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.

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.

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.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

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.

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

NASA Astrophysics Data System (ADS)

Svehla, D.

2009-12-01

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

Geometrical Theory of Spherical Harmonics for Geosciences

NASA Astrophysics Data System (ADS)

Svehla, Drazen

2010-05-01

Spherical harmonics play a central role in the modelling of spatial and temporal processes in the system Earth. The gravity field of the Earth and its temporal variations, sea surface topography, geomagnetic field, ionosphere etc., are just a few examples where spherical harmonics are used to represent processes in the system Earth. We introduce a novel method for the computation and rotation of spherical harmonics, Legendre polynomials and associated Legendre functions without making use of recursive relations. This novel geometrical approach allows calculation of spherical harmonics without any numerical instability up to an arbitrary degree and order, e.g. up to degree and order 106 and beyond. The algorithm is based on the trigonometric reduction of Legendre polynomials and the geometric rotation in hyperspace. It is shown that Legendre polynomials can be computed using trigonometric series by pre-computing amplitudes and translation terms for all angular arguments. It is shown that they can be treated as vectors in the Hilbert hyperspace leading to unitary hermitian rotation matrices with geometric properties. Thus, rotation of spherical harmonics about e.g. a polar or an equatorial axis can be represented in the similar way. This novel method allows stable calculation of spherical harmonics up to an arbitrary degree and order, i.e. up to degree and order 106 and beyond.

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.

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.

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.

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.

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 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

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.

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.

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

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.

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.

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.

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.

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.

Simulating The Prompt Electromagnetic Pulse In 3D Using Vector Spherical Harmonics

NASA Astrophysics Data System (ADS)

Friedman, Alex; Cohen, Bruce I.; Eng, Chester D.; Farmer, William A.; Grote, David P.; Kruger, Hans W.; Larson, David J.

2017-10-01

We describe a new, efficient code for simulating the prompt electromagnetic pulse. In SHEMP (``Spherical Harmonic EMP''), we extend to 3-D the methods pioneered in C. Longmire's CHAP code. The geomagnetic field and air density are consistent with CHAP's assumed spherical symmetry only for narrow domains of influence about the line of sight, limiting validity to very early times. Also, we seek to model inherently 3-D situations. In CHAP and our own CHAP-lite, the independent coordinates are r (the distance from the source) and τ = t-r/c; the pulse varies slowly with r at fixed τ, so a coarse radial grid suffices. We add non-spherically-symmetric physics via a vector spherical harmonic decomposition. For each (l,m) harmonic, the radial equation is similar to that in CHAP and CHAP-lite. We present our methodology and results on model problems. This work was performed under the auspices of the U.S. DOE by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.

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.

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.

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.

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.

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.

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

Euler potentials of current-free fields expressed in spherical harmonics

NASA Technical Reports Server (NTRS)

Stern, David P.

1994-01-01

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

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.

Electron correlation by polarization of interacting densities

NASA Astrophysics Data System (ADS)

Whitten, Jerry L.

2017-02-01

Coulomb interactions that occur in electronic structure calculations are correlated by allowing basis function components of the interacting densities to polarize dynamically, thereby reducing the magnitude of the interaction. Exchange integrals of molecular orbitals are not correlated. The modified Coulomb interactions are used in single-determinant or configuration interaction calculations. The objective is to account for dynamical correlation effects without explicitly introducing higher spherical harmonic functions into the molecular orbital basis. Molecular orbital densities are decomposed into a distribution of spherical components that conserve the charge and each of the interacting components is considered as a two-electron wavefunction embedded in the system acted on by an average field Hamiltonian plus r12-1. A method of avoiding redundancy is described. Applications to atoms, negative ions, and molecules representing different types of bonding and spin states are discussed.

Spherical integral transforms of second-order gravitational tensor components onto third-order gravitational tensor components

NASA Astrophysics Data System (ADS)

Šprlák, Michal; Novák, Pavel

2017-02-01

New spherical integral formulas between components of the second- and third-order gravitational tensors are formulated in this article. First, we review the nomenclature and basic properties of the second- and third-order gravitational tensors. Initial points of mathematical derivations, i.e., the second- and third-order differential operators defined in the spherical local North-oriented reference frame and the analytical solutions of the gradiometric boundary-value problem, are also summarized. Secondly, we apply the third-order differential operators to the analytical solutions of the gradiometric boundary-value problem which gives 30 new integral formulas transforming (1) vertical-vertical, (2) vertical-horizontal and (3) horizontal-horizontal second-order gravitational tensor components onto their third-order counterparts. Using spherical polar coordinates related sub-integral kernels can efficiently be decomposed into azimuthal and isotropic parts. Both spectral and closed forms of the isotropic kernels are provided and their limits are investigated. Thirdly, numerical experiments are performed to test the consistency of the new integral transforms and to investigate properties of the sub-integral kernels. The new mathematical apparatus is valid for any harmonic potential field and may be exploited, e.g., when gravitational/magnetic second- and third-order tensor components become available in the future. The new integral formulas also extend the well-known Meissl diagram and enrich the theoretical apparatus of geodesy.

Localized sudden changes in the geomagnetic secular variation.

USGS Publications Warehouse

Alldredge, L.R.

1987-01-01

There is much debate as to whether there was a worldwide geomagnetic jerk in 1969 or 1970. It is agreed that there was an unusual sharp change in the secular variation in the east component, Y, in Europe at that time. This note points out how a localized sudden change in the secular variation pattern of one component in Europe can occur without having any large worldwide effects in any of the components. The accompanying changes in the spherical harmonic coefficients for such a localized change are also discussed. -after Author

Spherical harmonic results for the 3D Kobayashi Benchmark suite

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

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

1999-03-02

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

Spherical harmonic expansion of the Levitus Sea surface topography

NASA Technical Reports Server (NTRS)

Engelis, Theodossios

1987-01-01

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

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.

YORP torque as the function of shape harmonics

NASA Astrophysics Data System (ADS)

Breiter, Sławomir; Michalska, Hanna

2008-08-01

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

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.

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).

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.

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

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.

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

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.

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.

The Local Stellar Velocity Field via Vector Spherical Harmonics

NASA Technical Reports Server (NTRS)

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

2007-01-01

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

USGS Publications Warehouse

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

1986-01-01

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

Solar quiet day ionospheric source current in the West African region.

PubMed

Obiekezie, Theresa N; Okeke, Francisca N

2013-05-01

The Solar Quiet (Sq) day source current were calculated using the magnetic data obtained from a chain of 10 magnetotelluric stations installed in the African sector during the French participation in the International Equatorial Electrojet Year (IEEY) experiment in Africa. The components of geomagnetic field recorded at the stations from January-December in 1993 during the experiment were separated into the source and (induced) components of Sq using Spherical Harmonics Analysis (SHA) method. The range of the source current was calculated and this enabled the viewing of a full year's change in the source current system of Sq.

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

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.

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

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.

Solar quiet day ionospheric source current in the West African region

PubMed Central

Obiekezie, Theresa N.; Okeke, Francisca N.

2012-01-01

The Solar Quiet (Sq) day source current were calculated using the magnetic data obtained from a chain of 10 magnetotelluric stations installed in the African sector during the French participation in the International Equatorial Electrojet Year (IEEY) experiment in Africa. The components of geomagnetic field recorded at the stations from January–December in 1993 during the experiment were separated into the source and (induced) components of Sq using Spherical Harmonics Analysis (SHA) method. The range of the source current was calculated and this enabled the viewing of a full year’s change in the source current system of Sq. PMID:25685434

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.

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.

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

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

DOE PAGES

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

2015-03-19

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

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.).

The ITSG-Grace2014 Gravity Field Model

NASA Astrophysics Data System (ADS)

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

2015-04-01

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2015-07-01

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

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.

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.

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

Mapping gravitational-wave backgrounds using methods from CMB analysis: Application to pulsar timing arrays

NASA Astrophysics Data System (ADS)

Gair, Jonathan; Romano, Joseph D.; Taylor, Stephen; Mingarelli, Chiara M. F.

2014-10-01

We describe an alternative approach to the analysis of gravitational-wave backgrounds, based on the formalism used to characterize the polarization of the cosmic microwave background. In contrast to standard analyses, this approach makes no assumptions about the nature of the background and so has the potential to reveal much more about the physical processes that generated it. An arbitrary background can be decomposed into modes whose angular dependence on the sky is given by gradients and curls of spherical harmonics. We derive the pulsar timing overlap reduction functions for the individual modes, which are given by simple combinations of spherical harmonics evaluated at the pulsar locations. We show how these can be used to recover the components of an arbitrary background, giving explicit results for both isotropic and anisotropic uncorrelated backgrounds. We also find that the response of a pulsar timing array to curl modes is identically zero, so half of the gravitational-wave sky will never be observed using pulsar timing, no matter how many pulsars are included in the array. An isotropic, unpolarized and uncorrelated background can be accurately represented using only three modes, and so a search of this type will be only slightly more complicated than the standard cross-correlation search using the Hellings and Downs overlap reduction function. However, by measuring the components of individual modes of the background and checking for consistency with isotropy, this approach has the potential to reveal much more information. Each individual mode on its own describes a background that is correlated between different points on the sky. A measurement of the components that indicates the presence of correlations in the background on large angular scales would suggest startling new physics.

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.

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).

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2017-07-01

The surface structure and its fluctuation of spherical micelles were investigated using a series of density correlation functions newly defined by spherical harmonics and Legendre polynomials based on the molecular dynamics calculations. To investigate the influence of head-group charges on the micelle surface structure, ionic sodium dodecyl sulfate and nonionic octaethyleneglycol monododecylether (C12E8) micelles were investigated as model systems. Large-scale density fluctuations were observed for both micelles in the calculated surface static structure factor. The area compressibility of the micelle surface evaluated by the surface static structure factor was tens-of-times larger than a typical value of a lipid membrane surface. The structural relaxation time, which was evaluated from the surface intermediate scattering function, indicates that the relaxation mechanism of the long-range surface structure can be well described by the hydrostatic approximation. The density fluctuation on the two-dimensional micelle surface has similar characteristics to that of three-dimensional fluids near the critical point.

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

PubMed

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

2017-07-21

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

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

NASA Technical Reports Server (NTRS)

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

1982-01-01

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

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

Theory and design of compact hybrid microphone arrays on two-dimensional planes for three-dimensional soundfield analysis.

PubMed

Chen, Hanchi; Abhayapala, Thushara D; Zhang, Wen

2015-11-01

Soundfield analysis based on spherical harmonic decomposition has been widely used in various applications; however, a drawback is the three-dimensional geometry of the microphone arrays. In this paper, a method to design two-dimensional planar microphone arrays that are capable of capturing three-dimensional (3D) spatial soundfields is proposed. Through the utilization of both omni-directional and first order microphones, the proposed microphone array is capable of measuring soundfield components that are undetectable to conventional planar omni-directional microphone arrays, thus providing the same functionality as 3D arrays designed for the same purpose. Simulations show that the accuracy of the planar microphone array is comparable to traditional spherical microphone arrays. Due to its compact shape, the proposed microphone array greatly increases the feasibility of 3D soundfield analysis techniques in real-world applications.

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.

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.

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

NASA Technical Reports Server (NTRS)

Klumpar, D. M. (Principal Investigator)

1982-01-01

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

Small-scale features in the Earth's magnetic field observed by Magsat.

USGS Publications Warehouse

Cain, J.C.; Schmitz, D.R.; Muth, L.

1984-01-01

A spherical harmonic expansion to degree and order 29 is derived using a selected magnetically quiet sample of Magsat data. Global maps representing the contribution due to terms of the expansion above n = 13 at 400 km altitude are compared with previously published residual anomaly maps and shown to be similar, even in polar regions. An expansion with such a high degree and order displays all but the sharpest features seen by the satellite and gives a more consistent picture of the high-order field structure at a constant altitude than do component maps derived independently. -Authors

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.

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

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

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

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

Oceanic tide maps and spherical harmonic coefficients from Geosat altimetry

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2012-07-01

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

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

NASA Technical Reports Server (NTRS)

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

1978-01-01

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

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

PubMed Central

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

2009-01-01

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

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.

Interannual Variations in Earth's Low-Degree Gravity Field and the Connections With Geophysical/Climatic Changes

NASA Technical Reports Server (NTRS)

Chao, Benjamin F.; Cox, Christopher M.

2004-01-01

Long-wavelength time-variable gravity recently derived from satellite laser ranging (SLR) analysis have focused to a large extent on the effects of the recent (since 1998) large anomalous change in J2, or the Earth's oblateness, and the potential causes. However, it is relatively more difficult to determine whether there are corresponding signals in the shorter wavelength zonal harmonics from the existing SLR-derived time variable gravity results, although it appears that geophysical fluid mass transport is being observed. For example, the recovered J3 time series shows remarkable agreement with NCEP-derived estimates of atmospheric gravity variations. Likewise, some of the non-zonal spherical harmonic components have significant interannual signal that appears to be related to mass transport. The non-zonal degree-2 components show reasonable temporal correlation with atmospheric signals, as well as climatic effects such as El Nino Southern Oscillation. We will present recent updates on the J2 evolution, as well as a look at other low-degree components of the interannual variations of gravity, complete through degree 4. We will examine the possible geophysical and climatic causes of these low-degree time-variable gravity related to oceanic and hydrological mass transports, for example some anomalous but prominent signals found in the extratropic Pacific ocean related to the Pacific Decadal Oscillation.

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.

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

NASA Astrophysics Data System (ADS)

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

2018-05-01

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

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.

Possible role of cochlear nonlinearity in the detection of mistuning of a harmonic component in a harmonic complex

NASA Astrophysics Data System (ADS)

Stoelinga, Christophe; Heo, Inseok; Long, Glenis; Lee, Jungmee; Lutfi, Robert; Chang, An-Chieh

2015-12-01

The human auditory system has a remarkable ability to "hear out" a wanted sound (target) in the background of unwanted sounds. One important property of sound which helps us hear-out the target is inharmonicity. When a single harmonic component of a harmonic complex is slightly mistuned, that component is heard to separate from the rest. At high harmonic numbers, where components are unresolved, the harmonic segregation effect is thought to result from detection of modulation of the time envelope (roughness cue) resulting from the mistuning. Neurophysiological research provides evidence that such envelope modulations are represented early in the auditory system, at the level of the auditory nerve. When the mistuned harmonic is a low harmonic, where components are resolved, the harmonic segregation is attributed to more centrally-located auditory processes, leading harmonic components to form a perceptual group heard separately from the mistuned component. Here we consider an alternative explanation that attributes the harmonic segregation to detection of modulation when both high and low harmonic numbers are mistuned. Specifically, we evaluate the possibility that distortion products in the cochlea generated by the mistuned component introduce detectable beating patterns for both high and low harmonic numbers. Distortion product otoacoustic emissions (DPOAEs) were measured using 3, 7, or 12-tone harmonic complexes with a fundamental frequency (F0) of 200 or 400 Hz. One of two harmonic components was mistuned at each F0: one when harmonics are expected to be resulted and the other from unresolved harmonics. Many non-harmonic DPOAEs are present whenever a harmonic component is mistuned. These non-harmonic DPOAEs are often separated by the amount of the mistuning (ΔF). This small frequency difference will generate a slow beating pattern at ΔF, because this beating is only present when a harmonic component is mistuned, it could provide a cue for behavioral detection of harmonic complex mistuning and may also be associated with the modulation of auditory nerve responses.

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.

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.

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.

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.

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

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

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

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.

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.

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.

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

Semiannual variations in the neutral composition.

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Volland, H.

1971-01-01

Meteor trail observations of the meridional mesospheric wind field are analyzed in terms of spherical harmonics, showing a predominance in the P3 term for the semiannual component. This suggests two heat sources for the semiannual variations. One that peaks at the equator is associated with the semiannual migration of the sun between the two hemispheres. A second heat input of greater magnitude that peaks at high latitudes is presumably related to auroral heating associated with the semiannual component in the occurrence of magnetic storms. The wind circulation, consistent with these sources, is shown to cause a semiannual redistribution of the minor constituent O in the lower thermosphere with the effects of decreasing the ratios of O/N2 and O/O2 at high latitudes and of enhancing these ratios at mid to low latitudes during equinox.

On the regularity of the covariance matrix of a discretized scalar field on the sphere

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

Bilbao-Ahedo, J.D.; Barreiro, R.B.; Herranz, D.

2017-02-01

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizationsmore » that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.« less

Nearly steady flows in GONG prototype data

NASA Technical Reports Server (NTRS)

Hathaway, David H.

1993-01-01

Doppler velocity images obtained with the GONG prototype instrument were analyzed to measure the nearly steady photospheric flows. The data consists of 88 images each of velocity, intensity, and modulation obtained at 20:00 UT on 88 days from July 1992 to February 1994. Each velocity image was temporally filtered to remove the p-mode oscillations, masked to exclude active regions, and then analyzed using spherical harmonics and orthogonal functions as described by Hathaway (1992). The spectral coefficients show very consistent results for the entire time interval with some evidence of year-to-year variations. The rotation profile agrees well with previous results and exhibits a north-south asymmetry that reverses sign during the 20 month interval. The residual rotation velocities exhibit structures with amplitudes of approximately 5 m/s that may be related to torsional oscillations. The meridional circulation is directed from the equator toward the poles with a peak velocity in the photosphere of approximately 50 m/s. The higher order components are very weak but indicate a divergent flow from the mid-latitudes (opposite that found for the June 1989 data). The convective limb shift is well fit by a 3rd order polynomial. The convection spectrum has a prominent peak at spherical harmonic degrees of l approximately 150 with very little signal in the low degree modes. Analysis of this signal shows that there is no evidence for giant cell convection at the level of approximately 10 m/s for all modes up to l = 32.

