EEG-distributed inverse solutions for a spherical head model

NASA Astrophysics Data System (ADS)

Riera, J. J.; Fuentes, M. E.; Valdés, P. A.; Ohárriz, Y.

1998-08-01

The theoretical study of the minimum norm solution to the MEG inverse problem has been carried out in previous papers for the particular case of spherical symmetry. However, a similar study for the EEG is remarkably more difficult due to the very complicated nature of the expression relating the voltage differences on the scalp to the primary current density (PCD) even for this simple symmetry. This paper introduces the use of the electric lead field (ELF) on the dyadic formalism in the spherical coordinate system to overcome such a drawback using an expansion of the ELF in terms of longitudinal and orthogonal vector fields. This approach allows us to represent EEG Fourier coefficients on a 2-sphere in terms of a current multipole expansion. The choice of a suitable basis for the Hilbert space of the PCDs on the brain region allows the current multipole moments to be related by spatial transfer functions to the PCD spectral coefficients. Properties of the most used distributed inverse solutions are explored on the basis of these results. Also, a part of the ELF null space is completely characterized and those spherical components of the PCD which are possible silent candidates are discussed.

Impact of Primary Spherical Aberration, Spatial Frequency and Stiles Crawford Apodization on Wavefront determined Refractive Error: A Computational Study

PubMed Central

Xu, Renfeng; Bradley, Arthur; Thibos, Larry N.

2013-01-01

Purpose We tested the hypothesis that pupil apodization is the basis for central pupil bias of spherical refractions in eyes with spherical aberration. Methods We employed Fourier computational optics in which we vary spherical aberration levels, pupil size, and pupil apodization (Stiles Crawford Effect) within the pupil function, from which point spread functions and optical transfer functions were computed. Through-focus analysis determined the refractive correction that optimized retinal image quality. Results For a large pupil (7 mm), as spherical aberration levels increase, refractions that optimize the visual Strehl ratio mirror refractions that maximize high spatial frequency modulation in the image and both focus a near paraxial region of the pupil. These refractions are not affected by Stiles Crawford Effect apodization. Refractions that optimize low spatial frequency modulation come close to minimizing wavefront RMS, and vary with level of spherical aberration and Stiles Crawford Effect. In the presence of significant levels of spherical aberration (e.g. C40 = 0.4 µm, 7mm pupil), low spatial frequency refractions can induce −0.7D myopic shift compared to high SF refraction, and refractions that maximize image contrast of a 3 cycle per degree square-wave grating can cause −0.75D myopic drift relative to refractions that maximize image sharpness. Discussion Because of small depth of focus associated with high spatial frequency stimuli, the large change in dioptric power across the pupil caused by spherical aberration limits the effective aperture contributing to the image of high spatial frequencies. Thus, when imaging high spatial frequencies, spherical aberration effectively induces an annular aperture defining that portion of the pupil contributing to a well-focused image. As spherical focus is manipulated during the refraction procedure, the dimensions of the annular aperture change. Image quality is maximized when the inner radius of the induced annulus falls to zero, thus defining a circular near paraxial region of the pupil that determines refraction outcome. PMID:23683093

Theoretical investigation of gas-surface interactions

NASA Technical Reports Server (NTRS)

Dyall, Kenneth G.

1990-01-01

A Dirac-Hartree-Fock code was developed for polyatomic molecules. The program uses integrals over symmetry-adapted real spherical harmonic Gaussian basis functions generated by a modification of the MOLECULE integrals program. A single Gaussian function is used for the nuclear charge distribution, to ensure proper boundary conditions at the nuclei. The Gaussian primitive functions are chosen to satisfy the kinetic balance condition. However, contracted functions which do not necessarily satisfy this condition may be used. The Fock matrix is constructed in the scalar basis and transformed to a jj-coupled 2-spinor basis before diagonalization. The program was tested against numerical results for atoms with a Gaussian nucleus and diatomic molecules with point nuclei. The energies converge on the numerical values as the basis set size is increased. Full use of molecular symmetry (restricted to D sub 2h and subgroups) is yet to be implemented.

MONOCULAR DIPLOPIA DUE TO SPHEROCYLINDRICAL REFRACTIVE ERRORS (AN AMERICAN OPHTHALMOLOGICAL SOCIETY THESIS)

PubMed Central

Archer, Steven M.

2007-01-01

Purpose Ordinary spherocylindrical refractive errors have been recognized as a cause of monocular diplopia for over a century, yet explanation of this phenomenon using geometrical optics has remained problematic. This study tests the hypothesis that the diffraction theory treatment of refractive errors will provide a more satisfactory explanation of monocular diplopia. Methods Diffraction theory calculations were carried out for modulation transfer functions, point spread functions, and line spread functions under conditions of defocus, astigmatism, and mixed spherocylindrical refractive errors. Defocused photographs of inked and projected black lines were made to demonstrate the predicted consequences of the theoretical calculations. Results For certain amounts of defocus, line spread functions resulting from spherical defocus are predicted to have a bimodal intensity distribution that could provide the basis for diplopia with line targets. Multimodal intensity distributions are predicted in point spread functions and provide a basis for diplopia or polyopia of point targets under conditions of astigmatism. The predicted doubling effect is evident in defocused photographs of black lines, but the effect is not as robust as the subjective experience of monocular diplopia. Conclusions Monocular diplopia due to ordinary refractive errors can be predicted from diffraction theory. Higher-order aberrations—such as spherical aberration—are not necessary but may, under some circumstances, enhance the features of monocular diplopia. The physical basis for monocular diplopia is relatively subtle, and enhancement by neural processing is probably needed to account for the robustness of the percept. PMID:18427616

Robust reconstruction of B1 (+) maps by projection into a spherical functions space.

PubMed

Sbrizzi, Alessandro; Hoogduin, Hans; Lagendijk, Jan J; Luijten, Peter; van den Berg, Cornelis A T

2014-01-01

Several parallel transmit MRI techniques require knowledge of the transmit radiofrequency field profiles (B1 (+) ). During the past years, various methods have been developed to acquire this information. Often, these methods suffer from long measurement times and produce maps exhibiting regions with poor signal-to-noise ratio and artifacts. In this article, a model-based reconstruction procedure is introduced that improves the robustness of B1 (+) mapping. The missing information from undersampled B1 (+) maps and the regions of poor signal to noise ratio are reconstructed through projection into the space of spherical functions that arise naturally from the solution of the Helmholtz equations in the spherical coordinate system. As a result, B1 (+) data over a limited range of the field of view/volume is sufficient to reconstruct the B1 (+) over the full spatial domain in a fast and robust way. The same model is exploited to filter the noise of the measured maps. Results from simulations and in vivo measurements confirm the validity of the proposed method. A spherical functions model can well approximate the magnetic fields inside the body with few basis terms. Exploiting this compression capability, B1 (+) maps are reconstructed in regions of unknown or corrupted values. Copyright © 2013 Wiley Periodicals, Inc.

Nucleation and evolution of spherical crystals with allowance for their unsteady-state growth rates

NASA Astrophysics Data System (ADS)

Alexandrov, D. V.

2018-02-01

The growth dynamics of a spherical crystal in a metastable liquid is analyzed theoretically. The unsteady-state contributions to the crystal radius and its growth rate are found as explicit functions of metastability level Δ and time t. It is shown that the fundamental contribution to the growth rate represents the time independent solution of a similar temperature conductivity problem (Alexandrov and Malygin 2013 J. Phys. A: Math. Theor. 46 455101) whereas the next unsteady-state contribution is proportional to Δ2 t . On the basis of these explicit unsteady-state solutions, the process of transient nucleation and growth of spherical crystals in a metastable system is theoretically studied at the intermediate stage of phase transformation. A complete analytical solution for the particle-radius distribution function and metastability level is constructed with allowance for the Weber-Volmer-Frenkel-Zel’dovich and Meirs kinetic mechanisms. It is shown that the obtained unsteady-state contribution to the crystal growth rate plays an important role in the nucleation process and drastically changes the particle-radius distribution function.

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.

Orthogonal basis with a conicoid first mode for shape specification of optical surfaces.

PubMed

Ferreira, Chelo; López, José L; Navarro, Rafael; Sinusía, Ester Pérez

2016-03-07

A rigorous and powerful theoretical framework is proposed to obtain systems of orthogonal functions (or shape modes) to represent optical surfaces. The method is general so it can be applied to different initial shapes and different polynomials. Here we present results for surfaces with circular apertures when the first basis function (mode) is a conicoid. The system for aspheres with rotational symmetry is obtained applying an appropriate change of variables to Legendre polynomials, whereas the system for general freeform case is obtained applying a similar procedure to spherical harmonics. Numerical comparisons with standard systems, such as Forbes and Zernike polynomials, are performed and discussed.

Expansion of Tabulated Scattering Matrices in Generalized Spherical Functions

NASA Technical Reports Server (NTRS)

Mishchenko, Michael I.; Geogdzhayev, Igor V.; Yang, Ping

2016-01-01

An efficient way to solve the vector radiative transfer equation for plane-parallel turbid media is to Fourier-decompose it in azimuth. This methodology is typically based on the analytical computation of the Fourier components of the phase matrix and is predicated on the knowledge of the coefficients appearing in the expansion of the normalized scattering matrix in generalized spherical functions. Quite often the expansion coefficients have to be determined from tabulated values of the scattering matrix obtained from measurements or calculated by solving the Maxwell equations. In such cases one needs an efficient and accurate computer procedure converting a tabulated scattering matrix into the corresponding set of expansion coefficients. This short communication summarizes the theoretical basis of this procedure and serves as the user guide to a simple public-domain FORTRAN program.

A complete analytical solution for the inverse instantaneous kinematics of a spherical-revolute-spherical (7R) redundant manipulator

NASA Technical Reports Server (NTRS)

Podhorodeski, R. P.; Fenton, R. G.; Goldenberg, A. A.

1989-01-01

Using a method based upon resolving joint velocities using reciprocal screw quantities, compact analytical expressions are generated for the inverse solution of the joint rates of a seven revolute (spherical-revolute-spherical) manipulator. The method uses a sequential decomposition of screw coordinates to identify reciprocal screw quantities used in the resolution of a particular joint rate solution, and also to identify a Jacobian null-space basis used for the direct solution of optimal joint rates. The results of the screw decomposition are used to study special configurations of the manipulator, generating expressions for the inverse velocity solution for all non-singular configurations of the manipulator, and identifying singular configurations and their characteristics. Two functions are therefore served: a new general method for the solution of the inverse velocity problem is presented; and complete analytical expressions are derived for the resolution of the joint rates of a seven degree of freedom manipulator useful for telerobotic and industrial robotic application.

Nuclear longitudinal form factors for axially deformed charge distributions expanded by nonorthogonal basis functions

NASA Astrophysics Data System (ADS)

Liu, Jian; Zhang, Jinjuan; Xu, Chang; Ren, Zhongzhou

2017-05-01

In this paper, the nuclear longitudinal form factors are systematically studied from the intrinsic charge multipoles. For axially deformed nuclei, two different types of density profiles are used to describe their charge distributions. For the same charge distributions expanded with different basis functions, the corresponding longitudinal form factors are derived and compared with each other. Results show the multipoles Cλ of longitudinal form factors are independent of the basis functions of charge distributions. Further numerical calculations of longitudinal form factors of 12C indicates that the C 0 multipole reflects the contributions of spherical components of all nonorthogonal basis functions. For deformed nuclei, their charge RMS radii can also be determined accurately by the C 0 measurement. The studies in this paper examine the model-independent properties of electron scattering, which are useful for interpreting electron scattering experiments on exotic deformed nuclei. Supported by National Natural Science Foundation of China (11505292, 11175085, 11575082, 11235001, 11275138, and 11447226), by Shandong Provincial Natural Science Foundation, China (BS2014SF007), Fundamental Research Funds for Central Universities (15CX02072A).

Light scattering by lunar-like particle size distributions

NASA Technical Reports Server (NTRS)

Goguen, Jay D.

1991-01-01

A fundamental input to models of light scattering from planetary regoliths is the mean phase function of the regolith particles. Using the known size distribution for typical lunar soils, the mean phase function and mean linear polarization for a regolith volume element of spherical particles of any composition were calculated from Mie theory. The two contour plots given here summarize the changes in the mean phase function and linear polarization with changes in the real part of the complex index of refraction, n - ik, for k equals 0.01, the visible wavelength 0.55 micrometers, and the particle size distribution of the typical mature lunar soil 72141. A second figure is a similar index-phase surface, except with k equals 0.1. The index-phase surfaces from this survey are a first order description of scattering by lunar-like regoliths of spherical particles of arbitrary composition. They form the basis of functions that span a large range of parameter-space.

Solving the Self-Interaction Problem in Kohn-Sham Density Functional Theory. Application to Atoms

DOE PAGES

Daene, M.; Gonis, A.; Nicholson, D. M.; ...

2014-10-14

Previously, we proposed a computational methodology that addresses the elimination of the self-interaction error from the Kohn–Sham formulation of the density functional theory. We demonstrated how the exchange potential can be obtained, and presented results of calculations for atomic systems up to Kr carried out within a Cartesian coordinate system. In our paper, we provide complete details of this self-interaction free method formulated in spherical coordinates based on the explicit equidensity basis ansatz. We also prove analytically that derivatives obtained using this method satisfy the Virial theorem for spherical orbitals, where the problem can be reduced to one dimension. Wemore » present the results of calculations of ground-state energies of atomic systems throughout the periodic table carried out within the exchange-only mode.« less

Observation and Kinematic Description of Long Actin Tracks Induced by Spherical Beads

PubMed Central

Kang, Hyeran; Perlmutter, David S.; Shenoy, Vivek B.; Tang, Jay X.

2010-01-01

We report an in vitro study comparing the growth of long actin tails induced by spherical beads coated with the verprolin central acidic domain of the polymerization enzyme N-WASP to that induced by Listeria monocytogenes in similar cellular extracts. The tracks behind the beads show characteristic differences in shape and curvature from those left by the bacteria, which have an elongated shape and a similar polymerization-inducing enzyme distributed only on the rear surface of the cell. The experimental tracks are simulated using a generalized kinematic model, which incorporates three modes of bead rotation with respect to the tail. The results show that the trajectories of spherical beads are mechanically deterministic rather than random, as suggested by stochastic models. Assessment of the bead rotation and its mechanistic basis offers insights into the biological function of actin-based motility. PMID:21044576

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.

Axial acoustic radiation force on a sphere in Gaussian field

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

Wu, Rongrong; Liu, Xiaozhou, E-mail: xzliu@nju.edu.cn; Gong, Xiufen

2015-10-28

Based on the finite series method, the acoustical radiation force resulting from a Gaussian beam incident on a spherical object is investigated analytically. When the position of the particles deviating from the center of the beam, the Gaussian beam is expanded as a spherical function at the center of the particles and the expanded coefficients of the Gaussian beam is calculated. The analytical expression of the acoustic radiation force on spherical particles deviating from the Gaussian beam center is deduced. The acoustic radiation force affected by the acoustic frequency and the offset distance from the Gaussian beam center is investigated.more » Results have been presented for Gaussian beams with different wavelengths and it has been shown that the interaction of a Gaussian beam with a sphere can result in attractive axial force under specific operational conditions. Results indicate the capability of manipulating and separating spherical spheres based on their mechanical and acoustical properties, the results provided here may provide a theoretical basis for development of single-beam acoustical tweezers.« less

The Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 aerosol extinction retrieval algorithm: theoretical basis

NASA Astrophysics Data System (ADS)

Loughman, Robert; Bhartia, Pawan K.; Chen, Zhong; Xu, Philippe; Nyaku, Ernest; Taha, Ghassan

2018-05-01

The theoretical basis of the Ozone Mapping and Profiler Suite (OMPS) Limb Profiler (LP) Version 1 aerosol extinction retrieval algorithm is presented. The algorithm uses an assumed bimodal lognormal aerosol size distribution to retrieve aerosol extinction profiles at 675 nm from OMPS LP radiance measurements. A first-guess aerosol extinction profile is updated by iteration using the Chahine nonlinear relaxation method, based on comparisons between the measured radiance profile at 675 nm and the radiance profile calculated by the Gauss-Seidel limb-scattering (GSLS) radiative transfer model for a spherical-shell atmosphere. This algorithm is discussed in the context of previous limb-scattering aerosol extinction retrieval algorithms, and the most significant error sources are enumerated. The retrieval algorithm is limited primarily by uncertainty about the aerosol phase function. Horizontal variations in aerosol extinction, which violate the spherical-shell atmosphere assumed in the version 1 algorithm, may also limit the quality of the retrieved aerosol extinction profiles significantly.

Tolerance analysis of optical telescopes using coherent addition of wavefront errors

NASA Technical Reports Server (NTRS)

Davenport, J. W.

1982-01-01

A near diffraction-limited telescope requires that tolerance analysis be done on the basis of system wavefront error. One method of analyzing the wavefront error is to represent the wavefront error function in terms of its Zernike polynomial expansion. A Ramsey-Korsch ray trace package, a computer program that simulates the tracing of rays through an optical telescope system, was expanded to include the Zernike polynomial expansion up through the fifth-order spherical term. An option to determine a 3 dimensional plot of the wavefront error function was also included in the Ramsey-Korsch package. Several assimulation runs were analyzed to determine the particular set of coefficients in the Zernike expansion that are effected by various errors such as tilt, decenter and despace. A 3 dimensional plot of each error up through the fifth-order spherical term was also included in the study. Tolerance analysis data are presented.

High-temperature electronic structure with the Korringa-Kohn-Rostoker Green's function method

NASA Astrophysics Data System (ADS)

Starrett, C. E.

2018-05-01

Modeling high-temperature (tens or hundreds of eV), dense plasmas is challenging due to the multitude of non-negligible physical effects including significant partial ionization and multisite effects. These effects cause the breakdown or intractability of common methods and approximations used at low temperatures, such as pseudopotentials or plane-wave basis sets. Here we explore the Korringa-Kohn-Rostoker Green's function method at these high-temperature conditions. The method is all electron, does not rely on pseudopotentials, and uses a spherical harmonic basis set, and so avoids the aforementioned limitations. It is found to be accurate for solid density aluminum and iron plasmas when compared to a plane-wave method at low temperature, while being able to access high temperatures.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters

NASA Astrophysics Data System (ADS)

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-01

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Matrix elements of N-particle explicitly correlated Gaussian basis functions with complex exponential parameters.

PubMed

Bubin, Sergiy; Adamowicz, Ludwik

2006-06-14

In this work we present analytical expressions for Hamiltonian matrix elements with spherically symmetric, explicitly correlated Gaussian basis functions with complex exponential parameters for an arbitrary number of particles. The expressions are derived using the formalism of matrix differential calculus. In addition, we present expressions for the energy gradient that includes derivatives of the Hamiltonian integrals with respect to the exponential parameters. The gradient is used in the variational optimization of the parameters. All the expressions are presented in the matrix form suitable for both numerical implementation and theoretical analysis. The energy and gradient formulas have been programmed and used to calculate ground and excited states of the He atom using an approach that does not involve the Born-Oppenheimer approximation.

Local gravity field modeling using spherical radial basis functions and a genetic algorithm

NASA Astrophysics Data System (ADS)

Mahbuby, Hany; Safari, Abdolreza; Foroughi, Ismael

2017-05-01

Spherical Radial Basis Functions (SRBFs) can express the local gravity field model of the Earth if they are parameterized optimally on or below the Bjerhammar sphere. This parameterization is generally defined as the shape of the base functions, their number, center locations, bandwidths, and scale coefficients. The number/location and bandwidths of the base functions are the most important parameters for accurately representing the gravity field; once they are determined, the scale coefficients can then be computed accordingly. In this study, the point-mass kernel, as the simplest shape of SRBFs, is chosen to evaluate the synthesized free-air gravity anomalies over the rough area in Auvergne and GNSS/Leveling points (synthetic height anomalies) are used to validate the results. A two-step automatic approach is proposed to determine the optimum distribution of the base functions. First, the location of the base functions and their bandwidths are found using the genetic algorithm; second, the conjugate gradient least squares method is employed to estimate the scale coefficients. The proposed methodology shows promising results. On the one hand, when using the genetic algorithm, the base functions do not need to be set to a regular grid and they can move according to the roughness of topography. In this way, the models meet the desired accuracy with a low number of base functions. On the other hand, the conjugate gradient method removes the bias between derived quasigeoid heights from the model and from the GNSS/leveling points; this means there is no need for a corrector surface. The numerical test on the area of interest revealed an RMS of 0.48 mGal for the differences between predicted and observed gravity anomalies, and a corresponding 9 cm for the differences in GNSS/leveling points.

A spherical parallel three degrees-of-freedom robot for ankle-foot neuro-rehabilitation.

PubMed

Malosio, Matteo; Negri, Simone Pio; Pedrocchi, Nicola; Vicentini, Federico; Caimmi, Marco; Molinari Tosatti, Lorenzo

2012-01-01

The ankle represents a fairly complex bone structure, resulting in kinematics that hinders a flawless robot-assisted recovery of foot motility in impaired subjects. The paper proposes a novel device for ankle-foot neuro-rehabilitation based on a mechatronic redesign of the remarkable Agile Eye spherical robot on the basis of clinical requisites. The kinematic design allows the positioning of the ankle articular center close to the machine rotation center with valuable benefits in term of therapy functions. The prototype, named PKAnkle, Parallel Kinematic machine for Ankle rehabilitation, provides a 6-axes load cell for the measure of subject interaction forces/torques, and it integrates a commercial EMG-acquisition system. Robot control provides active and passive therapeutic exercises.

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

NASA Technical Reports Server (NTRS)

Hahne, G. E.

1993-01-01

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

A Parallel Product-Convolution approach for representing the depth varying Point Spread Functions in 3D widefield microscopy based on principal component analysis.

PubMed

Arigovindan, Muthuvel; Shaevitz, Joshua; McGowan, John; Sedat, John W; Agard, David A

2010-03-29

We address the problem of computational representation of image formation in 3D widefield fluorescence microscopy with depth varying spherical aberrations. We first represent 3D depth-dependent point spread functions (PSFs) as a weighted sum of basis functions that are obtained by principal component analysis (PCA) of experimental data. This representation is then used to derive an approximating structure that compactly expresses the depth variant response as a sum of few depth invariant convolutions pre-multiplied by a set of 1D depth functions, where the convolving functions are the PCA-derived basis functions. The model offers an efficient and convenient trade-off between complexity and accuracy. For a given number of approximating PSFs, the proposed method results in a much better accuracy than the strata based approximation scheme that is currently used in the literature. In addition to yielding better accuracy, the proposed methods automatically eliminate the noise in the measured PSFs.

Kinetic damping in the spectra of the spherical impedance probe

NASA Astrophysics Data System (ADS)

Oberrath, J.

2018-04-01

The impedance probe is a measurement device to measure plasma parameters, such as electron density. It consists of one electrode connected to a network analyzer via a coaxial cable and is immersed into a plasma. A bias potential superposed with an alternating potential is applied to the electrode and the response of the plasma is measured. Its dynamical interaction with the plasma in an electrostatic, kinetic description can be modeled in an abstract notation based on functional analytic methods. These methods provide the opportunity to derive a general solution, which is given as the response function of the probe–plasma system. It is defined by the matrix elements of the resolvent of an appropriate dynamical operator. Based on the general solution, a residual damping for vanishing pressure can be predicted and can only be explained by kinetic effects. In this paper, an explicit response function of the spherical impedance probe is derived. Therefore, the resolvent is determined by its algebraic representation based on an expansion in orthogonal basis functions. This allows one to compute an approximated response function and its corresponding spectra. These spectra show additional damping due to kinetic effects and are in good agreement with former kinetically determined spectra.

Overset grid implementation of the complex Kohn variational method for electron-polyatomic molecule scattering

NASA Astrophysics Data System (ADS)

McCurdy, C. William; Lucchese, Robert L.; Greenman, Loren

2017-04-01

The complex Kohn variational method, which represents the continuum wave function in each channel using a combination of Gaussians and Bessel or Coulomb functions, has been successful in numerous applications to electron-polyatomic molecule scattering and molecular photoionization. The hybrid basis representation limits it to relatively low energies (< 50 eV) , requires an approximation to exchange matrix elements involving continuum functions, and hampers its coupling to modern electronic structure codes for the description of correlated target states. We describe a successful implementation of the method using completely adaptive overset grids to describe continuum functions, in which spherical subgrids are placed on every atomic center to complement a spherical master grid that describes the behavior at large distances. An accurate method for applying the free-particle Green's function on the grid eliminates the need to operate explicitly with the kinetic energy, enabling a rapidly convergent Arnoldi algorithm for solving linear equations on the grid, and no approximations to exchange operators are made. Results for electron scattering from several polyatomic molecules will be presented. Army Research Office, MURI, WN911NF-14-1-0383 and U. S. DOE DE-SC0012198 (at Texas A&M).

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.).

Efficient visibility encoding for dynamic illumination in direct volume rendering.

PubMed

Kronander, Joel; Jönsson, Daniel; Löw, Joakim; Ljung, Patric; Ynnerman, Anders; Unger, Jonas

2012-03-01

We present an algorithm that enables real-time dynamic shading in direct volume rendering using general lighting, including directional lights, point lights, and environment maps. Real-time performance is achieved by encoding local and global volumetric visibility using spherical harmonic (SH) basis functions stored in an efficient multiresolution grid over the extent of the volume. Our method enables high-frequency shadows in the spatial domain, but is limited to a low-frequency approximation of visibility and illumination in the angular domain. In a first pass, level of detail (LOD) selection in the grid is based on the current transfer function setting. This enables rapid online computation and SH projection of the local spherical distribution of visibility information. Using a piecewise integration of the SH coefficients over the local regions, the global visibility within the volume is then computed. By representing the light sources using their SH projections, the integral over lighting, visibility, and isotropic phase functions can be efficiently computed during rendering. The utility of our method is demonstrated in several examples showing the generality and interactive performance of the approach.

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.

Non-Negative Spherical Deconvolution (NNSD) for estimation of fiber Orientation Distribution Function in single-/multi-shell diffusion MRI.

PubMed

Cheng, Jian; Deriche, Rachid; Jiang, Tianzi; Shen, Dinggang; Yap, Pew-Thian

2014-11-01

Spherical Deconvolution (SD) is commonly used for estimating fiber Orientation Distribution Functions (fODFs) from diffusion-weighted signals. Existing SD methods can be classified into two categories: 1) Continuous Representation based SD (CR-SD), where typically Spherical Harmonic (SH) representation is used for convenient analytical solutions, and 2) Discrete Representation based SD (DR-SD), where the signal profile is represented by a discrete set of basis functions uniformly oriented on the unit sphere. A feasible fODF should be non-negative and should integrate to unity throughout the unit sphere S(2). However, to our knowledge, most existing SH-based SD methods enforce non-negativity only on discretized points and not the whole continuum of S(2). Maximum Entropy SD (MESD) and Cartesian Tensor Fiber Orientation Distributions (CT-FOD) are the only SD methods that ensure non-negativity throughout the unit sphere. They are however computational intensive and are susceptible to errors caused by numerical spherical integration. Existing SD methods are also known to overestimate the number of fiber directions, especially in regions with low anisotropy. DR-SD introduces additional error in peak detection owing to the angular discretization of the unit sphere. This paper proposes a SD framework, called Non-Negative SD (NNSD), to overcome all the limitations above. NNSD is significantly less susceptible to the false-positive peaks, uses SH representation for efficient analytical spherical deconvolution, and allows accurate peak detection throughout the whole unit sphere. We further show that NNSD and most existing SD methods can be extended to work on multi-shell data by introducing a three-dimensional fiber response function. We evaluated NNSD in comparison with Constrained SD (CSD), a quadratic programming variant of CSD, MESD, and an L1-norm regularized non-negative least-squares DR-SD. Experiments on synthetic and real single-/multi-shell data indicate that NNSD improves estimation performance in terms of mean difference of angles, peak detection consistency, and anisotropy contrast between isotropic and anisotropic regions. Copyright © 2014 Elsevier Inc. All rights reserved.

On the importance of local orbitals using second energy derivatives for d and f electrons

NASA Astrophysics Data System (ADS)

Karsai, Ferenc; Tran, Fabien; Blaha, Peter

2017-11-01

The all-electron linearized augmented plane wave (LAPW) methods are among the most accurate to solve the Kohn-Sham equations of density functional theory for periodic solids. In the LAPW methods, the unit cell is partitioned into spheres surrounding the atoms, inside which the wave functions are expanded into spherical harmonics, and the interstitial region, where the wave functions are expanded in Fourier series. Recently, Michalicek et al. (2013) reported an analysis of the so-called linearization error, which is inherent to the basis functions inside the spheres, and advocated the use of local orbital basis functions involving the second energy derivative of the radial part (HDLO). In the present work, we report the implementation of such basis functions into the WIEN2k code, and discuss in detail the improvement in terms of accuracy. From our tests, which involve atoms from the whole periodic table, it is concluded that for ground-state properties (e.g., equilibrium volume) the use of HDLO is necessary only for atoms with d or f electrons in the valence and large atomic spheres. For unoccupied states which are not too high above the Fermi energy, HDLO systematically improve the band structure, which may be of importance for the calculation of optical properties.

Earth Structure, Ice Mass Changes, and the Local Dynamic Geoid

NASA Astrophysics Data System (ADS)

Harig, C.; Simons, F. J.

2014-12-01

Spherical Slepian localization functions are a useful method for studying regional mass changes observed by satellite gravimetry. By projecting data onto a sparse basis set, the local field can be estimated more easily than with the full spherical harmonic basis. We have used this method previously to estimate the ice mass change in Greenland from GRACE data, and it can also be applied to other planetary problems such as global magnetic fields. Earth's static geoid, in contrast to the time-variable field, is in large part related to the internal density and rheological structure of the Earth. Past studies have used dynamic geoid kernels to relate this density structure and the internal deformation it induces to the surface geopotential at large scales. These now classical studies of the eighties and nineties were able to estimate the mantle's radial rheological profile, placing constraints on the ratio between upper and lower mantle viscosity. By combining these two methods, spherical Slepian localization and dynamic geoid kernels, we have created local dynamic geoid kernels which are sensitive only to density variations within an area of interest. With these kernels we can estimate the approximate local radial rheological structure that best explains the locally observed geoid on a regional basis. First-order differences of the regional mantle viscosity structure are accessible to this technique. In this contribution we present our latest, as yet unpublished results on the geographical and temporal pattern of ice mass changes in Antarctica over the past decade, and we introduce a new approach to extract regional information about the internal structure of the Earth from the static global gravity field. Both sets of results are linked in terms of the relevant physics, but also in being developed from the marriage of Slepian functions and geoid kernels. We make predictions on the utility of our approach to derive fully three-dimensional rheological Earth models, to be used for corrections for glacio-isostatic adjustment, as necessary for the interpretation of time-variable gravity observations in terms of ice sheet mass-balance studies.

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

The energy-release rate and “self-force” of dynamically expanding spherical and plane inclusion boundaries with dilatational eigenstrain

NASA Astrophysics Data System (ADS)

Markenscoff, Xanthippi; Ni, Luqun

2010-01-01

In the context of the linear theory of elasticity with eigenstrains, the radiated field including inertia effects of a spherical inclusion with dilatational eigenstrain radially expanding is obtained on the basis of the dynamic Green's function, and one of the half-space inclusion boundary (with dilatational eigenstrain) moving from rest in general subsonic motion is obtained by a limiting process from the spherically expanding inclusion as the radius tends to infinity while the eigenstrain remains constrained, and this is the minimum energy solution. The global energy-release rate required to move the plane inclusion boundary and to create an incremental region of eigenstrain is defined analogously to the one for moving cracks and dislocations and represents the mechanical rate of work needed to be provide for the expansion of the inclusion. The calculated value, which is the "self-force" of the expanding inclusion, has a static component plus a dynamic one depending only on the current value of the velocity, while in the case of the spherical boundary, there is an additional contribution accounting for the jump in the strain at the farthest part at the back of the inclusion having the time to reach the front boundary, thus making the dynamic "self-force" history dependent.

Convoluted Quasi Sturmian basis for the two-electron continuum

NASA Astrophysics Data System (ADS)

Ancarani, Lorenzo Ugo; Zaytsev, A. S.; Zaytsev, S. A.

2016-09-01

In the construction of solutions for the Coulomb three-body scattering problem one encounters a series of mathematical and numerical difficulties, one of which are the cumbersome boundary conditions the wave function should obey. We propose to describe a Coulomb three-body system continuum with a set of two-particle functions, named Convoluted Quasi Sturmian (CQS) in. They are built using recently introduced Quasi Sturmian (QS) functions which have the merit of possessing a closed form. Unlike a simple product of two one-particle functions, by construction, the CQS functions look asymptotically like a six-dimensional outgoing spherical wave. The proposed CQS basis is tested through the study of the double ionization of helium by high-energy electron impact in the framework of the Temkin-Poet model. An adequate logarithmic-like phase factor is further included in order to take into account the Coulomb interelectronic interaction and formally build the correct asymptotic behavior when all interparticle distances are large. With such a phase-factor (that can be easily extended to take into account higher partial waves) rapid convergence of the expansion can be obtained.

Evolution and statistics of non-sphericity of dark matter halos from cosmological N-body simulation

NASA Astrophysics Data System (ADS)

Suto, Daichi; Kitayama, Tetsu; Nishimichi, Takahiro; Sasaki, Shin; Suto, Yasushi

2016-12-01

We revisit the non-sphericity of cluster-mass-scale halos from cosmological N-body simulation on the basis of triaxial modeling. In order to understand the difference between the simulation results and the conventional ellipsoidal collapse model (EC), we first consider the evolution of individual simulated halos. The major difference between EC and the simulation becomes appreciable after the turnaround epoch. Moreover, it is sensitive to the individual evolution history of each halo. Despite such strong dependence on individual halos, the resulting non-sphericity of halos exhibits weak but robust mass dependence in a statistical fashion; massive halos are more spherical up to the turnaround, but gradually become less spherical by z = 0. This is clearly inconsistent with the EC prediction: massive halos are usually more spherical. In addition, at z = 0, inner regions of the simulated halos are less spherical than outer regions; that is, the density distribution inside the halos is highly inhomogeneous and therefore not self-similar (concentric ellipsoids with the same axis ratio and orientation). This is also inconsistent with the homogeneous density distribution that is commonly assumed in EC. Since most of previous fitting formulae for the probability distribution function (PDF) of the axis ratio of triaxial ellipsoids have been constructed under the self-similarity assumption, they are not accurate. Indeed, we compute the PDF of the projected axis ratio a1/a2 directly from the simulation data without the self-similarity assumption, and find that it is very sensitive to the assumption. The latter needs to be carefully taken into account in direct comparison with observations, and therefore we provide an empirical fitting formula for the PDF of a1/a2. Our preliminary analysis suggests that the derived PDF of a1/a2 roughly agrees with the current weak-lensing observations. More importantly, the present results will be useful for future exploration of the non-sphericity of clusters in X-ray and optical observations.

