Gravimeters (SGs) can be used to constrain the geocenter motion. Two major difficulties have to be tackled: (1) the sensitivity of surface gravimetric measurements to local mass changes, and in particular hydrological and atmospheric variabilities; (2) the spatial aliasing (spectral leakage) of spherical harmonic degrees higher than 1 induced by the under-sampling of station distribution. The largest gravity variations can be removed from the SG data by subtracting solid and oceanic tides as well as atmospheric and hydrologic effects using global models. However some hydrological signal may still remain. Since surface water content is well-modelled using GRACE observations, we investigate how the spatial aliasing in SG data can be reduced by employing GRACE solutions when retrieving geocenter motion. We show synthetic simulations using complete surface loading models together with GRACE solutions computed at SG stations. In order to retrieve the degree-one gravity variations that are associated with the geocenter motion, we use a multi-station stacking method that performs better than a classical spherical harmonic stacking when the station distribution is inhomogeneous. We also test the influence of the network configuration on the estimate of the geocenter motion. An inversion using SG and GRACE observations is finally presented and the results are compared with previous geocenter estimates.

CORRELATED AND ZONAL ERRORS OF GLOBAL ASTROMETRIC MISSIONS: A SPHERICAL HARMONIC SOLUTION

DOE Office of Scientific and Technical Information (OSTI.GOV)

Makarov, V. V.; Dorland, B. N.; Gaume, R. A.

We propose a computer-efficient and accurate method of estimating spatially correlated errors in astrometric positions, parallaxes, and proper motions obtained by space- and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects in space astrometry, such as SIM or JASMINE.

Oceanic tide maps and spherical harmonic coefficients from Geosat altimetry

NASA Technical Reports Server (NTRS)

Cartwright, D. E.; Ray, R. D.; Sanchez, B. V.

1991-01-01

Maps and tables for the global ocean tides, 69 degree N to 68 degree S, derived from two years of Geosat altimetry are presented. Global maps of local and Greenwich admittance of the (altimetric) ocean tide, and maps of amplitude and Greenwich phase lag of the ocean tide are shown for M(sub 2), S(sub 2), N(sub 2), O(sub 1), and K(sub 1). Larger scale maps of amplitude and phases are also shown for regional areas of special interest. Spherical harmonic coefficients of the ocean tide through degree and order 8 are tabulated for the six major constituents.

Correlated and Zonal Errors of Global Astrometric Missions: A Spherical Harmonic Solution

NASA Astrophysics Data System (ADS)

Makarov, V. V.; Dorland, B. N.; Gaume, R. A.; Hennessy, G. S.; Berghea, C. T.; Dudik, R. P.; Schmitt, H. R.

2012-07-01

We propose a computer-efficient and accurate method of estimating spatially correlated errors in astrometric positions, parallaxes, and proper motions obtained by space- and ground-based astrometry missions. In our method, the simulated observational equations are set up and solved for the coefficients of scalar and vector spherical harmonics representing the output errors rather than for individual objects in the output catalog. Both accidental and systematic correlated errors of astrometric parameters can be accurately estimated. The method is demonstrated on the example of the JMAPS mission, but can be used for other projects in space astrometry, such as SIM or JASMINE.

Parameter estimation applied to Nimbus 6 wide-angle longwave radiation measurements

NASA Technical Reports Server (NTRS)

Green, R. N.; Smith, G. L.

1978-01-01

A parameter estimation technique was used to analyze the August 1975 Nimbus 6 Earth radiation budget data to demonstrate the concept of deconvolution. The longwave radiation field at the top of the atmosphere is defined from satellite data by a fifth degree and fifth order spherical harmonic representation. The variations of the major features of the radiation field are defined by analyzing the data separately for each two-day duty cycle. A table of coefficient values for each spherical harmonic representation is given along with global mean, gradients, degree variances, and contour plots. In addition, the entire data set is analyzed to define the monthly average radiation field.

AUTOMATIC GENERATION OF FFT FOR TRANSLATIONS OF MULTIPOLE EXPANSIONS IN SPHERICAL HARMONICS

PubMed Central

Mirkovic, Dragan; Pettitt, B. Montgomery; Johnsson, S. Lennart

2009-01-01

The fast multipole method (FMM) is an efficient algorithm for calculating electrostatic interactions in molecular simulations and a promising alternative to Ewald summation methods. Translation of multipole expansion in spherical harmonics is the most important operation of the fast multipole method and the fast Fourier transform (FFT) acceleration of this operation is among the fastest methods of improving its performance. The technique relies on highly optimized implementation of fast Fourier transform routines for the desired expansion sizes, which need to incorporate the knowledge of symmetries and zero elements in the input arrays. Here a method is presented for automatic generation of such, highly optimized, routines. PMID:19763233

Efficient molecular density functional theory using generalized spherical harmonics expansions.

PubMed

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.

Flyby Characterization of Lower-Degree Spherical Harmonics Around Small Bodies

NASA Technical Reports Server (NTRS)

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.

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

PubMed

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.

Deconstructing the shallow internal structure of the Moon using GRAIL gravity and LOLA topography

NASA Astrophysics Data System (ADS)

Zuber, M. T.

2015-12-01

Globally-distributed, high-resolution gravity and topography observations of the Moon from the Gravity Recovery and Interior Laboratory (GRAIL) mission and Lunar Orbiter Laser Altimeter (LOLA) instrument aboard the Lunar Reconnaissance Orbiter (LRO) spacecraft afford the unprecedented opportunity to explore the shallow internal structure of the Moon. Gravity and topography can be combined to produce Bouguer gravity that reveals the distribution of mass in the subsurface, with high degrees in the spherical harmonic expansion of the Bouguer anomalies sensitive to shallowest structure. For isolated regions of the lunar highlands and several basins we have deconstructed the gravity field and mapped the subsurface distribution of density anomalies. While specified spherical harmonic degree ranges can be used to estimate contributions at different depths, such analyses require considerable caution in interpretation. A comparison of filtered Bouguer gravity with forward models of disk masses with plausible densities illustrates the interdependencies of the gravitational power of density anomalies with depth and spatial scale. The results have implications regarding the limits of interpretation of lunar subsurface structure.

On the frequency spectra of the core magnetic field Gauss coefficients

NASA Astrophysics Data System (ADS)

Lesur, Vincent; Wardinski, Ingo; Baerenzung, Julien; Holschneider, Matthias

2018-03-01

From monthly mean observatory data spanning 1957-2014, geomagnetic field secular variation values were calculated by annual differences. Estimates of the spherical harmonic Gauss coefficients of the core field secular variation were then derived by applying a correlation based modelling. Finally, a Fourier transform was applied to the time series of the Gauss coefficients. This process led to reliable temporal spectra of the Gauss coefficients up to spherical harmonic degree 5 or 6, and down to periods as short as 1 or 2 years depending on the coefficient. We observed that a k-2 slope, where k is the frequency, is an acceptable approximation for these spectra, with possibly an exception for the dipole field. The monthly estimates of the core field secular variation at the observatory sites also show that large and rapid variations of the latter happen. This is an indication that geomagnetic jerks are frequent phenomena and that significant secular variation signals at short time scales - i.e. less than 2 years, could still be extracted from data to reveal an unexplored part of the core dynamics.

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

NASA Technical Reports Server (NTRS)

Rapp, Richard H.; Wang, Yan Ming; Pavlis, Nikolaos K.

1991-01-01

The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

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

PubMed

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.

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

PubMed Central

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

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

NASA Technical Reports Server (NTRS)

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.

Present-day secular variations in the zonal harmonics of earth's geopotential

NASA Technical Reports Server (NTRS)

Mitrovica, J. X.; Peltier, W. R.

1993-01-01

The mathematical formulation required for predicting secular variation in the geopotential is developed for the case of a spherically symmetric, self-gravitating, viscoelastic earth model and an arbitrary surface load which can include a gravitational self-consistent ocean loading component. The theory is specifically applied to predict the present-day secular variation in the zonal harmonics of the geopotenial arising from the surface mass loading associated with the late Pleistocene glacial cycles. A procedure is outlined in which predictions of the present-day geopotential signal due to the late Pleistocene glacial cycles may be used to derive bounds on the net present-day mass flux from the Antarctic and Greenland ice sheets to the local oceans.

Analytic Reflected Lightcurves for Exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-04-01

The disk-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motion coupled with an inhomogeneous albedo map. We have previously derived analytic reflected lightcurves for spherical harmonic albedo maps in the special case of a synchronously-rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard 2013). In this letter, we present analytic reflected lightcurves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_l^m-maps). In particular, we use Wigner D-matrices to express an harmonic lightcurve for an arbitrary viewing geometry as a non-linear combination of harmonic lightcurves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected lightcurves, as well as fast calculation of lightcurves for mapping exoplanets based on time-resolved photometry. To these ends we make available Exoplanet Analytic Reflected Lightcurves (EARL), a simple open-source code that allows rapid computation of reflected lightcurves.

A harmonic analysis of lunar topography

NASA Technical Reports Server (NTRS)

Bills, B. G.; Ferrari, A. J.

1977-01-01

A global lunar topographic map has been derived from existing earth-based and orbital observations supplemented in areas without data by a linear autocovariance predictor. Of 2592 bins, each 5 deg square, 1380 (64.7% by area) contain at least one measurement. A spherical harmonic analysis to degree 12 yields a mean radius of 1737.53 plus or minus 0.03 km (formal standard error) and an offset of the center of figure of 1.98 plus or minus 0.06 km toward (19 plus or minus 2) deg S, (194 plus or minus 1) deg E. A Bouguer gravity map, derived from a 12-degree free-air gravity model and the present topography data, is presented for an elevation of 100 km above the mean surface. It is confirmed that the low-degree gravity harmonics are determined primarily by surface height variations and only secondarily by lateral density variations.

Extending radiative transfer models by use of Bayes rule. [in atmospheric science

NASA Technical Reports Server (NTRS)

Whitney, C.

1977-01-01

This paper presents a procedure that extends some existing radiative transfer modeling techniques to problems in atmospheric science where curvature and layering of the medium and dynamic range and angular resolution of the signal are important. Example problems include twilight and limb scan simulations. Techniques that are extended include successive orders of scattering, matrix operator, doubling, Gauss-Seidel iteration, discrete ordinates and spherical harmonics. The procedure for extending them is based on Bayes' rule from probability theory.

Eshelby's problem of a spherical inclusion eccentrically embedded in a finite spherical body

PubMed Central

He, Q.-C.

2017-01-01

Resorting to the superposition principle, the solution of Eshelby's problem of a spherical inclusion located eccentrically inside a finite spherical domain is obtained in two steps: (i) the solution to the problem of a spherical inclusion in an infinite space; (ii) the solution to the auxiliary problem of the corresponding finite spherical domain subjected to appropriate boundary conditions. Moreover, a set of functions called the sectional and harmonic deviators are proposed and developed to work out the auxiliary solution in a series form, including the displacement and Eshelby tensor fields. The analytical solutions are explicitly obtained and illustrated when the geometric and physical parameters and the boundary condition are specified. PMID:28293141

Comment on "An Assessment of the ICE-6G_C (VM5a) Glacial Isostatic Adjustment Model" by Purcell et al.

NASA Astrophysics Data System (ADS)

Richard Peltier, W.; Argus, Donald F.; Drummond, Rosemarie

2018-02-01

The most recently published model of the glacial isostatic adjustment process in the ICE-NG (VMX) sequence from the University of Toronto, denoted ICE-6G_C (VM5a), was originally developed to degree and order 256 in spherical harmonics and has been shown to provide accurate fits to a voluminous database of GPS observations from North America, Eurasia, and Antarctica, to time dependent gravity data being provided by the GRACE satellites, and to radiocarbon-dated relative sea level histories through the Holocene epoch. The authors of the Purcell et al. (2016, https://doi.org/10.1002/2015JB012742) paper have suggested this model to be flawed. We have produced a further version of our model, denoted ICE-6G_D (VM5a), by employing the same BEDMAP2 bathymetry for the Southern Ocean as employed in their analysis which has somewhat reduced the differences between our results. However, significant physically important differences remain, including the magnitude of present-day vertical crustal motion in the embayments and in the spectrum of Stokes coefficients for present-day geoid height time dependence which continues to "flatten" at high spherical harmonic degree. We explore the reasons for these differences and trace them to the use by Purcell et al. of a loading history for the embayments that differs significantly from that tabulated for both the original and modified versions of our model.

High-order perturbations of a spherical collapsing star

DOE Office of Scientific and Technical Information (OSTI.GOV)

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

2010-11-15

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.more » 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.« less

Acoustic centering of sources measured by surrounding spherical microphone arrays.

PubMed

Hagai, Ilan Ben; Pollow, Martin; Vorländer, Michael; Rafaely, Boaz

2011-10-01

The radiation patterns of acoustic sources have great significance in a wide range of applications, such as measuring the directivity of loudspeakers and investigating the radiation of musical instruments for auralization. Recently, surrounding spherical microphone arrays have been studied for sound field analysis, facilitating measurement of the pressure around a sphere and the computation of the spherical harmonics spectrum of the sound source. However, the sound radiation pattern may be affected by the location of the source inside the microphone array, which is an undesirable property when aiming to characterize source radiation in a unique manner. This paper presents a theoretical analysis of the spherical harmonics spectrum of spatially translated sources and defines four measures for the misalignment of the acoustic center of a radiating source. Optimization is used to promote optimal alignment based on the proposed measures and the errors caused by numerical and array-order limitations are investigated. This methodology is examined using both simulated and experimental data in order to investigate the performance and limitations of the different alignment methods. © 2011 Acoustical Society of America

Ozone data and mission sampling analysis

NASA Technical Reports Server (NTRS)

Robbins, J. L.

1980-01-01

A methodology was developed to analyze discrete data obtained from the global distribution of ozone. Statistical analysis techniques were applied to describe the distribution of data variance in terms of empirical orthogonal functions and components of spherical harmonic models. The effects of uneven data distribution and missing data were considered. Data fill based on the autocorrelation structure of the data is described. Computer coding of the analysis techniques is included.

VLBI2020: From Reality to Vision

NASA Technical Reports Server (NTRS)

Titov, Oleg

2010-01-01

The individual apparent motions of distant radio sources are believed to be caused by the effect of intrinsic structure variations of the active galactic nuclei (AGN). However, some cosmological models of the expanded Universe predict that systematic astrometric proper motions of distant quasars do not vanish as the radial distance from the observer to the quasar grows. These systematic effects can even increase with the distance, making it possible to measure them with high-precision astrometric techniques like VLBI. The Galactocentric acceleration of the Solar System barycenter may cause a secular aberration drift with a magnitude of 4 uas/yr. The Solar System motion relative to the cosmic microwave background produces an additional dipole effect, proportional to red shift. We analyzed geodetic VLBI data spanning from 1979 until 2009 to estimate the vector spherical harmonics in the expansion of the vector field of the proper motion of 687 radio sources. The dipole and quadrupole vector spherical harmonics were estimated with an accuracy of 1-5 as/yr. We have shown that over the next decade the geodetic VLBI may approach the level of accuracy on which the cosmological models of the Universe could be tested. Hence, it is important to organize a dedicated observational program to increase the number of measured proper motions to 3000.

Confirmation of a change in the global shear velocity pattern at around 1000 km depth

NASA Astrophysics Data System (ADS)

Durand, S.; Debayle, E.; Ricard, Y.; Zaroli, C.; Lambotte, S.

2017-12-01

In this study, we confirm the existence of a change in the shear velocity spectrum around 1000 km depth based on a new shear velocity tomographic model of the Earth's mantle, SEISGLOB2. This model is based on Rayleigh surface wave phase velocities, self- and cross-coupling structure coefficients of spheroidal normal modes and body wave traveltimes which are, for the first time, combined in a tomographic inversion. SEISGLOB2 is developed up to spherical harmonic degree 40 and in 21 radial spline functions. The spectrum of SEISGLOB2 is the flattest (i.e. richest in 'short' wavelengths corresponding to spherical harmonic degrees greater than 10) around 1000 km depth and this flattening occurs between 670 and 1500 km depth. We also confirm various changes in the continuity of slabs and mantle plumes all around 1000 km depth where we also observed the upper boundary of Large Low Shear Velocity Provinces. The existence of a flatter spectrum, richer in short-wavelength heterogeneities, in a region of the mid-mantle can have great impacts on our understanding of the mantle dynamics and should thus be better understood in the future. Although a viscosity increase, a phase change or a compositional change can all concur to induce this change of pattern, its precise origin is still very uncertain.

Statistical validation of brain tumor shape approximation via spherical harmonics for image-guided neurosurgery.

PubMed

Goldberg-Zimring, Daniel; Talos, Ion-Florin; Bhagwat, Jui G; Haker, Steven J; Black, Peter M; Zou, Kelly H

2005-04-01

Surgical planning now routinely uses both two-dimensional (2D) and three-dimensional (3D) models that integrate data from multiple imaging modalities, each highlighting one or more aspects of morphology or function. We performed a preliminary evaluation of the use of spherical harmonics (SH) in approximating the 3D shape and estimating the volume of brain tumors of varying characteristics. Magnetic resonance (MR) images from five patients with brain tumors were selected randomly from our MR-guided neurosurgical practice. Standardized mean square reconstruction errors (SMSRE) by tumor volume were measured. Validation metrics for comparing performances of the SH method against segmented contours (SC) were the dice similarity coefficient (DSC) and standardized Euclidean distance (SED) measure. Tumor volume range was 22,413-85,189 mm3, and range of number of vertices in triangulated models was 3674-6544. At SH approximations with degree of at least 30, SMSRE were within 1.66 x 10(-5) mm(-1). Summary measures yielded a DSC range of 0.89-0.99 (pooled median, 0.97 and significantly >0.7; P < .001) and an SED range of 0.0002-0.0028 (pooled median, 0.0005). 3D shapes of tumors may be approximated by using SH for neurosurgical applications.

2017 Updates: Earth Gravitational Model 2020

NASA Astrophysics Data System (ADS)

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

Rates of change of the earth's magnetic field measured by recent analyses

NASA Technical Reports Server (NTRS)

Harrison, C. G. A.; Huang, Qilin

1990-01-01

Typical rates of change of the earth's magnetic field are presented as a function of the earth's spherical harmonics. Harmonics up to the eight degree are analyzed. With the increase in the degree of the harmonics an increase in the relative rate of change can be observed. For higher degrees, the rate of change can be predicted. This enables a differentiation between harmonics originating in the core and harmonics caused by crustal magnetization. The westward drift of the magnetic field depends on the longitudinal gradient of the field. In order to determine the longitudinal motions, harmonics up to degree 20 can be utilized. The average rate of secular acceleration increases with the degree of harmonics from 0.001 deg/sq yr for a dipole term to an average of 0.05 deg/sq yr for degree eight harmonics.

Investigation of the effects of external current systems on the MAGSAT data utilizing grid cell modeling techniques

NASA Technical Reports Server (NTRS)

Klumpar, D. M. (Principal Investigator)

1982-01-01

Efforts in support of the development of a model of the magnetic fields due to ionospheric and magnetospheric electrical currents are discussed. Specifically, progress made in reading MAGSAT tapes and plotting the deviation of the measured magnetic field components with respect to a spherical harmonic model of the main geomagnetic field is reported. Initial tests of the modeling procedure developed to compute the ionosphere/magnetosphere-induced fields at satellite orbit are also described. The modeling technique utilizes a liner current element representation of the large scale current system.

A method of evaluating quantitative magnetospheric field models by an angular parameter alpha

NASA Technical Reports Server (NTRS)

Sugiura, M.; Poros, D. J.

1979-01-01

The paper introduces an angular parameter, termed alpha, which represents the angular difference between the observed, or model, field and the internal model field. The study discusses why this parameter is chosen and demonstrates its usefulness by applying it to both observations and models. In certain areas alpha is more sensitive than delta-B (the difference between the magnitude of the observed magnetic field and that of the earth's internal field calculated from a spherical harmonic expansion) in expressing magnetospheric field distortions. It is recommended to use both alpha and delta-B in comparing models with observations.

Image-based gradient non-linearity characterization to determine higher-order spherical harmonic coefficients for improved spatial position accuracy in magnetic resonance imaging.

PubMed

Weavers, Paul T; Tao, Shengzhen; Trzasko, Joshua D; Shu, Yunhong; Tryggestad, Erik J; Gunter, Jeffrey L; McGee, Kiaran P; Litwiller, Daniel V; Hwang, Ken-Pin; Bernstein, Matt A

2017-05-01

Spatial position accuracy in magnetic resonance imaging (MRI) is an important concern for a variety of applications, including radiation therapy planning, surgical planning, and longitudinal studies of morphologic changes to study neurodegenerative diseases. Spatial accuracy is strongly influenced by gradient linearity. This work presents a method for characterizing the gradient non-linearity fields on a per-system basis, and using this information to provide improved and higher-order (9th vs. 5th) spherical harmonic coefficients for better spatial accuracy in MRI. A large fiducial phantom containing 5229 water-filled spheres in a grid pattern is scanned with the MR system, and the positions all the fiducials are measured and compared to the corresponding ground truth fiducial positions as reported from a computed tomography (CT) scan of the object. Systematic errors from off-resonance (i.e., B0) effects are minimized with the use of increased receiver bandwidth (±125kHz) and two acquisitions with reversed readout gradient polarity. The spherical harmonic coefficients are estimated using an iterative process, and can be subsequently used to correct for gradient non-linearity. Test-retest stability was assessed with five repeated measurements on a single scanner, and cross-scanner variation on four different, identically-configured 3T wide-bore systems. A decrease in the root-mean-square error (RMSE) over a 50cm diameter spherical volume from 1.80mm to 0.77mm is reported here in the case of replacing the vendor's standard 5th order spherical harmonic coefficients with custom fitted 9th order coefficients, and from 1.5mm to 1mm by extending custom fitted 5th order correction to the 9th order. Minimum RMSE varied between scanners, but was stable with repeated measurements in the same scanner. The results suggest that the proposed methods may be used on a per-system basis to more accurately calibrate MR gradient non-linearity coefficients when compared to vendor standard corrections. Copyright © 2016 Elsevier Inc. All rights reserved.

An analytic study on bounds for the associated Legendre functions. [for truncation of geopotential series in spherical harmonics in orbital analyses

NASA Technical Reports Server (NTRS)

Payne, M. H.

1973-01-01

The bounds for the normalized associated Legendre functions P sub nm were studied to provide a rational basis for the truncation of the geopotential series in spherical harmonics in various orbital analyses. The conjecture is made that the largest maximum of the normalized associated Legendre function lies in the interval which indicates the greatest integer function. A procedure is developed for verifying this conjecture. An on-line algebraic manipulator, IAM, is used to implement the procedure and the verification is carried out for all n equal to or less than 2m, for m = 1 through 6. A rigorous proof of the conjecture is not available.

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

PubMed

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.

Modeling real shim fields for very high degree (and order) B0 shimming of the human brain at 9.4 T.

PubMed

Chang, Paul; Nassirpour, Sahar; Henning, Anke

2018-01-01

To describe the process of calibrating a B 0 shim system using high-degree (or high order) spherical harmonic models of the measured shim fields, to provide a method that considers amplitude dependency of these models, and to show the advantage of very high-degree B 0 shimming for whole-brain and single-slice applications at 9.4 Tesla (T). An insert shim with up to fourth and partial fifth/sixth degree (order) spherical harmonics was used with a Siemens 9.4T scanner. Each shim field was measured and modeled as input for the shimming algorithm. Optimal shim currents can therefore be calculated in a single iteration. A range of shim currents was used in the modeling to account for possible amplitude nonlinearities. The modeled shim fields were used to compare different degrees of whole-brain B 0 shimming on healthy subjects. The ideal shim fields did not correctly shim the subject brains. However, using the modeled shim fields improved the B 0 homogeneity from 55.1 (second degree) to 44.68 Hz (partial fifth/sixth degree) on the whole brains of 9 healthy volunteers, with a total applied current of 0.77 and 6.8 A, respectively. The necessity of calibrating the shim system was shown. Better B 0 homogeneity drastically reduces signal dropout and distortions for echo-planar imaging, and significantly improves the linewidths of MR spectroscopy imaging. Magn Reson Med 79:529-540, 2018. © 2017 International Society for Magnetic Resonance in Medicine. © 2017 International Society for Magnetic Resonance in Medicine.

Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

NASA Astrophysics Data System (ADS)

Casadio, Roberto; Giugno, Andrea; Giusti, Andrea; Micu, Octavian

2018-04-01

The Horizon Quantum Mechanics is an approach that allows one to analyse the gravitational radius of spherically symmetric systems and compute the probability that a given quantum state is a black hole. We first review the (global) formalism and show how it reproduces a gravitationally inspired GUP relation. This results leads to unacceptably large fluctuations in the horizon size of astrophysical black holes if one insists in describing them as (smeared) central singularities. On the other hand, if they are extended systems, like in the corpuscular models, no such issue arises and one can in fact extend the formalism to include asymptotic mass and angular momentum with the harmonic model of rotating corpuscular black holes. The Horizon Quantum Mechanics then shows that, in simple configurations, the appearance of the inner horizon is suppressed and extremal (macroscopic) geometries seem disfavoured.

Introduction to Radar Polarimetry

DTIC Science & Technology

1991-04-23

Coulomb force 11 1,2 Static etectric fields 13 1.3 Summary 15 2 ELECTROMAGNETIC WAVES 16 2.1 Harmonic plane waves 16 2.2 The average intensity of a...harmonic plane wave 17 2.3 Spherical harmonic waves 18 2.4 Summary 19 3 THE POLARIZATION OF AN ELECTROMAGNETIC WAVE 20 3.1 The polarization ellipse 20 3.2...CHANGE OF POLARIZATION 31 4.1 Simple examples 31 4.2 Scattering at a plane interface 33 4.3 Summary 36 5 THE SCATTERING MATRIX 37 5.1 Transmission

Global Simultaneous Estimation of Present-Day Surface Mass Trend and GIA Using Multi-Sensor Geodetic Data Combination

NASA Astrophysics Data System (ADS)

Wu, X.; Heflin, M. B.; Schotman, H.; Vermeersen, B. L.; Dong, D.; Gross, R. S.; Ivins, E. R.; Moore, A. W.; Owen, S. E.

2009-12-01

Separating geodetic signatures of present-day surface mass trend and Glacial Isostatic Adjustment (GIA) requires multi-data types of different physical characteristics. We take a kinematic approach to the global simultaneous estimation problem. Three sets of global spherical harmonic coefficients from degree 1 to 60 of the present-day surface mass trend, vertical and horizontal GIA induced surface velocity fields, as well as rotation vectors of 15 major tectonic plates are solved for. The estimation is carried out using GRACE geoid trend, 3-dimensional velocities measured at 664 SLR/VLBI/GPS sites, the data-assimilated JPL ECCO ocean model. The ICE-5G/IJ05 (VM2) predictions are used as a priori GIA mean model. An a priori covariance matrix is constructed in the spherical harmonic domain for the GIA model by propagating the covariance matrices of random and geographically correlated ice thickness errors and upper/lower mantle viscosity errors so that the resulting magnitude and geographic pattern of the geoid uncertainties roughly reflect the difference between two recent GIA models. Unprecedented high-precision results are achieved. For example, geocenter velocities due to present-day surface mass trend and due to GIA are both determined to uncertainties of better than 0.1 mm/yr without using direct geodetic geocenter information. Information content of the data sets, future improvements, and benefits from new data will also be explored in the global inverse framework.

Statistically optimal estimation of Greenland Ice Sheet mass variations from GRACE monthly solutions using an improved mascon approach

NASA Astrophysics Data System (ADS)

Ran, J.; Ditmar, P.; Klees, R.; Farahani, H. H.

2018-03-01

We present an improved mascon approach to transform monthly spherical harmonic solutions based on GRACE satellite data into mass anomaly estimates in Greenland. The GRACE-based spherical harmonic coefficients are used to synthesize gravity anomalies at satellite altitude, which are then inverted into mass anomalies per mascon. The limited spectral content of the gravity anomalies is properly accounted for by applying a low-pass filter as part of the inversion procedure to make the functional model spectrally consistent with the data. The full error covariance matrices of the monthly GRACE solutions are properly propagated using the law of covariance propagation. Using numerical experiments, we demonstrate the importance of a proper data weighting and of the spectral consistency between functional model and data. The developed methodology is applied to process real GRACE level-2 data (CSR RL05). The obtained mass anomaly estimates are integrated over five drainage systems, as well as over entire Greenland. We find that the statistically optimal data weighting reduces random noise by 35-69%, depending on the drainage system. The obtained mass anomaly time-series are de-trended to eliminate the contribution of ice discharge and are compared with de-trended surface mass balance (SMB) time-series computed with the Regional Atmospheric Climate Model (RACMO 2.3). We show that when using a statistically optimal data weighting in GRACE data processing, the discrepancies between GRACE-based estimates of SMB and modelled SMB are reduced by 24-47%.

TIME-DEPENDENT MULTI-GROUP MULTI-DIMENSIONAL RELATIVISTIC RADIATIVE TRANSFER CODE BASED ON SPHERICAL HARMONIC DISCRETE ORDINATE METHOD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tominaga, Nozomu; Shibata, Sanshiro; Blinnikov, Sergei I., E-mail: tominaga@konan-u.ac.jp, E-mail: sshibata@post.kek.jp, E-mail: Sergei.Blinnikov@itep.ru

We develop a time-dependent, multi-group, multi-dimensional relativistic radiative transfer code, which is required to numerically investigate radiation from relativistic fluids that are involved in, e.g., gamma-ray bursts and active galactic nuclei. The code is based on the spherical harmonic discrete ordinate method (SHDOM) which evaluates a source function including anisotropic scattering in spherical harmonics and implicitly solves the static radiative transfer equation with ray tracing in discrete ordinates. We implement treatments of time dependence, multi-frequency bins, Lorentz transformation, and elastic Thomson and inelastic Compton scattering to the publicly available SHDOM code. Our code adopts a mixed-frame approach; the source functionmore » is evaluated in the comoving frame, whereas the radiative transfer equation is solved in the laboratory frame. This implementation is validated using various test problems and comparisons with the results from a relativistic Monte Carlo code. These validations confirm that the code correctly calculates the intensity and its evolution in the computational domain. The code enables us to obtain an Eddington tensor that relates the first and third moments of intensity (energy density and radiation pressure) and is frequently used as a closure relation in radiation hydrodynamics calculations.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khamzin, A. A., E-mail: airat.khamzin@rambler.ru; Sitdikov, A. S.; Nikitin, A. S.

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.

Mercury's Interior from MESSENGER Radio Science Data

NASA Astrophysics Data System (ADS)

Genova, A.; Mazarico, E.; Goossens, S. J.; Lemoine, F. G.; Neumann, G. A.; Smith, D. E.; Zuber, M. T.

2017-12-01

The MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft provided precise radio tracking data in orbit about Mercury for more than 4 years, from March 2011 to April 2015. These geodetic measurements enable us to investigate the interior structure of the planet from the inner core to the crust. The first three years of radio data allowed us to determine the gravity field of Mercury with a resolution of 150 km in the northern hemisphere (degree and order 50 in spherical harmonics) since the periapsis was located at higher latitudes (>65˚N) and 200-500 km altitudes. The comparison of this gravity solution with Mercury's topography, which was retrieved by using over 25 million individual measurements of the Mercury Laser Altimeter (MLA), resulted in a preliminary map of the crustal thickness of the planet. However, those results were limited by the resolution of the gravity field since the topography was defined in spherical harmonics up to degree and order 125. The last year of the MESSENGER extended mission was dedicated to a low-altitude campaign, where the spacecraft periapsis was maintained at altitudes between 25 and 100 km. The radio data collected during this mission phase allowed us to significantly improve the resolution of the gravity field locally in the northern hemisphere up to degree and order 100 in spherical harmonics. We present the gravity anomalies and crustal thickness maps that lead to a better understanding on the formation and evolution of specific regions. We present our estimated orientation model, which slightly differs from the solutions that were obtained by using Earth-based radar measurements and the co-registration of MESSENGER imaging and altimetry data. These previous estimates provide a direct measurement of the surface response, whereas the orientation model from gravity is more sensitive to the inner and outer core. A discrepancy between core and surface obliquities may provide fundamental information on the status of the outer core and the presence of a solid inner core. We also present the latest solution of the tidal Love number k2 that enables us to constrain the basal temperature and rigidity of the outer molten core.

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raskin, Cody; Owen, J. Michael

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here in this paper, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such asmore » planets with core–mantle boundaries.« less

Rapid Optimal SPH Particle Distributions in Spherical Geometries For Creating Astrophysical Initial Conditions

DOE PAGES

Raskin, Cody; Owen, J. Michael

2016-03-24

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here in this paper, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such asmore » planets with core–mantle boundaries.« less

RAPID OPTIMAL SPH PARTICLE DISTRIBUTIONS IN SPHERICAL GEOMETRIES FOR CREATING ASTROPHYSICAL INITIAL CONDITIONS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Raskin, Cody; Owen, J. Michael

2016-04-01

Creating spherical initial conditions in smoothed particle hydrodynamics simulations that are spherically conformal is a difficult task. Here, we describe two algorithmic methods for evenly distributing points on surfaces that when paired can be used to build three-dimensional spherical objects with optimal equipartition of volume between particles, commensurate with an arbitrary radial density function. We demonstrate the efficacy of our method against stretched lattice arrangements on the metrics of hydrodynamic stability, spherical conformity, and the harmonic power distribution of gravitational settling oscillations. We further demonstrate how our method is highly optimized for simulating multi-material spheres, such as planets with core–mantlemore » boundaries.« less

Dynamically supported geoid highs over hotspots: Observation and theory

NASA Technical Reports Server (NTRS)

Richards, M. A.; Hager, B. H.; Sleep, N. H.

1986-01-01

Hotspots are associated with long wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. These associations are quantified by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is essentially white, with peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2 to 6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. A variety of fluid mechanical models were tested for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. The preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large scale background temperature highs in a mantle with substantial viscosity increase with depth, although other models are possible.

Dynamically supported geoid highs over hotspots - Observation and theory

NASA Technical Reports Server (NTRS)

Richards, Mark A.; Hager, Bradford H.; Sleep, Norman H.

1988-01-01

Hotspots are associated with long wavelength geoid highs, an association that is even stronger when the geoid highs associated with subduction zones are removed. These associations are quantified by expanding the hotspot distribution in spherical harmonics and calculating correlation coefficients as a function of harmonic degree. The hotspot distribution spectrum is essentially white, with peaks at degrees 2 and 6. It is correlated positively with the slab residual geoid for degrees 2 to 6, with low seismic velocity in the lower mantle at degree 2, and with low seismic velocity in the upper mantle at degree 6. A variety of fluid mechanical models were tested for hotspots, including lithospheric delamination and hot plumes, by calculating their predicted dynamic geoid responses and comparing them to the observations. These models include the effects of temperature dependent rheology. The preferred hotspot model, based on observations of the geoid and seismic tomography, has plumes preferentially occurring in regions of large scale background temperature highs in a mantle with substantial viscosity increase with depth, although other models are possible.

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

ERIC Educational Resources Information Center

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…

A study of isotropic-nematic transition of quadrupolar Gay-Berne fluid using density-functional theory approach

NASA Astrophysics Data System (ADS)

Singh, Ram Chandra; Ram, Jokhan

2011-11-01

The effects of quadrupole moments on the isotropic-nematic (IN) phase transitions are studied using the density-functional theory (DFT) for a Gay-Berne (GB) fluid for a range of length-to-breadth parameters ? in the reduced temperature range ? . The pair-correlation functions of the isotropic phase, which enter into the DFT as input parameters are found by solving the Percus-Yevick integral equation theory. The method used involves an expansion of angle-dependent functions appearing in the integral equations in terms of spherical harmonics and the harmonic coefficients are obtained by an iterative algorithm. All the terms of harmonic coefficients which involve l indices up to less than or equal to 6 are considered. The numerical accuracy of the results depends on the number of spherical harmonic coefficients considered for each orientation-dependent function. As the length-to-breadth ratio of quadrupolar GB molecules is increased, the IN transition is seen to move to lower density (and pressure) at a given temperature. It has been observed that the DFT is good to study the IN transitions in such fluids. The theoretical results have also been compared with the computer simulation results wherever they are available.

Analytic reflected light curves for exoplanets

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-07-01

The disc-integrated reflected brightness of an exoplanet changes as a function of time due to orbital and rotational motions coupled with an inhomogeneous albedo map. We have previously derived analytic reflected light curves for spherical harmonic albedo maps in the special case of a synchronously rotating planet on an edge-on orbit (Cowan, Fuentes & Haggard). In this paper, we present analytic reflected light curves for the general case of a planet on an inclined orbit, with arbitrary spin period and non-zero obliquity. We do so for two different albedo basis maps: bright points (δ-maps), and spherical harmonics (Y_ l^m-maps). In particular, we use Wigner D-matrices to express an harmonic light curve for an arbitrary viewing geometry as a non-linear combination of harmonic light curves for the simpler edge-on, synchronously rotating geometry. These solutions will enable future exploration of the degeneracies and information content of reflected light curves, as well as fast calculation of light curves for mapping exoplanets based on time-resolved photometry. To these ends, we make available Exoplanet Analytic Reflected Lightcurves, a simple open-source code that allows rapid computation of reflected light curves.