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.

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.

A new method of presentation the large-scale magnetic field structure on the Sun and solar corona

NASA Technical Reports Server (NTRS)

Ponyavin, D. I.

1995-01-01

The large-scale photospheric magnetic field, measured at Stanford, has been analyzed in terms of surface harmonics. Changes of the photospheric field which occur within whole solar rotation period can be resolved by this analysis. For this reason we used daily magnetograms of the line-of-sight magnetic field component observed from Earth over solar disc. We have estimated the period during which day-to-day full disc magnetograms must be collected. An original algorithm was applied to resolve time variations of spherical harmonics that reflect time evolution of large-scale magnetic field within solar rotation period. This method of magnetic field presentation can be useful enough in lack of direct magnetograph observations due to sometimes bad weather conditions. We have used the calculated surface harmonics to reconstruct the large-scale magnetic field structure on the source surface near the sun - the origin of heliospheric current sheet and solar wind streams. The obtained results have been compared with spacecraft in situ observations and geomagnetic activity. We tried to show that proposed technique can trace shon-time variations of heliospheric current sheet and short-lived solar wind streams. We have compared also our results with those obtained traditionally from potential field approximation and extrapolation using synoptic charts as initial boundary conditions.

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.

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.

Properties of thermospheric gravity waves on earth, Venus and Mars

NASA Technical Reports Server (NTRS)

Mayr, H. G.; Harris, I.; Pesnell, W. D.

1992-01-01

A spectral model with spherical harmonics and Fourier components that can simulate atmospheric perturbations in the global geometry of a multiconstituent atmosphere is presented. The boundaries are the planetary surface where the transport velocities vanish and the exobase where molecular heat conduction and viscosity dominate. The time consuming integration of the conservation equations is reduced to computing the transfer function (TF) which describes the dynamic properties of the medium divorced from the complexities in the temporal and horizontal variations of the excitation source. Given the TF, the atmospheric response to a chosen source distribution is then obtained in short order. Theoretical studies are presented to illuminate some properties of gravity waves on earth, Venus and Mars.

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.

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

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.

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.

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.

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

PubMed

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

2017-01-21

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

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

NASA Technical Reports Server (NTRS)

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

1981-01-01

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

High-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.

Early results from Magsat. [studies of near-earth magnetic fields

NASA Technical Reports Server (NTRS)

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

1981-01-01

Papers presented at the May 27, 1981 meeting of the American Geophysical Union concerning early results from the Magsat satellite program, which was designed to study the near-earth magnetic fields originating in the core and lithosphere, are discussed. The satellite was launched on October 30, 1979 into a sun-synchronous (twilight) orbit, and re-entered the atmosphere on June 11, 1980. Instruments carried included a cesium vapor magnetometer to measure field magnitudes, a fluxgate magnetometer to measure field components and an optical system to measure fluxgate magnetometer orientation. Early results concerned spherical harmonic models, fields due to ionospheric and magnetospheric currents, the identification and interpretation of fields from lithospheric sources. The preliminary results confirm the possibility of separating the measured field into core, crustal and external components, and represent significant developments in analytical techniques in main-field modelling and the physics of the field sources.

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)

Calculation and Analysis of magnetic gradient tensor components of global magnetic models

NASA Astrophysics Data System (ADS)

Schiffler, Markus; Queitsch, Matthias; Schneider, Michael; Stolz, Ronny; Krech, Wolfram; Meyer, Hans-Georg; Kukowski, Nina

2014-05-01

Magnetic mapping missions like SWARM and its predecessors, e.g. the CHAMP and MAGSAT programs, offer high resolution Earth's magnetic field data. These datasets are usually combined with magnetic observatory and survey data, and subject to harmonic analysis. The derived spherical harmonic coefficients enable magnetic field modelling using a potential series expansion. Recently, new instruments like the JeSSY STAR Full Tensor Magnetic Gradiometry system equipped with very high sensitive sensors can directly measure the magnetic field gradient tensor components. The full understanding of the quality of the measured data requires the extension of magnetic field models to gradient tensor components. In this study, we focus on the extension of the derivation of the magnetic field out of the potential series magnetic field gradient tensor components and apply the new theoretical framework to the International Geomagnetic Reference Field (IGRF) and the High Definition Magnetic Model (HDGM). The gradient tensor component maps for entire Earth's surface produced for the IGRF show low values and smooth variations reflecting the core and mantle contributions whereas those for the HDGM gives a novel tool to unravel crustal structure and deep-situated ore bodies. For example, the Thor Suture and the Sorgenfrei-Thornquist Zone in Europe are delineated by a strong northward gradient. Derived from Eigenvalue decomposition of the magnetic gradient tensor, the scaled magnetic moment, normalized source strength (NSS) and the bearing of the lithospheric sources are presented. The NSS serves as a tool for estimating the lithosphere-asthenosphere boundary as well as the depth of plutons and ore bodies. Furthermore changes in magnetization direction parallel to the mid-ocean ridges can be obtained from the scaled magnetic moment and the normalized source strength discriminates the boundaries between the anomalies of major continental provinces like southern Africa or the Eastern European Craton.

Modified ADALINE algorithm for harmonic estimation and selective harmonic elimination in inverters

NASA Astrophysics Data System (ADS)

Vasumathi, B.; Moorthi, S.

2011-11-01

In digital signal processing, algorithms are very well developed for the estimation of harmonic components. In power electronic applications, an objective like fast response of a system is of primary importance. An effective method for the estimation of instantaneous harmonic components, along with conventional harmonic elimination technique, is presented in this article. The primary function is to eliminate undesirable higher harmonic components from the selected signal (current or voltage) and it requires only the knowledge of the frequency of the component to be eliminated. A signal processing technique using modified ADALINE algorithm has been proposed for harmonic estimation. The proposed method stays effective as it converges to a minimum error and brings out a finer estimation. A conventional control based on pulse width modulation for selective harmonic elimination is used to eliminate harmonic components after its estimation. This method can be applied to a wide range of equipment. The validity of the proposed method to estimate and eliminate voltage harmonics is proved with a dc/ac inverter as a simulation example. Then, the results are compared with existing ADALINE algorithm for illustrating its effectiveness.

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

The source of the intermediate wavelength component of the Earth's magnetic field

NASA Technical Reports Server (NTRS)

Harrison, C. G. A.

1985-01-01

The intermediate wavelength component of the Earth's magnetic field has been well documented by observations made by MAGSAT. It has been shown that some significant fraction of this component is likely to be caused within the core of the Earth. Evidence for this comes from analysis of the intermediate wavelength component revealed by spherical harmonics between degrees 14 and 23, in which it is shown that it is unlikely that all of this signal is crustal. Firstly, there is no difference between average continental source strength and average oceanic source strength, which is unlikely to be the case if the anomalies reside within the crust, taking into account the very different nature and thickness of continental and oceanic crust. Secondly, there is almost no latitudinal variation in the source strength, which is puzzling if the sources are within the crust and have been formed by present or past magnetic fields with a factor of two difference in intensity between the equator and the poles. If however most of the sources for this field reside within the core, then these observations are not very surprising.

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.

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.

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.

The GRACE Mission: Meeting the Technical Challenges

NASA Technical Reports Server (NTRS)

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

2000-01-01

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

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

NASA Astrophysics Data System (ADS)

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

2015-12-01

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

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction.

PubMed

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-02-27

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 10 16 electrons/m²) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area.

Kriging with Unknown Variance Components for Regional Ionospheric Reconstruction

PubMed Central

Huang, Ling; Zhang, Hongping; Xu, Peiliang; Geng, Jianghui; Wang, Cheng; Liu, Jingnan

2017-01-01

Ionospheric delay effect is a critical issue that limits the accuracy of precise Global Navigation Satellite System (GNSS) positioning and navigation for single-frequency users, especially in mid- and low-latitude regions where variations in the ionosphere are larger. Kriging spatial interpolation techniques have been recently introduced to model the spatial correlation and variability of ionosphere, which intrinsically assume that the ionosphere field is stochastically stationary but does not take the random observational errors into account. In this paper, by treating the spatial statistical information on ionosphere as prior knowledge and based on Total Electron Content (TEC) semivariogram analysis, we use Kriging techniques to spatially interpolate TEC values. By assuming that the stochastic models of both the ionospheric signals and measurement errors are only known up to some unknown factors, we propose a new Kriging spatial interpolation method with unknown variance components for both the signals of ionosphere and TEC measurements. Variance component estimation has been integrated with Kriging to reconstruct regional ionospheric delays. The method has been applied to data from the Crustal Movement Observation Network of China (CMONOC) and compared with the ordinary Kriging and polynomial interpolations with spherical cap harmonic functions, polynomial functions and low-degree spherical harmonic functions. The statistics of results indicate that the daily ionospheric variations during the experimental period characterized by the proposed approach have good agreement with the other methods, ranging from 10 to 80 TEC Unit (TECU, 1 TECU = 1 × 1016 electrons/m2) with an overall mean of 28.2 TECU. The proposed method can produce more appropriate estimations whose general TEC level is as smooth as the ordinary Kriging but with a smaller standard deviation around 3 TECU than others. The residual results show that the interpolation precision of the new proposed method is better than the ordinary Kriging and polynomial interpolation by about 1.2 TECU and 0.7 TECU, respectively. The root mean squared error of the proposed new Kriging with variance components is within 1.5 TECU and is smaller than those from other methods under comparison by about 1 TECU. When compared with ionospheric grid points, the mean squared error of the proposed method is within 6 TECU and smaller than Kriging, indicating that the proposed method can produce more accurate ionospheric delays and better estimation accuracy over China regional area. PMID:28264424

A simple method for correcting spatially resolved solar intensity oscillation observations for variations in scattered light

NASA Technical Reports Server (NTRS)

Jefferies, S. M.; Duvall, T. L., Jr.

1991-01-01

A measurement of the intensity distribution in an image of the solar disk will be corrupted by a spatial redistribution of the light that is caused by the earth's atmosphere and the observing instrument. A simple correction method is introduced here that is applicable for solar p-mode intensity observations obtained over a period of time in which there is a significant change in the scattering component of the point spread function. The method circumvents the problems incurred with an accurate determination of the spatial point spread function and its subsequent deconvolution from the observations. The method only corrects the spherical harmonic coefficients that represent the spatial frequencies present in the image and does not correct the image itself.

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.

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.

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.

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.

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.

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

PubMed

Grinter, Roger; Jones, Garth A

2018-02-01

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

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

NASA Astrophysics Data System (ADS)

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

1999-07-01

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

Libsharp - spherical harmonic transforms revisited

NASA Astrophysics Data System (ADS)

Reinecke, M.; Seljebotn, D. S.

2013-06-01

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

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

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

NASA Astrophysics Data System (ADS)

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

2014-12-01

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

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.

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.

Research in Celestial Mechanics and Differential Equations.

DTIC Science & Technology

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

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

DTIC Science & Technology

1991-09-01

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

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.

Transfer function analysis of thermospheric perturbations

NASA Technical Reports Server (NTRS)

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

1986-01-01

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

Transfer function analysis of thermospheric perturbations

NASA Astrophysics Data System (ADS)

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

1986-06-01

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

A theoretical formulation of the electrophysiological inverse problem on the sphere

NASA Astrophysics Data System (ADS)

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

2006-04-01

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

Equivalent source modeling of the main field using MAGSAT data

NASA Technical Reports Server (NTRS)

1980-01-01

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

Ladder Operators for Some Spherically Symmetric Potentials in Quantum Mechanics

ERIC Educational Resources Information Center

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

1978-01-01

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

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.

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.

On the geomagnetic jerk of 1969

NASA Technical Reports Server (NTRS)

Mcleod, M. G.

1985-01-01

Courtillot et al. (1978) have first reported a sudden change in the slope of the first time derivatives of the geomagnetic field components which occurred around 1970. It was found that the change took place in a large part of the northern hemisphere. Malin and Hodder (1982) reported on studies which were conducted to determine whether this 1970 step change in the second time derivative of the geomagnetic field components, which they termed a geomagnetic 'jerk', was of internal or external origin. It was concluded that internal sources can give rise to changes in secular variation on time scales as short as one or two years and that these were the major factor in the geomagnetic jerk which occurred around 1970. The present paper provides new supporting evidence for the existence of a worldwide geomagnetic jerk, its (average) time of occurrence, and its internal nature. New estimates are given of the spherical harmonic coefficients of the jerk and of the pre-1969 and post-1969 secular acceleration.

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.

Anapoles in Free-Standing III-V Nanodisks Enhancing Second-Harmonic Generation.

PubMed

Timofeeva, Maria; Lang, Lukas; Timpu, Flavia; Renaut, Claude; Bouravleuv, Alexei; Shtrom, Igor; Cirlin, George; Grange, Rachel

2018-06-13

Nonradiating electromagnetic configurations in nanostructures open new horizons for applications due to two essential features: a lack of energy losses and invisibility to the propagating electromagnetic field. Such radiationless configurations form a basis for new types of nanophotonic devices, in which a strong electromagnetic field confinement can be achieved together with lossless interactions between nearby components. In our work, we present a new design of free-standing disk nanoantennas with nonradiating current distributions for the optical near-infrared range. We show a novel approach to creating nanoantennas by slicing III-V nanowires into standing disks using focused ion-beam milling. We experimentally demonstrate the suppression of the far-field radiation and the associated strong enhancement of the second-harmonic generation from the disk nanoantennas. With a theoretical analysis of the electromagnetic field distribution using multipole expansions in both spherical and Cartesian coordinates, we confirm that the demonstrated nonradiating configurations are anapoles. We expect that the presented procedure of designing and producing disk nanoantennas from nanowires becomes one of the standard approaches to fabricating controlled chains of standing nanodisks with different designs and configurations. These chains can be essential building blocks for new types of lasers and sensors with low power consumption.

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.

Harmonic generation with a dual frequency pulse.

PubMed

Keravnou, Christina P; Averkiou, Michalakis A

2014-05-01

Nonlinear imaging was implemented in commercial ultrasound systems over the last 15 years offering major advantages in many clinical applications. In this work, pulsing schemes coupled with a dual frequency pulse are presented. The pulsing schemes considered were pulse inversion, power modulation, and power modulated pulse inversion. The pulse contains a fundamental frequency f and a specified amount of its second harmonic 2f. The advantages and limitations of this method were evaluated with both acoustic measurements of harmonic generation and theoretical simulations based on the KZK equation. The use of two frequencies in a pulse results in the generation of the sum and difference frequency components in addition to the other harmonic components. While with single frequency pulses, only power modulation and power modulated pulse inversion contained odd harmonic components, with the dual frequency pulse, pulse inversion now also contains odd harmonic components.

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.

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

PubMed Central

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

2017-01-01

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

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.

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).

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.

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.

Mixed poloidal-toroidal magnetic configuration and surface abundance distributions of the Bp star 36 Lyn

NASA Astrophysics Data System (ADS)

Oksala, M. E.; Silvester, J.; Kochukhov, O.; Neiner, C.; Wade, G. A.; the MiMeS Collaboration

2018-01-01

Previous studies of the chemically peculiar Bp star 36 Lyn revealed a moderately strong magnetic field, circumstellar material and inhomogeneous surface abundance distributions of certain elements. We present in this paper an analysis of 33 high signal-to-noise ratio, high-resolution Stokes IV observations of 36 Lyn obtained with the Narval spectropolarimeter at the Bernard Lyot Telescope at Pic du Midi Observatory. From these data, we compute new measurements of the mean longitudinal magnetic field, Bℓ, using the multiline least-squares deconvolution (LSD) technique. A rotationally phased Bℓ curve reveals a strong magnetic field, with indications for deviation from a pure dipole field. We derive magnetic maps and chemical abundance distributions from the LSD profiles, produced using the Zeeman-Doppler imaging code INVERSLSD. Using a spherical harmonic expansion to characterize the magnetic field, we find that the harmonic energy is concentrated predominantly in the dipole mode (ℓ = 1), with significant contribution from both the poloidal and toroidal components. This toroidal field component is predicted theoretically, but not typically observed for Ap/Bp stars. Chemical abundance maps reveal a helium enhancement in a distinct region where the radial magnetic field is strong. Silicon enhancements are located in two regions, also where the radial field is stronger. Titanium and iron enhancements are slightly offset from the helium enhancements, and are located in areas where the radial field is weak, close to the magnetic equator.

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.

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

Vortices in a rotating two-component Bose–Einstein condensate with tunable interactions and harmonic potential

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

Zhang, Xiao-Fei, E-mail: xfzhang@ntsc.ac.cn; Du, Zhi-Jing; Tan, Ren-Bing

We consider a pair of coupled nonlinear Schrödinger equations modeling a rotating two-component Bose–Einstein condensate with tunable interactions and harmonic potential, with emphasis on the structure of vortex states by varying the strength of inter-component interaction, rotational frequency, and the aspect ratio of the harmonic potential. Our results show that the inter-component interaction greatly enhances the effect of rotation. For the case of isotropic harmonic potential and small inter-component interaction, the initial vortex structure remains unchanged. As the ratio of inter- to intra-component interactions increases, each component undergoes a transition from a vortex lattice (vortex line) in an isotropic (anisotropic)more » harmonic potential to an alternatively arranged stripe pattern, and eventually to the interwoven “serpentine” vortex sheets. Moreover, in the case of anisotropic harmonic potential the system can develop to a rotating droplet structure. -- Highlights: •Different vortex structures are obtained within the full parameter space. •Effects of system parameters on the ground state structure are discussed. •Phase transition between different vortex structures is also examined. •Present one possible way to obtain the rotating droplet structure. •Provide many possibilities to manipulate vortex in two-component BEC.« less

Rigorous covariance propagation of geoid errors to geodetic MDT estimates

NASA Astrophysics Data System (ADS)

Pail, R.; Albertella, A.; Fecher, T.; Savcenko, R.