Research on modeling and motion simulation of a spherical space robot with telescopic manipulator based on virtual prototype technology

NASA Astrophysics Data System (ADS)

Shi, Chengkun; Sun, Hanxu; Jia, Qingxuan; Zhao, Kailiang

2009-05-01

For realizing omni-directional movement and operating task of spherical space robot system, this paper describes an innovated prototype and analyzes dynamic characteristics of a spherical rolling robot with telescopic manipulator. Based on the Newton-Euler equations, the kinematics and dynamic equations of the spherical robot's motion are instructed detailedly. Then the motion simulations of the robot in different environments are developed with ADAMS. The simulation results validate the mathematics model of the system. And the dynamic model establishes theoretical basis for the latter job.

Zernike Basis to Cartesian Transformations

NASA Astrophysics Data System (ADS)

Mathar, R. J.

2009-12-01

The radial polynomials of the 2D (circular) and 3D (spherical) Zernike functions are tabulated as powers of the radial distance. The reciprocal tabulation of powers of the radial distance in series of radial polynomials is also given, based on projections that take advantage of the orthogonality of the polynomials over the unit interval. They play a role in the expansion of products of the polynomials into sums, which is demonstrated by some examples. Multiplication of the polynomials by the angular bases (azimuth, polar angle) defines the Zernike functions, for which we derive transformations to and from the Cartesian coordinate system centered at the middle of the circle or sphere.

High-order nonlinear susceptibilities of He

NASA Astrophysics Data System (ADS)

Liu, W.-C.; Clark, Charles W.

1996-05-01

High-order nonlinear optical response of noble gases to intense laser radiation is of considerable experimental interest, but is difficult to measure or calculate accurately. We have begun a set of calculations of frequency-dependent nonlinear susceptibilities of He 1s^2, within the framework of Rayleigh-Schrödinger perturbation theory at lowest applicable order, with the goal of providing critically evaluated atomic data for modelling high harmonic generation processes. The atomic Hamiltonian is decomposed in term of Hylleraas coordinates and spherical harmonics using the formalism of Pont and Shakeshaft (M. Pont and R. Shakeshaft, Phy. Rev. A 51), 257 (1995), and the hierarchy of inhomogeneous equations of perturbation theory is solved iteratively. A combination of Hylleraas and Frankowski basis functions is used(J. D. Baker, Master thesis, U. Delaware (1988); J. D. Baker, R. N. Hill, and J. D. Morgan, AIP Conference Proceedings 189) 123(1989); the compact Hylleraas basis provides a highly accurate representation of the ground state wavefunction, whereas the diffuse Frankowski basis functions efficiently reproduce the correct asymptotic structure of the perturbed orbitals.

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.

Decomposition of Atmospheric Aerosol Phase Function by Particle Size and Morphology via Single Particle Scattering Measurements

NASA Astrophysics Data System (ADS)

Aptowicz, K. B.; Pan, Y.; Martin, S.; Fernandez, E.; Chang, R.; Pinnick, R. G.

2013-12-01

We report upon an experimental approach that provides insight into how particle size and shape affect the scattering phase function of atmospheric aerosol particles. Central to our approach is the design of an apparatus that measures the forward and backward scattering hemispheres (scattering patterns) of individual atmospheric aerosol particles in the coarse mode range. The size and shape of each particle is discerned from the corresponding scattering pattern. In particular, autocorrelation analysis is used to differentiate between spherical and non-spherical particles, the calculated asphericity factor is used to characterize the morphology of non-spherical particles, and the integrated irradiance is used for particle sizing. We found the fraction of spherical particles decays exponentially with particle size, decreasing from 11% for particles on the order of 1 micrometer to less than 1% for particles over 5 micrometer. The average phase functions of subpopulations of particles, grouped by size and morphology, are determined by averaging their corresponding scattering patterns. The phase functions of spherical and non-spherical atmospheric particles are shown to diverge with increasing size. In addition, the phase function of non-spherical particles is found to vary little as a function of the asphericity factor.

Deformation properties of lead isotopes

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

Tolokonnikov, S. V.; Borzov, I. N.; Lutostansky, Yu. S.

2016-01-15

The deformation properties of a long lead isotopic chain up to the neutron drip line are analyzed on the basis of the energy density functional (EDF) in the FaNDF{sup 0} Fayans form. The question of whether the ground state of neutron-deficient lead isotopes can have a stable deformation is studied in detail. The prediction of this deformation is contained in the results obtained on the basis of the HFB-17 and HFB-27 Skyrme EDF versions and reported on Internet. The present analysis reveals that this is at odds with experimental data on charge radii and magnetic moments of odd lead isotopes.more » The Fayans EDF version predicts a spherical ground state for all light lead isotopes, but some of them (for example, {sup 180}Pb and {sup 184}Pb) prove to be very soft—that is, close to the point of a phase transition to a deformed state. Also, the results obtained in our present study are compared with the predictions of some other Skyrme EDF versions, including SKM*, SLy4, SLy6, and UNE1. By and large, their predictions are closer to the results arising upon the application of the Fayans functional. For example, the SLy4 functional predicts, in just the same way as the FaNDF{sup 0} functional, a spherical shape for all nuclei of this region. The remaining three Skyrme EDF versions lead to a deformation of some light lead isotopes, but their number is substantially smaller than that in the case of the HFB-17 and HFB-27 functionals. Moreover, the respective deformation energy is substantially lower, which gives grounds to hope for the restoration of a spherical shape upon going beyond the mean-field approximation, which we use here. Also, the deformation properties of neutron-rich lead isotopes are studied up to the neutron drip line. Here, the results obtained with the FaNDF{sup 0} functional are compared with the predictions of the HFB-17, HFB-27, SKM*, and SLy4 Skyrme EDF versions. All of the EDF versions considered here predict the existence of a region where neutron-rich lead isotopes undergo deformations, but the size of this region is substantially different for the different functionals being considered. Once again, it is maximal for the HFB-17 and HFB-27 functionals, is substantially narrower for the FaNDF{sup 0} functional, and is still narrower for the SKM* and SLy4 functionals. The two-neutron drip line proved to be A{sub drip}{sup 2n} = 266 for all of the EDF versions considered here, with the exception of SKM*, for which it is shifted to A{sub drip}{sup 2n}(SKM*) = 272.« less

Experimental evaluation and basis function optimization of the spatially variant image-space PSF on the Ingenuity PET/MR scanner

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

Kotasidis, Fotis A., E-mail: Fotis.Kotasidis@unige.ch; Zaidi, Habib; Geneva Neuroscience Centre, Geneva University, CH-1205 Geneva

2014-06-15

Purpose: The Ingenuity time-of-flight (TF) PET/MR is a recently developed hybrid scanner combining the molecular imaging capabilities of PET with the excellent soft tissue contrast of MRI. It is becoming common practice to characterize the system's point spread function (PSF) and understand its variation under spatial transformations to guide clinical studies and potentially use it within resolution recovery image reconstruction algorithms. Furthermore, due to the system's utilization of overlapping and spherical symmetric Kaiser-Bessel basis functions during image reconstruction, its image space PSF and reconstructed spatial resolution could be affected by the selection of the basis function parameters. Hence, a detailedmore » investigation into the multidimensional basis function parameter space is needed to evaluate the impact of these parameters on spatial resolution. Methods: Using an array of 12 × 7 printed point sources, along with a custom made phantom, and with the MR magnet on, the system's spatially variant image-based PSF was characterized in detail. Moreover, basis function parameters were systematically varied during reconstruction (list-mode TF OSEM) to evaluate their impact on the reconstructed resolution and the image space PSF. Following the spatial resolution optimization, phantom, and clinical studies were subsequently reconstructed using representative basis function parameters. Results: Based on the analysis and under standard basis function parameters, the axial and tangential components of the PSF were found to be almost invariant under spatial transformations (∼4 mm) while the radial component varied modestly from 4 to 6.7 mm. Using a systematic investigation into the basis function parameter space, the spatial resolution was found to degrade for basis functions with a large radius and small shape parameter. However, it was found that optimizing the spatial resolution in the reconstructed PET images, while having a good basis function superposition and keeping the image representation error to a minimum, is feasible, with the parameter combination range depending upon the scanner's intrinsic resolution characteristics. Conclusions: Using the printed point source array as a MR compatible methodology for experimentally measuring the scanner's PSF, the system's spatially variant resolution properties were successfully evaluated in image space. Overall the PET subsystem exhibits excellent resolution characteristics mainly due to the fact that the raw data are not under-sampled/rebinned, enabling the spatial resolution to be dictated by the scanner's intrinsic resolution and the image reconstruction parameters. Due to the impact of these parameters on the resolution properties of the reconstructed images, the image space PSF varies both under spatial transformations and due to basis function parameter selection. Nonetheless, for a range of basis function parameters, the image space PSF remains unaffected, with the range depending on the scanner's intrinsic resolution properties.« less

Frequency-radial duality based photoacoustic image reconstruction.

PubMed

Akramus Salehin, S M; Abhayapala, Thushara D

2012-07-01

Photoacoustic image reconstruction algorithms are usually slow due to the large sizes of data that are processed. This paper proposes a method for exact photoacoustic reconstruction for the spherical geometry in the limiting case of a continuous aperture and infinite measurement bandwidth that is faster than existing methods namely (1) backprojection method and (2) the Norton-Linzer method [S. J. Norton and M. Linzer, "Ultrasonic reflectivity imaging in three dimensions: Exact inverse scattering solution for plane, cylindrical and spherical apertures," Biomedical Engineering, IEEE Trans. BME 28, 202-220 (1981)]. The initial pressure distribution is expanded using a spherical Fourier Bessel series. The proposed method estimates the Fourier Bessel coefficients and subsequently recovers the pressure distribution. A concept of frequency-radial duality is introduced that separates the information from the different radial basis functions by using frequencies corresponding to the Bessel zeros. This approach provides a means to analyze the information obtained given a measurement bandwidth. Using order analysis and numerical experiments, the proposed method is shown to be faster than both the backprojection and the Norton-Linzer methods. Further, the reconstructed images using the proposed methodology were of similar quality to the Norton-Linzer method and were better than the approximate backprojection method.

On the addition theorem of spherical functions

NASA Astrophysics Data System (ADS)

Shkodrov, V. G.

The addition theorem of spherical functions is expressed in two reference systems, viz., an inertial system and a system rigidly fixed to a planet. A generalized addition theorem of spherical functions and a particular addition theorem for the rigidly fixed system are derived. The results are applied to the theory of a planetary potential.

Numerically Exact Calculation of Rovibrational Levels of Cl^-H_2O

NASA Astrophysics Data System (ADS)

Wang, Xiao-Gang; Carrington, Tucker

2014-06-01

Large amplitude vibrations of Van der Waals clusters are important because they reveal large regions of a potential energy surface (PES). To calculate spectra of Van der Waals clusters it is common to use an adiabatic approximation. When coupling between intra- and inter-molecular coordinates is important non-adiabatic coupling cannot be neglected and it is therefore critical to develop and test theoretical methods that couple both types of coordinates. We have developed new product basis and contracted basis Lanczos methods for Van der Waals complexes and tested them by computing rovibrational energy levels of Cl^-H_2O. The new product basis is made of functions of the inter-monomer distance, Wigner functions that depend on Euler angles specifying the orientation of H_2O with respect to a frame attached to the inter-monomer Jacobi vector, basis functions for H_2O vibration, and Wigner functions that depend on Euler angles specifying the orientation of the inter-monomer Jacobi vector with respect to a space-fixed frame. An advantage of this product basis is that it can be used to make an efficient contracted basis by replacing the vibrational basis functions for the monomer with monomer vibrational wavefunctions. Due to weak coupling between intra- and inter-molecular coordinates, only a few tens of monomer vibrational wavefunctions are necessary. The validity of the two new methods is established by comparing energy levels with benchmark rovibrational levels obtained with polyspherical coordinates and spherical harmonic type basis functions. For all bases, product structure is exploited to calculate eigenvalues with the Lanczos algorithm. For Cl^-H_2O, we are able, for the first time, to compute accurate splittings due to tunnelling between the two equivalent C_s minima. We use the PES of Rheinecker and Bowman (RB). Our results are in good agreement with experiment for the five fundamental bands observed. J. Rheinecker and J. M. Bowman, J. Chem. Phys. 124 131102 (2006) J. Rheinecker and J. M. Bowman, J. Chem. Phys. 125 133206 (2006)} S. Horvath, A. B. McCoy, B. M. Elliott, G. H. Weddle, J. R. Roscioli, and M. A. Johnson J. Phys. Chem. A 114 1556 (2010)

Analyses of scattering characteristics of chosen anthropogenic aerosols

NASA Astrophysics Data System (ADS)

Kaszczuk, Miroslawa; Mierczyk, Zygmunt; Muzal, Michal

2008-10-01

In the work, analyses of scattering profile of chosen anthropogenic aerosols for two wavelengths (λ1 = 1064 nm and λ2 = 532 nm) were made. As an example of anthropogenic aerosol three different pyrotechnic mixtures (DM11, M2, M16) were taken. Main parameters of smoke particles were firstly analyzed and well described, taking particle shape and size into special consideration. Shape of particles was analyzed on the basis of SEM pictures, and particle size was measured. Participation of particles in each fixed fraction characterized by range of sizes was analyzed and parameters of smoke particles of characteristic sizes and function describing aerosol size distribution (ASD) were determinated. Analyses of scattering profiles were carried out on the basis of both model of scattering on spherical and nonspherical particles. In the case of spherical particles Rayleigh-Mie model was used and for nonspherical particles analyses firstly model of spheroids was used, and then Rayleigh-Mie one. For each characteristic particle one calculated value of four parameters (effective scattering cross section σSCA, effective backscattering cross section σBSCA, scattering efficiency QSCA, backscattering efficiency QBSCA) and value of backscattering coefficient β for whole particles population. Obtained results were compared with the same parameters calculated for natural aerosol (cirrus cloud).

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.

On the completeness and the linear dependence of the Cartesian multipole series in representing the solution to the Helmholtz equation.

PubMed

Liu, Yangfan; Bolton, J Stuart

2016-08-01

The (Cartesian) multipole series, i.e., the series comprising monopole, dipoles, quadrupoles, etc., can be used, as an alternative to the spherical or cylindrical wave series, in representing sound fields in a wide range of problems, such as source radiation, sound scattering, etc. The proofs of the completeness of the spherical and cylindrical wave series in these problems are classical results, and it is also generally agreed that the Cartesian multipole series spans the same space as the spherical waves: a rigorous mathematical proof of that statement has, however, not been presented. In the present work, such a proof of the completeness of the Cartesian multipole series, both in two and three dimensions, is given, and the linear dependence relations among different orders of multipoles are discussed, which then allows one to easily extract a basis from the multipole series. In particular, it is concluded that the multipoles comprising the two highest orders in the series form a basis of the whole series, since the multipoles of all the lower source orders can be expressed as a linear combination of that basis.

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.

Eulerian formulation of the interacting particle representation model of homogeneous turbulence

DOE PAGES

Campos, Alejandro; Duraisamy, Karthik; Iaccarino, Gianluca

2016-10-21

The Interacting Particle Representation Model (IPRM) of homogeneous turbulence incorporates information about the morphology of turbulent structures within the con nes of a one-point model. In the original formulation [Kassinos & Reynolds, Center for Turbulence Research: Annual Research Briefs, 31{51, (1996)], the IPRM was developed in a Lagrangian setting by evolving second moments of velocity conditional on a given gradient vector. In the present work, the IPRM is re-formulated in an Eulerian framework and evolution equations are developed for the marginal PDFs. Eulerian methods avoid the issues associated with statistical estimators used by Lagrangian approaches, such as slow convergence. Amore » specific emphasis of this work is to use the IPRM to examine the long time evolution of homogeneous turbulence. We first describe the derivation of the marginal PDF in spherical coordinates, which reduces the number of independent variables and the cost associated with Eulerian simulations of PDF models. Next, a numerical method based on radial basis functions over a spherical domain is adapted to the IPRM. Finally, results obtained with the new Eulerian solution method are thoroughly analyzed. The sensitivity of the Eulerian simulations to parameters of the numerical scheme, such as the size of the time step and the shape parameter of the radial basis functions, is examined. A comparison between Eulerian and Lagrangian simulations is performed to discern the capabilities of each of the methods. Finally, a linear stability analysis based on the eigenvalues of the discrete differential operators is carried out for both the new Eulerian solution method and the original Lagrangian approach.« less

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.

The Fatigue Life Prediction of Train Wheel Rims Containing Spherical Inclusions

NASA Astrophysics Data System (ADS)

Li, Yajie; Chen, Huanguo; Cai, Li; Chen, Pei; Qian, Jiacheng; Wu, Jianwei

2018-03-01

It is a common phenomenon that fatigue crack initiation occurs frequently in the inclusions of wheel rims. Research on the fatigue life of wheel rims with spherical inclusions is of great significance on the reliability of wheels. To find the danger point and working condition of a wheel, the stress state of the wheel rim with spherical inclusions was analyzed using the finite element method. Results revealed that curve conditions are dangerous. The critical plane method, based on the cumulative fatigue damage theory, was used to predict the fatigue life of the wheel rim and whether it contained spherical inclusions or not under curve conditions. It was found that the fatigue life of the wheel rim is significantly shorter when the wheel rim contains spherical inclusions. Analysis of the results can provide a theoretical basis and technical support for train operations and maintenance.

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.

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).

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.

Isotropic enhancement in the critical current density of YBCO thin films incorporating nanoscale Y2BaCuO5 inclusions

NASA Astrophysics Data System (ADS)

Jha, Alok K.; Matsumoto, Kaname; Horide, Tomoya; Saini, Shrikant; Mele, Paolo; Ichinose, Ataru; Yoshida, Yutaka; Awaji, Satoshi

2017-09-01

The effect of incorporation of nanoscale Y2BaCuO5 (Y211) inclusions on the vortex pinning properties of YBa2Cu3O7-δ (YBCO or Y123) superconducting thin films is investigated in detail on the basis of variation of critical current density (JC) with applied magnetic field and also with the orientation of the applied magnetic field at two different temperatures: 77 K and 65 K. Surface modified target approach is employed to incorporate nanoscale Y211 inclusions into the superconducting YBCO matrix. The efficiency of Y211 nanoinclusions in reducing the angular anisotropy of critical current density is found to be significant. The observed angular dependence of the critical current density is discussed on the basis of mutually occupied volume by a vortex and spherical and/or planar defect. A dip in JC near the ab-plane is also observed which has been analyzed on the basis of variation of pinning potential corresponding to a spherical (3-D) or planar (2-D) pinning center and has been attributed to a reduced interaction volume of the vortices with a pinning center and competing nature of the potentials due to spherical and planar defects.

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

NASA Astrophysics Data System (ADS)

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

2010-05-01

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

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.

On Nonlinear Functionals of Random Spherical Eigenfunctions

NASA Astrophysics Data System (ADS)

Marinucci, Domenico; Wigman, Igor

2014-05-01

We prove central limit theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combines asymptotic analysis of higher order moments for Legendre polynomials and, in addition, recent results on Malliavin calculus and total variation bounds for Gaussian subordinated fields. We discuss applications to geometric functionals like the defect and invariant statistics, e.g., polyspectra of isotropic spherical random fields. Both of these have relevance for applications, especially in an astrophysical environment.

Integral Equations in Computational Electromagnetics: Formulations, Properties and Isogeometric Analysis

NASA Astrophysics Data System (ADS)

Lovell, Amy Elizabeth

Computational electromagnetics (CEM) provides numerical methods to simulate electromagnetic waves interacting with its environment. Boundary integral equation (BIE) based methods, that solve the Maxwell's equations in the homogeneous or piecewise homogeneous medium, are both efficient and accurate, especially for scattering and radiation problems. Development and analysis electromagnetic BIEs has been a very active topic in CEM research. Indeed, there are still many open problems that need to be addressed or further studied. A short and important list includes (1) closed-form or quasi-analytical solutions to time-domain integral equations, (2) catastrophic cancellations at low frequencies, (3) ill-conditioning due to high mesh density, multi-scale discretization, and growing electrical size, and (4) lack of flexibility due to re-meshing when increasing number of forward numerical simulations are involved in the electromagnetic design process. This dissertation will address those several aspects of boundary integral equations in computational electromagnetics. The first contribution of the dissertation is to construct quasi-analytical solutions to time-dependent boundary integral equations using a direct approach. Direct inverse Fourier transform of the time-harmonic solutions is not stable due to the non-existence of the inverse Fourier transform of spherical Hankel functions. Using new addition theorems for the time-domain Green's function and dyadic Green's functions, time-domain integral equations governing transient scattering problems of spherical objects are solved directly and stably for the first time. Additional, the direct time-dependent solutions, together with the newly proposed time-domain dyadic Green's functions, can enrich the time-domain spherical multipole theory. The second contribution is to create a novel method of moments (MoM) framework to solve electromagnetic boundary integral equation on subdivision surfaces. The aim is to avoid the meshing and re-meshing stages to accelerate the design process when the geometry needs to be updated. Two schemes to construct basis functions on the subdivision surface have been explored. One is to use the div-conforming basis function, and the other one is to create a rigorous iso-geometric approach based on the subdivision basis function with better smoothness properties. This new framework provides us better accuracy, more stability and high flexibility. The third contribution is a new stable integral equation formulation to avoid catastrophic cancellations due to low-frequency breakdown or dense-mesh breakdown. Many of the conventional integral equations and their associated post-processing operations suffer from numerical catastrophic cancellations, which can lead to ill-conditioning of the linear systems or serious accuracy problems. Examples includes low-frequency breakdown and dense mesh breakdown. Another instability may come from nontrivial null spaces of involving integral operators that might be related with spurious resonance or topology breakdown. This dissertation presents several sets of new boundary integral equations and studies their analytical properties. The first proposed formulation leads to the scalar boundary integral equations where only scalar unknowns are involved. Besides the requirements of gaining more stability and better conditioning in the resulting linear systems, multi-physics simulation is another driving force for new formulations. Scalar and vector potentials (rather than electromagnetic field) based formulation have been studied for this purpose. Those new contributions focus on different stages of boundary integral equations in an almost independent manner, e.g. isogeometric analysis framework can be used to solve different boundary integral equations, and the time-dependent solutions to integral equations from different formulations can be achieved through the same methodology proposed.

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.

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.

Spherical hashing: binary code embedding with hyperspheres.

PubMed

Heo, Jae-Pil; Lee, Youngwoon; He, Junfeng; Chang, Shih-Fu; Yoon, Sung-Eui

2015-11-01

Many binary code embedding schemes have been actively studied recently, since they can provide efficient similarity search, and compact data representations suitable for handling large scale image databases. Existing binary code embedding techniques encode high-dimensional data by using hyperplane-based hashing functions. In this paper we propose a novel hypersphere-based hashing function, spherical hashing, to map more spatially coherent data points into a binary code compared to hyperplane-based hashing functions. We also propose a new binary code distance function, spherical Hamming distance, tailored for our hypersphere-based binary coding scheme, and design an efficient iterative optimization process to achieve both balanced partitioning for each hash function and independence between hashing functions. Furthermore, we generalize spherical hashing to support various similarity measures defined by kernel functions. Our extensive experiments show that our spherical hashing technique significantly outperforms state-of-the-art techniques based on hyperplanes across various benchmarks with sizes ranging from one to 75 million of GIST, BoW and VLAD descriptors. The performance gains are consistent and large, up to 100 percent improvements over the second best method among tested methods. These results confirm the unique merits of using hyperspheres to encode proximity regions in high-dimensional spaces. Finally, our method is intuitive and easy to implement.

Four-zone varifocus mirrors with adaptive control of primary and higher-order spherical aberration

PubMed Central

Lukes, Sarah J.; Downey, Ryan D.; Kreitinger, Seth T.; Dickensheets, David L.

2017-01-01

Electrostatically actuated deformable mirrors with four concentric annular electrodes can exert independent control over defocus as well as primary, secondary, and tertiary spherical aberration. In this paper we use both numerical modeling and physical measurements to characterize recently developed deformable mirrors with respect to the amount of spherical aberration each can impart, and the dependence of that aberration control on the amount of defocus the mirror is providing. We find that a four-zone, 4 mm diameter mirror can generate surface shapes with arbitrary primary, secondary, and tertiary spherical aberration over ranges of ±0.4, ±0.2, and ±0.15 μm, respectively, referred to a non-normalized Zernike polynomial basis. We demonstrate the utility of this mirror for aberration-compensated focusing of a high NA optical system. PMID:27409212

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

NASA Astrophysics Data System (ADS)

Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; Nicholson, D. M.; Johnson, Duane D.

2014-11-01

The Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an efficient site-centered, electronic-structure technique for addressing an assembly of N scatterers. Wave functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number Lmax=(l,mmax), while scattering matrices, which determine spectral properties, are truncated at Lt r=(l,mt r) where phase shifts δl >ltr are negligible. Historically, Lmax is set equal to Lt r, which is correct for large enough Lmax but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for Lmax>Lt r with δl >ltr set to zero [X.-G. Zhang and W. H. Butler, Phys. Rev. B 46, 7433 (1992), 10.1103/PhysRevB.46.7433]. We present a numerically efficient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R3 process with rank N (ltr+1 ) 2 ] and includes higher-L contributions via linear algebra [R2 process with rank N (lmax+1) 2 ]. The augmented-KKR approach yields properly normalized wave functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe, and L 1 0 CoPt and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus Lmax for a given Lt r.

Green's function multiple-scattering theory with a truncated basis set: An augmented-KKR formalism

DOE PAGES

Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.; ...

2014-11-04

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L max = (l,m) max, while scattering matrices, which determine spectral properties, are truncated at L tr = (l,m) tr where phase shifts δl>l tr are negligible. Historically, L max is set equal to L tr, which is correct for large enough L max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L maxmore » > L tr with δl>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N(l tr + 1) 2] and includes higher-L contributions via linear algebra [R 2 process with rank N(l max +1) 2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 0 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L max for a given L tr.« less

Scattering and extinction by spherical particles immersed in an absorbing host medium

NASA Astrophysics Data System (ADS)

Mishchenko, Michael I.; Dlugach, Janna M.

2018-05-01

Many applications of electromagnetic scattering involve particles immersed in an absorbing rather than lossless medium, thereby making the conventional scattering theory potentially inapplicable. To analyze this issue quantitatively, we employ the FORTRAN program developed recently on the basis of the first-principles electromagnetic theory to study far-field scattering by spherical particles embedded in an absorbing infinite host medium. We further examine the phenomenon of negative extinction identified recently for monodisperse spheres and uncover additional evidence in favor of its interference origin. We identify the main effects of increasing the width of the size distribution on the ensemble-averaged extinction efficiency factor and show that negative extinction can be eradicated by averaging over a very narrow size distribution. We also analyze, for the first time, the effects of absorption inside the host medium and ensemble averaging on the phase function and other elements of the Stokes scattering matrix. It is shown in particular that increasing absorption significantly suppresses the interference structure and can result in a dramatic expansion of the areas of positive polarization. Furthermore, the phase functions computed for larger effective size parameters can develop a very deep minimum at side-scattering angles bracketed by a strong diffraction peak in the forward direction and a pronounced backscattering maximum.

Reconstruction of vibroacoustic responses of a highly nonspherical structure using Helmholtz equation least-squares method.

PubMed

Lu, Huancai; Wu, Sean F

2009-03-01

The vibroacoustic responses of a highly nonspherical vibrating object are reconstructed using Helmholtz equation least-squares (HELS) method. The objectives of this study are to examine the accuracy of reconstruction and the impacts of various parameters involved in reconstruction using HELS. The test object is a simply supported and baffled thin plate. The reason for selecting this object is that it represents a class of structures that cannot be exactly described by the spherical Hankel functions and spherical harmonics, which are taken as the basis functions in the HELS formulation, yet the analytic solutions to vibroacoustic responses of a baffled plate are readily available so the accuracy of reconstruction can be checked accurately. The input field acoustic pressures for reconstruction are generated by the Rayleigh integral. The reconstructed normal surface velocities are validated against the benchmark values, and the out-of-plane vibration patterns at several natural frequencies are compared with the natural modes of a simply supported plate. The impacts of various parameters such as number of measurement points, measurement distance, location of the origin of the coordinate system, microphone spacing, and ratio of measurement aperture size to the area of source surface of reconstruction on the resultant accuracy of reconstruction are examined.

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.

Theoretical nuclear physics

NASA Astrophysics Data System (ADS)

Rost, E.; Shephard, J. R.

1992-08-01

This report discusses the following topics: Exact 1-loop vacuum polarization effects in 1 + 1 dimensional QHD; exact 1-fermion loop contributions in 1 + 1 dimensional solitons; exact scalar 1-loop contributions in 1 + 3 dimensions; exact vacuum calculations in a hyper-spherical basis; relativistic nuclear matter with self-consistent correlation energy; consistent RHA-RPA for finite nuclei; transverse response functions in the (triangle)-resonance region; hadronic matter in a nontopological soliton model; scalar and vector contributions to (bar p)p yields (bar lambda)lambda reaction; 0+ and 2+ strengths in pion double-charge exchange to double giant-dipole resonances; and nucleons in a hybrid sigma model including a quantized pion field.

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.

Compression of head-related transfer function using autoregressive-moving-average models and Legendre polynomials.

PubMed

Shekarchi, Sayedali; Hallam, John; Christensen-Dalsgaard, Jakob

2013-11-01

Head-related transfer functions (HRTFs) are generally large datasets, which can be an important constraint for embedded real-time applications. A method is proposed here to reduce redundancy and compress the datasets. In this method, HRTFs are first compressed by conversion into autoregressive-moving-average (ARMA) filters whose coefficients are calculated using Prony's method. Such filters are specified by a few coefficients which can generate the full head-related impulse responses (HRIRs). Next, Legendre polynomials (LPs) are used to compress the ARMA filter coefficients. LPs are derived on the sphere and form an orthonormal basis set for spherical functions. Higher-order LPs capture increasingly fine spatial details. The number of LPs needed to represent an HRTF, therefore, is indicative of its spatial complexity. The results indicate that compression ratios can exceed 98% while maintaining a spectral error of less than 4 dB in the recovered HRTFs.

Application of the dual-kinetic-balance sets in the relativistic many-body problem of atomic structure

NASA Astrophysics Data System (ADS)

Beloy, Kyle; Derevianko, Andrei

2008-09-01

The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V.M. Shabaev et al., Phys. Rev. Lett. 93 (2004) 130405] is extended to problems with a non-local spherically-symmetric Dirac-Hartree-Fock potential. We implement the DKB method using B-spline basis sets and compare its performance with the widely-employed approach of Notre Dame (ND) group [W.R. Johnson, S.A. Blundell, J. Sapirstein, Phys. Rev. A 37 (1988) 307-315]. We compare the performance of the ND and DKB methods by computing various properties of Cs atom: energies, hyperfine integrals, the parity-non-conserving amplitude of the 6s-7s transition, and the second-order many-body correction to the removal energy of the valence electrons. We find that for a comparable size of the basis set the accuracy of both methods is similar for matrix elements accumulated far from the nuclear region. However, for atomic properties determined by small distances, the DKB method outperforms the ND approach. In addition, we present a strategy for optimizing the size of the basis sets by choosing progressively smaller number of basis functions for increasingly higher partial waves. This strategy exploits suppression of contributions of high partial waves to typical many-body correlation corrections.

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.

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.

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.

Parameterization of single-scattering properties of snow

NASA Astrophysics Data System (ADS)

Räisänen, Petri; Kokhanovsky, Alexander; Guyot, Gwennole; Jourdan, Olivier; Nousiainen, Timo

2015-04-01

Snow consists of non-spherical ice grains of various shapes and sizes, which are surrounded by air and sometimes covered by films of liquid water. Still, in many studies, homogeneous spherical snow grains have been assumed in radiative transfer calculations, due to the convenience of using Mie theory. More recently, second-generation Koch fractals have been employed. While they produce a relatively flat scattering phase function typical of deformed non-spherical particles, this is still a rather ad-hoc choice. Here, angular scattering measurements for blowing snow conducted during the CLimate IMpacts of Short-Lived pollutants In the Polar region (CLIMSLIP) campaign at Ny Ålesund, Svalbard, are used to construct a reference phase function for snow. Based on this phase function, an optimized habit combination (OHC) consisting of severely rough (SR) droxtals, aggregates of SR plates and strongly distorted Koch fractals is selected. The single-scattering properties of snow are then computed for the OHC as a function of wavelength λ and snow grain volume-to-projected area equivalent radius rvp. Parameterization equations are developed for λ=0.199-2.7 μm and rvp = 10-2000 μm, which express the single-scattering co-albedo β, the asymmetry parameter g and the phase function as functions of the size parameter and the real and imaginary parts of the refractive index. Compared to the reference values computed for the OHC, the accuracy of the parameterization is very high for β and g. This is also true for the phase function parameterization, except for strongly absorbing cases (β > 0.3). Finally, we consider snow albedo and reflected radiances for the suggested snow optics parameterization, making comparisons with spheres and distorted Koch fractals. Further evaluation and validation of the proposed approach against (e.g.) bidirectional reflectance and polarization measurements for snow is planned. At any rate, it seems safe to assume that the OHC selected here provides a substantially better basis for representing the single-scattering properties of snow than spheres do. Moreover, the parameterizations developed here are analytic and simple to use, and they can also be applied to the treatment of dirty snow following (e.g.) the approach of Kokhanovsky (The Cryosphere, 7, 1325-1331, doi:10.5194/tc-7-1325-2013, 2013). This should make them an attractive option for use in radiative transfer applications involving snow.

On the Contribution of Curl-Free Current Patterns to the Ultimate Intrinsic Signal-to-Noise Ratio at Ultra-High Field Strength.

PubMed

Pfrommer, Andreas; Henning, Anke

2017-05-01

The ultimate intrinsic signal-to-noise ratio (SNR) is a coil independent performance measure to compare different receive coil designs. To evaluate this benchmark in a sample, a complete electromagnetic basis set is required. The basis set can be obtained by curl-free and divergence-free surface current distributions, which excite linearly independent solutions to Maxwell's equations. In this work, we quantitatively investigate the contribution of curl-free current patterns to the ultimate intrinsic SNR in a spherical head-sized model at 9.4 T. Therefore, we compare the ultimate intrinsic SNR obtained with having only curl-free or divergence-free current patterns, with the ultimate intrinsic SNR obtained from a combination of curl-free and divergence-free current patterns. The influence of parallel imaging is studied for various acceleration factors. Moreover results for different field strengths (1.5 T up to 11.7 T) are presented at specific voxel positions and acceleration factors. The full-wave electromagnetic problem is analytically solved using dyadic Green's functions. We show, that at ultra-high field strength (B 0 ⩾7T) a combination of curl-free and divergence-free current patterns is required to achieve the best possible SNR at any position in a spherical head-sized model. On 1.5- and 3T platforms, divergence-free current patterns are sufficient to cover more than 90% of the ultimate intrinsic SNR. Copyright © 2017 John Wiley & Sons, Ltd.