Cortical geometry as a determinant of brain activity eigenmodes: Neural field analysis

NASA Astrophysics Data System (ADS)

Gabay, Natasha C.; Robinson, P. A.

2017-09-01

Perturbation analysis of neural field theory is used to derive eigenmodes of neural activity on a cortical hemisphere, which have previously been calculated numerically and found to be close analogs of spherical harmonics, despite heavy cortical folding. The present perturbation method treats cortical folding as a first-order perturbation from a spherical geometry. The first nine spatial eigenmodes on a population-averaged cortical hemisphere are derived and compared with previous numerical solutions. These eigenmodes contribute most to brain activity patterns such as those seen in electroencephalography and functional magnetic resonance imaging. The eigenvalues of these eigenmodes are found to agree with the previous numerical solutions to within their uncertainties. Also in agreement with the previous numerics, all eigenmodes are found to closely resemble spherical harmonics. The first seven eigenmodes exhibit a one-to-one correspondence with their numerical counterparts, with overlaps that are close to unity. The next two eigenmodes overlap the corresponding pair of numerical eigenmodes, having been rotated within the subspace spanned by that pair, likely due to second-order effects. The spatial orientations of the eigenmodes are found to be fixed by gross cortical shape rather than finer-scale cortical properties, which is consistent with the observed intersubject consistency of functional connectivity patterns. However, the eigenvalues depend more sensitively on finer-scale cortical structure, implying that the eigenfrequencies and consequent dynamical properties of functional connectivity depend more strongly on details of individual cortical folding. Overall, these results imply that well-established tools from perturbation theory and spherical harmonic analysis can be used to calculate the main properties and dynamics of low-order brain eigenmodes.

Harmony: EEG/MEG Linear Inverse Source Reconstruction in the Anatomical Basis of Spherical Harmonics

PubMed Central

Petrov, Yury

2012-01-01

EEG/MEG source localization based on a “distributed solution” is severely underdetermined, because the number of sources is much larger than the number of measurements. In particular, this makes the solution strongly affected by sensor noise. A new way to constrain the problem is presented. By using the anatomical basis of spherical harmonics (or spherical splines) instead of single dipoles the dimensionality of the inverse solution is greatly reduced without sacrificing the quality of the data fit. The smoothness of the resulting solution reduces the surface bias and scatter of the sources (incoherency) compared to the popular minimum-norm algorithms where single-dipole basis is used (MNE, depth-weighted MNE, dSPM, sLORETA, LORETA, IBF) and allows to efficiently reduce the effect of sensor noise. This approach, termed Harmony, performed well when applied to experimental data (two exemplars of early evoked potentials) and showed better localization precision and solution coherence than the other tested algorithms when applied to realistically simulated data. PMID:23071497

A plane wave generation method by wave number domain point focusing.

PubMed

Chang, Ji-Ho; Choi, Jung-Woo; Kim, Yang-Hann

2010-11-01

A method for generation of a wave-field that is a plane wave is described. This method uses an array of loudspeakers phased so that the field in the wave-number domain is nearly concentrated at a point, this point being at the wave-number vector of the desired plane wave. The method described here for such a wave-number concentration makes use of an expansion in spherical harmonics, and requires a relatively small number of measurement points for a good approximate achievement of a plane wave. The measurement points are on a spherical surface surrounding the array of loudspeakers. The input signals for the individual loudspeakers can be derived without a matrix inversion or without explicit assumptions about the loudspeakers. The mathematical development involves spherical harmonics and three-dimensional Fourier transforms. Some numerical examples are given, with various assumptions concerning the nature of the loudspeakers, that support the premise that the method described in the present paper may be useful in applications.

Global maps of the magnetic thickness and magnetization of the Earth's lithosphere

NASA Astrophysics Data System (ADS)

Vervelidou, Foteini; Thébault, Erwan

2015-10-01

We have constructed global maps of the large-scale magnetic thickness and magnetization of Earth's lithosphere. Deriving such large-scale maps based on lithospheric magnetic field measurements faces the challenge of the masking effect of the core field. In this study, the maps were obtained through analyses in the spectral domain by means of a new regional spatial power spectrum based on the Revised Spherical Cap Harmonic Analysis (R-SCHA) formalism. A series of regional spectral analyses were conducted covering the entire Earth. The R-SCHA surface power spectrum for each region was estimated using the NGDC-720 spherical harmonic (SH) model of the lithospheric magnetic field, which is based on satellite, aeromagnetic, and marine measurements. These observational regional spectra were fitted to a recently proposed statistical expression of the power spectrum of Earth's lithospheric magnetic field, whose free parameters include the thickness and magnetization of the magnetic sources. The resulting global magnetic thickness map is compared to other crustal and magnetic thickness maps based upon different geophysical data. We conclude that the large-scale magnetic thickness of the lithosphere is on average confined to a layer that does not exceed the Moho.

On the Relation Between Spherical Harmonics and Simplified Spherical Harmonics Methods

NASA Astrophysics Data System (ADS)

Coppa, G. G. M.; Giusti, V.; Montagnini, B.; Ravetto, P.

2010-03-01

The purpose of the paper is, first, to recall the proof that the AN method and, therefore, the SP2N-1 method (of which AN was shown to be a variant) are equivalent to the odd order P2N-1, at least for a particular class of multi-region problems; namely the problems for which the total cross section has the same value for all the regions and the scattering is supposed to be isotropic. By virtue of the introduction of quadrature formulas representing first collision probabilities, this class is then enlarged in order to encompass the systems in which the regions may have different total cross sections. Some examples are reported to numerically validate the procedure.

Transition operators in electromagnetic-wave diffraction theory. II - Applications to optics

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1993-01-01

The theory developed by Hahne (1992) for the diffraction of time-harmonic electromagnetic waves from fixed obstacles is briefly summarized and extended. Applications of the theory are considered which comprise, first, a spherical harmonic expansion of the so-called radiation impedance operator in the theory, for a spherical surface, and second, a reconsideration of familiar short-wavelength approximation from the new standpoint, including a derivation of the so-called physical optics method on the basis of quasi-planar approximation to the radiation impedance operator, augmented by the method of stationary phase. The latter includes a rederivation of the geometrical optics approximation for the complete Green's function for the electromagnetic field in the presence of a smooth- and a convex-surfaced perfectly electrically conductive obstacle.

A simplified model for the gravitational potential of the atmosphere and its effect on the geoid

NASA Technical Reports Server (NTRS)

Madden, S. J., Jr.

1972-01-01

The earth's atmosphere is considered as made up of oblate spheroidal layers of variable density lying over an oblate spheroidal earth. The gravitational attraction of the atmosphere at exterior points is computed and its contribution to the usual spherical harmonic gravitational expansion is assessed. The potential is also found for points at the bottom of the model atmosphere. This latter result is of interest for determination of the potential at the surface of the geoid. The atmospheric correction to the geoid determination from satellite coefficients is given.

Modeling of the Earth's gravity field using the New Global Earth Model (NEWGEM)

NASA Technical Reports Server (NTRS)

Kim, Yeong E.; Braswell, W. Danny

1989-01-01

Traditionally, the global gravity field was described by representations based on the spherical harmonics (SH) expansion of the geopotential. The SH expansion coefficients were determined by fitting the Earth's gravity data as measured by many different methods including the use of artificial satellites. As gravity data have accumulated with increasingly better accuracies, more of the higher order SH expansion coefficients were determined. The SH representation is useful for describing the gravity field exterior to the Earth but is theoretically invalid on the Earth's surface and in the Earth's interior. A new global Earth model (NEWGEM) (KIM, 1987 and 1988a) was recently proposed to provide a unified description of the Earth's gravity field inside, on, and outside the Earth's surface using the Earth's mass density profile as deduced from seismic studies, elevation and bathymetric information, and local and global gravity data. Using NEWGEM, it is possible to determine the constraints on the mass distribution of the Earth imposed by gravity, topography, and seismic data. NEWGEM is useful in investigating a variety of geophysical phenomena. It is currently being utilized to develop a geophysical interpretation of Kaula's rule. The zeroth order NEWGEM is being used to numerically integrate spherical harmonic expansion coefficients and simultaneously determine the contribution of each layer in the model to a given coefficient. The numerically determined SH expansion coefficients are also being used to test the validity of SH expansions at the surface of the Earth by comparing the resulting SH expansion gravity model with exact calculations of the gravity at the Earth's surface.

Scattering of plane transverse waves by spherical inclusions in a poroelastic medium

NASA Astrophysics Data System (ADS)

Liu, Xu; Greenhalgh, Stewart; Zhou, Bing

2009-03-01

The scattering of plane transverse waves by a spherical inclusion embedded in an infinite poroelastic medium is treated for the first time in this paper. The vector displacement wave equations of Biot's theory are solved as an infinite series of vector spherical harmonics for the case of a plane S-wave impinging from a porous medium onto a spherical inclusion which itself is assumed to be another porous medium. Based on the single spherical scattering theory and dynamic composite elastic medium theory, the non-self-consistent shear wavenumber is derived for a porous rock having numerous spherical inclusions of another medium. The frequency dependences of the shear wave velocity and the shear wave attenuation have been calculated for both the patchy saturation model (inclusions having the same solid frame as the host but with a different pore fluid from the host medium) and the double porosity model (inclusions having a different solid frame than the host but the same pore fluid as the host medium) with dilute concentrations of identical inclusions. Unlike the case of incident P-wave scattering, we show that although the fluid and the heterogeneity of the rock determine the shear wave velocity of the composite, the attenuation of the shear wave caused by scattering is actually contributed by the heterogeneity of the rock for spherical inclusions. The scattering of incident shear waves in the patchy saturation model is quite different from that of the double porosity model. For the patchy saturation model, the gas inclusions do not significantly affect the shear wave dispersion characteristic of the water-filled host medium. However, the softer inclusion with higher porosity in the double porosity model can cause significant shear wave scattering attenuation which occurs at a frequency at which the wavelength of the shear wave is approximately equal to the characteristic size of the inclusion and depends on the volume fraction. Compared with analytic formulae for the low frequency limit of the shear velocity, our scattering model yields discrepancies within 4.0 per cent. All calculated shear velocities of the composite medium with dilute inclusion concentrations approach the high frequency limit of the host material.

Experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum tube

NASA Astrophysics Data System (ADS)

Toufexis, Filippos; Tantawi, Sami G.; Jensen, Aaron; Dolgashev, Valery A.; Haase, Andrew; Fazio, Michael V.; Borchard, Philipp

2017-06-01

We report the experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum electronic device, which uses an over-moded spherical sector output cavity. In this device, a pencil electron beam is helically deflected in a transverse deflecting cavity before entering the output cavity. No magnetic field is required to focus or guide the beam. We built and tested a proof-of-principle device with an output frequency of 57.12 GHz. The measured peak power was 52.67 W at the 5th harmonic of the drive frequency. Power at the 4th, 6th, and 7th harmonics was 33.28 dB lower than that at the 5th harmonic.

Experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum tube

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toufexis, Filippos; Tantawi, Sami G.; Jensen, Aaron

Here, we report the experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum electronic device, which uses an over-moded spherical sector output cavity. In this device, a pencil electron beam is helically deflected in a transverse deflecting cavity before entering the output cavity. No magnetic field is required to focus or guide the beam. We built and tested a proof-of-principle device with an output frequency of 57.12 GHz. The measured peak power was 52.67 W at the 5th harmonic of the drive frequency. Power at the 4th, 6th, and 7th harmonics was 33.28 dB lower than that at themore » 5th harmonic.« less

Experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum tube

DOE PAGES

Toufexis, Filippos; Tantawi, Sami G.; Jensen, Aaron; ...

2017-06-26

Here, we report the experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum electronic device, which uses an over-moded spherical sector output cavity. In this device, a pencil electron beam is helically deflected in a transverse deflecting cavity before entering the output cavity. No magnetic field is required to focus or guide the beam. We built and tested a proof-of-principle device with an output frequency of 57.12 GHz. The measured peak power was 52.67 W at the 5th harmonic of the drive frequency. Power at the 4th, 6th, and 7th harmonics was 33.28 dB lower than that at themore » 5th harmonic.« less

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

PubMed

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 .

Gradient nonlinearity calibration and correction for a compact, asymmetric magnetic resonance imaging gradient system

PubMed Central

Tao, S; Trzasko, J D; Gunter, J L; Weavers, P T; Shu, Y; Huston, J; Lee, S K; Tan, E T; Bernstein, M A

2017-01-01

Due to engineering limitations, the spatial encoding gradient fields in conventional magnetic resonance imaging cannot be perfectly linear and always contain higher-order, nonlinear components. If ignored during image reconstruction, gradient nonlinearity (GNL) manifests as image geometric distortion. Given an estimate of the GNL field, this distortion can be corrected to a degree proportional to the accuracy of the field estimate. The GNL of a gradient system is typically characterized using a spherical harmonic polynomial model with model coefficients obtained from electromagnetic simulation. Conventional whole-body gradient systems are symmetric in design; typically, only odd-order terms up to the 5th-order are required for GNL modeling. Recently, a high-performance, asymmetric gradient system was developed, which exhibits more complex GNL that requires higher-order terms including both odd- and even-orders for accurate modeling. This work characterizes the GNL of this system using an iterative calibration method and a fiducial phantom used in ADNI (Alzheimer’s Disease Neuroimaging Initiative). The phantom was scanned at different locations inside the 26-cm diameter-spherical-volume of this gradient, and the positions of fiducials in the phantom were estimated. An iterative calibration procedure was utilized to identify the model coefficients that minimize the mean-squared-error between the true fiducial positions and the positions estimated from images corrected using these coefficients. To examine the effect of higher-order and even-order terms, this calibration was performed using spherical harmonic polynomial of different orders up to the 10th-order including even- and odd-order terms, or odd-order only. The results showed that the model coefficients of this gradient can be successfully estimated. The residual root-mean-squared-error after correction using up to the 10th-order coefficients was reduced to 0.36 mm, yielding spatial accuracy comparable to conventional whole-body gradients. The even-order terms were necessary for accurate GNL modeling. In addition, the calibrated coefficients improved image geometric accuracy compared with the simulation-based coefficients. PMID:28033119

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

NASA Astrophysics Data System (ADS)

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 Intelligence Agency (NGA) (Pavlis et al., 2008) and the DTU10 (Andersen, 2010) who represents the best up-to-date global gravity models (including surface gravity measurements from land, marine and airborne surveys as well as gravity and altimetry satellite measurements). The surface free-air anomaly is computed at the Earth's surface in the context of Molodensky theory and includes corrections from the mass of the atmosphere. The way gravity anomalies are computed on a worldwide basis slightly differs from the classical usage, but meets modern concerns which tend to take into account of the real Earth. The resulting anomaly maps and grids will be distributed for scientific and education purposes by the Commission for the Geological Map of the World (CGMW) (http://ccgm.free.fr) and by the Bureau Gravimetrique International (BGI) (http://bgi.omp.obs-mip.fr). Upgraded versions might be done as soon as new global gravity model will be available (including satellite GOCE data for instance). Institutions who are interested to contribute with new datasets of surface gravity measurements (i.e. ground, marine or airborne gravity data) are also invited to contact BGI bgi@cnes.fr.

NORDA’s Pattern Analysis Laboratory: Current Contributions to Naval Mapping, Charting, and Geodesy

DTIC Science & Technology

1989-04-01

magnetic observatories (McLeod, 1988). Using system integrates a suite of sensors and control devices the PAL’s VAX 11/780, spherical harmonic models to...DJAO:[FPS]*.OLB 5. Miscellaneous Utilities CALENDAR (NORDA events) 780 $ CALENDAR (menu-driven) DIALER modem controller 780 $ R AUTO DIAL:DIALER DTC...Utilities CALENDAR (NORDA events) 780 CALENDAR (menu-driven) DIALER modem controller 780 $ R AUTO DIAL:DIALER DTC Desk Top Calendar 780 $ DTC (menu-driven

Confirmation of a change in the global shear velocity pattern at around 1,000 km depth

NASA Astrophysics Data System (ADS)

Debayle, E.; Durand, S.; Ricard, Y. R.; Zaroli, C.; Lambotte, S.

2017-12-01

In this study, we confirm the existence of a change in the shear velocity spectrum around 1,000 km depth based on a new shear velocity tomographic model of the Earth's mantle, SEISGLOB2. This model is based on Rayleigh surface wave phase velocities, self- and cross- coupling structure coefficients of spheroidal normal modes and body wave travel times which are, for the first time, combined in a tomographic inversion. SEISGLOB2 is developed up to spherical harmonic degree 40 and in 21 radial spline functions. The spectrum of SEISGLOB2 is the flattest (i.e., richest in "short" wavelengths corresponding to spherical harmonic degrees greater than 10) around 1,000 km depth and this flattening occurs between 670 and 1,500 km depth. We also confirm various changes in the continuity of slabs and mantle plumes all around 1,000 km depth where we also observed the upper boundary of LLSVPs. The existence of a flatter spectrum, richer in short wavelength heterogeneities, in a region of the mid-mantle can have great impacts on our understanding of the mantle dynamics and should thus be better understood in the future. Although a viscosity increase, a phase change or a compositional change can all concur to induce this change of pattern, its precise origin is still very uncertain.

Statistical Validation of Brain Tumor Shape Approximation via Spherical Harmonics for Image-Guided Neurosurgery1

PubMed Central

Goldberg-Zimring, Daniel; Talos, Ion-Florin; Bhagwat, Jui G.; Haker, Steven J.; Black, Peter M.; Zou, Kelly H.

2005-01-01

Rationale and Objectives Surgical planning now routinely uses both two-dimensional (2D) and three-dimensional (3D) models that integrate data from multiple imaging modalities, each highlighting one or more aspects of morphology or function. We performed a preliminary evaluation of the use of spherical harmonics (SH) in approximating the 3D shape and estimating the volume of brain tumors of varying characteristics. Materials and Methods Magnetic resonance (MR) images from five patients with brain tumors were selected randomly from our MR-guided neurosurgical practice. Standardized mean square reconstruction errors (SMSRE) by tumor volume were measured. Validation metrics for comparing performances of the SH method against segmented contours (SC) were the dice similarity coefficient (DSC) and standardized Euclidean distance (SED) measure. Results Tumor volume range was 22413–85189 mm3, and range of number of vertices in triangulated models was 3674–6544. At SH approximations with degree of at least 30, SMSRE were within 1.66 × 10−5 mm−1. Summary measures yielded a DSC range of 0.89–0.99 (pooled median, 0.97 and significantly >0.7; P < .001) and an SED range of 0.0002–0.0028 (pooled median, 0.0005). Conclusion 3D shapes of tumors may be approximated by using SH for neurosurgical applications. PMID:15831419

Connecting the large- and the small-scale magnetic fields of solar-like stars

NASA Astrophysics Data System (ADS)

Lehmann, L. T.; Jardine, M. M.; Mackay, D. H.; Vidotto, A. A.

2018-05-01

A key question in understanding the observed magnetic field topologies of cool stars is the link between the small- and the large-scale magnetic field and the influence of the stellar parameters on the magnetic field topology. We examine various simulated stars to connect the small-scale with the observable large-scale field. The highly resolved 3D simulations we used couple a flux transport model with a non-potential coronal model using a magnetofrictional technique. The surface magnetic field of these simulations is decomposed into spherical harmonics which enables us to analyse the magnetic field topologies on a wide range of length scales and to filter the large-scale magnetic field for a direct comparison with the observations. We show that the large-scale field of the self-consistent simulations fits the observed solar-like stars and is mainly set up by the global dipolar field and the large-scale properties of the flux pattern, e.g. the averaged latitudinal position of the emerging small-scale field and its global polarity pattern. The stellar parameters flux emergence rate, differential rotation and meridional flow affect the large-scale magnetic field topology. An increased flux emergence rate increases the magnetic flux in all field components and an increased differential rotation increases the toroidal field fraction by decreasing the poloidal field. The meridional flow affects the distribution of the magnetic energy across the spherical harmonic modes.

Earth Gravitational Model 2020

NASA Astrophysics Data System (ADS)

Barnes, Daniel; Holmes, Simon; Factor, John; Ingalls, Sarah; Presicci, Manny; Beale, James

2017-04-01

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 likely 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 ship borne) of gravimetric data over specific geographical areas, 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 where possible, and generating improved error models that will inform the final combination with the latest satellite gravity models. Outdated data gridding procedures have been replaced with improved approaches. For EGM2020, NGA intends to extract maximum value from the proprietary data that overlaps geographically with unrestricted data, whilst also making sure to respect and honor its proprietary agreements with its data-sharing partners. Approved for Public Release, 15-564

Earth Gravitational Model 2020

NASA Astrophysics Data System (ADS)

Barnes, D.; Factor, J. K.; Holmes, S. A.; Ingalls, S.; Presicci, M. R.; Beale, J.; Fecher, T.

2015-12-01

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 likely 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, 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 where possible, and generating improved error models that will inform the final combination with the latest satellite gravity models. Outdated data gridding procedures have been replaced with improved approaches. For EGM2020, NGA intends to extract maximum value from the proprietary data that overlaps geographically with unrestricted data, whilst also making sure to respect and honor its proprietary agreements with its data-sharing partners.

Development of fully non-inductive plasmas heated by medium and high-harmonic fast waves in the national spherical torus experiment upgrade

NASA Astrophysics Data System (ADS)

Taylor, G.; Poli, F.; Bertelli, N.; Harvey, R. W.; Hosea, J. C.; Mueller, D.; Perkins, R. J.; Phillips, C. K.; Raman, R.

2015-12-01

A major challenge for spherical tokamak development is to start-up and ramp-up the plasma current (Ip) without using a central solenoid. Experiments in the National Spherical Torus eXperiment (NSTX) demonstrated that 1.4 MW of 30 MHz high-harmonic fast wave (HHFW) power could generate an Ip = 300 kA H-mode discharge with a non-inductive Ip fraction, fNI ˜ 0.7. The discharge had an axial toroidal magnetic field (BT(0)) of 0.55 T, the maximum BT(0) available on NSTX. NSTX has undergone a major upgrade (NSTX-U), that will eventually allow the generation of BT(0) ≤ 1 T and Ip ≤ 2 MA plasmas. Full wave simulations of 30 MHz HHFW and medium harmonic fast wave (MHFW) heating in NSTX-U predict significantly reduced FW power loss in the plasma edge at the higher BT(0) achievable in NSTX-U. HHFW experiments will aim to generate stable, fNI ˜ 1, Ip = 300 kA H-mode plasmas and to ramp Ip from 250 to 400 kA with FW power. Time-dependent TRANSP simulations are used to develop non-inductive Ip ramp-up and sustainment using 30 MHz FW power. This paper presents results from these RF simulations and plans for developing non-inductive plasmas heated by FW power.

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

NASA Astrophysics Data System (ADS)

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.

On Facilitating the use of HARDI in population studies by creating Rotation-Invariant Markers

PubMed Central

Caruyer, Emmanuel; Verma, Ragini

2014-01-01

We design and evaluate a novel method to compute rotationally invariant features using High Angular Resolution Diffusion Imaging (HARDI) data. These measures quantify the complexity of the angular diffusion profile modeled using a higher order model, thereby giving more information than classical diffusion tensor-derived parameters. The method is based on the spherical harmonic (SH) representation of the angular diffusion information, and is generalizable to a range of HARDI reconstruction models. These scalars are obtained as homogeneous polynomials of the SH representation of a HARDI reconstruction model. We show that finding such polynomials is equivalent to solving a large linear system of equations, and present a numerical method based on sparse matrices to efficiently solve this system. Among the solutions, we only keep a subset of algebraically independent polynomials, using an algorithm based on a numerical implementation of the Jacobian criterion. We compute a set of 12 or 25 rotationally invariant measures representative of the underlying white matter for the rank-4 or rank-6 spherical harmonics (SH) representation of the apparent diffusion coefficient (ADC) profile, respectively. Synthetic data was used to investigate and quantify the difference in contrast. Real data acquired with multiple repetitions showed that within subject variation in the invariants was less than the difference across subjects - facilitating their use to study population differences. These results demonstrate that our measures are able to characterize white matter, especially complex white matter found in regions of fiber crossings and hence can be used to derive new biomarkers for HARDI and can be used for HARDI-based population analysis. PMID:25465846

DOE Office of Scientific and Technical Information (OSTI.GOV)

Toufexis, Filippos; Tantawi, Sami G.; Jensen, Aaron

Here, we report the experimental demonstration of a 5th harmonic mm-wave frequency multiplying vacuum electronic device, which uses an over-moded spherical sector output cavity. In this device, a pencil electron beam is helically deflected in a transverse deflecting cavity before entering the output cavity. No magnetic field is required to focus or guide the beam. We built and tested a proof-of-principle device with an output frequency of 57.12 GHz. The measured peak power was 52.67 W at the 5th harmonic of the drive frequency. Power at the 4th, 6th, and 7th harmonics was 33.28 dB lower than that at themore » 5th harmonic.« less

Time-variable and static gravity field of Mars from MGS, Mars Odyssey, and MRO

NASA Astrophysics Data System (ADS)

Genova, Antonio; Goossens, Sander; Lemoine, Frank G.; Mazarico, Erwan; Neumann, Gregory A.; Smith, David E.; Zuber, Maria T.

2016-04-01

The Mars Global Surveyor (MGS), Mars Odyssey (ODY), and Mars Reconnaissance Orbiter (MRO) missions have significantly contributed to the determination of global high-resolution global gravity fields of Mars for the last 16 years. All three spacecraft were located in sun-synchronous, near-circular polar mapping orbits for their primary mission phases at different altitudes and Local Solar Time (LST). X-Band tracking data have been acquired from the NASA Deep Space Network (DSN) providing information on the time-variable and static gravity field of Mars. MGS operated between 1999 and 2006 at 390 km altitude. ODY and MRO are still orbiting Mars with periapsis altitudes of 400 km and 255 km, respectively. Before entering these mapping phases, all three spacecraft collected radio tracking data at lower altitudes (˜170-200 km) that help improve the resolution of the gravity field of Mars in specific regions. We analyzed the entire MGS radio tracking data set, and ODY and MRO radio data until 2015. These observations were processed using a batch least-squares filter through the NASA GSFC GEODYN II software. We combined all 2- and 3-way range rate data to estimate the global gravity field of Mars to degree and order 120, the seasonal variations of gravity harmonic coefficients C20, C30, C40 and C50 and the Love number k2. The gravity contribution of Mars atmospheric pressures on the surface of the planet has been discerned from the time-varying and static gravity harmonic coefficients. Surface pressure grids computed using the Mars-GRAM 2010 atmospheric model, with 2.5° x2.5° spatial and 2-h resolution, are converted into gravity spherical harmonic coefficients. Consequently, the estimated gravity and tides provide direct information on the solid planet. We will present the new Goddard Mars Model (GMM-3) of Mars gravity field in spherical harmonics to degree and order 120. The solution includes the Love number k2 and the 3-frequencies (annual, semi-annual, and tri-annual) time-variable coefficients of the gravity zonal harmonics C20, C30, C40 and C50. The seasonal gravity coefficients led us to determine the inter-annual mass exchange between the polar caps over ˜11 years from October 2002 to November 2014.

Analysis of regional crustal magnetization in Vector Cartesian Harmonics

NASA Astrophysics Data System (ADS)

Gubbins, D.; Ivers, D. J.; Williams, S.

2017-12-01

We introduce a set of basis functions for analysing magnetization in a plane layer, called Vector Cartesian Harmonics, that separate the part of the magnetization responsible for generating the external potential field from the part that generates no observable field. They are counterparts of similar functions defined on a sphere, Vector Spherical Harmonics, which we introduced earlier for magnetization in a spherical shell. We expand four example magnetizations in these functions and determine which parts are responsible for the observed magnetic field above the layer. For a point dipole, the component of magnetization responsible for the external potential field is the sum of a point dipole of half strength and a distributed magnetization that gives the same field. The dipping prism has no magnetic field if magnetized along strike; otherwise it, like the point dipole, has the correct dipping structure but of half the correct intensity accompanied by a distributed magnetization producing the same magnetic field. Interestingly, the distributed magnetization has singularities at the edges of the dipping slab. The buried cube is done numerically and again only a fraction of the true magnetization appears along with distributed magnetizations, strongest at the edges of the cube, making up the rest of the field. The Bishop model, a model of magnetization often used to test analysis methods, behaves similarly. In cases where the magnetization is induced by a known, non-horizontal field it is always possible to recover the vertically averaged susceptibility except for its horizontal average. Simple damped inversion of magnetic data will return only the harmonics responsible for the external field, so the analysis gives a clear indication of how any combination of induced and remanent magnetization would be returned. In practice, most interpretations of magnetic surveys are done in combination with other geological data and insights. We propose using this prior information to construct a quantitative magnetization that can be expanded in Vector Cartesian Harmonics to determine the part that generates the observed magnetic anomalies; this part can be refined to fit the data while the remaining part can only be improved using different information. The separation is simple and fast to implement using standard software because it involves only elementary manipulations of 2-dimensional Fourier transforms.

Elementary Theoretical Forms for the Spatial Power Spectrum of Earth's Crustal Magnetic Field

NASA Technical Reports Server (NTRS)

Voorhies, C.

1998-01-01

The magnetic field produced by magnetization in Earth's crust and lithosphere can be distinguished from the field produced by electric currents in Earth's core because the spatial magnetic power spectrum of the crustal field differs from that of the core field. Theoretical forms for the spectrum of the crustal field are derived by treating each magnetic domain in the crust as the point source of a dipole field. The geologic null-hypothesis that such moments are uncorrelated is used to obtain the magnetic spectrum expected from a randomly magnetized, or unstructured, spherical crust of negligible thickness. This simplest spectral form is modified to allow for uniform crustal thickness, ellipsoidality, and the polarization of domains by an periodically reversing, geocentric axial dipole field from Earth's core. Such spectra are intended to describe the background crustal field. Magnetic anomalies due to correlated magnetization within coherent geologic structures may well be superimposed upon this background; yet representing each such anomaly with a single point dipole may lead to similar spectral forms. Results from attempts to fit these forms to observational spectra, determined via spherical harmonic analysis of MAGSAT data, are summarized in terms of amplitude, source depth, and misfit. Each theoretical spectrum reduces to a source factor multiplied by the usual exponential function of spherical harmonic degree n due to geometric attenuation with attitude above the source layer. The source factors always vary with n and are approximately proportional to n(exp 3) for degrees 12 through 120. The theoretical spectra are therefore not directly proportional to an exponential function of spherical harmonic degree n. There is no radius at which these spectra are flat, level, or otherwise independent of n.

Atlas of wide-field-of-view outgoing longwave radiation derived from Nimbus 6 Earth radiation budget data set, July 1975 to June 1978

NASA Technical Reports Server (NTRS)

Bess, T. Dale; Smith, G. Louis

1987-01-01

An atlas of monthly mean outgoing longwave radiation global contour maps and associated spherical harmonic coefficients is presented. The atlas contains 36 months of continuous data from July 1975 to June 1978. The data were derived from the first Earth radiation budget experiment, which was flown on the Nimbus-6 Sun-synchronous satellite in 1975. Only the wide-field-of-view longwave measurements are cataloged in this atlas. The contour maps along with the associated sets of spherical harmonic coefficients form a valuable data set for studying different aspects of our changing climate over monthly, annual, and interannual scales in the time domain, and over regional, zonal, and global scales in the spatial domain.

Determination of some dominant parameters of the global dynamic sea surface topography from GEOS-3 altimetry

NASA Technical Reports Server (NTRS)

Mather, R. S.; Lerch, F. J.; Rizos, C.; Masters, E. G.; Hirsch, B.

1978-01-01

The 1977 altimetry data bank is analyzed for the geometrical shape of the sea surface expressed as surface spherical harmonics after referral to the higher reference model defined by GEM 9. The resulting determination is expressed as quasi-stationary dynamic SST. Solutions are obtained from different sets of long arcs in the GEOS-3 altimeter data bank as well as from sub-sets related to the September 1975 and March 1976 equinoxes assembled with a view to minimizing seasonal effects. The results are compared with equivalent parameters obtained from the hydrostatic analysis of sporadic temperature, pressure and salinity measurements of the oceans and the known major steady state current systems with comparable wavelengths. The most clearly defined parameter (the zonal harmonic of degree 2) is obtained with an uncertainty of + or - 6 cm. The preferred numerical value is smaller than the oceanographic value due to the effect of the correction for the permanent earth tide. Similar precision is achieved for the zonal harmonic of degree 3. The precision obtained for the fourth degree zonal harmonic reflects more closely the accuracy expected from the level of noise in the orbital solutions.

Modeling of Focused Acoustic Field of a Concave Multi-annular Phased Array Using Spheroidal Beam Equation

NASA Astrophysics Data System (ADS)

Yu, Li-Li; Shou, Wen-De; Hui, Chun

2012-02-01

A theoretical model of focused acoustic field for a multi-annular phased array on concave spherical surface is proposed. In this model, the source boundary conditions of the spheroidal beam equation (SBE) for multi-annular phased elements are studied. Acoustic field calculated by the dynamic focusing model of SBE is compared with numerical results of the O'Neil and Khokhlov—Zabolotskaya—Kuznetsov (KZK) model, respectively. Axial dynamic focusing and the harmonic effects are presented. The results demonstrate that the dynamic focusing model of SBE is good valid for a concave multi-annular phased array with a large aperture angle in the linear or nonlinear field.

Initial geomagnetic field model from MAGSAT

NASA Technical Reports Server (NTRS)

Langel, R. A.; Estes, R. H.; Mead, G. D.; Fabiano, E. B.; Lancaster, E. R.

1980-01-01

Magsat data from magnetically quiet days were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(3/80). The model utilized both scalar and vector data and fit that data with standard deviations of 8, 52, 55 and 97 nT for the scalar magnitude, B sub r, B sub theta and B sub phi respectively. When compared with earlier models, the Earth's dipole moment continues to decrease at a rate of about 26 nT/year. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the AWC/75 and IGS/75 are better for predicting vector fields.

International geomagnetic reference field 1980: a report by IAGA Division I working group.

USGS Publications Warehouse

Peddie, N.W.

1982-01-01

Describes the recommendations of the working group, which suggested additions to IGRF because of the cumulative effect of the inevitable uncertainties in the secular variation models which had led to unacceptable inaccuracies in the IGRF by the late 1970's. The recommendations were accepted by the International Association of Geomagnetism and Aeronomy on August 15, 1981 at the 4th Scientific Assembly, Edinburgh. An extended table sets out spherical harmonic coefficients of the IGRF 1980.-R.House

Near earth magnetic disturbance in total field at high latitudes. 1: Summary of data from OGO's 2, 4, and 6

NASA Technical Reports Server (NTRS)

Langel, R. A.

1973-01-01

Variations in the total (i.e. scalar) magnetic field data from the polar orbiting OGO-2, 4, and 6 spacecraft (altitudes 400-1510 km) are summarized for invariant latitudes above 55 deg. Data from all degrees of magnetic disturbance are included. The data are presented in terms of the quantity delta B(= measured field magnitude minus the field magnitude from a spherical harmonic model of the quiet field).

Some anticipated contributions to core fluid dynamics from the GRM

NASA Technical Reports Server (NTRS)

Vanvorhies, C.

1985-01-01

It is broadly maintained that the secular variation (SV) of the large scale geomagnetic field contains information on the fluid dynamics of Earth's electrically conducting outer core. The electromagnetic theory appropriate to a simple Earth model has recently been combined with reduced geomagnetic data in order to extract some of this information and ascertain its significance. The simple Earth model consists of a rigid, electrically insulating mantle surrounding a spherical, inviscid, and perfectly conducting liquid outer core. This model was tested against seismology by using truncated spherical harmonic models of the observed geomagnetic field to locate Earth's core-mantle boundary, CMB. Further electromagnetic theory has been developed and applied to the problem of estimating the horizontal fluid motion just beneath CMB. Of particular geophysical interest are the hypotheses that these motions: (1) include appreciable surface divergence indicative of vertical motion at depth, and (2) are steady for time intervals of a decade or more. In addition to the extended testing of the basic Earth model, the proposed GRM provides a unique opportunity to test these dynamical hypotheses.

Accuracy estimates for some global analytical models of the Earth's main magnetic field on the basis of data on gradient magnetic surveys at stratospheric balloons

NASA Astrophysics Data System (ADS)

Tsvetkov, Yu. P.; Brekhov, O. M.; Bondar, T. N.; Filippov, S. V.; Petrov, V. G.; Tsvetkova, N. M.; Frunze, A. Kh.