2012-04-01

The mean dynamic topography (MDT) is defined as the difference between the mean sea surface (MSS) derived from satellite altimetry, averaged over several years, and the static geoid. Assuming geostrophic conditions, from the MDT the ocean surface velocities as important component of global ocean circulation can be derived from it. Due to the availability of GOCE gravity field models, for the very first time MDT can now be derived solely from satellite observations (altimetry and gravity) down to spatial length-scales of 100 km and even below. Global gravity field models, parameterized in terms of spherical harmonic coefficients, are complemented by the full variance-covariance matrix (VCM). Therefore, for the geoid component a realistic statistical error estimate is available, while the error description of the altimetric component is still an open issue and is, if at all, attacked empirically. In this study we make the attempt to perform, based on the full gravity VCM, rigorous error propagation to derived geostrophic surface velocities, thus also considering all correlations. For the definition of the static geoid we use the third release of the time-wise GOCE model, as well as the satellite-only combination model GOCO03S. In detail, we will investigate the velocity errors resulting from the geoid component in dependence of the harmonic degree, and the impact of using/no using covariances on the MDT errors and its correlations. When deriving an MDT, it is spectrally filtered to a certain maximum degree, which is usually driven by the signal content of the geoid model, by applying isotropic or non-isotropic filters. Since this filtering is acting also on the geoid component, the consistent integration of this filter process into the covariance propagation shall be performed, and its impact shall be quantified. The study will be performed for MDT estimates in specific test areas of particular oceanographic interest.

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.

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).

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.

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.

Complex metabolic oscillations in plants forced by harmonic irradiance.

PubMed Central

Nedbal, Ladislav; Brezina, Vítezslav

2002-01-01

Plants exposed to harmonically modulated irradiance, approximately 1 + cos(omegat), exhibit a complex periodic pattern of chlorophyll fluorescence emission that can be deconvoluted into a steady-state component, a component that is modulated with the frequency of the irradiance (omega), and into at least two upper harmonic components (2omega and 3omega). A model is proposed that accounts for the upper harmonics in fluorescence emission by nonlinear negative feedback regulation of photosynthesis. In contrast to simpler linear models, the model predicts that the steady-state fluorescence component will depend on the frequency of light modulation, and that amplitudes of all fluorescence components will exhibit resonance peak(s) when the irradiance frequency is tuned to an internal frequency of a regulatory component. The experiments confirmed that the upper harmonic components appear and exhibit distinct resonant peaks. The frequency of autonomous oscillations observed earlier upon an abrupt increase in CO(2) concentration corresponds to the sharpest of the resonant peaks of the forced oscillations. We propose that the underlying principles are general for a wide spectrum of negative-feedback regulatory mechanisms. The analysis by forced harmonic oscillations will enable us to examine internal dynamics of regulatory processes that have not been accessible to noninvasive fluorescence monitoring to date. PMID:12324435

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.

Magnetic models for the United States for 1985

USGS Publications Warehouse

Peddie, Norman W.; Zunde, Audronis K.

1990-01-01

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

Ocean tides for satellite geodesy

NASA Technical Reports Server (NTRS)

Dickman, S. R.

1990-01-01

Spherical harmonic tidal solutions have been obtained at the frequencies of the 32 largest luni-solar tides using prior theory of the author. That theory was developed for turbulent, nonglobal, self-gravitating, and loading oceans possessing realistic bathymetry and linearized bottom friction; the oceans satisfy no-flow boundary conditions at coastlines. In this theory the eddy viscosity and bottom drag coefficients are treated as spatially uniform. Comparison of the predicted degree-2 components of the Mf, P1, and M2 tides with those from numerical and satellite-based tide models allows the ocean friction parameters to be estimated at long and short periods. Using the 32 tide solutions, the frequency dependence of tidal admittance is investigated, and the validity of sideband tide models used in satellite orbit analysis is examined. The implications of admittance variability for oceanic resonances are also explored.

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

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

The quasi-biennial variation in the geomagnetic field: a global characteristics analysis

NASA Astrophysics Data System (ADS)

Ou, Jiaming; Du, Aimin

2016-04-01

The periodicity of 1.5-3 years, namely the quasi-biennial oscillation (QBO), has been identified in the solar, geophysical, and atmospheric variability. Sugiura (1976) investigated the observatory annual means over 1900-1970 and confirmed the QBO in the geomagnetic field. At present, studying the quasi-biennial oscillation becomes substantial for separating the internal/external parts in the geomagnetic observations. For the internal field, two typical periodicities, namely the 6-year oscillation in the geomagnetic secular acceleration (SA) and the geomagnetic jerk (occurs in 1-2 years), have close period to the QBO. Recently, a global quasi-biennial fluctuation was identified in the geomagnetic core field model (Silva et al., 2012). Silva et al. speculated this 2.5 years signal to either external source remaining in the core field model or consequence of the methods used to construct the model. As more high-quality data from global observatories are available, it is a good opportunity to characterize the geomagnetic QBO in the global range. In this paper, we investigate the QBO in the observatory monthly geomagnetic field X, Y, and Z components spanning 1985-2010. We employ the observatory hourly means database from the World Data Center for Geomagnetism (WDC) for the investigation. Wavelet analysis is used to detect and identify the QBO, while Fast Fourier Transform (FFT) analysis to obtain the statistics of the QBO. We apply the spherical harmonic analysis on QBO's amplitude, in order to quantify and separate internal and external sources. Three salient periods respectively at 2.9, 2.2, and 1.7 years, are identified in the amplitude spectrum over 1988-2008. The oscillation with the period of ~2.2 years is most prominent in all field components and further studied. In the X component the QBO is attenuated towards the polar regions, while in the Z component the amplitude of QBO increases with increasing of the geomagnetic latitude. At the high latitudes, the QBO exhibits distinct anisotropic in the local time distribution. The QBO of the X and Z components are both stronger over LT 00:00-06:00. The results of spherical harmonic analysis indicate that the QBO is mainly contributed by the external sources. The QBO is highly correlated with various parameters of solar activity, solar wind at 1AU, and geomagnetic activity. Reference 1. Sugiura, M. (1976). Quasi-biennial geomagnetic variation caused by the Sun. Geophys. Res. Lett., 3(11), 643-646. 2. Silva, L., Jackson, L., and Mound, J., (2012), Assessing the importance and expression of the 6 year geomagnetic oscillation, J. Geophys. Res.: Solid Earth (1978-2012), 117.

On the possibility of a place code for the low pitch of high-frequency complex tonesa

PubMed Central

Santurette, Sébastien; Dau, Torsten; Oxenham, Andrew J.

2012-01-01

Harmonics are considered unresolved when they interact with neighboring harmonics and cannot be heard out separately. Several studies have suggested that the pitch derived from unresolved harmonics is coded via temporal fine-structure cues emerging from their peripheral interactions. Such conclusions rely on the assumption that the components of complex tones with harmonic ranks down to at least 9 were indeed unresolved. The present study tested this assumption via three different measures: (1) the effects of relative component phase on pitch matches, (2) the effects of dichotic presentation on pitch matches, and (3) listeners' ability to hear out the individual components. No effects of relative component phase or dichotic presentation on pitch matches were found in the tested conditions. Large individual differences were found in listeners' ability to hear out individual components. Overall, the results are consistent with the coding of individual harmonic frequencies, based on the tonotopic activity pattern or phase locking to individual harmonics, rather than with temporal coding of single-channel interactions. However, they are also consistent with more general temporal theories of pitch involving the across-channel summation of information from resolved and/or unresolved harmonics. Simulations of auditory-nerve responses to the stimuli suggest potential benefits to a spatiotemporal mechanism. PMID:23231119

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.

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

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.

Geomagnetic polarity transitions

NASA Astrophysics Data System (ADS)

Merrill, Ronald T.; McFadden, Phillip L.

1999-05-01

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

Project MANTIS: A MANTle Induction Simulator for coupling geodynamic and electromagnetic modeling

NASA Astrophysics Data System (ADS)

Weiss, C. J.

2009-12-01

A key component to testing geodynamic hypotheses resulting from the 3D mantle convection simulations is the ability to easily translate the predicted physiochemical state to the model space relevant for an independent geophysical observation, such as earth's seismic, geodetic or electromagnetic response. In this contribution a new parallel code for simulating low-frequency, global-scale electromagnetic induction phenomena is introduced that has the same Earth discretization as the popular CitcomS mantle convection code. Hence, projection of the CitcomS model into the model space of electrical conductivity is greatly simplified, and focuses solely on the node-to-node, physics-based relationship between these Earth parameters without the need for "upscaling", "downscaling", averaging or harmonizing with some other model basis such as spherical harmonics. Preliminary performance tests of the MANTIS code on shared and distributed memory parallel compute platforms shows favorable scaling (>70% efficiency) for up to 500 processors. As with CitcomS, an OpenDX visualization widget (VISMAN) is also provided for 3D rendering and interactive interrogation of model results. Details of the MANTIS code will be briefly discussed here, focusing on compatibility with CitcomS modeling, as will be preliminary results in which the electromagnetic response of a CitcomS model is evaluated. VISMAN rendering of electrical tomography-derived electrical conductivity model overlain by an a 1x1 deg crustal conductivity map. Grey scale represents the log_10 magnitude of conductivity [S/m]. Arrows are horiztonal components of a hypothetical magnetospheric source field used to electromagnetically excite the conductivity model.

Analysis of Even Harmonics Generation in an Isolated Electric Power System

NASA Astrophysics Data System (ADS)

Kanao, Norikazu; Hayashi, Yasuhiro; Matsuki, Junya

Harmonics bred from loads are mainly odd order because the current waveform has half-wave symmetry. Since the even harmonics are negligibly small, those are not generally measured in electric power systems. However, even harmonics were measured at a 500/275/154kV substation in Hokuriku Electric Power Company after removal of a transmission line fault. The even harmonics caused malfunctions of protective digital relays because the relays used 4th harmonics at the input filter as automatic supervisory signal. This paper describes the mechanism of generation of the even harmonics by comparing measured waveforms with ATP-EMTP simulation results. As a result of analysis, it is cleared that even harmonics are generated by three causes. The first cause is a magnetizing current of transformers due to flux deviation by DC component of a fault current. The second one is due to harmonic conversion of a synchronous machine which generates even harmonics when direct current component or even harmonic current flow into the machine. The third one is that increase of harmonic impedance due to an isolated power system produces harmonic voltages. The design of the input filter of protective digital relays should consider even harmonics generation in an isolated power system.

Probe for high resolution NMR with sample reorientation

DOEpatents

Pines, A.; Samoson, A.

1990-02-06

An improved NMR probe and method are described which substantially improve the resolution of NMR measurements made on powdered or amorphous or otherwise orientationally disordered samples. The apparatus mechanically varies the orientation of the sample such that the time average of two or more sets of spherical harmonic functions are zero. 8 figs.

An iterative inversion of weighted Radon transforms along hyperplanes

NASA Astrophysics Data System (ADS)

Goncharov, F. O.

2017-12-01

We propose iterative inversion algorithms for weighted Radon transforms R W along hyperplanes in {R}3 . More precisely, expanding the weight W=W(x, θ), x\\in {R}^3, θ\\in {S}^2, into the series of spherical harmonics in θ and assuming that the zero order term w0, 0(x)\

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

PubMed

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

2017-05-28

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

Electromagnetic deep-probing (100-1000 kms) of the Earth's interior from artificial satellites: Constraints on the regional emplacement of crustal resources

NASA Technical Reports Server (NTRS)

Hermance, J. F. (Principal Investigator)

1981-01-01

A spherical harmonic analysis program is being tested which takes magnetic data in universal time from a set of arbitrarily space observatories and calculates a value for the instantaneous magnetic field at any point on the globe. The calculation is done as a least mean-squares value fit to a set of spherical harmonics up to any desired order. The program accepts as a set of input the orbit position of a satellite coordinates it with ground-based magnetic data for a given time. The output is a predicted time series for the magnetic field on the Earth's surface at the (r, theta) position directly under the hypothetically orbiting satellite for the duration of the time period of the input data set. By tracking the surface magnetic field beneath the satellite, narrow-band averages crosspowers between the spatially coordinated satellite and the ground-based data sets are computed. These crosspowers are used to calculate field transfer coefficients with minimum noise distortion. The application of this technique to calculating the vector response function W is discussed.

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.

Fluorescence/depolarization lidar for mid-range stand-off detection of biological agents

NASA Astrophysics Data System (ADS)

Mierczyk, Z.; Kopczyński, K.; Zygmunt, M.; Wojtanowski, J.; Młynczak, J.; Gawlikowski, A.; Młodzianko, A.; Piotrowski, W.; Gietka, A.; Knysak, P.; Drozd, T.; Muzal, M.; Kaszczuk, M.; Ostrowski, R.; Jakubaszek, M.

2011-06-01

LIDAR system for real-time standoff detection of bio-agents is presented and preliminary experimental results are discussed. The detection approach is based on two independent physical phenomena: (1) laser induced fluorescence (LIF), (2) depolarization resulting from elastic scattering on non-spherical particles. The device includes three laser sources, two receiving telescopes, depolarization component and spectral signature analyzing spectrograph. It was designed to provide the stand-off detection capability at ranges from 200 m up to several kilometers. The system as a whole forms a mobile platform for vehicle or building installation. Additionally, it's combined with a scanning mechanics and advanced software, which enable to conduct the semi-automatic monitoring of a specified space sector. For fluorescence excitation, 3-rd (355 nm) and 4-th (266 nm) harmonics of Nd:YAG pulsed lasers are used. They emit short (~6 ns) pulses with the repetition rate of 20 Hz. Collecting optics for fluorescence echo detection and spectral content analysis includes 25 mm diameter f/4 Newton telescope, Czerny Turner spectrograph and 32-channel PMT. Depending on the grating applied, the spectral resolution from 20 nm up to 3 nm per channel can be achieved. The system is also equipped with an eye-safe (1.5 μm) Nd:YAG OPO laser for elastic backscattering/depolarization detection. The optical echo signal is collected by Cassegrain telescope with aperture diameter of 12.5 mm. Depolarization detection component based on polarizing beam-splitter serves as the stand-off particle-shape analyzer, which is very valuable in case of non-spherical bio-aerosols sensing.

Gaussian statistics of the cosmic microwave background: Correlation of temperature extrema in the COBE DMR two-year sky maps

NASA Technical Reports Server (NTRS)

Kogut, A.; Banday, A. J.; Bennett, C. L.; Hinshaw, G.; Lubin, P. M.; Smoot, G. F.

1995-01-01

We use the two-point correlation function of the extrema points (peaks and valleys) in the Cosmic Background Explorer (COBE) Differential Microwave Radiometers (DMR) 2 year sky maps as a test for non-Gaussian temperature distribution in the cosmic microwave background anisotropy. A maximum-likelihood analysis compares the DMR data to n = 1 toy models whose random-phase spherical harmonic components a(sub lm) are drawn from either Gaussian, chi-square, or log-normal parent populations. The likelihood of the 53 GHz (A+B)/2 data is greatest for the exact Gaussian model. There is less than 10% chance that the non-Gaussian models tested describe the DMR data, limited primarily by type II errors in the statistical inference. The extrema correlation function is a stronger test for this class of non-Gaussian models than topological statistics such as the genus.

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.

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.

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.

Gravity field models from kinematic orbits of CHAMP, GRACE and GOCE satellites

NASA Astrophysics Data System (ADS)

Bezděk, Aleš; Sebera, Josef; Klokočník, Jaroslav; Kostelecký, Jan

2014-02-01

The aim of our work is to generate Earth's gravity field models from GPS positions of low Earth orbiters. Our inversion method is based on Newton's second law, which relates the observed acceleration of the satellite with forces acting on it. The observed acceleration is obtained as numerical second derivative of kinematic positions. Observation equations are formulated using the gradient of the spherical harmonic expansion of the geopotential. Other forces are either modelled (lunisolar perturbations, tides) or provided by onboard measurements (nongravitational perturbations). From this linear regression model the geopotential harmonic coefficients are obtained. To this basic scheme of the acceleration approach we added some original elements, which may be useful in other inversion techniques as well. We tried to develop simple, straightforward and still statistically correct model of observations. (i) The model is linear in the harmonic coefficients, no a priori gravity field model is needed, no regularization is applied. (ii) We use the generalized least squares to successfully mitigate the strong amplification of noise due to numerical second derivative. (iii) The number of other fitted parameters is very small, in fact we use only daily biases, thus we can monitor their behaviour. (iv) GPS positions have correlated errors. The sample autocorrelation function and especially the partial autocorrelation function indicate suitability of an autoregressive model to represent the correlation structure. The decorrelation of residuals improved the accuracy of harmonic coefficients by a factor of 2-3. (v) We found it better to compute separate solutions in the three local reference frame directions than to compute them together at the same time; having obtained separate solutions for along-track, cross-track and radial components, we combine them using the normal matrices. Relative contribution of the along-track component to the combined solution is 50 percent on average. (vi) The computations were performed on an ordinary PC up to maximum degree and order 120. We applied the presented method to orbits of CHAMP and GRACE spanning seven years (2003-2009) and to two months of GOCE (Nov/Dec 2009). The obtained long-term static gravity field models are of similar or better quality compared to other published solutions. We also tried to extract the time-variable gravity signal from CHAMP and GRACE orbits. The acquired average annual signal shows clearly the continental areas with important and known hydrological variations.

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.

