Mercury's Crustal Magnetic Field from MESSENGER Data

NASA Astrophysics Data System (ADS)

Plattner, A.; Johnson, C.

2017-12-01

We present a regional spherical-harmonic based crustal magnetic field model for Mercury between latitudes 45° and 70° N, derived from MESSENGER magnetic field data. In addition to contributions from the core dynamo, the bow shock, and the magnetotail, Mercury's magnetic field is also influenced by interactions with the solar wind. The resulting field-aligned currents generate magnetic fields that are typically an order of magnitude stronger at spacecraft altitude than the field from sources within Mercury's crust. These current sources lie within the satellite path and so the resulting magnetic field can not be modeled using potential-field approaches. However, these fields are organized in the local-time frame and their spatial structure differs from that of the smaller-scale crustal field. We account for large-scale magnetic fields in the local-time reference frame by subtracting from the data a low-degree localized vector spherical-harmonic model including curl components fitted at satellite altitude. The residual data exhibit consistent signals across individual satellite tracks in the body fixed reference frame, similar to those obtained via more rudimentary along-track filtering approaches. We fit a regional internal-source spherical-harmonic model to the night-time radial component of the residual data, allowing a maximum spherical-harmonic degree of L = 150. Due to the cross-track spacing of the satellite tracks, spherical-harmonic degrees beyond L = 90 are damped. The strongest signals in the resulting model are in the region around the Caloris Basin and over Suisei Planitia, as observed previously. Regularization imposed in the modeling allows the field to be downward continued to the surface. The strongest surface fields are 30 nT. Furthermore, the regional power spectrum of the model shows a downward dipping slope between spherical-harmonic degrees 40 and 80, hinting that the main component of the crustal field lies deep within the crust.

Mathematical Methods for Optical Physics and Engineering

NASA Astrophysics Data System (ADS)

Gbur, Gregory J.

2011-01-01

1. Vector algebra; 2. Vector calculus; 3. Vector calculus in curvilinear coordinate systems; 4. Matrices and linear algebra; 5. Advanced matrix techniques and tensors; 6. Distributions; 7. Infinite series; 8. Fourier series; 9. Complex analysis; 10. Advanced complex analysis; 11. Fourier transforms; 12. Other integral transforms; 13. Discrete transforms; 14. Ordinary differential equations; 15. Partial differential equations; 16. Bessel functions; 17. Legendre functions and spherical harmonics; 18. Orthogonal functions; 19. Green's functions; 20. The calculus of variations; 21. Asymptotic techniques; Appendices; References; Index.

Multipole Vectors: Decomposing Functions on a Sphere

NASA Astrophysics Data System (ADS)

Copi, C. J.; Huterer, D.; Starkman, G. D.

2011-09-01

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These "multipole vectors and scalars" transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients, alm, in a nonlinear way, and are therefore sensitive to different aspects of the CMB anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. Using the WMAP full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2<=l1!=l2<=8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the ILC map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the l=3 and l=8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

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.

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.

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.

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.

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.

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).

Truncation of Spherical Harmonic Series and its Influence on Gravity Field Modelling

NASA Astrophysics Data System (ADS)

Fecher, T.; Gruber, T.; Rummel, R.

2009-04-01

Least-squares adjustment is a very common and effective tool for the calculation of global gravity field models in terms of spherical harmonic series. However, since the gravity field is a continuous field function its optimal representation by a finite series of spherical harmonics is connected with a set of fundamental problems. Particularly worth mentioning here are cut off errors and aliasing effects. These problems stem from the truncation of the spherical harmonic series and from the fact that the spherical harmonic coefficients cannot be determined independently of each other within the adjustment process in case of discrete observations. The latter is shown by the non-diagonal variance-covariance matrices of gravity field solutions. Sneeuw described in 1994 that the off-diagonal matrix elements - at least if data are equally weighted - are the result of a loss of orthogonality of Legendre polynomials on regular grids. The poster addresses questions arising from the truncation of spherical harmonic series in spherical harmonic analysis and synthesis. Such questions are: (1) How does the high frequency data content (outside the parameter space) affect the estimated spherical harmonic coefficients; (2) Where to truncate the spherical harmonic series in the adjustment process in order to avoid high frequency leakage?; (3) Given a set of spherical harmonic coefficients resulting from an adjustment, what is the effect of using only a truncated version of it?

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.

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.

Spherical Harmonic Inductive Detection Coils and their use In Dynamic Pre-emphasis for Magnetic Resonance Imaging

NASA Astrophysics Data System (ADS)

Edler, Karl T.

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field -- an inverse curl operation -- and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI. Keywords: magnetic resonance imaging, eddy currents, dynamic shimming, negative feedback, quasi-static fields, vector potential, inverse curl

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.

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.

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.

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.

Vector matter waves in two-component Bose-Einstein condensates with spatially modulated nonlinearities

NASA Astrophysics Data System (ADS)

Xu, Si-Liu; He, Jun-Rong; Xue, Li; Belić, Milivoj R.

2018-02-01

We demonstrate three-dimensional (3D) vector solitary waves in the coupled (3 + 1)-D nonlinear Gross-Pitaevskii equations with variable nonlinearity coefficients. The analysis is carried out in spherical coordinates, providing novel localized solutions that depend on three modal numbers, l, m, and n. Using the similarity transformation (ST) method in 3D, vector solitary waves are built with the help of a combination of harmonic and trapping potentials, including multipole solutions and necklace rings. In general, the solutions found are stable for low values of the modal numbers; for values larger than 2, the solutions are found to be unstable. Variable nonlinearity allows the utilization of soliton management methods.

A surface spherical harmonic expansion of gravity anomalies on the ellipsoid

NASA Astrophysics Data System (ADS)

Claessens, S. J.; Hirt, C.

2015-10-01

A surface spherical harmonic expansion of gravity anomalies with respect to a geodetic reference ellipsoid can be used to model the global gravity field and reveal its spectral properties. In this paper, a direct and rigorous transformation between solid spherical harmonic coefficients of the Earth's disturbing potential and surface spherical harmonic coefficients of gravity anomalies in ellipsoidal approximation with respect to a reference ellipsoid is derived. This transformation cannot rigorously be achieved by the Hotine-Jekeli transformation between spherical and ellipsoidal harmonic coefficients. The method derived here is used to create a surface spherical harmonic model of gravity anomalies with respect to the GRS80 ellipsoid from the EGM2008 global gravity model. Internal validation of the model shows a global RMS precision of 1 nGal. This is significantly more precise than previous solutions based on spherical approximation or approximations to order or , which are shown to be insufficient for the generation of surface spherical harmonic coefficients with respect to a geodetic reference ellipsoid. Numerical results of two applications of the new method (the computation of ellipsoidal corrections to gravimetric geoid computation, and area means of gravity anomalies in ellipsoidal approximation) are provided.

Multipole vectors: A new representation of the CMB sky and evidence for statistical anisotropy or non-Gaussianity at 2⩽l⩽8

NASA Astrophysics Data System (ADS)

Copi, Craig J.; Huterer, Dragan; Starkman, Glenn D.

2004-08-01

We propose a novel representation of cosmic microwave anisotropy maps, where each multipole order l is represented by l unit vectors pointing in directions on the sky and an overall magnitude. These “multipole vectors and scalars” transform as vectors under rotations. Like the usual spherical harmonics, multipole vectors form an irreducible representation of the proper rotation group SO(3). However, they are related to the familiar spherical harmonic coefficients alm in a nonlinear way and are therefore sensitive to different aspects of the cosmic microwave background (CMB) anisotropy. Nevertheless, it is straightforward to determine the multipole vectors for a given CMB map and we present an algorithm to compute them. A code implementing this algorithm is available at http://www.phys.cwru.edu/projects/mpvectors/. Using the Wilkinson Microwave Anisotropy Probe (WMAP) full-sky maps, we perform several tests of the hypothesis that the CMB anisotropy is statistically isotropic and Gaussian random. We find that the result from comparing the oriented area of planes defined by these vectors between multipole pairs 2⩽l1≠l2⩽8 is inconsistent with the isotropic Gaussian hypothesis at the 99.4% level for the internal linear combination map and at 98.9% level for the cleaned map of Tegmark et al. A particular correlation is suggested between the l=3 and l=8 multipoles, as well as several other pairs. This effect is entirely different from the now familiar planarity and alignment of the quadrupole and octupole: while the aforementioned is fairly unlikely, the multipole vectors indicate correlations not expected in Gaussian random skies that make them unusually likely. The result persists after accounting for pixel noise and after assuming a residual 10% dust contamination in the cleaned WMAP map. While the definitive analysis of these results will require more work, we hope that multipole vectors will become a valuable tool for various cosmological tests, in particular those of cosmic isotropy.

Spherical Harmonic Analysis of Particle Velocity Distribution Function: Comparison of Moments and Anisotropies using Cluster Data

NASA Technical Reports Server (NTRS)

Gurgiolo, Chris; Vinas, Adolfo F.

2009-01-01

This paper presents a spherical harmonic analysis of the plasma velocity distribution function using high-angular, energy, and time resolution Cluster data obtained from the PEACE spectrometer instrument to demonstrate how this analysis models the particle distribution function and its moments and anisotropies. The results show that spherical harmonic analysis produced a robust physical representation model of the velocity distribution function, resolving the main features of the measured distributions. From the spherical harmonic analysis, a minimum set of nine spectral coefficients was obtained from which the moment (up to the heat flux), anisotropy, and asymmetry calculations of the velocity distribution function were obtained. The spherical harmonic method provides a potentially effective "compression" technique that can be easily carried out onboard a spacecraft to determine the moments and anisotropies of the particle velocity distribution function for any species. These calculations were implemented using three different approaches, namely, the standard traditional integration, the spherical harmonic (SPH) spectral coefficients integration, and the singular value decomposition (SVD) on the spherical harmonic methods. A comparison among the various methods shows that both SPH and SVD approaches provide remarkable agreement with the standard moment integration method.

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).

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.

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.

Orientational Order on Surfaces: The Coupling of Topology, Geometry, and Dynamics

NASA Astrophysics Data System (ADS)

Nestler, M.; Nitschke, I.; Praetorius, S.; Voigt, A.

2018-02-01

We consider the numerical investigation of surface bound orientational order using unit tangential vector fields by means of a gradient flow equation of a weak surface Frank-Oseen energy. The energy is composed of intrinsic and extrinsic contributions, as well as a penalization term to enforce the unity of the vector field. Four different numerical discretizations, namely a discrete exterior calculus approach, a method based on vector spherical harmonics, a surface finite element method, and an approach utilizing an implicit surface description, the diffuse interface method, are described and compared with each other for surfaces with Euler characteristic 2. We demonstrate the influence of geometric properties on realizations of the Poincaré-Hopf theorem and show examples where the energy is decreased by introducing additional orientational defects.

Region Spherical Harmonic Magnetic Modeling from Near-Surface and Satellite-Altitude Anomlaies

NASA Technical Reports Server (NTRS)

Kim, Hyung Rae; von Frese, Ralph R. B.; Taylor, Patrick T.

2013-01-01

The compiled near-surface data and satellite crustal magnetic measured data are modeled with a regionally concentrated spherical harmonic presentation technique over Australia and Antarctica. Global crustal magnetic anomaly studies have used a spherical harmonic analysis to represent the Earth's magnetic crustal field. This global approach, however is best applied where the data are uniformly distributed over the entire Earth. Satellite observations generally meet this requirement, but unequally distributed data cannot be easily adapted in global modeling. Even for the satellite observations, due to the errors spread over the globe, data smoothing is inevitable in the global spherical harmonic presentations. In addition, global high-resolution modeling requires a great number of global spherical harmonic coefficients for the regional presentation of crustal magnetic anomalies, whereas a lesser number of localized spherical coefficients will satisfy. We compared methods in both global and regional approaches and for a case where the errors were propagated outside the region of interest. For observations from the upcoming Swarm constellation, the regional modeling will allow the production a lesser number of spherical coefficients that are relevant to the region of interest

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.

Approximating high angular resolution apparent diffusion coefficient profiles using spherical harmonics under BiGaussian assumption

NASA Astrophysics Data System (ADS)

Cao, Ning; Liang, Xuwei; Zhuang, Qi; Zhang, Jun

2009-02-01

Magnetic Resonance Imaging (MRI) techniques have achieved much importance in providing visual and quantitative information of human body. Diffusion MRI is the only non-invasive tool to obtain information of the neural fiber networks of the human brain. The traditional Diffusion Tensor Imaging (DTI) is only capable of characterizing Gaussian diffusion. High Angular Resolution Diffusion Imaging (HARDI) extends its ability to model more complex diffusion processes. Spherical harmonic series truncated to a certain degree is used in recent studies to describe the measured non-Gaussian Apparent Diffusion Coefficient (ADC) profile. In this study, we use the sampling theorem on band-limited spherical harmonics to choose a suitable degree to truncate the spherical harmonic series in the sense of Signal-to-Noise Ratio (SNR), and use Monte Carlo integration to compute the spherical harmonic transform of human brain data obtained from icosahedral schema.

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

A proposed International Geomagnetic Reference Field for 1965- 1985.

USGS Publications Warehouse

Peddie, N.W.; Fabiano, E.B.

1982-01-01

A set of spherical harmonic models describing the Earth's main magnetic field from 1965 to 1985 has been developed and is proposed as the next revision of the International Geomagnetic Reference Field (IGRF). A tenth degree and order spherical harmonic model of the main field was derived from Magsat data. A series of eighth degree and order spherical harmonic models of the secular variation of the main field was derived from magnetic observatory annual mean values. Models of the main field at 1965, 1970, 1975, and 1980 were obtained by extrapolating the main-field model using the secular variation models.-Authors spherical harmonic models Earth main magnetic field Magsat data

A T Matrix Method Based upon Scalar Basis Functions

NASA Technical Reports Server (NTRS)

Mackowski, D.W.; Kahnert, F. M.; Mishchenko, Michael I.

2013-01-01

A surface integral formulation is developed for the T matrix of a homogenous and isotropic particle of arbitrary shape, which employs scalar basis functions represented by the translation matrix elements of the vector spherical wave functions. The formulation begins with the volume integral equation for scattering by the particle, which is transformed so that the vector and dyadic components in the equation are replaced with associated dipole and multipole level scalar harmonic wave functions. The approach leads to a volume integral formulation for the T matrix, which can be extended, by use of Green's identities, to the surface integral formulation. The result is shown to be equivalent to the traditional surface integral formulas based on the VSWF basis.

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.

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

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.

Quantitative maps of geomagnetic perturbation vectors during substorm onset and recovery

PubMed Central

Pothier, N M; Weimer, D R; Moore, W B

2015-01-01

We have produced the first series of spherical harmonic, numerical maps of the time-dependent surface perturbations in the Earth's magnetic field following the onset of substorms. Data from 124 ground magnetometer stations in the Northern Hemisphere at geomagnetic latitudes above 33° were used. Ground station data averaged over 5 min intervals covering 8 years (1998–2005) were used to construct pseudo auroral upper, auroral lower, and auroral electrojet (AU*, AL*, and AE*) indices. These indices were used to generate a list of substorms that extended from 1998 to 2005, through a combination of automated processing and visual checks. Events were sorted by interplanetary magnetic field (IMF) orientation (at the Advanced Composition Explorer (ACE) satellite), dipole tilt angle, and substorm magnitude. Within each category, the events were aligned on substorm onset. A spherical cap harmonic analysis was used to obtain a least error fit of the substorm disturbance patterns at 5 min intervals up to 90 min after onset. The fits obtained at onset time were subtracted from all subsequent fits, for each group of substorm events. Maps of the three vector components of the averaged magnetic perturbations were constructed to show the effects of substorm currents. These maps are produced for several specific ranges of values for the peak |AL*| index, IMF orientation, and dipole tilt angle. We demonstrate an influence of the dipole tilt angle on the response to substorms. Our results indicate that there are downward currents poleward and upward currents just equatorward of the peak in the substorms' westward electrojet. Key Points Show quantitative maps of ground geomagnetic perturbations due to substorms Three vector components mapped as function of time during onset and recovery Compare/contrast results for different tilt angle and sign of IMF Y-component PMID:26167445

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.

How should spin-weighted spherical functions be defined?

NASA Astrophysics Data System (ADS)

Boyle, Michael

2016-09-01

Spin-weighted spherical functions provide a useful tool for analyzing tensor-valued functions on the sphere. A tensor field can be decomposed into complex-valued functions by taking contractions with tangent vectors on the sphere and the normal to the sphere. These component functions are usually presented as functions on the sphere itself, but this requires an implicit choice of distinguished tangent vectors with which to contract. Thus, we may more accurately say that spin-weighted spherical functions are functions of both a point on the sphere and a choice of frame in the tangent space at that point. The distinction becomes extremely important when transforming the coordinates in which these functions are expressed, because the implicit choice of frame will also transform. Here, it is proposed that spin-weighted spherical functions should be treated as functions on the spin or rotation groups, which simultaneously tracks the point on the sphere and the choice of tangent frame by rotating elements of an orthonormal basis. In practice, the functions simply take a quaternion argument and produce a complex value. This approach more cleanly reflects the geometry involved, and allows for a more elegant description of the behavior of spin-weighted functions. In this form, the spin-weighted spherical harmonics have simple expressions as elements of the Wigner 𝔇 representations, and transformations under rotation are simple. Two variants of the angular-momentum operator are defined directly in terms of the spin group; one is the standard angular-momentum operator L, while the other is shown to be related to the spin-raising operator ð.

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.

Direct solution of the H(1s)-H + long-range interaction problem in momentum space

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu

1985-02-01

Perturbation equations for the H(1s)-H+ long-range interaction are solved directly in momentum space up to the fourth order with respect to the reciprocal of the internuclear distance. As in the hydrogen atom problem, the Fock transformation is used which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere. Solutions are given as linear combinations of several four-dimensional spherical harmonics. The present results add an example to the momentum-space solution of the nonspherical potential problem.

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.

Sensitivity of selected geomagnetic properties to truncation level of spherical harmonic expansions

NASA Technical Reports Server (NTRS)

Benton, E. R.; Estes, R. H.; Langel, R. A.; Muth, L. A.

1982-01-01

The model dependence of Gauss coefficients associated with a lack of spherical harmonic orthogonality on a nonuniform Magsat data grid is shown to be minor, where the fitting level exceeds the harmonic order by a value of approximately four. The shape of the magnetic energy spectrum outside the core, and the sensitivity to truncation level of magnetic contour location and the number of their intersections on the core-mantle boundary, suggest that spherical harmonic expansions of the main geomagnetic field should be truncated at a truncation level value of not more than eight if they are to be extrapolated to the core.

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.

Fast calculation of low altitude disturbing gravity for ballistics

NASA Astrophysics Data System (ADS)

Wang, Jianqiang; Wang, Fanghao; Tian, Shasha

2018-03-01

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

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.

Permutation-symmetric three-particle hyper-spherical harmonics based on the S3 ⊗ SO(3)rot ⊂ O(2)⊗SO(3)rot ⊂ U(3)⋊S2 ⊂ O(6) subgroup chain

NASA Astrophysics Data System (ADS)

Salom, Igor; Dmitrašinović, V.

2017-07-01

We construct the three-body permutation symmetric hyperspherical harmonics to be used in the non-relativistic three-body Schrödinger equation in three spatial dimensions (3D). We label the state vectors according to the S3 ⊗ SO(3)rot ⊂ O (2) ⊗ SO(3)rot ⊂ U (3) ⋊S2 ⊂ O (6) subgroup chain, where S3 is the three-body permutation group and S2 is its two element subgroup containing transposition of first two particles, O (2) is the ;democracy transformation;, or ;kinematic rotation; group for three particles; SO(3)rot is the 3D rotation group, and U (3) , O (6) are the usual Lie groups. We discuss the good quantum numbers implied by the above chain of algebras, as well as their relation to the S3 permutation properties of the harmonics, particularly in view of the SO(3)rot ⊂ SU (3) degeneracy. We provide a definite, practically implementable algorithm for the calculation of harmonics with arbitrary finite integer values of the hyper angular momentum K, and show an explicit example of this construction in a specific case with degeneracy, as well as tables of K ≤ 6 harmonics. All harmonics are expressed as homogeneous polynomials in the Jacobi vectors (λ , ρ) with coefficients given as algebraic numbers unless the ;operator method; is chosen for the lifting of the SO(3)rot ⊂ SU (3) multiplicity and the dimension of the degenerate subspace is greater than four - in which case one must resort to numerical diagonalization; the latter condition is not met by any K ≤ 15 harmonic, or by any L ≤ 7 harmonic with arbitrary K. We also calculate a certain type of matrix elements (the Gaunt integrals of products of three harmonics) in two ways: 1) by explicit evaluation of integrals and 2) by reduction to known SU (3) Clebsch-Gordan coefficients. In this way we complete the calculation of the ingredients sufficient for the solution to the quantum-mechanical three-body bound state problem.

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.

Circular current loops, magnetic dipoles and spherical harmonic analysis.

USGS Publications Warehouse

Alldredge, L.R.

1980-01-01

Spherical harmonic analysis (SHA) is the most used method of describing the Earth's magnetic field, even though spherical harmonic coefficients (SHC) almost completely defy interpretation in terms of real sources. Some moderately successful efforts have been made to represent the field in terms of dipoles placed in the core in an effort to have the model come closer to representing real sources. Dipole sources are only a first approximation to the real sources which are thought to be a very complicated network of electrical currents in the core of the Earth. -Author

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.

Spectral simulations of an axisymmetric force-free pulsar magnetosphere

NASA Astrophysics Data System (ADS)

Cao, Gang; Zhang, Li; Sun, Sineng

2016-02-01

A pseudo-spectral method with an absorbing outer boundary is used to solve a set of time-dependent force-free equations. In this method, both electric and magnetic fields are expanded in terms of the vector spherical harmonic (VSH) functions in spherical geometry and the divergence-free state of the magnetic field is enforced analytically by a projection method. Our simulations show that the Deutsch vacuum solution and the Michel monopole solution can be reproduced well by our pseudo-spectral code. Further, the method is used to present a time-dependent simulation of the force-free pulsar magnetosphere for an aligned rotator. The simulations show that the current sheet in the equatorial plane can be resolved well and the spin-down luminosity obtained in the steady state is in good agreement with the value given by Spitkovsky.