2014-03-01

Two global analytical models of the main magnetic field of the Earth (MFE) have been used to determine their potential in deriving an anomalous MFE from balloon magnetic surveys conducted at altitudes of ˜30 km. The daily mean spherical harmonic model (DMSHM) constructed from satellite data on the day of balloon magnetic surveys was analyzed. This model for the day of magnetic surveys was shown to be almost free of errors associated with secular variations and can be recommended for deriving an anomalous MFE. The error of the enhanced magnetic model (EMM) was estimated depending on the number of harmonics used in the model. The model limited by the first 13 harmonics was shown to be able to lead to errors in the main MFE of around 15 nT. The EMM developed to n = m = 720 and constructed on the basis of satellite and ground-based magnetic data fails to adequately simulate the anomalous MFE at altitudes of 30 km. To construct a representative model developed to m = n = 720, ground-based magnetic data should be replaced by data of balloon magnetic surveys for altitudes of ˜30 km. The results of investigations were confirmed by a balloon experiment conducted by Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation of the Russian Academy of Sciences and the Moscow Aviation Institute.

Autonomous optimal trajectory design employing convex optimization for powered descent on an asteroid

NASA Astrophysics Data System (ADS)

Pinson, Robin Marie

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant (fuel) optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from ground control. The goal is to autonomously design the optimal powered descent trajectory onboard the spacecraft immediately prior to the descent burn for use during the burn. Compared to a planetary powered landing problem, the challenges that arise from designing an asteroid powered descent trajectory include complicated nonlinear gravity fields, small rotating bodies, and low thrust vehicles. The nonlinear gravity fields cannot be represented by a constant gravity model nor a Newtonian model. The trajectory design algorithm needs to be robust and efficient to guarantee a designed trajectory and complete the calculations in a reasonable time frame. This research investigates the following questions: Can convex optimization be used to design the minimum propellant powered descent trajectory for a soft landing on an asteroid? Is this method robust and reliable to allow autonomy onboard the spacecraft without interaction from ground control? This research designed a convex optimization based method that rapidly generates the propellant optimal asteroid powered descent trajectory. The solution to the convex optimization problem is the thrust magnitude and direction, which designs and determines the trajectory. The propellant optimal problem was formulated as a second order cone program, a subset of convex optimization, through relaxation techniques by including a slack variable, change of variables, and incorporation of the successive solution method. Convex optimization solvers, especially second order cone programs, are robust, reliable, and are guaranteed to find the global minimum provided one exists. In addition, an outer optimization loop using Brent's method determines the optimal flight time corresponding to the minimum propellant usage over all flight times. Inclusion of additional trajectory constraints, solely vertical motion near the landing site and glide slope, were evaluated. Through a theoretical proof involving the Minimum Principle from Optimal Control Theory and the Karush-Kuhn-Tucker conditions it was shown that the relaxed problem is identical to the original problem at the minimum point. Therefore, the optimal solution of the relaxed problem is an optimal solution of the original problem, referred to as lossless convexification. A key finding is that this holds for all levels of gravity model fidelity. The designed thrust magnitude profiles were the bang-bang predicted by Optimal Control Theory. The first high fidelity gravity model employed was the 2x2 spherical harmonics model assuming a perfect triaxial ellipsoid and placement of the coordinate frame at the asteroid's center of mass and aligned with the semi-major axes. The spherical harmonics model is not valid inside the Brillouin sphere and this becomes relevant for irregularly shaped asteroids. Then, a higher fidelity model was implemented combining the 4x4 spherical harmonics gravity model with the interior spherical Bessel gravity model. All gravitational terms in the equations of motion are evaluated with the position vector from the previous iteration, creating the successive solution method. Methodology success was shown by applying the algorithm to three triaxial ellipsoidal asteroids with four different rotation speeds using the 2x2 gravity model. Finally, the algorithm was tested using the irregularly shaped asteroid, Castalia.

Obtaining high g-values with low degree expansion of the phasefunction

NASA Astrophysics Data System (ADS)

Rinzema, Kees; ten Bosch, Jaap J.; Ferwerda, Hedzer A.; Hoenders, Bernhard J.

1994-02-01

Analytic theory of anisotropic random flight requires the expansion of phase-functions in spherical harmonics. The number of terms should be limited while a g value should be obtained that is as high as possible. We describe how such a phase function can be constructed for a given number N of spherical components of the phasefunction, while obtaining a maximum value of the asymmetry parameter g.

Second-harmonic generation from a thin spherical layer and No-generation conditions

NASA Astrophysics Data System (ADS)

Kapshai, V. N.; Shamyna, A. A.

2017-09-01

In the Rayleigh-Gans-Debye approximation, we solve the problem of second-harmonic generation by an elliptically polarized electromagnetic wave incident on the surface of a spherical particle that is coated by an optically nonlinear layer and is placed in a dielectric. The formulas obtained characterize the spatial distribution of the electric field of the second harmonic in the far-field zone. The most general form of the second-order dielectric susceptibility tensor is considered, which contains four independent components, with three of them being nonchiral and one, chiral. Consistency and inconsistencies between the obtained solution and formulas from works of other authors are found. We analyze the directivity patterns that characterize the spatial distribution of the generated radiation for the nonchiral layer and their dependences on the anisotropy and ellipticity coefficients of the incident wave. It is found that, with increasing radius of the nonlinear layer, the generated radiation becomes more directional. Combinations of parameters for which no radiation is generated are revealed. Based on this, we propose methods for experimental determination of the anisotropy coefficients.

Implications of postseismic gravity change following the great 2004 Sumatra-Andaman earthquake from the regional harmonic analysis of GRACE intersatellite tracking data

USGS Publications Warehouse

Han, S.-C.; Sauber, J.; Luthcke, S.B.; Ji, C.; Pollitz., F. F.

2008-01-01

We report Gravity Recovery and Climate Experiment (GRACE) satellite observations of coseismic displacements and postseismic transients from the great Sumatra-Andaman Islands (thrust event; Mw ???9.2) earthquake in December 2004. Instead of using global spherical harmonic solutions of monthly gravity fields, we estimated the gravity changes directly using intersatellite range-rate data with regionally concentrated spherical Slepian basis functions every 15-day interval. We found significant step-like (coseismic) and exponential-like (postseismic) behavior in the time series of estimated coefficients (from May 2003 to April 2007) for the spherical Slepian function's. After deriving coseismic slip estimates from seismic and geodetic data that spanned different time intervals, we estimated and evaluated postseismic relaxation mechanisms with alternate asthenosphere viscosity models. The large spatial coverage and uniform accuracy of our GRACE solution enabled us to clearly delineate a postseismic transient signal in the first 2 years of postearthquake GRACE data. Our preferred interpretation of the long-wavelength components of the postseismic avity change is biviscous viscoelastic flow. We estimated a transient viscosity of 5 ??17 Pa s and a steady state viscosity of 5 ?? 1018 - 1019 Pa s. Additional years of the GRACE observations should provide improved steady state viscosity estimates. In contrast to our interpretation of coseismic gravity change, the prominent postearthquake positive gravity change around the Nicobar Islands is accounted for by seafloor uplift with less postseismic perturbation in intrinsic density in the region surrounding the earthquake. Copyright 2008 by the American Geophysical Union.

Constraints on Ceres' Internal Structure and Evolution From Its Shape and Gravity Measured by the Dawn Spacecraft

NASA Astrophysics Data System (ADS)

Ermakov, A. I.; Fu, R. R.; Castillo-Rogez, J. C.; Raymond, C. A.; Park, R. S.; Preusker, F.; Russell, C. T.; Smith, D. E.; Zuber, M. T.

2017-11-01

Ceres is the largest body in the asteroid belt with a radius of approximately 470 km. In part due to its large mass, Ceres more closely approaches hydrostatic equilibrium than major asteroids. Pre-Dawn mission shape observations of Ceres revealed a shape consistent with a hydrostatic ellipsoid of revolution. The Dawn spacecraft Framing Camera has been imaging Ceres since March 2015, which has led to high-resolution shape models of the dwarf planet, while the gravity field has been globally determined to a spherical harmonic degree 14 (equivalent to a spatial wavelength of 211 km) and locally to 18 (a wavelength of 164 km). We use these shape and gravity models to constrain Ceres' internal structure. We find a negative correlation and admittance between topography and gravity at degree 2 and order 2. Low admittances between spherical harmonic degrees 3 and 16 are well explained by Airy isostatic compensation mechanism. Different models of isostasy give crustal densities between 1,200 and 1,400 kg/m3 with our preferred model giving a crustal density of 1,287+70-87 kg/m3. The mantle density is constrained to be 2,434+5-8 kg/m3. We compute isostatic gravity anomaly and find evidence for mascon-like structures in the two biggest basins. The topographic power spectrum of Ceres and its latitude dependence suggest that viscous relaxation occurred at the long wavelengths (>246 km). Our density constraints combined with finite element modeling of viscous relaxation suggests that the rheology and density of the shallow surface are most consistent with a rock, ice, salt and clathrate mixture.

Terrestrial Water Mass Load Changes from Gravity Recovery and Climate Experiment (GRACE)

NASA Technical Reports Server (NTRS)

Seo, K.-W.; Wilson, C. R.; Famiglietti, J. S.; Chen, J. L.; Rodell M.

2006-01-01

Recent studies show that data from the Gravity Recovery and Climate Experiment (GRACE) is promising for basin- to global-scale water cycle research. This study provides varied assessments of errors associated with GRACE water storage estimates. Thirteen monthly GRACE gravity solutions from August 2002 to December 2004 are examined, along with synthesized GRACE gravity fields for the same period that incorporate simulated errors. The synthetic GRACE fields are calculated using numerical climate models and GRACE internal error estimates. We consider the influence of measurement noise, spatial leakage error, and atmospheric and ocean dealiasing (AOD) model error as the major contributors to the error budget. Leakage error arises from the limited range of GRACE spherical harmonics not corrupted by noise. AOD model error is due to imperfect correction for atmosphere and ocean mass redistribution applied during GRACE processing. Four methods of forming water storage estimates from GRACE spherical harmonics (four different basin filters) are applied to both GRACE and synthetic data. Two basin filters use Gaussian smoothing, and the other two are dynamic basin filters which use knowledge of geographical locations where water storage variations are expected. Global maps of measurement noise, leakage error, and AOD model errors are estimated for each basin filter. Dynamic basin filters yield the smallest errors and highest signal-to-noise ratio. Within 12 selected basins, GRACE and synthetic data show similar amplitudes of water storage change. Using 53 river basins, covering most of Earth's land surface excluding Antarctica and Greenland, we document how error changes with basin size, latitude, and shape. Leakage error is most affected by basin size and latitude, and AOD model error is most dependent on basin latitude.

Weakly nonlinear incompressible Rayleigh-Taylor instability in spherical geometry

NASA Astrophysics Data System (ADS)

Zhang, J.; Wang, L. F.; Ye, W. H.; Wu, J. F.; Guo, H. Y.; Zhang, W. Y.; He, X. T.

2017-06-01

In this research, a weakly nonlinear (WN) model for the incompressible Rayleigh-Taylor instability in cylindrical geometry [Wang et al., Phys. Plasmas 20, 042708 (2013)] is generalized to spherical geometry. The evolution of the interface with an initial small-amplitude single-mode perturbation in the form of Legendre mode (Pn) is analysed with the third-order WN solutions. The transition of the small-amplitude perturbed spherical interface to the bubble-and-spike structure can be observed by our model. For single-mode perturbation Pn, besides the generation of P 2 n and P 3 n , which are similar to the second and third harmonics in planar and cylindrical geometries, many other modes in the range of P0- P 3 n are generated by mode-coupling effects up to the third order. With the same initial amplitude, the bubbles at the pole grow faster than those at the equator in the WN regime. Furthermore, it is found that the behavior of the bubbles at the pole is similar to that of three-dimensional axisymmetric bubbles, while the behavior of the bubbles at the equator is similar to that of two-dimensional bubbles.

Venus geology, geochemistry, and geophysics - Research results from the USSR

NASA Astrophysics Data System (ADS)

Barsukov, V. L.; Basilevsky, A. T.; Volkov, V. P.; Zharkov, V. N.

The book includes papers on the Venusian volcanism, hot-spot structures, the Lakshmi phenomenon, tesserae, ridge belts on plains, impact craters, evidence on the crustal dichotomy, the global tectonic style, resurfacing, and Venusian igneous rocks. Special attention is given to volatiles in the atmosphere and crust, the expansion of topography into spherical harmonics, rotation, statistical properties of topography and the gravity field, a physical model of Venus, and models of the thermal evolution of Venus. Also presented are an atlas of Venusian surface images and a table listing topographic features on Venus and their coordinates.

Are higher degree even zonals really harmful for the LARES/LAGEOS frame-dragging experiment?

NASA Astrophysics Data System (ADS)

Renzetti, G.

2012-08-01

The low-altitude effects of LARES are examined to determined how they can impact the outcome of the hoped 1% frame-dragging measurement in the LARES-LAGEOS experiment. This analysis, based on a different approach than other studies recently appearing in the literature, shows that the spherical harmonics of the Earth gravity field with degree ℓ > 60 may represent a threat because their errors map significantly into LARES orbital disturbances compared to frame-dragging. The GIF48 model was used. It is questionable whether future Earth gravity models by GRACE and GOCE will be of sufficient accuracy.

Multipath calibration in GPS pseudorange measurements

NASA Technical Reports Server (NTRS)

Kee, Changdon (Inventor); Parkinson, Bradford W. (Inventor)

1998-01-01

Novel techniques are disclosed for eliminating multipath errors, including mean bias errors, in pseudorange measurements made by conventional global positioning system receivers. By correlating the multipath signals of different satellites at their cross-over points in the sky, multipath mean bias errors are effectively eliminated. By then taking advantage of the geometrical dependence of multipath, a linear combination of spherical harmonics are fit to the satellite multipath data to create a hemispherical model of the multipath. This calibration model can then be used to compensate for multipath in subsequent measurements and thereby obtain GPS positioning to centimeter accuracy.

Comparative mapping of Pluto's sub-Charon hemisphere - Three least squares models based on mutual event lightcurves

NASA Technical Reports Server (NTRS)

Young, Eliot F.; Binzel, Richard P.

1993-01-01

Observations of Charon transits are used here to derive preliminary maps of Pluto's sub-Charon hemisphere. Three models are used to describe the brightness of Pluto's surface as functions of latitude and longitude. Mapping results are presented using spherical harmonic functions, polynomial functions, and finite elements. A smoothing algorithm applied to the maps is described and the validity and resolution of the maps is tested by reconstruction from synthetic data. A preliminary finding from the maps is that the south polar region has the highest albedo of any location on the planet.

Forecasting longitudinal changes in oropharyngeal tumor morphology throughout the course of head and neck radiation therapy

PubMed Central

Yock, Adam D.; Rao, Arvind; Dong, Lei; Beadle, Beth M.; Garden, Adam S.; Kudchadker, Rajat J.; Court, Laurence E.

2014-01-01

Purpose: To create models that forecast longitudinal trends in changing tumor morphology and to evaluate and compare their predictive potential throughout the course of radiation therapy. Methods: Two morphology feature vectors were used to describe 35 gross tumor volumes (GTVs) throughout the course of intensity-modulated radiation therapy for oropharyngeal tumors. The feature vectors comprised the coordinates of the GTV centroids and a description of GTV shape using either interlandmark distances or a spherical harmonic decomposition of these distances. The change in the morphology feature vector observed at 33 time points throughout the course of treatment was described using static, linear, and mean models. Models were adjusted at 0, 1, 2, 3, or 5 different time points (adjustment points) to improve prediction accuracy. The potential of these models to forecast GTV morphology was evaluated using leave-one-out cross-validation, and the accuracy of the models was compared using Wilcoxon signed-rank tests. Results: Adding a single adjustment point to the static model without any adjustment points decreased the median error in forecasting the position of GTV surface landmarks by the largest amount (1.2 mm). Additional adjustment points further decreased the forecast error by about 0.4 mm each. Selection of the linear model decreased the forecast error for both the distance-based and spherical harmonic morphology descriptors (0.2 mm), while the mean model decreased the forecast error for the distance-based descriptor only (0.2 mm). The magnitude and statistical significance of these improvements decreased with each additional adjustment point, and the effect from model selection was not as large as that from adding the initial points. Conclusions: The authors present models that anticipate longitudinal changes in tumor morphology using various models and model adjustment schemes. The accuracy of these models depended on their form, and the utility of these models includes the characterization of patient-specific response with implications for treatment management and research study design. PMID:25086518

Forecasting longitudinal changes in oropharyngeal tumor morphology throughout the course of head and neck radiation therapy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yock, Adam D.; Kudchadker, Rajat J.; Rao, Arvind

2014-08-15

Purpose: To create models that forecast longitudinal trends in changing tumor morphology and to evaluate and compare their predictive potential throughout the course of radiation therapy. Methods: Two morphology feature vectors were used to describe 35 gross tumor volumes (GTVs) throughout the course of intensity-modulated radiation therapy for oropharyngeal tumors. The feature vectors comprised the coordinates of the GTV centroids and a description of GTV shape using either interlandmark distances or a spherical harmonic decomposition of these distances. The change in the morphology feature vector observed at 33 time points throughout the course of treatment was described using static, linear,more » and mean models. Models were adjusted at 0, 1, 2, 3, or 5 different time points (adjustment points) to improve prediction accuracy. The potential of these models to forecast GTV morphology was evaluated using leave-one-out cross-validation, and the accuracy of the models was compared using Wilcoxon signed-rank tests. Results: Adding a single adjustment point to the static model without any adjustment points decreased the median error in forecasting the position of GTV surface landmarks by the largest amount (1.2 mm). Additional adjustment points further decreased the forecast error by about 0.4 mm each. Selection of the linear model decreased the forecast error for both the distance-based and spherical harmonic morphology descriptors (0.2 mm), while the mean model decreased the forecast error for the distance-based descriptor only (0.2 mm). The magnitude and statistical significance of these improvements decreased with each additional adjustment point, and the effect from model selection was not as large as that from adding the initial points. Conclusions: The authors present models that anticipate longitudinal changes in tumor morphology using various models and model adjustment schemes. The accuracy of these models depended on their form, and the utility of these models includes the characterization of patient-specific response with implications for treatment management and research study design.« less

Analysis of geomagnetic secular variation during 1980-1985 and 1985- 1990, and geomagnetic models proposed for the 1991 revision of the International Geomagnetic Reference Field

USGS Publications Warehouse

Peddie, N.W.

1992-01-01

The secular variation of the main geomagnetic field during the periods 1980-1985 and 1985-1990 was analyzed in terms of spherical harmonics up to the eighth degree and order. Data from worldwide magnetic observatories and the Navy's Project MAGNET aerial surveys were used. The resulting pair of secular-variation models was used to update the Definitive Geomagnetic Reference Field (DGRF) model for 1980, resulting in new mainfield models for 1985.0 and 1990.0. These, along with the secular-variation model for 1985-1990, were proposed for the 1991 revision of the International Geomagnetic Reference Field (IGRF). -Author

Analysis of the Reference Systems of Modern Selenographic Systems

NASA Astrophysics Data System (ADS)

Nefedyev, Yuri; Petrova, Natalia; Andreev, Alexey; Demina, Natalya

2016-07-01

In this work analysis of the reference systems of modern selenographic systems was made. The center of the Moon's mass position relative to its center of figure was determined from the data of "Clementine" and "Kaguya" missions and "ULCN" and "KSC-1162" catalogues. The knowledge of the Moon's center of mass position relative to its center of figure is important for researches of the lunar origin, structure and evolution and in terms of precision solutions circumlunar navigation tasks. At the present this task is the most relevant and demanded for cosmic lunar missions.The expansions by spherical harmonics N=5 degree and order of the lunar function h (λ, β) using the package ASNI USTU were executed. Module of the expansion of the local area to surfaces to full sphere was used. The parameters of cosmic missions are given for comparison (SAI; Bills, Ferrari). The normalized coefficients from expansions for eight sources of hypsometric information are obtained: "Clementine" (N=40), "KSC-1162" (N=5), "Kiev" (N=5), "SAI" (N=10; Chuikova (1975)), "Bills, Ferrari", "Kaguya" (Selena, Japan mission), "ULCN" (The Unified Lunar Control Network 2005). The displacements of the lunar center of figure relative to the lunar center of the mass were defined from equations (Chuikova (1975)): Δ ξ = C_{11} √{3}, Δ η= S_{11} √{3}, Δ ζ = C_{10} √{3}, where ξ is the axis directed towards the Earth, η is equatorial axis directed perpendicularly to ξ , ζ is rotation axis of the Moon, C_{11} , S_{11} , C_{10} are the normalized amplitudes of the harmonics of the first order expansion of the relief. After that we considered: - mathematical models in the form of expansions in spherical functions - methods for estimating the model parameters; - information technology data processing. As a model describing the behavior of the relief on the lunar sphere is used the expansion of the height in a series of spherical harmonics (Sagitov (1979)) in the form of a regression model (Valeev (2001)). To obtain the expansions in spherical harmonics in order to create a digital model and determine estimations of the center of mass position of the Moon relative to its center of the figure required in the future was usedsoftware package ASSR "Sphere" (an automated system of scientific research).ASSR "Sphere" is intended to describe the distribution of various values of the parameters (topography, gravity, magnetic, and other types of potential fields) on the sphere and its parts which were measured in points with known coordinates. Using this bundled software one can generate models of the specificform,carry out forecasting in the form of cross-sections, contour, tone and three-dimensional representation of the distribution of characteristicsvalues. The formation of models is accompanied by estimation of their quality and diagnostic of adherence of least square method. After all we can conclude that the "KSC-1162" catalogue, which was obtained in the center of mass and principal axes of inertia of the Moon, has the closest agreement with the results of recent space missions.It should be noted that the correction of the first measurements of the "Clementine" mission data, which were obtained by the authors of the "ULCN 2005" catalogue, was apparently related to the data on the visible side of the Moon because the amplitudes and offsets for the ("KSC-1162" + "Clementine") option close to the results of the "ULCN 2005" optionbut not to"Clementine".The results of defining relative position of the lunar center of mass and center of figure in "KSC-1162"selenocentric catalogue gave some good agreement with modern space mission data. Work was supported by grants RFBR 15-02-01638-a, 16-32-60071-mol-dk-a and 16-02-00496-a.

Short spatial filters with spherical lenses for high-power pulsed lasers

DOE Office of Scientific and Technical Information (OSTI.GOV)

Burdonov, K F; Soloviev, A A; Shaikin, A A

We report possible employment of short spatial filters based on spherical lenses in a pulsed laser source (neodymium glass, 300 J, 1 ns). The influence of the spherical aberration on the quality of output radiation and coefficient of conversion to the second harmonics is studied. The ultra-short aberration spatial filter of length 1.9 m with an aperture of 122 mm is experimentally tested. A considerable shortening of multi-cascade pump lasers for modern petawatt laser systems is demonstrated by the employment of short spatial filters without expensive aspherical optics. (elements of laser systems)

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

PubMed

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.

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

PubMed Central

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

2017-01-01

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. PMID:28287453

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

PubMed

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.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Sen; Luo, Sheng-Nian

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, fundamentalmore » harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.« less

Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow

DOE PAGES

Giacomin, A. J.; Gilbert, P. H.; Schmalzer, A. M.

2015-03-19

In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of themore » polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number λω is zero and the Weissenberg number λγ 0 is above unity), (ii) nonlinear viscoelasticity (where both λω and λγ 0 exceed unity), and (iii) linear viscoelasticity (where λω exceeds unity and where λγ 0 approaches zero). We learn that the polymer orientation distribution is spherical in the linear viscoelastic regime, and otherwise tilted and peanut-shaped. We find that the peanut-shaping is mainly caused by the zeroth harmonic, and the tilting, by the second. The first, third, and fourth harmonics of the orientation distribution make only slight contributions to the overall polymer motion.« less

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Sen; Luo, Sheng-Nian

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, fundamentalmore » harmonic bandwidth and high harmonics. The effects of bandwidth, spectral shape and high harmonics on particle size determination are evaluated quantitatively.« less

Redesigning existing transcranial magnetic stimulation coils to reduce energy: application to low field magnetic stimulation

NASA Astrophysics Data System (ADS)

Wang, Boshuo; Shen, Michael R.; Deng, Zhi-De; Smith, J. Evan; Tharayil, Joseph J.; Gurrey, Clement J.; Gomez, Luis J.; Peterchev, Angel V.

2018-06-01

Objective. To present a systematic framework and exemplar for the development of a compact and energy-efficient coil that replicates the electric field (E-field) distribution induced by an existing transcranial magnetic stimulation coil. Approach. The E-field generated by a conventional low field magnetic stimulation (LFMS) coil was measured for a spherical head model and simulated in both spherical and realistic head models. Then, using a spherical head model and spatial harmonic decomposition, a spherical-shaped cap coil was synthesized such that its windings conformed to a spherical surface and replicated the E-field on the cortical surface while requiring less energy. A prototype coil was built and electrically characterized. The effect of constraining the windings to the upper half of the head was also explored via an alternative coil design. Main results. The LFMS E-field distribution resembled that of a large double-cone coil, with a peak field strength around 350 mV m‑1 in the cortex. The E-field distributions of the cap coil designs were validated against the original coil, with mean errors of 1%–3%. The cap coil required as little as 2% of the original coil energy and was significantly smaller in size. Significance. The redesigned LFMS coil is substantially smaller and more energy-efficient than the original, improving cost, power consumption, and portability. These improvements could facilitate deployment of LFMS in the clinic and potentially at home. This coil redesign approach can also be applied to other magnetic stimulation paradigms. Finally, the anatomically-accurate E-field simulation of LFMS can be used to interpret clinical LFMS data.

The Early Shape of the Moon

NASA Astrophysics Data System (ADS)

Garrick-Bethell, I.; Perera, V.; Nimmo, F.; Zuber, M. T.

2013-12-01

The origin and nature of the long-wavelength shape of the Moon has been a puzzle for at least 100 years [1-5]. Understanding its origin would provide insight into the patterns of mare volcanism, early thermal evolution, the history of the Moon's orientation, and the Moon's orbital evolution. Previously, we explained the shape and structure of the lunar farside highlands with a model of early tidal heating in the crust [6]. However, we left open the problem of the rest of the Moon's low-order shape, and we did not consider the lunar gravity field together with topography. To address these problems, and further assess the tidal-rotation (spherical harmonic degree-2) origins of the lunar shape, we consider three effects: the Moon's degree-1 spherical harmonics, the Moon's largest basins and mascons, and the choice of reference frame in which we analyze topography. We find that removing the degree-1 terms from a topography map helps illustrate the Moon's degree-2 shape, since the degree-1 harmonics have relatively high power. More importantly, however, when we fit spherical harmonics to topography outside of the largest lunar basins (including South-Pole Aitken, Imbrium, Serenitatis, Nectaris, and Orientale), the degree-2 coefficient values change significantly. When these best-fit harmonics are rotated into a reference frame that only contains the C2,0 and C2,2 harmonics (equivalent to the frame that would have once faced the Earth if the early Moon's shape controlled the moments of inertia), we find that gravity and topography data together imply a mixture of compensated and uncompensated degree-2 topography components. The compensated topography component can be explained by global-scale tidal heating in the early crust, while the uncompensated component can be explained by a frozen 'fossil bulge' that formed at a semi-major axis of about 32 Earth radii. To check these explanations, we can examine the ratios of the C2,0 and C2,2 harmonics for each component. We find that the values of C2,0/C2,2 are approximately equal to the values expected for each unique process: -1.3 and -1.0, for compensated (tidal-heating) and uncompensated (fossil bulge) topography components, respectively. However, if we had not removed the effects of large basins, the ratios would not be in agreement. In conclusion, a combination of early tidal heating in the crust and a frozen fossil bulge can help explain the global, pre-basin shape of the Moon. References [1] W.F. Sedgwick, On the figure of the Moon, Messenger Math. 27 (1898) 171. [2] H. Jeffreys, On the figures of the Earth and Moon, Geophys. J. Int. 4 (1937) 1-13. [3] H.C. Urey, et al., Note on the internal structure of the Moon, Ap. J. 129 (1959) 842. [4] K. Lambeck, S. Pullan, The lunar fossil bulge hypothesis revisited, Phys. Earth Planet. Inter. 22 (1980) 29-35. [5] D.J. Stevenson, Origin and implications of the degree two lunar gravity field, Proc. Lunar Sci. Conf. 32nd (2001) 1175. [6] I. Garrick-Bethell, et al., Structure and formation of the lunar farside highlands, Science 330 (2010) 949-951.

Geomagnetism of earth's core

NASA Technical Reports Server (NTRS)

Benton, E. R.

1983-01-01

Instrumentation, analytical methods, and research goals for understanding the behavior and source of geophysical magnetism are reviewed. Magsat, launched in 1979, collected global magnetometer data and identified the main terrestrial magnetic fields. The data has been treated by representing the curl-free field in terms of a scalar potential which is decomposed into a truncated series of spherical harmonics. Solutions to the Laplace equation then extend the field upward or downward from the measurement level through intervening spaces with no source. Further research is necessary on the interaction between harmonics of various spatial scales. Attempts are also being made to analytically model the main field and its secular variation at the core-mantle boundary. Work is also being done on characterizing the core structure, composition, thermodynamics, energetics, and formation, as well as designing a new Magsat or a tethered satellite to be flown on the Shuttle.

YORP torque as the function of shape harmonics

NASA Astrophysics Data System (ADS)

Breiter, Sławomir; Michalska, Hanna

2008-08-01

The second-order analytical approximation of the mean Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) torque components is given as an explicit function of the shape spherical harmonics coefficients for a sufficiently regular minor body. The results are based upon a new expression for the insolation function, significantly simpler than in previous works. Linearized plane-parallel model of the temperature distribution derived from the insolation function allows us to take into account a non-zero conductivity. Final expressions for the three average components of the YORP torque related with rotation period, obliquity and precession are given in a form of the Legendre series of the cosine of obliquity. The series have good numerical properties and can be easily truncated according to the degree of the Legendre polynomials or associated functions, with first two terms playing the principal role.

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

PubMed

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.

Development and analysis of a twelfth degree and order gravity model for Mars

NASA Technical Reports Server (NTRS)

Christensen, E. J.; Balmino, G.

1979-01-01

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

An oblate ellipsoidal approach to update a high-resolution geopotential model over the oceans: Study case of EGM2008 and DTU10

NASA Astrophysics Data System (ADS)

Sebera, Josef; Bezděk, Aleš; Kostelecký, Jan; Pešek, Ivan; Shum, C. K.

2016-01-01

The most important high-resolution geopotential models such as EGM96 and EGM2008 have been released approximately once per decade. In light of the ability of modern satellite, airborne or terrestrial techniques to provide new data sets every year (e.g., in polar and ocean areas), these data can be readily included in existing models without waiting for a new release. In this article, we present a novel ellipsoidal approach for updating high-resolution models over the oceans with new gridded data. The problem is demonstrated using the EGM2008 model updated with DTU10 geoid and gravity grids that provide additional signal over the Arctic oceans. The result of the procedure are the ellipsoidal and the spherical harmonic coefficients up to degree 4320 and 4400, respectively. These coefficients represent the input data set to within 0.08 mGal globally, with the largest differences located at the land-ocean boundaries, which is two orders of magnitude less than real accuracy of gravity data from satellite altimetry. Along with the harmonic coefficients a detailed map of the second vertical derivative of the anomalous potential (or vertical gravitational gradient) on 1 arc-min grid is anticipated to improve or complement the original DTU10 geoid model. Finally, an optimized set of Jekeli's functions is provided as they allow for computing oblate ellipsoidal harmonics up to a very high degree and order (>10,000) in terms of the hypergeometric formulation.

General Multivariate Linear Modeling of Surface Shapes Using SurfStat

PubMed Central

Chung, Moo K.; Worsley, Keith J.; Nacewicz, Brendon, M.; Dalton, Kim M.; Davidson, Richard J.

2010-01-01

Although there are many imaging studies on traditional ROI-based amygdala volumetry, there are very few studies on modeling amygdala shape variations. This paper present a unified computational and statistical framework for modeling amygdala shape variations in a clinical population. The weighted spherical harmonic representation is used as to parameterize, to smooth out, and to normalize amygdala surfaces. The representation is subsequently used as an input for multivariate linear models accounting for nuisance covariates such as age and brain size difference using SurfStat package that completely avoids the complexity of specifying design matrices. The methodology has been applied for quantifying abnormal local amygdala shape variations in 22 high functioning autistic subjects. PMID:20620211

Evaluation of GOCE-based global gravity field models over Japan after the full mission using free-air gravity anomalies and geoid undulations

NASA Astrophysics Data System (ADS)

Odera, Patroba Achola; Fukuda, Yoichi

2017-09-01

The performance of Gravity field and steady-state Ocean Circulation Explorer (GOCE) global gravity field models (GGMs), at the end of GOCE mission covering 42 months, is evaluated using geoid undulations and free-air gravity anomalies over Japan, including six sub-regions (Hokkaido, north Honshu, central Honshu, west Honshu, Shikoku and Kyushu). Seventeen GOCE-based GGMs are evaluated and compared with EGM2008. The evaluations are carried out at 150, 180, 210, 240 and 270 spherical harmonics degrees. Results show that EGM2008 performs better than GOCE and related GGMs in Japan and three sub-regions (Hokkaido, central Honshu and Kyushu). However, GOCE and related GGMs perform better than EGM2008 in north Honshu, west Honshu and Shikoku up to degree 240. This means that GOCE data can improve geoid model over half of Japan. The improvement is only evident between degrees 150 and 240 beyond which EGM2008 performs better than GOCE GGMs in all the six regions. In general, the latest GOCE GGMs (releases 4 and 5) perform better than the earlier GOCE GGMs (releases 1, 2 and 3), indicating the contribution of data collected by GOCE in the last months before the mission ended on 11 November 2013. The results indicate that a more accurate geoid model over Japan is achievable, based on a combination of GOCE, EGM2008 and terrestrial gravity data sets. [Figure not available: see fulltext. Caption: Standard deviations of the differences between observed and GGMs implied ( a) free-air gravity anomalies over Japan, ( b) geoid undulations over Japan. n represents the spherical harmonic degrees

A boundary element method for particle and droplet electrohydrodynamics in the Quincke regime

NASA Astrophysics Data System (ADS)

Das, Debasish; Saintillan, David

2014-11-01

Quincke electrorotation is the spontaneous rotation of dielectric particles suspended in a dielectric liquid of higher conductivity when placed in a sufficiently strong electric field. This phenomenon of Quincke rotation has interesting implications for the rheology of these suspensions, whose effective viscosity can be controlled and reduced by application of an external field. While spherical harmonics can be used to solve the governing equations for a spherical particle, they cannot be used to study the dynamics of particles of more complex shapes or deformable particles or droplets. Here, we develop a novel boundary element formulation to model the dynamics of a dielectric particle under Quincke rotation based on the Taylor-Melcher leaky dielectric model, and compare the numerical results to theoretical predictions. We then employ this boundary element method to analyze the dynamics of a two-dimensional drop under Quincke rotation, where we allow the drop to deform under the electric field. Extensions to three-dimensions and to the electrohydrodynamic interactions of multiple droplets are also discussed.

Radiative transfer code SHARM for atmospheric and terrestrial applications

NASA Astrophysics Data System (ADS)

Lyapustin, A. I.

2005-12-01

An overview of the publicly available radiative transfer Spherical Harmonics code (SHARM) is presented. SHARM is a rigorous code, as accurate as the Discrete Ordinate Radiative Transfer (DISORT) code, yet faster. It performs simultaneous calculations for different solar zenith angles, view zenith angles, and view azimuths and allows the user to make multiwavelength calculations in one run. The Δ-M method is implemented for calculations with highly anisotropic phase functions. Rayleigh scattering is automatically included as a function of wavelength, surface elevation, and the selected vertical profile of one of the standard atmospheric models. The current version of the SHARM code does not explicitly include atmospheric gaseous absorption, which should be provided by the user. The SHARM code has several built-in models of the bidirectional reflectance of land and wind-ruffled water surfaces that are most widely used in research and satellite data processing. A modification of the SHARM code with the built-in Mie algorithm designed for calculations with spherical aerosols is also described.

Radiative transfer code SHARM for atmospheric and terrestrial applications.

PubMed

Lyapustin, A I

2005-12-20

An overview of the publicly available radiative transfer Spherical Harmonics code (SHARM) is presented. SHARM is a rigorous code, as accurate as the Discrete Ordinate Radiative Transfer (DISORT) code, yet faster. It performs simultaneous calculations for different solar zenith angles, view zenith angles, and view azimuths and allows the user to make multiwavelength calculations in one run. The Delta-M method is implemented for calculations with highly anisotropic phase functions. Rayleigh scattering is automatically included as a function of wavelength, surface elevation, and the selected vertical profile of one of the standard atmospheric models. The current version of the SHARM code does not explicitly include atmospheric gaseous absorption, which should be provided by the user. The SHARM code has several built-in models of the bidirectional reflectance of land and wind-ruffled water surfaces that are most widely used in research and satellite data processing. A modification of the SHARM code with the built-in Mie algorithm designed for calculations with spherical aerosols is also described.