Spherical sila- and germa-homoaromaticity.

PubMed

Chen, Zhongfang; Hirsch, Andreas; Nagase, Shigeru; Thiel, Walter; Schleyer, Paul von Ragué

2003-12-17

Guided by the 2(N + 1)2 electron-counting rule for spherical aromatic molecules, we have designed various spherical sila- and germa-homoaromatic systems rich in group 14 elements. Their aromaticity is revealed by density-functional computations of their structures and the nucleus-independent chemical shifts (NICS). Besides the formerly used endohedral inclusion strategy, spherical homoaromaticity is another way to stabilize silicon and germanium clusters.

A source with a 10{sup 13} DT neutron yield on the basis of a spherical plasma focus chamber

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

Zavyalov, N. V.; Maslov, V. V.; Rumyantsev, V. G., E-mail: rumyantsev@expd.vniief.ru

2013-03-15

Results from preliminary experimental research of neutron emission generated by a spherical plasma focus chamber filled with an equal-component deuterium-tritium mixture are presented. At a maximum current amplitude in the discharge chamber of {approx}1.5 MA, neutron pulses with a full width at half-maximum of 75-80 ns and an integral yield of {approx}1.3 Multiplication-Sign 10{sup 13} DT neutrons have been recorded.

Using radial NMR profiles to characterize pore size distributions

NASA Astrophysics Data System (ADS)

Deriche, Rachid; Treilhard, John

2012-02-01

Extracting information about axon diameter distributions in the brain is a challenging task which provides useful information for medical purposes; for example, the ability to characterize and monitor axon diameters would be useful in diagnosing and investigating diseases like amyotrophic lateral sclerosis (ALS)1 or autism.2 Three families of operators are defined by Ozarslan,3 whose action upon an NMR attenuation signal extracts the moments of the pore size distribution of the ensemble under consideration; also a numerical method is proposed to continuously reconstruct a discretely sampled attenuation profile using the eigenfunctions of the simple harmonic oscillator Hamiltonian: the SHORE basis. The work presented here extends Ozarlan's method to other bases that can offer a better description of attenuation signal behaviour; in particular, we propose the use of the radial Spherical Polar Fourier (SPF) basis. Testing is performed to contrast the efficacy of the radial SPF basis and SHORE basis in practical attenuation signal reconstruction. The robustness of the method to additive noise is tested and analysed. We demonstrate that a low-order attenuation signal reconstruction outperforms a higher-order reconstruction in subsequent moment estimation under noisy conditions. We propose the simulated annealing algorithm for basis function scale parameter estimation. Finally, analytic expressions are derived and presented for the action of the operators on the radial SPF basis (obviating the need for numerical integration, thus avoiding a spectrum of possible sources of error).

A new family of distribution functions for spherical galaxies

NASA Astrophysics Data System (ADS)

Gerhard, Ortwin E.

1991-06-01

The present study describes a new family of anisotropic distribution functions for stellar systems designed to keep control of the orbit distribution at fixed energy. These are quasi-separable functions of energy and angular momentum, and they are specified in terms of a circularity function h(x) which fixes the distribution of orbits on the potential's energy surfaces outside some anisotropy radius. Detailed results are presented for a particular set of radially anisotropic circularity functions h-alpha(x). In the scale-free logarithmic potential, exact analytic solutions are shown to exist for all scale-free circularity functions. Intrinsic and projected velocity dispersions are calculated and the expected properties are presented in extensive tables and graphs. Several applications of the quasi-separable distribution functions are discussed. They include the effects of anisotropy or a dark halo on line-broadening functions, the radial orbit instability in anisotropic spherical systems, and violent relaxation in spherical collapse.

The super-NFW model: an analytic dynamical model for cold dark matter haloes and elliptical galaxies

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Evans, N. Wyn; Sanders, Jason L.

2018-05-01

An analytic galaxy model with ρ ˜ r-1 at small radii and ρ ˜ r-3.5 at large radii is presented. The asymptotic density fall-off is slower than the Hernquist model, but faster than the Navarro-Frenk-White (NFW) profile for dark matter haloes, and so in accord with recent evidence from cosmological simulations. The model provides the zeroth-order term in a biorthornomal basis function expansion, meaning that axisymmetric, triaxial, and lopsided distortions can easily be added (much like the Hernquist model itself which is the zeroth-order term of the Hernquist-Ostriker expansion). The properties of the spherical model, including analytic distribution functions which are either isotropic, radially anisotropic, or tangentially anisotropic, are discussed in some detail. The analogue of the mass-concentration relation for cosmological haloes is provided.

Uniform electron gases. III. Low-density gases on three-dimensional spheres.

PubMed

Agboola, Davids; Knol, Anneke L; Gill, Peter M W; Loos, Pierre-François

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids - the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) - and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.

One- and two-center ETF-integrals of first order in relativistic calculation of NMR parameters

NASA Astrophysics Data System (ADS)

Slevinsky, R. M.; Temga, T.; Mouattamid, M.; Safouhi, H.

2010-06-01

The present work focuses on the analytical and numerical developments of first-order integrals involved in the relativistic calculation of the shielding tensor using exponential-type functions as a basis set of atomic orbitals. For the analytical development, we use the Fourier integral transformation and practical properties of spherical harmonics and the Rayleigh expansion of the plane wavefunctions. The Fourier transforms of the operators were derived in previous work and they are used for analytical development. In both the one- and two-center integrals, Cauchy's residue theorem is used in the final developments of the analytical expressions, which are shown to be accurate to machine precision.

Spherically Actuated Motor

NASA Technical Reports Server (NTRS)

Peeples, Steven

2015-01-01

A three degree of freedom (DOF) spherical actuator is proposed that will replace functions requiring three single DOF actuators in robotic manipulators providing space and weight savings while reducing the overall failure rate. Exploration satellites, Space Station payload manipulators, and rovers requiring pan, tilt, and rotate movements need an actuator for each function. Not only does each actuator introduce additional failure modes and require bulky mechanical gimbals, each contains many moving parts, decreasing mean time to failure. A conventional robotic manipulator is shown in figure 1. Spherical motors perform all three actuation functions, i.e., three DOF, with only one moving part. Given a standard three actuator system whose actuators have a given failure rate compared to a spherical motor with an equal failure rate, the three actuator system is three times as likely to fail over the latter. The Jet Propulsion Laboratory reliability studies of NASA robotic spacecraft have shown that mechanical hardware/mechanism failures are more frequent and more likely to significantly affect mission success than are electronic failures. Unfortunately, previously designed spherical motors have been unable to provide the performance needed by space missions. This inadequacy is also why they are unavailable commercially. An improved patentable spherically actuated motor (SAM) is proposed to provide the performance and versatility required by NASA missions.

Analytical expression for a class of spherically symmetric solutions in Lorentz-breaking massive gravity

NASA Astrophysics Data System (ADS)

Li, Ping; Li, Xin-zhou; Xi, Ping

2016-06-01

We present a detailed study of the spherically symmetric solutions in Lorentz-breaking massive gravity. There is an undetermined function { F }(X,{w}1,{w}2,{w}3) in the action of Stückelberg fields {S}φ ={{{Λ }}}4\\int {{{d}}}4x\\sqrt{-g}{ F }, which should be resolved through physical means. In general relativity, the spherically symmetric solution to the Einstein equation is a benchmark and its massive deformation also plays a crucial role in Lorentz-breaking massive gravity. { F } will satisfy the constraint equation {T}01=0 from the spherically symmetric Einstein tensor {G}01=0, if we maintain that any reasonable physical theory should possess the spherically symmetric solutions. The Stückelberg field {φ }i is taken as a ‘hedgehog’ configuration {φ }i=φ (r){x}i/r, whose stability is guaranteed by the topological one. Under this ansätz, {T}01=0 is reduced to d{ F }=0. The functions { F } for d{ F }=0 form a commutative ring {R}{ F }. We obtain an expression of the solution to the functional differential equation with spherical symmetry if { F }\\in {R}{ F }. If { F }\\in {R}{ F } and \\partial { F }/\\partial X=0, the functions { F } form a subring {S}{ F }\\subset {R}{ F }. We show that the metric is Schwarzschild, Schwarzschild-AdS or Schwarzschild-dS if { F }\\in {S}{ F }. When { F }\\in {R}{ F } but { F }\

X ray microscope assembly and alignment support and advanced x ray microscope design and analysis

NASA Technical Reports Server (NTRS)

Shealy, David L.

1991-01-01

Considerable efforts have been devoted recently to the design, analysis, fabrication, and testing of spherical Schwarzschild microscopes for soft x ray application in microscopy and projection lithography. The spherical Schwarzschild microscope consists of two concentric spherical mirrors configured such that the third order spherical aberration and coma are zero. Since multilayers are used on the mirror substrates for x ray applications, it is desirable to have only two reflecting surfaces in a microscope. In order to reduce microscope aberrations and increase the field of view, generalized mirror surface profiles have been considered in this investigation. Based on incoherent and sine wave modulation transfer function (MTF) calculations, the object plane resolution of a microscope has been analyzed as a function of the object height and numerical aperture (NA) of the primary for several spherical Schwarzschild, conic, and aspherical head reflecting two mirror microscope configurations.

Orbital dependent functionals: An atom projector augmented wave method implementation

NASA Astrophysics Data System (ADS)

Xu, Xiao

This thesis explores the formulation and numerical implementation of orbital dependent exchange-correlation functionals within electronic structure calculations. These orbital-dependent exchange-correlation functionals have recently received renewed attention as a means to improve the physical representation of electron interactions within electronic structure calculations. In particular, electron self-interaction terms can be avoided. In this thesis, an orbital-dependent functional is considered in the context of Hartree-Fock (HF) theory as well as the Optimized Effective Potential (OEP) method and the approximate OEP method developed by Krieger, Li, and Iafrate, known as the KLI approximation. In this thesis, the Fock exchange term is used as a simple well-defined example of an orbital-dependent functional. The Projected Augmented Wave (PAW) method developed by P. E. Blochl has proven to be accurate and efficient for electronic structure calculations for local and semi-local functions because of its accurate evaluation of interaction integrals by controlling multiple moments. We have extended the PAW method to treat orbital-dependent functionals in Hartree-Fock theory and the Optimized Effective Potential method, particularly in the KLI approximation. In the course of study we develop a frozen-core orbital approximation that accurately treats the core electron contributions for above three methods. The main part of the thesis focuses on the treatment of spherical atoms. We have investigated the behavior of PAW-Hartree Fock and PAW-KLI basis, projector, and pseudopotential functions for several elements throughout the periodic table. We have also extended the formalism to the treatment of solids in a plane wave basis and implemented PWPAW-KLI code, which will appear in future publications.

Effects of zonal flows on correlation between energy balance and energy conservation associated with nonlinear nonviscous atmospheric dynamics in a thin rotating spherical shell

NASA Astrophysics Data System (ADS)

Ibragimov, Ranis N.

2018-03-01

The nonlinear Euler equations are used to model two-dimensional atmosphere dynamics in a thin rotating spherical shell. The energy balance is deduced on the basis of two classes of functorially independent invariant solutions associated with the model. It it shown that the energy balance is exactly the conservation law for one class of the solutions whereas the second class of invariant solutions provides and asymptotic convergence of the energy balance to the conservation law.

Magnitude of finite-nucleus-size effects in relativistic density functional computations of indirect NMR nuclear spin-spin coupling constants.

PubMed

Autschbach, Jochen

2009-09-14

A spherical Gaussian nuclear charge distribution model has been implemented for spin-free (scalar) and two-component (spin-orbit) relativistic density functional calculations of indirect NMR nuclear spin-spin coupling (J-coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J-couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg(2) (2+), and Tl--X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite-nucleus effects.

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

NASA Astrophysics Data System (ADS)

Cai, Lin; Zhou, Zebing

2017-04-01

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

Implementation of Kane's Method for a Spacecraft Composed of Multiple Rigid Bodies

NASA Technical Reports Server (NTRS)

Stoneking, Eric T.

2013-01-01

Equations of motion are derived for a general spacecraft composed of rigid bodies connected via rotary (spherical or gimballed) joints in a tree topology. Several supporting concepts are developed in depth. Basis dyads aid in the transition from basis-free vector equations to component-wise equations. Joint partials allow abstraction of 1-DOF, 2-DOF, 3-DOF gimballed and spherical rotational joints to a common notation. The basic building block consisting of an "inner" body and an "outer" body connected by a joint enables efficient organization of arbitrary tree structures. Kane's equation is recast in a form which facilitates systematic assembly of large systems of equations, and exposes a relationship of Kane's equation to Newton and Euler's equations which is obscured by the usual presentation. The resulting system of dynamic equations is of minimum dimension, and is suitable for numerical solution by computer. Implementation is ·discussed, and illustrative simulation results are presented.

Spherical aberration yielding optimum visual performance: Evaluation of intraocular lenses using adaptive optics simulation

PubMed Central

Werner, John S.; Elliott, Sarah L.; Choi, Stacey S.; Doble, Nathan

2009-01-01

PURPOSE To evaluate the influence of spherical aberration on contrast sensitivity using adaptive optics. SETTING Vision Science and Advanced Retinal Imaging Laboratory, Department of Ophthalmology & Vision Science, University of California, Davis Medical Center, Sacramento, California, USA. METHODS Contrast sensitivity at 8 cycles per degree was evaluated using an adaptive optics system that permitted aberrations to be measured with a Shack-Hartman wavefront sensor and controlled by a 109 actuator continuous-surface deformable mirror that was at a plane conjugate to the observer’s pupil. Vertical Gabor patches were viewed through a 6.3 mm diameter pupil conjugate aperture. Contrast sensitivity was measured with the deformable mirror set to produce 1 of 5 spherical aberration profiles (−0.2 to +0.2 μm). Contrast sensitivity over the range of spherical aberration was fitted with a polynomial function. RESULTS Three observers (age 21 to 24 years) participated. The measured total mean spherical aberration resulting from the spherical aberration profiles produced by the deformable mirror was between −0.15 μm and +0.25 μm. The peak contrast sensitivity of this function for the 3 observers combined occurred at +0.06 μm of spherical aberration. The peak contrast sensitivity was also achieved with positive spherical aberration for observer (mean 0.09). CONCLUSION There was intersubject variability in the measurements; however, the average visual performance was best with the introduction of a small positive spherical aberration. PMID:19545813

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

Design and analysis of aspherical multilayer imaging X-ray microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.; Jiang, WU; Hoover, Richard B.

1991-01-01

Spherical Schwarzschild microscopes for soft X-ray applications in microscopy and projection lithography employ two concentric spherical mirrors that are configured such that the third-order spherical aberration and coma are zero. Based on incoherent, sine-wave MTF calculations, the object-plane resolution of a magnification-factor-20 microscope is presently analyzed as a function of object height and numerical aperture of the primary for several spherical Schwarzschild, conic, and aspherical two-mirror microscope configurations.

A numerical study of viscous vortex rings using a spectral method

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Discretising the velocity distribution for directional dark matter experiments

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

Kavanagh, Bradley J., E-mail: bradley.kavanagh@cea.fr

2015-07-01

Dark matter (DM) direct detection experiments which are directionally-sensitive may be the only method of probing the full velocity distribution function (VDF) of the Galactic DM halo. We present an angular basis for the DM VDF which can be used to parametrise the distribution in order to mitigate astrophysical uncertainties in future directional experiments and extract information about the DM halo. This basis consists of discretising the VDF in a series of angular bins, with the VDF being only a function of the DM speed v within each bin. In contrast to other methods, such as spherical harmonic expansions, themore » use of this basis allows us to guarantee that the resulting VDF is everywhere positive and therefore physical. We present a recipe for calculating the event rates corresponding to the discrete VDF for an arbitrary number of angular bins N and investigate the discretisation error which is introduced in this way. For smooth, Standard Halo Model-like distribution functions, only N=3 angular bins are required to achieve an accuracy of around 01–30% in the number of events in each bin. Shortly after confirmation of the DM origin of the signal with around 50 events, this accuracy should be sufficient to allow the discretised velocity distribution to be employed reliably. For more extreme VDFs (such as streams), the discretisation error is typically much larger, but can be improved with increasing N. This method paves the way towards an astrophysics-independent analysis framework for the directional detection of dark matter.« less

Discretising the velocity distribution for directional dark matter experiments

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

Kavanagh, Bradley J.; School of Physics & Astronomy, University of Nottingham,University Park, Nottingham, NG7 2RD

2015-07-13

Dark matter (DM) direct detection experiments which are directionally-sensitive may be the only method of probing the full velocity distribution function (VDF) of the Galactic DM halo. We present an angular basis for the DM VDF which can be used to parametrise the distribution in order to mitigate astrophysical uncertainties in future directional experiments and extract information about the DM halo. This basis consists of discretising the VDF in a series of angular bins, with the VDF being only a function of the DM speed v within each bin. In contrast to other methods, such as spherical harmonic expansions, themore » use of this basis allows us to guarantee that the resulting VDF is everywhere positive and therefore physical. We present a recipe for calculating the event rates corresponding to the discrete VDF for an arbitrary number of angular bins N and investigate the discretisation error which is introduced in this way. For smooth, Standard Halo Model-like distribution functions, only N=3 angular bins are required to achieve an accuracy of around 10–30% in the number of events in each bin. Shortly after confirmation of the DM origin of the signal with around 50 events, this accuracy should be sufficient to allow the discretised velocity distribution to be employed reliably. For more extreme VDFs (such as streams), the discretisation error is typically much larger, but can be improved with increasing N. This method paves the way towards an astrophysics-independent analysis framework for the directional detection of dark matter.« less

A coherent discrete variable representation method on a sphere

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

Yu, Hua -Gen

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

A coherent discrete variable representation method on a sphere

DOE PAGES

Yu, Hua -Gen

2017-09-05

Here, the coherent discrete variable representation (ZDVR) has been extended for construct- ing a multidimensional potential-optimized DVR basis on a sphere. In order to deal with the non-constant Jacobian in spherical angles, two direct product primitive basis methods are proposed so that the original ZDVR technique can be properly implemented. The method has been demonstrated by computing the lowest states of a two dimensional (2D) vibrational model. Results show that the extended ZDVR method gives accurate eigenval- ues and exponential convergence with increasing ZDVR basis size.

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.

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.

Underscreening in ionic liquids: a first principles analysis.

PubMed

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-07

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these 'primitive' and 'semi-primitive' models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length [Formula: see text], which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where [Formula: see text] increases with density beyond a critical density at which the Debye length [Formula: see text] becomes comparable to the ion diameter. In this high density regime the ratio [Formula: see text] increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

Underscreening in ionic liquids: a first principles analysis

NASA Astrophysics Data System (ADS)

Rotenberg, Benjamin; Bernard, Olivier; Hansen, Jean-Pierre

2018-02-01

An attempt is made to understand the underscreening effect, observed in concentrated electrolyte solutions or melts, on the basis of simple, admittedly crude models involving charged (for the ions) and neutral (for the solvent molecules) hard spheres. The thermodynamic and structural properties of these ‘primitive’ and ‘semi-primitive’ models are calculated within mean spherical approximation, which provides the basic input required to determine the partial density response functions. The screening length λS , which is unambiguously defined in terms of the wave-number-dependent response functions, exhibits a cross-over from a low density, Debye-like regime, to a regime where λS increases with density beyond a critical density at which the Debye length λD becomes comparable to the ion diameter. In this high density regime the ratio λ_S/λD increases according to a power law, in qualitative agreement with experimental measurements, albeit at a much slower rate.

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.

Tumour functional sphericity from PET images: prognostic value in NSCLC and impact of delineation method.

PubMed

Hatt, Mathieu; Laurent, Baptiste; Fayad, Hadi; Jaouen, Vincent; Visvikis, Dimitris; Le Rest, Catherine Cheze

2018-04-01

Sphericity has been proposed as a parameter for characterizing PET tumour volumes, with complementary prognostic value with respect to SUV and volume in both head and neck cancer and lung cancer. The objective of the present study was to investigate its dependency on tumour delineation and the resulting impact on its prognostic value. Five segmentation methods were considered: two thresholds (40% and 50% of SUV max ), ant colony optimization, fuzzy locally adaptive Bayesian (FLAB), and gradient-aided region-based active contour. The accuracy of each method in extracting sphericity was evaluated using a dataset of 176 simulated, phantom and clinical PET images of tumours with associated ground truth. The prognostic value of sphericity and its complementary value with respect to volume for each segmentation method was evaluated in a cohort of 87 patients with stage II/III lung cancer. Volume and associated sphericity values were dependent on the segmentation method. The correlation between segmentation accuracy and sphericity error was moderate (|ρ| from 0.24 to 0.57). The accuracy in measuring sphericity was not dependent on volume (|ρ| < 0.4). In the patients with lung cancer, sphericity had prognostic value, although lower than that of volume, except for that derived using FLAB for which when combined with volume showed a small improvement over volume alone (hazard ratio 2.67, compared with 2.5). Substantial differences in patient prognosis stratification were observed depending on the segmentation method used. Tumour functional sphericity was found to be dependent on the segmentation method, although the accuracy in retrieving the true sphericity was not dependent on tumour volume. In addition, even accurate segmentation can lead to an inaccurate sphericity value, and vice versa. Sphericity had similar or lower prognostic value than volume alone in the patients with lung cancer, except when determined using the FLAB method for which there was a small improvement in stratification when the parameters were combined.

Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields.

PubMed

Zhu, Wuming; Trickey, S B

2017-12-28

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li + , Be + , and B + , in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field.

Accurate and balanced anisotropic Gaussian type orbital basis sets for atoms in strong magnetic fields

NASA Astrophysics Data System (ADS)

Zhu, Wuming; Trickey, S. B.

2017-12-01

In high magnetic field calculations, anisotropic Gaussian type orbital (AGTO) basis functions are capable of reconciling the competing demands of the spherically symmetric Coulombic interaction and cylindrical magnetic (B field) confinement. However, the best available a priori procedure for composing highly accurate AGTO sets for atoms in a strong B field [W. Zhu et al., Phys. Rev. A 90, 022504 (2014)] yields very large basis sets. Their size is problematical for use in any calculation with unfavorable computational cost scaling. Here we provide an alternative constructive procedure. It is based upon analysis of the underlying physics of atoms in B fields that allow identification of several principles for the construction of AGTO basis sets. Aided by numerical optimization and parameter fitting, followed by fine tuning of fitting parameters, we devise formulae for generating accurate AGTO basis sets in an arbitrary B field. For the hydrogen iso-electronic sequence, a set depends on B field strength, nuclear charge, and orbital quantum numbers. For multi-electron systems, the basis set formulae also include adjustment to account for orbital occupations. Tests of the new basis sets for atoms H through C (1 ≤ Z ≤ 6) and ions Li+, Be+, and B+, in a wide B field range (0 ≤ B ≤ 2000 a.u.), show an accuracy better than a few μhartree for single-electron systems and a few hundredths to a few mHs for multi-electron atoms. The relative errors are similar for different atoms and ions in a large B field range, from a few to a couple of tens of millionths, thereby confirming rather uniform accuracy across the nuclear charge Z and B field strength values. Residual basis set errors are two to three orders of magnitude smaller than the electronic correlation energies in multi-electron atoms, a signal of the usefulness of the new AGTO basis sets in correlated wavefunction or density functional calculations for atomic and molecular systems in an external strong B field.

[Application of ordinary Kriging method in entomologic ecology].

PubMed

Zhang, Runjie; Zhou, Qiang; Chen, Cuixian; Wang, Shousong

2003-01-01

Geostatistics is a statistic method based on regional variables and using the tool of variogram to analyze the spatial structure and the patterns of organism. In simulating the variogram within a great range, though optimal simulation cannot be obtained, the simulation method of a dialogue between human and computer can be used to optimize the parameters of the spherical models. In this paper, the method mentioned above and the weighted polynomial regression were utilized to simulate the one-step spherical model, the two-step spherical model and linear function model, and the available nearby samples were used to draw on the ordinary Kriging procedure, which provided a best linear unbiased estimate of the constraint of the unbiased estimation. The sum of square deviation between the estimating and measuring values of varying theory models were figured out, and the relative graphs were shown. It was showed that the simulation based on the two-step spherical model was the best simulation, and the one-step spherical model was better than the linear function model.

Structure of spherical electric double layers with fully asymmetric electrolytes: a systematic study by Monte Carlo simulations and density functional theory.

PubMed

Patra, Chandra N

2014-11-14

A systematic investigation of the spherical electric double layers with the electrolytes having size as well as charge asymmetry is carried out using density functional theory and Monte Carlo simulations. The system is considered within the primitive model, where the macroion is a structureless hard spherical colloid, the small ions as charged hard spheres of different size, and the solvent is represented as a dielectric continuum. The present theory approximates the hard sphere part of the one particle correlation function using a weighted density approach whereas a perturbation expansion around the uniform fluid is applied to evaluate the ionic contribution. The theory is in quantitative agreement with Monte Carlo simulation for the density and the mean electrostatic potential profiles over a wide range of electrolyte concentrations, surface charge densities, valence of small ions, and macroion sizes. The theory provides distinctive evidence of charge and size correlations within the electrode-electrolyte interface in spherical geometry.

A hyper-spherical adaptive sparse-grid method for high-dimensional discontinuity detection

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

Zhang, Guannan; Webster, Clayton G.; Gunzburger, Max D.

This work proposes and analyzes a hyper-spherical adaptive hierarchical sparse-grid method for detecting jump discontinuities of functions in high-dimensional spaces is proposed. The method is motivated by the theoretical and computational inefficiencies of well-known adaptive sparse-grid methods for discontinuity detection. Our novel approach constructs a function representation of the discontinuity hyper-surface of an N-dimensional dis- continuous quantity of interest, by virtue of a hyper-spherical transformation. Then, a sparse-grid approximation of the transformed function is built in the hyper-spherical coordinate system, whose value at each point is estimated by solving a one-dimensional discontinuity detection problem. Due to the smoothness of themore » hyper-surface, the new technique can identify jump discontinuities with significantly reduced computational cost, compared to existing methods. Moreover, hierarchical acceleration techniques are also incorporated to further reduce the overall complexity. Rigorous error estimates and complexity analyses of the new method are provided as are several numerical examples that illustrate the effectiveness of the approach.« less

Variation in band gap energy and electrical analysis of double doped cobalt ferrite

NASA Astrophysics Data System (ADS)

Parveen, Azra; Agrawal, Shraddha; Azam, Ameer

2018-05-01

The Ca and Cr doped cobalt ferrite nanoparticles (Co0.9Ca0.1) (Fe0.8 Cr0.2)2O4 were synthesized by microwave gel combustion method. Microstructural studies were carried out by XRD and SEM. Structural studies suggest that the crystal system remains spinal even with the doping of calcium and chromium. The SEM image shows the spherical morphology of surface of the sample. Optical properties of Ca and Cr doped cobalt ferrite were studied by UV-visible technique in the range of 400-600 nm. The electrical conductivity of pure and doped cobalt ferrite were studied as a function of frequency and were explained on the basis of electron hopping.

Towards anti-causal Green's function for three-dimensional sub-diffraction focusing

NASA Astrophysics Data System (ADS)

Ma, Guancong; Fan, Xiying; Ma, Fuyin; de Rosny, Julien; Sheng, Ping; Fink, Mathias

2018-06-01

In causal physics, the causal Green's function describes the radiation of a point source. Its counterpart, the anti-causal Green's function, depicts a spherically converging wave. However, in free space, any converging wave must be followed by a diverging one. Their interference gives rise to the diffraction limit that constrains the smallest possible dimension of a wave's focal spot in free space, which is half the wavelength. Here, we show with three-dimensional acoustic experiments that we can realize a stand-alone anti-causal Green's function in a large portion of space up to a subwavelength distance from the focus point by introducing a near-perfect absorber for spherical waves at the focus. We build this subwavelength absorber based on membrane-type acoustic metamaterial, and experimentally demonstrate focusing of spherical waves beyond the diffraction limit.

A Novel Richardson-Lucy Model with Dictionary Basis and Spatial Regularization for Isolating Isotropic Signals.

PubMed

Xu, Tiantian; Feng, Yuanjing; Wu, Ye; Zeng, Qingrun; Zhang, Jun; He, Jianzhong; Zhuge, Qichuan

2017-01-01

Diffusion-weighted magnetic resonance imaging is a non-invasive imaging method that has been increasingly used in neuroscience imaging over the last decade. Partial volume effects (PVEs) exist in sampling signal for many physical and actual reasons, which lead to inaccurate fiber imaging. We overcome the influence of PVEs by separating isotropic signal from diffusion-weighted signal, which can provide more accurate estimation of fiber orientations. In this work, we use a novel response function (RF) and the correspondent fiber orientation distribution function (fODF) to construct different signal models, in which case the fODF is represented using dictionary basis function. We then put forward a new index Piso, which is a part of fODF to quantify white and gray matter. The classic Richardson-Lucy (RL) model is usually used in the field of digital image processing to solve the problem of spherical deconvolution caused by highly ill-posed least-squares algorithm. In this case, we propose an innovative model integrating RL model with spatial regularization to settle the suggested double-models, which improve noise resistance and accuracy of imaging. Experimental results of simulated and real data show that the proposal method, which we call iRL, can robustly reconstruct a more accurate fODF and the quantitative index Piso performs better than fractional anisotropy and general fractional anisotropy.

A Novel Richardson-Lucy Model with Dictionary Basis and Spatial Regularization for Isolating Isotropic Signals

PubMed Central

Feng, Yuanjing; Wu, Ye; Zeng, Qingrun; Zhang, Jun; He, Jianzhong; Zhuge, Qichuan

2017-01-01

Diffusion-weighted magnetic resonance imaging is a non-invasive imaging method that has been increasingly used in neuroscience imaging over the last decade. Partial volume effects (PVEs) exist in sampling signal for many physical and actual reasons, which lead to inaccurate fiber imaging. We overcome the influence of PVEs by separating isotropic signal from diffusion-weighted signal, which can provide more accurate estimation of fiber orientations. In this work, we use a novel response function (RF) and the correspondent fiber orientation distribution function (fODF) to construct different signal models, in which case the fODF is represented using dictionary basis function. We then put forward a new index Piso, which is a part of fODF to quantify white and gray matter. The classic Richardson-Lucy (RL) model is usually used in the field of digital image processing to solve the problem of spherical deconvolution caused by highly ill-posed least-squares algorithm. In this case, we propose an innovative model integrating RL model with spatial regularization to settle the suggested double-models, which improve noise resistance and accuracy of imaging. Experimental results of simulated and real data show that the proposal method, which we call iRL, can robustly reconstruct a more accurate fODF and the quantitative index Piso performs better than fractional anisotropy and general fractional anisotropy. PMID:28081561

Uniform electron gases. III. Low-density gases on three-dimensional spheres

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

Agboola, Davids; Knol, Anneke L.; Gill, Peter M. W., E-mail: peter.gill@anu.edu.au

2015-08-28

By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGFmore » centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.« less

Stable computations with flat radial basis functions using vector-valued rational approximations

NASA Astrophysics Data System (ADS)

Wright, Grady B.; Fornberg, Bengt

2017-02-01

One commonly finds in applications of smooth radial basis functions (RBFs) that scaling the kernels so they are 'flat' leads to smaller discretization errors. However, the direct numerical approach for computing with flat RBFs (RBF-Direct) is severely ill-conditioned. We present an algorithm for bypassing this ill-conditioning that is based on a new method for rational approximation (RA) of vector-valued analytic functions with the property that all components of the vector share the same singularities. This new algorithm (RBF-RA) is more accurate, robust, and easier to implement than the Contour-Padé method, which is similarly based on vector-valued rational approximation. In contrast to the stable RBF-QR and RBF-GA algorithms, which are based on finding a better conditioned base in the same RBF-space, the new algorithm can be used with any type of smooth radial kernel, and it is also applicable to a wider range of tasks (including calculating Hermite type implicit RBF-FD stencils). We present a series of numerical experiments demonstrating the effectiveness of this new method for computing RBF interpolants in the flat regime. We also demonstrate the flexibility of the method by using it to compute implicit RBF-FD formulas in the flat regime and then using these for solving Poisson's equation in a 3-D spherical shell.

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

Alam, Aftab; Khan, Suffian N.; Smirnov, A. V.

Korringa-Kohn-Rostoker (KKR) Green's function, multiple-scattering theory is an ecient sitecentered, electronic-structure technique for addressing an assembly of N scatterers. Wave-functions are expanded in a spherical-wave basis on each scattering center and indexed up to a maximum orbital and azimuthal number L max = (l,m) max, while scattering matrices, which determine spectral properties, are truncated at L tr = (l,m) tr where phase shifts δl>l tr are negligible. Historically, L max is set equal to L tr, which is correct for large enough L max but not computationally expedient; a better procedure retains higher-order (free-electron and single-site) contributions for L maxmore » > L tr with δl>l tr set to zero [Zhang and Butler, Phys. Rev. B 46, 7433]. We present a numerically ecient and accurate augmented-KKR Green's function formalism that solves the KKR equations by exact matrix inversion [R 3 process with rank N(l tr + 1) 2] and includes higher-L contributions via linear algebra [R 2 process with rank N(l max +1) 2]. Augmented-KKR approach yields properly normalized wave-functions, numerically cheaper basis-set convergence, and a total charge density and electron count that agrees with Lloyd's formula. We apply our formalism to fcc Cu, bcc Fe and L1 0 CoPt, and present the numerical results for accuracy and for the convergence of the total energies, Fermi energies, and magnetic moments versus L max for a given L tr.« less

Effect of 3-D viscoelastic structure on post-seismic relaxation from the 2004 M = 9.2 Sumatra earthquake

USGS Publications Warehouse

Pollitz, F.; Banerjee, P.; Grijalva, K.; Nagarajan, B.; Burgmann, R.

2008-01-01

The 2004 M=9.2 Sumatra-Andaman earthquake profoundly altered the state of stress in a large volume surrounding the ???1400 km long rupture. Induced mantle flow fields and coupled surface deformation are sensitive to the 3-D rheology structure. To predict the post-seismic motions from this earthquake, relaxation of a 3-D spherical viscoelastic earth model is simulated using the theory of coupled normal modes. The quasi-static deformation basis set and solution on the 3-D model is constructed using: a spherically stratified viscoelastic earth model with a linear stress-strain relation; an aspherical perturbation in viscoelastic structure; a 'static'mode basis set consisting of Earth's spheroidal and toroidal free oscillations; a "viscoelastic" mode basis set; and interaction kernels that describe the coupling among viscoelastic and static modes. Application to the 2004 Sumatra-Andaman earthquake illustrates the profound modification of the post-seismic flow field at depth by a slab structure and similarly large effects on the near-field post-seismic deformation field at Earth's surface. Comparison with post-seismic GPS observations illustrates the extent to which viscoelastic relaxation contributes to the regional post-seismic deformation. ?? Journal compilation ?? 2008 RAS.