Spherical harmonic analysis of a synoptic climatology generated with a global general circulation model

NASA Technical Reports Server (NTRS)

Christidis, Z. D.; Spar, J.

1980-01-01

Spherical harmonic analysis was used to analyze the observed climatological (C) fields of temperature at 850 mb, geopotential height at 500 mb, and sea level pressure. The spherical harmonic method was also applied to the corresponding "model climatological" fields (M) generated by a general circulation model, the "GISS climate model." The climate model was initialized with observed data for the first of December 1976 at 00. GMT and allowed to generate five years of meteorological history. Monthly means of the above fields for the five years were computed and subjected to spherical harmonic analysis. It was found from the comparison of the spectral components of both sets, M and C, that the climate model generated reasonable 500 mb geopotential heights. The model temperature field at 850 mb exhibited a generally correct structure. However, the meridional temperature gradient was overestimated and overheating of the continents was observed in summer.

Spherical Cap Harmonic Modelling of 400 Years of Secular Variation in the South-west Pacific

NASA Astrophysics Data System (ADS)

Ingham, M.; Alfheid, M.; Ingham, E. M.; Turner, G. M.

2014-12-01

Historical magnetic data recorded in ship's logs on voyages of exploration and trade in the south-west Pacific have been used as a basis for constructing a model of secular variation in the region using spherical cap harmonic (SCH) analysis. The spherical cap used is centred on colatitude 115° and longitude 160° and has a radius of 50°, thus covering New Zealand, Australia and parts of Antarctica. Gaps in the observational data have been filled by an iterative procedure started by using IGRF field values to obtain SCH models for 2000, 1950 and 1900 and assuming that the spherical cap coefficients have a linear variation in time over the 400 year time period of the model, as is observed to a first approximation for Gauss coefficients calculated from a global spherical harmonic analysis. The resulting field models have generally smooth spatial and temporal variations in declination, inclination and intensity which show some differences from the variations calculated using the global spherical harmonic model gufm1. The technique clearly shows promise for producing more refined models of secular variation in the south-west Pacific when the historical data are supplemented by archeomagnetic and paleomagnetic data.

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

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.

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.

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.

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.

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.

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.

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.

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.

A Semi-Vectorization Algorithm to Synthesis of Gravitational Anomaly Quantities on the Earth

NASA Astrophysics Data System (ADS)

Abdollahzadeh, M.; Eshagh, M.; Najafi Alamdari, M.

2009-04-01

The Earth's gravitational potential can be expressed by the well-known spherical harmonic expansion. The computational time of summing up this expansion is an important practical issue which can be reduced by an efficient numerical algorithm. This paper proposes such a method for block-wise synthesizing the anomaly quantities on the Earth surface using vectorization. Fully-vectorization means transformation of the summations to the simple matrix and vector products. It is not a practical for the matrices with large dimensions. Here a semi-vectorization algorithm is proposed to avoid working with large vectors and matrices. It speeds up the computations by using one loop for the summation either on degrees or on orders. The former is a good option to synthesize the anomaly quantities on the Earth surface considering a digital elevation model (DEM). This approach is more efficient than the two-step method which computes the quantities on the reference ellipsoid and continues them upward to the Earth surface. The algorithm has been coded in MATLAB which synthesizes a global grid of 5′Ã- 5′ (corresponding 9 million points) of gravity anomaly or geoid height using a geopotential model to degree 360 in 10000 seconds by an ordinary computer with 2G RAM.

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.

Computer-implemented method and apparatus for autonomous position determination using magnetic field data

NASA Technical Reports Server (NTRS)

Ketchum, Eleanor A. (Inventor)

2000-01-01

A computer-implemented method and apparatus for determining position of a vehicle within 100 km autonomously from magnetic field measurements and attitude data without a priori knowledge of position. An inverted dipole solution of two possible position solutions for each measurement of magnetic field data are deterministically calculated by a program controlled processor solving the inverted first order spherical harmonic representation of the geomagnetic field for two unit position vectors 180 degrees apart and a vehicle distance from the center of the earth. Correction schemes such as a successive substitutions and a Newton-Raphson method are applied to each dipole. The two position solutions for each measurement are saved separately. Velocity vectors for the position solutions are calculated so that a total energy difference for each of the two resultant position paths is computed. The position path with the smaller absolute total energy difference is chosen as the true position path of the vehicle.

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.

Spherical harmonic analysis of a harmonic function given on a spheroid

NASA Astrophysics Data System (ADS)

Claessens, S. J.

2016-07-01

A new analytical method for the computation of a truncated series of solid spherical harmonic coefficients (HCs) from data on a spheroid (i.e. an oblate ellipsoid of revolution) is derived, using a transformation between surface and solid spherical HCs. A two-step procedure is derived to extend this transformation beyond degree and order (d/o) 520. The method is compared to the Hotine-Jekeli transformation in a numerical study based on the EGM2008 global gravity model. Both methods are shown to achieve submicrometre precision in terms of height anomalies for a model to d/o 2239. However, both methods result in spherical harmonic models that are different by up to 7.6 mm in height anomalies and 2.5 mGal in gravity disturbances due to the different coordinate system used. While the Hotine-Jekeli transformation requires the use of an ellipsoidal coordinate system, the new method uses only spherical polar coordinates. The Hotine-Jekeli transformation is numerically more efficient, but the new method can more easily be extended to cases where (a linear combination of) normal derivatives of the function under consideration are given on the surface of the spheroid. It therefore provides a solution to many types of ellipsoidal boundary-value problems in the spectral domain.

Black hole perturbation under a 2 +2 decomposition in the action

NASA Astrophysics Data System (ADS)

Ripley, Justin L.; Yagi, Kent

2018-01-01

Black hole perturbation theory is useful for studying the stability of black holes and calculating ringdown gravitational waves after the collision of two black holes. Most previous calculations were carried out at the level of the field equations instead of the action. In this work, we compute the Einstein-Hilbert action to quadratic order in linear metric perturbations about a spherically symmetric vacuum background in Regge-Wheeler gauge. Using a 2 +2 splitting of spacetime, we expand the metric perturbations into a sum over scalar, vector, and tensor spherical harmonics, and dimensionally reduce the action to two dimensions by integrating over the two sphere. We find that the axial perturbation degree of freedom is described by a two-dimensional massive vector action, and that the polar perturbation degree of freedom is described by a two-dimensional dilaton massive gravity action. Varying the dimensionally reduced actions, we rederive covariant and gauge-invariant master equations for the axial and polar degrees of freedom. Thus, the two-dimensional massive vector and massive gravity actions we derive by dimensionally reducing the perturbed Einstein-Hilbert action describe the dynamics of a well-studied physical system: the metric perturbations of a static black hole. The 2 +2 formalism we present can be generalized to m +n -dimensional spacetime splittings, which may be useful in more generic situations, such as expanding metric perturbations in higher dimensional gravity. We provide a self-contained presentation of m +n formalism for vacuum spacetime splittings.

Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies

NASA Astrophysics Data System (ADS)

Balmino, G.; Vales, N.; Bonvalot, S.; Briais, A.

2012-07-01

The availability of high-resolution global digital elevation data sets has raised a growing interest in the feasibility of obtaining their spherical harmonic representation at matching resolution, and from there in the modelling of induced gravity perturbations. We have therefore estimated spherical Bouguer and Airy isostatic anomalies whose spherical harmonic models are derived from the Earth's topography harmonic expansion. These spherical anomalies differ from the classical planar ones and may be used in the context of new applications. We succeeded in meeting a number of challenges to build spherical harmonic models with no theoretical limitation on the resolution. A specific algorithm was developed to enable the computation of associated Legendre functions to any degree and order. It was successfully tested up to degree 32,400. All analyses and syntheses were performed, in 64 bits arithmetic and with semi-empirical control of the significant terms to prevent from calculus underflows and overflows, according to IEEE limitations, also in preserving the speed of a specific regular grid processing scheme. Finally, the continuation from the reference ellipsoid's surface to the Earth's surface was performed by high-order Taylor expansion with all grids of required partial derivatives being computed in parallel. The main application was the production of a 1' × 1' equiangular global Bouguer anomaly grid which was computed by spherical harmonic analysis of the Earth's topography-bathymetry ETOPO1 data set up to degree and order 10,800, taking into account the precise boundaries and densities of major lakes and inner seas, with their own altitude, polar caps with bedrock information, and land areas below sea level. The harmonic coefficients for each entity were derived by analyzing the corresponding ETOPO1 part, and free surface data when required, at one arc minute resolution. The following approximations were made: the land, ocean and ice cap gravity spherical harmonic coefficients were computed up to the third degree of the altitude, and the harmonics of the other, smaller parts up to the second degree. Their sum constitutes what we call ETOPG1, the Earth's TOPography derived Gravity model at 1' resolution (half-wavelength). The EGM2008 gravity field model and ETOPG1 were then used to rigorously compute 1' × 1' point values of surface gravity anomalies and disturbances, respectively, worldwide, at the real Earth's surface, i.e. at the lower limit of the atmosphere. The disturbance grid is the most interesting product of this study and can be used in various contexts. The surface gravity anomaly grid is an accurate product associated with EGM2008 and ETOPO1, but its gravity information contents are those of EGM2008. Our method was validated by comparison with a direct numerical integration approach applied to a test area in Morocco-South of Spain (Kuhn, private communication 2011) and the agreement was satisfactory. Finally isostatic corrections according to the Airy model, but in spherical geometry, with harmonic coefficients derived from the sets of the ETOPO1 different parts, were computed with a uniform depth of compensation of 30 km. The new world Bouguer and isostatic gravity maps and grids here produced will be made available through the Commission for the Geological Map of the World. Since gravity values are those of the EGM2008 model, geophysical interpretation from these products should not be done for spatial scales below 5 arc minutes (half-wavelength).

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

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=({+-}1,0)

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

Schmid, Christoph

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein's static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes. -more » The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity {omega}-vector{sub gyro} of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B-vector{sub g}{identical_to}-2{omega}-vector{sub gyro}. The gravitomagnetic field is caused by energy currents J-vector{sub {epsilon}} via the momentum constraint, Einstein's G{sup 0-}circumflex{sub i-circumflex} equation, (-{delta}+{mu}{sup 2})A-vector{sub g}=-16{pi}G{sub N}J-vector{sub {epsilon}} with B-vector{sub g}=curl A-vector{sub g}. This equation is analogous to Ampere's law, but it holds for all time-dependent situations. {delta} is the de Rham-Hodge Laplacian, and {delta}=-curl curl for the vorticity sector in Riemannian 3-space. - In the solution for an open universe the 1/r{sup 2}-force of Ampere is replaced by a Yukawa force Y{sub {mu}}(r)=(-d/dr)[(1/R)exp(-{mu}r)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2{pi}R is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and {mu}{sup 2}=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein's closed static universe.--We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.--We show that only energy currents in the toroidal vorticity sector with l=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X-vector{sub lm}{sup -} has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions. - The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenboeck formula for the difference between the de Rham-Hodge Laplacian {delta} and the ''rough'' Laplacian {nabla}{sup 2} on vector fields.« less

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.

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

The NASA/MSFC global reference atmospheric model: MOD 3 (with spherical harmonic wind model)

NASA Technical Reports Server (NTRS)

Justus, C. G.; Fletcher, G. R.; Gramling, F. E.; Pace, W. B.

1980-01-01

Improvements to the global reference atmospheric model are described. The basic model includes monthly mean values of pressure, density, temperature, and geostrophic winds, as well as quasi-biennial and small and large scale random perturbations. A spherical harmonic wind model for the 25 to 90 km height range is included. Below 25 km and above 90 km, the GRAM program uses the geostrophic wind equations and pressure data to compute the mean wind. In the altitudes where the geostrophic wind relations are used, an interpolation scheme is employed for estimating winds at low latitudes where the geostrophic wind relations being to mesh down. Several sample wind profiles are given, as computed by the spherical harmonic model. User and programmer manuals are presented.

Radiative transfer codes for atmospheric correction and aerosol retrieval: intercomparison study.

PubMed

Kotchenova, Svetlana Y; Vermote, Eric F; Levy, Robert; Lyapustin, Alexei

2008-05-01

Results are summarized for a scientific project devoted to the comparison of four atmospheric radiative transfer codes incorporated into different satellite data processing algorithms, namely, 6SV1.1 (second simulation of a satellite signal in the solar spectrum, vector, version 1.1), RT3 (radiative transfer), MODTRAN (moderate resolution atmospheric transmittance and radiance code), and SHARM (spherical harmonics). The performance of the codes is tested against well-known benchmarks, such as Coulson's tabulated values and a Monte Carlo code. The influence of revealed differences on aerosol optical thickness and surface reflectance retrieval is estimated theoretically by using a simple mathematical approach. All information about the project can be found at http://rtcodes.ltdri.org.

Radiative transfer codes for atmospheric correction and aerosol retrieval: intercomparison study

NASA Astrophysics Data System (ADS)

Kotchenova, Svetlana Y.; Vermote, Eric F.; Levy, Robert; Lyapustin, Alexei

2008-05-01

Results are summarized for a scientific project devoted to the comparison of four atmospheric radiative transfer codes incorporated into different satellite data processing algorithms, namely, 6SV1.1 (second simulation of a satellite signal in the solar spectrum, vector, version 1.1), RT3 (radiative transfer), MODTRAN (moderate resolution atmospheric transmittance and radiance code), and SHARM (spherical harmonics). The performance of the codes is tested against well-known benchmarks, such as Coulson's tabulated values and a Monte Carlo code. The influence of revealed differences on aerosol optical thickness and surface reflectance retrieval is estimated theoretically by using a simple mathematical approach. All information about the project can be found at http://rtcodes.ltdri.org.

Modeling study of seated reach envelopes based on spherical harmonics with consideration of the difficulty ratings.

PubMed

Yu, Xiaozhi; Ren, Jindong; Zhang, Qian; Liu, Qun; Liu, Honghao

2017-04-01

Reach envelopes are very useful for the design and layout of controls. In building reach envelopes, one of the key problems is to represent the reach limits accurately and conveniently. Spherical harmonics are proved to be accurate and convenient method for fitting of the reach capability envelopes. However, extensive study are required on what components of spherical harmonics are needed in fitting the envelope surfaces. For applications in the vehicle industry, an inevitable issue is to construct reach limit surfaces with consideration of the seating positions of the drivers, and it is desirable to use population envelopes rather than individual envelopes. However, it is relatively inconvenient to acquire reach envelopes via a test considering the seating positions of the drivers. In addition, the acquired envelopes are usually unsuitable for use with other vehicle models because they are dependent on the current cab packaging parameters. Therefore, it is of great significance to construct reach envelopes for real vehicle conditions based on individual capability data considering seating positions. Moreover, traditional reach envelopes provide little information regarding the assessment of reach difficulty. The application of reach envelopes will improve design quality by providing difficulty-rating information about reach operations. In this paper, using the laboratory data of seated reach with consideration of the subjective difficulty ratings, the method of modeling reach envelopes is studied based on spherical harmonics. The surface fitting using spherical harmonics is conducted for circumstances both with and without seat adjustments. For use with adjustable seat, the seating position model is introduced to re-locate the test data. The surface fitting is conducted for both population and individual reach envelopes, as well as for boundary envelopes. Comparison of the envelopes of adjustable seat and the SAE J287 control reach envelope shows that the latter is nearly at the middle difficulty level. It is also found that the abilities of reach envelope models in expressing the shape of the reach limits based on spherical harmonics depends both on the terms in the model expression and on the data used to fit the envelope surfaces. Copyright © 2016 Elsevier Ltd. All rights reserved.

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.

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.

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.

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

Dyadic Green's function of an eccentrically stratified sphere.

PubMed

Moneda, Angela P; Chrissoulidis, Dimitrios P

2014-03-01

The electric dyadic Green's function (dGf) of an eccentrically stratified sphere is built by use of the superposition principle, dyadic algebra, and the addition theorem of vector spherical harmonics. The end result of the analytical formulation is a set of linear equations for the unknown vector wave amplitudes of the dGf. The unknowns are calculated by truncation of the infinite sums and matrix inversion. The theory is exact, as no simplifying assumptions are required in any one of the analytical steps leading to the dGf, and it is general in the sense that any number, position, size, and electrical properties can be considered for the layers of the sphere. The point source can be placed outside of or in any lossless part of the sphere. Energy conservation, reciprocity, and other checks verify that the dGf is correct. A numerical application is made to a stratified sphere made of gold and glass, which operates as a lens.

Spherical harmonic analysis of a model-generated climatology

NASA Technical Reports Server (NTRS)

Christidis, Z. D.; Spar, J.

1981-01-01

Monthly mean fields of 850 mb temperature (T850), 500 mb geopotential height (G500) and sea level pressure (SLP) were generated in the course of a five-year climate simulation run with a global general circulation model. Both the model-generated climatology and an observed climatology were subjected to spherical harmonic analysis, with separate analyses of the globe and the Northern Hemisphere. Comparison of the dominant harmonics of the two climatologies indicates that more than 95% of the area-weighted spatial variance of G500 and more than 90% of that of T850 are explained by fewer than three components, and that the model adequately simulates these large-scale characteristics. On the other hand, as many as 25 harmonics are needed to explain 95% of the observed variance of SLP, and the model simulation of this field is much less satisfactory. The model climatology is also evaluated in terms of the annual cycles of the dominant harmonics.

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.

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.

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.

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.

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions.

PubMed

Harris, Frank E

2016-05-28

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance rij. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validated by showing that they yield correct results for a large number of integrals published by other investigators.

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.

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.

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.

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.

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.

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.

Harmonic reduction of Direct Torque Control of six-phase induction motor.

PubMed

Taheri, A

2016-07-01

In this paper, a new switching method in Direct Torque Control (DTC) of a six-phase induction machine for reduction of current harmonics is introduced. Selecting a suitable vector in each sampling period is an ordinal method in the ST-DTC drive of a six-phase induction machine. The six-phase induction machine has 64 voltage vectors and divided further into four groups. In the proposed DTC method, the suitable voltage vectors are selected from two vector groups. By a suitable selection of two vectors in each sampling period, the harmonic amplitude is decreased more, in and various comparison to that of the ST-DTC drive. The harmonics loss is greater reduced, while the electromechanical energy is decreased with switching loss showing a little increase. Spectrum analysis of the phase current in the standard and new switching table DTC of the six-phase induction machine and determination for the amplitude of each harmonics is proposed in this paper. The proposed method has a less sampling time in comparison to the ordinary method. The Harmonic analyses of the current in the low and high speed shows the performance of the presented method. The simplicity of the proposed method and its implementation without any extra hardware is other advantages of the proposed method. The simulation and experimental results show the preference of the proposed method. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Vector solitons in harmonic mode-locked erbium-doped fiber lasers

NASA Astrophysics Data System (ADS)

Habruseva, Tatiana; Mkhitaryan, Mkhitar; Mou, Chengbo; Rozhin, Aleksey; Turitsyn, Sergei K.; Sergeyev, Sergey V.

2014-05-01

We report experimental study of vector solitons for the fundamental and harmonic mode-locked operation in erbiumdoper fiber lasers with carbon nanotubes based saturable absorbers and anomalous dispersion cavities. We measure evolution of the output pulses polarization and demonstrate vector solitons with various polarization attractors, including locked polarization, periodic polarization switching, and polarization precession.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

An exact solution of the van der Waals interaction between two ground-state hydrogen atoms

NASA Astrophysics Data System (ADS)

Koga, Toshikatsu; Matsumoto, Shinya

1985-06-01

A momentum space treatment shows that perturbation equations for the H(1s)-H(1s) van der Waals interaction can be exactly solved in their Schrödinger forms without invoking any variational methods. Using the Fock transformation, which projects the momentum vector of an electron from the three-dimensional hyperplane onto the four-dimensional hypersphere, we solve the third order integral-type perturbation equation with respect to the reciprocal of the internuclear distance R. An exact third order wave function is found as a linear combination of infinite number of four-dimensional spherical harmonics. The result allows us to evaluate the exact dispersion energy E6R-6, which is completely determined by the first three coefficients of the above linear combination.

Kinetic-energy matrix elements for atomic Hylleraas-CI wave functions

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

Harris, Frank E., E-mail: harris@qtp.ufl.edu

Hylleraas-CI is a superposition-of-configurations method in which each configuration is constructed from a Slater-type orbital (STO) product to which is appended (linearly) at most one interelectron distance r{sub ij}. Computations of the kinetic energy for atoms by this method have been difficult due to the lack of formulas expressing these matrix elements for general angular momentum in terms of overlap and potential-energy integrals. It is shown here that a strategic application of angular-momentum theory, including the use of vector spherical harmonics, enables the reduction of all atomic kinetic-energy integrals to overlap and potential-energy matrix elements. The new formulas are validatedmore » by showing that they yield correct results for a large number of integrals published by other investigators.« less

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.

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

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.

Geodesic synchrotron radiation in the Kerr geometry by the method of asymptotically factorized Green's functions

NASA Technical Reports Server (NTRS)

Chrzanowski, P. L.; Misner, C. W.

1974-01-01

The scalar, electromagnetic, and gravitational geodesic-synchrotron-radiation (GSR) spectra are determined for the case of a test particle moving on a highly relativistic circular orbit about a rotating (Kerr) black hole. It is found that the spectral shape depends only weakly on the value of the angular-momentum parameter (a/M) of the black hole, but the total radiated power drops unexpectedly for a value of at least 0.95 and vanishes as the value approaches unity. A spin-dependent factor (involving the inner product of the polarization of a radiated quantum with the source) is isolated to explain the dependence of the spectral shape on the spin of the radiated field. Although the scalar wave equation is solved by separation of variables, this procedure is avoided for the vector and tensor cases by postulating a sum-over-states expansion for the Green's function similar to that found to hold in the scalar case. The terms in this sum, significant for GSR, can then be evaluated in the geometric-optics approximation without requiring the use of vector or tensor spherical harmonics.