On Weyl wormholes supported by massless K-essence

DOE Office of Scientific and Technical Information (OSTI.GOV)

Estevez-Delgado, J.; Zannias, T.

We show that Weyl wormholes supported by mass-less K-essence can be generated by a pair of axisymmetric harmonic functions. We study properties of space-times generated by harmonic functions describing the exterior potential of a thin conducting disk held at fixed potential. We find that within this family, only a particular subfamily generates wormholes and the resulting wormholes are necessarily spherical. In general, the topology of the space-times generated by an arbitrary pair is multi sheeted.

Calculation and Analysis of Magnetic Gradient Tensor Components of Global Magnetic Models

NASA Astrophysics Data System (ADS)

Schiffler, M.; Queitsch, M.; Schneider, M.; Goepel, A.; Stolz, R.; Krech, W.; Meyer, H. G.; Kukowski, N.

2014-12-01

Global Earth's magnetic field models like the International Geomagnetic Reference Field (IGRF), the World Magnetic Model (WMM) or the High Definition Geomagnetic Model (HDGM) are harmonic analysis regressions to available magnetic observations stored as spherical harmonic coefficients. Input data combine recordings from magnetic observatories, airborne magnetic surveys and satellite data. The advance of recent magnetic satellite missions like SWARM and its predecessors like CHAMP offer high resolution measurements while providing a full global coverage. This deserves expansion of the theoretical framework of harmonic synthesis to magnetic gradient tensor components. Measurement setups for Full Tensor Magnetic Gradiometry equipped with high sensitive gradiometers like the JeSSY STAR system can directly measure the gradient tensor components, which requires precise knowledge about the background regional gradients which can be calculated with this extension. In this study we develop the theoretical framework for calculation of the magnetic gradient tensor components from the harmonic series expansion and apply our approach to the IGRF and HDGM. The gradient tensor component maps for entire Earth's surface produced for the IGRF show low gradients reflecting the variation from the dipolar character, whereas maps for the HDGM (up to degree N=729) reveal new information about crustal structure, especially across the oceans, and deeply situated ore bodies. From the gradient tensor components, the rotational invariants, the Eigenvalues, and the normalized source strength (NSS) are calculated. The NSS focuses on shallower and stronger anomalies. Euler deconvolution using either the tensor components or the NSS applied to the HDGM reveals an estimate of the average source depth for the entire magnetic crust as well as individual plutons and ore bodies. The NSS reveals the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

4D Hyperspherical Harmonic (HyperSPHARM) Representation of Multiple Disconnected Brain Subcortical Structures

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Schaefer, Stacey M.; van Reekum, Carien M.; Peschke-Schmitz, Lara; Sutterer, Matt; Alexander, Andrew L.; Davidson, Richard J.

2014-01-01

We present a novel surface parameterization technique using hyperspherical harmonics (HSH) in representing compact, multiple, disconnected brain subcortical structures as a single analytic function. The proposed hyperspherical harmonic representation (HyperSPHARM) has many advantages over the widely used spherical harmonic (SPHARM) parameterization technique. SPHARM requires flattening 3D surfaces to 3D sphere which can be time consuming for large surface meshes, and can’t represent multiple disconnected objects with single parameterization. On the other hand, HyperSPHARM treats 3D object, via simple stereographic projection, as a surface of 4D hypersphere with extremely large radius, hence avoiding the computationally demanding flattening process. HyperSPHARM is shown to achieve a better reconstruction with only 5 basis compared to SPHARM that requires more than 441. PMID:24505716

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

Transition probability functions for applications of inelastic electron scattering

PubMed Central

Löffler, Stefan; Schattschneider, Peter

2012-01-01

In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations. PMID:22560709

Understanding microstrain anisotropy in yttrium oxide synthesized by sol-gel route

NASA Astrophysics Data System (ADS)

Murugesan, S.; Thirumurugesan, R.; Parameswaran, P.

2018-04-01

Yttrium oxide was synthesized by wet chemical route and calcined at various temperatures. On x-ray diffraction analysis of the material using Williamson-Hall analysis followed by Rietveld analysis indicates that the powder exists in nano crystallite size with lattice strain. The spherical harmonics analysis model of microstrain indicates the presence of strain anisotropy. The change in crystal structure lattice parameter, atomic coordinates of Y, O in yttria and the bond length analysis of the calcined powder reveals the presence of oxygen vacancies in the system.

Non-Newtonian gravity or gravity anomalies?

NASA Technical Reports Server (NTRS)

Rubincam, David P.; Chao, B. Fong; Schatten, Kenneth H.; Sager, William W.

1988-01-01

Geophysical measurements of G differ from laboratory values, indicating that gravity may be non-Newtonian. A spherical harmonic formulation is presented for the variation of (Newtonian) gravity inside the Earth. Using the GEM-10B Earth Gravitational Field Model, it is shown that long-wavelength gravity anomalies, if not corrected, may masquerade as non-Newtonian gravity by providing significant influences on experimental observation of delta g/delta r and G. An apparent contradiction in other studies is also resolved: i.e., local densities appear in equations when average densities of layers seem to be called for.

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

PubMed

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.

An ``Openable,'' High-Strength Gradient Set for Orthopedic MRI

NASA Astrophysics Data System (ADS)

Crozier, Stuart; Roffmann, Wolfgang U.; Luescher, Kurt; Snape-Jenkinson, Christopher; Forbes, Lawrence K.; Doddrell, David M.

1999-07-01

A novel three-axis gradient set and RF resonator for orthopedic MRI has been designed and constructed. The set is openable and may be wrapped around injured joints. The design methodology used was the minimization of magnetic field spherical harmonics by simulated annealing. Splitting of the longitudinal coil presents the major design challenge to a fully openable gradient set and in order to efficiently design such coils, we have developed a new fast algorithm for determining the magnetic field spherical harmonics generated by an arc of multiturn wire. The algorithm allows a realistic impression of the effect of split longitudinal designs. A prototype set was constructed based on the new designs and tested in a 2-T clinical research system. The set generated 12 mT/m/A with a linear region of 12 cm and a switching time of 100 μs, conforming closely with theoretical predictions. Preliminary images from the set are presented.

Testing Limits on Matte Surface Color Perception in Three-Dimensional Scenes with Complex Light Fields

PubMed Central

Doerschner, K.; Boyaci, H.; Maloney, L. T.

2007-01-01

We investigated limits on the human visual system’s ability to discount directional variation in complex lights field when estimating Lambertian surface color. Directional variation in the light field was represented in the frequency domain using spherical harmonics. The bidirectional reflectance distribution function of a Lambertian surface acts as a low-pass filter on directional variation in the light field. Consequently, the visual system needs to discount only the low-pass component of the incident light corresponding to the first nine terms of a spherical harmonics expansion (Basri & Jacobs, 2001; Ramamoorthi & Hanrahan, 2001) to accurately estimate surface color. We test experimentally whether the visual system discounts directional variation in the light field up to this physical limit. Our results are consistent with the claim that the visual system can compensate for all of the complexity in the light field that affects the appearance of Lambertian surfaces. PMID:18053846

Libsharp - spherical harmonic transforms revisited

NASA Astrophysics Data System (ADS)

Reinecke, M.; Seljebotn, D. S.

2013-06-01

We present libsharp, a code library for spherical harmonic transforms (SHTs), which evolved from the libpsht library and addresses several of its shortcomings, such as adding MPI support for distributed memory systems and SHTs of fields with arbitrary spin, but also supporting new developments in CPU instruction sets like the Advanced Vector Extensions (AVX) or fused multiply-accumulate (FMA) instructions. The library is implemented in portable C99 and provides an interface that can be easily accessed from other programming languages such as C++, Fortran, Python, etc. Generally, libsharp's performance is at least on par with that of its predecessor; however, significant improvements were made to the algorithms for scalar SHTs, which are roughly twice as fast when using the same CPU capabilities. The library is available at http://sourceforge.net/projects/libsharp/ under the terms of the GNU General Public License.

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

NASA Astrophysics Data System (ADS)

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.

Earth System Data Records of Mass Transport from Time-Variable Gravity Data

NASA Astrophysics Data System (ADS)

Zlotnicki, V.; Talpe, M.; Nerem, R. S.; Landerer, F. W.; Watkins, M. M.

2014-12-01

Satellite measurements of time variable gravity have revolutionized the study of Earth, by measuring the ice losses of Greenland, Antarctica and land glaciers, changes in groundwater including unsustainable losses due to extraction of groundwater, the mass and currents of the oceans and their redistribution during El Niño events, among other findings. Satellite measurements of gravity have been made primarily by four techniques: satellite tracking from land stations using either lasers or Doppler radio systems, satellite positioning by GNSS/GPS, satellite to satellite tracking over distances of a few hundred km using microwaves, and through a gravity gradiometer (radar altimeters also measure the gravity field, but over the oceans only). We discuss the challenges in the measurement of gravity by different instruments, especially time-variable gravity. A special concern is how to bridge a possible gap in time between the end of life of the current GRACE satellite pair, launched in 2002, and a future GRACE Follow-On pair to be launched in 2017. One challenge in combining data from different measurement systems consists of their different spatial and temporal resolutions and the different ways in which they alias short time scale signals. Typically satellite measurements of gravity are expressed in spherical harmonic coefficients (although expansions in terms of 'mascons', the masses of small spherical caps, has certain advantages). Taking advantage of correlations among spherical harmonic coefficients described by empirical orthogonal functions and derived from GRACE data it is possible to localize the otherwise coarse spatial resolution of the laser and Doppler derived gravity models. This presentation discusses the issues facing a climate data record of time variable mass flux using these different data sources, including its validation.

An inverse hyper-spherical harmonics-based formulation for reconstructing 3D volumetric lung deformations

NASA Astrophysics Data System (ADS)

Santhanam, Anand P.; Min, Yugang; Mudur, Sudhir P.; Rastogi, Abhinav; Ruddy, Bari H.; Shah, Amish; Divo, Eduardo; Kassab, Alain; Rolland, Jannick P.; Kupelian, Patrick

2010-07-01

A method to estimate the deformation operator for the 3D volumetric lung dynamics of human subjects is described in this paper. For known values of air flow and volumetric displacement, the deformation operator and subsequently the elastic properties of the lung are estimated in terms of a Green's function. A Hyper-Spherical Harmonic (HSH) transformation is employed to compute the deformation operator. The hyper-spherical coordinate transformation method discussed in this paper facilitates accounting for the heterogeneity of the deformation operator using a finite number of frequency coefficients. Spirometry measurements are used to provide values for the airflow inside the lung. Using a 3D optical flow-based method, the 3D volumetric displacement of the left and right lungs, which represents the local anatomy and deformation of a human subject, was estimated from 4D-CT dataset. Results from an implementation of the method show the estimation of the deformation operator for the left and right lungs of a human subject with non-small cell lung cancer. Validation of the proposed method shows that we can estimate the Young's modulus of each voxel within a 2% error level.

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

NASA Astrophysics Data System (ADS)

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.

2003-05-01

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.

Fast and accurate computation of projected two-point functions

NASA Astrophysics Data System (ADS)

Grasshorn Gebhardt, Henry S.; Jeong, Donghui

2018-01-01

We present the two-point function from the fast and accurate spherical Bessel transformation (2-FAST) algorithm1Our code is available at https://github.com/hsgg/twoFAST. for a fast and accurate computation of integrals involving one or two spherical Bessel functions. These types of integrals occur when projecting the galaxy power spectrum P (k ) onto the configuration space, ξℓν(r ), or spherical harmonic space, Cℓ(χ ,χ'). First, we employ the FFTLog transformation of the power spectrum to divide the calculation into P (k )-dependent coefficients and P (k )-independent integrations of basis functions multiplied by spherical Bessel functions. We find analytical expressions for the latter integrals in terms of special functions, for which recursion provides a fast and accurate evaluation. The algorithm, therefore, circumvents direct integration of highly oscillating spherical Bessel functions.

Spheroidal and Toroidal Modes for Tidal Kinetic Energy in Spherical Elastic Bodies

NASA Astrophysics Data System (ADS)

Getino, Juan; Escapa, Alberto; Garcia, Amelia

In this work, the total expression of the perturbation of the kinetic energy of rotation, when an elastic spherical solid is deformed due to the gravitational attraction of external bodies, is studied. We do not limit this study to any order in the expansion of the perturbing potential in spherical harmonics, and we consider in the expression of the displacement vector the complete solution, composed by spheroidal and toroidal modes. We show in a very simple way, by using the properties of the Legendre polynomials, that the toroidal modes have no contribution at all under the hypothesis of spherical body, and, among the spheroidal modes, only the term n=2 acts, therefore the perturbation produced by the spheroidal component for n=2 gathers the total perturbation.

A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders

NASA Astrophysics Data System (ADS)

Bucha, Blažej; Janák, Juraj

2013-07-01

We present a novel graphical user interface program GrafLab (GRAvity Field LABoratory) for spherical harmonic synthesis (SHS) created in MATLAB®. This program allows to comfortably compute 38 various functionals of the geopotential up to ultra-high degrees and orders of spherical harmonic expansion. For the most difficult part of the SHS, namely the evaluation of the fully normalized associated Legendre functions (fnALFs), we used three different approaches according to required maximum degree: (i) the standard forward column method (up to maximum degree 1800, in some cases up to degree 2190); (ii) the modified forward column method combined with Horner's scheme (up to maximum degree 2700); (iii) the extended-range arithmetic (up to an arbitrary maximum degree). For the maximum degree 2190, the SHS with fnALFs evaluated using the extended-range arithmetic approach takes only approximately 2-3 times longer than its standard arithmetic counterpart, i.e. the standard forward column method. In the GrafLab, the functionals of the geopotential can be evaluated on a regular grid or point-wise, while the input coordinates can either be read from a data file or entered manually. For the computation on a regular grid we decided to apply the lumped coefficients approach due to significant time-efficiency of this method. Furthermore, if a full variance-covariances matrix of spherical harmonic coefficients is available, it is possible to compute the commission errors of the functionals. When computing on a regular grid, the output functionals or their commission errors may be depicted on a map using automatically selected cartographic projection.

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

PubMed

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.

Medial Demons Registration Localizes The Degree of Genetic Influence Over Subcortical Shape Variability: An N= 1480 Meta-Analysis

PubMed Central

Gutman, Boris A.; Jahanshad, Neda; Ching, Christopher R.K.; Wang, Yalin; Kochunov, Peter V.; Nichols, Thomas E.; Thompson, Paul M.

2015-01-01

We present a multi-cohort shape heritability study, extending the fast spherical demons registration to subcortical shapes via medial modeling. A multi-channel demons registration based on vector spherical harmonics is applied to medial and curvature features, while controlling for metric distortion. We registered and compared seven subcortical structures of 1480 twins and siblings from the Queensland Twin Imaging Study and Human Connectome Project: Thalamus, Caudate, Putamen, Pallidum, Hippocampus, Amygdala, and Nucleus Accumbens. Radial distance and tensor-based morphometry (TBM) features were found to be highly heritable throughout the entire basal ganglia and limbic system. Surface maps reveal subtle variation in heritability across functionally distinct parts of each structure. Medial Demons reveals more significantly heritable regions than two previously described surface registration methods. This approach may help to prioritize features and measures for genome-wide association studies. PMID:26413211

Medial Demons Registration Localizes The Degree of Genetic Influence Over Subcortical Shape Variability: An N= 1480 Meta-Analysis.

PubMed

Gutman, Boris A; Jahanshad, Neda; Ching, Christopher R K; Wang, Yalin; Kochunov, Peter V; Nichols, Thomas E; Thompson, Paul M

2015-04-01

We present a multi-cohort shape heritability study, extending the fast spherical demons registration to subcortical shapes via medial modeling. A multi-channel demons registration based on vector spherical harmonics is applied to medial and curvature features, while controlling for metric distortion. We registered and compared seven subcortical structures of 1480 twins and siblings from the Queensland Twin Imaging Study and Human Connectome Project: Thalamus, Caudate, Putamen, Pallidum, Hippocampus, Amygdala, and Nucleus Accumbens . Radial distance and tensor-based morphometry (TBM) features were found to be highly heritable throughout the entire basal ganglia and limbic system. Surface maps reveal subtle variation in heritability across functionally distinct parts of each structure. Medial Demons reveals more significantly heritable regions than two previously described surface registration methods. This approach may help to prioritize features and measures for genome-wide association studies.

Research in Celestial Mechanics and Differential Equations.

DTIC Science & Technology

Contents: A geopotential representation with sampling functions; Sampling functions as an alternative to spherical harmonics; The Levi - Civita ...restricted problem of three bodies ; Secular perturbations of periodic comets; Resonance in the restricted problem of three bodies ; Two centers of

Electromagnetic Fields of a Uniform Sphere in a Uniform Conducting Medium with Application to Dipole Sources

DTIC Science & Technology

1991-09-01

12b. DISTRIBUTION CODE Approved for public release; distribution is unlimited. 13. ABSTRACT (Maximum 200 words) Vector spherical harmonic expansions are...electric and magnetic field vectors from E rand B - r alone. Genural expressions are given relating the scattered field expansion coefficients to the source...Prescnbed by ANSI Std. Z39-18 29W-102 NCSC TR 426-90 CONTENTS Pag o INTRODUCTION 1 BACKGROUND 1 ANGULAR MOMENTUM OPERATOR AND VECTOR SPHERICAL

GLGM-3: A Degree-ISO Lunar Gravity Model from the Historical Tracking Data of NASA Moon Orbiters

NASA Technical Reports Server (NTRS)

Mazarico, E.; Lemoine, F. G.; Han, Shin-Chan; Smith, D. E.

2010-01-01

In preparation for the radio science experiment of the Lunar Reconnaissance Orbiter (LRO) mission, we analyzed the available radio tracking data of previous NASA lunar orbiters. Our goal was to use these historical observations in combination with the new low-altitude data to be obtained by LRO. We performed Precision Orbit Determination on trajectory arcs from Lunar Orbiter 1 in 1966 to Lunar Prospector in 1998, using the GEODYN II program developed at NASA Goddard Space Flight Center. We then created a set of normal equations and solved for the coefficients of a spherical harmonics expansion of the lunar gravity potential up to degree and order 150. The GLGM-3 solution obtained with a global Kaula constraint (2.5 x 10(exp -4)/sq l) shows good agreement with model LP150Q from the Jet Propulsion Laboratory, especially over the nearside. The levels of data fit with both gravity models are very similar (Doppler RMS of approx.0.2 and approx. 1-2 mm/s in the nominal and extended phases, respectiVely). Orbit overlaps and uncertainties estimated from the covariance matrix also agree well. GLGM-3 shows better correlation with lunar topography and admittance over the nearside at high degrees of expansion (l > 100), particularly near the poles. We also present three companion solutions, obtained with the same data set but using alternate inversion strategies that modify the power law constraint and expectation of the individual spherical harmonics coefficients. We give a detailed discussion of the performance of this family of gravity field solutions in terms of observation fit, orbit quality, and geophysical consistency.

A quasi-hemispheric model of the Hermean's magnetic field

NASA Astrophysics Data System (ADS)

Thebault, E.; Oliveira, J.; Langlais, B.; Amit, H.

2015-10-01

We analyse and process magnetic field measurements provided by the MErcury Surface, Space ENvironment, Geochemistry, and Ranging (MESSENGER) mission. The vect or magnetic field measurements are modelled with a dedicated regional scheme expanded in space and in time. Compared to the widely used global Spherical Harmonics (SH), the regional approach is particularly well suited because the partial and quasi hemispheric distribution of the MESSENGER data represents no major numerical difficulty. We confirm that the internal magnetic field of Mercury is mostly axisymmetric with a magnetic equator shifted northward. However, we also observe a time dependency in the model that is at present hardly explained only by time variations of the external magnetic fields. We present the major spatial and temporal structures shown by the regional model.

Hyperspherical von Mises-Fisher mixture (HvMF) modelling of high angular resolution diffusion MRI.

PubMed

Bhalerao, Abhir; Westin, Carl-Fredrik

2007-01-01

A mapping of unit vectors onto a 5D hypersphere is used to model and partition ODFs from HARDI data. This mapping has a number of useful and interesting properties and we make a link to interpretation of the second order spherical harmonic decompositions of HARDI data. The paper presents the working theory and experiments of using a von Mises-Fisher mixture model for directional samples. The MLE of the second moment of the HvMF pdf can also be related to fractional anisotropy. We perform error analysis of the estimation scheme in single and multi-fibre regions and then show how a penalised-likelihood model selection method can be employed to differentiate single and multiple fibre regions.

The quadrupole model for rigid-body gravity simulations

NASA Astrophysics Data System (ADS)

Dobrovolskis, Anthony R.; Korycansky, D. G.

2013-07-01

We introduce two new models for gravitational simulations of systems of non-spherical bodies, such as comets and asteroids. In both models, one body (the "primary") may be represented by any convenient means, to arbitrary accuracy. In our first model, all of the other bodies are represented by small gravitational "molecules" consisting of a few point masses, rigidly linked together. In our second model, all of the other bodies are treated as point quadrupoles, with gravitational potentials including spherical harmonic terms up to the third degree (rather than only the first degree, as for ideal spheres or point masses). This quadrupole formulation may be regarded as a generalization of MacCullagh's approximation. Both models permit the efficient calculation of the interaction energy, the force, and the torque acting on a small body in an arbitrary external gravitational potential. We test both models for the cases of a triaxial ellipsoid, a rectangular parallelepiped, and "duplex" combinations of two spheres, all in a point-mass potential. These examples were chosen in order to compare the accuracy of our technique with known analytical results, but the ellipsoid and duplex are also useful models for comets and asteroids. We find that both approaches show significant promise for more efficient gravitational simulations of binary asteroids, for example. An appendix also describes the duplex model in detail.

Ion absorption of the high harmonic fast wave in the National Spherical Torus Experiment

NASA Astrophysics Data System (ADS)

Rosenberg, Adam Lewis

Ion absorption of the high harmonic fast wave in a spherical torus is of critical importance to assessing the viability of the wave as a means of heating and driving current. Analysis of recent NSTX shots has revealed that under some conditions when neutral beam and RF power are injected into the plasma simultaneously, a fast ion population with energy above the beam injection energy is sustained by the wave. In agreement with modeling, these experiments find the RF-induced fast ion tail strength and neutron rate at lower B-fields to be less enhanced, likely due to a larger β profile, which promotes greater off-axis absorption where the fast ion population is small. Ion loss codes find the increased loss fraction with decreased B insufficient to account for the changes in tail strength, providing further evidence that this is an RF interaction effect. Though greater ion absorption is predicted with lower k∥, surprisingly little variation in the tail was observed, along with a neutron rate enhancement with higher k∥. Data from the neutral particle analyzer, neutron detectors, x-ray crystal spectrometer, and Thomson scattering is presented, along with results from the TRANSP transport analysis code, ray-tracing codes HPRT and CURRAY, full-wave code and AORSA, quasilinear code CQL3D, and ion loss codes EIGOL and CONBEAM.

Direct measurement of density oscillation induced by a radio-frequency wave.

PubMed

Yamada, T; Ejiri, A; Shimada, Y; Oosako, T; Tsujimura, J; Takase, Y; Kasahara, H

2007-08-01

An O-mode reflectometer at a frequency of 25.85 GHz was applied to plasmas heated by the high harmonic fast wave (21 MHz) in the TST-2 spherical tokamak. An oscillation in the phase of the reflected microwave in the rf range was observed directly for the first time. In TST-2, the rf (250 kW) induced density oscillation depends mainly on the poloidal rf electric field, which is estimated to be about 0.2 kV/m rms by the reflectometer measurement. Sideband peaks separated in frequency by ion cyclotron harmonics from 21 MHz, and peaks at ion cyclotron harmonics which are suggested to be quasimodes generated by parametric decay, were detected.

Observed tidal braking in the earth/moon/sun system

NASA Technical Reports Server (NTRS)

Christodoulidis, D. C.; Smith, D. E.; Williamson, R. G.; Klosko, S. M.

1988-01-01

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century-squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century-squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 X 10 to the -22 rad/second-squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change in the earth's rotation rate of -4.69 + or - 0.36 X 10 to the -22 rad/second-squared.

The GRACE Mission: Meeting the Technical Challenges

NASA Technical Reports Server (NTRS)

Davis, E. S.; Dunn, C. E.; Stanton, R. H.; Thomas, J. B.

2000-01-01

The Gravity Recovery and Climate Experiment (GRACE) Mission is scheduled for launch in June 2001. Within the first year of the GRACE Mission, the project has a minimum science requirement to deliver a new model of the Earth's static geoid with an error of less than 1 cm to spherical harmonic degree seventy (70). However, the performance of the GRACE Mission is designed to exceed this minimum requirement by a factor of 25 or more. For spherical harmonic degrees of up to 40, we expect to improve the current knowledge of the gravity field by one thousand (1000x). The GRACE Mission uses the satellite-to-satellite tracking (SST) technique. The twin GRACE satellites are the instruments that measure the nonuniformities in the Earth's gravity field. Nonuniformities in the gravity field cause the relative distance between the centers-of-mass of the two satellites to vary as they fly over the Earth. Atmospheric drag is the largest non-gravitational disturbing force. Drag is measured and will be used to correct changes in the satellite-to-satellite range measured by an SST microwave link. The microwave link will measure changes in the range between the two GRACE satellites with an error approaching 1 micron. We will discuss how these instrumentation requirements affect the configuration, the mass balance, the thermal control and the aerodynamic design of the satellites, and the design of the microwave SST link and the accelerometer. Finally, the question of how noise in these components limits the overall accuracy of the gravity models will be addressed.

GRACE Mass Flux Measurements of Inland and Marginal Seas from Mascons: Analysis and Validation

NASA Astrophysics Data System (ADS)

Loomis, B.; Luthcke, S. B.; Sabaka, T. J.

2015-12-01

The latest GRACE time-variable gravity mascon solution from the NASA Goddard Space Flight Center (GSFC) applies an optimized set of models and constraints towards the direct measurement of 1-arc-degree global mass flux parameters each month. Separate mascon spatial constraint regions have been defined for the largest inland and marginal seas: Mediterranean Sea, Black Sea, Caspian Sea, Red Sea, and Hudson Bay. The mascon estimation approach, when applied with well-designed constraints, minimizes signal leakage across regional boundaries and eliminates the need for post-processing strategies. These post-processing techniques (e.g. smoothed averaging kernels) are necessary for computing regional mass change from the unconstrained spherical harmonics provided by the GRACE project to reduce the effect of noisy high degree and order terms, but introduce signal leakage into and out of the considered region. These mass signals are also difficult to obtain from altimetry measurements due to the comparatively sparse temperature and salinity data in these regions, which is needed to compute and remove the steric component of sea level variations. We provide new GSFC mascon measurements of these inland and marginal seas and compare to results obtained from kernel-averaged spherical harmonic solutions and steric-corrected altimetry measurements. The relative accuracy of the various solutions is determined by incorporating their output into the set of forward models applied in our processing of the GRACE Level-1B data and analyzing the effect on the inter-satellite range-rate residuals, where a reduction in residuals is a direct validation of improved solution quality.

New Crustal Field Models of Mars

NASA Astrophysics Data System (ADS)

Mittelholz, A.; Morschhauser, A.; Johnson, C.

2017-12-01

The crustal magnetic field on Mars has been subject of extensive analysis, as it provides us with information about the history of the dynamo, the iron mineralogy of the crust, and the processes that have affected the acquisition and any subsequent modification of crustal magnetization. Mars Global Surveyor (MGS) measured strong, localized crustal magnetic fields, mostly occurring in the southern hemisphere. MGS data were taken mostly at altitudes of 360 - 440 km, with limited (geographically and in local time) observations obtained at lower altitudes. The Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft has been in orbit since 2014. MAVEN magnetic field data complement those from MGS by globally expanding the spatial data distribution down to altitudes of 130 km, thus constraining shorter-wavelength structure in the field. Morschhauser et al. (2014) used the full MGS data set to build a spherical harmonic model for the crustal magnetic field up to spherical harmonic degree (l) and order (m) 110 ( λ≈195 km), while accounting for large-scale fields of non-crustal origin. We adopt a similar modeling approach, incorporating MAVEN data and inverting to higher l,m (e.g., λ≈130 km corresponds to l≈165). In order to avoid leakage of external field signals into the crustal field model, we select only nighttime data, use a modified Huber-Norm to treat data outliers and co-estimate a time-variable external field. We have also used another technique to model the field regionally. In this Equivalent Source Dipole (ESD) approach we solve for the magnetization of an assumed uniformly-magnetized layer, represented by equidistant dipoles placed at a single source depth. The ESD inversions indicate that shorter wavelength, weak signals are indeed resolvable in the MAVEN data. A comparison of the field models resulting from the two inversion techniques allows us to confidently identify new lithospheric field information available from the MAVEN observations.

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

NASA Astrophysics Data System (ADS)

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.

Equivalent source modeling of the main field using MAGSAT data

NASA Technical Reports Server (NTRS)

1980-01-01

The software was considerably enhanced to accommodate a more comprehensive examination of data available for field modeling using the equivalent sources method by (1) implementing a dynamic core allocation capability into the software system for the automatic dimensioning of the normal matrix; (2) implementing a time dependent model for the dipoles; (3) incorporating the capability to input specialized data formats in a fashion similar to models in spherical harmonics; and (4) implementing the optional ability to simultaneously estimate observatory anomaly biases where annual means data is utilized. The time dependence capability was demonstrated by estimating a component model of 21 deg resolution using the 14 day MAGSAT data set of Goddard's MGST (12/80). The equivalent source model reproduced both the constant and the secular variation found in MGST (12/80).

Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics

ERIC Educational Resources Information Center

Newmarch, J. D.; Golding, R. M.

1978-01-01

The energy levels of the free field, Coulomb potential, and the three-dimensional harmonic oscillator are found using the Dirac operator formalism by the construction of suitable ladder operators. The degeneracy of each level is also discussed. (Author/GA)

Spherical tensor analysis of polar liquid crystals with biaxial and chiral molecules

NASA Astrophysics Data System (ADS)

Iwamoto, Mitsumasa; Zhong-can, Ou-Yang

2012-11-01

With the help of spherical tensor expression, an irreducible calculus of a Lth-rank macroscopic susceptibility χ for a polar liquid crystal (PLC) of biaxial and chiral molecules written as the average of molecular hyperpolarizability tensor β associated with their spherical orientational order parameters (0⩽l⩽L) is presented. Comprehensive formulas of L=1,2 have been obtained and the latter explains the optical activity and spontaneous splay texture observed in bent-core PLC. The expression of L=3 specifies for the molecules with D2 symmetry which can be applied to analyze the nonlinear optical second harmonic generation (SHG) observed in proteins, peptides, and double-stranded DNA at interfaces.

New trend- trigonometric model for interpolation and prediction of the geomagnetic field utilizing the new DGRF models.

USGS Publications Warehouse

Alldredge, L.R.

1988-01-01

At the IUGG Assembly at Vancouver during August 1987 new definitive geomagnetic reference field (DGRF) models to degree 10 for 1945, 1950, 1955, and 1960 were adopted by IAGA. Before these new DGRF models were accepted, the author developed a trend and trigonometric model (old trig model) based on the models IGRF 1945, IGRF 1950, IGRF 1955, IGRF 1960, DGRF 1965, DGRF 1970, DGRF 1975, DGRF 1980, and IGRF 1985, which were all approved by IAGA in Prague in August 1985. The old trig model consists of 720 trend and trigonometric coefficients for the calculation of spherical harmonic coefficients (SHC) only to degree eight because the early IGRF models were truncated there. These trend and Fourier sine coefficients can replace the equal number of SHC contained in the 9 DGRF-IGRF models. -from Authors

Thermodynamic stability in elastic systems: Hard spheres embedded in a finite spherical elastic solid.

PubMed

Solano-Altamirano, J M; Goldman, Saul

2015-12-01

We determined the total system elastic Helmholtz free energy, under the constraints of constant temperature and volume, for systems comprised of one or more perfectly bonded hard spherical inclusions (i.e. "hard spheres") embedded in a finite spherical elastic solid. Dirichlet boundary conditions were applied both at the surface(s) of the hard spheres, and at the outer surface of the elastic solid. The boundary conditions at the surface of the spheres were used to describe the rigid displacements of the spheres, relative to their initial location(s) in the unstressed initial state. These displacements, together with the initial positions, provided the final shape of the strained elastic solid. The boundary conditions at the outer surface of the elastic medium were used to ensure constancy of the system volume. We determined the strain and stress tensors numerically, using a method that combines the Neuber-Papkovich spherical harmonic decomposition, the Schwartz alternating method, and Least-squares for determining the spherical harmonic expansion coefficients. The total system elastic Helmholtz free energy was determined by numerically integrating the elastic Helmholtz free energy density over the volume of the elastic solid, either by a quadrature, or a Monte Carlo method, or both. Depending on the initial position of the hard sphere(s) (or equivalently, the shape of the un-deformed stress-free elastic solid), and the displacements, either stationary or non-stationary Helmholtz free energy minima were found. The non-stationary minima, which involved the hard spheres nearly in contact with one another, corresponded to lower Helmholtz free energies, than did the stationary minima, for which the hard spheres were further away from one another.

RUSHMAPS: Real-Time Uploadable Spherical Harmonic Moment Analysis for Particle Spectrometers

NASA Technical Reports Server (NTRS)

Figueroa-Vinas, Adolfo

2013-01-01

RUSHMAPS is a new onboard data reduction scheme that gives real-time access to key science parameters (e.g. moments) of a class of heliophysics science and/or solar system exploration investigation that includes plasma particle spectrometers (PPS), but requires moments reporting (density, bulk-velocity, temperature, pressure, etc.) of higher-level quality, and tolerates a lowpass (variable quality) spectral representation of the corresponding particle velocity distributions, such that telemetry use is minimized. The proposed methodology trades access to the full-resolution velocity distribution data, saving on telemetry, for real-time access to both the moments and an adjustable-quality (increasing quality increases volume) spectral representation of distribution functions. Traditional onboard data storage and downlink bandwidth constraints severely limit PPS system functionality and drive cost, which, as a consequence, drives a limited data collection and lower angular energy and time resolution. This prototypical system exploit, using high-performance processing technology at GSFC (Goddard Space Flight Center), uses a SpaceCube and/or Maestro-type platform for processing. These processing platforms are currently being used on the International Space Station as a technology demonstration, and work is currently ongoing in a new onboard computation system for the Earth Science missions, but they have never been implemented in heliospheric science or solar system exploration missions. Preliminary analysis confirms that the targeted processor platforms possess the processing resources required for realtime application of these algorithms to the spectrometer data. SpaceCube platforms demonstrate that the target architecture possesses the sort of compact, low-mass/power, radiation-tolerant characteristics needed for flight. These high-performing hybrid systems embed unprecedented amounts of onboard processing power in the CPU (central processing unit), FPGAs (field programmable gate arrays), and DSP (digital signal processing) elements. The fundamental computational algorithm de constructs 3D velocity distributions in terms of spherical harmonic spectral coefficients (which are analogous to a Fourier sine-cosine decomposition), but uses instead spherical harmonics Legendre polynomial orthogonal functions as a basis for the expansion, portraying each 2D angular distribution at every energy or, geometrically, spherical speed-shell swept by the particle spectrometer. Optionally, these spherical harmonic spectral coefficients may be telemetered to the ground. These will provide a smoothed description of the velocity distribution function whose quality will depend on the number of coefficients determined. Successfully implemented on the GSFC-developed processor, the capability to integrate the proposed methodology with both heritage and anticipated future plasma particle spectrometer designs is demonstrated (with sufficiently detailed design analysis to advance TRL) to show specific science relevancy with future HSD (Heliophysics Science Division) solar-interplanetary, planetary missions, sounding rockets and/or CubeSat missions.

Constraints on geomagnetic secular variation modeling from electromagnetism and fluid dynamics of the Earth's core

NASA Technical Reports Server (NTRS)

Benton, E. R.

1986-01-01

A spherical harmonic representation of the geomagnetic field and its secular variation for epoch 1980, designated GSFC(9/84), is derived and evaluated. At three epochs (1977.5, 1980.0, 1982.5) this model incorporates conservation of magnetic flux through five selected patches of area on the core/mantle boundary bounded by the zero contours of vertical magnetic field. These fifteen nonlinear constraints are included like data in an iterative least squares parameter estimation procedure that starts with the recently derived unconstrained field model GSFC (12/83). Convergence is approached within three iterations. The constrained model is evaluated by comparing its predictive capability outside the time span of its data, in terms of residuals at magnetic observatories, with that for the unconstrained model.