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

NASA Astrophysics Data System (ADS)

Plattner, Alain; Simons, Frederik J.

2017-10-01

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

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

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.

Physiological and harmonic components in neural and muscular coherence in Parkinsonian tremor.

PubMed

Wang, Shouyan; Aziz, Tipu Z; Stein, John F; Bain, Peter G; Liu, Xuguang

2006-07-01

To differentiate physiological from harmonic components in coherence analysis of the tremor-related neural and muscular signals by comparing power, cross-power and coherence spectra. Influences of waveform, burst-width and additional noise on generating harmonic peaks in the power, cross-power and coherence spectra were studied using simulated signals. The local field potentials (LFPs) of the subthalamic nucleus (STN) and the EMGs of the contralateral forearm muscles in PD patients with rest tremor were analysed. (1) Waveform had significant effect on generating harmonics; (2) noise significantly decreased the coherence values in a frequency-dependent fashion; and (3) cross-spectrum showed high resistance to harmonics. Among six examples of paired LFP-EMG signals, significant coherence appeared at the tremor frequency only, both the tremor and double tremor frequencies and the double-tremor frequency only. In coherence analysis of neural and muscular signals, distortion in waveform generates significant harmonic peaks in the coherence spectra and the coherence values of both physiological and harmonic components are modulated by extra noise or non-tremor related activity. The physiological or harmonic nature of a coherence peak at the double tremor frequency may be differentiated when the coherence spectra are compared with the power and in particular the cross-power spectra.

Failure of Harmonic Gears During Verification of a Two-Axis Gimbal for the Mars Reconnaissance Orbiter Spacecraft

NASA Technical Reports Server (NTRS)

Johnson, Michael R.; Gehling, Russ; Head, Ray

2006-01-01

The Mars Reconnaissance Orbiter (MRO) spacecraft has three two-axis gimbal assemblies that support and move the High Gain Antenna and two solar array wings. The gimbal assemblies are required to move almost continuously throughout the mission's seven-year lifetime, requiring a large number of output revolutions for each actuator in the gimbal assemblies. The actuator for each of the six axes consists of a two-phase brushless dc motor with a direct drive to the wave generator of a size-32 cup-type harmonic gear. During life testing of an actuator assembly, the harmonic gear teeth failed completely, leaving the size-32 harmonic gear with a maximum output torque capability less than 10% of its design capability. The investigation that followed the failure revealed limitations of the heritage material choices that were made for the harmonic gear components that had passed similar life requirements on several previous programs. Additionally, the methods used to increase the stiffness of a standard harmonic gear component set, while accepted practice for harmonic gears, is limited in its range. The stiffness of harmonic gear assemblies can be increased up to a maximum stiffness point that, if exceeded, compromises the reliability of the gear components for long life applications.

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.

Numerical solution of the exterior oblique derivative BVP using the direct BEM formulation

NASA Astrophysics Data System (ADS)

Čunderlík, Róbert; Špir, Róbert; Mikula, Karol

2016-04-01

The fixed gravimetric boundary value problem (FGBVP) represents an exterior oblique derivative problem for the Laplace equation. A direct formulation of the boundary element method (BEM) for the Laplace equation leads to a boundary integral equation (BIE) where a harmonic function is represented as a superposition of the single-layer and double-layer potential. Such a potential representation is applied to obtain a numerical solution of FGBVP. The oblique derivative problem is treated by a decomposition of the gradient of the unknown disturbing potential into its normal and tangential components. Our numerical scheme uses the collocation with linear basis functions. It involves a triangulated discretization of the Earth's surface as our computational domain considering its complicated topography. To achieve high-resolution numerical solutions, parallel implementations using the MPI subroutines as well as an iterative elimination of far zones' contributions are performed. Numerical experiments present a reconstruction of a harmonic function above the Earth's topography given by the spherical harmonic approach, namely by the EGM2008 geopotential model up to degree 2160. The SRTM30 global topography model is used to approximate the Earth's surface by the triangulated discretization. The obtained BEM solution with the resolution 0.05 deg (12,960,002 nodes) is compared with EGM2008. The standard deviation of residuals 5.6 cm indicates a good agreement. The largest residuals are obviously in high mountainous regions. They are negative reaching up to -0.7 m in Himalayas and about -0.3 m in Andes and Rocky Mountains. A local refinement in the area of Slovakia confirms an improvement of the numerical solution in this mountainous region despite of the fact that the Earth's topography is here considered in more details.

Ship Detection and Measurement of Ship Motion by Multi-Aperture Synthetic Aperture Radar

DTIC Science & Technology

2014-06-01

Reconstructed periodic components of the Doppler histories shown in Fig. 27, (b) splined harmonic component amplitudes as a function of range...78 Figure 42: (a) Reconstructed periodic components of the Doppler histories shown in Figure 30, (b) Splined amplitudes of the...Figure 29 (b) Splined amplitudes of the harmonic components. ............................................ 79 Figure 44: Ship focusing by standard

Dual aperture dipole magnet with second harmonic component

DOEpatents

Praeg, Walter F.

1985-01-01

An improved dual aperture dipole electromagnet includes a second-harmonic frequency magnetic guide field winding which surrounds first harmonic frequency magnetic guide field windings associated with each aperture. The second harmonic winding and the first harmonic windings cooperate to produce resultant magnetic waveforms in the apertures which have extended acceleration and shortened reset portions of electromagnet operation.

Dual aperture dipole magnet with second harmonic component

DOEpatents

Praeg, W.F.

1983-08-31

An improved dual aperture dipole electromagnet includes a second-harmonic frequency magnetic guide field winding which surrounds first harmonic frequency magnetic guide field windings associated with each aperture. The second harmonic winding and the first harmonic windings cooperate to produce resultant magnetic waveforms in the apertures which have extended acceleration and shortened reset portions of electromagnet operation.

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.

Harmonic component detection: Optimized Spectral Kurtosis for operational modal analysis

NASA Astrophysics Data System (ADS)

Dion, J.-L.; Tawfiq, I.; Chevallier, G.

2012-01-01

This work is a contribution in the field of Operational Modal Analysis to identify the modal parameters of mechanical structures using only measured responses. The study deals with structural responses coupled with harmonic components amplitude and frequency modulated in a short range, a common combination for mechanical systems with engines and other rotating machines in operation. These harmonic components generate misleading data interpreted erroneously by the classical methods used in OMA. The present work attempts to differentiate maxima in spectra stemming from harmonic components and structural modes. The detection method proposed is based on the so-called Optimized Spectral Kurtosis and compared with others definitions of Spectral Kurtosis described in the literature. After a parametric study of the method, a critical study is performed on numerical simulations and then on an experimental structure in operation in order to assess the method's performance.

The non-hydrostatic figures of the terrestrial planets

NASA Technical Reports Server (NTRS)

Runcorn, S. K.

1985-01-01

Solid state creep being exponentially dependent on temperature must dominate the mechanical behavior of the mantles of terrestrial planets beneath their lithospheres. General arguments suggest that the lithospheres of the Moon and Mars are about 200 km thick; the Earth, Venus and Mercury much less. Short wavelength gravity anomalies are explained by the finite strength of the lithosphere: the lunar mascons being an example. The good correlation of the Venus and Mars gravity anomalies with topography up to spherical harmonics of degrees 10-15 is in striking contrast to the lack of correlation between the long wavelength components of the geoid and the continent-ocean distribution or even the plates. Attempts have been made to explain the former correlations by isostatic models but the depths of compensation seem implausible. Low degree harmonics of the gravity fields of the terrestrial planets as is certainly the case in the Earth must arise from the density variations driving solid state convection. In the case of Venus the less dense differentiated materials of the highlands seems to be positioned over the singular points of the convection pattern. Thus the correlated gravity field does not arise from the highlands but from the density difference in the convecting interior. In the Earth lack of correlation seems to arise from the fact that the plates have moved relative to the convection pattern the last 100 M yr.

Properties of Decameter IIIb-III Pairs

NASA Astrophysics Data System (ADS)

Melnik, V. N.; Brazhenko, A. I.; Frantsuzenko, A. V.; Dorovskyy, V. V.; Rucker, H. O.

2018-02-01

A large number of Type IIIb-III pairs, in which the first component is a Type IIIb burst and the second one is a Type III burst, are often recorded during decameter Type III burst storms. From the beginning of their observation, the question of whether the components of these pairs are the first and the second harmonics of radio emission or not has remained open. We discuss properties of decameter IIIb-III pairs in detail to answer this question. The components of these pairs, Type IIIb bursts and Type III bursts, have essentially different durations and polarizations. At the same time their frequency drift rates are rather close, provided that the drift rates of Type IIIb bursts are a little larger those of Type III bursts at the same frequency. Frequency ratios of the bursts at the same moment are close to two. This points at a harmonic connection of the components in IIIb-III pairs. At the same time there was a serious difficulty, namely why the first harmonic had fine frequency structure in the form of striae and the second harmonic did not have it. Recently Loi, Cairns, and Li ( Astrophys. J. 790, 67, 2014) succeeded in solving this problem. The physical aspects of observational properties of decameter IIIb-III pairs are discussed and pros and cons of harmonic character of Type IIIb bursts and Type III bursts in IIIb-III pairs are presented. We conclude that practically all properties of the IIIb-III pair components can be understood in the framework of the harmonic relation of the components of the IIIb-III pairs.

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.

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.

Constraints and vibrations in static packings of ellipsoidal particles.

PubMed

Schreck, Carl F; Mailman, Mitch; Chakraborty, Bulbul; O'Hern, Corey S

2012-06-01

We numerically investigate the mechanical properties of static packings of frictionless ellipsoidal particles in two and three dimensions over a range of aspect ratio and compression Δφ. While amorphous packings of spherical particles at jamming onset (Δφ=0) are isostatic and possess the minimum contact number z_{iso} required for them to be collectively jammed, amorphous packings of ellipsoidal particles generally possess fewer contacts than expected for collective jamming (z

High Power Klystrons for Efficient Reliable High Power Amplifiers.

DTIC Science & Technology

1980-11-01

techniques to obtain high overall efficiency. One is second harmonic space charge bunching. This is a process whereby the fundamental and second harmonic...components of the space charge waves in the electron beam of a microwave tube are combined to produce more highly concentrated electron bunches raising the...the drift lengths to enhance the 2nd harmonic component in the space charge waves. The latter method was utilized in the VKC-7790. Computer

Positional stability and radial dynamics of sonoluminescent bubbles under bi-harmonic driving: Effect of the high-frequency component and its relative phase.

PubMed

Rosselló, J M; Dellavale, D; Bonetto, F J

2016-07-01

The use of bi-frequency driving in sonoluminescence has proved to be an effective way to avoid the spatial instability (pseudo-orbits) developed by bubbles in systems with high viscous liquids like sulfuric or phosphoric acids. In this work, we present extensive experimental and numerical evidence in order to assess the effect of the high frequency component (PAc(HF)) of a bi-harmonic acoustic pressure field on the dynamic of sonoluminescent bubbles in an aqueous solution of sulfuric acid. The present study is mainly focused on the role of the harmonic frequency (Nf0) and the relative phase between the two frequency components (φb) of the acoustic field on the spatial, positional and diffusive stability of the bubbles. The results presented in this work were analyzed by means of three different approaches. First, we discussed some qualitative considerations about the changes observed in the radial dynamics, and the stability of similar bubbles under distinct bi-harmonic drivings. Later, we have investigated, through a series of numerical simulations, how the use of high frequency harmonic components of different order N, affects the positional stability of the SL bubbles. Furthermore, the influence of φb in their radius temporal evolution is systematically explored for harmonics ranging from the second to the fifteenth harmonic (N=2-15). Finally, a multivariate analysis based on the covariance method is performed to study the dependences among the parameters characterizing the SL bubble. Both experimental and numerical results indicate that the impact of PAc(HF) on the positional instability and the radial dynamics turns to be progressively negligible as the order of the high frequency harmonic component grows (i.e. N ≫ 1), however its effectiveness on the reduction of the spatial instability remains unaltered or even improved. Copyright © 2016 Elsevier B.V. All rights reserved.

Discrimination of radiation quality through second harmonic out-of-phase cw-ESR detection.

PubMed

Marrale, Maurizio; Longo, Anna; Brai, Maria; Barbon, Antonio; Brustolon, Marina

2014-02-01

The ability to discriminate the quality of ionizing radiation is important because the biological effects produced in tissue strongly depends on both absorbed dose and linear energy transfer (LET) of ionizing particles. Here we present an experimental electron spin resonance (ESR) analysis aimed at discriminating the effective LETs of various radiation beams (e.g., 19.3 MeV protons, (60)Co photons and thermal neutrons). The measurement of the intensities of the continuous wave spectrometer signal channel first harmonic in-phase and the second harmonic out-of-phase components are used to distinguish the radiation quality. A computational analysis, was carried out to evaluate the dependence of the first harmonic in-phase and second harmonic out-of-phase components on microwave power, modulation amplitude and relaxation times, and highlights that these components could be used to point out differences in the relaxation times. On the basis of this numerical analysis the experimental results are discussed. The methodology described in this study has the potential to provide information on radiation quality.

Long-Term Prediction of the Arctic Ionospheric TEC Based on Time-Varying Periodograms

PubMed Central

Liu, Jingbin; Chen, Ruizhi; Wang, Zemin; An, Jiachun; Hyyppä, Juha

2014-01-01

Knowledge of the polar ionospheric total electron content (TEC) and its future variations is of scientific and engineering relevance. In this study, a new method is developed to predict Arctic mean TEC on the scale of a solar cycle using previous data covering 14 years. The Arctic TEC is derived from global positioning system measurements using the spherical cap harmonic analysis mapping method. The study indicates that the variability of the Arctic TEC results in highly time-varying periodograms, which are utilized for prediction in the proposed method. The TEC time series is divided into two components of periodic oscillations and the average TEC. The newly developed method of TEC prediction is based on an extrapolation method that requires no input of physical observations of the time interval of prediction, and it is performed in both temporally backward and forward directions by summing the extrapolation of the two components. The backward prediction indicates that the Arctic TEC variability includes a 9 years period for the study duration, in addition to the well-established periods. The long-term prediction has an uncertainty of 4.8–5.6 TECU for different period sets. PMID:25369066

How Perturbing Ocean Floor Disturbs Tsunami Waves

NASA Astrophysics Data System (ADS)

Salaree, A.; Okal, E.

2017-12-01

Bathymetry maps play, perhaps the most crucial role in optimal tsunami simulations. Regardless of the simulation method, on one hand, it is desirable to include every detailed bathymetry feature in the simulation grids in order to predict tsunami amplitudes as accurately as possible, but on the other hand, large grids result in long simulation times. It is therefore, of interest to investigate a "sufficiency" level - if any - for the amount of details in bathymetry grids needed to reconstruct the most important features in tsunami simulations, as obtained from the actual bathymetry. In this context, we use a spherical harmonics series approach to decompose the bathymetry of the Pacific ocean into its components down to a resolution of 4 degrees (l=100) and create bathymetry grids by accumulating the resulting terms. We then use these grids to simulate the tsunami behavior from pure thrust events around the Pacific through the MOST algorithm (e.g. Titov & Synolakis, 1995; Titov & Synolakis, 1998). Our preliminary results reveal that one would only need to consider the sum of the first 40 coefficients (equivalent to a resolution of 1000 km) to reproduce the main components of the "real" results. This would result in simpler simulations, and potentially allowing for more efficient tsunami warning algorithms.

Non-linear Min protein interactions generate harmonics that signal mid-cell division in Escherichia coli

PubMed Central

Walsh, James C.; Angstmann, Christopher N.; Duggin, Iain G.

2017-01-01

The Min protein system creates a dynamic spatial pattern in Escherichia coli cells where the proteins MinD and MinE oscillate from pole to pole. MinD positions MinC, an inhibitor of FtsZ ring formation, contributing to the mid-cell localization of cell division. In this paper, Fourier analysis is used to decompose experimental and model MinD spatial distributions into time-dependent harmonic components. In both experiment and model, the second harmonic component is responsible for producing a mid-cell minimum in MinD concentration. The features of this harmonic are robust in both experiment and model. Fourier analysis reveals a close correspondence between the time-dependent behaviour of the harmonic components in the experimental data and model. Given this, each molecular species in the model was analysed individually. This analysis revealed that membrane-bound MinD dimer shows the mid-cell minimum with the highest contrast when averaged over time, carrying the strongest signal for positioning the cell division ring. This concurs with previous data showing that the MinD dimer binds to MinC inhibiting FtsZ ring formation. These results show that non-linear interactions of Min proteins are essential for producing the mid-cell positioning signal via the generation of second-order harmonic components in the time-dependent spatial protein distribution. PMID:29040283

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.