Waveform inversion for 3-D earth structure using the Direct Solution Method implemented on vector-parallel supercomputer

NASA Astrophysics Data System (ADS)

Hara, Tatsuhiko

2004-08-01

We implement the Direct Solution Method (DSM) on a vector-parallel supercomputer and show that it is possible to significantly improve its computational efficiency through parallel computing. We apply the parallel DSM calculation to waveform inversion of long period (250-500 s) surface wave data for three-dimensional (3-D) S-wave velocity structure in the upper and uppermost lower mantle. We use a spherical harmonic expansion to represent lateral variation with the maximum angular degree 16. We find significant low velocities under south Pacific hot spots in the transition zone. This is consistent with other seismological studies conducted in the Superplume project, which suggests deep roots of these hot spots. We also perform simultaneous waveform inversion for 3-D S-wave velocity and Q structure. Since resolution for Q is not good, we develop a new technique in which power spectra are used as data for inversion. We find good correlation between long wavelength patterns of Vs and Q in the transition zone such as high Vs and high Q under the western Pacific.

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

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

The BGS magnetic field candidate models for the 12th generation IGRF

NASA Astrophysics Data System (ADS)

Hamilton, Brian; Ridley, Victoria A.; Beggan, Ciarán D.; Macmillan, Susan

2015-05-01

We describe the candidate models submitted by the British Geological Survey for the 12th generation International Geomagnetic Reference Field. These models are extracted from a spherical harmonic `parent model' derived from vector and scalar magnetic field data from satellite and observatory sources. These data cover the period 2009.0 to 2014.7 and include measurements from the recently launched European Space Agency (ESA) Swarm satellite constellation. The parent model's internal field time dependence for degrees 1 to 13 is represented by order 6 B-splines with knots at yearly intervals. The parent model's degree 1 external field time dependence is described by periodic functions for the annual and semi-annual signals and by dependence on the 20-min Vector Magnetic Disturbance index. Signals induced by these external fields are also parameterized. Satellite data are weighted by spatial density and by two different noise estimators: (a) by standard deviation along segments of the satellite track and (b) a larger-scale noise estimator defined in terms of a measure of vector activity at the geographically closest magnetic observatories to the sample point. Forecasting of the magnetic field secular variation beyond the span of data is by advection of the main field using core surface flows.

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.

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.

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.

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.

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).

Existence and uniqueness of weak solutions of the compressible spherically symmetric Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Huang, Xiangdi

2017-02-01

One of the most influential fundamental tools in harmonic analysis is the Riesz transforms. It maps Lp functions to Lp functions for any p ∈ (1 , ∞) which plays an important role in singular operators. As an application in fluid dynamics, the norm equivalence between ‖∇u‖Lp and ‖ div u ‖ Lp +‖ curl u ‖ Lp is well established for p ∈ (1 , ∞). However, since Riesz operators sent bounded functions only to BMO functions, there is no hope to bound ‖∇u‖L∞ in terms of ‖ div u ‖ L∞ +‖ curl u ‖ L∞. As pointed out by Hoff (2006) [11], this is the main obstacle to obtain uniqueness of weak solutions for isentropic compressible flows. Fortunately, based on new observations, see Lemma 2.2, we derive an exact estimate for ‖∇u‖L∞ ≤ (2 + 1 / N)‖ div u ‖ L∞ for any N-dimensional radially symmetric vector functions u. As a direct application, we give an affirmative answer to the open problem of uniqueness of some weak solutions to the compressible spherically symmetric flows in a bounded ball.

Boundary integral equation analysis for suspension of spheres in Stokes flow

NASA Astrophysics Data System (ADS)

Corona, Eduardo; Veerapaneni, Shravan

2018-06-01

We show that the standard boundary integral operators, defined on the unit sphere, for the Stokes equations diagonalize on a specific set of vector spherical harmonics and provide formulas for their spectra. We also derive analytical expressions for evaluating the operators away from the boundary. When two particle are located close to each other, we use a truncated series expansion to compute the hydrodynamic interaction. On the other hand, we use the standard spectrally accurate quadrature scheme to evaluate smooth integrals on the far-field, and accelerate the resulting discrete sums using the fast multipole method (FMM). We employ this discretization scheme to analyze several boundary integral formulations of interest including those arising in porous media flow, active matter and magneto-hydrodynamics of rigid particles. We provide numerical results verifying the accuracy and scaling of their evaluation.

Unified heat kernel regression for diffusion, kernel smoothing and wavelets on manifolds and its application to mandible growth modeling in CT images.

PubMed

Chung, Moo K; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K

2015-05-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel method is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, the method is applied to characterize the localized growth pattern of mandible surfaces obtained in CT images between ages 0 and 20 by regressing the length of displacement vectors with respect to a surface template. Copyright © 2015 Elsevier B.V. All rights reserved.

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.

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.

Coherent states for the relativistic harmonic oscillator

NASA Technical Reports Server (NTRS)

Aldaya, Victor; Guerrero, J.

1995-01-01

Recently we have obtained, on the basis of a group approach to quantization, a Bargmann-Fock-like realization of the Relativistic Harmonic Oscillator as well as a generalized Bargmann transform relating fock wave functions and a set of relativistic Hermite polynomials. Nevertheless, the relativistic creation and annihilation operators satisfy typical relativistic commutation relations of the Lie product (vector-z, vector-z(sup dagger)) approximately equals Energy (an SL(2,R) algebra). Here we find higher-order polarization operators on the SL(2,R) group, providing canonical creation and annihilation operators satisfying the Lie product (vector-a, vector-a(sup dagger)) = identity vector 1, the eigenstates of which are 'true' coherent states.

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.

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

Assessment of polarization effect on aerosol retrievals from MODIS

NASA Astrophysics Data System (ADS)

Korkin, S.; Lyapustin, A.

2010-12-01

Light polarization affects the total intensity of scattered radiation. In this work, we compare aerosol retrievals performed by code MAIAC [1] with and without taking polarization into account. The MAIAC retrievals are based on the look-up tables (LUT). For this work, MAIAC was run using two different LUTs, the first one generated using the scalar code SHARM [2], and the second one generated with the vector code Modified Vector Discrete Ordinates Method (MVDOM). MVDOM is a new code suitable for computations with highly anisotropic phase functions, including cirrus clouds and snow [3]. To this end, the solution of the vector radiative transfer equation (VRTE) is represented as a sum of anisotropic and regular components. The anisotropic component is evaluated in the Small Angle Modification of the Spherical Harmonics Method (MSH) [4]. The MSH is formulated in the frame of reference of the solar beam where z-axis lies along the solar beam direction. In this case, the MSH solution for anisotropic part is nearly symmetric in azimuth, and is computed analytically. In scalar case, this solution coincides with the Goudsmit-Saunderson small-angle approximation [5]. To correct for an analytical separation of the anisotropic part of the signal, the transfer equation for the regular part contains a correction source function term [6]. Several examples of polarization impact on aerosol retrievals over different surface types will be presented. 1. Lyapustin A., Wang Y., Laszlo I., Kahn R., Korkin S., Remer L., Levy R., and Reid J. S. Multi-Angle Implementation of Atmospheric Correction (MAIAC): Part 2. Aerosol Algorithm. J. Geophys. Res., submitted (2010). 2. Lyapustin A., Muldashev T., Wang Y. Code SHARM: fast and accurate radiative transfer over spatially variable anisotropic surfaces. In: Light Scattering Reviews 5. Chichester: Springer, 205 - 247 (2010). 3. Budak, V.P., Korkin S.V. On the solution of a vectorial radiative transfer equation in an arbitrary three-dimensional turbid medium with anisotropic scattering. JQSRT, 109, 220-234 (2008). 4. Budak V.P., Sarmin S.E. Solution of radiative transfer equation by the method of spherical harmonics in the small angle modification. Atmospheric and Oceanic Optics, 3, 898-903 (1990). 5. Goudsmit S., Saunderson J.L. Multiple scattering of electrons. Phys. Rev., 57, 24-29 (1940). 6. Budak V.P, Klyuykov D.A., Korkin S.V. Convergence acceleration of radiative transfer equation solution at strongly anisotropic scattering. In: Light Scattering Reviews 5. Chichester: Springer, 147 - 204 (2010).

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.

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.

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.

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.

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.

Multipole Vector Anomalies in the First-Year WMAP Data: A Cut-Sky Analysis

NASA Astrophysics Data System (ADS)

Bielewicz, P.; Eriksen, H. K.; Banday, A. J.; Górski, K. M.; Lilje, P. B.

2005-12-01

We apply the recently defined multipole vector framework to the frequency-specific first-year WMAP sky maps, estimating the low-l multipole coefficients from the high-latitude sky by means of a power equalization filter. While most previous analyses of this type have considered only heavily processed (and foreground-contaminated) full-sky maps, the present approach allows for greater control of residual foregrounds and therefore potentially also for cosmologically important conclusions. The low-l spherical harmonic coefficients and corresponding multipole vectors are tabulated for easy reference. Using this formalism, we reassess a set of earlier claims of both cosmological and noncosmological low-l correlations on the basis of multipole vectors. First, we show that the apparent l=3 and 8 correlation claimed by Copi and coworkers is present only in the heavily processed map produced by Tegmark and coworkers and must therefore be considered an artifact of that map. Second, the well-known quadrupole-octopole correlation is confirmed at the 99% significance level and shown to be robust with respect to frequency and sky cut. Previous claims are thus supported by our analysis. Finally, the low-l alignment with respect to the ecliptic claimed by Schwarz and coworkers is nominally confirmed in this analysis, but also shown to be very dependent on severe a posteriori choices. Indeed, we show that given the peculiar quadrupole-octopole arrangement, finding such a strong alignment with the ecliptic is not unusual.

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.

Contribution of zonal harmonics to gravitational moment

NASA Technical Reports Server (NTRS)

Roithmayr, Carlos M.

1991-01-01

It is presently demonstrated that a recursive vector-dyadic expression for the contribution of a zonal harmonic of degree n to the gravitational moment about a small body's center-of-mass is obtainable with a procedure that involves twice differentiating a celestial body's gravitational potential with respect to a vector. The recursive property proceeds from taking advantage of a recursion relation for Legendre polynomials which appear in the gravitational potential. The contribution of the zonal harmonic of degree 2 is consistent with the gravitational moment exerted by an oblate spheroid.

Contribution of zonal harmonics to gravitational moment

NASA Astrophysics Data System (ADS)

Roithmayr, Carlos M.

1991-02-01

It is presently demonstrated that a recursive vector-dyadic expression for the contribution of a zonal harmonic of degree n to the gravitational moment about a small body's center-of-mass is obtainable with a procedure that involves twice differentiating a celestial body's gravitational potential with respect to a vector. The recursive property proceeds from taking advantage of a recursion relation for Legendre polynomials which appear in the gravitational potential. The contribution of the zonal harmonic of degree 2 is consistent with the gravitational moment exerted by an oblate spheroid.

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.

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

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.

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.

Magnetic and gravity anomalies in the Americas

NASA Technical Reports Server (NTRS)

Braile, L. W.; Hinze, W. J.; Vonfrese, R. R. B. (Principal Investigator)

1981-01-01

The cleaning and magnetic tape storage of spherical Earth processing programs are reported. These programs include: NVERTSM which inverts total or vector magnetic anomaly data on a distribution of point dipoles in spherical coordinates; SMFLD which utilizes output from NVERTSM to compute total or vector magnetic anomaly fields for a distribution of point dipoles in spherical coordinates; NVERTG; and GFLD. Abstracts are presented for papers dealing with the mapping and modeling of magnetic and gravity anomalies, and with the verification of crustal components in satellite data.

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.

Current harmonics elimination control method for six-phase PM synchronous motor drives.

PubMed

Yuan, Lei; Chen, Ming-liang; Shen, Jian-qing; Xiao, Fei

2015-11-01

To reduce the undesired 5th and 7th stator harmonic current in the six-phase permanent magnet synchronous motor (PMSM), an improved vector control algorithm was proposed based on vector space decomposition (VSD) transformation method, which can control the fundamental and harmonic subspace separately. To improve the traditional VSD technology, a novel synchronous rotating coordinate transformation matrix was presented in this paper, and only using the traditional PI controller in d-q subspace can meet the non-static difference adjustment, the controller parameter design method is given by employing internal model principle. Moreover, the current PI controller parallel with resonant controller is employed in x-y subspace to realize the specific 5th and 7th harmonic component compensation. In addition, a new six-phase SVPWM algorithm based on VSD transformation theory is also proposed. Simulation and experimental results verify the effectiveness of current decoupling vector controller. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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).

Temporal and spatial foliations of spacetimes.

NASA Astrophysics Data System (ADS)

Herold, H.

For the solution of initial-value problems in numerical relativity usually the (3+1) splitting of Einstein's equations is employed. An important part of this splitting is the choice of the temporal gauge condition. In order to estimate the quality of time-evolution schemes, different time slicings of given well-known spherically symmetric spacetimes have been studied. Besides the maximal slicing condition the harmonic slicing prescription has been used to calculate temporal foliations of the Schwarzschild and the Oppenheimer-Snyder spacetime. Additionally, the author has studied a recently proposed, geometrically motivated spatial gauge condition, which is defined by considering the foliations of the three-dimensional space-like hypersurfaces by 2-surfaces of constant mean extrinsic curvature. Apart from the equations for the shift vector, which can be derived for this gauge condition, he has investigated such spatial foliations for well-known stationary axially symmetric spacetimes, namely for the Kerr metric and for numerically determined solutions for rapidly rotating neutron stars.

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

PubMed Central

Chung, Moo K.; Qiu, Anqi; Seo, Seongho; Vorperian, Houri K.

2014-01-01

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface. PMID:25791435

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.

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

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

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.

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.

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.

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.

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.

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.

Gravity Compensation Using EGM2008 for High-Precision Long-Term Inertial Navigation Systems

PubMed Central

Wu, Ruonan; Wu, Qiuping; Han, Fengtian; Liu, Tianyi; Hu, Peida; Li, Haixia

2016-01-01

The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs. PMID:27999351

Gravity Compensation Using EGM2008 for High-Precision Long-Term Inertial Navigation Systems.

PubMed

Wu, Ruonan; Wu, Qiuping; Han, Fengtian; Liu, Tianyi; Hu, Peida; Li, Haixia

2016-12-18

The gravity disturbance vector is one of the major error sources in high-precision and long-term inertial navigation applications. Specific to the inertial navigation systems (INSs) with high-order horizontal damping networks, analyses of the error propagation show that the gravity-induced errors exist almost exclusively in the horizontal channels and are mostly caused by deflections of the vertical (DOV). Low-frequency components of the DOV propagate into the latitude and longitude errors at a ratio of 1:1 and time-varying fluctuations in the DOV excite Schuler oscillation. This paper presents two gravity compensation methods using the Earth Gravitational Model 2008 (EGM2008), namely, interpolation from the off-line database and computing gravity vectors directly using the spherical harmonic model. Particular attention is given to the error contribution of the gravity update interval and computing time delay. It is recommended for the marine navigation that a gravity vector should be calculated within 1 s and updated every 100 s at most. To meet this demand, the time duration of calculating the current gravity vector using EGM2008 has been reduced to less than 1 s by optimizing the calculation procedure. A few off-line experiments were conducted using the data of a shipborne INS collected during an actual sea test. With the aid of EGM2008, most of the low-frequency components of the position errors caused by the gravity disturbance vector have been removed and the Schuler oscillation has been attenuated effectively. In the rugged terrain, the horizontal position error could be reduced at best 48.85% of its regional maximum. The experimental results match with the theoretical analysis and indicate that EGM2008 is suitable for gravity compensation of the high-precision and long-term INSs.

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.

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.

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.

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.

Charged reflecting stars supporting charged massive scalar field configurations

NASA Astrophysics Data System (ADS)

Hod, Shahar

2018-03-01

The recently published no-hair theorems of Hod, Bhattacharjee, and Sarkar have revealed the intriguing fact that horizonless compact reflecting stars cannot support spatially regular configurations made of scalar, vector and tensor fields. In the present paper we explicitly prove that the interesting no-hair behavior observed in these studies is not a generic feature of compact reflecting stars. In particular, we shall prove that charged reflecting stars can support charged massive scalar field configurations in their exterior spacetime regions. To this end, we solve analytically the characteristic Klein-Gordon wave equation for a linearized charged scalar field of mass μ , charge coupling constant q, and spherical harmonic index l in the background of a spherically symmetric compact reflecting star of mass M, electric charge Q, and radius R_{ {s}}≫ M,Q. Interestingly, it is proved that the discrete set {R_{ {s}}(M,Q,μ ,q,l;n)}^{n=∞}_{n=1} of star radii that can support the charged massive scalar field configurations is determined by the characteristic zeroes of the confluent hypergeometric function. Following this simple observation, we derive a remarkably compact analytical formula for the discrete spectrum of star radii in the intermediate regime M≪ R_{ {s}}≪ 1/μ . The analytically derived resonance spectrum is confirmed by direct numerical computations.

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

Methods, systems and apparatus for optimization of third harmonic current injection in a multi-phase machine

DOEpatents

Gallegos-Lopez, Gabriel

2012-10-02

Methods, system and apparatus are provided for increasing voltage utilization in a five-phase vector controlled machine drive system that employs third harmonic current injection to increase torque and power output by a five-phase machine. To do so, a fundamental current angle of a fundamental current vector is optimized for each particular torque-speed of operating point of the five-phase machine.

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.

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

A vectorized Poisson solver over a spherical shell and its application to the quasi-geostrophic omega-equation

NASA Technical Reports Server (NTRS)

Mullenmeister, Paul

1988-01-01

The quasi-geostrophic omega-equation in flux form is developed as an example of a Poisson problem over a spherical shell. Solutions of this equation are obtained by applying a two-parameter Chebyshev solver in vector layout for CDC 200 series computers. The performance of this vectorized algorithm greatly exceeds the performance of its scalar analog. The algorithm generates solutions of the omega-equation which are compared with the omega fields calculated with the aid of the mass continuity equation.

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

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.

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

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.

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.

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

Methods, systems and apparatus for controlling third harmonic voltage when operating a multi-space machine in an overmodulation region

DOEpatents

Perisic, Milun; Kinoshita, Michael H; Ranson, Ray M; Gallegos-Lopez, Gabriel

2014-06-03

Methods, system and apparatus are provided for controlling third harmonic voltages when operating a multi-phase machine in an overmodulation region. The multi-phase machine can be, for example, a five-phase machine in a vector controlled motor drive system that includes a five-phase PWM controlled inverter module that drives the five-phase machine. Techniques for overmodulating a reference voltage vector are provided. For example, when the reference voltage vector is determined to be within the overmodulation region, an angle of the reference voltage vector can be modified to generate a reference voltage overmodulation control angle, and a magnitude of the reference voltage vector can be modified, based on the reference voltage overmodulation control angle, to generate a modified magnitude of the reference voltage vector. By modifying the reference voltage vector, voltage command signals that control a five-phase inverter module can be optimized to increase output voltages generated by the five-phase inverter module.

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.

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

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.

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

Magnetic Coordinate Systems

NASA Astrophysics Data System (ADS)

Laundal, K. M.; Richmond, A. D.

2017-03-01

Geospace phenomena such as the aurora, plasma motion, ionospheric currents and associated magnetic field disturbances are highly organized by Earth's main magnetic field. This is due to the fact that the charged particles that comprise space plasma can move almost freely along magnetic field lines, but not across them. For this reason it is sensible to present such phenomena relative to Earth's magnetic field. A large variety of magnetic coordinate systems exist, designed for different purposes and regions, ranging from the magnetopause to the ionosphere. In this paper we review the most common magnetic coordinate systems and describe how they are defined, where they are used, and how to convert between them. The definitions are presented based on the spherical harmonic expansion coefficients of the International Geomagnetic Reference Field (IGRF) and, in some of the coordinate systems, the position of the Sun which we show how to calculate from the time and date. The most detailed coordinate systems take the full IGRF into account and define magnetic latitude and longitude such that they are constant along field lines. These coordinate systems, which are useful at ionospheric altitudes, are non-orthogonal. We show how to handle vectors and vector calculus in such coordinates, and discuss how systematic errors may appear if this is not done correctly.

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.

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.

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.

Polarizability tensor retrieval for magnetic and plasmonic antenna design

NASA Astrophysics Data System (ADS)

Bernal Arango, Felipe; Femius Koenderink, A.

2013-07-01

A key quantity in the design of plasmonic antennas and metasurfaces, as well as metamaterials, is the electrodynamic polarizability of a single scattering building block. In particular, in the current merging of plasmonics and metamaterials, subwavelength scatterers are judged by their ability to present a large, generally anisotropic electric and magnetic polarizability, as well as a bi-anisotropic magnetoelectric polarizability. This bi-anisotropic response, whereby a magnetic dipole is induced through electric driving, and vice versa, is strongly linked to the optical activity and chiral response of plasmonic metamolecules. We present two distinct methods to retrieve the polarizibility tensor from electrodynamic simulations. As a basis for both, we use the surface integral equation (SIE) method to solve for the scattering response of arbitrary objects exactly. In the first retrieval method, we project scattered fields onto vector spherical harmonics with the aid of an exact discrete spherical harmonic Fourier transform on the unit sphere. In the second, we take the effective current distributions generated by SIE as a basis to calculate dipole moments. We verify that the first approach holds for scatterers of any size, while the second is only approximately correct for small scatterers. We present benchmark calculations, revisiting the zero-forward scattering paradox of Kerker et al (1983 J. Opt. Soc. Am. 73 765-7) and Alù and Engheta (2010 J. Nanophoton. 4 041590), relevant in dielectric scattering cancelation and sensor cloaking designs. Finally, we report the polarizability tensor of split rings, and show that split rings will strongly influence the emission of dipolar single emitters. In the context of plasmon-enhanced emission, split rings can imbue their large magnetic dipole moment on the emission of simple electric dipole emitters. We present a split ring antenna array design that is capable of converting the emission of a single linear dipole emitter in forward and backward beams of directional emission of opposite handedness. This design can, for instance, find application in the spin angular momentum encoding of quantum information.