Modelling the core magnetic field of the earth

NASA Technical Reports Server (NTRS)

Harrison, C. G. A.; Carle, H. M.

1982-01-01

It is suggested that radial off-center dipoles located within the core of the earth be used instead of spherical harmonics of the magnetic potential in modeling the core magnetic field. The off-center dipoles, in addition to more realistically modeling the physical current systems within the core, are if located deep within the core more effective at removing long wavelength signals of either potential or field. Their disadvantage is that their positions and strengths are more difficult to compute, and such effects as upward and downward continuation are more difficult to manipulate. It is nevertheless agreed with Cox (1975) and Alldredge and Hurwitz (1964) that physical realism in models is more important than mathematical convenience. A radial dipole model is presented which agrees with observations of secular variation and excursions.

EARL: Exoplanet Analytic Reflected Lightcurves package

NASA Astrophysics Data System (ADS)

Haggard, Hal M.; Cowan, Nicolas B.

2018-05-01

EARL (Exoplanet Analytic Reflected Lightcurves) computes the analytic form of a reflected lightcurve, given a spherical harmonic decomposition of the planet albedo map and the viewing and orbital geometries. The EARL Mathematica notebook allows rapid computation of reflected lightcurves, thus making lightcurve numerical experiments accessible.

The Development of a Degree 360 Expansion of the Dynamic Ocean Topography of the POCM_4B Global Circulation Model

NASA Technical Reports Server (NTRS)

Rapp, Richard H.

1998-01-01

This paper documents the development of a degree 360 expansion of the dynamic ocean topography (DOT) of the POCM_4B ocean circulation model. The principles and software used that led to the final model are described. A key principle was the development of interpolated DOT values into land areas to avoid discontinuities at or near the land/ocean interface. The power spectrum of the POCM_4B is also presented with comparisons made between orthonormal (ON) and spherical harmonic magnitudes to degree 24. A merged file of ON and SH computed degree variances is proposed for applications where the DOT power spectrum from low to high (360) degrees is needed.

Coupled BE/FE/BE approach for scattering from fluid-filled structures

NASA Technical Reports Server (NTRS)

Everstine, Gordon C.; Cheng, Raymond S.

1990-01-01

NASHUA is a coupled finite element/boundary element capability built around NASTRAN for calculating the low frequency far-field acoustic pressure field radiated or scattered by an arbitrary, submerged, three-dimensional, elastic structure subjected to either internal time-harmonic mechanical loads or external time-harmonic incident loadings. Described here are the formulation and use of NASHUA for solving such structural acoustics problems when the structure is fluid-filled. NASTRAN is used to generate the structural finite element model and to perform most of the required matrix operations. Both fluid domains are modeled using the boundary element capability in NASHUA, whose matrix formulation (and the associated NASTRAN DMAP) for evacuated structures can be used with suitable interpretation of the matrix definitions. After computing surface pressures and normal velocities, far-field pressures are evaluated using an asymptotic form of the Helmholtz exterior integral equation. The proposed numerical approach is validated by comparing the acoustic field scattered from a submerged fluid-filled spherical thin shell to that obtained with a series solution, which is also derived here.

A general model of the planetary radiation pressure on a satellite with a complex shape

NASA Technical Reports Server (NTRS)

Borderies, Nicole

1990-01-01

The purpose of this paper is to present a general model for the acceleration exerted on a spacecraft by the radiation coming from a planet. Both the solar radiation reflected by the planet and the thermal emission associated with its temperature are considered. The planet albedo and the planet emissive power are expanded in spherical harmonics with respect to an equatorial reference frame attached to the planet. The satellite external surface is assumed to consist of a juxtaposition of planar surfaces. A particular choice of variables allows to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimension integrals.

Fourier power spectra of the geomagnetic field for circular paths on the Earth's surface.

USGS Publications Warehouse

Alldredge, L.R.; Benton, E.R.

1986-01-01

The Fourier power spectra of geomagnetic component values, synthesized from spherical harmonic models, have been computed for circular paths on the Earth's surface. They are not found to be more useful than is the spectrum of magnetic energy outside the Earth for the purpose of separating core and crustal sources of the geomagnetic field. The Fourier power spectra of N and E geomagnetic components along nearly polar great circle paths exhibit some unusual characteristics that are explained by the geometric perspective of Fourier series on spheres developed by Yee. -Authors

2D and 3D Models of Convective Turbulence and Oscillations in Intermediate-Mass Main-Sequence Stars

NASA Astrophysics Data System (ADS)

Guzik, Joyce Ann; Morgan, Taylor H.; Nelson, Nicholas J.; Lovekin, Catherine; Kitiashvili, Irina N.; Mansour, Nagi N.; Kosovichev, Alexander

2015-08-01

We present multidimensional modeling of convection and oscillations in main-sequence stars somewhat more massive than the sun, using three separate approaches: 1) Applying the spherical 3D MHD ASH (Anelastic Spherical Harmonics) code to simulate the core convection and radiative zone. Our goal is to determine whether core convection can excite low-frequency gravity modes, and thereby explain the presence of low frequencies for some hybrid gamma Dor/delta Sct variables for which the envelope convection zone is too shallow for the convective blocking mechanism to drive g modes; 2) Using the 3D planar ‘StellarBox’ radiation hydrodynamics code to model the envelope convection zone and part of the radiative zone. Our goals are to examine the interaction of stellar pulsations with turbulent convection in the envelope, excitation of acoustic modes, and the role of convective overshooting; 3) Applying the ROTORC 2D stellar evolution and dynamics code to calculate evolution with a variety of initial rotation rates and extents of core convective overshooting. The nonradial adiabatic pulsation frequencies of these nonspherical models will be calculated using the 2D pulsation code NRO of Clement. We will present new insights into gamma Dor and delta Sct pulsations gained by multidimensional modeling compared to 1D model expectations.

High-harmonic fast magnetosonic wave coupling, propagation, and heating in a spherical torus plasma

NASA Astrophysics Data System (ADS)

Menard, J.; Majeski, R.; Kaita, R.; Ono, M.; Munsat, T.; Stutman, D.; Finkenthal, M.

1999-05-01

A novel rotatable two-strap antenna has been installed in the current drive experiment upgrade (CDX-U) [T. Jones, Ph.D. thesis, Princeton University (1995)] in order to investigate high-harmonic fast wave coupling, propagation, and electron heating as a function of strap angle and strap phasing in a spherical torus plasma. Radio-frequency-driven sheath effects are found to fit antenna loading trends at very low power and become negligible above a few kilowatts. At sufficiently high power, the measured coupling efficiency as a function of strap angle is found to agree favorably with cold plasma wave theory. Far-forward microwave scattering from wave-induced density fluctuations in the plasma core tracks the predicted fast wave loading as the antenna is rotated. Signs of electron heating during rf power injection have been observed in CDX-U with central Thomson scattering, impurity ion spectroscopy, and Langmuir probes. While these initial results appear promising, damping of the fast wave on thermal ions at high ion-cyclotron-harmonic number may compete with electron damping at sufficiently high ion β—possibly resulting in a significantly reduced current drive efficiency and production of a fast ion population. Preliminary results from ray-tracing calculations which include these ion damping effects are presented.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

J.R. Wilson; R.E. Bell; S. Bernabei

2003-02-11

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 STmore » 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.« less

A spherical harmonic approach for the determination of HCP texture from ultrasound: A solution to the inverse problem

NASA Astrophysics Data System (ADS)

Lan, Bo; Lowe, Michael J. S.; Dunne, Fionn P. E.

2015-10-01

A new spherical convolution approach has been presented which couples HCP single crystal wave speed (the kernel function) with polycrystal c-axis pole distribution function to give the resultant polycrystal wave speed response. The three functions have been expressed as spherical harmonic expansions thus enabling application of the de-convolution technique to enable any one of the three to be determined from knowledge of the other two. Hence, the forward problem of determination of polycrystal wave speed from knowledge of single crystal wave speed response and the polycrystal pole distribution has been solved for a broad range of experimentally representative HCP polycrystal textures. The technique provides near-perfect representation of the sensitivity of wave speed to polycrystal texture as well as quantitative prediction of polycrystal wave speed. More importantly, a solution to the inverse problem is presented in which texture, as a c-axis distribution function, is determined from knowledge of the kernel function and the polycrystal wave speed response. It has also been explained why it has been widely reported in the literature that only texture coefficients up to 4th degree may be obtained from ultrasonic measurements. Finally, the de-convolution approach presented provides the potential for the measurement of polycrystal texture from ultrasonic wave speed measurements.

Analytical study of the acoustic field in a spherical resonator for single bubble sonoluminescence.

PubMed

Dellavale, Damián; Urteaga, Raúl; Bonetto, Fabián J

2010-01-01

The acoustic field in the liquid within a spherical solid shell is calculated. The proposed model takes into account Stoke's wave equation in the viscous fluid, the membrane theory to describe the solid shell motion and the energy loss through the external couplings of the system. A point source at the resonator center is included to reproduce the acoustic emission of a sonoluminescence bubble. Particular calculations of the resulting acoustic field are performed for viscous liquids of interest in single bubble sonoluminescence. The model reveals that in case of radially symmetric modes of low frequency, the quality factor is mainly determined by the acoustic energy flowing through the mechanical coupling of the resonator. Alternatively, for high frequency modes the quality factor is mainly determined by the viscous dissipation in the liquid. Furthermore, the interaction between the bubble acoustic emission and the resonator modes is analyzed. It was found that the bubble acoustic emission produces local maxima in the resonator response. The calculated amplitudes and relative phases of the harmonics constituting the bubble acoustic environment can be used to improve multi-frequency driving in sonoluminescence.

Information theory lateral density distribution for Earth inferred from global gravity field

NASA Technical Reports Server (NTRS)

Rubincam, D. P.

1981-01-01

Information Theory Inference, better known as the Maximum Entropy Method, was used to infer the lateral density distribution inside the Earth. The approach assumed that the Earth consists of indistinguishable Maxwell-Boltzmann particles populating infinitesimal volume elements, and followed the standard methods of statistical mechanics (maximizing the entropy function). The GEM 10B spherical harmonic gravity field coefficients, complete to degree and order 36, were used as constraints on the lateral density distribution. The spherically symmetric part of the density distribution was assumed to be known. The lateral density variation was assumed to be small compared to the spherically symmetric part. The resulting information theory density distribution for the cases of no crust removed, 30 km of compensated crust removed, and 30 km of uncompensated crust removed all gave broad density anomalies extending deep into the mantle, but with the density contrasts being the greatest towards the surface (typically + or 0.004 g cm 3 in the first two cases and + or - 0.04 g cm 3 in the third). None of the density distributions resemble classical organized convection cells. The information theory approach may have use in choosing Standard Earth Models, but, the inclusion of seismic data into the approach appears difficult.

Geomagnetic polarity transitions

NASA Astrophysics Data System (ADS)

Merrill, Ronald T.; McFadden, Phillip L.

1999-05-01

The top of Earth's liquid outer core is nearly 2900 km beneath Earth's surface, so we will never be able to observe it directly. This hot, dense, molten iron-rich body is continuously in motion and is the source of Earth's magnetic field. One of the most dynamic manifestations at Earth's surface of this fluid body is, perhaps, a reversal of the geomagnetic field. Unfortunately, the most recent polarity transition occurred at about 780 ka, so we have never observed a transition directly. It seems that a polarity transition spans many human lifetimes, so no human will ever witness the phenomenon in its entirety. Thus we are left with the tantalizing prospect that paleomagnetic records of polarity transitions may betray some of the secrets of the deep Earth. Certainly, if there are systematics in the reversal process and they can be documented, then this will reveal substantial information about the nature of the lowermost mantle and of the outer core. Despite their slowness on a human timescale, polarity transitions occur almost instantaneously on a geological timescale. This rapidity, together with limitations in the paleomagnetic recording process, prohibits a comprehensive description of any reversal transition both now and into the foreseeable future, which limits the questions that may at this stage be sensibly asked. The natural model for the geomagnetic field is a set of spherical harmonic components, and we are not able to obtain a reliable model for even the first few harmonic terms during a transition. Nevertheless, it is possible, in principle, to make statements about the harmonic character of a geomagnetic polarity transition without having a rigorous spherical harmonic description of one. For example, harmonic descriptions of recent geomagnetic polarity transitions that are purely zonal can be ruled out (a zonal harmonic does not change along a line of latitude). Gleaning information about transitions has proven to be difficult, but it does seem reasonable to draw the following conclusions with varying degrees of confidence. There appears to be a substantial decrease in the mean intensity of the dipole field during a transition to ˜25% of its usual value. The duration of an average geomagnetic polarity transition is not well known but probably lies between 1000 and 8000 years. Values outside these bounds have been reported, but we give reasons as to why such outliers are likely to be artifacts. The reversal process is probably longer than the manifestation of the reversal at Earth's surface as recorded in paleomagnetic directional data. Convection hiatus during a geomagnetic polarity transition seems unlikely, and free-decay models for reversals appear to be generally incompatible with the data. This implies that certain theorems in dynamo theory, such as Cowling's theorem, should not be invoked to explain the origin of reversals. Unfortunately, the detailed description of directional changes during transitions remains controversial. Contrary to common belief, certain low-degree nondipole fields can produce significant longitudinal confinement of virtual geomagnetic poles (VGP) during a transition. The data are currently inadequate to refute or verify claims of longitudinal dipole confinement, VGP clustering, or other systematics during polarity transitions.

Geoid undulation accuracy

NASA Technical Reports Server (NTRS)

Rapp, Richard H.

1993-01-01

The determination of the geoid and equipotential surface of the Earth's gravity field, has long been of interest to geodesists and oceanographers. The geoid provides a surface to which the actual ocean surface can be compared with the differences implying information on the circulation patterns of the oceans. For use in oceanographic applications the geoid is ideally needed to a high accuracy and to a high resolution. There are applications that require geoid undulation information to an accuracy of +/- 10 cm with a resolution of 50 km. We are far from this goal today but substantial improvement in geoid determination has been made. In 1979 the cumulative geoid undulation error to spherical harmonic degree 20 was +/- 1.4 m for the GEM10 potential coefficient model. Today the corresponding value has been reduced to +/- 25 cm for GEM-T3 or +/- 11 cm for the OSU91A model. Similar improvements are noted by harmonic degree (wave-length) and in resolution. Potential coefficient models now exist to degree 360 based on a combination of data types. This paper discusses the accuracy changes that have taken place in the past 12 years in the determination of geoid undulations.

Preparation of spherical particles by vibrating orifice technique

NASA Astrophysics Data System (ADS)

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.

Numerical computation of spherical harmonics of arbitrary degree and order by extending exponent of floating point numbers

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2012-04-01

By extending the exponent of floating point numbers with an additional integer as the power index of a large radix, we compute fully normalized associated Legendre functions (ALF) by recursion without underflow problem. The new method enables us to evaluate ALFs of extremely high degree as 232 = 4,294,967,296, which corresponds to around 1 cm resolution on the Earth's surface. By limiting the application of exponent extension to a few working variables in the recursion, choosing a suitable large power of 2 as the radix, and embedding the contents of the basic arithmetic procedure of floating point numbers with the exponent extension directly in the program computing the recurrence formulas, we achieve the evaluation of ALFs in the double-precision environment at the cost of around 10% increase in computational time per single ALF. This formulation realizes meaningful execution of the spherical harmonic synthesis and/or analysis of arbitrary degree and order.

Libpsht - algorithms for efficient spherical harmonic transforms

NASA Astrophysics Data System (ADS)

Reinecke, M.

2011-02-01

Libpsht (or "library for performant spherical harmonic transforms") is a collection of algorithms for efficient conversion between spatial-domain and spectral-domain representations of data defined on the sphere. The package supports both transforms of scalars and spin-1 and spin-2 quantities, and can be used for a wide range of pixelisations (including HEALPix, GLESP, and ECP). It will take advantage of hardware features such as multiple processor cores and floating-point vector operations, if available. Even without this additional acceleration, the employed algorithms are among the most efficient (in terms of CPU time, as well as memory consumption) currently being used in the astronomical community. The library is written in strictly standard-conforming C90, ensuring portability to many different hard- and software platforms, and allowing straightforward integration with codes written in various programming languages like C, C++, Fortran, Python etc. Libpsht is distributed under the terms of the GNU General Public License (GPL) version 2 and can be downloaded from .

Libpsht: Algorithms for Efficient Spherical Harmonic Transforms

NASA Astrophysics Data System (ADS)

Reinecke, Martin

2010-10-01

Libpsht (or "library for Performing Spherical Harmonic Transforms") is a collection of algorithms for efficient conversion between spatial-domain and spectral-domain representations of data defined on the sphere. The package supports transforms of scalars as well as spin-1 and spin-2 quantities, and can be used for a wide range of pixelisations (including HEALPix, GLESP and ECP). It will take advantage of hardware features like multiple processor cores and floating-point vector operations, if available. Even without this additional acceleration, the employed algorithms are among the most efficient (in terms of CPU time as well as memory consumption) currently being used in the astronomical community. The library is written in strictly standard-conforming C90, ensuring portability to many different hard- and software platforms, and allowing straightforward integration with codes written in various programming languages like C, C++, Fortran, Python etc. Libpsht is distributed under the terms of the GNU General Public License (GPL) version 2. Development on this project has ended; its successor is libsharp (ascl:1402.033).

Use of Massive Parallel Computing Libraries in the Context of Global Gravity Field Determination from Satellite Data

NASA Astrophysics Data System (ADS)

Brockmann, J. M.; Schuh, W.-D.

2011-07-01

The estimation of the global Earth's gravity field parametrized as a finite spherical harmonic series is computationally demanding. The computational effort depends on the one hand on the maximal resolution of the spherical harmonic expansion (i.e. the number of parameters to be estimated) and on the other hand on the number of observations (which are several millions for e.g. observations from the GOCE satellite missions). To circumvent these restrictions, a massive parallel software based on high-performance computing (HPC) libraries as ScaLAPACK, PBLAS and BLACS was designed in the context of GOCE HPF WP6000 and the GOCO consortium. A prerequisite for the use of these libraries is that all matrices are block-cyclic distributed on a processor grid comprised by a large number of (distributed memory) computers. Using this set of standard HPC libraries has the benefit that once the matrices are distributed across the computer cluster, a huge set of efficient and highly scalable linear algebra operations can be used.

International Geomagnetic Reference Field: the 12th generation

NASA Astrophysics Data System (ADS)

Thébault, Erwan; Finlay, Christopher C.; Beggan, Ciarán D.; Alken, Patrick; Aubert, Julien; Barrois, Olivier; Bertrand, Francois; Bondar, Tatiana; Boness, Axel; Brocco, Laura; Canet, Elisabeth; Chambodut, Aude; Chulliat, Arnaud; Coïsson, Pierdavide; Civet, François; Du, Aimin; Fournier, Alexandre; Fratter, Isabelle; Gillet, Nicolas; Hamilton, Brian; Hamoudi, Mohamed; Hulot, Gauthier; Jager, Thomas; Korte, Monika; Kuang, Weijia; Lalanne, Xavier; Langlais, Benoit; Léger, Jean-Michel; Lesur, Vincent; Lowes, Frank J.; Macmillan, Susan; Mandea, Mioara; Manoj, Chandrasekharan; Maus, Stefan; Olsen, Nils; Petrov, Valeriy; Ridley, Victoria; Rother, Martin; Sabaka, Terence J.; Saturnino, Diana; Schachtschneider, Reyko; Sirol, Olivier; Tangborn, Andrew; Thomson, Alan; Tøffner-Clausen, Lars; Vigneron, Pierre; Wardinski, Ingo; Zvereva, Tatiana

2015-05-01

The 12th generation of the International Geomagnetic Reference Field (IGRF) was adopted in December 2014 by the Working Group V-MOD appointed by the International Association of Geomagnetism and Aeronomy (IAGA). It updates the previous IGRF generation with a definitive main field model for epoch 2010.0, a main field model for epoch 2015.0, and a linear annual predictive secular variation model for 2015.0-2020.0. Here, we present the equations defining the IGRF model, provide the spherical harmonic coefficients, and provide maps of the magnetic declination, inclination, and total intensity for epoch 2015.0 and their predicted rates of change for 2015.0-2020.0. We also update the magnetic pole positions and discuss briefly the latest changes and possible future trends of the Earth's magnetic field.

Local Lunar Gravity Field Analysis over the South Pole-aitken Basin from SELENE Farside Tracking Data

NASA Technical Reports Server (NTRS)

Goossens, Sander Johannes; Ishihara, Yoshiaki; Matsumoto, Koji; Sasaki, Sho

2012-01-01

We present a method with which we determined the local lunar gravity field model over the South Pole-Aitken (SPA) basin on the farside of the Moon by estimating adjustments to a global lunar gravity field model using SELENE tracking data. Our adjustments are expressed in localized functions concentrated over the SPA region in a spherical cap with a radius of 45deg centered at (191.1 deg E, 53.2 deg S), and the resolution is equivalent to a 150th degree and order spherical harmonics expansion. The new solution over SPA was used in several applications of geophysical analysis. It shows an increased correlation with high-resolution lunar topography in the frequency band l = 40-70, and admittance values are slightly different and more leveled when compared to other, global gravity field models using the same data. The adjustments expressed in free-air anomalies and differences in Bouguer anomalies between the local solution and the a priori global solution correlate with topographic surface features. The Moho structure beneath the SPA basin is slightly modified in our solution, most notably at the southern rim of the Apollo basin and around the Zeeman crater

Improvements in GRACE Gravity Field Determination through Stochastic Observation Modeling

NASA Astrophysics Data System (ADS)

McCullough, C.; Bettadpur, S. V.

2016-12-01

Current unconstrained Release 05 GRACE gravity field solutions from the Center for Space Research (CSR RL05) assume random observation errors following an independent multivariate Gaussian distribution. This modeling of observations, a simplifying assumption, fails to account for long period, correlated errors arising from inadequacies in the background force models. Fully modeling the errors inherent in the observation equations, through the use of a full observation covariance (modeling colored noise), enables optimal combination of GPS and inter-satellite range-rate data and obviates the need for estimating kinematic empirical parameters during the solution process. Most importantly, fully modeling the observation errors drastically improves formal error estimates of the spherical harmonic coefficients, potentially enabling improved uncertainty quantification of scientific results derived from GRACE and optimizing combinations of GRACE with independent data sets and a priori constraints.

Moho Modeling Using FFT Technique

NASA Astrophysics Data System (ADS)

Chen, Wenjin; Tenzer, Robert

2017-04-01

To improve the numerical efficiency, the Fast Fourier Transform (FFT) technique was facilitated in Parker-Oldenburg's method for a regional gravimetric Moho recovery, which assumes the Earth's planar approximation. In this study, we extend this definition for global applications while assuming a spherical approximation of the Earth. In particular, we utilize the FFT technique for a global Moho recovery, which is practically realized in two numerical steps. The gravimetric forward modeling is first applied, based on methods for a spherical harmonic analysis and synthesis of the global gravity and lithospheric structure models, to compute the refined gravity field, which comprises mainly the gravitational signature of the Moho geometry. The gravimetric inverse problem is then solved iteratively in order to determine the Moho depth. The application of FFT technique to both numerical steps reduces the computation time to a fraction of that required without applying this fast algorithm. The developed numerical producers are used to estimate the Moho depth globally, and the gravimetric result is validated using the global (CRUST1.0) and regional (ESC) seismic Moho models. The comparison reveals a relatively good agreement between the gravimetric and seismic models, with the RMS of differences (of 4-5 km) at the level of expected uncertainties of used input datasets, while without the presence of significant systematic bias.

Topology of the electron density of d0 transition metal compounds at subatomic resolution.

PubMed

Batke, Kilian; Eickerling, Georg

2013-11-14

Accurate X-ray diffraction experiments allow for a reconstruction of the electron density distribution of solids and molecules in a crystal. The basis for the reconstruction of the electron density is in many cases a multipolar expansion of the X-ray scattering factors in terms of spherical harmonics, a so-called multipolar model. This commonly used ansatz splits the total electron density of each pseudoatom in the crystal into (i) a spherical core, (ii) a spherical valence, and (iii) a nonspherical valence contribution. Previous studies, for example, on diamond and α-silicon have already shown that this approximation is no longer valid when ultrahigh-resolution diffraction data is taken into account. We report here the results of an analysis of the calculated electron density distribution in the d(0) transition metal compounds [TMCH3](2+) (TM = Sc, Y, and La) at subatomic resolution. By a detailed molecular orbital analysis, it is demonstrated that due to the radial nodal structure of the 3d, 4d, and 5d orbitals involved in the TM-C bond formation a significant polarization of the electron density in the inner electronic shells of the TM atoms is observed. We further show that these polarizations have to be taken into account by an extended multipolar model in order to recover accurate electron density distributions from high-resolution structure factors calculated for the title compounds.

The 2000 revision of the joint UK/US geomagnetic field models and an IGRF 2000 candidate model

USGS Publications Warehouse

Macmillan, S.; Quinn, J.M.

2000-01-01

The method of derivation of the joint UK/US spherical harmonic geomagnetic main-field and secular-variation models is presented. Early versions of these models, with the main field truncated at degree 10, are the UK/US candidates for the IGRF 2000 model. The main-field model describes the Earth's magnetic field at the 2000.0 epoch, while the secular-variation model predicts the evolution of this field between 2000.0 and 2005.0. A revised 1995.0 main-field model was also generated. Regional models for the continental US, Alaska and Hawaii were also produced as a by-product of the UK/US global modelling effort. Copy right?? The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences.

Dynamics of Compressible Convection and Thermochemical Mantle Convection

NASA Astrophysics Data System (ADS)

Liu, Xi

The Earth's long-wavelength geoid anomalies have long been used to constrain the dynamics and viscosity structure of the mantle in an isochemical, whole-mantle convection model. However, there is strong evidence that the seismically observed large low shear velocity provinces (LLSVPs) in the lowermost mantle are chemically distinct and denser than the ambient mantle. In this thesis, I investigated how chemically distinct and dense piles influence the geoid. I formulated dynamically self-consistent 3D spherical convection models with realistic mantle viscosity structure which reproduce Earth's dominantly spherical harmonic degree-2 convection. The models revealed a compensation effect of the chemically dense LLSVPs. Next, I formulated instantaneous flow models based on seismic tomography to compute the geoid and constrain mantle viscosity assuming thermochemical convection with the compensation effect. Thermochemical models reconcile the geoid observations. The viscosity structure inverted for thermochemical models is nearly identical to that of whole-mantle models, and both prefer weak transition zone. Our results have implications for mineral physics, seismic tomographic studies, and mantle convection modelling. Another part of this thesis describes analyses of the influence of mantle compressibility on thermal convection in an isoviscous and compressible fluid with infinite Prandtl number. A new formulation of the propagator matrix method is implemented to compute the critical Rayleigh number and the corresponding eigenfunctions for compressible convection. Heat flux and thermal boundary layer properties are quantified in numerical models and scaling laws are developed.

Comparison of approximate solutions to the phonon Boltzmann transport equation with the relaxation time approximation: Spherical harmonics expansions and the discrete ordinates method

NASA Astrophysics Data System (ADS)

Christenson, J. G.; Austin, R. A.; Phillips, R. J.

2018-05-01

The phonon Boltzmann transport equation is used to analyze model problems in one and two spatial dimensions, under transient and steady-state conditions. New, explicit solutions are obtained by using the P1 and P3 approximations, based on expansions in spherical harmonics, and are compared with solutions from the discrete ordinates method. For steady-state energy transfer, it is shown that analytic expressions derived using the P1 and P3 approximations agree quantitatively with the discrete ordinates method, in some cases for large Knudsen numbers, and always for Knudsen numbers less than unity. However, for time-dependent energy transfer, the PN solutions differ qualitatively from converged solutions obtained by the discrete ordinates method. Although they correctly capture the wave-like behavior of energy transfer at short times, the P1 and P3 approximations rely on one or two wave velocities, respectively, yielding abrupt, step-changes in temperature profiles that are absent when the angular dependence of the phonon velocities is captured more completely. It is shown that, with the gray approximation, the P1 approximation is formally equivalent to the so-called "hyperbolic heat equation." Overall, these results support the use of the PN approximation to find solutions to the phonon Boltzmann transport equation for steady-state conditions. Such solutions can be useful in the design and analysis of devices that involve heat transfer at nanometer length scales, where continuum-scale approaches become inaccurate.

Transfer function analysis of thermospheric perturbations

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Varosi, F.; Herrero, F. A.; Spencer, N. W.

1986-01-01

Applying perturbation theory, a spectral model in terms of vectors spherical harmonics (Legendre polynomials) is used to describe the short term thermospheric perturbations originating in the auroral regions. The source may be Joule heating, particle precipitation or ExB ion drift-momentum coupling. A multiconstituent atmosphere is considered, allowing for the collisional momentum exchange between species including Ar, O2, N2, O, He and H. The coupled equations of energy, mass and momentum conservation are solved simultaneously for the major species N2 and O. Applying homogeneous boundary conditions, the integration is carred out from the Earth's surface up to 700 km. In the analysis, the spherical harmonics are treated as eigenfunctions, assuming that the Earth's rotation (and prevailing circulation) do not significantly affect perturbations with periods which are typically much less than one day. Under these simplifying assumptions, and given a particular source distribution in the vertical, a two dimensional transfer function is constructed to describe the three dimensional response of the atmosphere. In the order of increasing horizontal wave numbers (order of polynomials), this transfer function reveals five components. To compile the transfer function, the numerical computations are very time consuming (about 100 hours on a VAX for one particular vertical source distribution). However, given the transfer function, the atmospheric response in space and time (using Fourier integral representation) can be constructed with a few seconds of a central processing unit. This model is applied in a case study of wind and temperature measurements on the Dynamics Explorer B, which show features characteristic of a ringlike excitation source in the auroral oval. The data can be interpreted as gravity waves which are focused (and amplified) in the polar region and then are reflected to propagate toward lower latitudes.

Transfer function analysis of thermospheric perturbations

NASA Astrophysics Data System (ADS)

Mayr, H. G.; Harris, I.; Varosi, F.; Herrero, F. A.; Spencer, N. W.

1986-06-01

Applying perturbation theory, a spectral model in terms of vectors spherical harmonics (Legendre polynomials) is used to describe the short term thermospheric perturbations originating in the auroral regions. The source may be Joule heating, particle precipitation or ExB ion drift-momentum coupling. A multiconstituent atmosphere is considered, allowing for the collisional momentum exchange between species including Ar, O2, N2, O, He and H. The coupled equations of energy, mass and momentum conservation are solved simultaneously for the major species N2 and O. Applying homogeneous boundary conditions, the integration is carred out from the Earth's surface up to 700 km. In the analysis, the spherical harmonics are treated as eigenfunctions, assuming that the Earth's rotation (and prevailing circulation) do not significantly affect perturbations with periods which are typically much less than one day. Under these simplifying assumptions, and given a particular source distribution in the vertical, a two dimensional transfer function is constructed to describe the three dimensional response of the atmosphere. In the order of increasing horizontal wave numbers (order of polynomials), this transfer function reveals five components. To compile the transfer function, the numerical computations are very time consuming (about 100 hours on a VAX for one particular vertical source distribution). However, given the transfer function, the atmospheric response in space and time (using Fourier integral representation) can be constructed with a few seconds of a central processing unit. This model is applied in a case study of wind and temperature measurements on the Dynamics Explorer B, which show features characteristic of a ringlike excitation source in the auroral oval. The data can be interpreted as gravity waves which are focused (and amplified) in the polar region and then are reflected to propagate toward lower latitudes.

A theoretical formulation of the electrophysiological inverse problem on the sphere

NASA Astrophysics Data System (ADS)

Riera, Jorge J.; Valdés, Pedro A.; Tanabe, Kunio; Kawashima, Ryuta

2006-04-01

The construction of three-dimensional images of the primary current density (PCD) produced by neuronal activity is a problem of great current interest in the neuroimaging community, though being initially formulated in the 1970s. There exist even now enthusiastic debates about the authenticity of most of the inverse solutions proposed in the literature, in which low resolution electrical tomography (LORETA) is a focus of attention. However, in our opinion, the capabilities and limitations of the electro and magneto encephalographic techniques to determine PCD configurations have not been extensively explored from a theoretical framework, even for simple volume conductor models of the head. In this paper, the electrophysiological inverse problem for the spherical head model is cast in terms of reproducing kernel Hilbert spaces (RKHS) formalism, which allows us to identify the null spaces of the implicated linear integral operators and also to define their representers. The PCD are described in terms of a continuous basis for the RKHS, which explicitly separates the harmonic and non-harmonic components. The RKHS concept permits us to bring LORETA into the scope of the general smoothing splines theory. A particular way of calculating the general smoothing splines is illustrated, avoiding a brute force discretization prematurely. The Bayes information criterion is used to handle dissimilarities in the signal/noise ratios and physical dimensions of the measurement modalities, which could affect the estimation of the amount of smoothness required for that class of inverse solution to be well specified. In order to validate the proposed method, we have estimated the 3D spherical smoothing splines from two data sets: electric potentials obtained from a skull phantom and magnetic fields recorded from subjects performing an experiment of human faces recognition.

Lq -Lp optimization for multigrid fluorescence tomography of small animals using simplified spherical harmonics

NASA Astrophysics Data System (ADS)

Edjlali, Ehsan; Bérubé-Lauzière, Yves

2018-01-01

We present the first Lq -Lp optimization scheme for fluorescence tomographic imaging. This is then applied to small animal imaging. Fluorescence tomography is an ill-posed, and in full generality, a nonlinear problem that seeks to image the 3D concentration distribution of a fluorescent agent inside a biological tissue. Standard candidates for regularization to deal with the ill-posedness of the image reconstruction problem include L1 and L2 regularization. In this work, a general Lq -Lp regularization framework (Lq discrepancy function - Lp regularization term) is introduced for fluorescence tomographic imaging. A method to calculate the gradient for this general framework is developed which allows evaluating the performance of different cost functions/regularization schemes in solving the fluorescence tomographic problem. The simplified spherical harmonics approximation is used to accurately model light propagation inside the tissue. Furthermore, a multigrid mesh is utilized to decrease the dimension of the inverse problem and reduce the computational cost of the solution. The inverse problem is solved iteratively using an lm-BFGS quasi-Newton optimization method. The simulations are performed under different scenarios of noisy measurements. These are carried out on the Digimouse numerical mouse model with the kidney being the target organ. The evaluation of the reconstructed images is performed both qualitatively and quantitatively using several metrics including QR, RMSE, CNR, and TVE under rigorous conditions. The best reconstruction results under different scenarios are obtained with an L1.5 -L1 scheme with premature termination of the optimization process. This is in contrast to approaches commonly found in the literature relying on L2 -L2 schemes.

Magnetic models for the United States for 1985

USGS Publications Warehouse

Peddie, Norman W.; Zunde, Audronis K.

1990-01-01

New models describing the magnetic field in the United States at the beginning of 1985 and the rate of change expected during the next few years have been developed. The models--which will serve as the basis for a new set of magnetic charts--were derived from several tens of thousands of original field measurements from land, marine, and aerial surveys; from values derived from the MAGSAT-based International Geomagnetic Reference Field; and from recent data from magnetic observatories and repeat stations. , They are in the form of spherical harmonic series that represent the scalar magnetic potential from which all the field components can be derived. The models for the conterminous States and Alaska are of maximum degree and order 4 (24 coefficients each) and the models for Hawaii are of maximum degree and order 2 (8 coefficients each).

Comparative Analysis of Models of the Earth's Gravity: 3. Accuracy of Predicting EAS Motion

NASA Astrophysics Data System (ADS)

Kuznetsov, E. D.; Berland, V. E.; Wiebe, Yu. S.; Glamazda, D. V.; Kajzer, G. T.; Kolesnikov, V. I.; Khremli, G. P.

2002-05-01

This paper continues a comparative analysis of modern satellite models of the Earth's gravity which we started in [6, 7]. In the cited works, the uniform norms of spherical functions were compared with their gradients for individual harmonics of the geopotential expansion [6] and the potential differences were compared with the gravitational accelerations obtained in various models of the Earth's gravity [7]. In practice, it is important to know how consistently the EAS motion is represented by various geopotential models. Unless otherwise stated, a model version in which the equations of motion are written using the classical Encke scheme and integrated together with the variation equations by the implicit one-step Everhart's algorithm [1] was used. When calculating coordinates and velocities on the integration step (at given instants of time), the approximate Everhart formula was employed.

Empirical wind model for the middle and lower atmosphere. Part 2: Local time variations

NASA Technical Reports Server (NTRS)

Hedin, A. E.; Fleming, E. L.; Manson, A. H.; Schmidlin, F. J.; Avery, S. K.; Clark, R. R.; Franke, S. J.; Fraser, G. J.; Tsuda, T.; Vial, F.