The determination of the most applicable PWV model for Turkey

NASA Astrophysics Data System (ADS)

Deniz, Ilke; Gurbuz, Gokhan; Mekik, Cetin

2016-07-01

Water vapor is a key component for modelling atmosphere and climate studies. Moreover, long-term water vapor changes can be an independent source for detecting climate changes. Since Global Navigation Satellite Systems (GNSS) use microwaves passing through the atmosphere, atmospheric effects are modeled with high accuracy. Tropospheric effects on GNSS signals are estimated with total zenith delay parameter (ZTD) which is the sum of hydrostatic (ZHD) and wet zenith delay (ZWD). The first component can be obtained from meteorological observations with high accuracy; the second component, however, can be computed by subtracting ZHD from ZTD (ZWD=ZTD-ZHD). Afterwards, the weighted mean temperature (Tm) or the conversion factor (Q) is used for the conversion between the precipitable water vapor (PWV) and ZWD. The parameters Tm and Q are derived from the analysis of radiosonde stations' profile observations. Numerous Q and Tm models have been developed for each radiosonde station, radiosonde station group, countries and global fields such as Bevis Tm model and Emardson and Derks' Q models. So, PWV models (Tm and Q models) applied for Turkey have been developed using a year of radiosonde data (2011) from 8 radiosonde stations. In this study the models developed are tested by comparing PWVGNSS computed applying Tm and Q models to the ZTD estimates derived by Bernese and GAMIT/GLOBK software at GNSS stations established at Istanbul and Ankara with those from the collocated radiosonde stations (PWVRS) from October 2013 to December 2014 with the data obtained from a project (no 112Y350) supported by the Scientific and Technological Research Council of Turkey (TUBITAK). The comparison results show that PWVGNSS and PWVRS are in high correlation (86 % for Ankara and 90% for Istanbul). Thus, the most applicable model for Turkey and the accuracy of GNSS meteorology are investigated. In addition, Tm model was applied to the ZTD estimates of 20 TUSAGA-Active (CORS-TR) stations in the 38.0°-42.0° northern latitudes and 28.0°-34.0° eastern longitudes of Turkey and PWV were computed. ZTD estimates of these stations were computed using Bernese GNSS Software v5.0 during the period from June 2013 to June 2014. Preceding the PWV estimation, meteorological parameters for these stations (temperature, pressure and humidity) are derived by applying spherical harmonics modelling and interpolation to the above-mentioned meteorological parameters measured by meteorological stations surrounding TUSAGA-Active stations. Results of spherical harmonics modelling and interpolation yield the precision of ±1.74 K in temperature, ±0.95 hPa in pressure and ±14.88 % in humidity. Also, the PWV of TUSAGA-Active stations selected were estimated.

Enhanced efficiency of the second harmonic inhomogeneous component in an opaque cavity.

PubMed

Roppo, V; Raineri, F; Raj, R; Sagnes, I; Trull, J; Vilaseca, R; Scalora, M; Cojocaru, C

2011-05-15

In this Letter, we experimentally demonstrate the enhancement of the inhomogeneous second harmonic conversion in the opaque region of a GaAs cavity with efficiencies of the order of 0.1% at 612 nm, using 3 ps pump pulses having peak intensities of the order of 10 MW/cm(2). We show that the conversion efficiency of the inhomogeneous, phase-locked second harmonic component is a quadratic function of the cavity factor Q. © 2011 Optical Society of America

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.

The OSIRIS-REx Radio Science Experiment at Bennu

NASA Astrophysics Data System (ADS)

McMahon, J. W.; Scheeres, D. J.; Hesar, S. G.; Farnocchia, D.; Chesley, S.; Lauretta, D.

2018-02-01

The OSIRIS-REx mission will conduct a Radio Science investigation of the asteroid Bennu with a primary goal of estimating the mass and gravity field of the asteroid. The spacecraft will conduct proximity operations around Bennu for over 1 year, during which time radiometric tracking data, optical landmark tracking images, and altimetry data will be obtained that can be used to make these estimates. Most significantly, the main Radio Science experiment will be a 9-day arc of quiescent operations in a 1-km nominally circular terminator orbit. The pristine data from this arc will allow the Radio Science team to determine the significant components of the gravity field up to the fourth spherical harmonic degree. The Radio Science team will also be responsible for estimating the surface accelerations, surface slopes, constraints on the internal density distribution of Bennu, the rotational state of Bennu to confirm YORP estimates, and the ephemeris of Bennu that incorporates a detailed model of the Yarkovsky effect.

Global excitation of wave phenomena in a dissipative multiconstituent medium. I - Transfer function of the earth's thermosphere. II - Impulsive perturbations in the earth's thermosphere

NASA Technical Reports Server (NTRS)

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

1984-01-01

A transfer function approach is taken in constructing a spectral model of the acoustic-gravity wave response in a multiconstituent thermosphere. The model is then applied to describing the thermospheric response to various sources around the globe. Zonal spherical harmonics serve to model the horizontal variations in propagating waves which, when integrated with respect to height, generate a transfer function for a vertical source distribution in the thermosphere. Four wave components are characterized as resonance phenomena and are associated with magnetic activity and ionospheric disturbances. The waves are either trapped or propagate, the latter becoming significant when possessing frequencies above 3 cycles/day. The energy input is distributed by thermospheric winds. The disturbances decay slowly, mainly due to heat conduction and diffusion. Gravity waves appear abruptly and are connected to a sudden switching on or off of a source. Turn off of a source coincides with a reversal of the local atmospheric circulation.

Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear

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

Ren, Zhen-Zhen; Wang, Feng; Fu, G. Y.

Linear and nonlinear simulations of high-order harmonics q=1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics (m=n>1) driven by energetic trapped particles can be higher than the m/n=1/1 component. The high m=n>1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonicsmore » modes, whereas there is only one precessional resonance for the m/n=1/1 harmonics. The fluid nonlinearity reduces the saturation level of the n=1 component, while it hardly affects those of the high n components, especially the modes with m=n=3,4. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. Lastly, in addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to m/n=1/1 component, although the m/n=1/1 component has a higher saturation amplitude.« less

Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear

DOE PAGES

Ren, Zhen-Zhen; Wang, Feng; Fu, G. Y.; ...

2017-04-24

Linear and nonlinear simulations of high-order harmonics q=1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics (m=n>1) driven by energetic trapped particles can be higher than the m/n=1/1 component. The high m=n>1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonicsmore » modes, whereas there is only one precessional resonance for the m/n=1/1 harmonics. The fluid nonlinearity reduces the saturation level of the n=1 component, while it hardly affects those of the high n components, especially the modes with m=n=3,4. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. Lastly, in addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to m/n=1/1 component, although the m/n=1/1 component has a higher saturation amplitude.« less

Balancing Vibrations at Harmonic Frequencies by Injecting Harmonic Balancing Signals into the Armature of a Linear Motor/Alternator Coupled to a Stirling Machine

NASA Technical Reports Server (NTRS)

Holliday, Ezekiel S. (Inventor)

2014-01-01

Vibrations at harmonic frequencies are reduced by injecting harmonic balancing signals into the armature of a linear motor/alternator coupled to a Stirling machine. The vibrations are sensed to provide a signal representing the mechanical vibrations. A harmonic balancing signal is generated for selected harmonics of the operating frequency by processing the sensed vibration signal with adaptive filter algorithms of adaptive filters for each harmonic. Reference inputs for each harmonic are applied to the adaptive filter algorithms at the frequency of the selected harmonic. The harmonic balancing signals for all of the harmonics are summed with a principal control signal. The harmonic balancing signals modify the principal electrical drive voltage and drive the motor/alternator with a drive voltage component in opposition to the vibration at each harmonic.

Biological Effects of Laser Radiation. Volume IV. Optical Second Harmonic Generation in Biological Tissues.

DTIC Science & Technology

1978-10-17

characteristics for optical second- harmonic generation. The collage component of conective tissue may be the principal site for the observed harmonic...Generation in Tissue ; Second Harmonic Generation in Collage; Glutathione, 5MB; Mechanisms; Conversion Efficiency; Significance of order UL AIM UY#m~wmev...sclera, and skin on 694 im. Q-switched ruby laser irradiation. A possible source of this second-harmonic generation was tissue collagen; because of

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.

Mover Position Detection for PMTLM Based on Linear Hall Sensors through EKF Processing

PubMed Central

Yan, Leyang; Zhang, Hui; Ye, Peiqing

2017-01-01

Accurate mover position is vital for a permanent magnet tubular linear motor (PMTLM) control system. In this paper, two linear Hall sensors are utilized to detect the mover position. However, Hall sensor signals contain third-order harmonics, creating errors in mover position detection. To filter out the third-order harmonics, a signal processing method based on the extended Kalman filter (EKF) is presented. The limitation of conventional processing method is first analyzed, and then EKF is adopted to detect the mover position. In the EKF model, the amplitude of the fundamental component and the percentage of the harmonic component are taken as state variables, and they can be estimated based solely on the measured sensor signals. Then, the harmonic component can be calculated and eliminated. The proposed method has the advantages of faster convergence, better stability and higher accuracy. Finally, experimental results validate the effectiveness and superiority of the proposed method. PMID:28383505

Investigation of superharmonic sound propagation and imaging in biological tissues in vitro.

PubMed

Ma, Qingyu; Zhang, Dong; Gong, Xiufen; Ma, Yong

2006-04-01

This article presents both theoretical and experimental studies on the superharmonic generation and its imaging in biological tissues. A superharmonic component is defined as a summation of the third-, fourth-, and fifth-order harmonics. A superharmonic signal is produced using an 8-mm-diam, 2.5-MHz planar piston source that is excited by eight-cycle, 2.5-MHz tone bursts. Axial and lateral field distributions of the superharmonic component and the second harmonic are first calculated based on the nonlinear KZK model and then compared with those experimentally determined at two different source pressures of 0.5 and 1 MPa. Results indicate that the amplitude of the superharmonic component can exceed that of the second harmonic, depending on the axial distance and the fundamental pressure amplitude. Also, the 3-dB beamwidth of the superharmonic component is about 23% narrower than that of the second harmonic. Additional experiments are performed in vitro using liver and fatty tissues in transmission mode and produced two-dimensional images using the fundamental, the second harmonic, and the superharmonic signals. Although the clinical applicability of this work still needs to be assessed, these results indicate that the superharmonic image quality is better than that of the other two images.

Assessment of foetal exposure to the homogeneous magnetic field harmonic spectrum generated by electricity transmission and distribution networks.

PubMed

Fiocchi, Serena; Liorni, Ilaria; Parazzini, Marta; Ravazzani, Paolo

2015-04-01

During the last decades studies addressing the effects of exposure to Extremely Low Frequency Electromagnetic Fields (ELF-EMF) have pointed out a possible link between those fields emitted by power lines and childhood leukaemia. They have also stressed the importance of also including in the assessment the contribution of frequency components, namely harmonics, other than the fundamental one. Based on the spectrum of supply voltage networks allowed by the European standard for electricity quality assessment, in this study the exposure of high-resolution three-dimensional models of foetuses to the whole harmonic content of a uniform magnetic field with a fundamental frequency of 50 Hz, was assessed. The results show that the main contribution in terms of induced electric fields to the foetal exposure is given by the fundamental frequency component. The harmonic components add some contributions to the overall level of electric fields, however, due to the extremely low permitted amplitude of the harmonic components with respect to the fundamental, their amplitudes are low. The level of the induced electric field is also much lower than the limits suggested by the guidelines for general public exposure, when the amplitude of the incident magnetic field is set at the maximum permitted level.

Assessment of Foetal Exposure to the Homogeneous Magnetic Field Harmonic Spectrum Generated by Electricity Transmission and Distribution Networks

PubMed Central

Fiocchi, Serena; Liorni, Ilaria; Parazzini, Marta; Ravazzani, Paolo

2015-01-01

During the last decades studies addressing the effects of exposure to Extremely Low Frequency Electromagnetic Fields (ELF-EMF) have pointed out a possible link between those fields emitted by power lines and childhood leukaemia. They have also stressed the importance of also including in the assessment the contribution of frequency components, namely harmonics, other than the fundamental one. Based on the spectrum of supply voltage networks allowed by the European standard for electricity quality assessment, in this study the exposure of high-resolution three-dimensional models of foetuses to the whole harmonic content of a uniform magnetic field with a fundamental frequency of 50 Hz, was assessed. The results show that the main contribution in terms of induced electric fields to the foetal exposure is given by the fundamental frequency component. The harmonic components add some contributions to the overall level of electric fields, however, due to the extremely low permitted amplitude of the harmonic components with respect to the fundamental, their amplitudes are low. The level of the induced electric field is also much lower than the limits suggested by the guidelines for general public exposure, when the amplitude of the incident magnetic field is set at the maximum permitted level. PMID:25837346

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.

Lunar and Solar Torques on the Oceanic Tides

NASA Technical Reports Server (NTRS)

Ray, Richard D.; Bills, Bruce G.; Chao, Benjamin F.

1998-01-01

Brosche and Seiler recently suggested that direct lunar and solar tidal torques on the oceanic tides play a significant role in the earth's short-period angular momentum balance ("short-period" here meaning daily and sub-daily). We reexamine that suggestion here, concentrating on axial torques and hence on variations in rotation rate. Only those spherical harmonic components of the ocean tide having the same degree and order as the tidal potential induce nonzero torques. Prograde components (those moving in the same direction as the tide-generating body) produce the familiar secular braking of the earth's rotation. Retrograde components, however, produce rapid variations in UTI at twice the tidal frequency. There also exist interaction torques between tidal constituents, e.g. solar torques on lunar tides. They generate UTI variations at frequencies equal to the sums and differences of the original tidal frequencies. We give estimates of the torques and angular momentum variations for each of the important regimes, secular to quarter-diurnal. For the M(sub 2) potential acting on the M(sub 2) ocean tide, we find an associated angular momentum variation of amplitude 3 x 10(exp 19) N m. This is 5 to 6 orders of magnitude smaller than the angular momentum variations associated with tidal currents. We conclude that these torques do not play a significant role in the short-period angular momentum balance.

Major Fault Patterns in Zanjan State of Iran Based of GECO Global Geoid Model

NASA Astrophysics Data System (ADS)

Beheshty, Sayyed Amir Hossein; Abrari Vajari, Mohammad; Raoufikelachayeh, SeyedehSusan

2016-04-01

A new Earth Gravitational Model (GECO) to degree 2190 has been developed incorporates EGM2008 and the latest GOCE based satellite solutions. Satellite gradiometry data are more sensitive information of the long- and medium- wavelengths of the gravity field than the conventional satellite tracking data. Hence, by utilizing this new technique, more accurate, reliable and higher degrees/orders of the spherical harmonic expansion of the gravity field can be achieved. Gravity gradients can also be useful in geophysical interpretation and prospecting. We have presented the concept of gravity gradients with some simple interpretations. A MATLAB based computer programs were developed and utilized for determining the gravity and gradient components of the gravity field using the GGMs, followed by a case study in Zanjan State of Iran. Our numerical studies show strong (more than 72%) correlations between gravity anomalies and the diagonal elements of the gradient tensor. Also, strong correlations were revealed between the components of the deflection of vertical and the off-diagonal elements as well as between the horizontal gradient and magnitude of the deflection of vertical. We clearly distinguished two big faults in North and South of Zanjan city based on the current information. Also, several minor faults were detected in the study area. Therefore, the same geophysical interpretation can be stated for gravity gradient components too. Our mathematical derivations support some of these correlations.

Optical harmonic generator

DOEpatents

Summers, M.A.; Eimerl, D.; Boyd, R.D.

1982-06-10

A pair of uniaxial birefringent crystal elements are fixed together to form a serially arranged, integral assembly which, alternatively, provides either a linearly or elliptically polarized second-harmonic output wave or a linearly polarized third-harmonic output wave. The extraordinary or e directions of the crystal elements are oriented in the integral assembly to be in quadrature (90/sup 0/). For a second-harmonic generation in the Type-II-Type-II angle tuned case, the input fundamental wave has equal amplitude o and e components. For a third-harmonic generation, the input fundamental wave has o and e components whose amplitudes are in a ratio of 2:1 (o:e reference first crystal). In the typical case of a linearly polarized input fundamental wave this can be accomplished by simply rotating the crystal assembly about the input beam direction by 10/sup 0/. For both second and third harmonic generation input precise phase-matching is achieved by tilting the crystal assembly about its two sensitive axeses (o).

Optical harmonic generator

DOEpatents

Summers, Mark A.; Eimerl, David; Boyd, Robert D.

1985-01-01

A pair of uniaxial birefringent crystal elements are fixed together to form a serially arranged, integral assembly which, alternatively, provides either a linearly or elliptically polarized second-harmonic output wave or a linearly polarized third-harmonic output wave. The "extraordinary" or "e" directions of the crystal elements are oriented in the integral assembly to be in quadrature (90.degree.). For a second-harmonic generation in the Type-II-Type-II angle tuned case, the input fundamental wave has equal amplitude "o" and "e" components. For a third-harmonic generation, the input fundamental wave has "o" and "e" components whose amplitudes are in a ratio of 2:1 ("o":"e" reference first crystal). In the typical case of a linearly polarized input fundamental wave this can be accomplished by simply rotating the crystal assembly about the input beam direction by 10.degree.. For both second and third harmonic generation input precise phase-matching is achieved by tilting the crystal assembly about its two sensitive axes ("o").

The NEAR laser ranging investigation

NASA Astrophysics Data System (ADS)

Zuber, M. T.; Smith, D. E.; Cheng, A. F.; Cole, T. D.

1997-10-01

The objective of the NEAR-Earth Asteriod Rendezvous (NEAR) laser ranging investigation is to obtain high integrity profiles and grids of topography for use in geophysical, geodetic and geological studies of asteroid 433 Eros. The NEAR laser rangefinder (NLR) will determine the slant range of the NEAR spacecraft to the asteroid surface by measuring precisely the round trip time of flight of individual laser pulses. Ranges will be converted to planetary radii measured with respect to the asteroid center of mass by subtracting the spacecraft orbit determined from X band Doppler tracking. The principal components of the NLR include a 1064 nm Cr:Nd:YAG laser, a gold-coated aluminum Dall-Kirkham Cassegrain telescope, an enhanced silicon avalanche photodiode hybrid detector, a 480-MHz crystal oscillator, and a digital processing unit. The instrument has a continuous in-flight calibration capability using a fiber-optic delay assembly. The single shot vertical resolution of the NLR is <6m, and the absolute accuracy of the global grid will be ~10m with respect to the asteroid center of mass. For the current mission orbital scenario, the laser spot size on the surface of Eros will vary from ~4-11m, and the along-track resolution for the nominal pulse repetition rate of 1 Hz will be approximately comparable to the spot size, resulting in contiguous along-track profiles. The across-track resolution will depend on the orbital mapping scenario, but will likely be <500m, which will define the spatial resolution of the global topographic model. Planned science investigations include global-scale analyses related to collisional and impact history and internal density distribution that utilize topographic grids as well as spherical harmonic topographic models that will be analyzed jointly with gravity at commensurate resolution. Attempts will be made to detect possible subtle time variations in internal structure that may be present if Eros is not a single coherent body, by analysis of low degree and order spherical harmonic coefficients. Local- to regional-scale analyses will utilize high-resolution three-dimensional topographic maps of specific surface structures to address surface geologic processes. Results from the NLR investigation will contribute significantly to understanding the origin, structure, and evolution of Eros and other asteroidal bodies.