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.

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.

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

Local Gram-Schmidt and covariant Lyapunov vectors and exponents for three harmonic oscillator problems

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.

2012-02-01

We compare the Gram-Schmidt and covariant phase-space-basis-vector descriptions for three time-reversible harmonic oscillator problems, in two, three, and four phase-space dimensions respectively. The two-dimensional problem can be solved analytically. The three-dimensional and four-dimensional problems studied here are simultaneously chaotic, time-reversible, and dissipative. Our treatment is intended to be pedagogical, for use in an updated version of our book on Time Reversibility, Computer Simulation, and Chaos. Comments are very welcome.

The harmonic oscillator and nuclear physics

NASA Technical Reports Server (NTRS)

Rowe, D. J.

1993-01-01

The three-dimensional harmonic oscillator plays a central role in nuclear physics. It provides the underlying structure of the independent-particle shell model and gives rise to the dynamical group structures on which models of nuclear collective motion are based. It is shown that the three-dimensional harmonic oscillator features a rich variety of coherent states, including vibrations of the monopole, dipole, and quadrupole types, and rotations of the rigid flow, vortex flow, and irrotational flow types. Nuclear collective states exhibit all of these flows. It is also shown that the coherent state representations, which have their origins in applications to the dynamical groups of the simple harmonic oscillator, can be extended to vector coherent state representations with a much wider range of applicability. As a result, coherent state theory and vector coherent state theory become powerful tools in the application of algebraic methods in physics.

Torque ripple reduction of brushless DC motor based on adaptive input-output feedback linearization.

PubMed

Shirvani Boroujeni, M; Markadeh, G R Arab; Soltani, J

2017-09-01

Torque ripple reduction of Brushless DC Motors (BLDCs) is an interesting subject in variable speed AC drives. In this paper at first, a mathematical expression for torque ripple harmonics is obtained. Then for a non-ideal BLDC motor with known harmonic contents of back-EMF, calculation of desired reference current amplitudes, which are required to eliminate some selected harmonics of torque ripple, are reviewed. In order to inject the reference harmonic currents to the motor windings, an Adaptive Input-Output Feedback Linearization (AIOFBL) control is proposed, which generates the reference voltages for three phases voltage source inverter in stationary reference frame. Experimental results are presented to show the capability and validity of the proposed control method and are compared with the vector control in Multi-Reference Frame (MRF) and Pseudo-Vector Control (P-VC) method results. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

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.

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.

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.

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.

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.

The analysis of initial Juno magnetometer data using a sparse magnetic field representation

NASA Astrophysics Data System (ADS)

Moore, Kimberly M.; Bloxham, Jeremy; Connerney, John E. P.; Jørgensen, John L.; Merayo, José M. G.

2017-05-01

The Juno spacecraft, now in polar orbit about Jupiter, passes much closer to Jupiter's surface than any previous spacecraft, presenting a unique opportunity to study the largest and most accessible planetary dynamo in the solar system. Here we present an analysis of magnetometer observations from Juno's first perijove pass (PJ1; to within 1.06 RJ of Jupiter's center). We calculate the residuals between the vector magnetic field observations and that calculated using the VIP4 spherical harmonic model and fit these residuals using an elastic net regression. The resulting model demonstrates how effective Juno's near-surface observations are in improving the spatial resolution of the magnetic field within the immediate vicinity of the orbit track. We identify two features resulting from our analyses: the presence of strong, oppositely signed pairs of flux patches near the equator and weak, possibly reversed-polarity patches of magnetic field over the polar regions. Additional orbits will be required to assess how robust these intriguing features are.

Saturn's Magnetic Field and Magnetosphere.

PubMed

Smith, E J; Davis, L; Jones, D E; Coleman, P J; Colburn, D S; Dyal, P; Sonett, C P

1980-01-25

The Pioneer Saturn vector helium magnetometer has detected a bow shock and magnetopause at Saturn and has provided an accurate characterization of the planetary field. The equatorial surface field is 0.20 gauss, a factor of 3 to 5 times smaller than anticipated on the basis of attempted scalings from Earth and Jupiter. The tilt angle between the magnetic dipole axis and Saturn's rotation axis is < 1 degrees , a surprisingly small value. Spherical harmonic analysis of the measurements shows that the ratio of quadrupole to dipole moments is < 10 percent, indicating that the field is more uniform than those of the Earth or Jupiter and consistent with Saturn having a relatively small core. The field in the outer magnetosphere shows systematic departures from the dipole field, principally a compression of the field near noon and an equatorial orientation associated with a current sheet near dawn. A hydromagnetic wake resulting from the interaction of Titan with the rotating magnetosphere appears to have been observed.

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.

Magnetic space-based field measurements

NASA Technical Reports Server (NTRS)

Langel, R. A.

1981-01-01

Because the near Earth magnetic field is a complex combination of fields from outside the Earth of fields from its core and of fields from its crust, measurements from space prove to be the only practical way to obtain timely, global surveys. Due to difficulty in making accurate vector measurements, early satellites such as Sputnik and Vanguard measured only the magnitude survey. The attitude accuracy was 20 arc sec. Both the Earth's core fields and the fields arising from its crust were mapped from satellite data. The standard model of the core consists of a scalar potential represented by a spherical harmonics series. Models of the crustal field are relatively new. Mathematical representation is achieved in localized areas by arrays of dipoles appropriately located in the Earth's crust. Measurements of the Earth's field are used in navigation, to map charged particles in the magnetosphere, to study fluid properties in the Earth's core, to infer conductivity of the upper mantels, and to delineate regional scale geological features.

Correction and update to 'The earth's C21 and S21 gravity coefficients and the rotation of the core'

NASA Technical Reports Server (NTRS)

Wahr, John

1990-01-01

Wahr (1987) used satellite constraints on C21 and S21 (the spherical harmonic coefficients of the earth's external gravitational potential) to infer certain properties of the core and core/mantle boundary. It is shown here, contrary to the claim by Wahr, that it is not possible to use C21 and S21 to placed bounds on the core's products of inertia. As a result, Wahr's constraints on the l = 2, m = 1 components of the core/mantle boundary topography and on the angular orientation of the inner core with respect to the earth's rotation vector are not justified. On the other hand, Wahr's conclusions about the time-averaged torque between the core and mantle and the resulting implications for the l = 2, m = 1 components of fluid pressure at the top of the core can be strengthened. Wahr's conclusions about the mean rotational flow in the core are unaltered.

Excitation of multipolar surface plasmon resonance in plasmonic nanoparticles by complex accelerating beams

NASA Astrophysics Data System (ADS)

Yang, Yang; Li, Jiafang; Li, Zhi-Yuan; Chen, Yue-Gang

2015-07-01

In this paper, through a vector-spherical harmonics approach, we investigate the optical spectra of plasmonic Au nanoparticles excited by two special accelerating beams: a non-paraxial Airy beam and a Bessel beam. We systematically analyze the impacts of the beam profile, phase, and helical wave front of the electromagnetic fields on the optical spectrum and the excitation of the surface plasmon resonance (SPR). We find that the high-order phase in the Airy beam would result in strong plasmonic oscillations in the optical spectra, while the cone angle and orbital angular momentum carried by the Bessel beam could be employed to engineer the plasmon modes excited in Au nanoparticles. Furthermore, the optical spectrum excited by a combined Airy-Bessel-Gauss beam is discussed. The study could help to deeply explore new ways to manipulate SPR in metal nanoparticles via the wave front engineering of optical beams for enhancing light-matter interaction and optical sensing performance.

Main field and secular variation modeling with Defense Meteorological Satellite Program magnetic measurements

NASA Astrophysics Data System (ADS)

Alken, P.; Olsen, N.; Finlay, C. C.; Chulliat, A.

2017-12-01

In order to investigate the spatial structure and development of rapid (sub-decadal) changes in the geomagnetic core field, including its secular variation and acceleration, global magnetic measurements from space play a crucial role. With the end of the CHAMP mission in September 2010, there has been a gap in high-quality satellite magnetic field measurements until the Swarm mission was launched in November 2013. Geomagnetic main field models during this period have relied on the global ground observatory network which, due to its sparse spatial configuration, has difficulty in resolving secular variation and acceleration at higher spherical harmonic degrees. In this presentation we will show new results in building main field models during this "gap period", based on vector magnetic measurements from four Defense Meteorological Satellite Program (DMSP) satellites. While the fluxgate instruments onboard DMSP were not designed for high-quality core field modeling, we find that the DMSP dataset can provide valuable information on secular variation and acceleration during the gap period.

3D-MHD Simulations of the Madison Dynamo Experiment

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Forest, C. B.; Wright, J. C.; O'Connell, R.

2003-10-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a 3-D pseudo-spectral simulation of the MHD equations; results of the simulations are used to predict behavior of the experiment. The code solves the self-consistent full evolution of the magnetic and velocity fields. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and fourth order finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James [Proc. R. Soc. Lond. A 425. 407-429 (1989)]. Initial results indicate that saturation of the magnetic field occurs so that the resulting perturbed backreaction of the induced magnetic field changes the velocity field such that it would no longer be linearly unstable, suggesting non-linear terms are necessary for explaining the resulting state. Saturation and self-excitation depend in detail upon the magnetic Prandtl number.

Numerical modelling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Wright, J. C.; Forest, C. B.; O'Connell, R.; Truitt, J. L.

2000-10-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a newly developed 3-D pseudo-spectral simulation of the MHD equations; results of the simulations will be compared to the experimental results obtained from the experiment. The code, Dynamo, is in Fortran90 and allows for full evolution of the magnetic and velocity fields. The induction equation governing B and the Navier-Stokes equation governing V are solved. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James (M.L. Dudley and R.W. James, Time-dependant kinematic dynamos with stationary flows, Proc. R. Soc. Lond. A 425, p. 407 (1989)). Initial results on magnetic field saturation, generated by the simultaneous evolution of magnetic and velocity fields be presented using a variety of mechanical forcing terms.

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.

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.

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.

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].

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).

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.

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.

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)

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

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

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.

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.

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.

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).

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.

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.

Extended phase matching of second-harmonic generation in periodically poled KTiOPO4 with zero group-velocity mismatch

NASA Astrophysics Data System (ADS)

König, Friedrich; Wong, Franco N. C.

2004-03-01

Under extended phase-matching conditions, the first frequency derivative of the wave-vector mismatch is zero and the phase-matching bandwidth is greatly increased. We present extensive three-wave mixing measurements of the wave-vector mismatch and obtain improved Sellmeier equations for KTiOPO4. We observed a type-II extended phase-matching bandwidth of 100 nm for second-harmonic generation in periodically poled KTiOPO4, centered at the fundamental wavelength of 1584 nm. Applications in quantum entanglement and frequency metrology are discussed.

Classification of Alzheimer's disease patients with hippocampal shape wrapper-based feature selection and support vector machine

NASA Astrophysics Data System (ADS)

Young, Jonathan; Ridgway, Gerard; Leung, Kelvin; Ourselin, Sebastien

2012-02-01

It is well known that hippocampal atrophy is a marker of the onset of Alzheimer's disease (AD) and as a result hippocampal volumetry has been used in a number of studies to provide early diagnosis of AD and predict conversion of mild cognitive impairment patients to AD. However, rates of atrophy are not uniform across the hippocampus making shape analysis a potentially more accurate biomarker. This study studies the hippocampi from 226 healthy controls, 148 AD patients and 330 MCI patients obtained from T1 weighted structural MRI images from the ADNI database. The hippocampi are anatomically segmented using the MAPS multi-atlas segmentation method, and the resulting binary images are then processed with SPHARM software to decompose their shapes as a weighted sum of spherical harmonic basis functions. The resulting parameterizations are then used as feature vectors in Support Vector Machine (SVM) classification. A wrapper based feature selection method was used as this considers the utility of features in discriminating classes in combination, fully exploiting the multivariate nature of the data and optimizing the selected set of features for the type of classifier that is used. The leave-one-out cross validated accuracy obtained on training data is 88.6% for classifying AD vs controls and 74% for classifying MCI-converters vs MCI-stable with very compact feature sets, showing that this is a highly promising method. There is currently a considerable fall in accuracy on unseen data indicating that the feature selection is sensitive to the data used, however feature ensemble methods may overcome this.

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.

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.

External field characterization using CHAMP satellite data for induction studies

NASA Astrophysics Data System (ADS)

Kunagu, Praveen; Chandrasekhar, E.

2013-06-01

Knowledge of external inducing source field morphology is essential for precise estimation of electromagnetic (EM) induction response. A better characterization of the external source field of magnetospheric origin can be achieved by decomposing it into outer and inner magnetospheric contributions, which are best represented in Geocentric Solar Magnetospheric (GSM) and Solar Magnetic (SM) reference frames, respectively. Thus we propose a spherical harmonic (SH) model to estimate the outer magnetospheric contribution, following the iterative reweighted least squares approach, using the vector magnetic data of the CHAMP satellite. The data covers almost a complete solar cycle from July 2001 to September 2010, spanning 54,474 orbits. The SH model, developed using orbit-averaged vector magnetic data, reveals the existence of a stable outer magnetospheric contribution of about 7.39 nT. This stable field was removed from the CHAMP data after transforming to SM frame. The residual field in the SM frame acts as a primary source for induction in the Earth. The analysis of this time-series using wavelet transformation showed a dominant 27-day periodicity of the geomagnetic field. Therefore, we calculated the inductive EM C-response function in a least squares sense considering the 27-day period variation as the inducing signal. From the estimated C-response, we have determined that the global depth to the perfect substitute conductor is about 1132 km and its conductivity is around 1.05 S/m.

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.

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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

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.

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)

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.

Observations of Upper Thermospheric Temperatures Using a Ground-Based Optical Instrument at the King Sejong Station, Antarctic

NASA Astrophysics Data System (ADS)

Chung, Jong-Kyun; Won, Young-In; Lee, Bang Yong; Kim, Jhoon

1998-06-01

We measured the terrestrial nightglow of OI 6300A in the thermosphere(~250km) using a ground-based Fabry-Perot interferometer at the King Sejong Station, Antarctic from March through September, 1997. The King Sejong Station is located at high latitude geographically (62.22 deg S, 301.25 deg E) but at mid-latitude geomagnetically (50.65 deg S, 7.51 deg E). It is therefore the strategic location to measure the temperatures of the thermosphere in the Southern Hemisphere associated with both solar and geomagnetic activities. In this study, we analyzed the observed temperatures in relation to F10.7 and Kp indices to examine the effect of the solar and the geomagnetic activities on high-latitude neutral thermosphere. During the observing period, the solar activity was at its minimum. The measured temperatures are usually in the range between about 600~1000 K with some seasonal variation and are higher than those predicted by semi-empirical model, VSH (Vector Spherical Harmonics) and empirical model, MSIS (Mass-Spectrometer-Incoherent-Scatter)-86.

Lateral heterogeneity and azimuthal anistropy of the upper mantle: Love and Rayleigh waves 100-250 sec

NASA Technical Reports Server (NTRS)

Tanimoto, T.; Anderson, D. L.

1983-01-01

The lateral heterogeneity and apparent anisotropy of the upper mantle are studied by measuring Rayleigh and Love wave phase velocities in the period range 100-250 sec. Spherical harmonic descriptions of the lateral heterogeneity are obtained for order and degree up to 1=m=10. Slow regions are evident at the East Pacific rise, northeast Africa, Tibet, Tasman sea, southwestern North America and triple junctions in the Northern Atlantic and Indian oceans. Fast regions occur in Australia, western Pacific and the eastern Atlantic. Details which are not evident in previous studies include two fast regions in the central Pacific and the subduction zone in the Scotia Arc region. Inversion for azimuthal dependence showed (1) little correlation between the fast phase velocity directions and the plate motion vector in plate interiors, but (2) correlation of the fast direction with the perpendicular direction to trenches and ridges. Phase velocity is high when waves propagate perpendicular to these structures. Severe tradeoffs exist between heterogeneity and azimuthal dependence because of the yet unsatisfactory path coverage.

Lateral heterogeneity and azimuthal anisotropy of the upper mantle - Love and Rayleigh waves 100-250 sec

NASA Technical Reports Server (NTRS)

Tanimoto, T.; Anderson, D. L.

1985-01-01

The lateral heterogeneity and apparent anisotropy of the upper mantle are studied by measuring Rayleigh and Love wave phase velocities in the period range 100-250 sec. Spherical harmonic descriptions of the lateral heterogeneity are obtained for order and degree up to 1=m=10. Slow regions are evident at the East Pacific rise, northeast Africa, Tibet, Tasman sea, southwestern North America and triple junctions in the Northern Atlantic and Indian oceans. Fast regions occur in Australia, western Pacific and the eastern Atlantic. Details which are not evident in previous studies include two fast regions in the central Pacific and the subduction zone in the Scotia Arc region. Inversion for azimuthal dependence showed (1) little correlation between the fast phase velocity directions and the plate motion vector in plate interiors, but (2) correlation of the fast direction with the perpendicular direction to trenches and ridges. Phase velocity is high when waves propagate perpendicular to these structures. Severe tradeoffs exist between heterogeneity and azimuthal dependence because of the yet unsatisfactory path coverage.

A study of different modeling choices for simulating platelets within the immersed boundary method

PubMed Central

Shankar, Varun; Wright, Grady B.; Fogelson, Aaron L.; Kirby, Robert M.

2012-01-01

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid–structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmitting information (forces and velocities) between these two representations. Most IB simulations represent their structures with piecewise linear approximations and utilize Hookean spring models to approximate structural forces. Our specific motivation is the modeling of platelets in hemodynamic flows. In this paper, we study two alternative representations – radial basis functions (RBFs) and Fourier-based (trigonometric polynomials and spherical harmonics) representations – for the modeling of platelets in two and three dimensions within the IB framework, and compare our results with the traditional piecewise linear approximation methodology. For different representative shapes, we examine the geometric modeling errors (position and normal vectors), force computation errors, and computational cost and provide an engineering trade-off strategy for when and why one might select to employ these different representations. PMID:23585704

Beyond Euler angles: exploiting the angle-axis parametrization in a multipole expansion of the rotation operator.

PubMed

Siemens, Mark; Hancock, Jason; Siminovitch, David

2007-02-01

Euler angles (alpha,beta,gamma) are cumbersome from a computational point of view, and their link to experimental parameters is oblique. The angle-axis {Phi, n} parametrization, especially in the form of quaternions (or Euler-Rodrigues parameters), has served as the most promising alternative, and they have enjoyed considerable success in rf pulse design and optimization. We focus on the benefits of angle-axis parameters by considering a multipole operator expansion of the rotation operator D(Phi, n), and a Clebsch-Gordan expansion of the rotation matrices D(MM')(J)(Phi, n). Each of the coefficients in the Clebsch-Gordan expansion is proportional to the product of a spherical harmonic of the vector n specifying the axis of rotation, Y(lambdamu)(n), with a fixed function of the rotation angle Phi, a Gegenbauer polynomial C(2J-lambda)(lambda+1)(cosPhi/2). Several application examples demonstrate that this Clebsch-Gordan expansion gives easy and direct access to many of the parameters of experimental interest, including coherence order changes (isolated in the Clebsch-Gordan coefficients), and rotation angle (isolated in the Gegenbauer polynomials).

Numerical modeling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

Bayliss, R. A.; Wright, J. C.; Forest, C. B.; O'Connell, R.

2002-11-01

Growth, saturation and turbulent evolution of the Madison dynamo experiment is investigated numerically using a 3-D pseudo-spectral simulation of the MHD equations; results of the simulations will be compared to results obtained from the experiment. The code, Dynamo (Fortran90), allows for full evolution of the magnetic and velocity fields. The induction equation governing B and the curl of the momentum equation governing V are separately or simultaneously solved. The code uses a spectral representation via spherical harmonic basis functions of the vector fields in longitude and latitude, and fourth order finite differences in the radial direction. The magnetic field evolution has been benchmarked against the laminar kinematic dynamo predicted by M.L. Dudley and R.W. James (M.L. Dudley and R.W. James, Time-dependent kinematic dynamos with stationary flows, Proc. R. Soc. Lond. A 425, p. 407 (1989)). Power balance in the system has been verified in both mechanically driven and perturbed hydrodynamic, kinematic, and dynamic cases. Evolution of the vacuum magnetic field has been added to facilitate comparison with the experiment. Modeling of the Madison Dynamo eXperiment will be presented.

Seismological versus geodetic reference frames for seismic dislocation: consistency under momentum conservations

NASA Astrophysics Data System (ADS)

Xu, Changyi; Chao, Benjamin F.

2015-02-01

We raise attention to the issue of consistency between the reference frame with respect to which the seismological model calculations of displacement are made on one hand, and that to which the geodetic measurements of crustal deformation refer (e.g. the ITRF) on the other. This issue is critical in principle if the seismologically calculated displacement (or gravity change) is to be compared or used in joint inversion with geodetic measurements. A necessary set of conditions to be satisfied by inertial frames is the conservations of linear and angular momentums: no net change in them can be induced by a seismic source indigenous to the Earth. We show that the momentums are embodied in the degree-1 terms of the vector spherical-harmonic expansion of the displacement field. Using three largest recent earthquakes as case examples we find that the algorithms of seismological dislocation modelling in the literature do not conserve the momentums. However, quantitatively this inconsistency amounts to two orders of magnitude smaller than the current precision in the definition of the ITRF, hence insignificant in practice. Some caveats are raised.

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.

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.

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.

Physical modeling with orthotropic material based on harmonic fields.