1993-01-01

The HWM90 thermospheric wind model was revised in the lower thermosphere and extended into the mesosphere and lower atmosphere to provide a single analytic model for calculating zonal and meridional wind profiles representative of the climatological average for various geophysical conditions. Local time variations in the mesosphere are derived from rocket soundings, incoherent scatter radar, MF radar, and meteor radar. Low-order spherical harmonics and Fourier series are used to describe these variations as a function of latitude and day of year with cubic spline interpolation in altitude. The model represents a smoothed compromise between the original data sources. Although agreement between various data sources is generally good, some systematic differences are noted. Overall root mean square differences between measured and model tidal components are on the order of 5 to 10 m/s.

Mapping quadrupole collectivity in the Cd isotopes: The breakdown of harmonic vibrational motion

NASA Astrophysics Data System (ADS)

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.

Generalized power-spectrum Larmor formula for an extended charged particle embedded in a harmonic oscillator

NASA Astrophysics Data System (ADS)

Marengo, Edwin A.; Khodja, Mohamed R.

2006-09-01

The nonrelativistic Larmor radiation formula, giving the power radiated by an accelerated charged point particle, is generalized for a spatially extended particle in the context of the classical charged harmonic oscillator. The particle is modeled as a spherically symmetric rigid charge distribution that possesses both translational and spinning degrees of freedom. The power spectrum obtained exhibits a structure that depends on the form factor of the particle, but reduces, in the limit of an infinitesimally small particle and for the charge distributions considered, to Larmor’s familiar result. It is found that for finite-duration small-enough accelerations as well as perpetual uniform accelerations the power spectrum of the spatially extended particle reduces to that of a point particle. It is also found that when the acceleration is violent or the size parameter of the particle is very large compared to the wavelength of the emitted radiation the power spectrum is highly suppressed. Possible applications are discussed.

Time-resolved second-harmonic generation from gold nanoparticle arrays

NASA Astrophysics Data System (ADS)

Ferrara, D. W.; Tetz, K. A.; McMahon, M. D.; Haglund, R. F., Jr.

2007-09-01

We have studied the effects of planar inversion symmetry and particle-coupling of gold nanoparticle (NP) arrays by angle dependent second-harmonic generation (SHG). Time- and angle- resolved measurements were made using a mode-locked Ti:sapphire 800 nm laser onto gold NP arrays with plasmon resonance tuned to match the laser wavelength in order to produce maximum SHG signal. Finite-difference time domain simulations are used to model the near-field distributions for the various geometries and compared to experiment. The arrays were fabricated by focused ion-beam lithography and metal vapor deposition followed by standard lift-off protocols, producing NPs approximately 20nm high with various in-plane dimensions and interparticle gaps. Above a threshold fluence of ~ 7.3 × 10 -5 mJ/cm2 we find that the SHG scales with the third power of intensity, rather than the second, and atomic-force microscopy shows that the NPs have undergone a reshaping process leading to more nearly spherical shapes.

Observed tidal braking in the earth/moon/sun system

NASA Technical Reports Server (NTRS)

Christodoulidis, D. C.; Smith, D. E.; Williamson, R. G.; Klosko, S. M.

1987-01-01

The low degree and order terms in the spherical harmonic model of the tidal potential were observed through the perturbations which are induced on near-earth satellite orbital motions. Evaluations of tracking observations from 17 satellites and a GEM-T1 geopotential model were used in the tidal recovery which was made in the presence of over 600 long-wavelength coefficients from 32 major and minor tides. Wahr's earth tidal model was used as a basis for the recovery of the ocean tidal terms. Using this tidal model, the secular change in the moon's mean motion due to tidal dissipation was found to be -25.27 + or - 0.61 arcsec/century squared. The estimation of lunar acceleration agreed with that observed from lunar laser ranging techniques (-24.9 + or - 1.0 arcsec/century squared), with the corresponding tidal braking of earth's rotation being -5.98 + or - 0.22 x 10 to the minus 22 rad/second squared. If the nontidal braking of the earth due to the observed secular change in the earth's second zonal harmonic is considered, satellite techniques yield a total value of the secular change of the earth's rotation rate of -4.69 + or - 0.36 x 10 to the minus 22 rad/second squared.

Continuing Development of a Hybrid Model (VSH) of the Neutral Thermosphere

NASA Technical Reports Server (NTRS)

Burns, Alan

1996-01-01

We propose to continue the development of a new operational model of neutral thermospheric density, composition, temperatures and winds to improve current engineering environment definitions of the neutral thermosphere. This model will be based on simulations made with the National Center for Atmospheric Research (NCAR) Thermosphere-Ionosphere- Electrodynamic General Circulation Model (TIEGCM) and on empirical data. It will be capable of using real-time geophysical indices or data from ground-based and satellite inputs and provides neutral variables at specified locations and times. This "hybrid" model will be based on a Vector Spherical Harmonic (VSH) analysis technique developed (over the last 8 years) at the University of Michigan that permits the incorporation of the TIGCM outputs and data into the model. The VSH model will be a more accurate version of existing models of the neutral thermospheric, and will thus improve density specification for satellites flying in low Earth orbit (LEO).

Probe for high resolution NMR with sample reorientation

DOEpatents

Pines, Alexander; Samoson, Ago

1990-01-01

An improved NMR probe and method are described which substantially improve the resolution of NMR measurements made on powdered or amorphous or otherwise orientationally disordered samples. The apparatus mechanically varies the orientation of the sample such that the time average of two or more sets of spherical harmonic functions are zero.

Alternate forms of the associated Legendre functions for use in geomagnetic modeling.

USGS Publications Warehouse

Alldredge, L.R.; Benton, E.R.

1986-01-01

An inconvenience attending traditional use of associated Legendre functions in global modeling is that the functions are not separable with respect to the 2 indices (order and degree). In 1973 Merilees suggested a way to avoid the problem by showing that associated Legendre functions of order m and degree m+k can be expressed in terms of elementary functions. This note calls attention to some possible gains in time savings and accuracy in geomagnetic modeling based upon this form. For this purpose, expansions of associated Legendre polynomials in terms of sines and cosines of multiple angles are displayed up to degree and order 10. Examples are also given explaining how some surface spherical harmonics can be transformed into true Fourier series for selected polar great circle paths. -from Authors

Double lens device for tunable harmonic generation of laser beams in KBBF/RBBF crystals or other non-linear optic materials

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kaminski, Adam

A method and apparatus to generate harmonically related laser wavelengths includes a pair of lenses at opposing faces of a non-linear optical material. The lenses are configured to promote incoming and outgoing beams to be normal to each outer lens surface over a range of acceptance angles of the incoming laser beam. This reduces reflection loss for higher efficiency operation. Additionally, the lenses allow a wider range of wavelengths for lasers for more universal application. Examples of the lenses include plano-cylindrical and plano-spherical form factors.

New models of Saturn's magnetic field using Pioneer 11 Vector Helium Magnetometer data

NASA Technical Reports Server (NTRS)

Davis, L., Jr.; Smith, E. J.

1986-01-01

In a reanalysis of the Vector Helium Magnetometer data taken by Pioneer 11 during its Saturn encounter in 1979, using improvements in the data set and in the procedures, studies are made of a variety of models. The best is the P(11)84 model, an axisymmetric spherical harmonic model of Saturn's magnetic field within 8 Saturn radii of the planet. The appropriately weighted root mean square average of the difference between the observed and the modeled field is 1.13 percent. For the Voyager-based Z3 model of Connerney, Acuna, and Ness, this average difference from the Pioneer 11 data is 1.81 percent. The external source currents in the magnetopause, tail, bow shock, and perhaps ring currents vary with time and can only be crudely modeled. An algebraic formula is derived for calculating the L shells on which energetic charged particles drift in axisymmetric fields.

Representation of magnetic fields in space. [special attention to Geomagnetic fields and Magnetospheric models

NASA Technical Reports Server (NTRS)

Stern, D. P.

1976-01-01

Several mathematical methods which are available for the description of magnetic fields in space are reviewed. Examples of the application of such methods are given, with particular emphasis on work related to the geomagnetic field, and their individual properties and associated problems are described. The methods are grouped in five main classes: (1) methods based on the current density, (2) methods using the scalar magnetic potential, (3) toroidal and poloidal components of the field and spherical vector harmonics, (4) Euler potentials, and (5) local expansions of the field near a given reference point. Special attention is devoted to models of the magnetosphere, to the uniqueness of the scalar potential as derived from observed data, and to the L parameter.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

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 asmore » 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.« less

Wigner tomography of multispin quantum states

NASA Astrophysics Data System (ADS)

Leiner, David; Zeier, Robert; Glaser, Steffen J.

2017-12-01

We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations of spherical harmonics [A. Garon, R. Zeier, and S. J. Glaser, Phys. Rev. A 91, 042122 (2015), 10.1103/PhysRevA.91.042122]. We develop a general methodology to experimentally recover these shapes by measuring expectation values of rotated axial spherical tensor operators and provide an interpretation in terms of fictitious multipole potentials. Our approach is experimentally demonstrated for quantum systems consisting of up to three spins using nuclear magnetic resonance spectroscopy.

An atlas of Rapp's 180-th order geopotential.

NASA Astrophysics Data System (ADS)

Melvin, P. J.

1986-08-01

Deprit's 1979 approach to the summation of the spherical harmonic expansion of the geopotential has been modified to spherical components and normalized Legendre polynomials. An algorithm has been developed which produces ten fields at the users option: the undulations of the geoid, three anomalous components of the gravity vector, or six components of the Hessian of the geopotential (gravity gradient). The algorithm is stable to high orders in single precision and does not treat the polar regions as a special case. Eleven contour maps of components of the anomalous geopotential on the surface of the ellipsoid are presented to validate the algorithm.

A Study of the Nearfield of an Excited Spherical Shell.

DTIC Science & Technology

1980-03-17

8217 tte exact wave harmonic series and the approximate Geometrical Theory of Diffraction (GTD) were used to predict the acoustic near field of an elastic...rr) )1/3 n 4 n14 XV e i+ (424 (ka) (2h (ka) nn an1 % Tte SkaI/ rA’ (k)2 nn in Ap ndi B]. =Q (ikc)~ (4.25)h(1 (a n Tn whee i adeayftore fo acosi prpaa3o...Approach to Scattering from Elastic Spherical Shells," NUC TP425, September 1974, Naval Undersea Center, San Diego, California. 36. Pathak, P. H. and

A semi-analytic theory for the motion of a close-earth artificial satellite with drag

NASA Technical Reports Server (NTRS)

Liu, J. J. F.; Alford, R. L.

1979-01-01

A semi-analytic method is used to estimate the decay history/lifetime and to generate orbital ephemeris for close-earth satellites perturbed by the atmospheric drag and earth oblateness due to the spherical harmonics J2, J3, and J4. The theory maintains efficiency through the application of the theory of a method of averaging and employs sufficient numerical emphasis to include a rather sophisticated atmospheric density model. The averaged drag effects with respect to mean anomaly are evaluated by a Gauss-Legendre quadrature while the averaged variational equations of motion are integrated numerically with automatic step size and error control.

Weakly nonlinear incompressible Rayleigh-Taylor instability in spherical and planar geometries

NASA Astrophysics Data System (ADS)

Zhang, J.; Wang, L. F.; Ye, W. H.; Guo, H. Y.; Wu, J. F.; Ding, Y. K.; Zhang, W. Y.; He, X. T.

2018-02-01

The relationship between the weakly nonlinear (WN) solutions of the Rayleigh-Taylor instability in spherical geometry [Zhang et al., Phys. Plasmas 24, 062703 (2017)] and those in planar geometry [Wang et al., Phys. Plasmas 19, 112706 (2012)] is analyzed. In the high-mode perturbation limit ( Pn(cos θ), n ≫1 ), it is found that at the equator, the contributions of mode P2 n along with its neighboring modes, mode P3 n along with its neighboring modes, and mode Pn at the third order along with its neighboring modes are equal to those of the second harmonic, the third harmonic, and the third-order feedback to the fundamental mode, respectively, in the planar case with a perturbation of the same wave vector and amplitude as those at the equator. The trends of WN results in spherical geometry towards the corresponding planar counterparts are found, and the convergence behaviors of the neighboring modes of Pn, P2 n , and P3 n are analyzed. Moreover, the spectra generated from the high-mode perturbations in the WN regime are provided. For low-mode perturbations, it is found that the fundamental modes saturate at larger amplitudes than the planar result. The geometry effect makes the bubbles at or near the equator grow faster than the bubbles in planar geometry in the WN regime.

Combining virtual observatory and equivalent source dipole approaches to describe the geomagnetic field with Swarm measurements

NASA Astrophysics Data System (ADS)

Saturnino, Diana; Langlais, Benoit; Amit, Hagay; Civet, François; Mandea, Mioara; Beucler, Éric

2018-03-01

A detailed description of the main geomagnetic field and of its temporal variations (i.e., the secular variation or SV) is crucial to understanding the geodynamo. Although the SV is known with high accuracy at ground magnetic observatory locations, the globally uneven distribution of the observatories hampers the determination of a detailed global pattern of the SV. Over the past two decades, satellites have provided global surveys of the geomagnetic field which have been used to derive global spherical harmonic (SH) models through some strict data selection schemes to minimise external field contributions. However, discrepancies remain between ground measurements and field predictions by these models; indeed the global models do not reproduce small spatial scales of the field temporal variations. To overcome this problem we propose to directly extract time series of the field and its temporal variation from satellite measurements as it is done at observatory locations. We follow a Virtual Observatory (VO) approach and define a global mesh of VOs at satellite altitude. For each VO and each given time interval we apply an Equivalent Source Dipole (ESD) technique to reduce all measurements to a unique location. Synthetic data are first used to validate the new VO-ESD approach. Then, we apply our scheme to data from the first two years of the Swarm mission. For the first time, a 2.5° resolution global mesh of VO time series is built. The VO-ESD derived time series are locally compared to ground observations as well as to satellite-based model predictions. Our approach is able to describe detailed temporal variations of the field at local scales. The VO-ESD time series are then used to derive global spherical harmonic models. For a simple SH parametrization the model describes well the secular trend of the magnetic field both at satellite altitude and at the surface. As more data will be made available, longer VO-ESD time series can be derived and consequently used to study sharp temporal variation features, such as geomagnetic jerks.

Global mean dynamic topography based on GOCE data and Wiener filters

NASA Astrophysics Data System (ADS)

Gilardoni, Maddalena; Reguzzoni, Mirko; Albertella, Alberta

2015-04-01

A mean dynamic ocean topography (MDT) has been computed by using a GOCE-only gravity model and a given mean sea surface (MSS) obtained from satellite altimetry. Since the used gravity model, i.e. the fifth release of the time-wise solution covering the full mission lifetime, is truncated at a maximum harmonic degree of 280, the obtained MDT has to be consistently filtered. This has been done globally by using the spherical harmonic representation and following a Wiener minimization principle. This global filtering approach is convenient from the computational point of view but requires to have MDT values all over the Earth surface and therefore to fill the continents with fictitious data. The main improvements with respect to the already presented results are in the MDT filling procedure (to guarantee that the global signal has the same covariance of the one over the oceans), in the error modelling of the input MSS and in the error estimation of the filtered MDT and of the corresponding geostrophic velocities. The impact of GOCE data in the ocean circulation global modelling has been assessed by comparing the pattern of the obtained geostrophic currents with those computed by using EGM2008. Comparisons with independent circulation data based on drifters and other MDT models have been also performed with the aim of evaluating the accuracy of the obtained results.

Probe for high resolution NMR with sample reorientation

DOEpatents

Pines, A.; Samoson, A.

1990-02-06

An improved NMR probe and method are described which substantially improve the resolution of NMR measurements made on powdered or amorphous or otherwise orientationally disordered samples. The apparatus mechanically varies the orientation of the sample such that the time average of two or more sets of spherical harmonic functions are zero. 8 figs.

An iterative inversion of weighted Radon transforms along hyperplanes

NASA Astrophysics Data System (ADS)

Goncharov, F. O.

2017-12-01

We propose iterative inversion algorithms for weighted Radon transforms R W along hyperplanes in {R}3 . More precisely, expanding the weight W=W(x, θ), x\\in {R}^3, θ\\in {S}^2, into the series of spherical harmonics in θ and assuming that the zero order term w0, 0(x)\

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

PubMed

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.

Electromagnetic deep-probing (100-1000 kms) of the Earth's interior from artificial satellites: Constraints on the regional emplacement of crustal resources

NASA Technical Reports Server (NTRS)

Hermance, J. F. (Principal Investigator)

1981-01-01

A spherical harmonic analysis program is being tested which takes magnetic data in universal time from a set of arbitrarily space observatories and calculates a value for the instantaneous magnetic field at any point on the globe. The calculation is done as a least mean-squares value fit to a set of spherical harmonics up to any desired order. The program accepts as a set of input the orbit position of a satellite coordinates it with ground-based magnetic data for a given time. The output is a predicted time series for the magnetic field on the Earth's surface at the (r, theta) position directly under the hypothetically orbiting satellite for the duration of the time period of the input data set. By tracking the surface magnetic field beneath the satellite, narrow-band averages crosspowers between the spatially coordinated satellite and the ground-based data sets are computed. These crosspowers are used to calculate field transfer coefficients with minimum noise distortion. The application of this technique to calculating the vector response function W is discussed.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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 (Au147), 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 Au147, 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 Au147 is performed, and it is concluded that Au147 has a dynamic surface, thus opening a new window for studying its reaction dynamics.

Searches for Large-scale Anisotropy in the Arrival Directions of Cosmic Rays Detected above Energy of 1019 eV at the Pierre Auger Observatory and the Telescope Array

NASA Astrophysics Data System (ADS)

Aab, A.; Abreu, P.; Aglietta, M.; Ahn, E. J.; Samarai, I. Al; Albuquerque, I. F. M.; Allekotte, I.; Allen, J.; Allison, P.; Almela, A.; Alvarez Castillo, J.; Alvarez-Muñiz, J.; Alves Batista, R.; Ambrosio, M.; Aminaei, A.; Anchordoqui, L.; Andringa, S.; Aramo, C.; Arqueros, F.; Asorey, H.; Assis, P.; Aublin, J.; Ave, M.; Avenier, M.; Avila, G.; Badescu, A. M.; Barber, K. B.; Bäuml, J.; Baus, C.; Beatty, J. J.; Becker, K. H.; Bellido, J. A.; Berat, C.; Bertaina, M. E.; Bertou, X.; Biermann, P. L.; Billoir, P.; Blanco, M.; Bleve, C.; Blümer, H.; Boháčová, M.; Boncioli, D.; Bonifazi, C.; Bonino, R.; Borodai, N.; Brack, J.; Brancus, I.; Brogueira, P.; Brown, W. C.; Buchholz, P.; Bueno, A.; Buitink, S.; Buscemi, M.; Caballero-Mora, K. S.; Caccianiga, B.; Caccianiga, L.; Candusso, M.; Caramete, L.; Caruso, R.; Castellina, A.; Cataldi, G.; Cazon, L.; Cester, R.; Chavez, A. G.; Chiavassa, A.; Chinellato, J. A.; Chudoba, J.; Cilmo, M.; Clay, R. W.; Cocciolo, G.; Colalillo, R.; Coleman, A.; Collica, L.; Coluccia, M. R.; Conceição, R.; Contreras, F.; Cooper, M. J.; Cordier, A.; Coutu, S.; Covault, C. E.; Cronin, J.; Curutiu, A.; Dallier, R.; Daniel, B.; Dasso, S.; Daumiller, K.; Dawson, B. R.; de Almeida, R. M.; De Domenico, M.; de Jong, S. J.; de Mello Neto, J. R. T.; De Mitri, I.; de Oliveira, J.; de Souza, V.; del Peral, L.; Deligny, O.; Dembinski, H.; Dhital, N.; Di Giulio, C.; Di Matteo, A.; Diaz, J. C.; Díaz Castro, M. L.; Diogo, F.; Dobrigkeit, C.; Docters, W.; D'Olivo, J. C.; Dorofeev, A.; Dorosti Hasankiadeh, Q.; Dova, M. T.; Ebr, J.; Engel, R.; Erdmann, M.; Erfani, M.; Escobar, C. O.; Espadanal, J.; Etchegoyen, A.; Facal San Luis, P.; Falcke, H.; Fang, K.; Farrar, G.; Fauth, A. C.; Fazzini, N.; Ferguson, A. P.; Fernandes, M.; Fick, B.; Figueira, J. M.; Filevich, A.; Filipčič, A.; Fox, B. D.; Fratu, O.; Fröhlich, U.; Fuchs, B.; Fuji, T.; Gaior, R.; García, B.; Garcia Roca, S. T.; Garcia-Gamez, D.; Garcia-Pinto, D.; Garilli, G.; Gascon Bravo, A.; Gate, F.; Gemmeke, H.; Ghia, P. L.; Giaccari, U.; Giammarchi, M.; Giller, M.; Glaser, C.; Glass, H.; Gómez Berisso, M.; Gómez Vitale, P. F.; Gonçalves, P.; Gonzalez, J. G.; González, N.; Gookin, B.; Gorgi, A.; Gorham, P.; Gouffon, P.; Grebe, S.; Griffith, N.; Grillo, A. F.; Grubb, T. D.; Guardincerri, Y.; Guarino, F.; Guedes, G. P.; Hampel, M. R.; Hansen, P.; Harari, D.; Harrison, T. A.; Hartmann, S.; Harton, J. L.; Haungs, A.; Hebbeker, T.; Heck, D.; Heimann, P.; Herve, A. E.; Hill, G. C.; Hojvat, C.; Hollon, N.; Holt, E.; Homola, P.; Hörandel, J. R.; Horvath, P.; Hrabovský, M.; Huber, D.; Huege, T.; Insolia, A.; Isar, P. G.; Islo, K.; Jandt, I.; Jansen, S.; Jarne, C.; Josebachuili, M.; Kääpä, A.; Kambeitz, O.; Kampert, K. H.; Kasper, P.; Katkov, I.; Kégl, B.; Keilhauer, B.; Keivani, A.; Kemp, E.; Kieckhafer, R. M.; Klages, H. O.; Kleifges, M.; Kleinfeller, J.; Krause, R.; Krohm, N.; Krömer, O.; Kruppke-Hansen, D.; Kuempel, D.; Kunka, N.; La Rosa, G.; LaHurd, D.; Latronico, L.; Lauer, R.; Lauscher, M.; Lautridou, P.; Le Coz, S.; Leão, M. S. A. B.; Lebrun, D.; Lebrun, P.; Leigui de Oliveira, M. A.; Letessier-Selvon, A.; Lhenry-Yvon, I.; Link, K.; López, R.; Lopez Agüera, A.; Louedec, K.; Lozano Bahilo, J.; Lu, L.; Lucero, A.; Ludwig, M.; Maccarone, M. C.; Malacari, M.; Maldera, S.; Mallamaci, M.; Maller, J.; Mandat, D.; Mantsch, P.; Mariazzi, A. G.; Marin, V.; Mariş, I. C.; Marsella, G.; Martello, D.; Martin, L.; Martinez, H.; Martínez Bravo, O.; Martraire, D.; Masías Meza, J. J.; Mathes, H. J.; Mathys, S.; Matthews, J. A. J.; Matthews, J.; Matthiae, G.; Maurel, D.; Maurizio, D.; Mayotte, E.; Mazur, P. O.; Medina, C.; Medina-Tanco, G.; Melissas, M.; Melo, D.; Menichetti, E.; Menshikov, A.; Messina, S.; Meyhandan, R.; Mićanović, S.; Micheletti, M. I.; Middendorf, L.; Minaya, I. A.; Miramonti, L.; Mitrica, B.; Molina-Bueno, L.; Mollerach, S.; Monasor, M.; Monnier Ragaigne, D.; Montanet, F.; Morello, C.; Mostafá, M.; Moura, C. A.; Muller, M. A.; Müller, G.; Münchmeyer, M.; Mussa, R.; Navarra, G.; Navas, S.; Necesal, P.; Nellen, L.; Nelles, A.; Neuser, J.; Niechciol, M.; Niemietz, L.; Niggemann, T.; Nitz, D.; Nosek, D.; Novotny, V.; Nožka, L.; Ochilo, L.; Olinto, A.; Oliveira, M.; Pacheco, N.; Pakk Selmi-Dei, D.; Palatka, M.; Pallotta, J.; Palmieri, N.; Papenbreer, P.; Parente, G.; Parra, A.; Paul, T.; Pech, M.; Pękala, J.; Pelayo, R.; Pepe, I. M.; Perrone, L.; Pesce, R.; Petermann, E.; Peters, C.; Petrera, S.; Petrolini, A.; Petrov, Y.; Phuntsok, J.; Piegaia, R.; Pierog, T.; Pieroni, P.; Pimenta, M.; Pirronello, V.; Platino, M.; Plum, M.; Porcelli, A.; Porowski, C.; Prado, R. R.; Privitera, P.; Prouza, M.; Purrello, V.; Quel, E. J.; Querchfeld, S.; Quinn, S.; Rautenberg, J.; Ravel, O.; Ravignani, D.; Revenu, B.; Ridky, J.; Riggi, S.; Risse, M.; Ristori, P.; Rizi, V.; Roberts, J.; Rodrigues de Carvalho, W.; Rodriguez Cabo, I.; Rodriguez Fernandez, G.; Rodriguez Rojo, J.; Rodríguez-Frías, M. D.; Ros, G.; Rosado, J.; Rossler, T.; Roth, M.; Roulet, E.; Rovero, A. C.; Saffi, S. J.; Saftoiu, A.; Salamida, F.; Salazar, H.; Saleh, A.; Salesa Greus, F.; Salina, G.; Sánchez, F.; Sanchez-Lucas, P.; Santo, C. E.; Santos, E.; Santos, E. M.; Sarazin, F.; Sarkar, B.; Sarmento, R.; Sato, R.; Scharf, N.; Scherini, V.; Schieler, H.; Schiffer, P.; Scholten, O.; Schoorlemmer, H.; Schovánek, P.; Schulz, A.; Schulz, J.; Schumacher, J.; Sciutto, S. J.; Segreto, A.; Settimo, M.; Shadkam, A.; Shellard, R. C.; Sidelnik, I.; Sigl, G.; Sima, O.; Śmiałkowski, A.; Šmída, R.; Snow, G. R.; Sommers, P.; Sorokin, J.; Squartini, R.; Srivastava, Y. N.; Stanič, S.; Stapleton, J.; Stasielak, J.; Stephan, M.; Stutz, A.; Suarez, F.; Suomijärvi, T.; Supanitsky, A. D.; Sutherland, M. S.; Swain, J.; Szadkowski, Z.; Szuba, M.; Taborda, O. A.; Tapia, A.; Tartare, M.; Theodoro, V. M.; Timmermans, C.; Todero Peixoto, C. J.; Toma, G.; Tomankova, L.; Tomé, B.; Tonachini, A.; Torralba Elipe, G.; Torres Machado, D.; Travnicek, P.; Trovato, E.; Tueros, M.; Ulrich, R.; Unger, M.; Urban, M.; Valdés Galicia, J. F.; Valiño, I.; Valore, L.; van Aar, G.; van den Berg, A. M.; van Velzen, S.; van Vliet, A.; Varela, E.; Vargas Cárdenas, B.; Varner, G.; Vázquez, J. R.; Vázquez, R. A.; Veberič, D.; Verzi, V.; Vicha, J.; Videla, M.; Villaseñor, L.; Vlcek, B.; Vorobiov, S.; Wahlberg, H.; Wainberg, O.; Walz, D.; Watson, A. A.; Weber, M.; Weidenhaupt, K.; Weindl, A.; Werner, F.; Widom, A.; Wiencke, L.; Wilczyńska, B.; Wilczyński, H.; Will, M.; Williams, C.; Winchen, T.; Wittkowski, D.; Wundheiler, B.; Wykes, S.; Yamamoto, T.; Yapici, T.; Younk, P.; Yuan, G.; Yushkov, A.; Zamorano, B.; Zas, E.; Zavrtanik, D.; Zavrtanik, M.; Zaw, I.; Zepeda, A.; Zhou, J.; Zhu, Y.; Zimbres Silva, M.; Ziolkowski, M.; Pierre Auger Collaboration; Abbasi, R. U.; Abe, M.; Abu-Zayyad, T.; Allen, M.; Anderson, R.; Azuma, R.; Barcikowski, E.; Belz, J. W.; Bergman, D. R.; Blake, S. A.; Cady, R.; Chae, M. J.; Cheon, B. G.; Chiba, J.; Chikawa, M.; Cho, W. R.; Fujii, T.; Fukushima, M.; Goto, T.; Hanlon, W.; Hayashi, Y.; Hayashida, N.; Hibino, K.; Honda, K.; Ikeda, D.; Inoue, N.; Ishii, T.; Ishimori, R.; Ito, H.; Ivanov, D.; Jui, C. C. H.; Kadota, K.; Kakimoto, F.; Kalashev, O.; Kasahara, K.; Kawai, H.; Kawakami, S.; Kawana, S.; Kawata, K.; Kido, E.; Kim, H. B.; Kim, J. H.; Kim, J. H.; Kitamura, S.; Kitamura, Y.; Kuzmin, V.; Kwon, Y. J.; Lan, J.; Lim, S. I.; Lundquist, J. P.; Machida, K.; Martens, K.; Matsuda, T.; Matsuyama, T.; Matthews, J. N.; Minamino, M.; Mukai, K.; Myers, I.; Nagasawa, K.; Nagataki, S.; Nakamura, T.; Nonaka, T.; Nozato, A.; Ogio, S.; Ogura, J.; Ohnishi, M.; Ohoka, H.; Oki, K.; Okuda, T.; Ono, M.; Oshima, A.; Ozawa, S.; Park, I. H.; Pshirkov, M. S.; Rodriguez, D. C.; Rubtsov, G.; Ryu, D.; Sagawa, H.; Sakurai, N.; Sampson, A. L.; Scott, L. M.; Shah, P. D.; Shibata, F.; Shibata, T.; Shimodaira, H.; Shin, B. K.; Smith, J. D.; Sokolsky, P.; Springer, R. W.; Stokes, B. T.; Stratton, S. R.; Stroman, T. A.; Suzawa, T.; Takamura, M.; Takeda, M.; Takeishi, R.; Taketa, A.; Takita, M.; Tameda, Y.; Tanaka, H.; Tanaka, K.; Tanaka, M.; Thomas, S. B.; Thomson, G. B.; Tinyakov, P.; Tkachev, I.; Tokuno, H.; Tomida, T.; Troitsky, S.; Tsunesada, Y.; Tsutsumi, K.; Uchihori, Y.; Udo, S.; Urban, F.; Vasiloff, G.; Wong, T.; Yamane, R.; Yamaoka, H.; Yamazaki, K.; Yang, J.; Yashiro, K.; Yoneda, Y.; Yoshida, S.; Yoshii, H.; Zollinger, R.; Zundel, Z.; Telescope Array Collaboration

2014-10-01

Spherical harmonic moments are well-suited for capturing anisotropy at any scale in the flux of cosmic rays. An unambiguous measurement of the full set of spherical harmonic coefficients requires full-sky coverage. This can be achieved by combining data from observatories located in both the northern and southern hemispheres. To this end, a joint analysis using data recorded at the Telescope Array and the Pierre Auger Observatory above 1019 eV is presented in this work. The resulting multipolar expansion of the flux of cosmic rays allows us to perform a series of anisotropy searches, and in particular to report on the angular power spectrum of cosmic rays above 1019 eV. No significant deviation from isotropic expectations is found throughout the analyses performed. Upper limits on the amplitudes of the dipole and quadrupole moments are derived as a function of the direction in the sky, varying between 7% and 13% for the dipole and between 7% and 10% for a symmetric quadrupole.

Background field removal technique using regularization enabled sophisticated harmonic artifact reduction for phase data with varying kernel sizes.

PubMed

Kan, Hirohito; Kasai, Harumasa; Arai, Nobuyuki; Kunitomo, Hiroshi; Hirose, Yasujiro; Shibamoto, Yuta

2016-09-01

An effective background field removal technique is desired for more accurate quantitative susceptibility mapping (QSM) prior to dipole inversion. The aim of this study was to evaluate the accuracy of regularization enabled sophisticated harmonic artifact reduction for phase data with varying spherical kernel sizes (REV-SHARP) method using a three-dimensional head phantom and human brain data. The proposed REV-SHARP method used the spherical mean value operation and Tikhonov regularization in the deconvolution process, with varying 2-14mm kernel sizes. The kernel sizes were gradually reduced, similar to the SHARP with varying spherical kernel (VSHARP) method. We determined the relative errors and relationships between the true local field and estimated local field in REV-SHARP, VSHARP, projection onto dipole fields (PDF), and regularization enabled SHARP (RESHARP). Human experiment was also conducted using REV-SHARP, VSHARP, PDF, and RESHARP. The relative errors in the numerical phantom study were 0.386, 0.448, 0.838, and 0.452 for REV-SHARP, VSHARP, PDF, and RESHARP. REV-SHARP result exhibited the highest correlation between the true local field and estimated local field. The linear regression slopes were 1.005, 1.124, 0.988, and 0.536 for REV-SHARP, VSHARP, PDF, and RESHARP in regions of interest on the three-dimensional head phantom. In human experiments, no obvious errors due to artifacts were present in REV-SHARP. The proposed REV-SHARP is a new method combined with variable spherical kernel size and Tikhonov regularization. This technique might make it possible to be more accurate backgroud field removal and help to achive better accuracy of QSM. Copyright © 2016 Elsevier Inc. All rights reserved.

Kinematics of our Galaxy from the PMA and TGAS catalogues

NASA Astrophysics Data System (ADS)

Velichko, Anna B.; Akhmetov, Volodymyr S.; Fedorov, Peter N.

2018-04-01

We derive and compare kinematic parameters of the Galaxy using the PMA and Gaia TGAS data. Two methods are used in calculations: evaluation of the Ogorodnikov-Milne model (OMM) parameters by the least square method (LSM) and a decomposition on a set of vector spherical harmonics (VSH). We trace dependencies on the distance of the derived parameters including the Oort constants A and B and the rotational velocity of the Galaxy V rot at the Solar distance for the common sample of stars of mixed spectral composition of the PMA and TGAS catalogues. The distances were obtained from the TGAS parallaxes or from reduced proper motions for fainter stars. The A, B and V rot parameters derived from proper motions of both catalogues used show identical behaviour but the values are systematically shifted by about 0.5 mas/yr. The Oort B parameter derived from the PMA sample of red giants shows gradual decrease with increasing the distance while the Oort A has a minimum at about 2 kpc and then gradually increases. As for models chosen for calculations, first, we confirm conclusions of other authors about the existence of extra-model harmonics in the stellar velocity field. Secondly, not all parameters of the OMM are statistically significant, and the set of parameters depends on the stellar sample used.

Crustal thickness inversions from recent Mars Reconnaissance Orbiter gravity solutions

NASA Astrophysics Data System (ADS)

Neumann, Gregory; Zuber, Maria T.; Lemoine, Frank; Neumann, Gregory A.; Smith, David E.

Recent Mars Reconnaissance Orbiter gravity solutions from low-altitude tracking of MRO, together with previous spacecraft, have dramatically improved correlation with MOLA topography at spherical harmonic degrees up to 95. We present several updated models of crustal thickness. These models are calculated to fit the Bouguer potential anomaly following the assumptions in Neumann et al. 2004, with much weaker a priori constraints applied to the topographic corrections and the downward continuation to the martian mantle. These models are available via anonymous ftp to "ftp://lepftp.gsfc.nasa.gov/pub/exports/tharsis/marscrust3". The higher-resolution models improve on those we produced in 2004-2005. They are appropriate for modeling impacts as small as 300 km diameter, and for processes related to the hemispheric dichotomy boundary. We discuss in particular the assumption of quasi-uniform crustal density and its likely failure in volcanic regions.

A model of geomagnetic secular variation for 1980-1983

USGS Publications Warehouse

Peddie, N.W.; Zunde, A.K.

1987-01-01

We developed an updated model of the secular variation of the main geomagnetic field during 1980 through 1983 based on annual mean values for that interval from 148 worldwide magnetic observatories. The model consists of a series of 80 spherical harmonics, up to and including those of degree and order 8. We used it to form a proposal for the 1985 revision of the International Geomagnetic Reference Field (IGRF). Comparison of the new model, whose mean epoch is approximately 1982.0, with the Provisional Geomagnetic Reference Field for 1975-1980 (PGRF 1975), indicates that the moment of the centered-dipole part of the geomagnetic field is now decreasing faster than it was 5 years ago. The rate (in field units) indicated by PGRF 1975 was about -25 nT a-1, while for the new model it is -28 nT a-1. ?? 1987.

Seismic sensitivity of normal-mode coupling to Lorentz stresses in the Sun

NASA Astrophysics Data System (ADS)

Hanasoge, Shravan M.