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

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.

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.

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

Crack detection using resonant ultrasound spectroscopy

DOEpatents

Migliori, A.; Bell, T.M.; Rhodes, G.W.

1994-10-04

Method and apparatus are provided for detecting crack-like flaws in components. A plurality of exciting frequencies are generated and applied to a component in a dry condition to obtain a first ultrasonic spectrum of the component. The component is then wet with a selected liquid to penetrate any crack-like flaws in the component. The plurality of exciting frequencies are again applied to the component and a second ultrasonic spectrum of the component is obtained. The wet and dry ultrasonic spectra are then analyzed to determine the second harmonic components in each of the ultrasonic resonance spectra and the second harmonic components are compared to ascertain the presence of crack-like flaws in the component. 5 figs.

Crack detection using resonant ultrasound spectroscopy

DOEpatents

Migliori, Albert; Bell, Thomas M.; Rhodes, George W.

1994-01-01

Method and apparatus are provided for detecting crack-like flaws in components. A plurality of exciting frequencies are generated and applied to a component in a dry condition to obtain a first ultrasonic spectrum of the component. The component is then wet with a selected liquid to penetrate any crack-like flaws in the component. The plurality of exciting frequencies are again applied to the component and a second ultrasonic spectrum of the component is obtained. The wet and dry ultrasonic spectra are then analyzed to determine the second harmonic components in each of the ultrasonic resonance spectra and the second harmonic components are compared to ascertain the presence of crack-like flaws in the component.

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.

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).

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.

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.

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.

The behavior of quantization spectra as a function of signal-to-noise ratio

NASA Technical Reports Server (NTRS)

Flanagan, M. J.

1991-01-01

An expression for the spectrum of quantization error in a discrete-time system whose input is a sinusoid plus white Gaussian noise is derived. This quantization spectrum consists of two components: a white-noise floor and spurious harmonics. The dithering effect of the input Gaussian noise in both components of the spectrum is considered. Quantitative results in a discrete Fourier transform (DFT) example show the behavior of spurious harmonics as a function of the signal-to-noise ratio (SNR). These results have strong implications for digital reception and signal analysis systems. At low SNRs, spurious harmonics decay exponentially on a log-log scale, and the resulting spectrum is white. As the SNR increases, the spurious harmonics figure prominently in the output spectrum. A useful expression is given that roughly bounds the magnitude of a spurious harmonic as a function of the SNR.

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.

Introduction to Fourier Optics

ERIC Educational Resources Information Center

Huggins, Elisha

2007-01-01

Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…

Harmonics distribution of iron oxide nanoparticles solutions under diamagnetic background

NASA Astrophysics Data System (ADS)

Saari, Mohd Mawardi; Che Lah, Nurul Akmal; Sakai, Kenji; Kiwa, Toshihiko; Tsukada, Keiji

2018-04-01

The static and dynamic magnetizations of low concentrated multi-core iron oxide nanoparticles solutions were investigated by a specially developed high-Tc Superconducting Quantum Interference Device (SQUID) magnetometer. The size distribution of iron oxide cores was determined from static magnetization curves concerning different concentrations. The simulated harmonics distribution was compared to the experimental results. Effect of the diamagnetic background from carrier liquid to harmonics distribution was investigated with respect to different intensity and position of peaks in the magnetic moment distribution using a numerical simulation. It was found that the diamagnetic background from carrier liquid of iron oxide nanoparticles affected the harmonics distribution as their concentration decreased and depending on their magnetic moment distribution. The first harmonic component was susceptible to the diamagnetic contribution of carrier liquid when the concentration was lower than 24 μg/ml. The second and third harmonics were affected when the peak position of magnetic moment distribution was smaller than m = 10-19 Am2 and the concentration was 10 ng/ml. A highly sensitive detection up to sub-nanogram of iron oxide nanoparticles in solutions can be achieved by utilizing second and third harmonic components.

Spatially resolved observation of the fundamental and second harmonic standing kink modes using SDO/AIA

NASA Astrophysics Data System (ADS)

Pascoe, D. J.; Goddard, C. R.; Nakariakov, V. M.

2016-09-01

Aims: We consider a coronal loop kink oscillation observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO) which demonstrates two strong spectral components. The period of the lower frequency component being approximately twice that of the shorter frequency component suggests the presence of harmonics. Methods: We examine the presence of two longitudinal harmonics by investigating the spatial dependence of the loop oscillation. The time-dependent displacement of the loop is measured at 15 locations along the loop axis. For each position the displacement is fitted as the sum of two damped sinusoids, having periods P1 and P2, and a damping time τ. The shorter period component exhibits anti-phase oscillations in the loop legs. Results: We interpret the observation in terms of the first (global or fundamental) and second longitudinal harmonics of the standing kink mode. The strong excitation of the second harmonic appears connected to the preceding coronal mass ejection (CME) which displaced one of the loop legs. The oscillation parameters found are P1 = 5.00±0.62 min, P2 = 2.20±0.23 min, P1/ 2P2 = 1.15±0.22, and τ/P = 3.35 ± 1.45. A movie associated to Fig. 5 is available in electronic form at http://www.aanda.org

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.

An atomic mean-field spin-orbit approach within exact two-component theory for a non-perturbative treatment of spin-orbit coupling

NASA Astrophysics Data System (ADS)

Liu, Junzi; Cheng, Lan

2018-04-01

An atomic mean-field (AMF) spin-orbit (SO) approach within exact two-component theory (X2C) is reported, thereby exploiting the exact decoupling scheme of X2C, the one-electron approximation for the scalar-relativistic contributions, the mean-field approximation for the treatment of the two-electron SO contribution, and the local nature of the SO interactions. The Hamiltonian of the proposed SOX2CAMF scheme comprises the one-electron X2C Hamiltonian, the instantaneous two-electron Coulomb interaction, and an AMF SO term derived from spherically averaged Dirac-Coulomb Hartree-Fock calculations of atoms; no molecular relativistic two-electron integrals are required. Benchmark calculations for bond lengths, harmonic frequencies, dipole moments, and electric-field gradients for a set of diatomic molecules containing elements across the periodic table show that the SOX2CAMF scheme offers a balanced treatment for SO and scalar-relativistic effects and appears to be a promising candidate for applications to heavy-element containing systems. SOX2CAMF coupled-cluster calculations of molecular properties for bismuth compounds (BiN, BiP, BiF, BiCl, and BiI) are also presented and compared with experimental results to further demonstrate the accuracy and applicability of the SOX2CAMF scheme.

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.

A global analysis of the 1991 geomagnetic jerk

NASA Astrophysics Data System (ADS)

De Michelis, Paola; Cafarella, Lili; Meloni, Antonio

2000-12-01

A recent examination of the geomagnetic annual mean values for the European magnetic observatories has shown the existence of a sudden change in the secular acceleration in about 1991 (Cafarella & Meloni 1995; Macmillan 1996). Using first differences of the Y (east geomagnetic field component) mean values from 74 observatories, the worldwide character of the 1991 impulse has been determined (De Michelis et al. 1998). Using data from 109 observatories widely distributed all over the world, the structure of the secular variation for the X (north) and Z (vertical) magnetic field intensities around 1990 was investigated, and evidence of this most recent jerk was found. External effects were removed from the annual mean data by comparing the long-term variations of the geomagnetic field components at individual observatories with the long-term variations of two geomagnetic indices, aa and Dst, and of a solar index, the Wolf number R. A careful analysis has been carried out on the amplitude of the external disturbance, on its dependence on latitude, and on the weights of the geomagnetic indices in the evaluation of the resulting external field. The secular variation has been evaluated from the corrected annual means. Around 1990, the secular variation can be fitted at many observatories by two straight lines with a sudden and marked change in slope. In this manner the jerk occurrence time and the intensity of the step in the second time derivative (ΔX'', ΔY'' and ΔZ'') were computed. Maps of ΔX'', ΔY'' and ΔZ'' provide information on the worldwide intensity distribution of the examined event. Maps of the jerk occurrence-time distributions are also given. The mean jerk occurrence time is 1990.1+/-0.6. Finally, a spherical harmonic analysis was used to complete the quantitative description of this phenomenon in order to study the trend of the energy density spectrum as a function of the harmonic degree n.

SPECIAL ISSUE DEVOTED TO THE 80TH BIRTHDAY OF S.A. AKHMANOV: Selective generation of a higher harmonic in plasma

NASA Astrophysics Data System (ADS)

Kulagin, I. A.; Usmanov, T.

2009-07-01

It is shown for the first time that the use of autoionisation states for phase matching leads to the efficient selection of a single harmonic generated in a plateau region in plasma. The selected harmonic frequency can be tuned by changing the relative concentration of plasma components and tuning the fundamental radiation frequency. It is shown that the contrast of the selected harmonic can exceed 104.

A framework to analyze the stochastic harmonics and resonance of wind energy grid interconnection

DOE PAGES

Cho, Youngho; Lee, Choongman; Hur, Kyeon; ...

2016-08-31

This study addresses a modeling and analysis methodology for investigating the stochastic harmonics and resonance concerns of wind power plants (WPPs). Wideband harmonics from modern wind turbines are observed to be stochastic, associated with real power production, and they may adversely interact with the grid impedance and cause unexpected harmonic resonance if not comprehensively addressed in the planning and commissioning of the WPPs. These issues should become more critical as wind penetration levels increase. We thus propose a planning study framework comprising the following functional steps: First, the best-fitted probability density functions (PDFs) of the harmonic components of interest inmore » the frequency domain are determined. In operations planning, maximum likelihood estimations followed by a chi-square test are used once field measurements or manufacturers' data are available. Second, harmonic currents from the WPP are represented by randomly-generating harmonic components based on their PDFs (frequency spectrum) and then synthesized for time-domain simulations via inverse Fourier transform. Finally, we conduct a comprehensive assessment by including the impacts of feeder configurations, harmonic filters, and the variability of parameters. We demonstrate the efficacy of the proposed study approach for a 100-MW offshore WPP consisting of 20 units of 5-MW full-converter turbines, a realistic benchmark system adapted from a WPP under development in Korea, and discuss lessons learned through this research.« less

Simultaneous Measurements of Harmonic Waves at Fatigue-Cracked Interfaces

NASA Astrophysics Data System (ADS)

Hyunjo, Jeong; Dan, Barnard

2011-08-01

Nonlinear harmonic waves generated at cracked interfaces are investigated theoretically and experimentally. A compact tension specimen is fabricated and the amplitude of the transmitted wave is analyzed as a function of position along the fatigued crack surface. In order to measure as many nonlinear harmonic components as possible, broadband lithium niobate (LiNbO3) transducers are employed together with a calibration technique for making absolute amplitude measurements with fluid-coupled receiving transducers. Cracked interfaces are shown to generate high acoustic nonlinearities, which are manifested as harmonics in the power spectrum of the received signal. The first subharmonic f/2 and the second harmonic 2f waves are found to be dominant nonlinear components for an incident toneburst signal of frequency f. To explain the observed nonlinear behavior, a partially closed crack is modeled by planar half interfaces that can account for crack parameters, such as crack opening displacement and crack surface conditions. The simulation results show reasonable agreement with the experimental results.

Optical system

NASA Technical Reports Server (NTRS)

Breckinridge, J. B.; Page, N. A.; Shack, R. V.; Shannon, R. R. (Inventor)

1985-01-01

Disclosed is an otpical system used in a spacecraft to observe a remote surface and provide a spatial and spectral image of this surface. The optical system includes aspheric and spherical mirrors aligned to focus at a first focal plane an image of the surface, and a mirror at this first focal plane which reflects light back on to the spherical mirror. This spherical mirror collimates the light and directs it through a prism which disperses it. The dispersed light is then focused on an array of light responsive elements disposed at a second focal plane. The prism is designed such that it disperses light into components of different wavelengths, with the components of shorter wavelengths being dispersed more than the components of longer wavelengths to present at the second focal plane a distribution pattern in which preselected groupings of the components are dispersed over essentially equal spacing intervals.

Planetary Volcanism

NASA Technical Reports Server (NTRS)

Antonenko, I.; Head, J. W.; Pieters, C. W.

1998-01-01

The final report consists of 10 journal articles concerning Planetary Volcanism. The articles discuss the following topics: (1) lunar stratigraphy; (2) cryptomare thickness measurements; (3) spherical harmonic spectra; (4) late stage activity of volcanoes on Venus; (5) stresses and calderas on Mars; (6) magma reservoir failure; (7) lunar mare basalt volcanism; (8) impact and volcanic glasses in the 79001/2 Core; (9) geology of the lunar regional dark mantle deposits; and (10) factors controlling the depths and sizes of magma reservoirs in Martian volcanoes.

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

DTIC Science & Technology

1989-04-01

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

On regional geomagnetic charts

USGS Publications Warehouse

Alldredge, L.R.

1987-01-01

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

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

NASA Astrophysics Data System (ADS)

Budak, Vladimir P.; Korkin, Sergey V.

2009-03-01

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

The magnetic lead field theorem in the quasi-static approximation and its use for magnetoencephalography forward calculation in realistic volume conductors.

PubMed

Nolte, Guido

2003-11-21

The equation for the magnetic lead field for a given magnetoencephalography (MEG) channel is well known for arbitrary frequencies omega but is not directly applicable to MEG in the quasi-static approximation. In this paper we derive an equation for omega = 0 starting from the very definition of the lead field instead of using Helmholtz's reciprocity theorems. The results are (a) the transpose of the conductivity times the lead field is divergence-free, and (b) the lead field differs from the one in any other volume conductor by a gradient of a scalar function. Consequently, for a piecewise homogeneous and isotropic volume conductor, the lead field is always tangential at the outermost surface. Based on this theoretical result, we formulated a simple and fast method for the MEG forward calculation for one shell of arbitrary shape: we correct the corresponding lead field for a spherical volume conductor by a superposition of basis functions, gradients of harmonic functions constructed here from spherical harmonics, with coefficients fitted to the boundary conditions. The algorithm was tested for a prolate spheroid of realistic shape for which the analytical solution is known. For high order in the expansion, we found the solutions to be essentially exact and for reasonable accuracies much fewer multiplications are needed than in typical implementations of the boundary element methods. The generalization to more shells is straightforward.

Single-shot imaging with higher-dimensional encoding using magnetic field monitoring and concomitant field correction.

PubMed

Testud, Frederik; Gallichan, Daniel; Layton, Kelvin J; Barmet, Christoph; Welz, Anna M; Dewdney, Andrew; Cocosco, Chris A; Pruessmann, Klaas P; Hennig, Jürgen; Zaitsev, Maxim

2015-03-01

PatLoc (Parallel Imaging Technique using Localized Gradients) accelerates imaging and introduces a resolution variation across the field-of-view. Higher-dimensional encoding employs more spatial encoding magnetic fields (SEMs) than the corresponding image dimensionality requires, e.g. by applying two quadratic and two linear spatial encoding magnetic fields to reconstruct a 2D image. Images acquired with higher-dimensional single-shot trajectories can exhibit strong artifacts and geometric distortions. In this work, the source of these artifacts is analyzed and a reliable correction strategy is derived. A dynamic field camera was built for encoding field calibration. Concomitant fields of linear and nonlinear spatial encoding magnetic fields were analyzed. A combined basis consisting of spherical harmonics and concomitant terms was proposed and used for encoding field calibration and image reconstruction. A good agreement between the analytical solution for the concomitant fields and the magnetic field simulations of the custom-built PatLoc SEM coil was observed. Substantial image quality improvements were obtained using a dynamic field camera for encoding field calibration combined with the proposed combined basis. The importance of trajectory calibration for single-shot higher-dimensional encoding is demonstrated using the combined basis including spherical harmonics and concomitant terms, which treats the concomitant fields as an integral part of the encoding. © 2014 Wiley Periodicals, Inc.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

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

NASA Astrophysics Data System (ADS)

Rosenberg, Adam Lewis

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

The contribution of radio-frequency rectification to field-aligned losses of high-harmonic fast wave power to the divertor in the National Spherical Torus eXperiment

DOE PAGES

Perkins, R. J.; Hosea, J. C.; Jaworski, M. A.; ...