PubMed

Liao, Sheng-Hui; Zou, Bei-Ji; Geng, Jian-Ping; Wang, Jin-Xiao; Ding, Xi

2012-11-01

Although it is well known that human bone tissues have obvious orthotropic material properties, most works in the physical modeling field adopted oversimplified isotropic or approximated transversely isotropic elasticity due to the simplicity. This paper presents a convenient methodology based on harmonic fields, to construct volumetric finite element mesh integrated with complete orthotropic material. The basic idea is taking advantage of the fact that the longitudinal axis direction indicated by the shape configuration of most bone tissues is compatible with the trajectory of the maximum material stiffness. First, surface harmonic fields of the longitudinal axis direction for individual bone models were generated, whose scalar distribution pattern tends to conform very well to the object shape. The scalar iso-contours were extracted and sampled adaptively to construct volumetric meshes of high quality. Following, the surface harmonic fields were expanded over the whole volumetric domain to create longitudinal and radial volumetric harmonic fields, from which the gradient vector fields were calculated and employed as the orthotropic principal axes vector fields. Contrastive finite element analyses demonstrated that elastic orthotropy has significant effect on simulating stresses and strains, including the value as well as distribution pattern, which underlines the relevance of our orthotropic modeling scheme. Copyright © 2011 Elsevier Ireland Ltd. All rights reserved.

Observation of High-Order Polarization-Locked Vector Solitons in a Fiber Laser

NASA Astrophysics Data System (ADS)

Tang, D. Y.; Zhang, H.; Zhao, L. M.; Wu, X.

2008-10-01

We report on the experimental observation of a new type of polarization-locked vector soliton in a passively mode-locked fiber laser. The vector soliton is characterized by the fact that not only are the two orthogonally polarized soliton components phase-locked, but also one of the components has a double-humped intensity profile. Multiple phase-locked high-order vector solitons with identical soliton parameters and harmonic mode locking of the vector solitons were also obtained in the laser. Numerical simulations confirmed the existence of stable high-order vector solitons in the fiber laser.

Observation of high-order polarization-locked vector solitons in a fiber laser.

PubMed

Tang, D Y; Zhang, H; Zhao, L M; Wu, X

2008-10-10

We report on the experimental observation of a new type of polarization-locked vector soliton in a passively mode-locked fiber laser. The vector soliton is characterized by the fact that not only are the two orthogonally polarized soliton components phase-locked, but also one of the components has a double-humped intensity profile. Multiple phase-locked high-order vector solitons with identical soliton parameters and harmonic mode locking of the vector solitons were also obtained in the laser. Numerical simulations confirmed the existence of stable high-order vector solitons in the fiber laser.

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.

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

Brown, J. David

An action principle for the generalized harmonic formulation of general relativity is presented. The action is a functional of the spacetime metric and the gauge source vector. An action principle for the Z4 formulation of general relativity has been proposed recently by Bona, Bona-Casas, and Palenzuela. The relationship between the generalized harmonic action and the Bona, Bona-Casas, and Palenzuela action is discussed in detail.

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.

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.

Holomorphic projections and Ramanujan’s mock theta functions

PubMed Central

Imamoğlu, Özlem; Raum, Martin; Richter, Olav K.

2014-01-01

We use spectral methods of automorphic forms to establish a holomorphic projection operator for tensor products of vector-valued harmonic weak Maass forms and vector-valued modular forms. We apply this operator to discover simple recursions for Fourier series coefficients of Ramanujan’s mock theta functions. PMID:24591582

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.

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

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.

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].

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).

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.

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.

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.

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.

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.

Exact simulation of polarized light reflectance by particle deposits

NASA Astrophysics Data System (ADS)

Ramezan Pour, B.; Mackowski, D. W.

2015-12-01

The use of polarimetric light reflection measurements as a means of identifying the physical and chemical characteristics of particulate materials obviously relies on an accurate model of predicting the effects of particle size, shape, concentration, and refractive index on polarized reflection. The research examines two methods for prediction of reflection from plane parallel layers of wavelength—sized particles. The first method is based on an exact superposition solution to Maxwell's time harmonic wave equations for a deposit of spherical particles that are exposed to a plane incident wave. We use a FORTRAN-90 implementation of this solution (the Multiple Sphere T Matrix (MSTM) code), coupled with parallel computational platforms, to directly simulate the reflection from particle layers. The second method examined is based upon the vector radiative transport equation (RTE). Mie theory is used in our RTE model to predict the extinction coefficient, albedo, and scattering phase function of the particles, and the solution of the RTE is obtained from adding—doubling method applied to a plane—parallel configuration. Our results show that the MSTM and RTE predictions of the Mueller matrix elements converge when particle volume fraction in the particle layer decreases below around five percent. At higher volume fractions the RTE can yield results that, depending on the particle size and refractive index, significantly depart from the exact predictions. The particle regimes which lead to dependent scattering effects, and the application of methods to correct the vector RTE for particle interaction, will be discussed.

Three-Dimensional Profiles Using a Spherical Cutting Bit: Problem Solving in Practice

ERIC Educational Resources Information Center

Ollerton, Richard L.; Iskov, Grant H.; Shannon, Anthony G.

2002-01-01

An engineering problem concerned with relating the coordinates of the centre of a spherical cutting tool to the actual cutting surface leads to a potentially rich example of problem-solving techniques. Basic calculus, Lagrange multipliers and vector calculus techniques are employed to produce solutions that may be compared to better understand…

Black hole and cosmos with multiple horizons and multiple singularities in vector-tensor theories

NASA Astrophysics Data System (ADS)

Gao, Changjun; Lu, Youjun; Yu, Shuang; Shen, You-Gen

2018-05-01

A stationary and spherically symmetric black hole (e.g., Reissner-Nordström black hole or Kerr-Newman black hole) has, at most, one singularity and two horizons. One horizon is the outer event horizon and the other is the inner Cauchy horizon. Can we construct static and spherically symmetric black hole solutions with N horizons and M singularities? The de Sitter cosmos has only one apparent horizon. Can we construct cosmos solutions with N horizons? In this article, we present the static and spherically symmetric black hole and cosmos solutions with N horizons and M singularities in the vector-tensor theories. Following these motivations, we also construct the black hole solutions with a firewall. The deviation of these black hole solutions from the usual ones can be potentially tested by future measurements of gravitational waves or the black hole continuum spectrum.

Electron Gyro-Harmonic Effects on Ionospheric Stimulated Brillouin Scatter

DTIC Science & Technology

2014-08-21

27709-2211 Brillouin, SBS, emission lines, pump frequency stepping, cyclotron , EIC, airglow, upper hybrid REPORT DOCUMENTATION PAGE 11. SPONSOR...direction and the background magnetic field vector, the excited electrostatic wave could be either ion acoustic (IA) or electrostatic ion cyclotron (EIC...A. Hedberg, B. Lundborg, P. Stubbe, H. Kopka, and M. T. Rietveld (1989), Stimulated electromagnetic emission near electron cyclotron harmonics in

Third harmonic generation of a short pulse laser in a plasma density ripple created by a machining beam

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

Liu, C. S.; Tripathi, V. K.

An intense machining laser beam, impinged on a gas jet target, causes space periodic ionization of the gas and heats the electrons. The nonuniform plasma pressure leads to atomic density redistribution. When, after a suitable time delay, a second more intense laser pulse is launched along the periodicity wave vector q-vector, a plasma density ripple n{sub q} is instantly created, leading to resonant third harmonic generation when q=4{omega}{sub p}{sup 2}/(3{omega}c{gamma}{sub 0}), where {omega}{sub p} is the plasma frequency, {omega} is the laser frequency, and {gamma}{sub 0} is the electron Lorentz factor. The third harmonic is produced through the beating ofmore » ponderomotive force induced second harmonic density oscillations and the quiver velocity of electrons at the fundamental. The relativistic mass nonlinearity plays no role in resonant coupling. The energy conversion efficiency scales as the square of plasma density and square of depth of density ripple, and is {approx}0.2% for normalized laser amplitude a{sub o}{approx}1 in a plasma of 1% critical density with 20% density ripple. The theory explains several features of a recent experiment.« less

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.

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.

Precise and Fast Computation of the Gravitational Field of a General Finite Body and Its Application to the Gravitational Study of Asteroid Eros

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

Fukushima, Toshio, E-mail: Toshio.Fukushima@nao.ac.jp

In order to obtain the gravitational field of a general finite body inside its Brillouin sphere, we developed a new method to compute the field accurately. First, the body is assumed to consist of some layers in a certain spherical polar coordinate system and the volume mass density of each layer is expanded as a Maclaurin series of the radial coordinate. Second, the line integral with respect to the radial coordinate is analytically evaluated in a closed form. Third, the resulting surface integrals are numerically integrated by the split quadrature method using the double exponential rule. Finally, the associated gravitationalmore » acceleration vector is obtained by numerically differentiating the numerically integrated potential. Numerical experiments confirmed that the new method is capable of computing the gravitational field independently of the location of the evaluation point, namely whether inside, on the surface of, or outside the body. It can also provide sufficiently precise field values, say of 14–15 digits for the potential and of 9–10 digits for the acceleration. Furthermore, its computational efficiency is better than that of the polyhedron approximation. This is because the computational error of the new method decreases much faster than that of the polyhedron models when the number of required transcendental function calls increases. As an application, we obtained the gravitational field of 433 Eros from its shape model expressed as the 24 × 24 spherical harmonic expansion by assuming homogeneity of the object.« less

Effect of DNA sequence of Fab fragment on yield characteristics and cell growth of E. coli.

PubMed

Kulmala, Antti; Huovinen, Tuomas; Lamminmäki, Urpo

2017-06-19

Codon usage is one of the factors influencing recombinant protein expression. We were interested in the codon usage of an antibody Fab fragment gene exhibiting extreme toxicity in the E. coli host. The toxic synthetic human Fab gene contained domains optimized by the "one amino acid-one codon" method. We redesigned five segments of the Fab gene with a "codon harmonization" method described by Angov et al. and studied the effects of these changes on cell viability, Fab yield and display on filamentous phage using different vectors and bacterial strains. The harmonization considerably reduced toxicity, increased Fab expression from negligible levels to 10 mg/l, and restored the display on phage. Testing the impact of the individual redesigned segments revealed that the most significant effects were conferred by changes in the constant domain of the light chain. For some of the Fab gene variants, we also observed striking differences in protein yields when cloned from a chloramphenicol resistant vector into an identical vector, except with ampicillin resistance. In conclusion, our results show that the expression of a heterodimeric secretory protein can be improved by harmonizing selected DNA segments by synonymous codons and reveal additional complexity involved in heterologous protein expression.

DC-magnetic field vector measurement

NASA Technical Reports Server (NTRS)

Schmidt, R.

1981-01-01

A magnetometer experiment was designed to determine the local magnetic field by measuring the total of the Earth's magnetic field and that of an unknown spacecraft. The measured field vector components are available to all onboard experiments via the Spacelab command and data management system. The experiment consists of two parts, an electronic box and the magnetic field sensor. The sensor includes three independent measuring flux-gate magnetometers, each measuring one component. The physical background is the nonlinearity of the B-H curve of a ferrite material. Two coils wound around a ferrite rod are necessary. One of them, a tank coil, pumps the ferrite rod at approximately 20 kilohertz. As a consequence of the nonlinearity, many harmonics can be produced. The second coil (i.e., the detection coil) resonates to the first harmonic. If an unknown dc or low-frequency magnetic field exists, the amplitude of the first harmonic is a measure for the unknown magnetic field. The voltages detected by the sensors are to be digitized and transferred to the command and data management system.

Dynamical Causal Modeling from a Quantum Dynamical Perspective

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

Demiralp, Emre; Demiralp, Metin

Recent research suggests that any set of first order linear vector ODEs can be converted to a set of specific vector ODEs adhering to what we have called ''Quantum Harmonical Form (QHF)''. QHF has been developed using a virtual quantum multi harmonic oscillator system where mass and force constants are considered to be time variant and the Hamiltonian is defined as a conic structure over positions and momenta to conserve the Hermiticity. As described in previous works, the conversion to QHF requires the matrix coefficient of the first set of ODEs to be a normal matrix. In this paper, thismore » limitation is circumvented using a space extension approach expanding the potential applicability of this method. Overall, conversion to QHF allows the investigation of a set of ODEs using mathematical tools available to the investigation of the physical concepts underlying quantum harmonic oscillators. The utility of QHF in the context of dynamical systems and dynamical causal modeling in behavioral and cognitive neuroscience is briefly discussed.« less

Development of apple latent spherical virus-based vaccines against three tospoviruses.

PubMed

Taki, Ayano; Yamagishi, Noriko; Yoshikawa, Nobuyuki

2013-09-01

Apple latent spherical virus (ALSV) is characterized by its relatively broad host range, latency in most host plants, and ability to induce gene silencing in host plants. Herein, we focus on the above characteristic of ALSV and describe our development of ALSV vector vaccines against three tospoviruses, namely, Impatiens necrotic spot virus (INSV), Iris yellow spot virus (IYSV), and Tomato spotted wilt virus (TSWV). DNA fragments of 201 nt of three tospovirus S-RNAs (silencing suppressor (NSS) and nucleocapsid protein (N) coding regions for each tospovirus) were inserted into an ALSV-RNA2 vector to obtain six types of ALSV vector vaccines. Nicotiana benthamiana plants at the five-leaf stage were inoculated with each ALSV vector vaccine and challenged with the corresponding tospovirus species. Tospovirus-induced symptoms and tospovirus replication after challenge were significantly suppressed in plants preinoculated with all ALSV vector vaccines having the N region fragment, indicating that strong resistance was acquired after infection with ALSV vector vaccines. On the other hand, cross protection was not significant in plants preinoculated with ALSV vectors having the NSs region fragment. Similarly, inoculation with an ALSV-RNA1 vector having the N region fragment in the 3'-noncoding region, but not the NSs region fragment, induced cross protection, indicating that cross protection is via RNA silencing, not via the function of the protein derived from the N region fragment. Our approach, wherein ALSV vectors and selected target inserts are used, enables rapid establishment of ALSV vector vaccines against many pathogenic RNA viruses with known sequences. Copyright © 2013 Elsevier B.V. All rights reserved.

Static Thrust and Vectoring Performance of a Spherical Convergent Flap Nozzle with a Nonrectangular Divergent Duct

NASA Technical Reports Server (NTRS)

Wing, David J.

1998-01-01

The static internal performance of a multiaxis-thrust-vectoring, spherical convergent flap (SCF) nozzle with a non-rectangular divergent duct was obtained in the model preparation area of the Langley 16-Foot Transonic Tunnel. Duct cross sections of hexagonal and bowtie shapes were tested. Additional geometric parameters included throat area (power setting), pitch flap deflection angle, and yaw gimbal angle. Nozzle pressure ratio was varied from 2 to 12 for dry power configurations and from 2 to 6 for afterburning power configurations. Approximately a 1-percent loss in thrust efficiency from SCF nozzles with a rectangular divergent duct was incurred as a result of internal oblique shocks in the flow field. The internal oblique shocks were the result of cross flow generated by the vee-shaped geometric throat. The hexagonal and bowtie nozzles had mirror-imaged flow fields and therefore similar thrust performance. Thrust vectoring was not hampered by the three-dimensional internal geometry of the nozzles. Flow visualization indicates pitch thrust-vector angles larger than 10' may be achievable with minimal adverse effect on or a possible gain in resultant thrust efficiency as compared with the performance at a pitch thrust-vector angle of 10 deg.

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.

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.

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.

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.

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

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

JPRS Report, Science & Technology, USSR: Earth Sciences

DTIC Science & Technology

1988-12-06

Vol 24 No 7, Jul 88] 14 Integral Characteristics of Light Scattering by Large Spherical Particles IE. P. Zege, A. A. Kokhanovskiy; IZVESTIYA AKADEMII...economical that the base not contain a grid model, but the initial contours, represented in vector format, in which case it is called a vector DRM. The...information make it possible to display both screen and vector DRM and from these, retrieve contours in the initial format. The automated forest mapping

An analytical solution for the elastic response to surface loads imposed on a layered, transversely isotropic and self-gravitating Earth

NASA Astrophysics Data System (ADS)

Pan, E.; Chen, J. Y.; Bevis, M.; Bordoni, A.; Barletta, V. R.; Molavi Tabrizi, A.

2015-12-01

We present an analytical solution for the elastic deformation of an elastic, transversely isotropic, layered and self-gravitating Earth by surface loads. We first introduce the vector spherical harmonics to express the physical quantities in the layered Earth. This reduces the governing equations to a linear system of equations for the expansion coefficients. We then solve for the expansion coefficients analytically under the assumption (i.e. approximation) that in the mantle, the density in each layer varies as 1/r (where r is the radial coordinate) while the gravity is constant and that in the core the gravity in each layer varies linearly in r with constant density. These approximations dramatically simplify the subsequent mathematical analysis and render closed-form expressions for the expansion coefficients. We implement our solution in a MATLAB code and perform a benchmark which shows both the correctness of our solution and the implementation. We also calculate the load Love numbers (LLNs) of the PREM Earth for different degrees of the Legendre function for both isotropic and transversely isotropic, layered mantles with different core models, demonstrating for the first time the effect of Earth anisotropy on the LLNs.

Particle definitions and the information loss paradox

NASA Astrophysics Data System (ADS)

Venditti, Alex

An investigation of information loss in black hole spacetimes is performed. We demonstrate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the radiation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schrodinger picture. We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric spacetime with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a selfsimilarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.

On the accuracy of palaeopole estimations from magnetic field measurements

NASA Astrophysics Data System (ADS)

Vervelidou, F.; Lesur, V.; Morschhauser, A.; Grott, M.; Thomas, P.

2017-12-01

Various techniques have been proposed for palaeopole position estimation based on magnetic field measurements. Such estimates can offer insights into the rotational dynamics and the dynamo history of moons and terrestrial planets carrying a crustal magnetic field. Motivated by discrepancies in the estimated palaeopole positions among various studies regarding the Moon and Mars, we examine the limitations of magnetic field measurements as source of information for palaeopole position studies. It is already known that magnetic field measurements cannot constrain the null space of the magnetization nor its full spectral content. However, the extent to which these limitations affect palaeopole estimates has not been previously investigated in a systematic way. In this study, by means of the vector Spherical Harmonics formalism, we show that inferring palaeopole positions from magnetic field measurements necessarily introduces, explicitly or implicitly, assumptions about both the null space and the full spectral content of the magnetization. Moreover, we demonstrate through synthetic tests that if these assumptions are inaccurate, then the resulting palaeopole position estimates are wrong. Based on this finding, we make suggestions that can allow future palaeopole studies to be conducted in a more constructive way.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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.

A new class of N=2 topological amplitudes

NASA Astrophysics Data System (ADS)

Antoniadis, I.; Hohenegger, S.; Narain, K. S.; Sokatchev, E.

2009-12-01

We describe a new class of N=2 topological amplitudes that compute a particular class of BPS terms in the low energy effective supergravity action. Specifically they compute the coupling F(( where F, λ and ϕ are gauge field strengths, gaugino and holomorphic vector multiplet scalars. The novel feature of these terms is that they depend both on the vector and hypermultiplet moduli. The BPS nature of these terms implies that they satisfy a holomorphicity condition with respect to vector moduli and a harmonicity condition as well as a second order differential equation with respect to hypermultiplet moduli. We study these conditions explicitly in heterotic string theory and show that they are indeed satisfied up to anomalous boundary terms in the world-sheet moduli space. We also analyze the boundary terms in the holomorphicity and harmonicity equations at a generic point in the vector and hyper moduli space. In particular we show that the obstruction to the holomorphicity arises from the one loop threshold correction to the gauge couplings and we argue that this is due to the contribution of non-holomorphic couplings to the connected graphs via elimination of the auxiliary fields.

Main field and secular variation candidate models for the 12th IGRF generation after 10 months of Swarm measurements

NASA Astrophysics Data System (ADS)

Saturnino, Diana; Langlais, Benoit; Civet, François; Thébault, Erwan; Mandea, Mioara

2015-06-01

We describe the main field and secular variation candidate models for the 12th generation of the International Geomagnetic Reference Field model. These two models are derived from the same parent model, in which the main field is extrapolated to epoch 2015.0 using its associated secular variation. The parent model is exclusively based on measurements acquired by the European Space Agency Swarm mission between its launch on 11/22/2013 and 09/18/2014. It is computed up to spherical harmonic degree and order 25 for the main field, 13 for the secular variation, and 2 for the external field. A selection on local time rather than on true illumination of the spacecraft was chosen in order to keep more measurements. Data selection based on geomagnetic indices was used to minimize the external field contributions. Measurements were screened and outliers were carefully removed. The model uses magnetic field intensity measurements at all latitudes and magnetic field vector measurements equatorward of 50° absolute quasi-dipole magnetic latitude. A second model using only the vertical component of the measured magnetic field and the total intensity was computed. This companion model offers a slightly better fit to the measurements. These two models are compared and discussed.We discuss in particular the quality of the model which does not use the full vector measurements and underline that this approach may be used when only partial directional information is known. The candidate models and their associated companion models are retrospectively compared to the adopted IGRF which allows us to criticize our own choices.

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.

Ranking of stopping criteria for log domain diffeomorphic demons application in clinical radiation therapy.

PubMed

Peroni, M; Golland, P; Sharp, G C; Baroni, G

2011-01-01

Deformable Image Registration is a complex optimization algorithm with the goal of modeling a non-rigid transformation between two images. A crucial issue in this field is guaranteeing the user a robust but computationally reasonable algorithm. We rank the performances of four stopping criteria and six stopping value computation strategies for a log domain deformable registration. The stopping criteria we test are: (a) velocity field update magnitude, (b) vector field Jacobian, (c) mean squared error, and (d) harmonic energy. Experiments demonstrate that comparing the metric value over the last three iterations with the metric minimum of between four and six previous iterations is a robust and appropriate strategy. The harmonic energy and vector field update magnitude metrics give the best results in terms of robustness and speed of convergence.

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

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.