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.

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.

Rough surfaces: Is the dark stuff just shadow?. ;Who knows what evil lurks in the hearts of men? The shadow knows!;☆

NASA Astrophysics Data System (ADS)

Cuzzi, Jeffrey N.; Chambers, Lindsey B.; Hendrix, Amanda R.

2017-06-01

Remote observations of the surfaces of airless planetary objects are fundamental to inferring the physical structure and compositional makeup of the surface material. A number of forward models have been developed to reproduce the photometric behavior of these surfaces, based on specific, assumed structural properties such as macroscopic roughness and associated shadowing. Most work of this type is applied to geometric albedos, which are affected by complicated effects near zero phase angle that represent only a tiny fraction of the net energy reflected by the object. Other applications include parameter fits to resolved portions of some planetary surface as viewed over a range of geometries. The spherical albedo of the entire object (when it can be determined) captures the net energy balance of the particle more robustly than the geometric albedo. In most treatments involving spherical albedos, spherical albedos and particle phase functions are often treated as if they are independent, neglecting the effects of roughness. In this paper we take a different approach. We note that whatever function captures the phase angle dependence of the brightness of a realistic rough, shadowed, flat surface element relative to that of a smooth granular surface of the same material, it is manifested directly in both the integral phase function and the spherical albedo of the object. We suggest that, where broad phase angle coverage is possible, spherical albedos may be easily corrected for the effects of shadowing using observed (or assumed) phase functions, and then modeled more robustly using smooth-surface regolith radiative transfer models without further imposed (forward-modeled) shadowing corrections. Our approach attributes observed "powerlaw" phase functions of various slope (and "linear" ranges of magnitude-vs.-phase angle) to shadowing, as have others, and goes in to suggest that regolith-model-based inferences of composition based on shadow-uncorrected spherical albedos overestimate the amount of absorbing material contained in the regolith.

Rough Surfaces: Is the Dark Stuff Just Shadow?: "Who knows what evil lurks in the hearts of men? The shadow knows!"

NASA Technical Reports Server (NTRS)

Cuzzi, Jeffrey N.; Chambers, Lindsey B.; Hendrix, Amanda R.

2016-01-01

Remote observations of the surfaces of airless planetary objects are fundamental to inferring the physical structure and compositional makeup of the surface material. A number of forward models have been developed to reproduce the photometric behavior of these surfaces, based on specific, assumed structural properties such as macroscopic roughness and associated shadowing. Most work of this type is applied to geometric albedos, which are affected by complicated effects near zero phase angle that represent only a tiny fraction of the net energy reflected by the object. Other applications include parameter fits to resolved portions of some planetary surface as viewed over a range of geometries. The spherical albedo of the entire object (when it can be determined) captures the net energy balance of the particle more robustly than the geometric albedo. In most treatments involving spherical albedos, spherical albedos and particle phase functions are often treated as if they are independent, neglecting the effects of roughness. In this paper we take a different approach. We note that whatever function captures the phase angle dependence of the brightness of a realistic rough, shadowed, flat surface element relative to that of a smooth granular surface of the same material, it is manifested directly in both the integral phase function and the spherical albedo of the object. We suggest that, where broad phase angle coverage is possible, spherical albedos may be easily corrected for the effects of shadowing using observed (or assumed) phase functions, and then modeled more robustly using smooth-surface regolith radiative transfer models without further imposed (forward-modeled) shadowing corrections. Our approach attributes observed "power law" phase functions of various slope (and "linear" ranges of magnitude-vs.-phase angle) to shadowing, as have others, and goes on to suggest that regolith-model-based inferences of composition based on shadow-uncorrected spherical albedos overestimate the amount of absorbing material contained in the regolith.

Expressions for the spherical-wave-structure function based on a bump spectrum model for the index of refraction

NASA Astrophysics Data System (ADS)

Richardson, Christina E.; Andrews, Larry C.

1991-07-01

New spectra models have recently been developed for the spatial power spectra of temperature and refractive index fluctuations in the atmospheric boundary layer showing the characteristic 'bump' just prior to the dissipation ranges. Theoretical work involving these new models has led to new expressions for the phase structure function associated with a plane optical wave, although most experimental work has involved spherical waves. Following techniques similar to those used for the plane wave analysis, new expressions valid in geometrical and diffraction regimes are developed here for the phase structure function of a spherical optical wave propagating through clear-air atmospheric turbulence. Useful asymptotic formulas for small separation distances and the inertial subrange are derived from these general expressions.

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

Spontaneous spherical symmetry breaking in atomic confinement

NASA Astrophysics Data System (ADS)

Sveshnikov, Konstantin; Tolokonnikov, Andrey

2017-07-01

The effect of spontaneous breaking of initial SO(3) symmetry is shown to be possible for an H-like atom in the ground state, when it is confined in a spherical box under general boundary conditions of "not going out" through the box surface (i.e. third kind or Robin's ones), for a wide range of physically reasonable values of system parameters. The most novel and nontrivial result, which has not been reported previously, is that such an effect takes place not only for attractive, but also for repulsive interactions of atomic electrons with the cavity environment. Moreover, in the limit of a large box size R ≫ aB the regime of an atom, soaring over a plane with boundary condition of "not going out", is reproduced, rather than a spherically symmetric configuration, which would be expected on the basis of the initial SO(3) symmetry of the problem.

Ion beam-induced shaping of Ni nanoparticles embedded in a silica matrix: from spherical to prolate shape

PubMed Central

2011-01-01

Present work reports the elongation of spherical Ni nanoparticles (NPs) parallel to each other, due to bombardment with 120 MeV Au+9 ions at a fluence of 5 × 1013 ions/cm2. The Ni NPs embedded in silica matrix have been prepared by atom beam sputtering technique and subsequent annealing. The elongation of Ni NPs due to interaction with Au+9 ions as investigated by cross-sectional transmission electron microscopy (TEM) shows a strong dependence on initial Ni particle size and is explained on the basis of thermal spike model. Irradiation induces a change from single crystalline nature of spherical particles to polycrystalline nature of elongated particles. Magnetization measurements indicate that changes in coercivity (Hc) and remanence ratio (Mr/Ms) are stronger in the ion beam direction due to the preferential easy axis of elongated particles in the beam direction. PMID:21711659

The numerical design of a spherical baroclinic experiment for Spacelab flights

NASA Technical Reports Server (NTRS)

Fowlis, W. W.; Roberts, G. O.

1982-01-01

The near-zero G environment of Spacelab is the basis of a true spherical experimental model of synoptic scale baroclinic atmospheric processes, using a radial dielectric body force analogous to gravity over a volume of liquid within two concentric spheres. The baroclinic motions are generated by corotating the spheres and imposing thermal boundary conditions, such that the liquid is subjected to a stable radial gradient and a latitudinal gradient. Owing to mathematical difficulties associated with the spherical geometry, quantitative design criteria can be acquired only by means of numerical models. The procedure adopted required the development of two computer codes based on the Navier-Stokes equations. The codes, of which the first calculates axisymmetric steady flow solutions and the second determines the growth or decay rates of linear wave perturbations with different wave numbers, are combined to generate marginal stability curves.

Electrowetting-actuated zoom lens with spherical-interface liquid lenses.

PubMed

Peng, Runling; Chen, Jiabi; Zhuang, Songlin

2008-11-01

The interface shape of two immiscible liquids in a conical chamber is discussed. The analytical solution of the differential equation describing the interface shape shows that the interface shape is completely spherical when the density difference of two liquids is zero. On the basis of the spherical-interface shape and an energy-minimization method, explicit calculations and detailed analyses of an extended Young-type equation for the conical double-liquid lens are given. Finally, a novel design of a zoom lens system without motorized movements is proposed. The lens system consists of a fixed lens and two conical double-liquid variable-focus lenses. The structure and principle of the lens system are introduced in this paper. Taking finite objects as example, detailed calculations and simulation examples are presented to predict how two liquid lenses are related to meet the basic requirements of zoom lenses.

A Phase-Space Approach to Collisionless Stellar Systems Using a Particle Method

NASA Astrophysics Data System (ADS)

Hozumi, Shunsuke

1997-10-01

A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem, which states that the distribution function (DF) at time t can be derived from tracing necessary orbits back to t = 0. To make this procedure feasible, a self-consistent field (SCF) method for solving Poisson's equation is adopted to compute the orbits of arbitrary stars. As an example, for the violent relaxation of a uniform density sphere, the phase-space evolution generated by the current method is compared to that obtained with a phase-space method for integrating the collisionless Boltzmann equation, on the assumption of spherical symmetry. Excellent agreement is found between the two methods if an optimal basis set for the SCF technique is chosen. Since this reproduction method requires only the functional form of initial DFs and does not require any assumptions to be made about the symmetry of the system, success in reproducing the phase-space evolution implies that there would be no need of directly solving the collisionless Boltzmann equation in order to access phase space even for systems without any special symmetries. The effects of basis sets used in SCF simulations on the reproduced phase space are also discussed.

A Practical Computational Method for the Anisotropic Redshift-Space 3-Point Correlation Function

NASA Astrophysics Data System (ADS)

Slepian, Zachary; Eisenstein, Daniel J.

2018-04-01

We present an algorithm enabling computation of the anisotropic redshift-space galaxy 3-point correlation function (3PCF) scaling as N2, with N the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with this scaling by expanding the radially-binned density field around each galaxy in the survey into spherical harmonics and combining these coefficients to form multipole moments. The N2 scaling occurred because this approach never explicitly required the relative angle between a galaxy pair about the primary galaxy. Here we generalize this work, demonstrating that in the presence of azimuthally-symmetric anisotropy produced by redshift-space distortions (RSD) the 3PCF can be described by two triangle side lengths, two independent total angular momenta, and a spin. This basis for the anisotropic 3PCF allows its computation with negligible additional work over the isotropic 3PCF. We also present the covariance matrix of the anisotropic 3PCF measured in this basis. Our algorithm tracks the full 5-D redshift-space 3PCF, uses an accurate line of sight to each triplet, is exact in angle, and easily handles edge correction. It will enable use of the anisotropic large-scale 3PCF as a probe of RSD in current and upcoming large-scale redshift surveys.

Gas Generation Testing of Spherical Resorcinol-Formaldehyde (sRF) Resin

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

Colburn, Heather A.; Bryan, Samuel A.; Camaioni, Donald M.

This report describes gas generation testing of the spherical resorcinol-formaldehyde (sRF) resin that was conducted to support the technology maturation of the LAWPS facility. The current safety basis for the LAWPS facility is based primarily on two studies that had limited or inconclusive data sets. The two studies indicated a 40% increase in hydrogen generation rate of water (as predicted by the Hu model) with sRF resin over water alone. However, the previous studies did not test the range of conditions (process fluids and temperatures) that are expected in the LAWPS facility. Additionally, the previous studies did not obtain replicatemore » test results or comparable liquid-only control samples. All of the testing described in this report, conducted with water, 0.45M nitric acid, and waste simulants with and without sRF resin, returned hydrogen generation rates that are within the current safety basis for the facility of 1.4 times the Hu model output for water.« less

A Kinect-Based Real-Time Compressive Tracking Prototype System for Amphibious Spherical Robots

PubMed Central

Pan, Shaowu; Shi, Liwei; Guo, Shuxiang

2015-01-01

A visual tracking system is essential as a basis for visual servoing, autonomous navigation, path planning, robot-human interaction and other robotic functions. To execute various tasks in diverse and ever-changing environments, a mobile robot requires high levels of robustness, precision, environmental adaptability and real-time performance of the visual tracking system. In keeping with the application characteristics of our amphibious spherical robot, which was proposed for flexible and economical underwater exploration in 2012, an improved RGB-D visual tracking algorithm is proposed and implemented. Given the limited power source and computational capabilities of mobile robots, compressive tracking (CT), which is the effective and efficient algorithm that was proposed in 2012, was selected as the basis of the proposed algorithm to process colour images. A Kalman filter with a second-order motion model was implemented to predict the state of the target and select candidate patches or samples for the CT tracker. In addition, a variance ratio features shift (VR-V) tracker with a Kalman estimation mechanism was used to process depth images. Using a feedback strategy, the depth tracking results were used to assist the CT tracker in updating classifier parameters at an adaptive rate. In this way, most of the deficiencies of CT, including drift and poor robustness to occlusion and high-speed target motion, were partly solved. To evaluate the proposed algorithm, a Microsoft Kinect sensor, which combines colour and infrared depth cameras, was adopted for use in a prototype of the robotic tracking system. The experimental results with various image sequences demonstrated the effectiveness, robustness and real-time performance of the tracking system. PMID:25856331

A Kinect-based real-time compressive tracking prototype system for amphibious spherical robots.

PubMed

Pan, Shaowu; Shi, Liwei; Guo, Shuxiang

2015-04-08

A visual tracking system is essential as a basis for visual servoing, autonomous navigation, path planning, robot-human interaction and other robotic functions. To execute various tasks in diverse and ever-changing environments, a mobile robot requires high levels of robustness, precision, environmental adaptability and real-time performance of the visual tracking system. In keeping with the application characteristics of our amphibious spherical robot, which was proposed for flexible and economical underwater exploration in 2012, an improved RGB-D visual tracking algorithm is proposed and implemented. Given the limited power source and computational capabilities of mobile robots, compressive tracking (CT), which is the effective and efficient algorithm that was proposed in 2012, was selected as the basis of the proposed algorithm to process colour images. A Kalman filter with a second-order motion model was implemented to predict the state of the target and select candidate patches or samples for the CT tracker. In addition, a variance ratio features shift (VR-V) tracker with a Kalman estimation mechanism was used to process depth images. Using a feedback strategy, the depth tracking results were used to assist the CT tracker in updating classifier parameters at an adaptive rate. In this way, most of the deficiencies of CT, including drift and poor robustness to occlusion and high-speed target motion, were partly solved. To evaluate the proposed algorithm, a Microsoft Kinect sensor, which combines colour and infrared depth cameras, was adopted for use in a prototype of the robotic tracking system. The experimental results with various image sequences demonstrated the effectiveness, robustness and real-time performance of the tracking system.

Application of close-packed structures in dental resin composites.

PubMed

Wang, Ruili; Habib, Eric; Zhu, X X

2017-03-01

The inorganic filler particles in dental resin composites serve to improve their mechanical properties and reduce polymerization shrinkage during their use. Efforts have been made in academia and industry to increase the filler particle content, but, few studies examine the theoretical basis for the maximum particle loading. This work evaluates the packing of spherical particles in a close-packed state for highly loaded composites. Calculations show that for low dispersity particles, the maximum amount of particles is 74.05vol%, regardless of the particle size. This can be further improved by using a mix of large and small particles or by the use of non-spherical particles. For representative spherical particles with a diameter of 1000nm, two types of secondary particles with respective sizes of 414nm (d I ) and 225nm (d II ) are selected. The results show that after embedding secondary particles I & II into primary spherical particles, the packing factor is increased to 81.19% for the close-packed structures, which shows an improvement of 9.64%, compared to the 74.05% obtained only with primary spherical particles. This packing factor is also higher than either structure with the embedded secondary particles I or II. Examples of these mixtures with different spherical particle sizes are shown as a theoretical estimation, serving as a guideline for the design and formulation of new dental resin composites with better properties and improved performance. Copyright © 2017 The Academy of Dental Materials. Published by Elsevier Ltd. All rights reserved.

On the efficiency of treating singularities in triatomic variational vibrational computations. The vibrational states of H(+)3 up to dissociation.

PubMed

Szidarovszky, Tamás; Császár, Attila G; Czakó, Gábor

2010-08-01

Several techniques of varying efficiency are investigated, which treat all singularities present in the triatomic vibrational kinetic energy operator given in orthogonal internal coordinates of the two distances-one angle type. The strategies are based on the use of a direct-product basis built from one-dimensional discrete variable representation (DVR) bases corresponding to the two distances and orthogonal Legendre polynomials, or the corresponding Legendre-DVR basis, corresponding to the angle. The use of Legendre functions ensures the efficient treatment of the angular singularity. Matrix elements of the singular radial operators are calculated employing DVRs using the quadrature approximation as well as special DVRs satisfying the boundary conditions and thus allowing for the use of exact DVR expressions. Potential optimized (PO) radial DVRs, based on one-dimensional Hamiltonians with potentials obtained by fixing or relaxing the two non-active coordinates, are also studied. The numerical calculations employed Hermite-DVR, spherical-oscillator-DVR, and Bessel-DVR bases as the primitive radial functions. A new analytical formula is given for the determination of the matrix elements of the singular radial operator using the Bessel-DVR basis. The usually claimed failure of the quadrature approximation in certain singular integrals is revisited in one and three dimensions. It is shown that as long as no potential optimization is carried out the quadrature approximation works almost as well as the exact DVR expressions. If wave functions with finite amplitude at the boundary are to be computed, the basis sets need to meet the required boundary conditions. The present numerical results also confirm that PO-DVRs should be constructed employing relaxed potentials and PO-DVRs can be useful for optimizing quadrature points for calculations applying large coordinate intervals and describing large-amplitude motions. The utility and efficiency of the different algorithms is demonstrated by the computation of converged near-dissociation vibrational energy levels for the H molecular ion.

Aircraft navigation and surveillance analysis for a spherical earth

DOT National Transportation Integrated Search

2014-10-01

This memorandum addresses a fundamental function in surveillance and navigation analysis : quantifying the geometry of two or more locations relative to each other and to a spherical earth. Here, geometry refers to: (a) points (idealized lo...

On the divergence of triangular and eccentric spherical sums of double Fourier series

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

Karagulyan, G A

We construct a continuous function on the torus with almost everywhere divergent triangular sums of double Fourier series. We also prove an analogous theorem for eccentric spherical sums. Bibliography: 14 titles.

Impact of spherical nanoparticles on nematic order parameters

NASA Astrophysics Data System (ADS)

Kyrou, C.; Kralj, S.; Panagopoulou, M.; Raptis, Y.; Nounesis, G.; Lelidis, I.

2018-04-01

We study experimentally the impact of spherical nanoparticles on the orientational order parameters of a host nematic liquid crystal. We use spherical core-shell quantum dots that are surface functionalized to promote homeotropic anchoring on their interface with the liquid crystal host. We show experimentally that the orientational order may be strongly affected by the presence of spherical nanoparticles even at low concentrations. The orientational order of the composite system is probed by means of polarized micro-Raman spectroscopy and by optical birefringence measurements as function of temperature and concentration. Our data show that the orientational order depends on the concentration in a nonlinear way, and the existence of a crossover concentration χc≈0.004 pw . It separates two different regimes exhibiting pure-liquid crystal like (χ <χc ) and distorted-nematic ordering (χ >χc ), respectively. In the latter phase the degree of ordering is lower with respect to the pure-liquid crystal nematic phase.

Estimation of the outer-sphere contribution to the activation volume for electron exchange reactions using the mean spherical approximation

NASA Astrophysics Data System (ADS)

Takagi, Hideo D.; Swaddle, Thomas W.

1996-01-01

The outer-sphere contribution to the volume of activation of homogeneous electron exchange reactions is estimated for selected solvents on the basis of the mean spherical approximation (MSA), and the calculated values are compared with those estimated by the Strank-Hush-Marcus (SHM) theory and with activation volumes obtained experimentally for the electron exchange reaction between tris(hexafluoroacetylacetonato)ruthenium(III) and -(II) in acetone, acetonitrile, methanol and chloroform. The MSA treatment, which recognizes the molecular nature of the solvent, does not improve significantly upon the continuous-dielectric SHM theory, which represents the experimental data adequately for the more polar solvents.

Spherical mirror grazing incidence x-ray optics

NASA Technical Reports Server (NTRS)

Cash, Jr., Webster C. (Inventor)

1997-01-01

An optical system for x-rays combines at least two spherical or near spherical mirrors for each dimension in grazing incidence orientation to provide the functions of a lens in the x-ray region. To focus x-ray radiation in both the X and the Y dimensions, one of the mirrors focusses the X dimension, a second mirror focusses the Y direction, a third mirror corrects the X dimension by removing comatic aberration and a fourth mirror corrects the Y dimension. Spherical aberration may also be removed for an even better focus. The order of the mirrors is unimportant.

Analysis of scattering by a linear chain of spherical inclusions in an optical fiber

NASA Astrophysics Data System (ADS)

Chremmos, Ioannis D.; Uzunoglu, Nikolaos K.

2006-12-01

The scattering by a linear chain of spherical dielectric inclusions, embedded along the axis of an optical fiber, is analyzed using a rigorous integral equation formulation, based on the dyadic Green's function theory. The coupled electric field integral equations are solved by applying the Galerkin technique with Mie-type expansion of the field inside the spheres in terms of spherical waves. The analysis extends the previously studied case of a single spherical inhomogeneity inside a fiber to the multisphere-scattering case, by utilizing the classic translational addition theorems for spherical waves in order to analytically extract the direct-intersphere-coupling coefficients. Results for the transmitted and reflected power, on incidence of the fundamental HE11 mode, are presented for several cases.

Modeling mantle convection in the spherical annulus

NASA Astrophysics Data System (ADS)

Hernlund, John W.; Tackley, Paul J.

2008-12-01

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

Three-body spectrum in a finite volume: The role of cubic symmetry

DOE PAGES

Doring, M.; Hammer, H. -W.; Mai, M.; ...

2018-06-15

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

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

Three-body spectrum in a finite volume: The role of cubic symmetry

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

Doring, M.; Hammer, H. -W.; Mai, M.

The three-particle quantization condition is partially diagonalized in the center-of-mass frame by using cubic symmetry on the lattice. To this end, instead of spherical harmonics, the kernel of the Bethe-Salpeter equation for particle-dimer scattering is expanded in the basis functions of different irreducible representations of the octahedral group. Such a projection is of particular importance for the three-body problem in the finite volume due to the occurrence of three-body singularities above breakup. Additionally, we study the numerical solution and properties of such a projected quantization condition in a simple model. It is shown that, for large volumes, these solutions allowmore » for an instructive interpretation of the energy eigenvalues in terms of bound and scattering states.« less

Numerical solutions of the macroscopic Maxwell equations for scattering by non-spherical particles: A tutorial review

NASA Astrophysics Data System (ADS)

Kahnert, Michael

2016-07-01

Numerical solution methods for electromagnetic scattering by non-spherical particles comprise a variety of different techniques, which can be traced back to different assumptions and solution strategies applied to the macroscopic Maxwell equations. One can distinguish between time- and frequency-domain methods; further, one can divide numerical techniques into finite-difference methods (which are based on approximating the differential operators), separation-of-variables methods (which are based on expanding the solution in a complete set of functions, thus approximating the fields), and volume integral-equation methods (which are usually solved by discretisation of the target volume and invoking the long-wave approximation in each volume cell). While existing reviews of the topic often tend to have a target audience of program developers and expert users, this tutorial review is intended to accommodate the needs of practitioners as well as novices to the field. The required conciseness is achieved by limiting the presentation to a selection of illustrative methods, and by omitting many technical details that are not essential at a first exposure to the subject. On the other hand, the theoretical basis of numerical methods is explained with little compromises in mathematical rigour; the rationale is that a good grasp of numerical light scattering methods is best achieved by understanding their foundation in Maxwell's theory.

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.

Large-Angle Magnetic Suspension (LAMS)

NASA Technical Reports Server (NTRS)

Oglevie, Ronald E.; Eisenhaure, David B.; Downer, James R.

1988-01-01

Spherical LAMS is magnetic syspension that provides dual functions of magnetic bearing and rotorgimbal system. Provides two degrees of angular freedom within single magnetic suspension system. Approach employs spherically-shaped magnetic-gap surfaces to achieve much-larger angular freedom than available from previous suspensions.

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.

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.

Electrostatic field and charge distribution in small charged dielectric droplets

NASA Astrophysics Data System (ADS)

Storozhev, V. B.

2004-08-01

The charge distribution in small dielectric droplets is calculated on the basis of continuum medium approximation. There are considered charged liquid spherical droplets of methanol in the range of nanometer sizes. The problem is solved by the following way. We find the free energy of some ion in dielectric droplet, which is a function of distribution of other ions in the droplet. The probability of location of the ion in some element of volume in the droplet is a function of its free energy in this element of volume. The same approach can be applied to other ions in the droplet. The obtained charge distribution differs considerably from the surface distribution. The curve of the charge distribution in the droplet as a function of radius has maximum near the surface. Relative concentration of charges in the vicinity of the center of the droplet does not equal to zero, and it is the higher, the less is the total charge of the droplet. According to the estimates the model is applicable if the droplet radius is larger than 10 nm.

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.

Analytic Description of Critical Point Nuclei in a Spherical-Axially Deformed Shape Phase Transition

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

Iachello, F.

2001-07-30

An approximate solution at the critical point of the spherical to axially deformed shape phase transition in nuclei is presented. The eigenvalues of the Hamiltonian are expressed in terms of zeros of Bessel functions of irrational order.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem.

PubMed

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-21

Quantum mechanical calculations of ro-vibrational energies of CH 4 , CHD 3 , CH 3 D, and CH 3 F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH 3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH 3 . Euler angles specifying the orientation of a frame attached to CH 3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH 4 , CHD 3 , and CH 3 D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH 3 F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Computing energy levels of CH4, CHD3, CH3D, and CH3F with a direct product basis and coordinates based on the methyl subsystem

NASA Astrophysics Data System (ADS)

Zhao, Zhiqiang; Chen, Jun; Zhang, Zhaojun; Zhang, Dong H.; Wang, Xiao-Gang; Carrington, Tucker; Gatti, Fabien

2018-02-01

Quantum mechanical calculations of ro-vibrational energies of CH4, CHD3, CH3D, and CH3F were made with two different numerical approaches. Both use polyspherical coordinates. The computed energy levels agree, confirming the accuracy of the methods. In the first approach, for all the molecules, the coordinates are defined using three Radau vectors for the CH3 subsystem and a Jacobi vector between the remaining atom and the centre of mass of CH3. Euler angles specifying the orientation of a frame attached to CH3 with respect to a frame attached to the Jacobi vector are used as vibrational coordinates. A direct product potential-optimized discrete variable vibrational basis is used to build a Hamiltonian matrix. Ro-vibrational energies are computed using a re-started Arnoldi eigensolver. In the second approach, the coordinates are the spherical coordinates associated with four Radau vectors or three Radau vectors and a Jacobi vector, and the frame is an Eckart frame. Vibrational basis functions are products of contracted stretch and bend functions, and eigenvalues are computed with the Lanczos algorithm. For CH4, CHD3, and CH3D, we report the first J > 0 energy levels computed on the Wang-Carrington potential energy surface [X.-G. Wang and T. Carrington, J. Chem. Phys. 141(15), 154106 (2014)]. For CH3F, the potential energy surface of Zhao et al. [J. Chem. Phys. 144, 204302 (2016)] was used. All the results are in good agreement with experimental data.

Radiative transfer in spherical shell atmospheres. 2: Asymmetric phase functions

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Adams, C. N.

1977-01-01

The effects are investigated of sphericity on the radiation reflected from a planet with a homogeneous, conservative scattering atmosphere of optical thicknesses of 0.25 and 1.0. A Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7 is considered. Significant differences were found when these results were compared with the plane-parallel calculations. Also large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle.

YASEIS: Yet Another computer program to calculate synthetic SEISmograms for a spherically multi-layered Earth model

NASA Astrophysics Data System (ADS)

Ma, Yanlu

2013-04-01

Although most researches focus on the lateral heterogeneity of 3D Earth nowadays, a spherically multi-layered model where the parameters depend only on depth still represents a good first order approximation of real Earth. Such 1D models could be used as starting models for seismic tomographic inversion or as background model where the source mechanisms are inverted. The problem of wave propagation in a spherically layered model had been solved theoretically long time ago (Takeuchi and Saito, 1972). The existing computer programs such as Mineos (developed by G. Master, J. Woodhouse and F. Gilbert), Gemini (Friederich and Dalkolmo 1995), DSM (Kawai et. al. 2006) and QSSP (Wang 1999) tackled the computational aspects of the problem. A new simple and fast program for computing the Green's function of a stack of spherical dissipative layers is presented here. The analytical solutions within each homogeneous spherical layer are joined through the continuous boundary conditions and propagated from the center of model up to the level of source depth. Another solution is built by propagating downwardly from the free surface of model to the source level. The final solution is then constructed in frequency domain from the previous two solutions to satisfy the discontinuities of displacements and stresses at the source level which are required by the focal mechanism. The numerical instability in the propagator approach is solved by complementing the matrix propagating with an orthonormalization procedure (Wang 1999). Another unstable difficulty due to the high attenuation in the upper mantle low velocity zone is overcome by switching the bases of solutions from the spherical Bessel functions to the spherical Hankel functions when necessary. We compared the synthetic seismograms obtained from the new program YASEIS with those computed by Gemini and QSSP. In the range of near distances, the synthetics by a reflectivity code for the horizontally layers are also compared with those from YASEIS. Finally the static displacements in the source region are computed by choosing a very small frequency value in YASEIS which is designed for computing the dynamic response, and compared with the results in a homogeneous half-space model (Okada 1992). [1] Friederich, W. and J. Dalkolmo (1995). Complete synthetic seismograms for a spherically symmetric Earth a numerical computation of the Green's function in the frequency domain, Geophys. J. Int., vol. 122, 537-550. [2] Kawai, K., N. Takeuchi, and R.J. Geller (2006). Complete synthetic seismograms up to 2Hz for transversely isotropic spherically symmetric media, Geophys. J. Int., vol. 164, 411-424. [3] Okada, Y. (1992). Internal deformation due to shear and tensile faults in a half space, Bull. Seismol. Soc. Am., vol. 82, no. 2, 1018-1040. [4] Takeuchi, H. and M. Saito (1972). Seismic surface waves, Methods in computational physics, vol. II, 217-295. [5] Wang, R. (1999). A simple orthonormalization method for stable and efficient computation of Green's functions, Bull. Seismol. Soc. Am., vol. 89, no. 3, 733-741.

MODIS Retrieval of Dust Aerosol

NASA Technical Reports Server (NTRS)

Remer, Lorraine A.; Kaufman, Yoram J.; Tanre, Didier

2003-01-01

The MODerate resolution Imaging Spectroradiometer (MODIS) currently aboard both the Terra and Aqua satellites produces a suite of products designed to characterize global aerosol distribution, optical thickness and particle size. Never before has a space-borne instrument been able to provide such detailed information, operationally, on a nearly global basis every day. The three years of Terra-MODIS data have been validated by comparing with co-located AERONET observations of aerosol optical thickness and derivations of aerosol size parameters. Some 8000 comparison points located at 133 AERONET sites around the globe show that the MODIS aerosol optical thickness retrievals are accurate to within the pre-launch expectations. However, the validation in regions dominated by desert dust is less accurate than in regions dominated by fine mode aerosol or background marine sea salt. The discrepancy is most apparent in retrievals of aerosol size parameters over ocean. In dust situations, the MODIS algorithm tends to under predict particle size because the reflectances at top of atmosphere measured by MODIS exhibit the stronger spectral signature expected by smaller particles. This pattern is consistent with the angular and spectral signature of non-spherical particles. All possible aerosol models in the MODIS Look-Up Tables were constructed from Mie theory, assuming a spherical shape. Using a combination of MODIS and AERONET observations, in regimes dominated by desert dust, we construct phase functions, empirically, with no assumption of particle shape. These new phase functions are introduced into the MODIS algorithm, in lieu of the original options for large dust-like particles. The results will be analyzed and examined.

Nonnegative definite EAP and ODF estimation via a unified multi-shell HARDI reconstruction.

PubMed

Cheng, Jian; Jiang, Tianzi; Deriche, Rachid

2012-01-01

In High Angular Resolution Diffusion Imaging (HARDI), Orientation Distribution Function (ODF) and Ensemble Average Propagator (EAP) are two important Probability Density Functions (PDFs) which reflect the water diffusion and fiber orientations. Spherical Polar Fourier Imaging (SPFI) is a recent model-free multi-shell HARDI method which estimates both EAP and ODF from the diffusion signals with multiple b values. As physical PDFs, ODFs and EAPs are nonnegative definite respectively in their domains S2 and R3. However, existing ODF/EAP estimation methods like SPFI seldom consider this natural constraint. Although some works considered the nonnegative constraint on the given discrete samples of ODF/EAP, the estimated ODF/EAP is not guaranteed to be nonnegative definite in the whole continuous domain. The Riemannian framework for ODFs and EAPs has been proposed via the square root parameterization based on pre-estimated ODFs and EAPs by other methods like SPFI. However, there is no work on how to estimate the square root of ODF/EAP called as the wavefuntion directly from diffusion signals. In this paper, based on the Riemannian framework for ODFs/EAPs and Spherical Polar Fourier (SPF) basis representation, we propose a unified model-free multi-shell HARDI method, named as Square Root Parameterized Estimation (SRPE), to simultaneously estimate both the wavefunction of EAPs and the nonnegative definite ODFs and EAPs from diffusion signals. The experiments on synthetic data and real data showed SRPE is more robust to noise and has better EAP reconstruction than SPFI, especially for EAP profiles at large radius.

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.

A comparison between space-time video descriptors

NASA Astrophysics Data System (ADS)

Costantini, Luca; Capodiferro, Licia; Neri, Alessandro

2013-02-01

The description of space-time patches is a fundamental task in many applications such as video retrieval or classification. Each space-time patch can be described by using a set of orthogonal functions that represent a subspace, for example a sphere or a cylinder, within the patch. In this work, our aim is to investigate the differences between the spherical descriptors and the cylindrical descriptors. In order to compute the descriptors, the 3D spherical and cylindrical Zernike polynomials are employed. This is important because both the functions are based on the same family of polynomials, and only the symmetry is different. Our experimental results show that the cylindrical descriptor outperforms the spherical descriptor. However, the performances of the two descriptors are similar.

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

NASA Astrophysics Data System (ADS)

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

2009-04-01

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

Surface Structure Spread Single Crystals (S4C): Preparation and characterization

NASA Astrophysics Data System (ADS)

de Alwis, A.; Holsclaw, B.; Pushkarev, V. V.; Reinicker, A.; Lawton, T. J.; Blecher, M. E.; Sykes, E. C. H.; Gellman, A. J.