2015-04-13

The National Spherical Torus eXperiment (NSTX) can exhibit a major loss of high-harmonic fast wave (HHFW) power along scrape-off layer (SOL) field lines passing in front of the antenna, resulting in bright and hot spirals on both the upper and lower divertor regions. One possible mechanism for this loss is RF sheaths forming at the divertors. We demonstrate that swept-voltage Langmuir probe characteristics for probes under the spiral are shifted relative to those not under the spiral in a manner consistent with RF rectification. We estimate both the magnitude of the RF voltage across the sheath and the sheath heatmore » flux transmission coefficient in the presence of the RF field. Though the precise comparison between computed heat flux and infrared (IR) thermography cannot yet be made, the computed heat deposition compares favorably with the projections from IR camera measurements. The RF sheath losses are significant and contribute substantially to the total SOL losses of HHFW power to the divertor for the cases studied. Our work will guide future experimentation on NSTX-U, where a wide-angle IR camera and a dedicated set of coaxial Langmuir probes for measuring the RF sheath voltage directly will quantify the contribution of RF sheath rectification to the heat deposition from the SOL to the divertor.« less

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

PubMed Central

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

2005-01-01

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

Inter-comparison of GRACE data over India

NASA Astrophysics Data System (ADS)

Banerjee, Chandan; Kumar, D. Nagesh

2016-05-01

The advent of satellite remote sensing and its use in hydrology has facilitated a huge leap in the understanding of the various water resources, its interaction with ecological systems and anthropogenic creations. Recently, NASA and German Aerospace Research Agency-DLR launched the Gravity Recovery and Climate Experiment (GRACE) satellite mission consisting of two satellites. They measure the time varying gravity which gives changes in the distribution of mass on the surface of the earth which after removing atmospheric and oceanic effects is majorly caused by changes in Terrestrial Water Storage (TWS) changes. GRACE data is generally available as spherical harmonic coefficients, which is difficult for hydrologists to understand and interpret. JPL's TELLUS website is now providing gridded global data set in the form of mass anomaly derived from the Level-2 data sets of spherical harmonic coefficients of 3 sources, viz. CSR, GFZ and JPL. Before using these data sets for solving hydrological problems, it is important to understand the differences and similarities between these data sets as direct calibration of GRACE data is not possible. In this study we do an inter-comparison of the Level-3 Release 05 data sets over India. We compare the data sets using Pearson, Spearman and Kendall correlation. CSR and GFZ data sets appear to be closest to each other whereas JPL and GFZ data sets are most different from each other.

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.

Geomagnetism of earth's core

NASA Technical Reports Server (NTRS)

Benton, E. R.

1983-01-01

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

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

NASA Technical Reports Server (NTRS)

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

1989-01-01

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

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

PubMed

Bardhan, Jaydeep P; Knepley, Matthew G

2011-09-28

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

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

PubMed

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

2015-01-01

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

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

PubMed Central

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

2015-01-01

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

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.

Harmonic analysis of spacecraft power systems using a personal computer

NASA Technical Reports Server (NTRS)

Williamson, Frank; Sheble, Gerald B.

1989-01-01

The effects that nonlinear devices such as ac/dc converters, HVDC transmission links, and motor drives have on spacecraft power systems are discussed. The nonsinusoidal currents, along with the corresponding voltages, are calculated by a harmonic power flow which decouples and solves for each harmonic component individually using an iterative Newton-Raphson algorithm. The sparsity of the harmonic equations and the overall Jacobian matrix is used to an advantage in terms of saving computer memory space and in terms of reducing computation time. The algorithm could also be modified to analyze each harmonic separately instead of all at the same time.

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.

Horizon Quantum Mechanics: Spherically Symmetric and Rotating Sources

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

HT-FRTC: a fast radiative transfer code using kernel regression

NASA Astrophysics Data System (ADS)

Thelen, Jean-Claude; Havemann, Stephan; Lewis, Warren

2016-09-01

The HT-FRTC is a principal component based fast radiative transfer code that can be used across the electromagnetic spectrum from the microwave through to the ultraviolet to calculate transmittance, radiance and flux spectra. The principal components cover the spectrum at a very high spectral resolution, which allows very fast line-by-line, hyperspectral and broadband simulations for satellite-based, airborne and ground-based sensors. The principal components are derived during a code training phase from line-by-line simulations for a diverse set of atmosphere and surface conditions. The derived principal components are sensor independent, i.e. no extra training is required to include additional sensors. During the training phase we also derive the predictors which are required by the fast radiative transfer code to determine the principal component scores from the monochromatic radiances (or fluxes, transmittances). These predictors are calculated for each training profile at a small number of frequencies, which are selected by a k-means cluster algorithm during the training phase. Until recently the predictors were calculated using a linear regression. However, during a recent rewrite of the code the linear regression was replaced by a Gaussian Process (GP) regression which resulted in a significant increase in accuracy when compared to the linear regression. The HT-FRTC has been trained with a large variety of gases, surface properties and scatterers. Rayleigh scattering as well as scattering by frozen/liquid clouds, hydrometeors and aerosols have all been included. The scattering phase function can be fully accounted for by an integrated line-by-line version of the Edwards-Slingo spherical harmonics radiation code or approximately by a modification to the extinction (Chou scaling).

Parallel transmit beamforming using orthogonal frequency division multiplexing applied to harmonic imaging--a feasibility study.

PubMed

Demi, Libertario; Verweij, Martin D; Van Dongen, Koen W A

2012-11-01

Real-time 2-D or 3-D ultrasound imaging systems are currently used for medical diagnosis. To achieve the required data acquisition rate, these systems rely on parallel beamforming, i.e., a single wide-angled beam is used for transmission and several narrow parallel beams are used for reception. When applied to harmonic imaging, the demand for high-amplitude pressure wave fields, necessary to generate the harmonic components, conflicts with the use of a wide-angled beam in transmission because this results in a large spatial decay of the acoustic pressure. To enhance the amplitude of the harmonics, it is preferable to do the reverse: transmit several narrow parallel beams and use a wide-angled beam in reception. Here, this concept is investigated to determine whether it can be used for harmonic imaging. The method proposed in this paper relies on orthogonal frequency division multiplexing (OFDM), which is used to create distinctive parallel beams in transmission. To test the proposed method, a numerical study has been performed, in which the transmit, receive, and combined beam profiles generated by a linear array have been simulated for the second-harmonic component. Compared with standard parallel beamforming, application of the proposed technique results in a gain of 12 dB for the main beam and in a reduction of the side lobes. Experimental verification in water has also been performed. Measurements obtained with a single-element emitting transducer and a hydrophone receiver confirm the possibility of exciting a practical ultrasound transducer with multiple Gaussian modulated pulses, each having a different center frequency, and the capability to generate distinguishable second-harmonic components.

Analysis of surgical smoke produced by various energy-based instruments and effect on laparoscopic visibility.

PubMed

Weld, Kyle J; Dryer, Stephen; Ames, Caroline D; Cho, Kuk; Hogan, Chris; Lee, Myonghwa; Biswas, Pratim; Landman, Jaime

2007-03-01

We analyzed the smoke plume produced by various energy-based laparoscopic instruments and determined its effect on laparoscopic visibility. The Bipolar Macroforceps, Harmonic Scalpel, Floating Ball, and Monopolar Shears were applied in vitro to porcine psoas muscle. An Aerodynamic Particle Sizer and Electrostatic Classifier provided a size distribution of the plume for particles >500 nm and <500 nm, and a geometric mean particle size was calculated. A Condensation Particle Counter provided the total particle-number concentration. Electron microscopy was used to characterize particle size and shape further. Visibility was calculated using the measured-size distribution data and the Rayleigh and Mie light-scattering theories. The real-time instruments were successful in measuring aerosolized particle size distributions in two size ranges. Electron microscopy revealed smaller, homogeneous, spherical particles and larger, irregular particles consistent with cellular components. The aerosol produced by the Bipolar Macroforceps obscured visibility the least (relative visibility 0.887) among the instruments tested. Particles from the Harmonic Scalpel resulted in a relative visibility of 0.801. Monopolar-based instruments produced plumes responsible for the poorest relative visibility (Floating Ball 0.252; Monopolar Shears 0.026). Surgical smoke is composed of two distinct particle populations caused by the nucleation of vapors as they cool (the small particles) and the entrainment of tissue secondary to mechanical aspects (the large particles). High concentrations of small particles are most responsible for the deterioration in laparoscopic vision. Bipolar and ultrasonic instruments generate a surgical plume that causes the least deterioration of visibility among the instruments tested.

Higher-order harmonics of limited diffraction Bessel beams

PubMed

Ding; Lu

2000-03-01

We investigate theoretically the nonlinear propagation of the limited diffraction Bessel beam in nonlinear media, under the successive approximation of the KZK equation. The result shows that the nth-order harmonic of the Bessel beam, like its fundamental component, is radially limited diffracting, and that the main beamwidth of the nth-order harmonic is exactly 1/n times that of the fundamental.

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.

Waveform and polarization of compressional Pc 5 waves at geosynchronous orbit

NASA Astrophysics Data System (ADS)

Higuchi, Tomoyuki; Kokubun, Susumu

1988-12-01

The factors controlling the occurrence and the properties of compressional Pc 5 waves were examined by studying the statistical characteristics of compressional Pc 5 waves, using magnetic-field data obtained by GOES 2 and GOES 3 satellites during the August 1978 - August 1980 period. The compressional Pc 5 waves could be classified into the harmonic, transitional, and normal types, on the basis of the second-harmonic component in the compressional component of the magnetic field oscillation. It was found that the harmonic and the transitional waves have significant azimuthal perturbations and show right-handed polarization with respect to the local magnetic field, while most of the normal-type waves have small amplitude in the azimuthal component. The polarization properties of transverse perturbation, which may reflect the spatial inhomogeneity of the medium, are investigated.

Improved Efficiency Type II Second Harmonic Generation

NASA Technical Reports Server (NTRS)

Barnes, Norman P.; Walsh, Brian M.; Reichle, Donald J., Jr.

2009-01-01

Second harmonic efficiency is limited by lateral and temporal separation of the ordinary and extraordinary components of the fundamental. A mode locked dual beam laser demonstrated these effects and a novel method to minimize them.

Planning for Coupling Effects in Bitoric Mixed Astigmatism Ablative Treatments.

PubMed

Alpins, Noel; Ong, James K Y; Stamatelatos, George

2017-08-01

To demonstrate how to determine the historical coupling adjustments of bitoric mixed astigmatism ablative treatments and how to use these historical coupling adjustments to adjust future bitoric treatments. The individual coupling adjustments of the myopic and hyperopic cylindrical components of a bitoric treatment were derived empirically from a retrospective study where the theoretical combined treatment effect on spherical equivalent was compared to the actual change in refractive spherical equivalent. The coupling adjustments that provided the best fit in both mean and standard deviation were determined to be the historical coupling adjustments. Theoretical treatments that incorporated the historical coupling adjustments were then calculated. The actual distribution of postoperative spherical equivalent errors was compared to the theoretically adjusted distribution. The study group comprised 242 eyes and included 118 virgin right eyes and 124 virgin left eyes of 155 individuals. For the laser used, the myopic coupling adjustment was -0.02 and the hyperopic coupling adjustment was 0.30, as derived by global nonlinear optimization. This implies that almost no adjustment of the myopic component of the bitoric treatment is necessary, but that the hyperopic component of the bitoric treatment generates a large amount of unintended spherical shift. The theoretically adjusted treatments targeted zero mean spherical equivalent error, as intended, and the distribution of the theoretical spherical equivalent errors had the same spread as the distribution of actual postoperative spherical equivalent errors. Bitoric mixed astigmatism ablative treatments may display non-trivial coupling effects. Historical coupling adjustments should be taken into consideration when planning mixed astigmatism treatments to improve surgical outcomes. [J Refract Surg. 2017;33(8):545-551.]. Copyright 2017, SLACK Incorporated.

A Spectral Algorithm for Solving the Relativistic Vlasov-Maxwell Equations

NASA Technical Reports Server (NTRS)

Shebalin, John V.

2001-01-01

A spectral method algorithm is developed for the numerical solution of the full six-dimensional Vlasov-Maxwell system of equations. Here, the focus is on the electron distribution function, with positive ions providing a constant background. The algorithm consists of a Jacobi polynomial-spherical harmonic formulation in velocity space and a trigonometric formulation in position space. A transform procedure is used to evaluate nonlinear terms. The algorithm is suitable for performing moderate resolution simulations on currently available supercomputers for both scientific and engineering applications.

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.

Reconstruction of SAXS Profiles from Protein Structures

PubMed Central

Putnam, Daniel K.; Lowe, Edward W.

2013-01-01

Small angle X-ray scattering (SAXS) is used for low resolution structural characterization of proteins often in combination with other experimental techniques. After briefly reviewing the theory of SAXS we discuss computational methods based on 1) the Debye equation and 2) Spherical Harmonics to compute intensity profiles from a particular macromolecular structure. Further, we review how these formulas are parameterized for solvent density and hydration shell adjustment. Finally we introduce our solution to compute SAXS profiles utilizing GPU acceleration. PMID:24688746

Linear perturbations of a Schwarzschild blackhole by thin disc - convergence

NASA Astrophysics Data System (ADS)

Čížek, P.; Semerák, O.

2012-07-01

In order to find the perturbation of a Schwarzschild space-time due to a rotating thin disc, we try to adjust the method used by [4] in the case of perturbation by a one-dimensional ring. This involves solution of stationary axisymmetric Einstein's equations in terms of spherical-harmonic expansions whose convergence however turned out questionable in numerical examples. Here we show, analytically, that the series are almost everywhere convergent, but in some regions the convergence is not absolute.

The role of zonally asymmetric heating in the vertical and temporal structure of the global scale flow fields during FGGE SOP-1

NASA Technical Reports Server (NTRS)

Paegle, J.; Kalnay, E.; Baker, W. E.

1981-01-01

The global scale structure of atmospheric flow is best documented on time scales longer than a few days. Theoretical and observational studies of ultralong waves have emphasized forcing due to global scale variations of topography and surface heat flux, possibly interacting with baroclinically unstable or vertically refracting basic flows. Analyses of SOP-1 data in terms of global scale spherical harmonics is documented with emphasis upon weekly transitions.

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

USGS Publications Warehouse

Peddie, N.W.

1982-01-01

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

Monterey Bay Geoid

DTIC Science & Technology

1994-03-01

thought to be a flat disk. The first scientific hypothesis that the earth was spherical is credited to Thales of Milet in 600 B.C. or Pythagoras in 550...acceleration can be integrated over the surface, by Gauss’s theorem and gives: 35 v1 Wv2 <v3 Figure 12. Equipotential Surfaces and Gravity: V,, V2, V3 are...continuous derivatives where they satisfy Laplace’s equation. Stokes’ theorem states that a harmonic function outside a surface is uniquely determined by

Resonances, radiation pressure and optical scattering phenomena of drops and bubbles

NASA Technical Reports Server (NTRS)

Marston, P. L.; Goosby, S. G.; Langley, D. S.; Loporto-Arione, S. E.

1982-01-01

Acoustic levitation and the response of fluid spheres to spherical harmonic projections of the radiation pressure are described. Simplified discussions of the projections are given. A relationship between the tangential radiation stress and the Konstantinov effect is introduced and fundamental streaming patterns for drops are predicted. Experiments on the forced shape oscillation of drops are described and photographs of drop fission are displayed. Photographs of critical angle and glory scattering by bubbles and rainbow scattering by drops are displayed.

Determination of stellar ages from asteroseismology

NASA Technical Reports Server (NTRS)

Ulrich, R. K.

1986-01-01

This Letter shows that measurements of the stellar analog of the solar five minute oscillations can permit the determination of the radius and age of isolated stars. The key frequencies of oscillation correspond to pairs of modes differing by two in the degree of the spherical harmonic describing the angular dependence of the motion and by one in the overtone order of the modes. The frequency pairs are very nearly degenerate, and adequate frequency resolution will require a nearly unbroken time sequence extending over 15 days.

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

NASA Technical Reports Server (NTRS)

Langel, R. A.

1973-01-01

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

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

NASA Technical Reports Server (NTRS)

Whitney, C.

1977-01-01

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

Steady-state visual evoked potential (SSVEP)-based communication: impact of harmonic frequency components

NASA Astrophysics Data System (ADS)

Müller-Putz, Gernot R.; Scherer, Reinhold; Brauneis, Christian; Pfurtscheller, Gert

2005-12-01

Brain-computer interfaces (BCIs) can be realized on the basis of steady-state evoked potentials (SSEPs). These types of brain signals resulting from repetitive stimulation have the same fundamental frequency as the stimulation but also include higher harmonics. This study investigated how the classification accuracy of a 4-class BCI system can be improved by incorporating visually evoked harmonic oscillations. The current study revealed that the use of three SSVEP harmonics yielded a significantly higher classification accuracy than was the case for one or two harmonics. During feedback experiments, the five subjects investigated reached a classification accuracy between 42.5% and 94.4%.

Steady-state visual evoked potential (SSVEP)-based communication: impact of harmonic frequency components.

PubMed

Müller-Putz, Gernot R; Scherer, Reinhold; Brauneis, Christian; Pfurtscheller, Gert

2005-12-01

Brain-computer interfaces (BCIs) can be realized on the basis of steady-state evoked potentials (SSEPs). These types of brain signals resulting from repetitive stimulation have the same fundamental frequency as the stimulation but also include higher harmonics. This study investigated how the classification accuracy of a 4-class BCI system can be improved by incorporating visually evoked harmonic oscillations. The current study revealed that the use of three SSVEP harmonics yielded a significantly higher classification accuracy than was the case for one or two harmonics. During feedback experiments, the five subjects investigated reached a classification accuracy between 42.5% and 94.4%.

Observations of z-dependent microbunching harmonic intensities using COTR in a SASE FEL.

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

Lumpkin, A. H.; Biedron, S. G.; Dejus, R. J.

The nonlinear generation of harmonics in a self-amplified spontaneous emission (SASE) free-electron laser (FEL) continues to be of interest. Complementary to such studies is the search for information on the electron beam microbunching harmonic components, which are revealed by coherent optical transition radiation (COTR) experiments. An initial z-dependent set of data has been obtained with the fundamental at 530 nm and the second harmonic at 265 nm. The latter data were collected after every other undulator in a nine-undulator string. These results are compared to estimates based on GINGER and an analytical model for nonlinear harmonic generation.