Role of Acentric Displacements on the Crystal Structure and Second-Harmonic Generating Properties of RbPbCO3F and CsPbCO3F

PubMed Central

2015-01-01

Two lead fluorocarbonates, RbPbCO3F and CsPbCO3F, were synthesized and characterized. The materials were synthesized through solvothermal and conventional solid-state techniques. RbPbCO3F and CsPbCO3F were structurally characterized by single-crystal X-ray diffraction and exhibit three-dimensional (3D) crystal structures consisting of corner-shared PbO6F2 polyhedra. For RbPbCO3F, infrared and ultraviolet–visible spectroscopy and thermogravimetric and differential thermal analysis measurements were performed. RbPbCO3F is a new noncentrosymmetric material and crystallizes in the achiral and nonpolar space group P6̅m2 (crystal class 6̅m2). Powder second-harmonic generation (SHG) measurements on RbPbCO3F and CsPbCO3F using 1064 nm radiation revealed an SHG efficiency of approximately 250 and 300 × α-SiO2, respectively. Charge constants d33 of approximately 72 and 94 pm/V were obtained for RbPbCO3F and CsPbCO3F, respectively, through converse piezoelectric measurements. Electronic structure calculations indicate that the nonlinear optical response originates from the distorted PbO6F2 polyhedra, because of the even–odd parity mixing of the O 2p states with the nearly spherically symmetric 6s electrons of Pb2+. The degree of inversion symmetry breaking is quantified using a mode-polarization vector analysis and is correlated with cation size mismatch, from which it is possible to deduce the acentric properties of 3D alkali-metal fluorocarbonates. PMID:24867361

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.

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.

Different evolution dynamics of vector solitons depending on their polarization states

NASA Astrophysics Data System (ADS)

Chen, Wei-Cheng; Chen, Guo-Jie

2014-03-01

There are three types of temporal evolution dynamics of vector solitons observed in a ring fiber laser with a semiconductor saturable absorption mirror (SESAM) as a mode-locker. It is found that the polarization property of vector solitons is an important factor for achieving different evolution dynamics. The vector soliton with a uniform polarization state across the whole pulse profile and zero polarization extinction ratio operates at a fundamental repetition rate with a single pulse profile. The elliptically polarized vector soliton with a larger polarization extinction ratio exhibits a harmonic pulse train. The soliton bunching with multi-peak structures exists between the above two states and shows elliptical polarization with a small polarization extinction ratio.

Experimental study of Bloch vector analysis in nonlinear, finite, dissipative systems

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

D'Aguanno, G.; Mattiucci, N.; C. M. Bowden Facility, Building 7804, RDECOM, Redstone Arsenal, Alabama 35898

2010-01-15

We have investigated and experimentally demonstrated the applicability of the Bloch vector for one-dimensional, nonlinear, finite, dissipative systems. The case studied is the second harmonic generation from metallodielectric multilayer filters. In particular, we have applied the Bloch vector analysis to Ag/Ta{sub 2}O{sub 5} thin-film multilayer samples and shown the importance of the phase matching calculated through the Bloch vector. The nonlinear coefficients extracted from experimental results are consistent with previous studies. Nowadays, metal-based nanostructures play a fundamental role in nonlinear nanophotonics and nanoplasmonics. Our results clearly suggest that even in these forefront fields the Bloch vector continues to play anmore » essential role.« less

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.

Induction and maintenance of DNA methylation in plant promoter sequences by apple latent spherical virus-induced transcriptional gene silencing

PubMed Central

Kon, Tatsuya; Yoshikawa, Nobuyuki

2014-01-01

Apple latent spherical virus (ALSV) is an efficient virus-induced gene silencing vector in functional genomics analyses of a broad range of plant species. Here, an Agrobacterium-mediated inoculation (agroinoculation) system was developed for the ALSV vector, and virus-induced transcriptional gene silencing (VITGS) is described in plants infected with the ALSV vector. The cDNAs of ALSV RNA1 and RNA2 were inserted between the cauliflower mosaic virus 35S promoter and the NOS-T sequences in a binary vector pCAMBIA1300 to produce pCALSR1 and pCALSR2-XSB or pCALSR2-XSB/MN. When these vector constructs were agroinoculated into Nicotiana benthamiana plants with a construct expressing a viral silencing suppressor, the infection efficiency of the vectors was 100%. A recombinant ALSV vector carrying part of the 35S promoter sequence induced transcriptional gene silencing of the green fluorescent protein gene in a line of N. benthamiana plants, resulting in the disappearance of green fluorescence of infected plants. Bisulfite sequencing showed that cytosine residues at CG and CHG sites of the 35S promoter sequence were highly methylated in the silenced generation zero plants infected with the ALSV carrying the promoter sequence as well as in progeny. The ALSV-mediated VITGS state was inherited by progeny for multiple generations. In addition, induction of VITGS of an endogenous gene (chalcone synthase-A) was demonstrated in petunia plants infected with an ALSV vector carrying the native promoter sequence. These results suggest that ALSV-based vectors can be applied to study DNA methylation in plant genomes, and provide a useful tool for plant breeding via epigenetic modification. PMID:25426109

Dynamics of axial torsional libration under the mantle-inner core gravitational interaction

NASA Astrophysics Data System (ADS)

Chao, B. F.

2017-01-01

The aims of this paper are (i) formulating the dynamics of the mantle-inner core gravitational (MICG) interaction in terms of the spherical-harmonic multipoles of mass density. The modeled MICG system is composed of two concentric rigid bodies (mantle and inner core) of near-spherical but otherwise heterogeneous configuration, with a fluid outer core in between playing a passive role. We derive the general equation of motion for the vector rotation but only focus on the polar component that describes the MICG axial torsional libration. The torsion constant and hence the square of the natural frequency of the libration is proportional to the product of the equatorial ellipticities of the mantle and inner-core geoid embodied in their multipoles (of two different types) of degree 2 and order 2 (such as the Large Low-Shear-Velocity Provinces above the core-mantle boundary) and (ii) studying the geophysical implications upon equating the said MICG libration to the steady 6 year oscillation that are observed in the Earth's spin rate or the length-of-day variation (ΔLOD). In particular, the MICG torsion constant is found to be Γ>˜z = CIC σz2 ≈ 6.5 × 1019 N m, while the inner core's (BIC - AIC) ≈ 1.08 × 1031 kg m2 gives the inner core triaxiality (BIC - AIC)/CIC ≈ 1.8 × 10-4, about 8 times the whole-Earth value. It is also asserted that the required inner-core ellipticity amounts to no more than 140 m in geoid height, much smaller than the sensitivity required for the seismic wave travel time to resolve the variation of the inner core.

Vector spherical quasi-Gaussian vortex beams

NASA Astrophysics Data System (ADS)

Mitri, F. G.

2014-02-01

Model equations for describing and efficiently computing the radiation profiles of tightly spherically focused higher-order electromagnetic beams of vortex nature are derived stemming from a vectorial analysis with the complex-source-point method. This solution, termed as a high-order quasi-Gaussian (qG) vortex beam, exactly satisfies the vector Helmholtz and Maxwell's equations. It is characterized by a nonzero integer degree and order (n,m), respectively, an arbitrary waist w0, a diffraction convergence length known as the Rayleigh range zR, and an azimuthal phase dependency in the form of a complex exponential corresponding to a vortex beam. An attractive feature of the high-order solution is the rigorous description of strongly focused (or strongly divergent) vortex wave fields without the need of either the higher-order corrections or the numerically intensive methods. Closed-form expressions and computational results illustrate the analysis and some properties of the high-order qG vortex beams based on the axial and transverse polarization schemes of the vector potentials with emphasis on the beam waist.

A phenomenological calculus of Wiener description space.

PubMed

Richardson, I W; Louie, A H

2007-10-01

The phenomenological calculus is a categorical example of Robert Rosen's modeling relation. This paper is an alligation of the phenomenological calculus and generalized harmonic analysis, another categorical example. Our epistemological exploration continues into the realm of Wiener description space, in which constitutive parameters are extended from vectors to vector-valued functions of a real variable. Inherent in the phenomenology are fundamental representations of time and nearness to equilibrium.

MO-C-17A-04: 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, A; UT Graduate School of Biomedical Sciences, Houston, TX; Rao, A

2014-06-15

Purpose: To generate, evaluate, and compare models that predict longitudinal changes in tumor morphology throughout the course of radiation therapy. Methods: Two morphology feature vectors were used to describe the size, shape, and position of 35 oropharyngeal GTVs at each treatment fraction during intensity-modulated radiation therapy. The feature vectors comprised the coordinates of the GTV centroids and one of two shape descriptors. One shape descriptor was based on radial distances between the GTV centroid and 614 GTV surface landmarks. The other was based on a spherical harmonic decomposition of these distances. Feature vectors over the course of therapy were describedmore » using static, linear, and mean models. The error of these models in forecasting GTV morphology was evaluated with leave-one-out cross-validation, and their accuracy was compared using Wilcoxon signed-rank tests. The effect of adjusting model parameters at 1, 2, 3, or 5 time points (adjustment points) was also evaluated. Results: The addition of a single adjustment point to the static model decreased the median error in forecasting the position of GTV surface landmarks by 1.2 mm (p<0.001). Additional adjustment points further decreased forecast error by about 0.4 mm each. The linear model decreased forecast error compared to the static model for feature vectors based on both shape descriptors (0.2 mm), while the mean model did so only for those based on the inter-landmark distances (0.2 mm). The decrease in forecast error due to adding adjustment points was greater than that due to model selection. Both effects diminished with subsequent adjustment points. Conclusion: Models of tumor morphology that include information from prior patients and/or prior treatment fractions are able to predict the tumor surface at each treatment fraction during radiation therapy. The predicted tumor morphology can be compared with patient anatomy or dose distributions, opening the possibility of anticipatory re-planning. American Legion Auxiliary Fellowship; The University of Texas Graduate School of Biomedical Sciences at Houston.« less

Improved definition of crustal magnetic anomalies for MAGSAT data

NASA Technical Reports Server (NTRS)

Brown, R. D.; Frawley, J. F.; Davis, W. M.; Ray, R. D.; Didwall, E.; Regan, R. D. (Principal Investigator)

1982-01-01

The routine correction of MAGSAT vector magnetometer data for external field effects such as the ring current and the daily variation by filtering long wavelength harmonics from the data is described. Separation of fields due to low altitude sources from those caused by high altitude sources is affected by means of dual harmonic expansions in the solution of Dirichlet's problem. This regression/harmonic filter procedure is applied on an orbit by orbit basis, and initial tests on MAGSAT data from orbit 1176 show reduction in external field residuals by 24.33 nT RMS in the horizontal component, and 10.95 nT RMS in the radial component.

KvN mechanics approach to the time-dependent frequency harmonic oscillator.

PubMed

Ramos-Prieto, Irán; Urzúa-Pineda, Alejandro R; Soto-Eguibar, Francisco; Moya-Cessa, Héctor M

2018-05-30

Using the Ermakov-Lewis invariants appearing in KvN mechanics, the time-dependent frequency harmonic oscillator is studied. The analysis builds upon the operational dynamical model, from which it is possible to infer quantum or classical dynamics; thus, the mathematical structure governing the evolution will be the same in both cases. The Liouville operator associated with the time-dependent frequency harmonic oscillator can be transformed using an Ermakov-Lewis invariant, which is also time dependent and commutes with itself at any time. Finally, because the solution of the Ermakov equation is involved in the evolution of the classical state vector, we explore some analytical and numerical solutions.

Correlation techniques and measurements of wave-height statistics

NASA Technical Reports Server (NTRS)

Guthart, H.; Taylor, W. C.; Graf, K. A.; Douglas, D. G.

1972-01-01

Statistical measurements of wave height fluctuations have been made in a wind wave tank. The power spectral density function of temporal wave height fluctuations evidenced second-harmonic components and an f to the minus 5th power law decay beyond the second harmonic. The observations of second harmonic effects agreed very well with a theoretical prediction. From the wave statistics, surface drift currents were inferred and compared to experimental measurements with satisfactory agreement. Measurements were made of the two dimensional correlation coefficient at 15 deg increments in angle with respect to the wind vector. An estimate of the two-dimensional spatial power spectral density function was also made.

Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories

NASA Astrophysics Data System (ADS)

Heisenberg, Lavinia; Tsujikawa, Shinji

2018-05-01

In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

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.

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.

Evaluation of candidate geomagnetic field models for IGRF-11

NASA Astrophysics Data System (ADS)

Finlay, C. C.; Maus, S.; Beggan, C. D.; Hamoudi, M.; Lowes, F. J.; Olsen, N.; Thébault, E.

2010-10-01

The eleventh generation of the International Geomagnetic Reference Field (IGRF) was agreed in December 2009 by a task force appointed by the International Association of Geomagnetism and Aeronomy (IAGA) Division V Working Group V-MOD. New spherical harmonic main field models for epochs 2005.0 (DGRF-2005) and 2010.0 (IGRF-2010), and predictive linear secular variation for the interval 2010.0-2015.0 (SV-2010-2015) were derived from weighted averages of candidate models submitted by teams led by DTU Space, Denmark (team A); NOAA/NGDC, U.S.A. (team B); BGS, U.K. (team C); IZMIRAN, Russia (team D); EOST, France (team E); IPGP, France (team F); GFZ, Germany (team G) and NASA-GSFC, U.S.A. (team H). Here, we report the evaluations of candidate models carried out by the IGRF-11 task force during October/November 2009 and describe the weightings used to derive the new IGRF-11 model. The evaluations include calculations of root mean square vector field differences between the candidates, comparisons of the power spectra, and degree correlations between the candidates and a mean model. Coefficient by coefficient analysis including determination of weighting factors used in a robust estimation of mean coefficients is also reported. Maps of differences in the vertical field intensity at Earth's surface between the candidates and weighted mean models are presented. Candidates with anomalous aspects are identified and efforts made to pinpoint both troublesome coefficients and geographical regions where large variations between candidates originate. A retrospective analysis of IGRF-10 main field candidates for epoch 2005.0 and predictive secular variation candidates for 2005.0-2010.0 using the new IGRF-11 models as a reference is also reported. The high quality and consistency of main field models derived using vector satellite data is demonstrated; based on internal consistency DGRF-2005 has a formal root mean square vector field error over Earth's surface of 1.0 nT. Difficulties nevertheless remain in accurately forecasting field evolution only five years into the future.

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.

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.

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.

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.

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.

Gaussian statistics for palaeomagnetic vectors

USGS Publications Warehouse

Love, J.J.; Constable, C.G.

2003-01-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimoda) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Re??union, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Gaussian statistics for palaeomagnetic vectors

NASA Astrophysics Data System (ADS)

Love, J. J.; Constable, C. G.

2003-03-01

With the aim of treating the statistics of palaeomagnetic directions and intensities jointly and consistently, we represent the mean and the variance of palaeomagnetic vectors, at a particular site and of a particular polarity, by a probability density function in a Cartesian three-space of orthogonal magnetic-field components consisting of a single (unimodal) non-zero mean, spherically-symmetrical (isotropic) Gaussian function. For palaeomagnetic data of mixed polarities, we consider a bimodal distribution consisting of a pair of such symmetrical Gaussian functions, with equal, but opposite, means and equal variances. For both the Gaussian and bi-Gaussian distributions, and in the spherical three-space of intensity, inclination, and declination, we obtain analytical expressions for the marginal density functions, the cumulative distributions, and the expected values and variances for each spherical coordinate (including the angle with respect to the axis of symmetry of the distributions). The mathematical expressions for the intensity and off-axis angle are closed-form and especially manageable, with the intensity distribution being Rayleigh-Rician. In the limit of small relative vectorial dispersion, the Gaussian (bi-Gaussian) directional distribution approaches a Fisher (Bingham) distribution and the intensity distribution approaches a normal distribution. In the opposite limit of large relative vectorial dispersion, the directional distributions approach a spherically-uniform distribution and the intensity distribution approaches a Maxwell distribution. We quantify biases in estimating the properties of the vector field resulting from the use of simple arithmetic averages, such as estimates of the intensity or the inclination of the mean vector, or the variances of these quantities. With the statistical framework developed here and using the maximum-likelihood method, which gives unbiased estimates in the limit of large data numbers, we demonstrate how to formulate the inverse problem, and how to estimate the mean and variance of the magnetic vector field, even when the data consist of mixed combinations of directions and intensities. We examine palaeomagnetic secular-variation data from Hawaii and Réunion, and although these two sites are on almost opposite latitudes, we find significant differences in the mean vector and differences in the local vectorial variances, with the Hawaiian data being particularly anisotropic. These observations are inconsistent with a description of the mean field as being a simple geocentric axial dipole and with secular variation being statistically symmetrical with respect to reflection through the equatorial plane. Finally, our analysis of palaeomagnetic acquisition data from the 1960 Kilauea flow in Hawaii and the Holocene Xitle flow in Mexico, is consistent with the widely held suspicion that directional data are more accurate than intensity data.

Spherical Demons: Fast Surface Registration

PubMed Central

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

2009-01-01

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

Spherical demons: fast surface registration.

PubMed

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

2008-01-01

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

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.

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.

Hidden symmetry in the confined hydrogen atom problem

NASA Astrophysics Data System (ADS)

Pupyshev, Vladimir I.; Scherbinin, Andrei V.

2002-07-01

The classical counterpart of the well-known quantum mechanical model of a spherically confined hydrogen atom is examined in terms of the Lenz vector, a dynamic variable featuring the conventional Kepler problem. It is shown that a conditional conservation law associated with the Lenz vector is true, in fair agreement with the corresponding quantum problem previously found to exhibit a hidden symmetry as well.

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.

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.

A new approach to global seismic tomography based on regularization by sparsity in a novel 3D spherical wavelet basis

NASA Astrophysics Data System (ADS)

Loris, Ignace; Simons, Frederik J.; Daubechies, Ingrid; Nolet, Guust; Fornasier, Massimo; Vetter, Philip; Judd, Stephen; Voronin, Sergey; Vonesch, Cédric; Charléty, Jean

2010-05-01

Global seismic wavespeed models are routinely parameterized in terms of spherical harmonics, networks of tetrahedral nodes, rectangular voxels, or spherical splines. Up to now, Earth model parametrizations by wavelets on the three-dimensional ball remain uncommon. Here we propose such a procedure with the following three goals in mind: (1) The multiresolution character of a wavelet basis allows for the models to be represented with an effective spatial resolution that varies as a function of position within the Earth. (2) This property can be used to great advantage in the regularization of seismic inversion schemes by seeking the most sparse solution vector, in wavelet space, through iterative minimization of a combination of the ℓ2 (to fit the data) and ℓ1 norms (to promote sparsity in wavelet space). (3) With the continuing increase in high-quality seismic data, our focus is also on numerical efficiency and the ability to use parallel computing in reconstructing the model. In this presentation we propose a new wavelet basis to take advantage of these three properties. To form the numerical grid we begin with a surface tesselation known as the 'cubed sphere', a construction popular in fluid dynamics and computational seismology, coupled with an semi-regular radial subdivison that honors the major seismic discontinuities between the core-mantle boundary and the surface. This mapping first divides the volume of the mantle into six portions. In each 'chunk' two angular and one radial variable are used for parametrization. In the new variables standard 'cartesian' algorithms can more easily be used to perform the wavelet transform (or other common transforms). Edges between chunks are handled by special boundary filters. We highlight the benefits of this construction and use it to analyze the information present in several published seismic compressional-wavespeed models of the mantle, paying special attention to the statistics of wavelet and scaling coefficients across scales. We also focus on the likely gains of future inversions of finite-frequency seismic data using a sparsity promoting penalty in combination with our new wavelet approach.

On the symplectic structure of harmonic superspace

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

Kachkachi, M.; Saidi, E.H.

In this paper, the symplectic properties of harmonic superspace are studied. It is shown that Diff(S[sup 2]) is isomorphic to Diff[sub 0](S[sup 3])/Ab(Diff[sub 0](S[sup 3])), where Diff[sub 0](S[sup 3]) is the group of the diffeomorphisms of S[sup 3] preserving the Cartan charge operator D[sup 0] and Ab(Diff[sub 0](S[sup 3])) is its Abelian subgroup generated by the Cartan vectors L[sub 0] = w[sup 0]D[sup 0]. The authors show also that the eigenvalue equation D[sup 0] [lambda](z) = 0 defines a symplectic structure in harmonic superspace, and the authors calculate the corresponding algebra. The general symplectic invariant coupling of the Maxwell prepotentialmore » is constructed in both flat and curved harmonic superspace. Other features are discussed.« less

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.

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

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.

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.

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.

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

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.

Generalized Preconditioned Locally Harmonic Residual Eigensolver (GPLHR) v0.1

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

VECHARYNSKI, EUGENE; YANG, CHAO

The software contains a MATLAB implementation of the Generalized Preconditioned Locally Harmonic Residual (GPLHR) method for solving standard and generalized non-Hermitian eigenproblems. The method is particularly useful for computing a subset of eigenvalues, and their eigen- or Schur vectors, closest to a given shift. The proposed method is based on block iterations and can take advantage of a preconditioner if it is available. It does not need to perform exact shift-and-invert transformation. Standard and generalized eigenproblems are handled in a unified framework.

Phase-matched second- and third-harmonic generation in plasmas with density ripple

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

Dahiya, Deepak; Sajal, Vivek; Sharma, A. K.

The generation of second and third harmonics by the interaction of an ultrashort laser pulse with underdense plasma having a density ripple is studied at intensities I{lambda}{sup 2}=10{sup 16}-10{sup 19} W cm{sup -2} {mu}m{sup 2} using fully relativistic two-dimensional particle-in-cell simulations with high spectral resolution. A theoretical model is developed for second- and third-harmonic conversion efficiencies. When the laser is plane polarized in the simulation plane even and odd harmonics are excited in the same polarization as the laser polarization. The highest efficiency of generation of a specific harmonic occurs when the ripple wave vector value k{sub q} satisfies phase-matchingmore » conditions. The efficiency of phase-matched harmonic generation is an order of magnitude higher than the one without phase matching. The efficiency increases rapidly in weak and moderate relativistic regime and tends to saturate in strong relativistic regime. At moderately relativistic intensities and low plasma densities, the simulation and recent experimental results are fairly reproduced by an analytical theory.« less

SPECIAL ISSUE DEVOTED TO THE 80TH BIRTHDAY OF S.A. AKHMANOV: Three-wave interactions of surface defect-deformation waves and their manifestations in the self-organisation of nano- and microstructures in solids exposed to laser radiation

NASA Astrophysics Data System (ADS)

Emel'yanov, Vladimir I.; Seval'nev, D. M.