2013-02-01

A set of six spherically curved Cu single crystals referred to as Surface Structure Spread Single Crystals (S4Cs) has been prepared in such a way that their exposed surfaces collectively span all possible crystallographic surface orientations that can be cleaved from the face centered cubic Cu lattice. The method for preparing these S4Cs and for finding the high symmetry pole point is described. Optical profilometry has been used to determine the true shapes of the S4Cs and show that over the majority of the surface, the shape is extremely close to that of a perfect sphere. The local orientations of the surfaces lie within ± 1° of the orientation expected on the basis of the spherical shape; their orientation is as good as that of many commercially prepared single crystals. STM imaging has been used to characterize the atomic level structure of the Cu(111) ± 11°-S4C. This has shown that the average step densities and the average step orientations match those expected based on the spherical shape. In other words, although there is some distribution of step-step spacing and step orientations, there is no evidence of large scale reconstruction or faceting. The Cu S4Cs have local structures based on the ideal termination of the face centered cubic Cu lattice in the direction of termination. The set of Cu S4Cs will serve as the basis for high throughput investigations of structure sensitive surface chemistry on Cu.

Weak solution concept and Galerkin's matrix for the exterior of an oblate ellipsoid of revolution in the representation of the Earth's gravity potential by buried masses

NASA Astrophysics Data System (ADS)

Holota, Petr; Nesvadba, Otakar

2017-04-01

The paper is motivated by the role of boundary value problems in Earth's gravity field studies. The discussion focuses on Neumann's problem formulated for the exterior of an oblate ellipsoid of revolution as this is considered a basis for an iteration solution of the linear gravimetric boundary value problem in the determination of the disturbing potential. The approach follows the concept of the weak solution and Galerkin's approximations are applied. This means that the solution of the problem is approximated by linear combinations of basis functions with scalar coefficients. The construction of Galerkin's matrix for basis functions generated by elementary potentials (point masses) is discussed. Ellipsoidal harmonics are used as a natural tool and the elementary potentials are expressed by means of series of ellipsoidal harmonics. The problem, however, is the summation of the series that represent the entries of Galerkin's matrix. It is difficult to reduce the number of summation indices since in the ellipsoidal case there is no analogue to the addition theorem known for spherical harmonics. Therefore, the straightforward application of series of ellipsoidal harmonics is complemented by deeper relations contained in the theory of ordinary differential equations of second order and in the theory of Legendre's functions. Subsequently, also hypergeometric functions and series are used. Moreover, within some approximations the entries are split into parts. Some of the resulting series may be summed relatively easily, apart from technical tricks. For the remaining series the summation was converted to elliptic integrals. The approach made it possible to deduce a closed (though approximate) form representation of the entries in Galerkin's matrix. The result rests on concepts and methods of mathematical analysis. In the paper it is confronted with a direct numerical approach applied for the implementation of Legendre's functions. The computation of the entries is more demanding in this case, but conceptually it avoids approximations. Finally, some specific features associated with function bases generated by elementary potentials in case the ellipsoidal solution domain are illustrated and discussed.

Beta-decay rate and beta-delayed neutron emission probability of improved gross theory

NASA Astrophysics Data System (ADS)

Koura, Hiroyuki

2014-09-01

A theoretical study has been carried out on beta-decay rate and beta-delayed neutron emission probability. The gross theory of the beta decay is based on an idea of the sum rule of the beta-decay strength function, and has succeeded in describing beta-decay half-lives of nuclei overall nuclear mass region. The gross theory includes not only the allowed transition as the Fermi and the Gamow-Teller, but also the first-forbidden transition. In this work, some improvements are introduced as the nuclear shell correction on nuclear level densities and the nuclear deformation for nuclear strength functions, those effects were not included in the original gross theory. The shell energy and the nuclear deformation for unmeasured nuclei are adopted from the KTUY nuclear mass formula, which is based on the spherical-basis method. Considering the properties of the integrated Fermi function, we can roughly categorized energy region of excited-state of a daughter nucleus into three regions: a highly-excited energy region, which fully affect a delayed neutron probability, a middle energy region, which is estimated to contribute the decay heat, and a region neighboring the ground-state, which determines the beta-decay rate. Some results will be given in the presentation. A theoretical study has been carried out on beta-decay rate and beta-delayed neutron emission probability. The gross theory of the beta decay is based on an idea of the sum rule of the beta-decay strength function, and has succeeded in describing beta-decay half-lives of nuclei overall nuclear mass region. The gross theory includes not only the allowed transition as the Fermi and the Gamow-Teller, but also the first-forbidden transition. In this work, some improvements are introduced as the nuclear shell correction on nuclear level densities and the nuclear deformation for nuclear strength functions, those effects were not included in the original gross theory. The shell energy and the nuclear deformation for unmeasured nuclei are adopted from the KTUY nuclear mass formula, which is based on the spherical-basis method. Considering the properties of the integrated Fermi function, we can roughly categorized energy region of excited-state of a daughter nucleus into three regions: a highly-excited energy region, which fully affect a delayed neutron probability, a middle energy region, which is estimated to contribute the decay heat, and a region neighboring the ground-state, which determines the beta-decay rate. Some results will be given in the presentation. This work is a result of Comprehensive study of delayed-neutron yields for accurate evaluation of kinetics of high-burn up reactors entrusted to Tokyo Institute of Technology by the Ministry of Education, Culture, Sports, Science and Technology of Japan.

The 4-parameter Compressible Packing Model (CPM) including a critical cavity size ratio

NASA Astrophysics Data System (ADS)

Roquier, Gerard

2017-06-01

The 4-parameter Compressible Packing Model (CPM) has been developed to predict the packing density of mixtures constituted by bidisperse spherical particles. The four parameters are: the wall effect and the loosening effect coefficients, the compaction index and a critical cavity size ratio. The two geometrical interactions have been studied theoretically on the basis of a spherical cell centered on a secondary class bead. For the loosening effect, a critical cavity size ratio, below which a fine particle can be inserted into a small cavity created by touching coarser particles, is introduced. This is the only parameter which requires adaptation to extend the model to other types of particles. The 4-parameter CPM demonstrates its efficiency on frictionless glass beads (300 values), spherical particles numerically simulated (20 values), round natural particles (125 values) and crushed particles (335 values) with correlation coefficients equal to respectively 99.0%, 98.7%, 97.8%, 96.4% and mean deviations equal to respectively 0.007, 0.006, 0.007, 0.010.

Navier-Stokes structure of merged layer flow on the spherical nose of a space vehicle

NASA Technical Reports Server (NTRS)

Jain, A. C.; Woods, G. H.

1988-01-01

Hypersonic merged layer flow on the forepart of a spherical surface of a space vehicle has been investigated on the basis of the full steady-state Navier-Stokes equations using slip and temperature jump boundary conditions at the surface and free-stream conditions far from the surface. The shockwave-like structure was determined as part of the computations. Using an equivalent body concept, computations were carried out under conditions that the Aeroassist Flight Experiment (AFE) Vehicle would encounter at 15 and 20 seconds in its flight path. Emphasis was placed on understanding the basic nature of the flow structure under low density conditions. Particular attention was paid to the understanding of the structure of the outer shockwave-like region as the fluid expands around the sphere. Plots were drawn for flow profiles and surface characteristics to understand the role of dissipation processes in the merged layer of the spherical nose of the vehicle.

Avian influenza a virus budding morphology: spherical or filamentous?

USDA-ARS?s Scientific Manuscript database

Most strains of influenza A virus (IAV) can produce long (µm length) filamentous virus particles as well as ~100 nm diameter spherical virions. The function of the filamentous particles is unclear but is hypothesized to facilitate transmission within or from the respiratory tract. In mammalian IAVs,...

Human exposure in low Earth orbit

NASA Technical Reports Server (NTRS)

Wilson, J. W.; Cucinotta, F.

1984-01-01

Human exposure to trapped electrons and protons in low Earth orbit (LEO) is evaluated on a basis of a simple approximation of the human geometry for spherical shell shields of varying thickness. A data base is presented that may be used to make preliminary assessment of the impact of radiation exposure constraints on human performance. Detailed shielding studies should be performed before final design considerations. A sample impact assessment is discussed on the basis of presently accepted allowable exposure limits. A brief discussion is given on the anticipated impact of an ongoing reassessment of allowable exposure limits.

Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates

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

Mezzacappa, Anthony; Endeve, Eirik; Hauck, Cory D.

We extend the positivity-preserving method of Zhang & Shu [49] to simulate the advection of neutral particles in phase space using curvilinear coordinates. The ability to utilize these coordinates is important for non-equilibrium transport problems in general relativity and also in science and engineering applications with specific geometries. The method achieves high-order accuracy using Discontinuous Galerkin (DG) discretization of phase space and strong stabilitypreserving, Runge-Kutta (SSP-RK) time integration. Special care in taken to ensure that the method preserves strict bounds for the phase space distribution function f; i.e., f ϵ [0, 1]. The combination of suitable CFL conditions and themore » use of the high-order limiter proposed in [49] is su cient to ensure positivity of the distribution function. However, to ensure that the distribution function satisfies the upper bound, the discretization must, in addition, preserve the divergencefree property of the phase space ow. Proofs that highlight the necessary conditions are presented for general curvilinear coordinates, and the details of these conditions are worked out for some commonly used coordinate systems (i.e., spherical polar spatial coordinates in spherical symmetry and cylindrical spatial coordinates in axial symmetry, both with spherical momentum coordinates). Results from numerical experiments - including one example in spherical symmetry adopting the Schwarzschild metric - demonstrate that the method achieves high-order accuracy and that the distribution function satisfies the maximum principle.« less

The evolution of void-filled cosmological structures

NASA Technical Reports Server (NTRS)

Regos, Eniko; Geller, Margaret J.

1991-01-01

1D, 2D, and 3D simulations are used here to investigate the salient features in the evolution of void-filled cosmological structures in universes with arbitrary values of Omega. It is found that the growth of a void as a function of time decreases significantly at the time corresponding to Omega = 0.5. In models constructed in 2D and 3D, suitable initial conditions lead to cellular structure with faceted voids similar to those observed in redshift surveys. Matter compressed to planes flows more rapidly toward condensations at the intersections than would be expected for spherical infall. The peculiar streaming velocities for void diameters of 5000 km/s should be observable. The simulations provide a more physical basis and dynamics for the bubbly and Voronois tesselation models used to derive statistical properties of cellular large-scale structure.

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.

The reduction, verification and interpretation of MAGSAT magnetic data over Canada

NASA Technical Reports Server (NTRS)

Coles, R. L. (Principal Investigator); Haines, G. V.; Vanbeek, G. J.; Walker, J. K.; Newitt, L. R.

1982-01-01

Consideration is being given to representing the magnetic field in the area 40 deg N to 83 deg N by means of functions in spherical coordinates. A solution to Laplace's equation for the magnetic potential over a restricted area was found, and programming and testing are currently being carried out. Magnetic anomaly modelling is proceeding. The program SPHERE, which was adapted to function correctly on the Cyber computer, is now operational, for deriving gravity and magnetic models in a spherical coordinate system.

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.

Self-similar dynamic converging shocks - I. An isothermal gas sphere with self-gravity

NASA Astrophysics Data System (ADS)

Lou, Yu-Qing; Shi, Chun-Hui

2014-07-01

We explore novel self-similar dynamic evolution of converging spherical shocks in a self-gravitating isothermal gas under conceivable astrophysical situations. The construction of such converging shocks involves a time-reversal operation on feasible flow profiles in self-similar expansion with a proper care for the increasing direction of the specific entropy. Pioneered by Guderley since 1942 but without self-gravity so far, self-similar converging shocks are important for implosion processes in aerodynamics, combustion, and inertial fusion. Self-gravity necessarily plays a key role for grossly spherical structures in very broad contexts of astrophysics and cosmology, such as planets, stars, molecular clouds (cores), compact objects, planetary nebulae, supernovae, gamma-ray bursts, supernova remnants, globular clusters, galactic bulges, elliptical galaxies, clusters of galaxies as well as relatively hollow cavity or bubble structures on diverse spatial and temporal scales. Large-scale dynamic flows associated with such quasi-spherical systems (including collapses, accretions, fall-backs, winds and outflows, explosions, etc.) in their initiation, formation, and evolution are likely encounter converging spherical shocks at times. Our formalism lays an important theoretical basis for pertinent astrophysical and cosmological applications of various converging shock solutions and for developing and calibrating numerical codes. As examples, we describe converging shock triggered star formation, supernova explosions, and void collapses.

Electromagnetic δ -function sphere

NASA Astrophysics Data System (ADS)

Parashar, Prachi; Milton, Kimball A.; Shajesh, K. V.; Brevik, Iver

2017-10-01

We develop a formalism to extend our previous work on the electromagnetic δ -function plates to a spherical surface. The electric (λe) and magnetic (λg) couplings to the surface are through δ -function potentials defining the dielectric permittivity and the diamagnetic permeability, with two anisotropic coupling tensors. The formalism incorporates dispersion. The electromagnetic Green's dyadic breaks up into transverse electric and transverse magnetic parts. We derive the Casimir interaction energy between two concentric δ -function spheres in this formalism and show that it has the correct asymptotic flat-plate limit. We systematically derive expressions for the Casimir self-energy and the total stress on a spherical shell using a δ -function potential, properly regulated by temporal and spatial point splitting, which are different from the conventional temporal point splitting. In the strong-coupling limit, we recover the usual result for the perfectly conducting spherical shell but in addition there is an integrated curvature-squared divergent contribution. For finite coupling, there are additional divergent contributions; in particular, there is a familiar logarithmic divergence occurring in the third order of the uniform asymptotic expansion that renders it impossible to extract a unique finite energy except in the case of an isorefractive sphere, which translates into λg=-λe.

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

Tide Gauge Records Reveal Improved Processing of Gravity Recovery and Climate Experiment Time-Variable Mass Solutions over the Coastal Ocean

NASA Astrophysics Data System (ADS)

Piecuch, Christopher G.; Landerer, Felix W.; Ponte, Rui M.

2018-05-01

Monthly ocean bottom pressure solutions from the Gravity Recovery and Climate Experiment (GRACE), derived using surface spherical cap mass concentration (MC) blocks and spherical harmonics (SH) basis functions, are compared to tide gauge (TG) monthly averaged sea level data over 2003-2015 to evaluate improved gravimetric data processing methods near the coast. MC solutions can explain ≳ 42% of the monthly variance in TG time series over broad shelf regions and in semi-enclosed marginal seas. MC solutions also generally explain ˜5-32 % more TG data variance than SH estimates. Applying a coastline resolution improvement algorithm in the GRACE data processing leads to ˜ 31% more variance in TG records explained by the MC solution on average compared to not using this algorithm. Synthetic observations sampled from an ocean general circulation model exhibit similar patterns of correspondence between modeled TG and MC time series and differences between MC and SH time series in terms of their relationship with TG time series, suggesting that observational results here are generally consistent with expectations from ocean dynamics. This work demonstrates the improved quality of recent MC solutions compared to earlier SH estimates over the coastal ocean, and suggests that the MC solutions could be a useful tool for understanding contemporary coastal sea level variability and change.

Numerical Solution of the Problem of the Expansion of the Universe in the Schwarzschild Metric

NASA Astrophysics Data System (ADS)

Vasenin, I. M.; Goiko, V. L.

2018-02-01

The statement and solution of the problem of the expansion of the Universe in nonstationary spherically-symmetric coordinates in the Schwarzschild metric are considered without pressure taken into account. The observational data of astronomers investigating the rates of recession of distant stars are explained on the basis of the obtained solutions.

Magnetic particles extracted from manganese nodules: Suggested origin from stony and iron meteorites

USGS Publications Warehouse

Finkelman, R.B.

1970-01-01

On the basis of x-ray diffraction and electron microprobe data, spherical and ellipsoidal particles extracted from manganese nodules were divided into three groups. Group I particles are believed to be derived from iron meteorites, and Group II particles from stony meteorites. Group III particles are believed to be volcanic in origin.

Spherical Demons: Fast Surface Registration

PubMed Central

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

2009-01-01

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

Spherical demons: fast surface registration.

PubMed

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

2008-01-01

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

On the Runge-Lenz-Pauli vector operator as an aid to the calculation of atomic processes in laboratory and astrophysical plasmas

NASA Astrophysics Data System (ADS)

Hey, J. D.

2015-09-01

On the basis of the original definition and analysis of the vector operator by Pauli (1926 Z. Phys. 36 336-63), and further developments by Flamand (1966 J. Math. Phys. 7 1924-31), and by Becker and Bleuler (1976 Z. Naturforsch. 31a 517-23), we consider the action of the operator on both spherical polar and parabolic basis state wave functions, both with and without direct use of Pauli’s identity (Valent 2003 Am. J. Phys. 71 171-75). Comparison of the results, with the aid of two earlier papers (Hey 2006 J. Phys. B: At. Mol. Opt. Phys. 39 2641-64, Hey 2007 J. Phys. B: At. Mol. Opt. Phys. 40 4077-96), yields a convenient ladder technique in the form of a recurrence relation for calculating the transformation coefficients between the two sets of basis states, without explicit use of generalized hypergeometric functions. This result is therefore very useful for application to Stark effect and impact broadening calculations applied to high-n radio recombination lines from tenuous space plasmas. We also demonstrate the versatility of the Runge-Lenz-Pauli vector operator as a means of obtaining recurrence relations between expectation values of successive powers of quantum mechanical operators, by using it to provide, as an example, a derivation of the Kramers-Pasternack relation. It is suggested that this operator, whose potential use in Stark- and Zeeman-effect calculations for magnetically confined fusion edge plasmas (Rosato, Marandet and Stamm 2014 J. Phys. B: At. Mol. Opt. Phys. 47 105702) and tenuous space plasmas ( H II regions) has not been fully explored and exploited, may yet be found to yield a number of valuable results for applications to plasma diagnostic techniques based upon rate calculations of atomic processes.

Characteristics and application of spherical-type activation detectors in neutron spectrum measurements at a boron neutron capture therapy (BNCT) facility

NASA Astrophysics Data System (ADS)

Lin, Heng-Xiao; Chen, Wei-Lin; Liu, Yuan-Hao; Sheu, Rong-Jiun

2016-03-01

A set of spherical-type activation detectors was developed aiming to provide better determination of the neutron spectrum at the Tsing Hua Open-pool Reactor (THOR) BNCT facility. An activation foil embedded in a specially designed spherical holder exhibits three advantages: (1) minimizing the effect of neutron angular dependence, (2) creating response functions with broadened coverage of neutron energies by introducing additional moderators or absorbers to the central activation foil, and (3) reducing irradiation time because of improved detection efficiencies to epithermal neutron beam. This paper presents the design concept and the calculated response functions of new detectors. Theoretical and experimental demonstrations of the performance of the detectors are provided through comparisons of the unfolded neutron spectra determined using this method and conventional multiple-foil activation techniques.

Data Assimilation on a Quantum Annealing Computer: Feasibility and Scalability

NASA Astrophysics Data System (ADS)

Nearing, G. S.; Halem, M.; Chapman, D. R.; Pelissier, C. S.

2014-12-01

Data assimilation is one of the ubiquitous and computationally hard problems in the Earth Sciences. In particular, ensemble-based methods require a large number of model evaluations to estimate the prior probability density over system states, and variational methods require adjoint calculations and iteration to locate the maximum a posteriori solution in the presence of nonlinear models and observation operators. Quantum annealing computers (QAC) like the new D-Wave housed at the NASA Ames Research Center can be used for optimization and sampling, and therefore offers a new possibility for efficiently solving hard data assimilation problems. Coding on the QAC is not straightforward: a problem must be posed as a Quadratic Unconstrained Binary Optimization (QUBO) and mapped to a spherical Chimera graph. We have developed a method for compiling nonlinear 4D-Var problems on the D-Wave that consists of five steps: Emulating the nonlinear model and/or observation function using radial basis functions (RBF) or Chebyshev polynomials. Truncating a Taylor series around each RBF kernel. Reducing the Taylor polynomial to a quadratic using ancilla gadgets. Mapping the real-valued quadratic to a fixed-precision binary quadratic. Mapping the fully coupled binary quadratic to a partially coupled spherical Chimera graph using ancilla gadgets. At present the D-Wave contains 512 qbits (with 1024 and 2048 qbit machines due in the next two years); this machine size allows us to estimate only 3 state variables at each satellite overpass. However, QAC's solve optimization problems using a physical (quantum) system, and therefore do not require iterations or calculation of model adjoints. This has the potential to revolutionize our ability to efficiently perform variational data assimilation, as the size of these computers grows in the coming years.

Radiative transfer in spherical shell atmospheres. II - Asymmetric phase functions

NASA Technical Reports Server (NTRS)

Kattawar, G. W.; Adams, C. N.

1978-01-01

This paper investigates the effects of sphericity on the radiation reflected from a planet with a homogeneous conservative-scattering atmosphere of optical thicknesses of 0.25 and 1.0. A Henyey-Greenstein phase function with asymmetry factors of 0.5 and 0.7 was considered. Significant differences were found when these results were compared with the plane-parallel calculations. Also, large violations of the reciprocity theorem, which is only true for plane-parallel calculations, were noted. Results are presented for the radiance versus height distributions as a function of planetary phase angle. These results will be useful to researchers in the field of remote sensing and planetary spectroscopy.

Influence of shape and gradient refractive index in the accommodative changes of spherical aberration in nonhuman primate crystalline lenses.

PubMed

de Castro, Alberto; Birkenfeld, Judith; Maceo, Bianca; Manns, Fabrice; Arrieta, Esdras; Parel, Jean-Marie; Marcos, Susana

2013-09-11

To estimate changes in surface shape and gradient refractive index (GRIN) profile in primate lenses as a function of accommodation. To quantify the contribution of surface shape and GRIN to spherical aberration changes with accommodation. Crystalline lenses from 15 cynomolgus monkeys were studied in vitro under different levels of accommodation produced by a stretching system. Lens shape was obtained from optical coherence tomography (OCT) cross-sectional images. The GRIN was reconstructed with a search algorithm using the optical path measured from OCT images and the measured back focal length. The spherical aberration of the lens was estimated as a function of accommodation using the reconstructed GRIN and a homogeneous refractive index. The lens anterior and posterior radii of curvature decreased with increasing lens power. Both surfaces exhibited negative asphericities in the unaccommodated state. The anterior surface conic constant shifted toward less negative values with accommodation, while the value of the posterior remained constant. GRIN parameters remained constant with accommodation. The lens spherical aberration with GRIN distribution was negative and higher in magnitude than that with a homogeneous equivalent refractive index (by 29% and 53% in the unaccommodated and fully accommodated states, respectively). Spherical aberration with the equivalent refractive index shifted with accommodation toward negative values (-0.070 μm/diopter [D]), but the reconstructed GRIN shifted it farther (-0.124 μm/D). When compared with the lens with the homogeneous equivalent refractive index, the reconstructed GRIN lens has more negative spherical aberration and a larger shift toward more negative values with accommodation.

The HCO+-H2 van der Waals interaction: Potential energy and scattering

NASA Astrophysics Data System (ADS)

Massó, H.; Wiesenfeld, L.

2014-11-01

We compute the rigid-body, four-dimensional interaction potential between HCO+ and H2. The ab initio energies are obtained at the coupled-cluster single double triple level of theory, corrected for Basis Set Superposition Errors. The ab initio points are fit onto the spherical basis relevant for quantum scattering. We present elastic and rotationally inelastic coupled channels scattering between low lying rotational levels of HCO+ and para-/ortho-H2. Results are compared with similar earlier computations with He or isotropic para-H2 as the projectile. Computations agree with earlier pressure broadening measurements.

The HCO⁺-H₂ van der Waals interaction: potential energy and scattering.

PubMed

Massó, H; Wiesenfeld, L

2014-11-14

We compute the rigid-body, four-dimensional interaction potential between HCO(+) and H2. The ab initio energies are obtained at the coupled-cluster single double triple level of theory, corrected for Basis Set Superposition Errors. The ab initio points are fit onto the spherical basis relevant for quantum scattering. We present elastic and rotationally inelastic coupled channels scattering between low lying rotational levels of HCO(+) and para-/ortho-H2. Results are compared with similar earlier computations with He or isotropic para-H2 as the projectile. Computations agree with earlier pressure broadening measurements.

Uncertainties of aerosol retrieval from neglecting non-sphericity of dust aerosols

NASA Astrophysics Data System (ADS)

Li, Chi; Xue, Yong; Yang, Leiku; Guang, Jie

2013-04-01

The Mie theory is conventionally applied to calculate aerosol optical properties in satellite remote sensing applications, while dust aerosols cannot be well modeled by the Mie calculation for their non-sphericity. It has been cited in Mishchenko et al. (1995; 1997) that neglecting non-sphericity can severely influence aerosol optical depth (AOD, ?) retrieval in case of dust aerosols because of large difference of phase functions under spherical and non-spherical assumptions, whereas this uncertainty has not been thoroughly studied. This paper aims at a better understanding of uncertainties on AOD retrieval caused by aerosol non-sphericity. A dust aerosol model with known refractive index and size distribution is generated from long-term AERONET observations since 1999 over China. Then aerosol optical properties, such as the extinction, phase function, single scattering albedo (SSA) are calculated respectively in the assumption of spherical and non-spherical aerosols. Mie calculation is carried out for spherical assumption, meanwhile for non-spherical aerosol modeling, we adopt the pre-calculated scattering kernels and software package presented by Dubovik et al. (2002; 2006), which describes dust as a shape mixture of randomly oriented polydisperse spheroids. Consequently we generate two lookup tables (LUTspheric and LUTspheroid) from simulated satellite received reflectance at top of atmosphere (TOA) under varieties of observing conditions and aerosol loadings using Second Simulation of a Satellite Signal in the Solar Spectrum - Vector (6SV) code. All the simulations are made at 550 nm, and for simplicity the Lambertian surface is assumed. Using the obtained LUTs we examine the differences of TOA reflectance (Δ?TOA = ?spheric - ?spheroid) under different surface reflectance and aerosol loadings. Afterwards AOD is retrieved using LUTspheric from the simulated TOA reflectance by LUTspheroid in order to detect the retrieval errors (Δ? = ?retreived -?input) induced by straightforwardly utilizing Mie theory in dust aerosol retrieval. As expected we find that the uncertainties mainly result from the obvious difference of phase functions (Pspheric and Pspheroid). Errors may be positive or negative, depending on the specific geometry. In scattering angle (θ) regions where Psphericis greater (30°~85° & 145°~180°), we generally get positive Δ?TOA and negative Δ?, and vice versa (85°~145°). For low aerosol loading (? ~0.25) and black surface, |Δ?TOA| could be greater than 0.004 and 0.012 around θ ~120° and θ ~170°, with |Δ?| of ~0.04 and ~0.12 respectively. In most back scattering cases (θ >100°), the magnitude of Δ? is about ten times that of Δ?TOA, while this ratio (|Δ?|/|Δ?TOA|) significantly reduces to as low as ~0.5 for forward scattering, and can reach ~20 at θ ~145°. Moreover, this errors and |Δ?|/|Δ?TOA| can increase more than ten times as aerosol loading gets higher and surface gets brighter. Therefore we conclude that the neglect of non-sphericity introduces substantial errors on radiative transfer simulation and AOD retrieval. As a result of this study, a representative aspheric aerosol model other than Mie calculation is recommended for inversion algorithms related with dust-like non-spherical aerosols. References Dubovik, O., Holben, B. N., Lapyonok, T., Sinyuk, A., Mishchenko, M. I., Yang, P., and Slutsker, I. (2002). Non-spherical aerosol retrieval method employing light scattering by spheroids. Geophyscal Research Letters, 29(10), 1415, doi:10.1029/2001GL014506. Dubovik, O., Sinyuk, A., Lapyonok, T., Holben, B. N., Mishchenko, M., Yang, P., Eck, T. F., Volten, H., Muñoz, O., Veihelmann, B., van der Zande, W. J., Leon, J.-F., Sorokin, M., and Slutsker, I. (2006). Application of spheroid models to account for aerosol particle nonsphericity in remote sensing of desert dust. Journal of Geophysical Research, 111, D11208, doi:10.1029/2005JD006619. Mishchenko, M. I., Lacis, A. A., Carlson, B. E., and Travis, L. D. (1995). Nonsphericity of dust-like aerosols: Implications for aerosol remote sensing and climate modeling, Geophyscal Research Letters, 22, 1077- 1080. Mishchenko, M. I., Travis, L. D., Kahn, R. A., and West, R. A. (1997). Modeling phase functions for dustlike tropospheric aerosols using a shape mixture of randomly oriented polydisperse spheroids, Journal of Geophysical Research, 102, 16831- 16847.

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).

Density-functional theory of spherical electric double layers and zeta potentials of colloidal particles in restricted-primitive-model electrolyte solutions.

PubMed

Yu, Yang-Xin; Wu, Jianzhong; Gao, Guang-Hua

2004-04-15

A density-functional theory is proposed to describe the density profiles of small ions around an isolated colloidal particle in the framework of the restricted primitive model where the small ions have uniform size and the solvent is represented by a dielectric continuum. The excess Helmholtz energy functional is derived from a modified fundamental measure theory for the hard-sphere repulsion and a quadratic functional Taylor expansion for the electrostatic interactions. The theoretical predictions are in good agreement with the results from Monte Carlo simulations and from previous investigations using integral-equation theory for the ionic density profiles and the zeta potentials of spherical particles at a variety of solution conditions. Like the integral-equation approaches, the density-functional theory is able to capture the oscillatory density profiles of small ions and the charge inversion (overcharging) phenomena for particles with elevated charge density. In particular, our density-functional theory predicts the formation of a second counterion layer near the surface of highly charged spherical particle. Conversely, the nonlinear Poisson-Boltzmann theory and its variations are unable to represent the oscillatory behavior of small ion distributions and charge inversion. Finally, our density-functional theory predicts charge inversion even in a 1:1 electrolyte solution as long as the salt concentration is sufficiently high. (c) 2004 American Institute of Physics.

Martian airfall dust on smooth, inclined surfaces as observed on the Phoenix Mars Lander telltale mirror

NASA Astrophysics Data System (ADS)

Moores, John E.; Ha, Taesung; Lemmon, Mark T.; Gunnlaugsson, Haraldur Páll

2015-10-01

The telltale mirror, a smooth inclined surface raised over 1 m above the deck of the Phoenix Mars Lander, was observed by the Surface Stereo Imager (SSI) several times per sol during the Phoenix Mars Lander mission. These observations were combined with a radiative transfer model to determine the thickness of dust on the wind telltale mirror as a function of time. 239 telltale sequences were analyzed and dustiness was determined on a diurnal and seasonal basis. The thickness of accumulated dust did not follow any particular diurnal or seasonal trend. The dust thickness on the mirror over the mission was 0.82±0.39 μm, which suggests a similar thickness to the modal scattering particle diameter. This suggests that inclining a surface beyond the angle of repose and polishing it to remove surface imperfections is an effective way to mitigate the accumulation of dust to less than a micron over a wide range of meteorological conditions and could be beneficial for surfaces which can tolerate some dust but not thick accumulations, such as solar panels. However, such a surface will not remain completely dust free through this action alone and mechanical or electrical clearing must be employed to remove adhered dust if a pristine surface is required. The single-scattering phase function of the dust on the mirror was consistent with the single-scattering phase function of martian aerosol dust at 450 nm, suggesting that this result is inconsistent with models of the atmosphere which require vertically or horizontally separated components or broad size distributions to explain the scattering behavior of these aerosols in the blue. The single-scattering behavior of the dust on the mirror is also consistent with Hapke modeling of spherical particles. The presence of a monolayer of particles would tend to support the spherical conclusion: such particles would be most strongly adhered electrostatically.

Hipparchus' coordinate system

NASA Astrophysics Data System (ADS)

Duke, Dennis W.

2002-07-01

In his "Histoire de l'Astronomie Ancienne" Delambre concludes unequivocally that Hipparchus knew and used a definite system of celestial spherical coordinates, namely the right ascension and declination system that we use today. The basis of Delambre's conclusion was disarmingly simple: he pointed out that in the "Commentary to Aratus" Hipparchus actually quotes the positions of numerous stars directly in right ascension and declination (or more often its complement, polar distance). Nearly two centuries later, in his "A History of Ancient Mathematical Astronomy", Neugebauer not only completely ignores Delambre's conclusion on this issue, but goes further to propose his own, as we shall see quite fanciful, theory that begins "From the Commentary to Aratus, it is quite obvious that at Hipparchus' time a definite system of spherical coordinates for stellar positions did not yet exist." and concludes "...nowhere in Greek astronomy before the catalogue of stars in the Almagest is it attested that orthogonal spherical coordinates are used to determine stellar positions." Today it is clear that Neugebauer's theory is conventionally accepted. It is the purpose of this paper to offer fresh arguments that Delambre was correct.

Self-assembled mesoporous Co and Ni-ferrite spherical clusters consisting of spinel nanocrystals prepared using a template-free approach.

PubMed

Yu, Byong Yong; Kwak, Seung-Yeop

2011-10-21

Based on a self-assembly strategy, spherical mesoporous cobalt and nickel ferrite nanocrystal clusters with a large surface area and narrow size distribution were successfully synthesized for the first time via a template-free solvothermal process in ethylene glycol and subsequent heat treatment. In this work, the mesopores in the ferrite clusters were derived mainly from interior voids between aggregated primary nanoparticles (with crystallite size of less than 7 nm) and disordered particle packing domains. The concentration of sodium acetate is shown herein to play a crucial role in the formation of mesoporous ferrite spherical clusters. These ferrite clusters were characterized in detail using wide-angle X-ray diffraction, thermogravimetric-differential thermal analysis, (57)Fe Mössbauer spectroscopy, X-ray photoelectron spectroscopy, field-emission scanning electron microscopy, standard and high-resolution transmission electron microscopy, and other techniques. The results confirmed the formation of both pure-phase ferrite clusters with highly crystalline spinel structure, uniform size (about 160 nm) and spherical morphology, and worm-like mesopore structures. The BET specific surface areas and mean pore sizes of the mesoporous Co and Ni-ferrite clusters were as high as 160 m(2) g(-1) and 182 m(2) g(-1), and 7.91 nm and 6.87 nm, respectively. A model for the formation of the spherical clusters in our system is proposed on the basis of the results. The magnetic properties of both samples were investigated at 300 K, and it was found that these materials are superparamagnetic. This journal is © The Royal Society of Chemistry 2011

Functionalized patchy particles using colloidal lenses

NASA Astrophysics Data System (ADS)

Middleton, Christine

2014-03-01

Colloidal assembly had been limited by the isotropic, nonspecific nature of interactions between spherical colloidal particles. By giving particles patches functionalized with single stranded DNA, these interactions can be made both directional and specific. We create patchy particles by adding patches to spherical emulsion droplets using the depletion interaction. First we make polystyrene particles in the shape of contact lenses to be the patches. The lenses are functionalized with single stranded DNA on their convex side. Then we put the lenses on the surface of oil emulsion droplets using the depletion interaction, creating a patch (or multiple patches) on the surface of each emulsion droplet. The emulsion droplets can now interact with each other in a specific, directional way through DNA functionalized patches.