2017-09-01

Understanding the governing mechanism of solar magnetism remains an outstanding challenge in astrophysics. Seismology is the most compelling technique to infer the internal properties of the Sun and stars. Waves in the Sun, nominally acoustic, are sensitive to the emergence and cyclical strengthening of magnetic field, evidenced by measured changes in resonant oscillation frequencies that are correlated with the solar cycle. The inference of internal Lorentz stresses from these measurements has the potential to significantly advance our appreciation of the dynamo. Indeed, seismological inverse theory for the Sun is well understood for perturbations in composition, thermal structure and flows but, is not fully developed for magnetism, owing to the complexity of the ideal magnetohydrodynamic (MHD) equation. Invoking first-Born perturbation theory to characterize departures from spherically symmetric hydrostatic models of the Sun and applying the notation of generalized spherical harmonics, we calculate sensitivity functions of seismic measurements to the general time-varying Lorentz stress tensor. We find that eigenstates of isotropic (I.e. acoustic only) background models are dominantly sensitive to isotropic deviations in the stress tensor and much more weakly than anisotropic stresses (and therefore challenging to infer). The apple cannot fall far from the tree.

Linear Stability Analysis of an Acoustically Vaporized Droplet

NASA Astrophysics Data System (ADS)

Siddiqui, Junaid; Qamar, Adnan; Samtaney, Ravi

2015-11-01

Acoustic droplet vaporization (ADV) is a phase transition phenomena of a superheat liquid (Dodecafluoropentane, C5F12) droplet to a gaseous bubble, instigated by a high-intensity acoustic pulse. This approach was first studied in imaging applications, and applicable in several therapeutic areas such as gas embolotherapy, thrombus dissolution, and drug delivery. High-speed imaging and theoretical modeling of ADV has elucidated several physical aspects, ranging from bubble nucleation to its subsequent growth. Surface instabilities are known to exist and considered responsible for evolving bubble shapes (non-spherical growth, bubble splitting and bubble droplet encapsulation). We present a linear stability analysis of the dynamically evolving interfaces of an acoustically vaporized micro-droplet (liquid A) in an infinite pool of a second liquid (liquid B). We propose a thermal ADV model for the base state. The linear analysis utilizes spherical harmonics (Ynm, of degree m and order n) and under various physical assumptions results in a time-dependent ODE of the perturbed interface amplitudes (one at the vapor/liquid A interface and the other at the liquid A/liquid B interface). The perturbation amplitudes are found to grow exponentially and do not depend on m. Supported by KAUST Baseline Research Funds.

Supercontinent cycles, true polar wander, and very long-wavelength mantle convection

NASA Astrophysics Data System (ADS)

Zhong, Shijie; Zhang, Nan; Li, Zheng-Xiang; Roberts, James H.

2007-09-01

We show in this paper that mobile-lid mantle convection in a three-dimensional spherical shell with observationally constrained mantle viscosity structure, and realistic convective vigor and internal heating rate is characterized by either a spherical harmonic degree-1 planform with a major upwelling in one hemisphere and a major downwelling in the other hemisphere when continents are absent, or a degree-2 planform with two antipodal major upwellings when a supercontinent is present. We propose that due to modulation of continents, these two modes of mantle convection alternate within the Earth's mantle, causing the cyclic processes of assembly and breakup of supercontinents including Rodinia and Pangea in the last 1 Ga. Our model suggests that the largely degree-2 structure for the present-day mantle with the Africa and Pacific antipodal superplumes, is a natural consequence of this dynamic process of very long-wavelength mantle convection interacting with supercontinent Pangea. Our model explains the basic features of true polar wander (TPW) events for Rodinia and Pangea including their equatorial locations and large variability of TPW inferred from paleomagnetic studies. Our model also suggests that TPW is expected to be more variable and large during supercontinent assembly, but small after a supercontinent acquires its equatorial location and during its subsequent dispersal.

SHPTS: towards a new method for generating precise global ionospheric TEC map based on spherical harmonic and generalized trigonometric series functions

NASA Astrophysics Data System (ADS)

Li, Zishen; Yuan, Yunbin; Wang, Ningbo; Hernandez-Pajares, Manuel; Huo, Xingliang

2015-04-01

To take maximum advantage of the increasing Global Navigation Satellite Systems (GNSS) data to improve the accuracy and resolution of global ionospheric TEC map (GIM), an approach, named Spherical Harmonic plus generalized Trigonometric Series functions (SHPTS), is proposed by integrating the spherical harmonic and the generalized trigonometric series functions on global and local scales, respectively. The SHPTS-based GIM from January 1st, 2001 to December 31st, 2011 (about one solar cycle) is validated by the ionospheric TEC from raw global GPS data, the GIM released by the current Ionospheric Associate Analysis Center (IAAC), the TOPEX/Poseidon satellite and the DORIS. The present results show that the SHPTS-based GIM over the area where no real data are available has the same accuracy level (approximately 2-6 TECu) to that released by the current IAAC. However, the ionospheric TEC in the SHPTS-based GIM over the area covered by real data is more accurate (approximately 1.5 TECu) than that of the GIM (approximately 3.0 TECu) released by the current IAAC. The external accuracy of the SHPTS-based GIM validated by the TOPEX/Poseidon and DORIS is approximately 2.5-5.5 and 1.5-4.5 TECu, respectively. In particular, the SHPTS-based GIM is the best or almost the best ranked, along with those of JPL and UPC, when they are compared with TOPEX/Poseidon measurements, and the best (in addition to UPC) when they are validated with DORIS data. With the increase in the number of GNSS satellites and contributing stations, the performance of the SHPTS-based GIM can be further improved. The SHPTS-based GIM routinely calculated using global GPS, GLONASS and BDS data will be found at the website http://www.gipp.org.cn.

Potential energy and dipole moment surfaces for HF@C60: Prediction of spectral and electric response properties

NASA Astrophysics Data System (ADS)

Kalugina, Yulia N.; Roy, Pierre-Nicholas

2017-12-01

We present a five-dimensional potential energy surface (PES) for the HF@C60 system computed at the DF-LMP2/cc-pVTZ level of theory. We also calculated a five-dimensional dipole moment surface (DMS) based on DFT(PBE0)/cc-pVTZ calculations. The HF and C60 molecules are considered rigid with bond length rHF = 0.9255 Å (gas phase ground rovibrational state geometry). The C60 geometry is of Ih symmetry. The ab initio points were fitted to obtain a PES in terms of bipolar spherical harmonics. The minimum of the PES corresponds to a geometry where the center of mass of HF is located 0.11 Å away from the center of the cage with an interaction energy of -6.929 kcal/mol. The DMS was also represented in terms of bipolar spherical harmonics. The PES was used to calculate the rotation-translation bound states of HF@C60, and good agreement was found relative to the available experimental data [A. Krachmalnicoff et al., Nat. Chem. 8, 953 (2016)] except for the splitting of the first rotational excitation levels. We propose an empirical adjustment to the PES in order to account for the experimentally observed symmetry breaking. The form of that effective PES is additive. We also propose an effective Hamiltonian with an adjusted rotational constant in order to quantitatively reproduce the experimental results including the splitting of the first rotational state. We use our models to compute the molecular volume polarizability of HF confined by C60 and obtain good agreement with experiment.

Potential energy and dipole moment surfaces for HF@C60: Prediction of spectral and electric response properties.

PubMed

Kalugina, Yulia N; Roy, Pierre-Nicholas

2017-12-28

We present a five-dimensional potential energy surface (PES) for the HF@C 60 system computed at the DF-LMP2/cc-pVTZ level of theory. We also calculated a five-dimensional dipole moment surface (DMS) based on DFT(PBE0)/cc-pVTZ calculations. The HF and C 60 molecules are considered rigid with bond length r HF = 0.9255 Å (gas phase ground rovibrational state geometry). The C 60 geometry is of I h symmetry. The ab initio points were fitted to obtain a PES in terms of bipolar spherical harmonics. The minimum of the PES corresponds to a geometry where the center of mass of HF is located 0.11 Å away from the center of the cage with an interaction energy of -6.929 kcal/mol. The DMS was also represented in terms of bipolar spherical harmonics. The PES was used to calculate the rotation-translation bound states of HF@C 60 , and good agreement was found relative to the available experimental data [A. Krachmalnicoff et al., Nat. Chem. 8, 953 (2016)] except for the splitting of the first rotational excitation levels. We propose an empirical adjustment to the PES in order to account for the experimentally observed symmetry breaking. The form of that effective PES is additive. We also propose an effective Hamiltonian with an adjusted rotational constant in order to quantitatively reproduce the experimental results including the splitting of the first rotational state. We use our models to compute the molecular volume polarizability of HF confined by C 60 and obtain good agreement with experiment.

An RBF-based compression method for image-based relighting.

PubMed

Leung, Chi-Sing; Wong, Tien-Tsin; Lam, Ping-Man; Choy, Kwok-Hung

2006-04-01

In image-based relighting, a pixel is associated with a number of sampled radiance values. This paper presents a two-level compression method. In the first level, the plenoptic property of a pixel is approximated by a spherical radial basis function (SRBF) network. That means that the spherical plenoptic function of each pixel is represented by a number of SRBF weights. In the second level, we apply a wavelet-based method to compress these SRBF weights. To reduce the visual artifact due to quantization noise, we develop a constrained method for estimating the SRBF weights. Our proposed approach is superior to JPEG, JPEG2000, and MPEG. Compared with the spherical harmonics approach, our approach has a lower complexity, while the visual quality is comparable. The real-time rendering method for our SRBF representation is also discussed.

Quiet Clean Short-haul Experimental Engine (QCSEE) whirl test of cam/harmonic pitch change actuation system

NASA Technical Reports Server (NTRS)

1976-01-01

A variable pitch fan actuation system, which incorporates a remote nacelle mounted blade angle regulator, was tested. The regulator drives a rotating fan mounted mechanical actuator through a flexible shaft and differential gear train. The actuator incorporates a high ratio harmonic drive attached to a multitrack spherical cam which changes blade pitch through individual cam follower arms attached to each blade trunnion. Testing of the actuator on a whirl rig, is reported. Results of tests conducted to verify that the unit satisfied the design requirements and was structurally adequate for use in an engine test are presented.

Quiet Clean Short-haul Experimental Engine (QCSEE): Hamilton Standard cam/harmonic drive variable pitch fan actuation system detail design report

NASA Technical Reports Server (NTRS)

1976-01-01

A variable pitch fan actuation system was designed which incorporates a remote nacelle-mounted blade angle regulator. The regulator drives a rotating fan-mounted mechanical actuator through a flexible shaft and differential gear train. The actuator incorporates a high ratio harmonic drive attached to a multitrack spherical cam which changes blade pitch through individual cam follower arms attached to each blade trunnion. Detail design parameters of the actuation system are presented. These include the following: design philosophies, operating limits, mechanical, hydraulic and thermal characteristics, mechanical efficiencies, materials, weights, lubrication, stress analyses, reliability and failure analyses.

Spherical and hyperspherical harmonics representation of van der Waals aggregates

NASA Astrophysics Data System (ADS)

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.

Empirical model of atomic nitrogen in the upper thermosphere

NASA Technical Reports Server (NTRS)

Engebretson, M. J.; Mauersberger, K.; Kayser, D. C.; Potter, W. E.; Nier, A. O.

1977-01-01

Atomic nitrogen number densities in the upper thermosphere measured by the open source neutral mass spectrometer (OSS) on Atmosphere Explorer-C during 1974 and part of 1975 have been used to construct a global empirical model at an altitude of 375 km based on a spherical harmonic expansion. The most evident features of the model are large diurnal and seasonal variations of atomic nitrogen and only a moderate and latitude-dependent density increase during periods of geomagnetic activity. Maximum and minimum N number densities at 375 km for periods of low solar activity are 3.6 x 10 to the 6th/cu cm at 1500 LST (local solar time) and low latitude in the summer hemisphere and 1.5 x 10 to the 5th/cu cm at 0200 LST at mid-latitudes in the winter hemisphere.

The Empirical Canadian High Arctic Ionospheric Model (E-CHAIM): Bottomside Parameterization

NASA Astrophysics Data System (ADS)

Themens, D. R.; Jayachandran, P. T.

2017-12-01

It is well known that the International Reference Ionosphere (IRI) suffers reduced accuracy in its representation of monthly median ionospheric electron density at high latitudes. These inaccuracies are believed to stem, at least in part, from a historical lack of data from these regions. Now, roughly thirty and forty years after the development of the original URSI and CCIR foF2 maps, respectively, there exists a much larger dataset of high latitude observations of ionospheric electron density. These new measurements come in the form of new ionosonde deployments, such as those of the Canadian High Arctic Ionospheric Network, the CHAMP, GRACE, and COSMIC radio occultation missions, and the construction of the Poker Flat, Resolute, and EISCAT Incoherent Scatter Radar systems. These new datasets afford an opportunity to revise the IRI's representation of the high latitude ionosphere. Using a spherical cap harmonic expansion to represent horizontal and diurnal variability and a Fourier expansion in day of year to represent seasonal variations, we have developed a new model of the bottomside ionosphere's electron density for the high latitude ionosphere, above 50N geomagnetic latitude. For the peak heights of the E and F1 layers (hmE and hmF1, respectively), current standards use a constant value for hmE and either use a single-parameter model for hmF1 (IRI) or scale hmF1 with the F peak (NeQuick). For E-CHAIM, we have diverged from this convention to account for the greater variability seen in these characteristics at high latitudes, opting to use a full spherical harmonic model description for each of these characteristics. For the description of the bottomside vertical electron density profile, we present a single-layer model with altitude-varying scale height. The scale height function is taken as the sum three scale height layer functions anchored to the F2 peak, hmF1, and hmE. This parameterization successfully reproduces the structure of the various bottomside layers while ensuring that the resulting electron density profile is free of strong vertical gradient artifacts and is doubly differentiable.

Revisiting the use of hyperdiffusivities in numerical dynamo models

NASA Astrophysics Data System (ADS)

Fournier, A.; Aubert, J.

2012-04-01

The groundbreaking numerical dynamo models of Glatzmaier & Roberts (1995) and Kuang & Bloxham (1997) received some criticism due to their use of hyperdiffusivities, whereby small scale processes artificially experience much stronger dissipation than large scale processes. This stronger dissipation they chose was anisotropic, in that it was only effective in the horizontal direction, and parameterized in spectral space using the following generic formula for any diffusive parameter ν ν(l) = ν0 ifl ≤ l0, ν(l) = ν0[1 + a(l- l0)n] ifl > l0, in which l is the spherical harmonic degree, ν0 is a reference value, l0 is the degree above which hyperdiffusivities start operating, and a and n are real numbers. Following the same choice as the studies mentioned above (which had most notably l0 = 0), Grote & Busse (2000) showed in a fully nonlinear context that the usage of hyperdiffusivities could lead to substantially different dynamics and magnetic field generation mechanisms. Without questioning the physical relevance of this parameterization of subgrid scale processes, we wish here to revisit the use of hyperdiffusivities (as defined mathematically above), on the account of the observation that today's models are run with a truncation at much larger spherical harmonic degree than early models. Consequently, they do not require hyperdiffusivities to kick in at the largest scales (l0 can be set to several tens). An exploration of those regions of parameter space less accessible to numerical models could therefore benefit from their use, provided they do not alter noticeably the largest scales of the dynamo (which are the ones expressing themselves in the record of the geomagnetic secular variation). We compare the statistics of a direct numerical simulation with the statistics of several hyperdiffusive simulations. In the prospect of exploring the parameter space and constructing statistics for their subsequent use for geomagnetic data assimilation practice, we conclude that a sensible use of hyperdiffusivities can lead to a much wanted decrease in computational cost, while not altering the nature of the solution.

Spectral analysis of the Earth's topographic potential via 2D-DFT: a new data-based degree variance model to degree 90,000

NASA Astrophysics Data System (ADS)

Rexer, Moritz; Hirt, Christian

2015-09-01

Classical degree variance models (such as Kaula's rule or the Tscherning-Rapp model) often rely on low-resolution gravity data and so are subject to extrapolation when used to describe the decay of the gravity field at short spatial scales. This paper presents a new degree variance model based on the recently published GGMplus near-global land areas 220 m resolution gravity maps (Geophys Res Lett 40(16):4279-4283, 2013). We investigate and use a 2D-DFT (discrete Fourier transform) approach to transform GGMplus gravity grids into degree variances. The method is described in detail and its approximation errors are studied using closed-loop experiments. Focus is placed on tiling, azimuth averaging, and windowing effects in the 2D-DFT method and on analytical fitting of degree variances. Approximation errors of the 2D-DFT procedure on the (spherical harmonic) degree variance are found to be at the 10-20 % level. The importance of the reference surface (sphere, ellipsoid or topography) of the gravity data for correct interpretation of degree variance spectra is highlighted. The effect of the underlying mass arrangement (spherical or ellipsoidal approximation) on the degree variances is found to be crucial at short spatial scales. A rule-of-thumb for transformation of spectra between spherical and ellipsoidal approximation is derived. Application of the 2D-DFT on GGMplus gravity maps yields a new degree variance model to degree 90,000. The model is supported by GRACE, GOCE, EGM2008 and forward-modelled gravity at 3 billion land points over all land areas within the SRTM data coverage and provides gravity signal variances at the surface of the topography. The model yields omission errors of 9 mGal for gravity (1.5 cm for geoid effects) at scales of 10 km, 4 mGal (1 mm) at 2-km scales, and 2 mGal (0.2 mm) at 1-km scales.

Gravity field models from kinematic orbits of CHAMP, GRACE and GOCE satellites

NASA Astrophysics Data System (ADS)

Bezděk, Aleš; Sebera, Josef; Klokočník, Jaroslav; Kostelecký, Jan

2014-02-01

The aim of our work is to generate Earth's gravity field models from GPS positions of low Earth orbiters. Our inversion method is based on Newton's second law, which relates the observed acceleration of the satellite with forces acting on it. The observed acceleration is obtained as numerical second derivative of kinematic positions. Observation equations are formulated using the gradient of the spherical harmonic expansion of the geopotential. Other forces are either modelled (lunisolar perturbations, tides) or provided by onboard measurements (nongravitational perturbations). From this linear regression model the geopotential harmonic coefficients are obtained. To this basic scheme of the acceleration approach we added some original elements, which may be useful in other inversion techniques as well. We tried to develop simple, straightforward and still statistically correct model of observations. (i) The model is linear in the harmonic coefficients, no a priori gravity field model is needed, no regularization is applied. (ii) We use the generalized least squares to successfully mitigate the strong amplification of noise due to numerical second derivative. (iii) The number of other fitted parameters is very small, in fact we use only daily biases, thus we can monitor their behaviour. (iv) GPS positions have correlated errors. The sample autocorrelation function and especially the partial autocorrelation function indicate suitability of an autoregressive model to represent the correlation structure. The decorrelation of residuals improved the accuracy of harmonic coefficients by a factor of 2-3. (v) We found it better to compute separate solutions in the three local reference frame directions than to compute them together at the same time; having obtained separate solutions for along-track, cross-track and radial components, we combine them using the normal matrices. Relative contribution of the along-track component to the combined solution is 50 percent on average. (vi) The computations were performed on an ordinary PC up to maximum degree and order 120. We applied the presented method to orbits of CHAMP and GRACE spanning seven years (2003-2009) and to two months of GOCE (Nov/Dec 2009). The obtained long-term static gravity field models are of similar or better quality compared to other published solutions. We also tried to extract the time-variable gravity signal from CHAMP and GRACE orbits. The acquired average annual signal shows clearly the continental areas with important and known hydrological variations.

The next generation Antarctic digital magnetic anomaly map

USGS Publications Warehouse

von Frese, R.R.B; Golynsky, A.V.; Kim, H.R.; Gaya-Piqué, L.; Thébault, E.; Chiappinii, M.; Ghidella, M.; Grunow, A.; ,

2007-01-01

S (Golynsky et al., 2001). This map synthesized over 7.1 million line-kms of survey data available up through 1999 from marine, airborne and Magsat satellite observations. Since the production of the initial map, a large number of new marine and airborne surveys and improved magnetic observations from the Ørsted and CHAMP satellite missions have become available. In addition, an improved core field model for the Antarctic has been developed to better isolate crustal anomalies in these data. The next generation compilation also will likely represent the magnetic survey observations of the region in terms of a high-resolution spherical cap harmonic model. In this paper, we review the progress and problems of developing an improved magnetic anomaly map to facilitate studies of the Antarctic crustal magnetic field

A study of the radiative transfer equation using a spherical harmonics-nodal collocation method

NASA Astrophysics Data System (ADS)

Capilla, M. T.; Talavera, C. F.; Ginestar, D.; Verdú, G.

2017-03-01

Optical tomography has found many medical applications that need to know how the photons interact with the different tissues. The majority of the photon transport simulations are done using the diffusion approximation, but this approximation has a limited validity when optical properties of the different tissues present large gradients, when structures near the photons source are studied or when anisotropic scattering has to be taken into account. As an alternative to the diffusion model, the PL equations for the radiative transfer problem are studied. These equations are discretized in a rectangular mesh using a nodal collocation method. The performance of this model is studied by solving different 1D and 2D benchmark problems of light propagation in tissue having media with isotropic and anisotropic scattering.

A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation.

PubMed

Tie, Junbo; Cao, Juliang; Chang, Lubing; Cai, Shaokun; Wu, Meiping; Lian, Junxiang

2018-03-16

Compensation of gravity disturbance can improve the precision of inertial navigation, but the effect of compensation will decrease due to the accelerometer bias, and estimation of the accelerometer bias is a crucial issue in gravity disturbance compensation. This paper first investigates the effect of accelerometer bias on gravity disturbance compensation, and the situation in which the accelerometer bias should be estimated is established. The accelerometer bias is estimated from the gravity vector measurement, and a model of measurement noise in gravity vector measurement is built. Based on this model, accelerometer bias is separated from the gravity vector measurement error by the method of least squares. Horizontal gravity disturbances are calculated through EGM2008 spherical harmonic model to build the simulation scene, and the simulation results indicate that precise estimations of the accelerometer bias can be obtained with the proposed method.

A Model of Gravity Vector Measurement Noise for Estimating Accelerometer Bias in Gravity Disturbance Compensation

PubMed Central

Cao, Juliang; Cai, Shaokun; Wu, Meiping; Lian, Junxiang

2018-01-01

Compensation of gravity disturbance can improve the precision of inertial navigation, but the effect of compensation will decrease due to the accelerometer bias, and estimation of the accelerometer bias is a crucial issue in gravity disturbance compensation. This paper first investigates the effect of accelerometer bias on gravity disturbance compensation, and the situation in which the accelerometer bias should be estimated is established. The accelerometer bias is estimated from the gravity vector measurement, and a model of measurement noise in gravity vector measurement is built. Based on this model, accelerometer bias is separated from the gravity vector measurement error by the method of least squares. Horizontal gravity disturbances are calculated through EGM2008 spherical harmonic model to build the simulation scene, and the simulation results indicate that precise estimations of the accelerometer bias can be obtained with the proposed method. PMID:29547552

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

NASA Technical Reports Server (NTRS)

Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.

1995-01-01

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

Algebraic special functions and SO(3,2)

DOE Office of Scientific and Technical Information (OSTI.GOV)

Celeghini, E., E-mail: celeghini@fi.infn.it; Olmo, M.A. del, E-mail: olmo@fta.uva.es

2013-06-15

A ladder structure of operators is presented for the associated Legendre polynomials and the sphericas harmonics. In both cases these operators belong to the irreducible representation of the Lie algebra so(3,2) with quadratic Casimir equals to −5/4. As both are also bases of square-integrable functions, the universal enveloping algebra of so(3,2) is thus shown to be homomorphic to the space of linear operators acting on the L{sup 2} functions defined on (−1,1)×Z and on the sphere S{sup 2}, respectively. The presence of a ladder structure is suggested to be the general condition to obtain a Lie algebra representation defining inmore » this way the “algebraic special functions” that are proposed to be the connection between Lie algebras and square-integrable functions so that the space of linear operators on the L{sup 2} functions is homomorphic to the universal enveloping algebra. The passage to the group, by means of the exponential map, shows that the associated Legendre polynomials and the spherical harmonics support the corresponding unitary irreducible representation of the group SO(3,2). -- Highlights: •The algebraic ladder structure is constructed for the associated Legendre polynomials (ALP). •ALP and spherical harmonics support a unitary irreducible SO(3,2)-representation. •A ladder structure is the condition to get a Lie group representation defining “algebraic special functions”. •The “algebraic special functions” connect Lie algebras and L{sup 2} functions.« less

High coupling efficiency of foam spherical hohlraum driven by 2ω laser light

NASA Astrophysics Data System (ADS)

Chen, Yao-Hua; Lan, Ke; Zheng, Wanguo; Campbell, E. M.

2018-02-01

The majority of solid state laser facilities built for laser fusion research irradiate targets with third harmonic light (0.35 μm) up-converted from the fundamental Nd wavelength at 1.05 μm. The motivation for this choice of wavelength is improved laser-plasma coupling. Significant disadvantages to this choice of wavelength are the reduced damage threshold of optical components and the efficiency of energy conversion to third harmonic light. Both these issues are significantly improved if second harmonic (0.53 μm) radiation is used, but theory and experiments have shown lower optical to x-ray energy conversion efficiency and increased levels of laser-plasma instabilities, resulting in reduced laser-target coupling. In this letter, we propose to use a 0.53 μm laser for the laser ignition facilities and use a low density foam wall to increase the coupling efficiency from the laser to the capsule and present two-dimensional radiation-hydrodynamic simulations of 0.53 μm laser light irradiating an octahedral-spherical hohlraum with a low density foam wall. The simulations show that the reduced optical depth of the foam wall leads to an increased laser-light conversion into thermal x-rays and about 10% higher radiation flux on the capsule than that achieved with 0.35 μm light irradiating a solid density wall commonly used in laser indirect drive fusion research. The details of the simulations and their implications and suggestions for wavelength scaling coupled with innovative hohlraum designs will be discussed.

Method and apparatus for measuring the NMR spectrum of an orientationally disordered sample

DOEpatents

Pines, Alexander; Samoson, Ago

1990-01-01

An improved NMR probe and method are described which substantially improve the resolution of NMR measurements made on powdered or amorphous or otherwise oreintationally disordered samples. The apparatus mechanically varies the orientation of the sample such that the time average of two or more sets of spherical harmonic functions is zero.

4D Hyperspherical Harmonic (HyperSPHARM) Representation of Surface Anatomy: A Holistic Treatment of Multiple Disconnected Anatomical Structures

PubMed Central

Hosseinbor, A. Pasha; Chung, Moo K.; Koay, Cheng Guan; Schaefer, Stacey M.; van Reekum, Carien M.; Schmitz, Lara Peschke; Sutterer, Matt; Alexander, Andrew L.; Davidson, Richard J.

2015-01-01

Image-based parcellation of the brain often leads to multiple disconnected anatomical structures, which pose significant challenges for analyses of morphological shapes. Existing shape models, such as the widely used spherical harmonic (SPHARM) representation, assume topological invariance, so are unable to simultaneously parameterize multiple disjoint structures. In such a situation, SPHARM has to be applied separately to each individual structure. We present a novel surface parameterization technique using 4D hyperspherical harmonics in representing multiple disjoint objects as a single analytic function, terming it HyperSPHARM. The underlying idea behind Hyper-SPHARM is to stereographically project an entire collection of disjoint 3D objects onto the 4D hypersphere and subsequently simultaneously parameterize them with the 4D hyperspherical harmonics. Hence, HyperSPHARM allows for a holistic treatment of multiple disjoint objects, unlike SPHARM. In an imaging dataset of healthy adult human brains, we apply HyperSPHARM to the hippocampi and amygdalae. The HyperSPHARM representations are employed as a data smoothing technique, while the HyperSPHARM coefficients are utilized in a support vector machine setting for object classification. HyperSPHARM yields nearly identical results as SPHARM, as will be shown in the paper. Its key advantage over SPHARM lies computationally; Hyper-SPHARM possess greater computational efficiency than SPHARM because it can parameterize multiple disjoint structures using much fewer basis functions and stereographic projection obviates SPHARM's burdensome surface flattening. In addition, HyperSPHARM can handle any type of topology, unlike SPHARM, whose analysis is confined to topologically invariant structures. PMID:25828650

Normal Gravity Fields and Equipotential Ellipsoids of Small Objects in the Solar System: A Closed-form Solution in Ellipsoidal Harmonics up to the Second Degree

NASA Astrophysics Data System (ADS)

Hu, Xuanyu

2017-11-01

We propose a definition for the normal gravity fields and normal figures of small objects in the solar system, such as asteroids, cometary nuclei, and planetary moons. Their gravity fields are represented as series of ellipsoidal harmonics, ensuring more robust field evaluation in the proximity of an arbitrary, convex shape than using spherical harmonics. The normal gravity field, approximate to the actual field, can be described by a finite series of three terms, that is, degree zero, and the zonal and sectoral harmonics of degree two. The normal gravity is that of an equipotential ellipsoid, defined as the normal ellipsoid of the body. The normal ellipsoid may be distinct from the actual figure. We present a rationale for specifying and a numerical method for determining the parameters of the normal ellipsoid. The definition presented here generalizes the convention of the normal spheroid of a large, hydrostatically equilibrated planet, such as Earth. Modeling the normal gravity and the normal ellipsoid is relevant to studying the formation of the “rubble pile” objects, which may have been accreted, or reorganized after disruption, under self-gravitation. While the proposed methodology applies to convex, approximately ellipsoidal objects, those bi-lobed objects can be treated as contact binaries comprising individual convex subunits. We study an exemplary case of the nearly ellipsoidal Martian moon, Phobos, subject to strong tidal influence in its present orbit around Mars. The results allude to the formation of Phobos via gravitational accretion at some further distance from Mars.

Global accuracy estimates of point and mean undulation differences obtained from gravity disturbances, gravity anomalies and potential coefficients

NASA Technical Reports Server (NTRS)

Jekeli, C.

1979-01-01

Through the method of truncation functions, the oceanic geoid undulation is divided into two constituents: an inner zone contribution expressed as an integral of surface gravity disturbances over a spherical cap; and an outer zone contribution derived from a finite set of potential harmonic coefficients. Global, average error estimates are formulated for undulation differences, thereby providing accuracies for a relative geoid. The error analysis focuses on the outer zone contribution for which the potential coefficient errors are modeled. The method of computing undulations based on gravity disturbance data for the inner zone is compared to the similar, conventional method which presupposes gravity anomaly data within this zone.

Properties of thermospheric gravity waves on earth, Venus and Mars

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Pesnell, W. D.

1992-01-01

A spectral model with spherical harmonics and Fourier components that can simulate atmospheric perturbations in the global geometry of a multiconstituent atmosphere is presented. The boundaries are the planetary surface where the transport velocities vanish and the exobase where molecular heat conduction and viscosity dominate. The time consuming integration of the conservation equations is reduced to computing the transfer function (TF) which describes the dynamic properties of the medium divorced from the complexities in the temporal and horizontal variations of the excitation source. Given the TF, the atmospheric response to a chosen source distribution is then obtained in short order. Theoretical studies are presented to illuminate some properties of gravity waves on earth, Venus and Mars.

The Mystery of the Mars North Polar Gravity-Topography Correlation(Or Lack Thereof)

NASA Technical Reports Server (NTRS)

Phillips, R. J.; Sjogren, W. L.; Johnson, C. L.

1999-01-01

Maps of moderately high resolution gravity data obtained from the Mars Global Surveyor (MGS) gravity calibration orbit campaign and high precision topography obtained from the Mars Orbiter Laser Altimeter (MOLA) experiment reveal relationships between gravity and topography in high northern latitudes of Mars. Figure 1 shows the results of a JPL spherical harmonic gravity model bandpass filtered between degrees 6 and 50 contoured over a MOLA topographic image. A positive gravity anomaly exists over the main North Polar cap, but there are at least six additional positive gravity anomalies, as well as a number of smaller negative anomalies, with no obvious correlation to topography. Additional information is contained in the original extended abstract.

Acoustic behavior of Halobacterium salinarum gas vesicles in the high frequency range: experiments and modeling

PubMed Central

Cherin, Emmanuel; Melis, Johan M.; Bourdeau, Raymond W.; Yin, Melissa; Kochmann, Dennis M.; Foster, F. Stuart; Shapiro, Mikhail G.

2017-01-01

Gas vesicles are a new and unique class of biologically derived ultrasound contrast agents with sub-micron size whose acoustic properties have not been fully elucidated. In this study, we investigated the acoustic collapse pressure and behavior of Halobacterium salinarum gas vesicles at transmit center frequencies ranging from 12.5 to 27.5 MHz. The acoustic collapse pressure was found to be above 550 kPa at all frequencies, 9 fold higher than the critical pressure observed in hydrostatic conditions. We show that gas vesicles behave non-linearly when exposed to ultrasound at incident pressure ranging from 160 kPa to the collapse pressure, and generate second harmonic amplitudes of −2 to −6 dB below the fundamental in media with viscosities ranging from 0.89 to 8 mPa.s. Simulations performed using a Rayleigh-Plesset type model accounting for buckling, and a dynamic finite element analysis, suggest that buckling is the mechanism behind the generation of harmonics. We found good agreement between the level of second harmonic relative to the fundamental measured at 20 MHz and the Rayleigh-Plesset model predictions. Finite element simulations extended these findings to a non-spherical geometry, confirmed that the acoustic buckling pressure corresponds to the critical pressure in hydrostatic conditions, and support the hypothesis of limited gas flow across the GV shell during the compression phase in the frequency range investigated. From simulations, estimates of GV bandwidth-limited scattering indicate that a single GV has a scattering cross-section comparable to that of a red blood cell. These findings will inform the development of GV-based contrast agents and pulse sequences to optimize their detection with ultrasound. PMID:28258771

High-order nonlinear susceptibilities of He

NASA Astrophysics Data System (ADS)

Liu, W.-C.; Clark, Charles W.

1996-05-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. We have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s^2, within the framework of Rayleigh-Schrödinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Pont and Shakeshaft (M. Pont and R. Shakeshaft, Phy. Rev. A 51), 257 (1995), and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used(J. D. Baker, Master thesis, U. Delaware (1988); J. D. Baker, R. N. Hill, and J. D. Morgan, AIP Conference Proceedings 189) 123(1989); the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals.

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

NASA Astrophysics Data System (ADS)

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.

An Online Gravity Modeling Method Applied for High Precision Free-INS

PubMed Central

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

2016-01-01

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS. PMID:27669261

An Online Gravity Modeling Method Applied for High Precision Free-INS.

PubMed

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

2016-09-23

For real-time solution of inertial navigation system (INS), the high-degree spherical harmonic gravity model (SHM) is not applicable because of its time and space complexity, in which traditional normal gravity model (NGM) has been the dominant technique for gravity compensation. In this paper, a two-dimensional second-order polynomial model is derived from SHM according to the approximate linear characteristic of regional disturbing potential. Firstly, deflections of vertical (DOVs) on dense grids are calculated with SHM in an external computer. And then, the polynomial coefficients are obtained using these DOVs. To achieve global navigation, the coefficients and applicable region of polynomial model are both updated synchronously in above computer. Compared with high-degree SHM, the polynomial model takes less storage and computational time at the expense of minor precision. Meanwhile, the model is more accurate than NGM. Finally, numerical test and INS experiment show that the proposed method outperforms traditional gravity models applied for high precision free-INS.

Project MANTIS: A MANTle Induction Simulator for coupling geodynamic and electromagnetic modeling

NASA Astrophysics Data System (ADS)

Weiss, C. J.

2009-12-01

A key component to testing geodynamic hypotheses resulting from the 3D mantle convection simulations is the ability to easily translate the predicted physiochemical state to the model space relevant for an independent geophysical observation, such as earth's seismic, geodetic or electromagnetic response. In this contribution a new parallel code for simulating low-frequency, global-scale electromagnetic induction phenomena is introduced that has the same Earth discretization as the popular CitcomS mantle convection code. Hence, projection of the CitcomS model into the model space of electrical conductivity is greatly simplified, and focuses solely on the node-to-node, physics-based relationship between these Earth parameters without the need for "upscaling", "downscaling", averaging or harmonizing with some other model basis such as spherical harmonics. Preliminary performance tests of the MANTIS code on shared and distributed memory parallel compute platforms shows favorable scaling (>70% efficiency) for up to 500 processors. As with CitcomS, an OpenDX visualization widget (VISMAN) is also provided for 3D rendering and interactive interrogation of model results. Details of the MANTIS code will be briefly discussed here, focusing on compatibility with CitcomS modeling, as will be preliminary results in which the electromagnetic response of a CitcomS model is evaluated. VISMAN rendering of electrical tomography-derived electrical conductivity model overlain by an a 1x1 deg crustal conductivity map. Grey scale represents the log_10 magnitude of conductivity [S/m]. Arrows are horiztonal components of a hypothetical magnetospheric source field used to electromagnetically excite the conductivity model.