2009-07-01

The self-organisation of the surface-relief nanostructures in solids under the action of energy and particle fluxes is interpreted as the instability of defect-deformation (DD) gratings produced by quasi-static Lamb and Rayleigh waves and defect-concentration waves. The allowance for the nonlocality in the defects—lattice atom interaction with a simultaneous account for both (normal and longitudinal) defect-induced forces bending the surface layer leads to the appearance of two maxima in the dependence of the instability growth rate of DD waves on the wave number. Three-wave interactions of quasi-static coupled DD waves (second harmonic generation and wave vector mixing) are considered for the first time, which are similar to three-wave interactions in nonlinear optics and acoustics and lead to the enrichment of the spectrum of surface-relief harmonics. Computer processing of experimental data on laser-induced generation of micro- and nanostructures of the surface relief reveals the presence of effects responsible for the second harmonic generation and wave vector mixing.

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.

Segmentation of discrete vector fields.

PubMed

Li, Hongyu; Chen, Wenbin; Shen, I-Fan

2006-01-01

In this paper, we propose an approach for 2D discrete vector field segmentation based on the Green function and normalized cut. The method is inspired by discrete Hodge Decomposition such that a discrete vector field can be broken down into three simpler components, namely, curl-free, divergence-free, and harmonic components. We show that the Green Function Method (GFM) can be used to approximate the curl-free and the divergence-free components to achieve our goal of the vector field segmentation. The final segmentation curves that represent the boundaries of the influence region of singularities are obtained from the optimal vector field segmentations. These curves are composed of piecewise smooth contours or streamlines. Our method is applicable to both linear and nonlinear discrete vector fields. Experiments show that the segmentations obtained using our approach essentially agree with human perceptual judgement.

Deriving Global Convection Maps From SuperDARN Measurements

NASA Astrophysics Data System (ADS)

Gjerloev, J. W.; Waters, C. L.; Barnes, R. J.

2018-04-01

A new statistical modeling technique for determining the global ionospheric convection is described. The principal component regression (PCR)-based technique is based on Super Dual Auroral Radar Network (SuperDARN) observations and is an advanced version of the PCR technique that Waters et al. (https//:doi.org.10.1002/2015JA021596) used for the SuperMAG data. While SuperMAG ground magnetic field perturbations are vector measurements, SuperDARN provides line-of-sight measurements of the ionospheric convection flow. Each line-of-sight flow has a known azimuth (or direction), which must be converted into the actual vector flow. However, the component perpendicular to the azimuth direction is unknown. Our method uses historical data from the SuperDARN database and PCR to determine a fill-in model convection distribution for any given universal time. The fill-in data process is driven by a list of state descriptors (magnetic indices and the solar zenith angle). The final solution is then derived from a spherical cap harmonic fit to the SuperDARN measurements and the fill-in model. When compared with the standard SuperDARN fill-in model, we find that our fill-in model provides improved solutions, and the final solutions are in better agreement with the SuperDARN measurements. Our solutions are far less dynamic than the standard SuperDARN solutions, which we interpret as being due to a lack of magnetosphere-ionosphere inertia and communication delays in the standard SuperDARN technique while it is inherently included in our approach. Rather, we argue that the magnetosphere-ionosphere system has inertia that prevents the global convection from changing abruptly in response to an interplanetary magnetic field change.

Magnetic effects of magnetospheric currents at ground and in low orbit

NASA Astrophysics Data System (ADS)

Stolle, C.; Willer, A.; Finlay, C. C.; Olsen, N.

2012-12-01

Since the advent of high precision vector magnetic field observations from satellites in low orbit it has been recognized that magnetospheric currents contribute by about 20nT to the geomagnetic field even during quiet times (when Dst=0nT) (Langel et al., 1980). Comparing spherical harmonic models of the magnetospheric field derived from ground observations with satellite data shows a similar offset. A robust linear fit between these two quantities reveals a slope of about 0.9, indicating that only 90% of the magnetospheric field as monitored on ground is seen by satellites. The intercept of ~20nT is found to diminish with reducing solar activity (as was previously noted by Lühr & Maus, 2010), while the slope is hardly affected. There have been several suggestions for the origin of this systematic difference between ground and space based observations of magnetospheric fields. We compare magnetic residuals of selected observatories with those of CHAMP satellite observations at times of conjunctions, separating the data pairs by criteria including local time and longitude, season, solar and magnetic activity. Obtaining rough estimates of the ionospheric conductivity in this way, we are able to discuss possible ionospheric sources for the observed intercept. Consideration of appropriate ordering in local time, also enables us to test for possible contributions from field aligned currents connecting the ionosphere and the magnetosphere. Langel RA, Mead GD, Lancaster ER, Estes RH, Fabiano EB. 1980. Initial geomagnetic field model from Magsat vector data. Geophys. Res. Lett. 7:793-96 Lühr H, Maus S. 2010. Solar cycle dependence of quiet-time magnetospheric currents and a model of their near-Earth magnetic fields. Earth Planets Space 62:843-48

Toward an improved determination of Earth's lithospheric magnetic field from satellite observations

NASA Astrophysics Data System (ADS)

Kotsiaros, S.

2016-12-01

An analytical and numerical analysis of the spectral properties of the gradient tensor, initially performed by Rummel and van Gelderen (1992) for the gravity potential, shows that when the tensor elements are grouped into sets of semi-tangential and pure-tangential parts, they produce almost identical signal content as the normal element. Moreover, simple eigenvalue relations can be derived between these sets and the spherical harmonic expansion of the potential. This theoretical development generally applies to any potential field. First, the analysis of Rummel and van Gelderen (1992) is adapted to the magnetic field case and then the elements of the magnetic gradient tensor are estimated by 2 years of Swarm data and grouped into Γ(1) = {[∇B]rθ,[∇B]rφ} resp. Γ(2) = {[∇B]θθ-[∇B]φφ, 2[∇B]θφ}. It is shown that the estimated combinations Γ(1) and Γ(2) produce similar signal content as the theoretical radial gradient [∇B]rr. These results demonstrate the ability of multi-satellite missions such as Swarm, which cannot directly measure the radial gradient, to retrieve similar signal content by means of the horizontal gradients. Finally, lithospheric field models are derived using the gradient combinations Γ(1) and Γ(2) and compared with models derived from traditional vector and gradient data. The model resulting from Γ(1) leads to a very similar, and in particular cases improved, model compared to models retrieved by using approximately three times more data, i.e. a full set of vector, North-South and East-West gradients. ReferencesRummel, R., and M. van Gelderen (1992), Spectral analysis of the full gravity tensor, Geophysical Journal International, 111 (1), 159-169.

Uncertainty principles for inverse source problems for electromagnetic and elastic waves

NASA Astrophysics Data System (ADS)

Griesmaier, Roland; Sylvester, John

2018-06-01

In isotropic homogeneous media, far fields of time-harmonic electromagnetic waves radiated by compactly supported volume currents, and elastic waves radiated by compactly supported body force densities can be modelled in very similar fashions. Both are projected restricted Fourier transforms of vector-valued source terms. In this work we generalize two types of uncertainty principles recently developed for far fields of scalar-valued time-harmonic waves in Griesmaier and Sylvester (2017 SIAM J. Appl. Math. 77 154–80) to this vector-valued setting. These uncertainty principles yield stability criteria and algorithms for splitting far fields radiated by collections of well-separated sources into the far fields radiated by individual source components, and for the restoration of missing data segments. We discuss proper regularization strategies for these inverse problems, provide stability estimates based on the new uncertainty principles, and comment on reconstruction schemes. A numerical example illustrates our theoretical findings.

Kinematics and constraints associated with swashplate blade pitch control

NASA Technical Reports Server (NTRS)

Leyland, Jane A.

1993-01-01

An important class of techniques to reduce helicopter vibration is based on using a Higher Harmonic controller to optimally define the Higher Harmonic blade pitch. These techniques typically require solution of a general optimization problem requiring the determination of a control vector which minimizes a performance index where functions of the control vector are subject to inequality constraints. Six possible constraint functions associated with swashplate blade pitch control were identified and defined. These functions constrain: (1) blade pitch Fourier Coefficients expressed in the Rotating System, (2) blade pitch Fourier Coefficients expressed in the Nonrotating System, (3) stroke of the individual actuators expressed in the Nonrotating System, (4) blade pitch expressed as a function of blade azimuth and actuator stroke, (5) time rate-of-change of the aforementioned parameters, and (6) required actuator power. The aforementioned constraints and the associated kinematics of swashplate blade pitch control by means of the strokes of the individual actuators are documented.

Vectorization and parallelization of the finite strip method for dynamic Mindlin plate problems

NASA Technical Reports Server (NTRS)

Chen, Hsin-Chu; He, Ai-Fang

1993-01-01

The finite strip method is a semi-analytical finite element process which allows for a discrete analysis of certain types of physical problems by discretizing the domain of the problem into finite strips. This method decomposes a single large problem into m smaller independent subproblems when m harmonic functions are employed, thus yielding natural parallelism at a very high level. In this paper we address vectorization and parallelization strategies for the dynamic analysis of simply-supported Mindlin plate bending problems and show how to prevent potential conflicts in memory access during the assemblage process. The vector and parallel implementations of this method and the performance results of a test problem under scalar, vector, and vector-concurrent execution modes on the Alliant FX/80 are also presented.

Parameters Estimation For A Patellofemoral Joint Of A Human Knee Using A Vector Method

NASA Astrophysics Data System (ADS)

Ciszkiewicz, A.; Knapczyk, J.

2015-08-01

Position and displacement analysis of a spherical model of a human knee joint using the vector method was presented. Sensitivity analysis and parameter estimation were performed using the evolutionary algorithm method. Computer simulations for the mechanism with estimated parameters proved the effectiveness of the prepared software. The method itself can be useful when solving problems concerning the displacement and loads analysis in the knee joint.

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.

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.

In Situ Observations of Harmonic Alfvén Waves and Associated Heavy Ion Heating

NASA Astrophysics Data System (ADS)

Chen, Huayue; Gao, Xinliang; Lu, Quanming; Wang, Shui

2018-06-01

Resonant ion heating by high-frequency Alfvén waves has long been believed to be the primary dissipation mechanism for solar coronal heating, and these high-frequency Alfvén waves are considered to be generated via cascade from low-frequency Alfvén waves. In this study, we report an unusual harmonic Alfvén event from in situ observations by the Van Allen Probes in the magnetosphere, having an environment similar to that in the solar corona. The harmonic Alfvén waves, which propagate almost along the wave vector of the fundamental waves, are considered to be generated due to the interaction between quasi-parallel Alfvén waves and plasma density fluctuations with almost identical frequency. These high-frequency harmonic Alfvén waves can then cyclotron resonantly heat the heavy ions. Our observations provide an important insight into solar corona heating by Alfvén waves.

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.

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.

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.

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.

Concepts for the design of a completely active helicopter isolation system using output vector feedback

NASA Technical Reports Server (NTRS)

Schulz, G.

1977-01-01

The theory of output vector feedback (a few measured quantities) is used to derive completely active oscillation isolation functions for helicopters. These feedback controller concepts are tested with various versions of the BO 105 helicopter and their performance is demonstrated. A compensation of the vibrational excitations from the rotor and harmonics of the number of blades are considered. There is also a fast and automatic trim function for maneuvers.

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.

Spherical earth gravity and magnetic anomaly analysis by equivalent point source inversion

NASA Technical Reports Server (NTRS)

Von Frese, R. R. B.; Hinze, W. J.; Braile, L. W.

1981-01-01

To facilitate geologic interpretation of satellite elevation potential field data, analysis techniques are developed and verified in the spherical domain that are commensurate with conventional flat earth methods of potential field interpretation. A powerful approach to the spherical earth problem relates potential field anomalies to a distribution of equivalent point sources by least squares matrix inversion. Linear transformations of the equivalent source field lead to corresponding geoidal anomalies, pseudo-anomalies, vector anomaly components, spatial derivatives, continuations, and differential magnetic pole reductions. A number of examples using 1 deg-averaged surface free-air gravity anomalies of POGO satellite magnetometer data for the United States, Mexico, and Central America illustrate the capabilities of the method.

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=(±1,0)

NASA Astrophysics Data System (ADS)

Schmid, Christoph

2009-03-01

We show that there is exact dragging of the axis directions of local inertial frames by a weighted average of the cosmological energy currents via gravitomagnetism for all linear perturbations of all Friedmann-Robertson-Walker (FRW) universes and of Einstein’s static closed universe, and for all energy-momentum-stress tensors and in the presence of a cosmological constant. This includes FRW universes arbitrarily close to the Milne Universe and the de Sitter universe. Hence the postulate formulated by Ernst Mach about the physical cause for the time-evolution of inertial axes is shown to hold in general relativity for linear perturbations of FRW universes.—The time-evolution of local inertial axes (relative to given local fiducial axes) is given experimentally by the precession angular velocity Ω→gyro of local gyroscopes, which in turn gives the operational definition of the gravitomagnetic field: B→g≡-2Ω→gyro. The gravitomagnetic field is caused by energy currents J→ɛ via the momentum constraint, Einstein’s G0^i^ equation, (-Δ+μ2)A→g=-16πGNJ→ɛ with B→g=curlA→g. This equation is analogous to Ampère’s law, but it holds for all time-dependent situations. Δ is the de Rham-Hodge Laplacian, and Δ=-curlcurl for the vorticity sector in Riemannian 3-space.—In the solution for an open universe the 1/r2-force of Ampère is replaced by a Yukawa force Yμ(r)=(-d/dr)[(1/R)exp⁡(-μr)], form-identical for FRW backgrounds with K=(-1,0). Here r is the measured geodesic distance from the gyroscope to the cosmological source, and 2πR is the measured circumference of the sphere centered at the gyroscope and going through the source point. The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, dot is the derivative with respect to cosmic time, and μ2=-4(dH/dt). Analogous results hold in closed FRW universes and in Einstein’s closed static universe.—We list six fundamental tests for the principle formulated by Mach: all of them are explicitly fulfilled by our solutions.—We show that only energy currents in the toroidal vorticity sector with ℓ=1 can affect the precession of gyroscopes. We show that the harmonic decomposition of toroidal vorticity fields in terms of vector spherical harmonics X→ℓm- has radial functions which are form-identical for the 3-sphere, the hyperbolic 3-space, and Euclidean 3-space, and are form-identical with the spherical Bessel-, Neumann-, and Hankel functions.—The Appendix gives the de Rham-Hodge Laplacian on vorticity fields in Riemannian 3-spaces by equations connecting the calculus of differential forms with the curl notation. We also give the derivation the Weitzenböck formula for the difference between the de Rham-Hodge Laplacian Δ and the “rough” Laplacian ∇2 on vector fields.

Did the Moon have a dipolar field?

NASA Astrophysics Data System (ADS)

Boutin, D.; Arkani-Hamed, J.

2012-12-01

Did the Moon have a dipolar core field? Daniel Boutin1 (dboutin003@sympatico.ca) Jafar Arkani-Hamed2 (jafar@physics.utoronto.ca) 1Earth and Planetary Sciences, McGill University, Montreal, QC, H3A-2A7, Canada 2Physics, University of Toronto, Toronto, ON M5S 1A7, Canada The lack of a global scale magnetic field at present and the observed strong magnetic anomalies of the Moon suggest that the magnetic source bodies have been magnetized in the past. The origin of the magnetizing field is poorly understood. Several scenarios have been proposed including a strong core dynamo [1] and the external origin due to giant impacts such as the enhancement of an existing weak field by impact-generated plasmas or a transient field possibly generated during the impacts [2,3]. It is also possible that the existing field was not very strong but the source bodies are highly magnetic [4]. Here we test the hypothesis that the magnetizing field was of internal origin using two sets of data: the 150 degree spherical harmonic representation of the lunar crustal field by Purucker [5] and the raw magnetic data acquired by the Lunar Prospector magnetometer. Although 17 isolated magnetic anomalies are easily identified on the basis of the spherical harmonic representation, we model only 10 anomalies because of the lack of sufficient raw data over others. The isolated magnetic anomalies allow us to model each anomaly by a simple uniformly magnetized elliptical source body. We model the radial component of the magnetic field following the procedure adopted by Boutin and Arkani-Hamed [6] for the martian magnetic anomalies, and determine the three components of the magnetization vector. Seven out of 10 anomalies result in consistent source bodies obtained using the two sets of data. Assuming that each of the source bodies is magnetized by a dipole core field, the paleomagnetic pole of the Moon is determined on the basis of the corresponding magnetization vector. The resulting paleomagnetic pole positions do not show any significant clustering. There is a general agreement between some of our pole positions with those reported by Wieczorek and Weiss [7]. The lack of consistent dipolar core field is probably due to (1) the core field was not dominated by the dipole component, or (2) the core field was mainly dipolar but there has been appreciable true polar wander during the time the source bodies acquired magnetization, or (3) the magnetizing field was not of internal origin. Further investigations are required to identify the characteristics of the magnetizing field. [1] D. R. Stegman, D.R., et al., Nature 421, 143, 2003. [2] Hood, L. And Z. Huang, J. Geophys. Res. 96, 9837, 1991. [3] Hood, L., Icarus 211, 1109 (2011). [4] Wieczorek, M.A. et al., Science, 335, 1212-1215, 2012. [5] Purucker, M.E. Icarus, 197(1), 19-23, 2008. [6] Boutin, D., and Arkani-Hamed, J., Icarus, 181, 13-25, 2006. [7] Wieczorek , M.A. and Weiss, B.P., EPSC Abstracts Vol. 5, EPSC2010-533, 2010.

Multiple polarization states of vector soliton in fiber laser

NASA Astrophysics Data System (ADS)

Chen, Weicheng; Xu, Wencheng; Cao, Hui; Han, Dingan

2007-11-01

Vector soliton is obtained in erbium-doped fiber laser via nonlinear polarization rotation techniques. In experiment, we observe the every 4- and 7-pulse sinusoidal peak modulation. Temporal pulse sinusoidal peak modulation owes to evolution behavior of vector solitons in multiple polarization states. The polarizer in the laser modulates the mode-locked pulses with different polarization states into periodical pulse train intensities modulation. Moreover, the increasing pumping power lead to the appearance of the harmonic pulses and change the equivalent beat length to accelerate the polarization rotation. When the laser cavity length is the n-th multiple ratios to the beat length to maintain the mode-locking, the mode-locked vector soliton is in n-th multiple polarization states, exhibiting every n-pulse sinusoidal peak modulation.

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.

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.

Improving liver fibrosis diagnosis based on forward and backward second harmonic generation signals

NASA Astrophysics Data System (ADS)

Peng, Qiwen; Zhuo, Shuangmu; So, Peter T. C.; Yu, Hanry

2015-02-01

The correlation of forward second harmonic generation (SHG) signal and backward SHG signal in different liver fibrosis stages was investigated. We found that three features, including the collagen percentage for forward SHG, the collagen percentage for backward SHG, and the average intensity ratio of two kinds of SHG signals, can quantitatively stage liver fibrosis in thioacetamide-induced rat model. We demonstrated that the combination of all three features by using a support vector machine classification algorithm can provide a more accurate prediction than each feature alone in fibrosis diagnosis.

Polarized Radiative Transfer of a Cirrus Cloud Consisting of Randomly Oriented Hexagonal Ice Crystals: The 3 x 3 Approximation for Non-Spherical Particles

NASA Technical Reports Server (NTRS)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K.N.; Stamnes, K.

2016-01-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 x 10(exp 3) so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling- adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5 for I and within 1.5 for Q for all viewing angles. In 1971 Hansen showed that for scattering by spherical particles the 3 x 3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3 x 3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3 x 3 approximation leads to an absolute error 2 x 10(exp -6) for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Polarized radiative transfer of a cirrus cloud consisting of randomly oriented hexagonal ice crystals: The 3×3 approximation for non-spherical particles

NASA Astrophysics Data System (ADS)

Stamnes, S.; Ou, S. C.; Lin, Z.; Takano, Y.; Tsay, S. C.; Liou, K. N.; Stamnes, K.

2017-05-01

The reflection and transmission of polarized light for a cirrus cloud consisting of randomly oriented hexagonal columns were calculated by two very different vector radiative transfer models. The forward peak of the phase function for the ensemble-averaged ice crystals has a value of order 6 ×103 so a truncation procedure was used to help produce numerically efficient yet accurate results. One of these models, the Vectorized Line-by-Line Equivalent model (VLBLE), is based on the doubling-adding principle, while the other is based on a vector discrete ordinates method (VDISORT). A comparison shows that the two models provide very close although not entirely identical results, which can be explained by differences in treatment of single scattering and the representation of the scattering phase matrix. The relative differences in the reflected I and Q Stokes parameters are within 0.5% for I and within 1.5% for Q for all viewing angles. In 1971 Hansen [1] showed that for scattering by spherical particles the 3×3 approximation is sufficient to produce accurate results for the reflected radiance I and the degree of polarization (DOP), and he conjectured that these results would hold also for non-spherical particles. Simulations were conducted to test Hansen's conjecture for the cirrus cloud particles considered in this study. It was found that the 3×3 approximation also gives accurate results for the transmitted light, and for Q and U in addition to I and DOP. For these non-spherical ice particles the 3×3 approximation leads to an absolute error < 2 ×10-6 for the reflected and transmitted I, Q and U Stokes parameters. Hence, it appears to be an excellent approximation, which significantly reduces the computational complexity and burden required for multiple scattering calculations.

Effect of difference of cupula and endolymph densities on the dynamics of semicircular canal.