Beta electron fluxes inside a magnetic plasma cavern: Calculation and comparison with experiment

NASA Astrophysics Data System (ADS)

Stupitskii, E. L.; Smirnov, E. V.; Kulikova, N. A.

2010-12-01

We study the possibility of electrostatic blanking of beta electrons in the expanding spherical blob of a radioactive plasma in a rarefied ionosphere. From numerical studies on the dynamics of beta electrons departing a cavern, we obtain the form of a function that determines the portion of departing electrons and calculate the flux density of beta electrons inside the cavern in relation to the Starfish Prime nuclear blast. We show that the flux density of electrons in geomagnetic flux tubes and inside the cavern depend on a correct allowance for the quantity of beta electrons returning to the cavern. On the basis of a physical analysis, we determine the approximate criterion for the return of electrons from a geomagnetic flux tube to the cavern. We compare calculation results in terms of the flux density of beta electrons inside the cavern with the recently published experimental results from operation Starfish Prime.

On the error in the nucleus-centered multipolar expansion of molecular electron density and its topology: A direct-space computational study.

PubMed

Michael, J Robert; Koritsanszky, Tibor

2017-05-28

The convergence of nucleus-centered multipolar expansion of the quantum-chemical electron density (QC-ED), gradient, and Laplacian is investigated in terms of numerical radial functions derived by projecting stockholder atoms onto real spherical harmonics at each center. The partial sums of this exact one-center expansion are compared with the corresponding Hansen-Coppens pseudoatom (HC-PA) formalism [Hansen, N. K. and Coppens, P., "Testing aspherical atom refinements on small-molecule data sets," Acta Crystallogr., Sect. A 34, 909-921 (1978)] commonly utilized in experimental electron density studies. It is found that the latter model, due to its inadequate radial part, lacks pointwise convergence and fails to reproduce the local topology of the target QC-ED even at a high-order expansion. The significance of the quantitative agreement often found between HC-PA-based (quadrupolar-level) experimental and extended-basis QC-EDs can thus be challenged.

q-Space Upsampling Using x-q Space Regularization.

PubMed

Chen, Geng; Dong, Bin; Zhang, Yong; Shen, Dinggang; Yap, Pew-Thian

2017-09-01

Acquisition time in diffusion MRI increases with the number of diffusion-weighted images that need to be acquired. Particularly in clinical settings, scan time is limited and only a sparse coverage of the vast q -space is possible. In this paper, we show how non-local self-similar information in the x - q space of diffusion MRI data can be harnessed for q -space upsampling. More specifically, we establish the relationships between signal measurements in x - q space using a patch matching mechanism that caters to unstructured data. We then encode these relationships in a graph and use it to regularize an inverse problem associated with recovering a high q -space resolution dataset from its low-resolution counterpart. Experimental results indicate that the high-resolution datasets reconstructed using the proposed method exhibit greater quality, both quantitatively and qualitatively, than those obtained using conventional methods, such as interpolation using spherical radial basis functions (SRBFs).

The derivative-free Fourier shell identity for photoacoustics.

PubMed

Baddour, Natalie

2016-01-01

In X-ray tomography, the Fourier slice theorem provides a relationship between the Fourier components of the object being imaged and the measured projection data. The Fourier slice theorem is the basis for X-ray Fourier-based tomographic inversion techniques. A similar relationship, referred to as the 'Fourier shell identity' has been previously derived for photoacoustic applications. However, this identity relates the pressure wavefield data function and its normal derivative measured on an arbitrary enclosing aperture to the three-dimensional Fourier transform of the enclosed object evaluated on a sphere. Since the normal derivative of pressure is not normally measured, the applicability of the formulation is limited in this form. In this paper, alternative derivations of the Fourier shell identity in 1D, 2D polar and 3D spherical polar coordinates are presented. The presented formulations do not require the normal derivative of pressure, thereby lending the formulas directly adaptable for Fourier based absorber reconstructions.

On the error in the nucleus-centered multipolar expansion of molecular electron density and its topology: A direct-space computational study

NASA Astrophysics Data System (ADS)

Michael, J. Robert; Koritsanszky, Tibor

2017-05-01

The convergence of nucleus-centered multipolar expansion of the quantum-chemical electron density (QC-ED), gradient, and Laplacian is investigated in terms of numerical radial functions derived by projecting stockholder atoms onto real spherical harmonics at each center. The partial sums of this exact one-center expansion are compared with the corresponding Hansen-Coppens pseudoatom (HC-PA) formalism [Hansen, N. K. and Coppens, P., "Testing aspherical atom refinements on small-molecule data sets," Acta Crystallogr., Sect. A 34, 909-921 (1978)] commonly utilized in experimental electron density studies. It is found that the latter model, due to its inadequate radial part, lacks pointwise convergence and fails to reproduce the local topology of the target QC-ED even at a high-order expansion. The significance of the quantitative agreement often found between HC-PA-based (quadrupolar-level) experimental and extended-basis QC-EDs can thus be challenged.

Modeling the directional reflectance from complete homogeneous vegetation canopies with various leaf-orientation distributions

NASA Technical Reports Server (NTRS)

Kimes, D. S.

1984-01-01

The directional-reflectance distributions of radiant flux from homogeneous vegetation canopies with greater than 90 percent ground cover are analyzed with a radiative-transfer model. The model assumes that the leaves consist of small finite planes with Lambertian properties. Four theoretical canopies with different leaf-orientation distributions were studied: erectophile, spherical, planophile, and heliotropic canopies. The directional-reflectance distributions from the model closely resemble reflectance distributions measured in the field. The physical scattering mechanisms operating in the model explain the variations observed in the reflectance distributions as a function of leaf-orientation distribution, solar zenith angle, and leaf transmittance and reflectance. The simulated reflectance distribution show unique characteristics for each canopy. The basic understanding of the physical scattering properties of the different canopy geometries gained in this study provide a basis for developing techniques to infer leaf-orientation distributions of vegetation canopies from directional remote-sensing measurements.

Ionic Asymmetry and Solvent Excluded Volume Effects on Spherical Electric Double Layers: A Density Functional Approach

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

Medasani, Bharat; Ovanesyan, Zaven; Thomas, Dennis G.

In this article we present a classical density functional theory for electrical double layers of spherical macroions that extends the capabilities of conventional approaches by accounting for electrostatic ion correlations, size asymmetry and excluded volume effects. The approach is based on a recent approximation introduced by Hansen-Goos and Roth for the hard sphere excess free energy of inhomogeneous fluids (J. Chem. Phys. 124, 154506). It accounts for the proper and efficient description of the effects of ionic asymmetry and solvent excluded volume, especially at high ion concentrations and size asymmetry ratios including those observed in experimental studies. Additionally, we utilizemore » a leading functional Taylor expansion approximation of the ion density profiles. In addition, we use the Mean Spherical Approximation for multi-component charged hard sphere fluids to account for the electrostatic ion correlation effects. These approximations are implemented in our theoretical formulation into a suitable decomposition of the excess free energy which plays a key role in capturing the complex interplay between charge correlations and excluded volume effects. We perform Monte Carlo simulations in various scenarios to validate the proposed approach, obtaining a good compromise between accuracy and computational cost. We use the proposed computational approach to study the effects of ion size, ion size asymmetry and solvent excluded volume on the ion profiles, integrated charge, mean electrostatic potential, and ionic coordination number around spherical macroions in various electrolyte mixtures. Our results show that both solvent hard sphere diameter and density play a dominant role in the distribution of ions around spherical macroions, mainly for experimental water molarity and size values where the counterion distribution is characterized by a tight binding to the macroion, similar to that predicted by the Stern model.« less

Spherical shock waves in general relativity

NASA Astrophysics Data System (ADS)

Nutku, Y.

1991-11-01

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-N vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-N Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the C0-form of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.

Director Field Analysis (DFA): Exploring Local White Matter Geometric Structure in Diffusion MRI.

PubMed

Cheng, Jian; Basser, Peter J

2018-01-01

In Diffusion Tensor Imaging (DTI) or High Angular Resolution Diffusion Imaging (HARDI), a tensor field or a spherical function field (e.g., an orientation distribution function field), can be estimated from measured diffusion weighted images. In this paper, inspired by the microscopic theoretical treatment of phases in liquid crystals, we introduce a novel mathematical framework, called Director Field Analysis (DFA), to study local geometric structural information of white matter based on the reconstructed tensor field or spherical function field: (1) We propose a set of mathematical tools to process general director data, which consists of dyadic tensors that have orientations but no direction. (2) We propose Orientational Order (OO) and Orientational Dispersion (OD) indices to describe the degree of alignment and dispersion of a spherical function in a single voxel or in a region, respectively; (3) We also show how to construct a local orthogonal coordinate frame in each voxel exhibiting anisotropic diffusion; (4) Finally, we define three indices to describe three types of orientational distortion (splay, bend, and twist) in a local spatial neighborhood, and a total distortion index to describe distortions of all three types. To our knowledge, this is the first work to quantitatively describe orientational distortion (splay, bend, and twist) in general spherical function fields from DTI or HARDI data. The proposed DFA and its related mathematical tools can be used to process not only diffusion MRI data but also general director field data, and the proposed scalar indices are useful for detecting local geometric changes of white matter for voxel-based or tract-based analysis in both DTI and HARDI acquisitions. The related codes and a tutorial for DFA will be released in DMRITool. Copyright © 2017 Elsevier B.V. All rights reserved.

In-flight performance of the Faint Object Camera of the Hubble Space Telescope

NASA Technical Reports Server (NTRS)

Greenfield, P.; Paresce, F.; Baxter, D.; Hodge, P.; Hook, R.; Jakobsen, P.; Jedrzejewski, R.; Nota, A.; Sparks, W. B.; Towers, N.

1991-01-01

An overview of the Faint Object Camera and its performance to date is presented. In particular, the detector's efficiency, the spatial uniformity of response, distortion characteristics, detector and sky background, detector linearity, spectrography, and operation are discussed. The effect of the severe spherical aberration of the telescope's primary mirror on the camera's point spread function is reviewed, as well as the impact it has on the camera's general performance. The scientific implications of the performance and the spherical aberration are outlined, with emphasis on possible remedies for spherical aberration, hardware remedies, and stellar population studies.

Dose in critical body organs in low Earth orbit

NASA Technical Reports Server (NTRS)

Wilson, J. W.; Cucinotta, F.

1984-01-01

Human exposure to trapped radiations in low Earth orbit (LEO) are evaluated on the basis of a simple approximation of the human geometry for spherical shell shields of varying thickness. A data base is presented that may be used to make preliminary assessment of the impact of radiation exposure constraints on human performance. A sample impact assessment is discussed.

Elastic energy of polyhedral bilayer vesicles

PubMed Central

Haselwandter, Christoph A.; Phillips, Rob

2011-01-01

In recent experiments the spontaneous formation of hollow bilayer vesicles with polyhedral symmetry has been observed. On the basis of the experimental phenomenology it was suggested that the mechanism for the formation of bilayer polyhedra is minimization of elastic bending energy. Motivated by these experiments, we study the elastic bending energy of polyhedral bilayer vesicles. In agreement with experiments, and provided that excess amphiphiles exhibiting spontaneous curvature are present in sufficient quantity, we find that polyhedral bilayer vesicles can indeed be energetically favorable compared to spherical bilayer vesicles. Consistent with experimental observations we also find that the bending energy associated with the vertices of bilayer polyhedra can be locally reduced through the formation of pores. However, the stabilization of polyhedral bilayer vesicles over spherical bilayer vesicles relies crucially on molecular segregation of excess amphiphiles along the ridges rather than the vertices of bilayer polyhedra. Furthermore, our analysis implies that, contrary to what has been suggested on the basis of experiments, the icosahedron does not minimize elastic bending energy among arbitrary polyhedral shapes and sizes. Instead, we find that, for large polyhedron sizes, the snub dodecahedron and the snub cube both have lower total bending energies than the icosahedron. PMID:21797397

GRACE L1b inversion through a self-consistent modified radial basis function approach

NASA Astrophysics Data System (ADS)

Yang, Fan; Kusche, Juergen; Rietbroek, Roelof; Eicker, Annette

2016-04-01

Implementing a regional geopotential representation such as mascons or, more general, RBFs (radial basis functions) has been widely accepted as an efficient and flexible approach to recover the gravity field from GRACE (Gravity Recovery and Climate Experiment), especially at higher latitude region like Greenland. This is since RBFs allow for regionally specific regularizations over areas which have sufficient and dense GRACE observations. Although existing RBF solutions show a better resolution than classical spherical harmonic solutions, the applied regularizations cause spatial leakage which should be carefully dealt with. It has been shown that leakage is a main error source which leads to an evident underestimation of yearly trend of ice-melting over Greenland. Unlike some popular post-processing techniques to mitigate leakage signals, this study, for the first time, attempts to reduce the leakage directly in the GRACE L1b inversion by constructing an innovative modified (MRBF) basis in place of the standard RBFs to retrieve a more realistic temporal gravity signal along the coastline. Our point of departure is that the surface mass loading associated with standard RBF is smooth but disregards physical consistency between continental mass and passive ocean response. In this contribution, based on earlier work by Clarke et al.(2007), a physically self-consistent MRBF representation is constructed from standard RBFs, with the help of the sea level equation: for a given standard RBF basis, the corresponding MRBF basis is first obtained by keeping the surface load over the continent unchanged, but imposing global mass conservation and equilibrium response of the oceans. Then, the updated set of MRBFs as well as standard RBFs are individually employed as the basis function to determine the temporal gravity field from GRACE L1b data. In this way, in the MRBF GRACE solution, the passive (e.g. ice melting and land hydrology response) sea level is automatically separated from ocean dynamic effects, and our hypothesis is that in this way we improve the partitioning of the GRACE signals into land and ocean contributions along the coastline. In particular, we inspect the ice-melting over Greenland from real GRACE data, and we evaluate the ability of the MRBF approach to recover true mass variations along the coastline. Finally, using independent measurements from multiple techniques including GPS vertical motion and altimetry, a validation will be presented to quantify to what extent it is possible to reduce the leakage through the MRBF approach.

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.

Comparison of Subjective Refraction under Binocular and Monocular Conditions in Myopic Subjects.

PubMed

Kobashi, Hidenaga; Kamiya, Kazutaka; Handa, Tomoya; Ando, Wakako; Kawamorita, Takushi; Igarashi, Akihito; Shimizu, Kimiya

2015-07-28

To compare subjective refraction under binocular and monocular conditions, and to investigate the clinical factors affecting the difference in spherical refraction between the two conditions. We examined thirty eyes of 30 healthy subjects. Binocular and monocular refraction without cycloplegia was measured through circular polarizing lenses in both eyes, using the Landolt-C chart of the 3D visual function trainer-ORTe. Stepwise multiple regression analysis was used to assess the relations among several pairs of variables and the difference in spherical refraction in binocular and monocular conditions. Subjective spherical refraction in the monocular condition was significantly more myopic than that in the binocular condition (p < 0.001), whereas no significant differences were seen in subjective cylindrical refraction (p = 0.99). The explanatory variable relevant to the difference in spherical refraction between binocular and monocular conditions was the binocular spherical refraction (p = 0.032, partial regression coefficient B = 0.029) (adjusted R(2) = 0.230). No significant correlation was seen with other clinical factors. Subjective spherical refraction in the monocular condition was significantly more myopic than that in the binocular condition. Eyes with higher degrees of myopia are more predisposed to show the large difference in spherical refraction between these two conditions.

Comparison of Subjective Refraction under Binocular and Monocular Conditions in Myopic Subjects

PubMed Central

Kobashi, Hidenaga; Kamiya, Kazutaka; Handa, Tomoya; Ando, Wakako; Kawamorita, Takushi; Igarashi, Akihito; Shimizu, Kimiya

2015-01-01

To compare subjective refraction under binocular and monocular conditions, and to investigate the clinical factors affecting the difference in spherical refraction between the two conditions. We examined thirty eyes of 30 healthy subjects. Binocular and monocular refraction without cycloplegia was measured through circular polarizing lenses in both eyes, using the Landolt-C chart of the 3D visual function trainer-ORTe. Stepwise multiple regression analysis was used to assess the relations among several pairs of variables and the difference in spherical refraction in binocular and monocular conditions. Subjective spherical refraction in the monocular condition was significantly more myopic than that in the binocular condition (p < 0.001), whereas no significant differences were seen in subjective cylindrical refraction (p = 0.99). The explanatory variable relevant to the difference in spherical refraction between binocular and monocular conditions was the binocular spherical refraction (p = 0.032, partial regression coefficient B = 0.029) (adjusted R2 = 0.230). No significant correlation was seen with other clinical factors. Subjective spherical refraction in the monocular condition was significantly more myopic than that in the binocular condition. Eyes with higher degrees of myopia are more predisposed to show the large difference in spherical refraction between these two conditions. PMID:26218972

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.

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.

Shape fluctuations of nearly spherical lipid vesicles and emulsion droplets.

PubMed

Bivas, Isak

2010-06-01

It is known that the relaxation of the shape fluctuations of nearly spherical lipid vesicles is accompanied by a lateral displacement of the monolayers, comprising their bilayers. In this work a dissipation mechanism of the mechanical energy stored in the fluctuation is revealed that concerns the viscous friction of the flow in the liquid around the vesicle caused by this displacement. The time correlation functions of each of the vesicle's fluctuation modes are calculated as a function of the mechanical and rheological properties of the system which are the tension of the vesicle bilayer, its bending elasticities at free and blocked flip-flop, the viscosities of the liquids bathing the bilayer, the friction coefficient between the two monolayers, as well as the vesicle's dimensions: its bilayer thickness and radius. The correlations of the shape fluctuations of nearly spherical emulsion droplets are also calculated for different viscosities of the liquid inside and outside the droplet.

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.

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.

Generalizations of the Toda molecule

NASA Astrophysics Data System (ADS)

Van Velthoven, W. P. G.; Bais, F. A.

1986-12-01

Finite-energy monopole solutions are constructed for the self-dual equations with spherical symmetry in an arbitrary integer graded Lie algebra. The constraint of spherical symmetry in a complex noncoordinate basis leads to a dimensional reduction. The resulting two-dimensional ( r, t) equations are of second order and furnish new generalizations of the Toda molecule equations. These are then solved by a technique which is due to Leznov and Saveliev. For time-independent solutions a further reduction is made, leading to an ansatz for all SU(2) embeddings of the Lie algebra. The regularity condition at the origin for the solutions, needed to ensure finite energy, is also solved for a special class of nonmaximal embeddings. Explicit solutions are given for the groups SU(2), SO(4), Sp(4) and SU(4).

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.

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.

Influence of Shape and Gradient Refractive Index in the Accommodative Changes of Spherical Aberration in Nonhuman Primate Crystalline Lenses

PubMed Central

de Castro, Alberto; Birkenfeld, Judith; Maceo, Bianca; Manns, Fabrice; Arrieta, Esdras; Parel, Jean-Marie; Marcos, Susana

2013-01-01

Purpose. To estimate changes in surface shape and gradient refractive index (GRIN) profile in primate lenses as a function of accommodation. To quantify the contribution of surface shape and GRIN to spherical aberration changes with accommodation. Methods. Crystalline lenses from 15 cynomolgus monkeys were studied in vitro under different levels of accommodation produced by a stretching system. Lens shape was obtained from optical coherence tomography (OCT) cross-sectional images. The GRIN was reconstructed with a search algorithm using the optical path measured from OCT images and the measured back focal length. The spherical aberration of the lens was estimated as a function of accommodation using the reconstructed GRIN and a homogeneous refractive index. Results. The lens anterior and posterior radii of curvature decreased with increasing lens power. Both surfaces exhibited negative asphericities in the unaccommodated state. The anterior surface conic constant shifted toward less negative values with accommodation, while the value of the posterior remained constant. GRIN parameters remained constant with accommodation. The lens spherical aberration with GRIN distribution was negative and higher in magnitude than that with a homogeneous equivalent refractive index (by 29% and 53% in the unaccommodated and fully accommodated states, respectively). Spherical aberration with the equivalent refractive index shifted with accommodation toward negative values (−0.070 μm/diopter [D]), but the reconstructed GRIN shifted it farther (−0.124 μm/D). Conclusions. When compared with the lens with the homogeneous equivalent refractive index, the reconstructed GRIN lens has more negative spherical aberration and a larger shift toward more negative values with accommodation. PMID:23927893

An Accurate Analytic Approximation for Light Scattering by Non-absorbing Spherical Aerosol Particles

NASA Astrophysics Data System (ADS)

Lewis, E. R.

2017-12-01

The scattering of light by particles in the atmosphere is a ubiquitous and important phenomenon, with applications to numerous fields of science and technology. The problem of scattering of electromagnetic radiation by a uniform spherical particle can be solved by the method of Mie and Debye as a series of terms depending on the size parameter, x=2πr/λ, and the complex index of refraction, m. However, this solution does not provide insight into the dependence of the scattering on the radius of the particle, the wavelength, or the index of refraction, or how the scattering varies with relative humidity. Van de Hulst demonstrated that the scattering efficiency (the scattering cross section divided by the geometric cross section) of a non-absorbing sphere, over a wide range of particle sizes of atmospheric importance, depends not on x and m separately, but on the quantity 2x(m-1); this is the basis for the anomalous diffraction approximation. Here an analytic approximation for the scattering efficiency of a non-absorbing spherical particle is presented in terms of this new quantity that is accurate over a wide range of particle sizes of atmospheric importance and which readily displays the dependences of the scattering efficiency on particle radius, index of refraction, and wavelength. For an aerosol for which the particle size distribution is parameterized as a gamma function, this approximation also yields analytical results for the scattering coefficient and for the Ångström exponent, with the dependences of scattering properties on wavelength and index of refraction clearly displayed. This approximation provides insight into the dependence of light scattering properties on factors such as relative humidity, readily enables conversion of scattering from one index of refraction to another, and demonstrates the conditions under which the aerosol index (the product of the aerosol optical depth and the Ångström exponent) is a useful proxy for the number of cloud condensation nuclei.

Ordered Self-Assembly Mechanism of a Spherical Oncoprotein Oligomer Triggered by Zinc Removal and Stabilized by an Intrinsically Disordered Domain

PubMed Central

Smal, Clara; Alonso, Leonardo G.; Wetzler, Diana E.; Heer, Angeles; de Prat Gay, Gonzalo

2012-01-01

Background Self-assembly is a common theme in proteins of unrelated sequences or functions. The human papillomavirus E7 oncoprotein is an extended dimer with an intrinsically disordered domain, that can form large spherical oligomers. These are the major species in the cytosol of HPV transformed and cancerous cells. E7 binds to a large number of targets, some of which lead to cell transformation. Thus, the assembly process not only is of biological relevance, but represents a model system to investigate a widely distributed mechanism. Methodology/Principal Findings Using various techniques, we monitored changes in secondary, tertiary and quaternary structure in a time course manner. By applying a robust kinetic model developed by Zlotnik, we determined the slow formation of a monomeric “Z-nucleus” after zinc removal, followed by an elongation phase consisting of sequential second-order events whereby one monomer is added at a time. This elongation process takes place at a strikingly slow overall average rate of one monomer added every 28 seconds at 20 µM protein concentration, strongly suggesting either a rearrangement of the growing complex after binding of each monomer or the existence of a “conformation editing” mechanism through which the monomer binds and releases until the appropriate conformation is adopted. The oligomerization determinant lies within its small 5 kDa C-terminal globular domain and, remarkably, the E7 N-terminal intrinsically disordered domain stabilizes the oligomer, preventing an insoluble amyloid route. Conclusion We described a controlled ordered mechanism with features in common with soluble amyloid precursors, chaperones, and other spherical oligomers, thus sharing determining factors for symmetry, size and shape. In addition, such a controlled and discrete polymerization reaction provides a valuable tool for nanotechnological applications. Finally, its increased immunogenicity related to its supramolecular structure is the basis for the development of a promising therapeutic vaccine candidate for treating HPV cancerous lesions. PMID:22590549

Bio-inspired synthesis of hybrid silica nanoparticles templated from elastin-like polypeptide micelles

NASA Astrophysics Data System (ADS)

Han, Wei; MacEwan, Sarah R.; Chilkoti, Ashutosh; López, Gabriel P.

2015-07-01

The programmed self-assembly of block copolymers into higher order nanoscale structures offers many attractive attributes for the development of new nanomaterials for numerous applications including drug delivery and biosensing. The incorporation of biomimetic silaffin peptides in these block copolymers enables the formation of hybrid organic-inorganic materials, which can potentially enhance the utility and stability of self-assembled nanostructures. We demonstrate the design, synthesis and characterization of amphiphilic elastin-like polypeptide (ELP) diblock copolymers that undergo temperature-triggered self-assembly into well-defined spherical micelles. Genetically encoded incorporation of the silaffin R5 peptide at the hydrophilic terminus of the diblock ELP leads to presentation of the silaffin R5 peptide on the coronae of the micelles, which results in localized condensation of silica and the formation of near-monodisperse, discrete, sub-100 nm diameter hybrid ELP-silica particles. This synthesis method, can be carried out under mild reaction conditions suitable for bioactive materials, and will serve as the basis for the development and application of functional nanomaterials. Beyond silicification, the general strategies described herein may also be adapted for the synthesis of other biohybrid nanomaterials as well.The programmed self-assembly of block copolymers into higher order nanoscale structures offers many attractive attributes for the development of new nanomaterials for numerous applications including drug delivery and biosensing. The incorporation of biomimetic silaffin peptides in these block copolymers enables the formation of hybrid organic-inorganic materials, which can potentially enhance the utility and stability of self-assembled nanostructures. We demonstrate the design, synthesis and characterization of amphiphilic elastin-like polypeptide (ELP) diblock copolymers that undergo temperature-triggered self-assembly into well-defined spherical micelles. Genetically encoded incorporation of the silaffin R5 peptide at the hydrophilic terminus of the diblock ELP leads to presentation of the silaffin R5 peptide on the coronae of the micelles, which results in localized condensation of silica and the formation of near-monodisperse, discrete, sub-100 nm diameter hybrid ELP-silica particles. This synthesis method, can be carried out under mild reaction conditions suitable for bioactive materials, and will serve as the basis for the development and application of functional nanomaterials. Beyond silicification, the general strategies described herein may also be adapted for the synthesis of other biohybrid nanomaterials as well. Electronic supplementary information (ESI) available. See DOI: 10.1039/c5nr01407g

Spherical demons: fast diffeomorphic landmark-free surface registration.

PubMed

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

2010-03-01

We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160 k nodes requires less than 5 min when warping the atlas and less than 3 min when warping the subject on a Xeon 3.2 GHz single processor machine. This is comparable to the fastest nondiffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image 1) parcellation of in vivo cortical surfaces and 2) Brodmann area localization in ex vivo cortical surfaces.

Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration

PubMed Central

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

2010-01-01

We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160k nodes requires less than 5 minutes when warping the atlas and less than 3 minutes when warping the subject on a Xeon 3.2GHz single processor machine. This is comparable to the fastest non-diffeomorphic landmark-free surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image: (1) parcellation of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces. PMID:19709963

Spherical shock waves in general relativity

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

Nutku, Y.

1991-11-15

We present the metric appropriate to a spherical shock wave in the framework of general relativity. This is a Petrov type-{ital N} vacuum solution of the Einstein field equations where the metric is continuous across the shock and the Riemann tensor suffers a step-function discontinuity. Spherical gravitational waves are described by type-{ital N} Robinson-Trautman metrics. However, for shock waves the Robinson-Trautman solutions are unacceptable because the metric becomes discontinuous in the Robinson-Trautman coordinate system. Other coordinate systems that have so far been introduced for describing Robinson-Trautman solutions also suffer from the same defect. We shall present the {ital C}{sup 0}-formmore » of the metric appropriate to spherical shock waves using Penrose's approach of identification with warp. Further extensions of Penrose's method yield accelerating, as well as coupled electromagnetic-gravitational shock-wave solutions.« less

Correcting spherical aberrations induced by an unknown medium through determination of its refractive index and thickness.

PubMed

Iwaniuk, Daniel; Rastogi, Pramod; Hack, Erwin

2011-09-26

In imaging and focusing applications, spherical aberration induces axial broadening of the point spread function (PSF). A transparent medium between lens and object of interest induces spherical aberration. We propose a method that first obtains both the physical thickness and the refractive index of the aberration inducing medium in situ by measuring the induced focal shifts for paraxial and large angle rays. Then, the fourth order angle dependence of the optical path difference inside the medium is used to correct the spherical aberration using a phase-only spatial light modulator. The obtained measurement accuracy of 3% is sufficient for a complete compensation as demonstrated in a model microscope with NA 0.3 with glass plate induced axial broadening of the PSF by a factor of 5. © 2011 Optical Society of America

On computing special functions in marine engineering

NASA Astrophysics Data System (ADS)

Constantinescu, E.; Bogdan, M.

2015-11-01

Important modeling applications in marine engineering conduct us to a special class of solutions for difficult differential equations with variable coefficients. In order to be able to solve and implement such models (in wave theory, in acoustics, in hydrodynamics, in electromagnetic waves, but also in many other engineering fields), it is necessary to compute so called special functions: Bessel functions, modified Bessel functions, spherical Bessel functions, Hankel functions. The aim of this paper is to develop numerical solutions in Matlab for the above mentioned special functions. Taking into account the main properties for Bessel and modified Bessel functions, we shortly present analytically solutions (where possible) in the form of series. Especially it is studied the behavior of these special functions using Matlab facilities: numerical solutions and plotting. Finally, it will be compared the behavior of the special functions and point out other directions for investigating properties of Bessel and spherical Bessel functions. The asymptotic forms of Bessel functions and modified Bessel functions allow determination of important properties of these functions. The modified Bessel functions tend to look more like decaying and growing exponentials.

Simulation of perturbation produced by an absorbing spherical body in collisionless plasma

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

Krasovsky, V. L., E-mail: vkrasov@iki.rssi.ru; Kiselyov, A. A., E-mail: alexander.kiselyov@stonehenge-3.net.ru; Dolgonosov, M. S.

2017-01-15

A steady plasma state reached in the course of charging of an absorbing spherical body is found using computational methods. Numerical simulations provide complete information on this process, thereby allowing one to find the spatiotemporal dependences of the physical quantities and observe the kinetic phenomena accompanying the formation of stable electron and ion distributions in phase space. The distribution function of trapped ions is obtained, and their contribution to the screening of the charged sphere is determined. The sphere charge and the charge of the trapped-ion cloud are determined as functions of the unperturbed plasma parameters.

New 2D dilaton gravity for nonsingular black holes

NASA Astrophysics Data System (ADS)

Kunstatter, Gabor; Maeda, Hideki; Taves, Tim

2016-05-01

We construct a two-dimensional action that is an extension of spherically symmetric Einstein-Lanczos-Lovelock (ELL) gravity. The action contains arbitrary functions of the areal radius and the norm squared of its gradient, but the field equations are second order and obey Birkhoff’s theorem. In complete analogy with spherically symmetric ELL gravity, the field equations admit the generalized Misner-Sharp mass as the first integral that determines the form of the vacuum solution. The arbitrary functions in the action allow for vacuum solutions that describe a larger class of interesting nonsingular black hole spacetimes than previously available.

Study of the geodesic equations of a spherical symmetric spacetime in conformal Weyl gravity

NASA Astrophysics Data System (ADS)

Hoseini, Bahareh; Saffari, Reza; Soroushfar, Saheb

2017-03-01

A set of analytic solutions of the geodesic equation in a spherical conformal spacetime is presented. Solutions of this geodesics can be expressed in terms of the Weierstrass \\wp function and the Kleinian σ function. Using conserved energy and angular momentum we can characterize the different orbits. Also, considering parametric diagrams and effective potentials, we plot some possible orbits. Moreover, with the help of analytical solutions, we investigate the light deflection for such an escape orbit. Finally, by using periastron advance we get to an upper bound for magnitude of γ.

The method of planes pressure tensor for a spherical subvolume

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

Heyes, D. M., E-mail: d.heyes@imperial.ac.uk; Smith, E. R., E-mail: edward.smith05@imperial.ac.uk; Dini, D., E-mail: d.dini@imperial.ac.uk

2014-02-07

Various formulas for the local pressure tensor based on a spherical subvolume of radius, R, are considered. An extension of the Method of Planes (MOP) formula of Todd et al. [Phys. Rev. E 52, 1627 (1995)] for a spherical geometry is derived using the recently proposed Control Volume formulation [E. R. Smith, D. M. Heyes, D. Dini, and T. A. Zaki, Phys. Rev. E 85, 056705 (2012)]. The MOP formula for the purely radial component of the pressure tensor is shown to be mathematically identical to the Radial Irving-Kirkwood formula. Novel offdiagonal elements which are important for momentum conservation emergemore » naturally from this treatment. The local pressure tensor formulas for a plane are shown to be the large radius limits of those for spherical surfaces. The radial-dependence of the pressure tensor computed by Molecular Dynamics simulation is reported for virtual spheres in a model bulk liquid where the sphere is positioned randomly or whose center is also that of a molecule in the liquid. The probability distributions of angles relating to pairs of atoms which cross the surface of the sphere, and the center of the sphere, are presented as a function of R. The variance in the shear stress calculated from the spherical Volume Averaging method is shown to converge slowly to the limiting values with increasing radius, and to be a strong function of the number of molecules in the simulation cell.« less

Local scattering stress distribution on surface of a spherical cell in optical stretcher

NASA Astrophysics Data System (ADS)

Bareil, Paul B.; Sheng, Yunlong; Chiou, Arthur

2006-12-01

We calculate stress distribution on the surface of a spherical cell trapped by two counter propagating beams in the optical stretcher in the ray optics regime. We demonstrate that the local scattering stress is perpendicular to the spherical refractive surface regardless of incident angle, polarization and the reflectance and transmittance at the surface. We explain the apparition of peaks in the stress distribution, which were not revealed in the existing theory. We consider the divergence of the incident beams from the fibers, and express the stress distribution as a function of fiber-to-cell distance. The new theory can predict the cell’s deformation more precisely.

GPS Recovery of Daily Hydrologic and Atmospheric Mass Variation: A Methodology and Results From the Australian Continent

NASA Astrophysics Data System (ADS)

Han, Shin-Chan; Razeghi, S. Mahdiyeh

2017-11-01

We present a methodology to invert a regional set of vertical displacement data from Global Positioning System (GPS) to determine the surface mass redistribution. It is assumed that GPS deformation is a result of the Earth's elastic response to the surface mass load of hydrology, atmosphere, and/or ocean. We develop an algorithm to estimate the spectral information of displacements from "regional" GPS data through regional spherical (Slepian) basis functions and apply the load Love numbers to estimate the mass load. The same approach is applied to determine global mass changes from "global" geopotential change data of Gravity Recovery and Climate Experiment (GRACE). We rigorously examine all systematic errors caused by various truncations (spherical harmonic series and Slepian series) and the smoothing constraint applied to the GPS inversion. We demonstrate the technique by processing 16 years of daily vertical motions determined from 114 GPS stations in Australia. The GPS-inverted surface mass changes are validated against GRACE data, atmosphere and ocean models, and a land surface model. Seasonal and interannual terrestrial mass variations from GPS are in good agreement with GRACE data and the water storage models. The GPS recovery compares better with the water storage model around the smaller coastal basins than two different GRACE solutions. The submonthly mass changes from GPS provide meaningful results agreeing with atmospheric mass changes in central Australia. Finally, it is suggested to integrate GPS and GRACE data to draw a comprehensive picture of daily mass changes on different continents.