Thermodynamic Theory of Spherically Trapped Coulomb Clusters

NASA Astrophysics Data System (ADS)

Wrighton, Jeffrey; Dufty, James; Bonitz, Michael; K"{A}Hlert, Hanno

2009-11-01

The radial density profile of a finite number of identical charged particles confined in a harmonic trap is computed over a wide ranges of temperatures (Coulomb coupling) and particle numbers. At low temperatures these systems form a Coulomb crystal with spherical shell structure which has been observed in ultracold trapped ions and in dusty plasmas. The shell structure is readily reproduced in simulations. However, analytical theories which used a mean field approachfootnotetext[1]C. Henning et al., Phys. Rev. E 74, 056403 (2006) or a local density approximationfootnotetext[2]C. Henning et al., Phys. Rev. E 76, 036404 (2007) have, so far, only been able to reproduce the average density profile. Here we present an approach to Coulomb correlations based on the hypernetted chain approximation with additional bridge diagrams. It is demonstrated that this model reproduces the correct shell structure within a few percent and provides the basis for a thermodynamic theory of Coulomb clusters in the strongly coupled fluid state.footnotetext[3]J. Wrighton, J.W. Dufty, H. K"ahlert and M. Bonitz, J. Phys. A 42, 214052 (2009) and Phys. Rev. E (2009) (to be submitted)

LCS-1: a high-resolution global model of the lithospheric magnetic field derived from CHAMP and Swarm satellite observations

NASA Astrophysics Data System (ADS)

Olsen, Nils; Ravat, Dhananjay; Finlay, Christopher C.; Kother, Livia K.

2017-12-01

We derive a new model, named LCS-1, of Earth's lithospheric field based on four years (2006 September-2010 September) of magnetic observations taken by the CHAMP satellite at altitudes lower than 350 km, as well as almost three years (2014 April-2016 December) of measurements taken by the two lower Swarm satellites Alpha and Charlie. The model is determined entirely from magnetic 'gradient' data (approximated by finite differences): the north-south gradient is approximated by first differences of 15 s along-track data (for CHAMP and each of the two Swarm satellites), while the east-west gradient is approximated by the difference between observations taken by Swarm Alpha and Charlie. In total, we used 6.2 mio data points. The model is parametrized by 35 000 equivalent point sources located on an almost equal-area grid at a depth of 100 km below the surface (WGS84 ellipsoid). The amplitudes of these point sources are determined by minimizing the misfit to the magnetic satellite 'gradient' data together with the global average of |Br| at the ellipsoid surface (i.e. applying an L1 model regularization of Br). In a final step, we transform the point-source representation to a spherical harmonic expansion. The model shows very good agreement with previous satellite-derived lithospheric field models at low degree (degree correlation above 0.8 for degrees n ≤ 133). Comparison with independent near-surface aeromagnetic data from Australia yields good agreement (coherence >0.55) at horizontal wavelengths down to at least 250 km, corresponding to spherical harmonic degree n ≈ 160. The LCS-1 vertical component and field intensity anomaly maps at Earth's surface show similar features to those exhibited by the WDMAM2 and EMM2015 lithospheric field models truncated at degree 185 in regions where they include near-surface data and provide unprecedented detail where they do not. Example regions of improvement include the Bangui anomaly region in central Africa, the west African cratons, the East African Rift region, the Bay of Bengal, the southern 90°E ridge, the Cretaceous quiet zone south of the Walvis Ridge and the younger parts of the South Atlantic.

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

DOE Office of Scientific and Technical Information (OSTI.GOV)

Takahashi, Kazuya; Yamada, Shoichi, E-mail: ktakahashi@heap.phys.waseda.ac.jp

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 solvedmore » 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.« less

Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models

NASA Astrophysics Data System (ADS)

Blackman, Jonathan; Field, Scott E.; Galley, Chad R.; Szilágyi, Béla; Scheel, Mark A.; Tiglio, Manuel; Hemberger, Daniel A.

2015-09-01

Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic -2Yℓm waveform modes resolved by the NR code up to ℓ=8 . We compare our surrogate model to effective one body waveforms from 50 M⊙ to 300 M⊙ for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).

Initial geomagnetic field model from Magsat vector data

NASA Technical Reports Server (NTRS)

Langel, R. A.; Mead, G. D.; Lancaster, E. R.; Estes, R. H.; Fabiano, E. B.

1980-01-01

Magsat data from the magnetically quiet days of November 5-6, 1979, were used to derive a thirteenth degree and order spherical harmonic geomagnetic field model, MGST(6/80). The model utilized both scalar and high-accuracy vector data and fit that data with root-mean-square deviations of 8.2, 6.9, 7.6 and 7.4 nT for the scalar magnitude, B(r), B(theta), and B(phi), respectively. The model includes the three first-order coefficients of the external field. Comparison with averaged Dst indicates that zero Dst corresponds with 25 nT of horizontal field from external sources. When compared with earlier models, the earth's dipole moment continues to decrease at a rate of about 26 nT/yr. Evaluation of earlier models with Magsat data shows that the scalar field at the Magsat epoch is best predicted by the POGO(2/72) model but that the WC80, AWC/75 and IGS/75 are better for predicting vector fields.

Fast and Accurate Prediction of Numerical Relativity Waveforms from Binary Black Hole Coalescences Using Surrogate Models.

PubMed

Blackman, Jonathan; Field, Scott E; Galley, Chad R; Szilágyi, Béla; Scheel, Mark A; Tiglio, Manuel; Hemberger, Daniel A

2015-09-18

Simulating a binary black hole coalescence by solving Einstein's equations is computationally expensive, requiring days to months of supercomputing time. Using reduced order modeling techniques, we construct an accurate surrogate model, which is evaluated in a millisecond to a second, for numerical relativity (NR) waveforms from nonspinning binary black hole coalescences with mass ratios in [1, 10] and durations corresponding to about 15 orbits before merger. We assess the model's uncertainty and show that our modeling strategy predicts NR waveforms not used for the surrogate's training with errors nearly as small as the numerical error of the NR code. Our model includes all spherical-harmonic _{-2}Y_{ℓm} waveform modes resolved by the NR code up to ℓ=8. We compare our surrogate model to effective one body waveforms from 50M_{⊙} to 300M_{⊙} for advanced LIGO detectors and find that the surrogate is always more faithful (by at least an order of magnitude in most cases).

Label-free three-dimensional imaging of cell nucleus using third-harmonic generation microscopy

NASA Astrophysics Data System (ADS)

Lin, Jian; Zheng, Wei; Wang, Zi; Huang, Zhiwei

2014-09-01

We report the implementation of the combined third-harmonic generation (THG) and two-photon excited fluorescence (TPEF) microscopy for label-free three-dimensional (3-D) imaging of cell nucleus morphological changes in liver tissue. THG imaging shows regular spherical shapes of normal hepatocytes nuclei with inner chromatin structures while revealing the condensation of chromatins and nuclear fragmentations in hepatocytes of diseased liver tissue. Colocalized THG and TPEF imaging provides complementary information of cell nuclei and cytoplasm in tissue. This work suggests that 3-D THG microscopy has the potential for quantitative analysis of nuclear morphology in cells at a submicron-resolution without the need for DNA staining.

Label-free three-dimensional imaging of cell nucleus using third-harmonic generation microscopy

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Jian; Zheng, Wei; Wang, Zi

2014-09-08

We report the implementation of the combined third-harmonic generation (THG) and two-photon excited fluorescence (TPEF) microscopy for label-free three-dimensional (3-D) imaging of cell nucleus morphological changes in liver tissue. THG imaging shows regular spherical shapes of normal hepatocytes nuclei with inner chromatin structures while revealing the condensation of chromatins and nuclear fragmentations in hepatocytes of diseased liver tissue. Colocalized THG and TPEF imaging provides complementary information of cell nuclei and cytoplasm in tissue. This work suggests that 3-D THG microscopy has the potential for quantitative analysis of nuclear morphology in cells at a submicron-resolution without the need for DNA staining.

Estimation and Validation of Oceanic Mass Circulation from the GRACE Mission

NASA Technical Reports Server (NTRS)

Boy, J.-P.; Rowlands, D. D.; Sabaka, T. J.; Luthcke, S. B.; Lemoine, F. G.

2011-01-01

Since the launch of the Gravity Recovery And Climate Experiment (GRACE) in March 2002, the Earth's surface mass variations have been monitored with unprecedented accuracy and resolution. Compared to the classical spherical harmonic solutions, global high-resolution mascon solutions allows the retrieval of mass variations with higher spatial and temporal sampling (2 degrees and 10 days). We present here the validation of the GRACE global mascon solutions by comparing mass estimates to a set of about 100 ocean bottom pressure (OSP) records, and show that the forward modelling of continental hydrology prior to the inversion of the K-band range rate data allows better estimates of ocean mass variations. We also validate our GRACE results to OSP variations modelled by different state-of-the-art ocean general circulation models, including ECCO (Estimating the Circulation and Climate of the Ocean) and operational and reanalysis from the MERCATOR project.

Cluster/Peace Electrons Velocity Distribution Function: Modeling the Strahl in the Solar Wind

NASA Technical Reports Server (NTRS)

Figueroa-Vinas, Adolfo; Gurgiolo, Chris; Goldstein, Melvyn L.

2008-01-01

We present a study of kinetic properties of the strahl electron velocity distribution functions (VDF's) in the solar wind. These are used to investigate the pitch-angle scattering and stability of the population to interactions with electromagnetic (whistler) fluctuations. The study is based on high time resolution data from the Cluster/PEACE electron spectrometer. Our study focuses on the mechanisms that control and regulate the pitch-angle and stability of strahl electrons in the solar wind; mechanisms that are not yet well understood. Various parameters are investigated such as the electron heat-flux and temperature anisotropy. The goal is to check whether the strahl electrons are constrained by some instability (e.g., the whistler instability), or are maintained by other types of processes. The electron heat-flux and temperature anisotropy are determined by fitting the VDF's to a spectral spherical harmonic model from which the moments are derived directly from the model coefficients.

A stochastic-dynamic model for global atmospheric mass field statistics

NASA Technical Reports Server (NTRS)

Ghil, M.; Balgovind, R.; Kalnay-Rivas, E.

1981-01-01

A model that yields the spatial correlation structure of atmospheric mass field forecast errors was developed. The model is governed by the potential vorticity equation forced by random noise. Expansion in spherical harmonics and correlation function was computed analytically using the expansion coefficients. The finite difference equivalent was solved using a fast Poisson solver and the correlation function was computed using stratified sampling of the individual realization of F(omega) and hence of phi(omega). A higher order equation for gamma was derived and solved directly in finite differences by two successive applications of the fast Poisson solver. The methods were compared for accuracy and efficiency and the third method was chosen as clearly superior. The results agree well with the latitude dependence of observed atmospheric correlation data. The value of the parameter c sub o which gives the best fit to the data is close to the value expected from dynamical considerations.

The Lunar Crustal Thickness from Analysis of the Lunar Prospector Gravity and Clementine Topography Datasets

NASA Technical Reports Server (NTRS)

Asmar, S.; Schubert, G.; Konopliv, A.; Moore, W.

1999-01-01

The Lunar Prospector spacecraft has mapped the gravity field of the Moon to a level of resolution never achieved before, and a spherical harmonic representation to degree and order 100 is available. When combined with the topography dataset produced by the Clementine mission, the resulting Bouguer anomaly map is interpreted to model the thickness of the lunar crust. Such models are crucial to understanding the lunar thermal history and the formation of geological features such as mascon basins, several more of which have been newly discovered from this dataset. A two-layer planetary model was used to compute the variations of the depth to the lunar Moho. The thickness values ranged from near 0 to 120 km. There is significant agreement with previous work using the Clementine gravitational field data with differences in specific locations such as South Pole-Aitken Basin, for example.

Odd Harmonics in Exoplanet Photometry: Weather or Artifact?

NASA Astrophysics Data System (ADS)

Chayes, Victoria; Cowan, Nicholas; Bouffard, Élie; Haggard, Hal

2017-01-01

In the Fourier decomposition of light curves of exoplanets observed by the Kepler mission, one expects to see power in the first mode, from the planet orbiting the star, and the second mode, from ellipsoidal variations. Observations of power in the third mode of planets such as HAT-P-7b and Kepler-13Ab are as of yet unexplained. Using a spherical harmonic basis we analyze planet maps to find their corresponding light curves and show that no planet observed edge-on can produce these third harmonics with either reflected light or thermal emissions. Further numerical and analytic calculations put upper bounds on the power in the third mode that can be produced by planets not transiting perfectly edge-on, or with time-variable maps. We find the expected order of magnitude of these contributions to be at most two orders of magnitude below the first harmonic. The North-South asymmetric features or time-variable maps that could produce such harmonics would suggest exoplanetary weather if observed. However, more careful analysis of tidal effects on the stars of HAT-P-7b and Kepler-13Ab suggest that these particular harmonics are stellar in origin. Élie Bouffard was supported by an iREx summer internship. We thank the International Space Science Institute in Bern, Switzerland, for hosting the Exo-Cartography workshop series.

The Temporal Morphology of Infrasound Propagation

NASA Astrophysics Data System (ADS)

Drob, Douglas P.; Garcés, Milton; Hedlin, Michael; Brachet, Nicolas

2010-05-01

Expert knowledge suggests that the performance of automated infrasound event association and source location algorithms could be greatly improved by the ability to continually update station travel-time curves to properly account for the hourly, daily, and seasonal changes of the atmospheric state. With the goal of reducing false alarm rates and improving network detection capability we endeavor to develop, validate, and integrate this capability into infrasound processing operations at the International Data Centre of the Comprehensive Nuclear Test-Ban Treaty Organization. Numerous studies have demonstrated that incorporation of hybrid ground-to-space (G2S) enviromental specifications in numerical calculations of infrasound signal travel time and azimuth deviation yields significantly improved results over that of climatological atmospheric specifications, specifically for tropospheric and stratospheric modes. A robust infrastructure currently exists to generate hybrid G2S vector spherical harmonic coefficients, based on existing operational and emperical models on a real-time basis (every 3- to 6-hours) (D rob et al., 2003). Thus the next requirement in this endeavor is to refine numerical procedures to calculate infrasound propagation characteristics for robust automatic infrasound arrival identification and network detection, location, and characterization algorithms. We present results from a new code that integrates the local (range-independent) τp ray equations to provide travel time, range, turning point, and azimuth deviation for any location on the globe given a G2S vector spherical harmonic coefficient set. The code employs an accurate numerical technique capable of handling square-root singularities. We investigate the seasonal variability of propagation characteristics over a five-year time series for two different stations within the International Monitoring System with the aim of understanding the capabilities of current working knowledge of the atmosphere and infrasound propagation models. The statistical behaviors or occurrence frequency of various propagation configurations are discussed. Representative examples of some of these propagation configuration states are also shown.

A new model for the (geo)magnetic power spectrum, with application to planetary dynamo radii

NASA Astrophysics Data System (ADS)

Langlais, Benoit; Amit, Hagay; Larnier, Hugo; Thébault, Erwan; Mocquet, Antoine

2014-09-01

We propose two new analytical expressions to fit the Mauersberger-Lowes geomagnetic field spectrum at the core-mantle boundary. These can be used to estimate the radius of the outer liquid core where the geodynamo operates, or more generally the radius of the planetary dynamo regions. We show that two sub-families of the geomagnetic field are independent of spherical harmonics degree n at the core-mantle boundary and exhibit flat spectra. The first is the non-zonal field, i.e., for spherical harmonics order m different from zero. The second is the quadrupole family, i.e., n+m even. The flatness of their spectra is motivated by the nearly axisymmetric time-average paleomagnetic field (for the non-zonal field) and the dominance of rotational effects in core dynamics (for the quadrupole family). We test our two expressions with two approaches using the reference case of the Earth. First we estimate at the seismic core radius the agreement between the actual spectrum and the theoretical one. Second we estimate the magnetic core radius, where the spectrum flattens. We show that both sub-families offer a better agreement with the actual spectrum compared with previously proposed analytical expressions, and predict a magnetic core radius within less than 10 km of the Earth's seismic core radius. These new expressions supersede previous ones to infer the core radius from geomagnetic field information because the low degree terms are not ignored. Our formalism is then applied to infer the radius of the dynamo regions on Jupiter, Saturn, Uranus and Neptune. The axisymmetric nature of the magnetic field of Saturn prevents the use of the non-zonal expression. For the three other planets both expressions converge and offer independent constraints on the internal structure of these planets. These non-zonal and quadrupole family expressions may be implemented to extrapolate the geomagnetic field spectrum beyond observable degrees, or to further regularize magnetic field models constructed from modern or historical observations.

Fast and accurate reference-free alignment of subtomograms.

PubMed

Chen, Yuxiang; Pfeffer, Stefan; Hrabe, Thomas; Schuller, Jan Michael; Förster, Friedrich

2013-06-01

In cryoelectron tomography alignment and averaging of subtomograms, each dnepicting the same macromolecule, improves the resolution compared to the individual subtomogram. Major challenges of subtomogram alignment are noise enhancement due to overfitting, the bias of an initial reference in the iterative alignment process, and the computational cost of processing increasingly large amounts of data. Here, we propose an efficient and accurate alignment algorithm via a generalized convolution theorem, which allows computation of a constrained correlation function using spherical harmonics. This formulation increases computational speed of rotational matching dramatically compared to rotation search in Cartesian space without sacrificing accuracy in contrast to other spherical harmonic based approaches. Using this sampling method, a reference-free alignment procedure is proposed to tackle reference bias and overfitting, which also includes contrast transfer function correction by Wiener filtering. Application of the method to simulated data allowed us to obtain resolutions near the ground truth. For two experimental datasets, ribosomes from yeast lysate and purified 20S proteasomes, we achieved reconstructions of approximately 20Å and 16Å, respectively. The software is ready-to-use and made public to the community. Copyright © 2013 Elsevier Inc. All rights reserved.

Multi-Coil Shimming of the Mouse Brain

PubMed Central

Juchem, Christoph; Brown, Peter B.; Nixon, Terence W.; McIntyre, Scott; Rothman, Douglas L.; de Graaf, Robin A.

2011-01-01

MR imaging and spectroscopy allow the non-invasive measurement of brain function and physiology, but excellent magnetic field homogeneity is required for meaningful results. The homogenization of the magnetic field distribution in the mouse brain (i.e. shimming) is a difficult task due to complex susceptibility-induced field distortions combined with the small size of the object. To date, the achievement of satisfactory whole brain shimming in the mouse remains a major challenge. The magnetic fields generated by a set of 48 circular coils (diameter 13 mm) that were arranged in a cylinder-shaped pattern of 32 mm diameter and driven with individual dynamic current ranges of ±1 A are shown to be capable of substantially reducing the field distortions encountered in the mouse brain at 9.4 Tesla. Static multi-coil shim fields allowed the reduction of the standard deviation of Larmor frequencies by 31% compared to second order spherical harmonics shimming and a 66% narrowing was achieved with the slice-specific application of the multi-coil shimming with a dynamic approach. For gradient echo imaging, multi-coil shimming minimized shim-related signal voids in the brain periphery and allowed overall signal gains of up to 51% compared to spherical harmonics shimming. PMID:21442653

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

PubMed

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.

The effects of patch-potentials on the gravity probe B gyroscopes.

PubMed

Buchman, S; Turneaure, J P

2011-07-01

Gravity probe B (GP-B) was designed to measure the geodetic and frame dragging precessions of gyroscopes in the near field of the Earth using a drag-free satellite in a 642 km polar orbit. Four electrostatically suspended cryogenic gyroscopes were designed to measure the precession of the local inertial frame of reference with a disturbance drift of about 0.1 marc sec/yr-0.2 marc sec/yr. A number of unexpected gyro disturbance effects were observed during the mission: spin-speed and polhode damping, misalignment and roll-polhode resonance torques, forces acting on the gyroscopes, and anomalies in the measurement of the gyro potentials. We show that all these effects except possibly polhode damping can be accounted for by electrostatic patch potentials on both the gyro rotors and the gyro housing suspension and ground-plane electrodes. We express the rotor and housing patch potentials as expansions in spherical harmonics Y(l,m)(θ,φ). Our analysis demonstrates that these disturbance effects are approximated by a power spectrum for the coefficients of the spherical harmonics of the form V(0)(2)/l(r) with V(0) ≈ 100 mV and r ≈ 1.7.

Simulations towards the achievement of non-inductive current ramp-up and sustainment in the National Spherical Torus Experiment Upgrade

DOE PAGES

Poli, F. M.; Andre, R. G.; Bertelli, N.; ...

2015-10-30

One of the goals of the National Spherical Torus Experiment Upgrade (NSTX-U) (Menard et al 2012 Nucl. Fusion 52 083015) is the demonstration of fully non-inductive start-up, current ramp-up and sustainment. This work discusses predictive simulations where the available heating and current drive systems are combined to maximize the non-inductive current and minimize the solenoidal contribution. Radio-frequency waves at harmonics higher than the ion cyclotron resonance (high-harmonic fast waves (HHFW)) and neutral beam injection are used to ramp the plasma current non-inductively starting from an initial Ohmic plasma. An interesting synergy is observed in the simulations between the HHFW andmore » electron cyclotron (EC) wave heating. Furthermore, time-dependent simulations indicate that, depending on the phasing of the HHFW antenna, EC wave heating can significantly increase the effectiveness of the radio-frequency power, by heating the electrons and increasing the current drive efficiency, thus relaxing the requirements on the level of HHFW power that needs to be absorbed in the core plasma to drive the same amount of fast-wave current.« less

On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.

2004-01-01

The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.

Empirical wind model for the middle and lower atmosphere. Part 1: Local time average

NASA Technical Reports Server (NTRS)

Hedin, A. E.; Fleming, E. L.; Manson, A. H.; Schmidlin, F. J.; Avery, S. K.; Franke, S. J.

1993-01-01

The HWM90 thermospheric wind model was revised in the lower thermosphere and extended into the mesosphere and lower atmosphere to provide a single analytic model for calculating zonal and meridional wind profiles representative of the climatological average for various geophysical conditions. Gradient winds from CIRA-86 plus rocket soundings, incoherent scatter radar, MF radar, and meteor radar provide the data base and are supplemented by previous data driven model summaries. Low-order spherical harmonics and Fourier series are used to describe the major variations throughout the atmosphere including latitude, annual, semiannual, and longitude (stationary wave 1). The model represents a smoothed compromise between the data sources. Although agreement between various data sources is generally good, some systematic differences are noted, particularly near the mesopause. Root mean square differences between data and model are on the order of 15 m/s in the mesosphere and 10 m/s in the stratosphere for zonal wind, and 10 m/s and 4 m/s, respectively, for meridional wind.

Airborne geoid mapping of land and sea areas of East Malaysia

NASA Astrophysics Data System (ADS)

Jamil, H.; Kadir, M.; Forsberg, R.; Olesen, A.; Isa, M. N.; Rasidi, S.; Mohamed, A.; Chihat, Z.; Nielsen, E.; Majid, F.; Talib, K.; Aman, S.

2017-02-01

This paper describes the development of a new geoid-based vertical datum from airborne gravity data, by the Department of Survey and Mapping Malaysia, on land and in the South China Sea out of the coast of East Malaysia region, covering an area of about 610,000 square kilometres. More than 107,000 km flight line of airborne gravity data over land and marine areas of East Malaysia has been combined to provide a seamless land-to-sea gravity field coverage; with an estimated accuracy of better than 2.0 mGal. The iMAR-IMU processed gravity anomaly data has been used during a 2014-2016 airborne survey to extend a composite gravity solution across a number of minor gaps on selected lines, using a draping technique. The geoid computations were all done with the GRAVSOFT suite of programs from DTU-Space. EGM2008 augmented with GOCE spherical harmonic model has been used to spherical harmonic degree N = 720. The gravimetric geoid first was tied at one tide-gauge (in Kota Kinabalu, KK2019) to produce a fitted geoid, my_geoid2017_fit_kk. The fitted geoid was offset from the gravimetric geoid by +0.852 m, based on the comparison at the tide-gauge benchmark KK2019. Consequently, orthometric height at the six other tide gauge stations was computed from HGPS Lev = hGPS - Nmy_geoid2017_.t_kk. Comparison of the conventional (HLev) and GPS-levelling heights (HGPS Lev) at the six tide gauge locations indicate RMS height difference of 2.6 cm. The final gravimetric geoidwas fitted to the seven tide gauge stations and is known as my_geoid2017_fit_east. The accuracy of the gravimetric geoid is estimated to be better than 5 cm across most of East Malaysia land and marine areas

Analyses of the solid earth and ocean tidal perturbations on the orbits of the Geos 1 and Geos 2 satellites

NASA Technical Reports Server (NTRS)

Felsentreger, T. L.; Marsh, J. G.; Agreen, R. W.

1976-01-01

Perturbations in the inclination of the Geos 1 and Geos 2 satellite orbits have been analyzed for the solid earth and ocean tide contributions. Precision reduced camera and Tranet Doppler observations spanning periods of over 600 days for each satellite were used to derive mean orbital elements. Perturbations due to the earth's gravity field, solar radiation pressure, and atmospheric drag were modeled, and the resulting inclination residuals were analyzed for tidal effects. The amplitudes of the observed total tidal effects were about 1.2 arc sec (36 m) in the inclination of Geos 1 and 4.5 arc sec (135 m) for Geos 2. The solid earth tides were then modeled by using the Love number 0.30. The resulting inclination residuals were then analyzed for ocean tide spherical harmonic parameters.

Ocean tides for satellite geodesy

NASA Technical Reports Server (NTRS)

Dickman, S. R.

1990-01-01

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

Stabilized determination of geopotential coefficients by the mixed hom-BLUP approach

NASA Technical Reports Server (NTRS)

Middel, B.; Schaffrin, B.

1989-01-01

For the determination of geopotential coefficients, data can be used from rather different sources, e.g., satellite tracking, gravimetry, or altimetry. As each data type is particularly sensitive to certain wavelengths of the spherical harmonic coefficients it is of essential importance how they are treated in a combination solution. For example the longer wavelengths are well described by the coefficients of a model derived by satellite tracking, while other observation types such as gravity anomalies, delta g, and geoid heights, N, from altimetry contain only poor information for these long wavelengths. Therefore, the lower coefficients of the satellite model should be treated as being superior in the combination. In the combination a new method is presented which turns out to be highly suitable for this purpose due to its great flexibility combined with robustness.

A lithospheric magnetic field model derived from the Swarm satellite magnetic field measurements

NASA Astrophysics Data System (ADS)

Hulot, G.; Thebault, E.; Vigneron, P.

2015-12-01

The Swarm constellation of satellites was launched in November 2013 and has since then delivered high quality scalar and vector magnetic field measurements. A consortium of several research institutions was selected by the European Space Agency (ESA) to provide a number of scientific products which will be made available to the scientific community. Within this framework, specific tools were tailor-made to better extract the magnetic signal emanating from Earth's the lithospheric. These tools rely on the scalar gradient measured by the lower pair of Swarm satellites and rely on a regional modeling scheme that is more sensitive to small spatial scales and weak signals than the standard spherical harmonic modeling. In this presentation, we report on various activities related to data analysis and processing. We assess the efficiency of this dedicated chain for modeling the lithospheric magnetic field using more than one year of measurements, and finally discuss refinements that are continuously implemented in order to further improve the robustness and the spatial resolution of the lithospheric field model.

High-temperature electronic structure with the Korringa-Kohn-Rostoker Green's function method

NASA Astrophysics Data System (ADS)

Starrett, C. E.

2018-05-01

Modeling high-temperature (tens or hundreds of eV), dense plasmas is challenging due to the multitude of non-negligible physical effects including significant partial ionization and multisite effects. These effects cause the breakdown or intractability of common methods and approximations used at low temperatures, such as pseudopotentials or plane-wave basis sets. Here we explore the Korringa-Kohn-Rostoker Green's function method at these high-temperature conditions. The method is all electron, does not rely on pseudopotentials, and uses a spherical harmonic basis set, and so avoids the aforementioned limitations. It is found to be accurate for solid density aluminum and iron plasmas when compared to a plane-wave method at low temperature, while being able to access high temperatures.

Simultaneous stochastic inversion for geomagnetic main field and secular variation. I - A large-scale inverse problem

NASA Technical Reports Server (NTRS)

Bloxham, Jeremy

1987-01-01

The method of stochastic inversion is extended to the simultaneous inversion of both main field and secular variation. In the present method, the time dependency is represented by an expansion in Legendre polynomials, resulting in a simple diagonal form for the a priori covariance matrix. The efficient preconditioned Broyden-Fletcher-Goldfarb-Shanno algorithm is used to solve the large system of equations resulting from expansion of the field spatially to spherical harmonic degree 14 and temporally to degree 8. Application of the method to observatory data spanning the 1900-1980 period results in a data fit of better than 30 nT, while providing temporally and spatially smoothly varying models of the magnetic field at the core-mantle boundary.

(abstract) Venus Gravity Field

NASA Technical Reports Server (NTRS)

Konopliv, A. S.; Sjogren, W. L.

1995-01-01

A global gravity field model of Venus to degree and order 75 (5772 spherical harmonic coefficients) has been estimated from Doppler radio tracking of the orbiting spacecraft Pioneer Venus Orbiter (1979-1992) and Magellan (1990-1994). After the successful aerobraking of Magellan, a near circular polar orbit was attained and relatively uniform gravity field resolution (approximately 200 km) was obtained with formal uncertainties of a few milligals. Detailed gravity for several highland features are displayed as gravity contours overlaying colored topography. The positive correlation of typography with gravity is very high being unlike that of the Earth, Moon, and Mars. The amplitudes are Earth-like, but have significantly different gravity-topography ratios for different features. Global gravity, geoid, and isostatic anomaly maps as well as the admittance function are displayed.

Quantum Metric of Classic Physics

NASA Astrophysics Data System (ADS)

Machusky, Eugene

2017-09-01

By methods of differential geometry and number theory the following has been established: All fundamental physical constants are the medians of quasi-harmonic functions of relative space and relative time. Basic quantum units are, in fact, the gradients of normal distribution of standing waves between the points of pulsating spherical spiral, which are determined only by functional bonds of transcendental numbers PI and E. Analytically obtained values of rotational speed, translational velocity, vibrational speed, background temperature and molar mass give the possibility to evaluate all basic quantum units with practically unlimited accuracy. Metric of quantum physics really is two-dimensional image of motion of waves in three-dimensional space. Standard physical model is correct, but SI metric system is insufficiently exact at submillimeter distances.

YORP on tumbling asteroids

NASA Astrophysics Data System (ADS)

Rozek, A.; Breiter, S.; Vokrouhlicky, D.

2011-10-01

A semi-analytical model of the Yarkovsky-O'Keefe- Radzievskii-Paddack (YORP) effect on an asteroid spin in non principal axis rotation state is presented. Assuming zero conductivity, the YORP torque is represented by spherical harmonics series with vector coefficients, allowing to use any degree and order of approximation. Within the quadrupole approximation of the illumination function we find the same first integrals involving rotational momentum, obliquity and dynamical inertia that were obtained by Cicaló and Scheeres [1]. The integrals do not exist when higher degree terms of illumination function are included and then the asymptotic states known from Vokrouhlický et al. [2] appear. This resolves an apparent contradiction between earlier results. Averaged equations of motion admit stable and unstable limit cycle solutions that were not detected previously.

The complex magnetic field of Jupiter

NASA Technical Reports Server (NTRS)

Acuna, M. H.; Ness, N. F.

1975-01-01

An analysis of the characteristics of the magnetic field of the planet Jupiter is presented. The data were obtained during the flight of Pioneer 11 space probe, using a high field triaxial fluxgate magnetometer. The data are analyzed in terms of traditional Schmitt normalized spherical harmonic expansion fitted to the observations in a least squares sense. Tables of data and graphs are provided to summarize the findings.

Computer-generated formulas for three-center nuclear-attraction integrals (electrostatic potential) for Slater-type orbitals

NASA Technical Reports Server (NTRS)

Jones, H. W.

1984-01-01

The computer-assisted C-matrix, Loewdin-alpha-function, single-center expansion method in spherical harmonics has been applied to the three-center nuclear-attraction integral (potential due to the product of separated Slater-type orbitals). Exact formulas are produced for 13 terms of an infinite series that permits evaluation to ten decimal digits of an example using 1s orbitals.

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

NASA Astrophysics Data System (ADS)

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 Ministry of Science and Technology of Thailand and King Mongkut's Institute of Technology Ladkrabang under grant no. A118-59-011.

Testing the dynamic coupling of the core-mantle and inner core boundaries

NASA Astrophysics Data System (ADS)

Driscoll, Peter E.

2015-07-01

The proposal that the seismically observed hemispherical asymmetry of Earth's inner core is controlled by the heat flux structure imposed on the outer core by the lower mantle is tested with numerical dynamo models driven by mixed thermochemical convection. We find that models driven by a single core-mantle boundary (CMB) spherical harmonic of degree and mode 2, the dominant mode in lower mantle seismic shear velocity tomography, produce a similar structure at the inner core boundary (ICB) shifted 30∘ westward. The sensitivity of the ICB to the CMB is further tested by increasing the CMB heterogeneity amplitude. In addition, two seismic tomographic models are tested: first with CMB resolution up to degree and order 4, and second with resolution up to degree and order 8. We find time-averaged ICB heat flux in these cases to be similar at large scale, with small-scale differences due to higher CMB harmonics (above degree 4). The tomographic models produce "Earth-like" magnetic fields, while similar models with twice the CMB heat flow amplitudes produce less Earth-like fields, implying that increasing CMB heterogeneity forces the model out of an Earth-like regime. The dynamic ICB heat fluxes are compared to the proposed translation mode of the inner core to test whether the CMB controls inner core growth and structure. This test indicates that, although CMB tomography is unlikely to be driving inner core translation, the ICB heat flux response is weak enough to not interfere with the most unstable translation mode, if it is occurring.

GPS Recovery of Daily Hydrologic and Atmospheric Mass Variation: A Methodology and Results From the Australian Continent

NASA Astrophysics Data System (ADS)

Han, Shin-Chan; Razeghi, S. Mahdiyeh

2017-11-01

We present a methodology to invert a regional set of vertical displacement data from Global Positioning System (GPS) to determine the surface mass redistribution. It is assumed that GPS deformation is a result of the Earth's elastic response to the surface mass load of hydrology, atmosphere, and/or ocean. We develop an algorithm to estimate the spectral information of displacements from "regional" GPS data through regional spherical (Slepian) basis functions and apply the load Love numbers to estimate the mass load. The same approach is applied to determine global mass changes from "global" geopotential change data of Gravity Recovery and Climate Experiment (GRACE). We rigorously examine all systematic errors caused by various truncations (spherical harmonic series and Slepian series) and the smoothing constraint applied to the GPS inversion. We demonstrate the technique by processing 16 years of daily vertical motions determined from 114 GPS stations in Australia. The GPS-inverted surface mass changes are validated against GRACE data, atmosphere and ocean models, and a land surface model. Seasonal and interannual terrestrial mass variations from GPS are in good agreement with GRACE data and the water storage models. The GPS recovery compares better with the water storage model around the smaller coastal basins than two different GRACE solutions. The submonthly mass changes from GPS provide meaningful results agreeing with atmospheric mass changes in central Australia. Finally, it is suggested to integrate GPS and GRACE data to draw a comprehensive picture of daily mass changes on different continents.

Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

2016-04-01

The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

Reduced Fokker-Planck models for fast particle distribution across a transition layer of disparate plasma temperatures

NASA Astrophysics Data System (ADS)

Tang, Xian-Zhu; Berk, H. L.; Guo, Zehua; McDevitt, C. J.

2014-03-01

Across a transition layer of disparate plasma temperatures, the high energy tail of the plasma distribution can have appreciable deviations from the local Maxwellian distribution due to the Knudson layer effect. The Fokker-Planck equation for the tail particle population can be simplified in a series of practically useful limiting cases. The first is the approximation of background Maxwellian distribution for linearizing the collision operator. The second is the supra-thermal particle speed ordering of vTi ≪ v ≪ vTe for the tail ions and vTi ≪ vTe ≪ v for the tail electrons. Keeping both the collisional drag and energy scattering is essential for the collision operator to produce a Maxwellian tail distribution. The Fokker-Planck model for following the tail ion distribution for a given background plasma profile is explicitly worked out for systems of one spatial dimension, in both slab and spherical geometry. A third simplification is an expansion of the tail particle distribution using the spherical harmonics, which are eigenfunctions of the pitch angle scattering operator. This produces a set of coupled Fokker-Planck equations that contain energy-dependent spatial diffusion terms in two coordinates (position and energy), which originate from pitch angle scattering in the original Fokker-Planck equation. It is shown that the well-known diffusive Fokker-Planck model is a poor approximation of the two-mode truncation model, which itself has fundamental deficiency compared with the three-mode truncation model. The cause is the lack of even-symmetry representation in pitch dependence in the two-mode truncation model.