PubMed

Kondrachuk, A V; Sirenko, S P; Boyle, R

2008-01-01

The effect of different densities of a cupula and endolymph on the dynamics of the semicircular canals is considered within the framework of a simplified one-dimensional mathematical model where the canal is approximated by a torus. If the densities are equal, the model is represented by Steinhausen's phenomenological equation. The difference of densities results in the complex dynamics of the cupulo-endolymphatic system, and leads to a dependence on the orientation of both the gravity vector relative to the canal plane and the axis of rotation, as well as on the distance between the axis of rotation and the center of the semicircular canal. Our analysis focused on two cases of canal stimulation: rotation with a constant velocity and a time-dependent (harmonically oscillating) angular velocity. Two types of spatial orientation of the axis of rotation, the axis of canal symmetry, and the vector of gravity were considered: i) the gravity vector and axis of rotation lie in the canal plane, and ii) the axis of rotation and gravity vector are normal to the canal plane. The difference of the cupula and endolymph densities reveals new features of cupula dynamics, for instance--a shift of the cupula to a new position of equilibrium that depends on the gravity vector and the parameters of head rotation, and the onset of cupula oscillations with multiple frequencies that results in the distortion of cupula dynamics relative to harmonic stimulation. Factors that might influence the density difference effects and the conditions under which these effects occur are 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.

Exploration of spherical torus physics in the NSTX device

NASA Astrophysics Data System (ADS)

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

2000-03-01

The National Spherical Torus Experiment (NSTX) is being built at Princeton Plasma Physics Laboratory to test the fusion physics principles for the spherical torus concept at the MA level. The NSTX nominal plasma parameters are R0 = 85 cm, a = 67 cm, R/a >= 1.26, Bt = 3 kG, Ip = 1 MA, q95 = 14, elongation κ <= 2.2, triangularity δ <= 0.5 and a plasma pulse length of up to 5 s. The plasma heating/current drive tools are high harmonic fast wave (6 MW, 5 s), neutral beam injection (5 MW, 80 keV, 5 s) and coaxial helicity injection. Theoretical calculations predict that NSTX should provide exciting possibilities for exploring a number of important new physics regimes, including very high plasma β, naturally high plasma elongation, high bootstrap current fraction, absolute magnetic well and high pressure driven sheared flow. In addition, the NSTX programme plans to explore fully non-inductive plasma startup as well as a dispersive scrape-off layer for heat and particle flux handling.

On the best mean-square approximations to a planet's gravitational potential

NASA Astrophysics Data System (ADS)

Lobkova, N. I.

1985-02-01

The continuous problem of approximating the gravitational potential of a planet in the form of polynomials of solid spherical functions is considered. The best mean-square polynomials, referred to different parts of space, are compared with each other. The harmonic coefficients corresponding to the surface of a planet are shown to be unstable with respect to the degree of the polynomial and to differ from the Stokes constants.

Earth's isostatic gravity anomaly field: Contributions to National Geodetic Satellite Program

NASA Technical Reports Server (NTRS)

Khan, M. A.

1973-01-01

On the assumption that the compensation for the topographic load is achieved in the manner of Airy-Heiskenenan hypothesis at a compensation depth of 30 kilometers, the spherical harmonic coefficients of the isostatic reduction potential U are computed. The degree power spectra of these coefficients are compared with the power spectra of the isostatic reduction coefficients given by Uotila. Results are presented in tabular form.

Series expansions of rotating two and three dimensional sound fields.

PubMed

Poletti, M A

2010-12-01

The cylindrical and spherical harmonic expansions of oscillating sound fields rotating at a constant rate are derived. These expansions are a generalized form of the stationary sound field expansions. The derivations are based on the representation of interior and exterior sound fields using the simple source approach and determination of the simple source solutions with uniform rotation. Numerical simulations of rotating sound fields are presented to verify the theory.

Nonsurgical Brain Activity Recovery From a Cap Containing Multiple Electroencephalogram Recording Sites

DTIC Science & Technology

2006-09-01

Astin, Director (December, 1965) [2] Agranovich, Y. Ya. “The theory of operators with dominant main diagonal. I.” Positiv - ity, Volume 2 (1998) pages 153...A Spherical Harmonics Solu- tion for Radiative Transfer Problems with Reflecting Boundaries and Internal Sources” Journal of Quantitative Spectroscopy...F. Huxley. “A Quantitative Description of Membrane Current and its Application to Conduction and Excitation in Nerve” Journal of Physiology (1952

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.

Different polarization dynamic states in a vector Yb-doped fiber laser.

PubMed

Li, Xingliang; Zhang, Shumin; Han, Huiyun; Han, Mengmeng; Zhang, Huaxing; Zhao, Luming; Wen, Fang; Yang, Zhenjun

2015-04-20

Different polarization dynamic states in an unidirectional, vector, Yb-doped fiber ring laser have been observed. A rich variety of dynamic states, including group velocity locked polarization domains and their splitting into regularly distributed multiple domains, polarization locked square pulses and their harmonic mode locking counterparts, and dissipative soliton resonances have all been observed with different operating parameters. We have also shown experimentally details of the conditions under which polarization-domain-wall dark pulses and bright square pulses form.

High Power Microwaves (HPM) (les Micro-ondes de forte puissance (MFP).

DTIC Science & Technology

1995-03-01

the polarization vector , [C/m 2], P1 is the polarization term which is linearly dependent on the electric field, and Pnl is The soliton laser [35...which utilizes Kerr nonlinearity in the polarization vector which is nonlinearly dependent on the optical fiber, has also been demonstrated. In the case...forward propa- then applied across the cathode. If the electric gating volume harmonics of the TMO1 mode, field is of the proper polarity , a phase tran- as

Debye-Waller Factor in Neutron Scattering by Ferromagnetic Metals

NASA Astrophysics Data System (ADS)

Paradezhenko, G. V.; Melnikov, N. B.; Reser, B. I.

2018-04-01

We obtain an expression for the neutron scattering cross section in the case of an arbitrary interaction of the neutron with the crystal. We give a concise, simple derivation of the Debye-Waller factor as a function of the scattering vector and the temperature. For ferromagnetic metals above the Curie temperature, we estimate the Debye-Waller factor in the range of scattering vectors characteristic of polarized magnetic neutron scattering experiments. In the example of iron, we compare the results of harmonic and anharmonic approximations.

Solving the multi-frequency electromagnetic inverse source problem by the Fourier method

NASA Astrophysics Data System (ADS)

Wang, Guan; Ma, Fuming; Guo, Yukun; Li, Jingzhi

2018-07-01

This work is concerned with an inverse problem of identifying the current source distribution of the time-harmonic Maxwell's equations from multi-frequency measurements. Motivated by the Fourier method for the scalar Helmholtz equation and the polarization vector decomposition, we propose a novel method for determining the source function in the full vector Maxwell's system. Rigorous mathematical justifications of the method are given and numerical examples are provided to demonstrate the feasibility and effectiveness of the method.

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.

Spherical Harmonic Solutions to the 3D Kobayashi Benchmark Suite

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

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

1999-12-29

Spherical harmonic solutions of order 5, 9 and 21 on spatial grids containing up to 3.3 million cells are presented for the Kobayashi benchmark suite. This suite of three problems with simple geometry of pure absorber with large void region was proposed by Professor Kobayashi at an OECD/NEA meeting in 1996. Each of the three problems contains a source, a void and a shield region. Problem 1 can best be described as a box in a box problem, where a source region is surrounded by a square void region which itself is embedded in a square shield region. Problems 2more » and 3 represent a shield with a void duct. Problem 2 having a straight and problem 3 a dog leg shaped duct. A pure absorber and a 50% scattering case are considered for each of the three problems. The solutions have been obtained with Ardra, a scalable, parallel neutron transport code developed at Lawrence Livermore National Laboratory (LLNL). The Ardra code takes advantage of a two-level parallelization strategy, which combines message passing between processing nodes and thread based parallelism amongst processors on each node. All calculations were performed on the IBM ASCI Blue-Pacific computer at LLNL.« less

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.

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.

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.

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.

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

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.

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.

A new radar determination of the spin vector of Venus

NASA Technical Reports Server (NTRS)

Zohar, S.; Goldstein, R. M.; Rumsey, H. C.

1980-01-01

Two radar observations of a set of three relatively small features on the surface of Venus have facilitated a refined determination of the spin vector of Venus. The period is found to be 243.019 + or 0.014 days, while the obliquity is 177.22 + or - 0.18 deg. The effects of deviations from exact sphericity on the interpretation of the measurements are discussed at length and the question of resonance with earth is reexamined.

Fierz bilinear formulation of the Maxwell–Dirac equations and symmetry reductions

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

Inglis, Shaun, E-mail: sminglis@utas.edu.au; Jarvis, Peter, E-mail: Peter.Jarvis@utas.edu.au

We study the Maxwell–Dirac equations in a manifestly gauge invariant presentation using only the spinor bilinear scalar and pseudoscalar densities, and the vector and pseudovector currents, together with their quadratic Fierz relations. The internally produced vector potential is expressed via algebraic manipulation of the Dirac equation, as a rational function of the Fierz bilinears and first derivatives (valid on the support of the scalar density), which allows a gauge invariant vector potential to be defined. This leads to a Fierz bilinear formulation of the Maxwell tensor and of the Maxwell–Dirac equations, without any reference to gauge dependent quantities. We showmore » how demanding invariance of tensor fields under the action of a fixed (but arbitrary) Lie subgroup of the Poincaré group leads to symmetry reduced equations. The procedure is illustrated, and the reduced equations worked out explicitly for standard spherical and cylindrical cases, which are coupled third order nonlinear PDEs. Spherical symmetry necessitates the existence of magnetic monopoles, which do not affect the coupled Maxwell–Dirac system due to magnetic terms cancelling. In this paper we do not take up numerical computations. As a demonstration of the power of our approach, we also work out the symmetry reduced equations for two distinct classes of dimension 4 one-parameter families of Poincaré subgroups, one splitting and one non-splitting. The splitting class yields no solutions, whereas for the non-splitting class we find a family of formal exact solutions in closed form. - Highlights: • Maxwell–Dirac equations derived in manifestly gauge invariant tensor form. • Invariant scalar and four vector fields for four Poincaré subgroups derived, including two unusual cases. • Symmetry reduction imposed on Maxwell–Dirac equations under example subgroups. • Magnetic monopole arises for spherically symmetric case, consistent with charge quantization condition.« less

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

NASA Technical Reports Server (NTRS)

Simpson, David G.

1998-01-01

In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable on-board computer resources.

Full-potential multiple scattering theory with space-filling cells for bound and continuum states.

PubMed

Hatada, Keisuke; Hayakawa, Kuniko; Benfatto, Maurizio; Natoli, Calogero R

2010-05-12

We present a rigorous derivation of a real-space full-potential multiple scattering theory (FP-MST) that is free from the drawbacks that up to now have impaired its development (in particular the need to expand cell shape functions in spherical harmonics and rectangular matrices), valid both for continuum and bound states, under conditions for space partitioning that are not excessively restrictive and easily implemented. In this connection we give a new scheme to generate local basis functions for the truncated potential cells that is simple, fast, efficient, valid for any shape of the cell and reduces to the minimum the number of spherical harmonics in the expansion of the scattering wavefunction. The method also avoids the need for saturating 'internal sums' due to the re-expansion of the spherical Hankel functions around another point in space (usually another cell center). Thus this approach provides a straightforward extension of MST in the muffin-tin (MT) approximation, with only one truncation parameter given by the classical relation l(max) = kR(b), where k is the electron wavevector (either in the excited or ground state of the system under consideration) and R(b) is the radius of the bounding sphere of the scattering cell. Moreover, the scattering path operator of the theory can be found in terms of an absolutely convergent procedure in the l(max) --> ∞ limit. Consequently, this feature provides a firm ground for the use of FP-MST as a viable method for electronic structure calculations and makes possible the computation of x-ray spectroscopies, notably photo-electron diffraction, absorption and anomalous scattering among others, with the ease and versatility of the corresponding MT theory. Some numerical applications of the theory are presented, both for continuum and bound states.

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.

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.

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.

Principal component analysis of the nonlinear coupling of harmonic modes in heavy-ion collisions

NASA Astrophysics Data System (ADS)

BoŻek, Piotr

2018-03-01

The principal component analysis of flow correlations in heavy-ion collisions is studied. The correlation matrix of harmonic flow is generalized to correlations involving several different flow vectors. The method can be applied to study the nonlinear coupling between different harmonic modes in a double differential way in transverse momentum or pseudorapidity. The procedure is illustrated with results from the hydrodynamic model applied to Pb + Pb collisions at √{sN N}=2760 GeV. Three examples of generalized correlations matrices in transverse momentum are constructed corresponding to the coupling of v22 and v4, of v2v3 and v5, or of v23,v33 , and v6. The principal component decomposition is applied to the correlation matrices and the dominant modes are calculated.

Analysis of harmonic spline gravity models for Venus and Mars

NASA Technical Reports Server (NTRS)

Bowin, Carl

1986-01-01

Methodology utilizing harmonic splines for determining the true gravity field from Line-Of-Sight (LOS) acceleration data from planetary spacecraft missions was tested. As is well known, the LOS data incorporate errors in the zero reference level that appear to be inherent in the processing procedure used to obtain the LOS vectors. The proposed method offers a solution to this problem. The harmonic spline program was converted from the VAX 11/780 to the Ridge 32C computer. The problem with the matrix inversion routine that improved inversion of the data matrices used in the Optimum Estimate program for global Earth studies was solved. The problem of obtaining a successful matrix inversion for a single rev supplemented by data for the two adjacent revs still remains.

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.

Group velocity locked vector dissipative solitons in a high repetition rate fiber laser

NASA Astrophysics Data System (ADS)

Luo, Yiyang; Li, Lei; Liu, Deming; Sun, Qizhen; Wu, Zhichao; Xu, Zhilin; Tang, Dingyuan; Fu, Songnian; Zhao, Luming

2016-08-01

Vectorial nature of dissipative solitons (DSs) with high repetition rates is studied for the first time in a normal-dispersion fiber laser. Despite the fact that the formed DSs are strongly chirped and the repetition rate is greater than 100 MHz, polarization locked and polarization rotating group velocity locked vector DSs can be formed under 129.3 MHz fundamental mode-locking and 258.6 MHz harmonic mode-locking of the fiber laser, respectively. The two orthogonally polarized components of these vector DSs possess distinctly different central wavelengths and travel together at the same group velocity in the laser cavity, resulting in a gradual spectral edge and small steps on the optical spectra, which can be considered as an auxiliary indicator of the group velocity locked vector DSs.

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)

1982-01-01

Progress in the harmonic analysis of MAGSAT data is reported. Single-day data sets were subdivided into information on the sunrise side of the Earth and information on the sunset side of the Earth. Data for the main and external fields each demonstrate a clear and consistent systematic difference between the sets of data which was determined to be, due to ionospheric currents which differ from the sunset to the sunrise terminator. A toroidal field was analyzed for and determined to be an apparent toroidal field resulting from electric currents concentrated in the two terminators. Progressive elimination of auroral zone data demonstrates that the information presented does not arise from complications due to Birkeland currents.

Transverse spin and transverse momentum in scattering of plane waves.

PubMed

Saha, Sudipta; Singh, Ankit K; Ray, Subir K; Banerjee, Ayan; Gupta, Subhasish Dutta; Ghosh, Nirmalya

2016-10-01

We study the near field to the far field evolution of spin angular momentum (SAM) density and the Poynting vector of the scattered waves from spherical scatterers. The results show that at the near field, the SAM density and the Poynting vector are dominated by their transverse components. While the former (transverse SAM) is independent of the helicity of the incident circular polarization state, the latter (transverse Poynting vector) depends upon the polarization state. It is further demonstrated that the interference of the transverse electric and transverse magnetic scattering modes enhances both the magnitudes and the spatial extent of the transverse SAM and the transverse momentum components.

Numerical computation of gravitational field of general extended body and its application to rotation curve study of galaxies

NASA Astrophysics Data System (ADS)

Fukushima, Toshio

2017-06-01

Reviewed are recently developed methods of the numerical integration of the gravitational field of general two- or three-dimensional bodies with arbitrary shape and mass density distribution: (i) an axisymmetric infinitely-thin disc (Fukushima 2016a, MNRAS, 456, 3702), (ii) a general infinitely-thin plate (Fukushima 2016b, MNRAS, 459, 3825), (iii) a plane-symmetric and axisymmetric ring-like object (Fukushima 2016c, AJ, 152, 35), (iv) an axisymmetric thick disc (Fukushima 2016d, MNRAS, 462, 2138), and (v) a general three-dimensional body (Fukushima 2016e, MNRAS, 463, 1500). The key techniques employed are (a) the split quadrature method using the double exponential rule (Takahashi and Mori, 1973, Numer. Math., 21, 206), (b) the precise and fast computation of complete elliptic integrals (Fukushima 2015, J. Comp. Appl. Math., 282, 71), (c) Ridder's algorithm of numerical differentiaion (Ridder 1982, Adv. Eng. Softw., 4, 75), (d) the recursive computation of the zonal toroidal harmonics, and (e) the integration variable transformation to the local spherical polar coordinates. These devices succesfully regularize the Newton kernel in the integrands so as to provide accurate integral values. For example, the general 3D potential is regularly integrated as Φ (\\vec{x}) = - G \\int_0^∞ ( \\int_{-1}^1 ( \\int_0^{2π} ρ (\\vec{x}+\\vec{q}) dψ ) dγ ) q dq, where \\vec{q} = q (√{1-γ^2} cos ψ, √{1-γ^2} sin ψ, γ), is the relative position vector referred to \\vec{x}, the position vector at which the potential is evaluated. As a result, the new methods can compute the potential and acceleration vector very accurately. In fact, the axisymmetric integration reproduces the Miyamoto-Nagai potential with 14 correct digits. The developed methods are applied to the gravitational field study of galaxies and protoplanetary discs. Among them, the investigation on the rotation curve of M33 supports a disc-like structure of the dark matter with a double-power-law surface mass density distribution. Fortran 90 subroutines to execute these methods and their test programs and sample outputs are available from the author's WEB site: https://www.researchgate.net/profile/Toshio_Fukushima/

Biot-Savart helicity versus physical helicity: A topological description of ideal flows

NASA Astrophysics Data System (ADS)

Sahihi, Taliya; Eshraghi, Homayoon

2014-08-01

For an isentropic (thus compressible) flow, fluid trajectories are considered as orbits of a family of one parameter, smooth, orientation-preserving, and nonsingular diffeomorphisms on a compact and smooth-boundary domain in the Euclidian 3-space which necessarily preserve a finite measure, later interpreted as the fluid mass. Under such diffeomorphisms the Biot-Savart helicity of the pushforward of a divergence-free and tangent to the boundary vector field is proved to be conserved and since these circumstances present an isentropic flow, the conservation of the "Biot-Savart helicity" is established for such flows. On the other hand, the well known helicity conservation in ideal flows which here we call it "physical helicity" is found to be an independent constant with respect to the Biot-Savart helicity. The difference between these two helicities reflects some topological features of the domain as well as the velocity and vorticity fields which is discussed and is shown for simply connected domains the two helicities coincide. The energy variation of the vorticity field is shown to be formally the same as for the incompressible flow obtained before. For fluid domains consisting of several disjoint solid tori, at each time, the harmonic knot subspace of smooth vector fields on the fluid domain is found to have two independent base sets with a special type of orthogonality between these two bases by which a topological description of the vortex and velocity fields depending on the helicity difference is achieved since this difference is shown to depend only on the harmonic knot parts of velocity, vorticity, and its Biot-Savart vector field. For an ideal magnetohydrodynamics (MHD) flow three independent constant helicities are reviewed while the helicity of magnetic potential is generalized for non-simply connected domains by inserting a special harmonic knot field in the dynamics of the magnetic potential. It is proved that the harmonic knot part of the vorticity in hydrodynamics and the magnetic field in MHD is presented by constant coefficients (fluxes) when expanded in terms of one of the time dependent base functions.

Recovery of Sparse Positive Signals on the Sphere from Low Resolution Measurements

NASA Astrophysics Data System (ADS)

Bendory, Tamir; Eldar, Yonina C.

2015-12-01

This letter considers the problem of recovering a positive stream of Diracs on a sphere from its projection onto the space of low-degree spherical harmonics, namely, from its low-resolution version. We suggest recovering the Diracs via a tractable convex optimization problem. The resulting recovery error is proportional to the noise level and depends on the density of the Diracs. We validate the theory by numerical experiments.

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.

A numerical study of viscous vortex rings using a spectral method

NASA Technical Reports Server (NTRS)

Stanaway, S. K.; Cantwell, B. J.; Spalart, Philippe R.

1988-01-01

Viscous, axisymmetric vortex rings are investigated numerically by solving the incompressible Navier-Stokes equations using a spectral method designed for this type of flow. The results presented are axisymmetric, but the method is developed to be naturally extended to three dimensions. The spectral method relies on divergence-free basis functions. The basis functions are formed in spherical coordinates using Vector Spherical Harmonics in the angular directions, and Jacobi polynomials together with a mapping in the radial direction. Simulations are performed of a single ring over a wide range of Reynolds numbers (Re approximately equal gamma/nu), 0.001 less than or equal to 1000, and of two interacting rings. At large times, regardless of the early history of the vortex ring, it is observed that the flow approaches a Stokes solution that depends only on the total hydrodynamic impulse, which is conserved for all time. At small times, from an infinitely thin ring, the propagation speeds of vortex rings of varying Re are computed and comparisons are made with the asymptotic theory by Saffman. The results are in agreement with the theory; furthermore, the error is found to be smaller than Saffman's own estimate by a factor square root ((nu x t)/R squared) (at least for Re=0). The error also decreases with increasing Re at fixed core-to-ring radius ratio, and appears to be independent of Re as Re approaches infinity). Following a single ring, with Re=500, the vorticity contours indicate shedding of vorticity into the wake and a settling of an initially circular core to a more elliptical shape, similar to Norbury's steady inviscid vortices. Finally, we consider the case of leapfrogging vortex rings with Re=1000. The results show severe straining of the inner vortex core in the first pass and merging of the two cores during the second pass.