Second rank direction cosine spherical tensor operators and the nuclear electric quadrupole hyperfine structure Hamiltonian of rotating molecules

NASA Astrophysics Data System (ADS)

di Lauro, C.

2018-03-01

Transformations of vector or tensor properties from a space-fixed to a molecule-fixed axis system are often required in the study of rotating molecules. Spherical components λμ,ν of a first rank irreducible tensor can be obtained from the direction cosines between the two axis systems, and a second rank tensor with spherical components λμ,ν(2) can be built from the direct product λ × λ. It is shown that the treatment of the interaction between molecular rotation and the electric quadrupole of a nucleus is greatly simplified, if the coefficients in the axis-system transformation of the gradient of the electric field of the outer charges at the coupled nucleus are arranged as spherical components λμ,ν(2). Then the reduced matrix elements of the field gradient operators in a symmetric top eigenfunction basis, including their dependence on the molecule-fixed z-angular momentum component k, can be determined from the knowledge of those of λ(2) . The hyperfine structure Hamiltonian Hq is expressed as the sum of terms characterized each by a value of the molecule-fixed index ν, whose matrix elements obey the rule Δk = ν. Some of these terms may vanish because of molecular symmetry, and the specific cases of linear and symmetric top molecules, orthorhombic molecules, and molecules with symmetry lower than orthorhombic are considered. Each ν-term consists of a contraction of the rotational tensor λ(2) and the nuclear quadrupole tensor in the space-fixed frame, and its matrix elements in the rotation-nuclear spin coupled representation can be determined by the standard spherical tensor methods.

Models for randomly distributed nanoscopic domains on spherical vesicles

NASA Astrophysics Data System (ADS)

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

2018-06-01

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

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.

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

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.

A symmetric integral identity for Bessel functions with applications to integral geometry

NASA Astrophysics Data System (ADS)

Salman, Yehonatan

2017-12-01

In the article of Kunyansky (Inverse Probl 23(1):373-383, 2007) a symmetric integral identity for Bessel functions of the first and second kind was proved in order to obtain an explicit inversion formula for the spherical mean transform where our data is given on the unit sphere in Rn . The aim of this paper is to prove an analogous symmetric integral identity in case where our data for the spherical mean transform is given on an ellipse E in R2 . For this, we will use the recent results obtained by Cohl and Volkmer (J Phys A Math Theor 45:355204, 2012) for the expansions into eigenfunctions of Bessel functions of the first and second kind in elliptical coordinates.

Topological structure prediction in binary nanoparticle superlattices

DOE PAGES

Travesset, A.

2017-04-27

Systems of spherical nanoparticles with capping ligands have been shown to self-assemble into beautiful superlattices of fascinating structure and complexity. Here, I show that the spherical geometry of the nanoparticle imposes constraints on the nature of the topological defects associated with the capping ligand and that such topological defects control the structure and stability of the superlattices that can be assembled. Furthermore, all of these considerations form the basis for the orbifold topological model (OTM) described in this paper. Finally, the model quantitatively predicts the structure of super-lattices where capping ligands are hydrocarbon chains in excellent agreement with experimental results,more » explains the appearance of low packing fraction lattices as equilibrium, why certain similar structures are more stable (bccAB 6vs. CaB 6, AuCu vs. CsCl, etc.) and many other experimental observations.« less

A temperature correction method for expanding atmospheres

NASA Astrophysics Data System (ADS)

Hamann, W.-R.; Gräfener, G.

2003-11-01

Model atmospheres form the basis for the interpretation of stellar spectra. A major problem in those model calculations is to establish the temperature stratification from the condition of radiative equilibrium. Dealing with non-LTE models for spherically expanding atmospheres of Wolf-Rayet stars, we developed a new temperature correction method. Its basic idea dates back to 1955 when it was proposed by Unsöld for grey, static and plane-parallel atmospheres in LTE. The equations were later generalized to the non-grey case by Lucy. In the present paper we furthermore drop the Eddington approximation, proceed to spherical geometry and allow for expansion of the atmosphere. Finally the concept of an ``approximate lambda operator'' is employed to speed up the convergence. Tests for Wolf-Rayet type models demonstrate that the method works fine even in situations of strong non-LTE.

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.

Effect of amine functionalization of spherical MCM-41 and SBA-15 on controlled drug release

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

Szegedi, A., E-mail: szegedi@chemres.h; Popova, M.; Goshev, I.

2011-05-15

MCM-41 and SBA-15 silica materials with spherical morphology and different particle sizes were synthesized and modified by post-synthesis method with 3-aminopropyltriethoxysilane (APTES). A comparative study of the adsorption and release of a model drug, ibuprofen, were carried out. The modified and drug loaded mesoporous materials were characterized by XRD, TEM, N{sub 2} physisorption, thermal analysis, elemental analysis and FT-IR spectroscopy. Surface modification with amino groups resulted in high degree of ibuprofen loading and slow rate of release for MCM-41, whereas it was the opposite for SBA-15. The adsorbed drug content and the delivery rate can be predetermined by the choicemore » of mesoporous material with the appropriate structural characteristics and surface functionality. -- Graphical Abstract: Ibuprofen delivery from the parent and amino-modified spherical MCM-41 materials with 100 nm (small) and 500 nm (large) particle sizes. Display Omitted Highlights: {yields} Spherical type MCM-41 and SBA-15 with different particle sizes were modified by APTES. {yields} Adsorption and release rate of ibuprofen were compared. {yields} High degree of ibuprofen loading, slow release rate for MCM-41, the opposite for SBA-15. {yields} MCM-41 with 100 nm particles was more stable and showed slower release rate« less

Receiving sensitivity and transmitting voltage response of a fluid loaded spherical piezoelectric transducer with an elastic coating.

PubMed

George, Jineesh; Ebenezer, D D; Bhattacharyya, S K

2010-10-01

A method is presented to determine the response of a spherical acoustic transducer that consists of a fluid-filled piezoelectric sphere with an elastic coating embedded in infinite fluid to electrical and plane-wave acoustic excitations. The exact spherically symmetric, linear, differential, governing equations are used for the interior and exterior fluids, and elastic and piezoelectric materials. Under acoustic excitation and open circuit boundary condition, the equation governing the piezoelectric sphere is homogeneous and the solution is expressed in terms of Bessel functions. Under electrical excitation, the equation governing the piezoelectric sphere is inhomogeneous and the complementary solution is expressed in terms of Bessel functions and the particular integral is expressed in terms of a power series. Numerical results are presented to illustrate the effect of dimensions of the piezoelectric sphere, fluid loading, elastic coating and internal material losses on the open-circuit receiving sensitivity and transmitting voltage response of the transducer.

Generalized seniority on a deformed single-particle basis

NASA Astrophysics Data System (ADS)

Jia, L. Y.

2017-09-01

Recently, I proposed a fast computing scheme for generalized seniority on a spherical single-particle basis [J. Phys. G: Nucl. Part. Phys. 42, 115105 (2015), 10.1088/0954-3899/42/11/115105]. This work redesigns the scheme to make it applicable to deformed single-particle basis. The algorithm is applied to the rare-earth-metal nucleus 94 64 158Gd for intrinsic (body-fixed frame) neutron excitations under the low-momentum NN interaction Vlow -k. By allowing as many as four broken pairs, I compute the lowest 300 intrinsic states of several multipolarities. These states converge well to the exact ones, showing generalized seniority is very effective in truncating the deformed shell model. Under realistic interactions, the picture remains approximately valid: The ground state is a coherent pair condensate and the pairs gradually break up as excitation energy increases.

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

DOE PAGES

Michael, J. Robert; Volkov, Anatoliy

2015-03-01

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

Cortical surface registration using spherical thin-plate spline with sulcal lines and mean curvature as features.

PubMed

Park, Hyunjin; Park, Jun-Sung; Seong, Joon-Kyung; Na, Duk L; Lee, Jong-Min

2012-04-30

Analysis of cortical patterns requires accurate cortical surface registration. Many researchers map the cortical surface onto a unit sphere and perform registration of two images defined on the unit sphere. Here we have developed a novel registration framework for the cortical surface based on spherical thin-plate splines. Small-scale composition of spherical thin-plate splines was used as the geometric interpolant to avoid folding in the geometric transform. Using an automatic algorithm based on anisotropic skeletons, we extracted seven sulcal lines, which we then incorporated as landmark information. Mean curvature was chosen as an additional feature for matching between spherical maps. We employed a two-term cost function to encourage matching of both sulcal lines and the mean curvature between the spherical maps. Application of our registration framework to fifty pairwise registrations of T1-weighted MRI scans resulted in improved registration accuracy, which was computed from sulcal lines. Our registration approach was tested as an additional procedure to improve an existing surface registration algorithm. Our registration framework maintained an accurate registration over the sulcal lines while significantly increasing the cross-correlation of mean curvature between the spherical maps being registered. Copyright © 2012 Elsevier B.V. All rights reserved.

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) 'The chemical basis of morphogenesis'.

PubMed

Ball, Philip

2015-04-19

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, 'The chemical basis of morphogenesis', on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of 'Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.

The elastic field induced by a hemispherical inclusion in the half-space

NASA Astrophysics Data System (ADS)

Wu, Linzhi

2003-06-01

The elastic field induced by a hekispherical inclusion with uniform eigenstrains in a semi-infinite elastic medium is solved by using the Green's function method and series expansion technique. The exact solutions are presented for the displacement and stress fields which can be expressed by complete elliptic integrals of the first, second, and third kinds and hypergeometric functions. The present method can be used to determine the corresponding elastic fields when the shape of the inclusion is a spherical crown or a spherical segment. Finally, numerical results are given for the displacement and stress fields along the axis of symmetry ( x 3-axis).

Dynamic equations for an isotropic spherical shell using the power series method and surface differential operators

NASA Astrophysics Data System (ADS)

Okhovat, Reza; Boström, Anders

2017-04-01

Dynamic equations for an isotropic spherical shell are derived by using a series expansion technique. The displacement field is split into a scalar (radial) part and a vector (tangential) part. Surface differential operators are introduced to decrease the length of all equations. The starting point is a power series expansion of the displacement components in the thickness coordinate relative to the mid-surface of the shell. By using the expansions of the displacement components, the three-dimensional elastodynamic equations yield a set of recursion relations among the expansion functions that can be used to eliminate all but the four of lowest order and to express higher order expansion functions in terms of those of lowest orders. Applying the boundary conditions on the surfaces of the spherical shell and eliminating all but the four lowest order expansion functions give the shell equations as a power series in the shell thickness. After lengthy manipulations, the final four shell equations are obtained in a relatively compact form which are given to second order in shell thickness explicitly. The eigenfrequencies are compared to exact three-dimensional theory with excellent agreement and to membrane theory.

Renormalizable Quantum Field Theories in the Large -n Limit

NASA Astrophysics Data System (ADS)

Guruswamy, Sathya

1995-01-01

In this thesis, we study two examples of renormalizable quantum field theories in the large-N limit. Chapter one is a general introduction describing physical motivations for studying such theories. In chapter two, we describe the large-N method in field theory and discuss the pioneering work of 't Hooft in large-N two-dimensional Quantum Chromodynamics (QCD). In chapter three we study a spherically symmetric approximation to four-dimensional QCD ('spherical QCD'). We recast spherical QCD into a bilocal (constrained) theory of hadrons which in the large-N limit is equivalent to large-N spherical QCD for all energy scales. The linear approximation to this theory gives an eigenvalue equation which is the analogue of the well-known 't Hooft's integral equation in two dimensions. This eigenvalue equation is a scale invariant one and therefore leads to divergences in the theory. We give a non-perturbative renormalization prescription to cure this and obtain a beta function which shows that large-N spherical QCD is asymptotically free. In chapter four, we review the essentials of conformal field theories in two and higher dimensions, particularly in the context of critical phenomena. In chapter five, we study the O(N) non-linear sigma model on three-dimensional curved spaces in the large-N limit and show that there is a non-trivial ultraviolet stable critical point at which it becomes conformally invariant. We study this model at this critical point on examples of spaces of constant curvature and compute the mass gap in the theory, the free energy density (which turns out to be a universal function of the information contained in the geometry of the manifold) and the two-point correlation functions. The results we get give an indication that this model is an example of a three-dimensional analogue of a rational conformal field theory. A conclusion with a brief summary and remarks follows at the end.

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

Saperstein, E. E., E-mail: saper@mbslab.kiae.ru; Tolokonnikov, S. V.

Recent results obtained on the basis of the self-consistent theory of finite Fermi systems by employing the energy density functional proposed by Fayans and his coauthors are surveyed. These results are compared with the predictions of Skyrme–Hartree–Fock theory involving several popular versions of the Skyrme energy density functional. Spherical nuclei are predominantly considered. The charge radii of even and odd nuclei and features of low-lying 2{sup +} excitations in semimagic nuclei are discussed briefly. The single-particle energies ofmagic nuclei are examined inmore detail with allowance for corrections to mean-field theory that are induced by particle coupling to low-lying collective surfacemore » excitations (phonons). The importance of taking into account, in this problem, nonpole (tadpole) diagrams, which are usually disregarded, is emphasized. The spectroscopic factors of magic and semimagic nuclei are also considered. In this problem, only the surface term stemming from the energy dependence induced in the mass operator by the exchange of surface phonons is usually taken into account. The volume contribution associated with the energy dependence initially present in the mass operator within the self-consistent theory of finite Fermi systems because of the exchange of high-lying particle–hole excitations is also included in the spectroscopic factor. The results of the first studies that employed the Fayans energy density functional for deformed nuclei are also presented.« less

Reynolds stress and heat flux in spherical shell convection

NASA Astrophysics Data System (ADS)

Käpylä, P. J.; Mantere, M. J.; Guerrero, G.; Brandenburg, A.; Chatterjee, P.

2011-07-01

Context. Turbulent fluxes of angular momentum and enthalpy or heat due to rotationally affected convection play a key role in determining differential rotation of stars. Their dependence on latitude and depth has been determined in the past from convection simulations in Cartesian or spherical simulations. Here we perform a systematic comparison between the two geometries as a function of the rotation rate. Aims: Here we want to extend the earlier studies by using spherical wedges to obtain turbulent angular momentum and heat transport as functions of the rotation rate from stratified convection. We compare results from spherical and Cartesian models in the same parameter regime in order to study whether restricted geometry introduces artefacts into the results. In particular, we want to clarify whether the sharp equatorial profile of the horizontal Reynolds stress found in earlier Cartesian models is also reproduced in spherical geometry. Methods: We employ direct numerical simulations of turbulent convection in spherical and Cartesian geometries. In order to alleviate the computational cost in the spherical runs, and to reach as high spatial resolution as possible, we model only parts of the latitude and longitude. The rotational influence, measured by the Coriolis number or inverse Rossby number, is varied from zero to roughly seven, which is the regime that is likely to be realised in the solar convection zone. Cartesian simulations are performed in overlapping parameter regimes. Results: For slow rotation we find that the radial and latitudinal turbulent angular momentum fluxes are directed inward and equatorward, respectively. In the rapid rotation regime the radial flux changes sign in accordance with earlier numerical results, but in contradiction with theory. The latitudinal flux remains mostly equatorward and develops a maximum close to the equator. In Cartesian simulations this peak can be explained by the strong "banana cells". Their effect in the spherical case does not appear to be as large. The latitudinal heat flux is mostly equatorward for slow rotation but changes sign for rapid rotation. Longitudinal heat flux is always in the retrograde direction. The rotation profiles vary from anti-solar (slow equator) for slow and intermediate rotation to solar-like (fast equator) for rapid rotation. The solar-like profiles are dominated by the Taylor-Proudman balance. Movies and Appendix A are available in electronic form at http://www.aanda.org

The Bargmann-Wigner equations in spherical space

NASA Astrophysics Data System (ADS)

McKeon, D. G. C.; Sherry, T. N.

2006-01-01

The Bargmann-Wigner formalism is adapted to spherical surfaces embedded in three to eleven dimensions. This is demonstrated to generate wave equations in spherical space for a variety of antisymmetric tensor fields. Some of these equations are gauge invariant for particular values of the parameters characterizing them. For spheres embedded in three, four, and five dimensions, this gauge invariance can be generalized so as to become non-Abelian. This non-Abelian gauge invariance is shown to be a property of second-order models for two index antisymmetric tensor fields in any number of dimensions. The O(3) model is quantized and the two-point function is shown to vanish at the one-loop order.

A meta-GGA level screened range-separated hybrid functional by employing short range Hartree-Fock with a long range semilocal functional.

PubMed

Jana, Subrata; Samal, Prasanjit

2018-03-28

The range-separated hybrid density functionals are very successful in describing a wide range of molecular and solid-state properties accurately. In principle, such functionals are designed from spherically averaged or system averaged as well as reverse engineered exchange holes. In the present attempt, the screened range-separated hybrid functional scheme has been applied to the meta-GGA rung by using the density matrix expansion based semilocal exchange hole (or functional). The hybrid functional proposed here utilizes the spherically averaged density matrix expansion based exchange hole in the range separation scheme. For slowly varying density correction the range separation scheme is employed only through the local density approximation based exchange hole coupled with the corresponding fourth order gradient approximate Tao-Mo enhancement factor. The comprehensive testing and performance of the newly constructed functional indicates its applicability in describing several molecular properties. The most appealing feature of this present screened hybrid functional is that it will be practically very useful in describing solid-state properties at the meta-GGA level.

Dyons and dyonic black holes in su (N ) Einstein-Yang-Mills theory in anti-de Sitter spacetime

NASA Astrophysics Data System (ADS)

Shepherd, Ben L.; Winstanley, Elizabeth

2016-03-01

We present new spherically symmetric, dyonic soliton and black hole solutions of the su (N ) Einstein-Yang-Mills equations in four-dimensional asymptotically anti-de Sitter spacetime. The gauge field has nontrivial electric and magnetic components and is described by N -1 magnetic gauge field functions and N -1 electric gauge field functions. We explore the phase space of solutions in detail for su (2 ) and su (3 ) gauge groups. Combinations of the electric gauge field functions are monotonic and have no zeros; in general the magnetic gauge field functions may have zeros. The phase space of solutions is extremely rich, and we find solutions in which the magnetic gauge field functions have more than fifty zeros. Of particular interest are solutions for which the magnetic gauge field functions have no zeros, which exist when the negative cosmological constant has sufficiently large magnitude. We conjecture that at least some of these nodeless solutions may be stable under linear, spherically symmetric, perturbations.

Some physical properties of ginkgo nuts and kernels

NASA Astrophysics Data System (ADS)

Ch'ng, P. E.; Abdullah, M. H. R. O.; Mathai, E. J.; Yunus, N. A.

2013-12-01

Some data of the physical properties of ginkgo nuts at a moisture content of 45.53% (±2.07) (wet basis) and of their kernels at 60.13% (± 2.00) (wet basis) are presented in this paper. It consists of the estimation of the mean length, width, thickness, the geometric mean diameter, sphericity, aspect ratio, unit mass, surface area, volume, true density, bulk density, and porosity measures. The coefficient of static friction for nuts and kernels was determined by using plywood, glass, rubber, and galvanized steel sheet. The data are essential in the field of food engineering especially dealing with design and development of machines, and equipment for processing and handling agriculture products.

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.

All silicon waveguide spherical microcavity coupler device.

PubMed

Xifré-Pérez, E; Domenech, J D; Fenollosa, R; Muñoz, P; Capmany, J; Meseguer, F

2011-02-14

A coupler based on silicon spherical microcavities coupled to silicon waveguides for telecom wavelengths is presented. The light scattered by the microcavity is detected and analyzed as a function of the wavelength. The transmittance signal through the waveguide is strongly attenuated (up to 25 dB) at wavelengths corresponding to the Mie resonances of the microcavity. The coupling between the microcavity and the waveguide is experimentally demonstrated and theoretically modeled with the help of FDTD calculations.

Contrast Density and mass function for spherical collapse of Lemaitre-Tolman-Bondi metric from fractal point of view

NASA Astrophysics Data System (ADS)

Chacón-Cardona, C. A.; Casas-Miranda, R. A.

2014-10-01

Recent works about large structure in the universe put in doubt the homogeneity transition almost universally accepted, (Joyce et al.2005), (Gaite 2007), (Chacón-Cardona & Casas-Miranda 2012). In the present work we develop theoretically the density contrast for the spherical collapse of an over-density of dark matter which evolve in a inhomogeneous universe inside a fractal cosmology presented by (Bondi 1947).

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.

Correlation energy, correlated electron density, and exchange-correlation potential in some spherically confined atoms.

PubMed

Vyboishchikov, Sergei F

2016-12-05

We report correlation energies, electron densities, and exchange-correlation potentials obtained from configuration interaction and density functional calculations on spherically confined He, Be, Be 2+ , and Ne atoms. The variation of the correlation energy with the confinement radius R c is relatively small for the He, Be 2+ , and Ne systems. Curiously, the Lee-Yang-Parr (LYP) functional works well for weak confinements but fails completely for small R c . However, in the neutral beryllium atom the CI correlation energy increases markedly with decreasing R c . This effect is less pronounced at the density-functional theory level. The LYP functional performs very well for the unconfined Be atom, but fails badly for small R c . The standard exchange-correlation potentials exhibit significant deviation from the "exact" potential obtained by inversion of Kohn-Sham equation. The LYP correlation potential behaves erratically at strong confinements. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.

Model for transport and reaction of defects and carriers within displacement cascades in gallium arsenide

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

Wampler, William R., E-mail: wrwampl@sandia.gov; Myers, Samuel M.

A model is presented for recombination of charge carriers at evolving displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with the details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers,more » and defects within a representative spherically symmetric cluster of defects. The initial radial defect profiles within the cluster were determined through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to displacement damage from energetic particle irradiation.« less

Computer-generated holograms (CGH) realization: the integration of dedicated software tool with digital slides printer

NASA Astrophysics Data System (ADS)

Guarnieri, Vittorio; Francini, Franco

1997-12-01

Last generation of digital printer is usually characterized by a spatial resolution enough high to allow the designer to realize a binary CGH directly on a transparent film avoiding photographic reduction techniques. These devices are able to produce slides or offset prints. Furthermore, services supplied by commercial printing company provide an inexpensive method to rapidly verify the validity of the design by means of a test-and-trial process. Notably, this low-cost approach appears to be suitable for a didactical environment. On the basis of these considerations, a set of software tools able to design CGH's has been developed. The guidelines inspiring the work have been the following ones: (1) ray-tracing approach, considering the object to be reproduced as source of spherical waves; (2) Optimization and speed-up of the algorithms used, in order to produce a portable code, runnable on several hardware platforms. In this paper calculation methods to obtain some fundamental geometric functions (points, lines, curves) are described. Furthermore, by the juxtaposition of these primitives functions it is possible to produce the holograms of more complex objects. Many examples of generated CGHs are presented.

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.

Two-dimensional time-resolved X-ray diffraction study of liquid/solid fraction and solid particle size in Fe-C binary system with an electrostatic levitator furnace

NASA Astrophysics Data System (ADS)

Yonemura, M.; Okada, J.; Watanabe, Y.; Ishikawa, T.; Nanao, S.; Shobu, T.; Toyokawa, H.

2013-03-01

Liquid state provides functions such as matter transport or a reaction field and plays an important role in manufacturing processes such as refining, forging or welding. However, experimental procedures are significantly difficult for an observation of solidification process of iron and iron-based alloys in order to identify rapid transformations subjected to fast temperature evolution. Therefore, in order to study the solidification in iron and iron-based alloys, we considered a combination of high energy X-ray diffraction measurements and an electrostatic levitation method (ESL). In order to analyze the liquid/solid fraction, the solidification of melted spherical specimens was measured at a time resolution of 0.1 seconds during rapid cooling using the two-dimensional time-resolved X-ray diffraction. Furthermore, the observation of particle sizes and phase identification was performed on a trial basis using X-ray small angle scattering with X-ray diffraction.

Oxidative stress–induced assembly of PML nuclear bodies controls sumoylation of partner proteins

PubMed Central

Sahin, Umut; Ferhi, Omar; Jeanne, Marion; Benhenda, Shirine; Berthier, Caroline; Jollivet, Florence; Niwa-Kawakita, Michiko; Faklaris, Orestis; Setterblad, Niclas; Lallemand-Breitenbach, Valérie

2014-01-01

The promyelocytic leukemia (PML) protein organizes PML nuclear bodies (NBs), which are stress-responsive domains where many partner proteins accumulate. Here, we clarify the basis for NB formation and identify stress-induced partner sumoylation as the primary NB function. NB nucleation does not rely primarily on intermolecular interactions between the PML SUMO-interacting motif (SIM) and SUMO, but instead results from oxidation-mediated PML multimerization. Oxidized PML spherical meshes recruit UBC9, which enhances PML sumoylation, allow partner recruitment through SIM interactions, and ultimately enhance partner sumoylation. Intermolecular SUMO–SIM interactions then enforce partner sequestration within the NB inner core. Accordingly, oxidative stress enhances NB formation and global sumoylation in vivo. Some NB-associated sumoylated partners also become polyubiquitinated by RNF4, precipitating their proteasomal degradation. As several partners are protein-modifying enzymes, NBs could act as sensors that facilitate and confer oxidative stress sensitivity not only to sumoylation but also to other post-translational modifications, thereby explaining alterations of stress response upon PML or NB loss. PMID:24637324

3D-MHD Simulations of the Madison Dynamo Experiment

NASA Astrophysics Data System (ADS)

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

2003-10-01

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

Numerical modelling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

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

2000-10-01

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

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.

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

PubMed

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

2017-08-01

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

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

NASA Astrophysics Data System (ADS)

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

2018-03-01

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

Wavefront shaping with an electrowetting liquid lens using surface harmonics (Conference Presentation)

NASA Astrophysics Data System (ADS)

Strauch, Matthias; Konijnenberg, Sander; Shao, Yifeng; Urbach, H. Paul

2017-02-01

Liquid lenses are used to correct for low order wavefront aberrations. Electrowetting liquid lenses can nowadays control defocus and astigmatism effectively, so they start being used for ophthalmology applications. To increase the performance and applicability, we introduce a new driving mechanism to create, detect and correct higher order aberrations using standing waves on the liquid interface. The speed of a liquid lens is in general limited, because the liquid surface cannot follow fast voltage changes, while providing a spherical surface. Surface waves are created instead and with them undesired aberrations. We try to control those surface waves to turn them into an effective wavefront shaping tool. We introduce a model, which treats the liquid lens as a circular vibrating membrane with adjusted boundary conditions. Similar to tunable acoustic gradient (TAG) lenses, the nature of the surface modes are predicted to be Bessel functions. Since Bessel functions are a full set of orthogonal basis functions any surface can be created as a linear combination of different Bessel functions. The model was investigated experimentally in two setups. First the point spread functions were studied and compared to a simulation of the intensity distribution created by Fresnel propagated Bessel surfaces. Second the wavefronts were measured directly using a spatial light modulator. The surface resonance frequencies confirm the predictions made by the model as well as the wavefront measurements. By superposition of known surface modes, it is possible to create new surface shapes, which can be used to simulate and measure the human eye.

Design and analysis of multilayer x ray/XUV microscope

NASA Technical Reports Server (NTRS)

Shealy, David L.

1990-01-01

The design and analysis of a large number of normal incidence multilayer x ray microscopes based on the spherical mirror Schwarzschild configuration is examined. Design equations for the spherical mirror Schwarzschild microscopes are summarized and used to evaluate mirror parameters for microscopes with magnifications ranging from 2 to 50x. Ray tracing and diffraction analyses are carried out for many microscope configurations to determine image resolution as a function of system parameters. The results are summarized in three publication included herein. A preliminary study of advanced reflecting microscope configurations, where aspherics are used in place of the spherical microscope mirror elements, has indicated that the aspherical elements will improve off-axis image resolution and increase the effective field of view.

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

Casimir self-entropy of a spherical electromagnetic δ -function shell

NASA Astrophysics Data System (ADS)

Milton, Kimball A.; Kalauni, Pushpa; Parashar, Prachi; Li, Yang

2017-10-01

In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic δ -function sphere ("semitransparent sphere") whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong-coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The transverse electric self-entropy is negative as expected, but the transverse magnetic self-entropy requires ultraviolet and infrared renormalization (subtraction), and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes. These rather surprising findings require further investigation.

Nonlinear optical susceptibility described with a spherical formalism applied to coherent anti-Stokes Raman scattering

NASA Astrophysics Data System (ADS)

Cleff, Carsten; Rigneault, Hervé; Brasselet, Sophie; Duboisset, Julien

2017-07-01

We describe coherent Raman scattering in a complete spherical formalism allowing a better understanding of the coherent Raman process with respect to its symmetry properties, which is especially helpful in polarized coherent Raman microscopy. We describe how to build the coherent Raman tensor from spontaneous Raman tensor for crystalline and disordered media. We introduce a distribution function for molecular bonds and show how this distribution function results in a new macroscopic symmetry which can be very different from the symmetry of vibrational modes. Finally, we explicitly show polarization configurations for coherent anti-Stokes Raman scattering to probe specific vibration symmetries in crystalline samples and lipid layers.

Optical equivalence of isotropic ensembles of ellipsoidal particles in the Rayleigh-Gans-Debye and anomalous diffraction approximations and its consequences

NASA Astrophysics Data System (ADS)

Paramonov, L. E.

2012-05-01

Light scattering by isotropic ensembles of ellipsoidal particles is considered in the Rayleigh-Gans-Debye approximation. It is proved that randomly oriented ellipsoidal particles are optically equivalent to polydisperse randomly oriented spheroidal particles and polydisperse spherical particles. Density functions of the shape and size distributions for equivalent ensembles of spheroidal and spherical particles are presented. In the anomalous diffraction approximation, equivalent ensembles of particles are shown to also have equal extinction, scattering, and absorption coefficients. Consequences of optical equivalence are considered. The results are illustrated by numerical calculations of the angular dependence of the scattering phase function using the T-matrix method and the Mie theory.

Use of the Digamma Function in Statistical Astrophysics Distributions

NASA Astrophysics Data System (ADS)

Cahill, Michael

2017-06-01

Relaxed astrophysical statistical distributions may be constructed by using the inverse of a most probable energy distribution equation giving the energy ei of each particle in cell i in terms of the cell’s particle population Ni. The digamma mediated equation is A + Bei = Ψ(1+ Ni), where the constants A & B are Lagrange multipliers and Ψ is the digamma function given by Ψ(1+x) = dln(x!)/dx. Results are discussed for a Monatomic Ideal Gas, Atmospheres of Spherical Planets or Satellites and for Spherical Globular Clusters. These distributions are self-terminating even if other factors do not cause a cutoff. The examples are discussed classically but relativistic extensions are possible.

Modulational Instability of Cylindrical and Spherical NLS Equations. Statistical Approach

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

Grecu, A. T.; Grecu, D.; Visinescu, Anca

2010-01-21

The modulational (Benjamin-Feir) instability for cylindrical and spherical NLS equations (c/s NLS equations) is studied using a statistical approach (SAMI). A kinetic equation for a two-point correlation function is written and analyzed using the Wigner-Moyal transform. The linear stability of the Fourier transform of the two-point correlation function is studied and an implicit integral form for the dispersion relation is found. This is solved for different expressions of the initial spectrum (delta-spectrum, Lorentzian, Gaussian), and in the case of a Lorentzian spectrum the total growth of the instability is calculated. The similarities and differences with the usual one-dimensional NLS equationmore » are emphasized.« less

Electron scattering intensities and Patterson functions of Skyrmions

NASA Astrophysics Data System (ADS)

Karliner, M.; King, C.; Manton, N. S.

2016-06-01

The scattering of electrons off nuclei is one of the best methods of probing nuclear structure. In this paper we focus on electron scattering off nuclei with spin and isospin zero within the Skyrme model. We consider two distinct methods and simplify our calculations by use of the Born approximation. The first method is to calculate the form factor of the spherically averaged Skyrmion charge density; the second uses the Patterson function to calculate the scattering intensity off randomly oriented Skyrmions, and spherically averages at the end. We compare our findings with experimental scattering data. We also find approximate analytical formulae for the first zero and first stationary point of a form factor.

Fresnel diffraction by spherical obstacles

NASA Technical Reports Server (NTRS)

Hovenac, Edward A.

1989-01-01

Lommel functions were used to solve the Fresnel-Kirchhoff diffraction integral for the case of a spherical obstacle. Comparisons were made between Fresnel diffraction theory and Mie scattering theory. Fresnel theory is then compared to experimental data. Experiment and theory typically deviated from one another by less than 10 percent. A unique experimental setup using mercury spheres suspended in a viscous fluid significantly reduced optical noise. The major source of error was due to the Gaussian-shaped laser beam.

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.

Wave Amplitude Dependent Engineering Model of Propellant Slosh in Spherical Tanks

NASA Technical Reports Server (NTRS)

Brodnick, Jacob; Westra, Douglas G.; Eberhart, Chad J.; Yang, Hong Q.; West, Jeffrey S.

2016-01-01

Liquid propellant slosh is often a concern for the controllability of flight vehicles. Anti-slosh devices are traditionally included in propellant tank designs to limit the amount of sloshing allowed during flight. These devices and any necessary supports can be quite heavy to meet various structural requirements. Some of the burden on anti-slosh devices can be relieved by exploiting the nonlinear behavior of slosh waves in bare smooth wall tanks. A nonlinear regime slosh model for bare spherical tanks was developed through a joint analytical and experimental effort by NASA/MSFC. The developed slosh model accounts for the large damping inherent in nonlinear slosh waves which is more accurate and drives conservatism from vehicle stability analyses that use traditional bare tank slosh models. A more accurate slosh model will result in more realistic predicted slosh forces during flight reducing or removing the need for active controls during a maneuver or baffles in the tank design. Lower control gains and smaller or fewer tank baffles can reduce cost and system complexity while increasing vehicle performance. Both Computational Fluid Dynamics (CFD) simulation and slosh testing of three different spherical tank geometries were performed to develop the proposed slosh model. Several important findings were made during this effort in addition to determining the parameters to the nonlinear regime slosh model. The linear regime slosh damping trend for spherical tanks reported in NASA SP-106 was shown to be inaccurate for certain regions of a tank. Additionally, transition to the nonlinear regime for spherical tanks was only found to occur at very large wave amplitudes in the lower hemisphere and was a strong function of the propellant fill level in the upper hemisphere. The nonlinear regime damping trend was also found to be a function of the propellant fill level.