The capture and recreation of 3D auditory scenes

NASA Astrophysics Data System (ADS)

Li, Zhiyun

The main goal of this research is to develop the theory and implement practical tools (in both software and hardware) for the capture and recreation of 3D auditory scenes. Our research is expected to have applications in virtual reality, telepresence, film, music, video games, auditory user interfaces, and sound-based surveillance. The first part of our research is concerned with sound capture via a spherical microphone array. The advantage of this array is that it can be steered into any 3D directions digitally with the same beampattern. We develop design methodologies to achieve flexible microphone layouts, optimal beampattern approximation and robustness constraint. We also design novel hemispherical and circular microphone array layouts for more spatially constrained auditory scenes. Using the captured audio, we then propose a unified and simple approach for recreating them by exploring the reciprocity principle that is satisfied between the two processes. Our approach makes the system easy to build, and practical. Using this approach, we can capture the 3D sound field by a spherical microphone array and recreate it using a spherical loudspeaker array, and ensure that the recreated sound field matches the recorded field up to a high order of spherical harmonics. For some regular or semi-regular microphone layouts, we design an efficient parallel implementation of the multi-directional spherical beamformer by using the rotational symmetries of the beampattern and of the spherical microphone array. This can be implemented in either software or hardware and easily adapted for other regular or semi-regular layouts of microphones. In addition, we extend this approach for headphone-based system. Design examples and simulation results are presented to verify our algorithms. Prototypes are built and tested in real-world auditory scenes.

Measurement of Jupiter’s asymmetric gravity field

NASA Astrophysics Data System (ADS)

Iess, L.; Folkner, W. M.; Durante, D.; Parisi, M.; Kaspi, Y.; Galanti, E.; Guillot, T.; Hubbard, W. B.; Stevenson, D. J.; Anderson, J. D.; Buccino, D. R.; Casajus, L. Gomez; Milani, A.; Park, R.; Racioppa, P.; Serra, D.; Tortora, P.; Zannoni, M.; Cao, H.; Helled, R.; Lunine, J. I.; Miguel, Y.; Militzer, B.; Wahl, S.; Connerney, J. E. P.; Levin, S. M.; Bolton, S. J.

2018-03-01

The gravity harmonics of a fluid, rotating planet can be decomposed into static components arising from solid-body rotation and dynamic components arising from flows. In the absence of internal dynamics, the gravity field is axially and hemispherically symmetric and is dominated by even zonal gravity harmonics J2n that are approximately proportional to qn, where q is the ratio between centrifugal acceleration and gravity at the planet’s equator. Any asymmetry in the gravity field is attributed to differential rotation and deep atmospheric flows. The odd harmonics, J3, J5, J7, J9 and higher, are a measure of the depth of the winds in the different zones of the atmosphere. Here we report measurements of Jupiter’s gravity harmonics (both even and odd) through precise Doppler tracking of the Juno spacecraft in its polar orbit around Jupiter. We find a north–south asymmetry, which is a signature of atmospheric and interior flows. Analysis of the harmonics, described in two accompanying papers, provides the vertical profile of the winds and precise constraints for the depth of Jupiter’s dynamical atmosphere.

Second harmonic generation from small particle aggregates

NASA Astrophysics Data System (ADS)

Mochan, W. Luis; Ortiz, Guillermo P.; Mendoza, Bernardo S.; Brudny, Vera L.

2001-03-01

Novel nanofabrication techniques are capable of producing nanoparticles with controled structures which include small clusters, self-assembled particles, quantum dots, vesicles, etc. The non-linear optical scattering of these structures are important for applications, and can be used for their physical characterization. The second harmonic (SH) field radiated by a single small spherical particle has surface and bulk, dipolar and quadrupolar contributions of similar intensities and is strongly dependent of the local environment of the particle [1], in contrast to the linear case. In this work we calculate the nonlinear scattering by particle aggregates and we investigate the effects on the SH generation of the disorder induced field fluctuations and of the localization of light. We acknowledge the partial support from DGAPA-UNAM (grant IN110999), Conacyt (31120-E and 26651-E), CIP and UBACyT. [1] Vera L. Brudny, Bernardo S. Mendoza, and W. Luis Mochán, Phys. Rev. B 62, 11152 (2000).

Emergent gauge field for a chiral bound state on curved surface

NASA Astrophysics Data System (ADS)

Shi, Zhe-Yu; Zhai, Hui

2017-09-01

Emergent physics is one of the most important concepts in modern physics, and one of the most intriguing examples is the emergent gauge field. Here we show that a gauge field emerges for a chiral bound state formed by two attractively interacting particles on a curved surface. We demonstrate explicitly that the center-of-mass wave function of such a deeply bound state is monopole harmonic instead of spherical harmonic, which means that the bound state experiences a magnetic monopole at the center of the sphere. This emergent gauge field is due to the coupling between the center-of-mass and the relative motion on a curved surface, and our results can be generalized to an arbitrary curved surface. This result establishes an intriguing connection between the space curvature and gauge field, and paves an alternative way to engineer a topological state with space curvature, and may be observed in a cold atom system.

A Search for r-Modes from 1825 to the Present

NASA Technical Reports Server (NTRS)

Wolff, Charles L.

1998-01-01

Global oscillations (r-modes) of the Sun's outer convective envelope with periods approximately 1 month and longer have been detected in several short data strings of several years duration. To test whether r-modes might persist beyond one 11 year cycle, the daily sunspot numbers from 1825 to the present were analyzed. Good evidence, but confidence level less than 3sigma, was found for most of the 14 r-modes with spherical harmonic index lambda less than or equal to 5 that can exist in the presence of solar differential rotation. The characteristic rotation rate of almost every such r-mode was detected, displaced systematically from its expected value by only 0.15%. If this probable detection is real, then most low harmonic r-modes have lifetimes exceeding one century and the rotation of the Sun's outer layers varies by less than 0.05%, except possibly at solar minimum.

On second harmonic generation and multiphoton-absorption induced luminescence from laser-reshaped silver nanoparticles embedded in glass.

PubMed

Zolotovskaya, S A; Tyrk, M A; Stalmashonak, A; Gillespie, W A; Abdolvand, A

2016-10-28

Spherical silver nanoparticles (NPs) of 30 nm diameter embedded in soda-lime glass were uniformly reshaped (elongated) after irradiation by a linearly polarised 250 fs pulsed laser operating within the NPs' surface plasmon resonance band. We observed second harmonic generation (SHG) and multiphoton-absorption-induced luminescence (MAIL) in the embedded laser-reshaped NPs upon picosecond (10 ps) pulsed laser excitation at 1064 nm. A complementary study of SHG and MAIL was conducted in soda-lime glass containing embedded, mechanically-reshaped silver NPs of a similar elongation ratio (aspect ratio) to the laser-reshaped NPs. This supports the notion that the observed difference in SHG and MAIL in the studied nanocomposite systems is due to the shape modification mechanism. The discrete dipole approximation method was used to assess the absorption and scattering cross-sections of the reshaped NPs with different elongation ratios.

The effect of tides on self-driven stellar pulsations

NASA Astrophysics Data System (ADS)

Balona, L. A.

2018-06-01

In addition to rotation, a tidal force in a binary introduces another axis of symmetry joining the two centres of mass. If the stars are in circular orbit and synchronous rotation, a pulsation with spherical harmonic degree l is split into l + 1 frequencies. In the observer's frame of reference, these in turn are further split into equidistant frequencies spaced by multiples of the orbital frequency. In the periodogram of a pulsating star, tidal action can be seen as low-amplitude equidistant splitting of each oscillation mode which are not harmonics of the orbital frequency. This effect is illustrated using Kepler observations of the heartbeat variable, KIC 4142768, which is also a δ Scuti star. Even though the theory is only applicable to circular orbits, the expected equidistant splitting is clearly seen in all four of the highest amplitude modes. This results in amplitude variability of each pulsation mode with a period equal to the orbital period.

On the Harmonic Coupling of Components in Pairs of IIIb-III Bursts at Decameter Wavelengths

NASA Astrophysics Data System (ADS)

Brazhenko, A. I.; Melnik, V. N.; Frantsuzenko, A. V.; Dorovskyy, V. V.; Rucker, H. O.; Panchenko, M.

2015-06-01

The properties of IIIb-III pairs observed by the URAN-2 radioThe properties of IIIb-III pairs observed by the URAN-2 radiotelescope at frequencies 16-32 MHz are analyzed. Observations of these bursts were hold in April, June and September 2011. Durations, frequency drift rates, simultaneous frequency ratio of pairs components and their polarizations are analyzed. Pro and contra of IIIb-III harmonic connection are discussed.

Ellipticity dependence of the near-threshold harmonics of H2 in an elliptical strong laser field.

PubMed

Yang, Hua; Liu, Peng; Li, Ruxin; Xu, Zhizhan

2013-11-18

We study the ellipticity dependence of the near-threshold (NT) harmonics of pre-aligned H2 molecules using the time-dependent density functional theory. The anomalous maximum appearing at a non-zero ellipticity for the generated NT harmonics can be attributed to multiphoton effects of the orthogonally polarized component of the elliptical driving laser field. Our calculation also shows that the structure of the bound-state, such as molecular alignment and bond length, can be sensitively reflected on the ellipticity dependence of the near-threshold harmonics.

LCS-1: a high-resolution global model of the lithospheric magnetic field derived from CHAMP and Swarm satellite observations

NASA Astrophysics Data System (ADS)

Olsen, Nils; Ravat, Dhananjay; Finlay, Christopher C.; Kother, Livia K.

2017-12-01

We derive a new model, named LCS-1, of Earth's lithospheric field based on four years (2006 September-2010 September) of magnetic observations taken by the CHAMP satellite at altitudes lower than 350 km, as well as almost three years (2014 April-2016 December) of measurements taken by the two lower Swarm satellites Alpha and Charlie. The model is determined entirely from magnetic 'gradient' data (approximated by finite differences): the north-south gradient is approximated by first differences of 15 s along-track data (for CHAMP and each of the two Swarm satellites), while the east-west gradient is approximated by the difference between observations taken by Swarm Alpha and Charlie. In total, we used 6.2 mio data points. The model is parametrized by 35 000 equivalent point sources located on an almost equal-area grid at a depth of 100 km below the surface (WGS84 ellipsoid). The amplitudes of these point sources are determined by minimizing the misfit to the magnetic satellite 'gradient' data together with the global average of |Br| at the ellipsoid surface (i.e. applying an L1 model regularization of Br). In a final step, we transform the point-source representation to a spherical harmonic expansion. The model shows very good agreement with previous satellite-derived lithospheric field models at low degree (degree correlation above 0.8 for degrees n ≤ 133). Comparison with independent near-surface aeromagnetic data from Australia yields good agreement (coherence >0.55) at horizontal wavelengths down to at least 250 km, corresponding to spherical harmonic degree n ≈ 160. The LCS-1 vertical component and field intensity anomaly maps at Earth's surface show similar features to those exhibited by the WDMAM2 and EMM2015 lithospheric field models truncated at degree 185 in regions where they include near-surface data and provide unprecedented detail where they do not. Example regions of improvement include the Bangui anomaly region in central Africa, the west African cratons, the East African Rift region, the Bay of Bengal, the southern 90°E ridge, the Cretaceous quiet zone south of the Walvis Ridge and the younger parts of the South Atlantic.

Grouping and the pitch of a mistuned fundamental component: Effects of applying simultaneous multiple mistunings to the other harmonics.

PubMed

Roberts, Brian; Holmes, Stephen D

2006-12-01

Mistuning a harmonic produces an exaggerated change in its pitch. This occurs because the component becomes inconsistent with the regular pattern that causes the other harmonics (constituting the spectral frame) to integrate perceptually. These pitch shifts were measured when the fundamental (F0) component of a complex tone (nominal F0 frequency = 200 Hz) was mistuned by +8% and -8%. The pitch-shift gradient was defined as the difference between these values and its magnitude was used as a measure of frame integration. An independent and random perturbation (spectral jitter) was applied simultaneously to most or all of the frame components. The gradient magnitude declined gradually as the degree of jitter increased from 0% to +/-40% of F0. The component adjacent to the mistuned target made the largest contribution to the gradient, but more distant components also contributed. The stimuli were passed through an auditory model, and the exponential height of the F0-period peak in the averaged summary autocorrelation function correlated well with the gradient magnitude. The fit improved when the weighting on more distant channels was attenuated by a factor of three per octave. The results are consistent with a grouping mechanism that computes a weighted average of periodicity strength across several components.

Accurate image-charge method by the use of the residue theorem for core-shell dielectric sphere

NASA Astrophysics Data System (ADS)

Fu, Jing; Xu, Zhenli

2018-02-01

An accurate image-charge method (ICM) is developed for ionic interactions outside a core-shell structured dielectric sphere. Core-shell particles have wide applications for which the theoretical investigation requires efficient methods for the Green's function used to calculate pairwise interactions of ions. The ICM is based on an inverse Mellin transform from the coefficients of spherical harmonic series of the Green's function such that the polarization charge due to dielectric boundaries is represented by a series of image point charges and an image line charge. The residue theorem is used to accurately calculate the density of the line charge. Numerical results show that the ICM is promising in fast evaluation of the Green's function, and thus it is useful for theoretical investigations of core-shell particles. This routine can also be applicable for solving other problems with spherical dielectric interfaces such as multilayered media and Debye-Hückel equations.

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.

Resolution-Enhanced Harmonic and Interharmonic Measurement for Power Quality Analysis in Cyber-Physical Energy System.

PubMed

Liu, Yanchi; Wang, Xue; Liu, Youda; Cui, Sujin

2016-06-27

Power quality analysis issues, especially the measurement of harmonic and interharmonic in cyber-physical energy systems, are addressed in this paper. As new situations are introduced to the power system, the impact of electric vehicles, distributed generation and renewable energy has introduced extra demands to distributed sensors, waveform-level information and power quality data analytics. Harmonics and interharmonics, as the most significant disturbances, require carefully designed detection methods for an accurate measurement of electric loads whose information is crucial to subsequent analyzing and control. This paper gives a detailed description of the power quality analysis framework in networked environment and presents a fast and resolution-enhanced method for harmonic and interharmonic measurement. The proposed method first extracts harmonic and interharmonic components efficiently using the single-channel version of Robust Independent Component Analysis (RobustICA), then estimates the high-resolution frequency from three discrete Fourier transform (DFT) samples with little additional computation, and finally computes the amplitudes and phases with the adaptive linear neuron network. The experiments show that the proposed method is time-efficient and leads to a better accuracy of the simulated and experimental signals in the presence of noise and fundamental frequency deviation, thus providing a deeper insight into the (inter)harmonic sources or even the whole system.

Resolution-Enhanced Harmonic and Interharmonic Measurement for Power Quality Analysis in Cyber-Physical Energy System

PubMed Central

Liu, Yanchi; Wang, Xue; Liu, Youda; Cui, Sujin

2016-01-01

Power quality analysis issues, especially the measurement of harmonic and interharmonic in cyber-physical energy systems, are addressed in this paper. As new situations are introduced to the power system, the impact of electric vehicles, distributed generation and renewable energy has introduced extra demands to distributed sensors, waveform-level information and power quality data analytics. Harmonics and interharmonics, as the most significant disturbances, require carefully designed detection methods for an accurate measurement of electric loads whose information is crucial to subsequent analyzing and control. This paper gives a detailed description of the power quality analysis framework in networked environment and presents a fast and resolution-enhanced method for harmonic and interharmonic measurement. The proposed method first extracts harmonic and interharmonic components efficiently using the single-channel version of Robust Independent Component Analysis (RobustICA), then estimates the high-resolution frequency from three discrete Fourier transform (DFT) samples with little additional computation, and finally computes the amplitudes and phases with the adaptive linear neuron network. The experiments show that the proposed method is time-efficient and leads to a better accuracy of the simulated and experimental signals in the presence of noise and fundamental frequency deviation, thus providing a deeper insight into the (inter)harmonic sources or even the whole system. PMID:27355946

Estimating Antarctic Near-Surface Magnetic Anomalies from Oersted and CHAMP Satellite Magnetometer Observations

NASA Technical Reports Server (NTRS)

vonFrese, Ralph R. B.; Kim, Hyung Rae; Gaya-Pique, Luis R.; Taylor, Patrick T.; Golynsky, Alexander V.; Kim, Jeong Woo

2004-01-01

Significant improvement in predicting near-surface magnetic anomalies can result from the highly accurate magnetic observations of the CHAMP satellite that is orbiting at about 400 km altitude. In general, regional magnetic signals of the crust are strongly masked by the core field and its secular variations due to wavelength coupling in the spherical harmonic representation and thus are difficult to isolate in the satellite measurements. However, efforts to isolate the regional lithospheric from core field components can exploit the correlations between the CHAMP magnetic anomalies and the pseudo magnetic effects inferred from gravity-derived crustal thickness variations. In addition, we can use spectral correlation theory to filter the static lithospheric field components from the dynamic external field effects. Employing these procedures, we processed the CHAMP magnetic conservations for an improved magnetic anomaly map of the Antarctic crust. Relative to the much higher altitude Oersted and noisier Magsat observations, CHAMP magnetic anomalies at 400 km altitude reveal new details on the effects of intra-crustal magnetic features and crustal thickness variations of the Antarctic. Moreover, these results greatly facilitate predicting magnetic anomalies in the regional coverage gaps of the ADMAP compilation of Antarctic magnetic anomalies from shipborne, airborne and ground surveys. Our analysis suggests that considerable new insights on the magnetic properties of the lithosphere may be revealed by a further order-of-magnitude improvement in the accuracy of the magnetometer.