Finite slice analysis (FINA) of sliced and velocity mapped images on a Cartesian grid

NASA Astrophysics Data System (ADS)

Thompson, J. O. F.; Amarasinghe, C.; Foley, C. D.; Rombes, N.; Gao, Z.; Vogels, S. N.; van de Meerakker, S. Y. T.; Suits, A. G.

2017-08-01

Although time-sliced imaging yields improved signal-to-noise and resolution compared with unsliced velocity mapped ion images, for finite slice widths as encountered in real experiments there is a loss of resolution and recovered intensities for the slow fragments. Recently, we reported a new approach that permits correction of these effects for an arbitrarily sliced distribution of a 3D charged particle cloud. This finite slice analysis (FinA) method utilizes basis functions that model the out-of-plane contribution of a given velocity component to the image for sequential subtraction in a spherical polar coordinate system. However, the original approach suffers from a slow processing time due to the weighting procedure needed to accurately model the out-of-plane projection of an anisotropic angular distribution. To overcome this issue we present a variant of the method in which the FinA approach is performed in a cylindrical coordinate system (Cartesian in the image plane) rather than a spherical polar coordinate system. Dubbed C-FinA, we show how this method is applied in much the same manner. We compare this variant to the polar FinA method and find that the processing time (of a 510 × 510 pixel image) in its most extreme case improves by a factor of 100. We also show that although the resulting velocity resolution is not quite as high as the polar version, this new approach shows superior resolution for fine structure in the differential cross sections. We demonstrate the method on a range of experimental and synthetic data at different effective slice widths.

Discontinuous Galerkin finite element methods for radiative transfer in spherical symmetry

NASA Astrophysics Data System (ADS)

Kitzmann, D.; Bolte, J.; Patzer, A. B. C.

2016-11-01

The discontinuous Galerkin finite element method (DG-FEM) is successfully applied to treat a broad variety of transport problems numerically. In this work, we use the full capacity of the DG-FEM to solve the radiative transfer equation in spherical symmetry. We present a discontinuous Galerkin method to directly solve the spherically symmetric radiative transfer equation as a two-dimensional problem. The transport equation in spherical atmospheres is more complicated than in the plane-parallel case owing to the appearance of an additional derivative with respect to the polar angle. The DG-FEM formalism allows for the exact integration of arbitrarily complex scattering phase functions, independent of the angular mesh resolution. We show that the discontinuous Galerkin method is able to describe accurately the radiative transfer in extended atmospheres and to capture discontinuities or complex scattering behaviour which might be present in the solution of certain radiative transfer tasks and can, therefore, cause severe numerical problems for other radiative transfer solution methods.

Resonance energy transfer: The unified theory via vector spherical harmonics

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

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

2016-08-21

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

Electric Double Layer electrostatics of spherical polyelectrolyte brushes with pH-dependent charge density

NASA Astrophysics Data System (ADS)

Li, Hao; Chen, Guang; Sinha, Shayandev; Das, Siddhartha; Soft Matter, Interfaces,; Energy Laboratory (Smiel) Team

Understanding the electric double layer (EDL) electrostatics of spherical polyelectrolyte (PE) brushes, which are spherical particles grafted with PE layers, is essential for appropriate use of PE-grfated micro-nanoparticles for targeted drug delivery, oil recovery, water harvesting, emulsion stabilization, emulsion breaking, etc. Here we elucidate the EDL electrostatics of spherical PE brushes for the case where the PE exhibits pH-dependent charge density. This pH-dependence necessitates the consideration of explicit hydrogen ion concentration, which in turn dictates the distribution of monomers along the length of the grafted PE. This monomer distribution is shown to be a function of the nature of the sphere (metallic or a charged or uncharged dielectric or a liquid-filled sphere). All the calculations are performed for the case where the PE electrostatics can be decoupled from the PE elastic and excluded volume effects. Initial predictions are also provided for the case where such decoupling is not possible.

Size-Dependent Surface Energy Density of Spherical Face-Centered-Cubic Metallic Nanoparticles.

PubMed

Wei, Yaochi; Chen, Shaohua

2015-12-01

The surface energy density of nano-sized elements exhibits a significantly size-dependent behavior. Spherical nanoparticle, as an important element in nano-devices and nano-composites, has attracted many interesting studies on size effect, most of which are molecular dynamics (MD) simulations. However, the existing MD calculations yield two opposite size-dependent trends of surface energy density of nanoparticles. In order to clarify such a real underlying problem, atomistic calculations are carried out in the present paper for various spherical face-centered-cubic (fcc) metallic nanoparticles. Both the embedded atom method (EAM) potential and the modified embedded atom method (MEAM) one are adopted. It is found that the size-dependent trend of surface energy density of nanoparticles is not governed by the chosen potential function or variation trend of surface energy, but by the defined radius of spherical nanoparticles in MD models. The finding in the present paper should be helpful for further theoretical studies on surface/interface effect of nanoparticles and nanoparticle-reinforced composites.

Parameterization of single-scattering properties of snow

NASA Astrophysics Data System (ADS)

Räisänen, P.; Kokhanovsky, A.; Guyot, G.; Jourdan, O.; Nousiainen, T.

2015-02-01

Snow consists of non-spherical grains of various shapes and sizes. Still, in many radiative transfer applications, single-scattering properties of snow have been based on the assumption of spherical grains. More recently, second-generation Koch fractals have been employed. While they produce a relatively flat phase function typical of deformed non-spherical particles, this is still a rather ad-hoc choice. Here, angular scattering measurements for blowing snow conducted during the CLimate IMpacts of Short-Lived pollutants In the Polar region (CLIMSLIP) campaign at Ny Ålesund, Svalbard, are used to construct a reference phase function for snow. Based on this phase function, an optimized habit combination (OHC) consisting of severely rough (SR) droxtals, aggregates of SR plates and strongly distorted Koch fractals is selected. The single-scattering properties of snow are then computed for the OHC as a function of wavelength λ and snow grain volume-to-projected area equivalent radius rvp. Parameterization equations are developed for λ = 0.199-2.7 μm and rvp = 10-2000 μm, which express the single-scattering co-albedo β, the asymmetry parameter g and the phase function P11 as functions of the size parameter and the real and imaginary parts of the refractive index. The parameterizations are analytic and simple to use in radiative transfer models. Compared to the reference values computed for the OHC, the accuracy of the parameterization is very high for β and g. This is also true for the phase function parameterization, except for strongly absorbing cases (β > 0.3). Finally, we consider snow albedo and reflected radiances for the suggested snow optics parameterization, making comparisons to spheres and distorted Koch fractals.

Parameterization of single-scattering properties of snow

NASA Astrophysics Data System (ADS)

Räisänen, P.; Kokhanovsky, A.; Guyot, G.; Jourdan, O.; Nousiainen, T.

2015-06-01

Snow consists of non-spherical grains of various shapes and sizes. Still, in many radiative transfer applications, single-scattering properties of snow have been based on the assumption of spherical grains. More recently, second-generation Koch fractals have been employed. While they produce a relatively flat phase function typical of deformed non-spherical particles, this is still a rather ad hoc choice. Here, angular scattering measurements for blowing snow conducted during the CLimate IMpacts of Short-Lived pollutants In the Polar region (CLIMSLIP) campaign at Ny Ålesund, Svalbard, are used to construct a reference phase function for snow. Based on this phase function, an optimized habit combination (OHC) consisting of severely rough (SR) droxtals, aggregates of SR plates and strongly distorted Koch fractals is selected. The single-scattering properties of snow are then computed for the OHC as a function of wavelength λ and snow grain volume-to-projected area equivalent radius rvp. Parameterization equations are developed for λ = 0.199-2.7 μm and rvp = 10-2000 μm, which express the single-scattering co-albedo β, the asymmetry parameter g and the phase function P11 as functions of the size parameter and the real and imaginary parts of the refractive index. The parameterizations are analytic and simple to use in radiative transfer models. Compared to the reference values computed for the OHC, the accuracy of the parameterization is very high for β and g. This is also true for the phase function parameterization, except for strongly absorbing cases (β > 0.3). Finally, we consider snow albedo and reflected radiances for the suggested snow optics parameterization, making comparisons to spheres and distorted Koch fractals.

G7 BiSpherical Acetabular Shell PMCF Study

ClinicalTrials.gov

2017-11-22

Rheumatoid Arthritis; Osteoarthritis; Noninflammatory Degenerative Joint Disease; Avascular Necrosis; Correction of Functional Deformity; Non-Union Fracture; Femoral Neck Fractures; Trochanteric Fractures

Development and application of a ray-based model of light propagation through a spherical acousto-optic lens

PubMed Central

Evans, Geoffrey J.; Kirkby, Paul A.; Nadella, K. M. Naga Srinivas; Marin, Bóris; Silver, R. Angus

2016-01-01

A spherical acousto-optic lens (AOL) consists of four acousto-optic deflectors (AODs) that can rapidly and precisely control the focal position of an optical beam in 3D space. Development and application of AOLs has increased the speed at which 3D random access point measurements can be performed with a two-photon microscope. This has been particularly useful for measuring brain activity with fluorescent reporter dyes because neuronal signalling is rapid and sparsely distributed in 3D space. However, a theoretical description of light propagation through AOLs has lagged behind their development, resulting in only a handful of simplified principles to guide AOL design and optimization. To address this we have developed a ray-based computer model of an AOL incorporating acousto-optic diffraction and refraction by anisotropic media. We extended an existing model of a single AOD with constant drive frequency to model a spherical AOL: four AODs in series driven with linear chirps. AOL model predictions of the relationship between optical transmission efficiency and acoustic drive frequency including second order diffraction effects closely matched experimental measurements from a 3D two-photon AOL microscope. Moreover, exploration of different AOL drive configurations identified a new simple rule for maximizing the field of view of our compact AOL design. By providing a theoretical basis for understanding optical transmission through spherical AOLs, our open source model is likely to be useful for comparing and improving different AOL designs, as well as identifying the acoustic drive configurations that provide the best transmission performance over the 3D focal region. PMID:26368449

Development and application of a ray-based model of light propagation through a spherical acousto-optic lens.

PubMed

Evans, Geoffrey J; Kirkby, Paul A; Naga Srinivas Nadella, K M; Marin, Bóris; Angus Silver, R

2015-09-07

A spherical acousto-optic lens (AOL) consists of four acousto-optic deflectors (AODs) that can rapidly and precisely control the focal position of an optical beam in 3D space. Development and application of AOLs has increased the speed at which 3D random access point measurements can be performed with a two-photon microscope. This has been particularly useful for measuring brain activity with fluorescent reporter dyes because neuronal signalling is rapid and sparsely distributed in 3D space. However, a theoretical description of light propagation through AOLs has lagged behind their development, resulting in only a handful of simplified principles to guide AOL design and optimization. To address this we have developed a ray-based computer model of an AOL incorporating acousto-optic diffraction and refraction by anisotropic media. We extended an existing model of a single AOD with constant drive frequency to model a spherical AOL: four AODs in series driven with linear chirps. AOL model predictions of the relationship between optical transmission efficiency and acoustic drive frequency including second order diffraction effects closely matched experimental measurements from a 3D two-photon AOL microscope. Moreover, exploration of different AOL drive configurations identified a new simple rule for maximizing the field of view of our compact AOL design. By providing a theoretical basis for understanding optical transmission through spherical AOLs, our open source model is likely to be useful for comparing and improving different AOL designs, as well as identifying the acoustic drive configurations that provide the best transmission performance over the 3D focal region.

Stresses in curved nematic membranes.

PubMed

Santiago, J A

2018-05-01

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

The Backscattering Phase Function for a Sphere with a Two-Scale Relief of Rough Surface

NASA Astrophysics Data System (ADS)

Klass, E. V.

2017-12-01

The backscattering of light from spherical surfaces characterized by one and two-scale roughness reliefs has been investigated. The analysis is performed using the three-dimensional Monte-Carlo program POKS-RG (geometrical-optics approximation), which makes it possible to take into account the roughness of objects under study by introducing local geometries of different levels. The geometric module of the program is aimed at describing objects by equations of second-order surfaces. One-scale roughness is set as an ensemble of geometric figures (convex or concave halves of ellipsoids or cones). The two-scale roughness is modeled by convex halves of ellipsoids, with surface containing ellipsoidal pores. It is shown that a spherical surface with one-scale convex inhomogeneities has a flatter backscattering phase function than a surface with concave inhomogeneities (pores). For a sphere with two-scale roughness, the dependence of the backscattering intensity is found to be determined mostly by the lower-level inhomogeneities. The influence of roughness on the dependence of the backscattering from different spatial regions of spherical surface is analyzed.

Stresses in curved nematic membranes

NASA Astrophysics Data System (ADS)

Santiago, J. A.

2018-05-01

Ordering configurations of a director field on a curved membrane induces stress. In this work, we present a theoretical framework to calculate the stress tensor and the torque as a consequence of the nematic ordering; we use the variational principle and invariance of the energy under Euclidean motions. Euler-Lagrange equations of the membrane as well as the corresponding boundary conditions also appear as natural results. The stress tensor found includes attraction-repulsion forces between defects; likewise, defects are attracted to patches with the same sign in Gaussian curvature. These forces are mediated by the Green function of the Laplace-Beltrami operator of the surface. In addition, we find nonisotropic forces that involve derivatives of the Green function and the Gaussian curvature, even in the normal direction to the membrane. We examine the case of axial membranes to analyze the spherical one. For spherical vesicles we find the modified Young-Laplace law as a consequence of the nematic texture. In the case of spherical cap with defect at the north pole, we find that the force is repulsive with respect to the north pole, indicating that it is an unstable equilibrium point.

Calculation of the acoustic radiation force on coated spherical shells in progressive and standing plane waves.

PubMed

Mitri, F G

2006-07-01

In this paper, analytical equations are derived for the time-averaged radiation force induced by progressive and standing acoustic waves incident on elastic spherical shells covered with a layer of viscoelastic and sound-absorbing material. The fluid surrounding the shells is considered compressible and nonviscous. The incident field is assumed to be moderate so that the scattered field from the shells is taken to linear approximation. The analytical results are illustrated by means of a numerical example in which the radiation force function curves are displayed, with particular emphasis on the coating thickness and the content of the hollow region of the shells. The fluid-loading on the radiation force function curves is analysed as well. This study attempts to generalize the various treatments of radiation force due to both progressive and standing waves on spherically-shaped structures immersed in ideal fluids. The results show that various ways can be effectively used for damping resonance peaks, such as by changing the fluid in the interior hollow region of the shells or by changing the coating thickness.

Hydrodynamic entrainment in micro-confined suspensions and its implications for two-point microrheology

NASA Astrophysics Data System (ADS)

Aponte-Rivera, Christian; Zia, Roseanna N.

2017-11-01

We study hydrodynamic entrainment in spherically confined colloidal suspensions of hydrodynamically interacting particles as a model system for intracellular and other micro-confined biophysical transport. Modeling of transport and rheology in such materials requires an accurate description of the microscopic forces driving particle motion and of particle interactions with nearby boundaries. We carry out dynamic simulations of concentrated, spherically confined colloids as a model system to study the effect of 3D confinement on entrainment and rheology. We show that entrainment between two tracer particles exhibits qualitatively different functional dependence on inter-particle separation as compared to an unbound suspension, and develop a scaling theory that collapses the concentrated mobility of spherically confined suspensions for all volume fractions and particle to cavity size ratios onto a master curve. For widely separated particles, the master curve can be predicted via a Green's function, which suggests a framework with which to conduct two-point microrheology measurements near confining boundaries. The implications of these results for experiments in micro-confined biophysical systems, such as the interior of eukaryotic cells, are discussed.

Cross-correlating 2D and 3D galaxy surveys

DOE PAGES

Passaglia, Samuel; Manzotti, Alessandro; Dodelson, Scott

2017-06-08

Galaxy surveys probe both structure formation and the expansion rate, making them promising avenues for understanding the dark universe. Photometric surveys accurately map the 2D distribution of galaxy positions and shapes in a given redshift range, while spectroscopic surveys provide sparser 3D maps of the galaxy distribution. We present a way to analyse overlapping 2D and 3D maps jointly and without loss of information. We represent 3D maps using spherical Fourier-Bessel (sFB) modes, which preserve radial coverage while accounting for the spherical sky geometry, and we decompose 2D maps in a spherical harmonic basis. In these bases, a simple expression exists for the cross-correlation of the two fields. One very powerful application is the ability to simultaneously constrain the redshift distribution of the photometric sample, the sample biases, and cosmological parameters. We use our framework to show that combined analysis of DESI and LSST can improve cosmological constraints by factors ofmore » $${\\sim}1.2$$ to $${\\sim}1.8$$ on the region where they overlap relative to identically sized disjoint regions. We also show that in the overlap of DES and SDSS-III in Stripe 82, cross-correlating improves photo-$z$ parameter constraints by factors of $${\\sim}2$$ to $${\\sim}12$$ over internal photo-$z$ reconstructions.« less

Numerical study on the lubrication performance of compression ring-cylinder liner system with spherical dimples

PubMed Central

Liu, Cheng; Zhang, Yong-Fang; Li, Sha; Müller, Norbert

2017-01-01

The effects of surface texture on the lubrication performance of a compression ring-cylinder liner system are studied in this paper. By considering the surface roughness of the compression ring and cylinder liner, a mixed lubrication model is presented to investigate the tribological behaviors of a barrel-shaped compression ring-cylinder liner system with spherical dimples on the liner. In order to determine the rupture and reformulation positions of fluid film accurately, the Jacoboson-Floberg-Olsson (JFO) cavitation boundary condition is applied to the mixed lubrication model for ensuring the mass-conservative law. On this basis, the minimum oil film thickness and average friction forces in the compression ring-cylinder liner system are investigated under the engine-like conditions by changing the dimple area density, radius, and depth. The wear load, average friction forces, and power loss of the compression ring-cylinder liner system with and without dimples are also compared for different compression ring face profiles. The results show that the spherical dimples can produce a larger reduction of friction in mixed lubrication region, and reduce power loss significantly in the middle of the strokes. In addition, higher reduction percentages of average friction forces and wear are obtained for smaller crown height or larger axial width. PMID:28732042

Cross-correlating 2D and 3D galaxy surveys

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

Passaglia, Samuel; Manzotti, Alessandro; Dodelson, Scott

Galaxy surveys probe both structure formation and the expansion rate, making them promising avenues for understanding the dark universe. Photometric surveys accurately map the 2D distribution of galaxy positions and shapes in a given redshift range, while spectroscopic surveys provide sparser 3D maps of the galaxy distribution. We present a way to analyse overlapping 2D and 3D maps jointly and without loss of information. We represent 3D maps using spherical Fourier-Bessel (sFB) modes, which preserve radial coverage while accounting for the spherical sky geometry, and we decompose 2D maps in a spherical harmonic basis. In these bases, a simple expression exists for the cross-correlation of the two fields. One very powerful application is the ability to simultaneously constrain the redshift distribution of the photometric sample, the sample biases, and cosmological parameters. We use our framework to show that combined analysis of DESI and LSST can improve cosmological constraints by factors ofmore » $${\\sim}1.2$$ to $${\\sim}1.8$$ on the region where they overlap relative to identically sized disjoint regions. We also show that in the overlap of DES and SDSS-III in Stripe 82, cross-correlating improves photo-$z$ parameter constraints by factors of $${\\sim}2$$ to $${\\sim}12$$ over internal photo-$z$ reconstructions.« less

Identification and onset of inertial modes in the wide-gap spherical Couette system

NASA Astrophysics Data System (ADS)

Barik, A.; Wicht, J.; Triana, S. A.; Hoff, M.

2016-12-01

The spherical Couette system consists of two concentric rotating spheres with a fluid filling the shell in between. The system has been studied for a long time by fluid dynamicists and is ideal for studying flow instabilities due to differential rotation and the interaction of the same with magnetic fields - important for understanding dynamics of planetary and stellar interiors. The system is also a basis for a new generation of dynamo experiments because of its closer geometrical resemblance to real astrophysical objects as compared to past experiments. We simulate this system using the two different pseudo-spectral codes MagIC and XSHELLS. We focus here on a very interesting and general instability in this system - inertial modes. A rotating body of fluid is known to sustain oscillatory waves due to the restoring action of the Coriolis force. In a bounded container, these form a discrete spectrum called inertial modes. These modes have been analytically known for a rotating full sphere for over a century now. In a spherical shell, they cannot be formulated analytically. However, many of these inertial modes are observed in spherical Couette experiments as well as in simulations. Past studies have tried to explain the onset of these modes invoking wave over-reflection or critical layer instabilities on the cylinder tangent to the inner sphere. In this study, we present the inertial modes found in our simulations and try to explain their onset as secondary instabilities due to the destabilization of the fundamental non-axisymmetric instability, forming a triadic resonance with the fundamental instability. We run various simulations varying the rotation rate of the inner sphere, while keeping the rotation rate of the outer sphere constant. We track velocities and induced magnetic field and produce spectrograms similar to those of the experiments. Our results match very well the experimental data from spherical Couette set-ups at BTU Cottbus and the University of Maryland.

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

NASA Astrophysics Data System (ADS)

Otsuka, Takaharu; Sugita, Michiaki

1988-12-01

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

Baroclinic instability with variable static stability - A design study for a spherical atmospheric model experiment. [for Spacelab flight

NASA Technical Reports Server (NTRS)

Giere, A. C.; Fowlis, W. W.

1980-01-01

The effect of a radially-variable, dielectric body force, analogous to gravity on baroclinic instability for the design of a spherical, synoptic-scale, atmospheric model experiment in a Spacelab flight is investigated. Exact solutions are examined for quasi-geostrophic baroclinic instability in which the rotational Froude number is a linear function of the height. Flow in a rotating rectilinear channel with a vertically variable body force without horizontal shear of the basic state is also discussed.

Dynamic properties of porous B sub 4 C. Interim report

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

Brar, N.S.; Rosenberg, Z.; Bless, S.J.

1990-01-25

The sound speed in porous B4C (Boron Carbide) was measured and predicted on the basis of a spherical void model and a penny crack model. Neither model does well for porosity exceeding 10 percent. Measured values of Hugoniot elastic limit for porous B4C agree well with those predicted by the Steinberg's model. Measured transverse stress in the elastic range of B4C under 1-d strain condition agrees with the predictions.

Forging patterns and making waves from biology to geology: a commentary on Turing (1952) ‘The chemical basis of morphogenesis’

PubMed Central

Ball, Philip

2015-01-01

Alan Turing was neither a biologist nor a chemist, and yet the paper he published in 1952, ‘The chemical basis of morphogenesis’, on the spontaneous formation of patterns in systems undergoing reaction and diffusion of their ingredients has had a substantial impact on both fields, as well as in other areas as disparate as geomorphology and criminology. Motivated by the question of how a spherical embryo becomes a decidedly non-spherical organism such as a human being, Turing devised a mathematical model that explained how random fluctuations can drive the emergence of pattern and structure from initial uniformity. The spontaneous appearance of pattern and form in a system far away from its equilibrium state occurs in many types of natural process, and in some artificial ones too. It is often driven by very general mechanisms, of which Turing's model supplies one of the most versatile. For that reason, these patterns show striking similarities in systems that seem superficially to share nothing in common, such as the stripes of sand ripples and of pigmentation on a zebra skin. New examples of ‘Turing patterns' in biology and beyond are still being discovered today. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750229

Size dependence of magneto-optical activity in silver nanoparticles with dimensions between 10 and 60 nm studied by MCD spectroscopy.

PubMed

Shiratsu, Taisuke; Yao, Hiroshi

2018-02-07

Size-dependent magneto-optical activity in Ag nanoparticles with dimensions from 10 to 60 nm is demonstrated with magnetic circular dichroism (MCD) spectroscopy. The Ag nanoparticles are prepared on the basis of a seeded-growth strategy using sodium citrate and/or tannic acid as reducing agents in aqueous solution. The obtained nanoparticles are roughly spherical, but those larger than ∼28 nm have a slight diversity of shapes with quasi-spherical polyhedrons. They exhibit a derivative-like MCD response in the localized surface plasmon resonance (LSPR) region, which originates from two circular modes of surface magnetoplasmons. With an increase in the nanoparticle diameter, the bisignated MCD signal is strongly distorted and weakened. Such a distortion for large-sized Ag nanoparticles can be phenomenologically simulated on the basis of both spectral inhomogeneity and MCD signal lobe asymmetry. Then the maximum value of MCD amplitude (MCD max ), which is obtained by normalization of the amplitude to the LSPR peak absorbance, first increases with increasing particle diameter and then decreases with a maximum for the 23 nm nanoparticle. Interestingly, the MCD max values are inversely correlated with the spectral bandwidth of LSPR extinction. This behaviour is discussed from a viewpoint of inhomogeneous effects of both spectral and size/shape distributions. We believe the present results will advance the design and application of optical devices based on magnetoplasmonics.

The Quantified Characterization Method of the Micro-Macro Contacts of Three-Dimensional Granular Materials on the Basis of Graph Theory.

PubMed

Guan, Yanpeng; Wang, Enzhi; Liu, Xiaoli; Wang, Sijing; Luan, Hebing

2017-08-03

We have attempted a multiscale and quantified characterization method of the contact in three-dimensional granular material made of spherical particles, particularly in cemented granular material. Particle contact is defined as a type of surface contact with voids in its surroundings, rather than a point contact. Macro contact is a particle contact set satisfying the restrictive condition of a two-dimensional manifold with a boundary. On the basis of graph theory, two dual geometrical systems are abstracted from the granular pack. The face and the face set, which satisfies the two-dimensional manifold with a boundary in the solid cell system, are extracted to characterize the particle contact and the macro contact, respectively. This characterization method is utilized to improve the post-processing in DEM (Discrete Element Method) from a micro perspective to describe the macro effect of the cemented granular material made of spherical particles. Since the crack has the same shape as its corresponding contact, this method is adopted to characterize the crack and realize its visualization. The integral failure route of the sample can be determined by a graph theory algorithm. The contact force is assigned to the weight value of the face characterizing the particle contact. Since the force vectors can be added, the macro contact force can be solved by adding the weight of its corresponding faces.

Morphology conserving aminopropyl functionalization of hollow silica nanospheres in toluene

NASA Astrophysics Data System (ADS)

Dobó, Dorina G.; Berkesi, Dániel; Kukovecz, Ákos

2017-07-01

Inorganic nanostructures containing cavities of monodisperse diameter distribution find applications in e.g. catalysis, adsorption and drug delivery. One of their possible synthesis routes is the template assisted core-shell synthesis. We synthesized hollow silica spheres around polystyrene cores by the sol-gel method. The polystyrene template was removed by heat treatment leaving behind a hollow spherical shell structure. The surface of the spheres was then modified by adding aminopropyl groups. Here we present the first experimental evidence that toluene is a suitable alternative functionalization medium for the resulting thin shells, and report the comprehensive characterization of the amino-functionalized hollow silica spheres based on scanning electron microscopy, transmission electron microscopy, N2 adsorption, FT-IR spectroscopy, Raman spectroscopy and electrokinetic potential measurement. Both the presence of the amino groups and the preservation of the hollow spherical morphology were unambiguously proven. The introduction of the amine functionality adds amphoteric character to the shell as shown by the zeta potential vs. pH function. Unlike pristine silica particles, amino-functionalized nanosphere aqueous sols can be stable at both acidic and basic conditions.

Variations in the expansion and shear scalars for dissipative fluids

NASA Astrophysics Data System (ADS)

Akram, A.; Ahmad, S.; Jami, A. Rehman; Sufyan, M.; Zahid, U.

2018-04-01

This work is devoted to the study of some dynamical features of spherical relativistic locally anisotropic stellar geometry in f(R) gravity. In this paper, a specific configuration of tanh f(R) cosmic model has been taken into account. The mass function through technique introduced by Misner-Sharp has been formulated and with the help of it, various fruitful relations are derived. After orthogonal decomposition of the Riemann tensor, the tanh modified structure scalars are calculated. The role of these tanh modified structure scalars (MSS) has been discussed through shear, expansion as well as Weyl scalar differential equations. The inhomogeneity factor has also been explored for the case of radiating viscous locally anisotropic spherical system and spherical dust cloud with and without constant Ricci scalar corrections.

Electrons on a spherical surface: Physical properties and hollow spherical clusters

NASA Astrophysics Data System (ADS)

Cricchio, Dario; Fiordilino, Emilio; Persico, Franco

2012-07-01

We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number N of electrons. The trends obtained with increasing N are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic numbers which follows a power law with critical exponent -0.5. We conclude that our completely mechanistic and analytically tractable model can be useful for the analysis of self-assembling complex systems.

The 27-28 October 1986 FIRE IFO Cirrus case study: Comparison of radiative transfer theory with observations by satellite and aircraft

NASA Technical Reports Server (NTRS)

Wielicki, Bruce A.; Suttles, J. T.; Heymsfield, Andrew J.; Welch, Ronald M.; Spinhirne, James D.; Wu, Man-Li C.; Starr, David OC.; Parker, Lindsay; Arduini, Robert F.

1989-01-01

Observations of cirrus and altocumulus clouds during the First International Satellite Cloud Climatology Project Regional Experiment (FIRE) are compared to theoretical models of cloud radiative properties. Three tests are performed. First, LANDSAT radiances are used to compare the relationship between nadir reflectance ot 0.83 micron and beam emittance at 11.5 microns with that predicted for model calculations using spherical and nonspherical phase functions. Good agreement is found between observations and theory when water droplets dominate. Poor agreement is found when ice particles dominate, especially using scattering phase functions for spherical particles. Even when compared to a laboratory measured ice particle phase function, the observations show increased side scattered radiation relative to the theoretical calculations. Second, the anisotropy of conservatively scattered radiation is examined using simultaneous multiple angle views of the cirrus from LANDSAT and ER-2 aircraft radiometers. Observed anisotropy gives good agreement with theoretical calculations using the laboratory measured ice particle phase function and poor agreement with a spherical particle phase function. Third, Landsat radiances at 0.83, 1.65, and 2.21 microns are used to infer particle phase and particle size. For water droplets, good agreement is found with King Air FSSP particle probe measurements in the cloud. For ice particles, the LANDSAT radiance observations predict an effective radius of 60 microns versus aircraft observations of about 200 microns. It is suggested that this descrepancy may be explained by uncertainty in the imaginary index of ice and by inadequate measurements of small ice particles by microphysical probes.

Bumps of the wave structure function in non-Kolmogorov turbulence

NASA Astrophysics Data System (ADS)

Qiao, Chunhong; Lu, Lu; Zhang, Pengfei; Wang, Haitao; Huang, Honghua; Fan, Chengyu

2015-10-01

The analytical expressions for wave structure function of plane and spherical waves are derived both in the viscous dissipation and inertial range. Due to previously research, there is a discrepancy between theoretical results and the experimental datum in viscous dissipation range. In this paper, only considering the inertial range, taking plane waves for example, we give a comparison of results of WSF calculated by the analytical formula obtained in this paper and the numerical calculations of the definition at the fixed parameter (i.e., the generalized exponent α), it can be seen that the two results are in agreement with each other exactly. Based on non-Kolmogorov power spectrum, new characteristics for wave structure function (WSF) have been found for plane and spherical wave models when the different ratio of inner scale l0 and outer scale of turbulence L0 is obtained. In outer scale assumed finite case (i.e., L0 =1m), WSF obtains the maximum when α approximates to 3.3 both for plane and spherical wave models. In outer scale assumed infinite case (i.e., L0 = ∞), the WSF can be sorted into three parts, including two rapid-rising regions (i.e., 3.0 < α < 3.3 and 3.8 < α < 4.0 ) and one gently rising region (i.e., 3.3 < α < 3.8 ).Further, the changes of scaled WSF versus the ratio of separation distance and inner scale ( p/ l0 ) are investigated under mentioned above conditions for two models. In L0 = 1m case, both for plane and spherical waves, the value of α determines the bump position of WSF. In L0 = ∞ case, the bump of scaled WSF disappears when the generalized exponent has large values. The changings of scaled WSF monotonically increase as α increased when the generalized exponent is larger than11/3 for two models. Besides, the properties of spherical waves are similar to plane waves, except which the values of WSF and the scaled WSF are smaller than plane ones.

Functionalized C@TiO2 hollow spherical architecture for multifunctional applications.

PubMed

Chattopadhyay, Shreyasi; Mishra, Manish Kr; De, Goutam

2016-03-28

Hierarchical anatase titania (TiO2) with a hollow spherical architecture decorated with functionalized carbon dots (C(F)@THS) was synthesized by a solvothermal decomposition of titanium(IV) isopropoxide (TTIP) in the presence of a solution mixture containing thiourea and citric acid. Interestingly, the concomitant presence of thiourea and citric acid has been found to be essential to obtain such hierarchical hollow architecture because individual constituents produced non-hollow spheres when hydrothermally treated with TTIP. The co-existence of these two constituents also accelerates the growth of hollow spheres. BET surface area study of C(F)@THS revealed the existence of a slit like mesoporosity with a surface area value of 81 m(2) g(-1). Time dependent FESEM and TEM studies confirmed the formation of nanoflake like structures in the intermediate stages followed by the growth of a hollow spherical architecture. We proposed that these nanoflakes get accumulated on the bubble surface to form such hollow spherical morphology. The PL spectral study and Raman shift of the as prepared C(F)@THS confirmed the presence of functionalized graphitic C dots on the surface. A thorough XPS analysis was conducted to explore the nature and relative atomic concentration of the functional groups (-COOH, -CONH2, -NH2). This C(F)@THS sample showed very fast and selective dye (methylene blue and methyl violet) adsorption ability (even from a mixture of two different dye solutions) due to these δ-site containing functional groups on the surface. As C(F)@THS showed only two times reusability for adsorption, the dye adsorbed C(F)@THS was calcined at 450 °C in air to yield organic free anatase TiO2 hollow spheres (THS) with a retention of the original structure. THS was recycled as an efficient and a reusable photocatalyst (k = 9.36 × 10(-2) min(-1)) as well as a photoanode in dye sensitized solar cells (DSSCs) having Jsc value of 19.58 mA cm(-2) with overall efficiency of 6.48%.

Spherical type integrable classical systems in a magnetic field

NASA Astrophysics Data System (ADS)

Marchesiello, A.; Šnobl, L.; Winternitz, P.

2018-04-01

We show that four classes of second order spherical type integrable classical systems in a magnetic field exist in the Euclidean space {E}3 , and construct the Hamiltonian and two second order integrals of motion in involution for each of them. For one of the classes the Hamiltonian depends on four arbitrary functions of one variable. This class contains the magnetic monopole as a special case. Two further classes have Hamiltonians depending on one arbitrary function of one variable and four or six constants, respectively. The magnetic field in these cases is radial. The remaining system corresponds to a constant magnetic field and the Hamiltonian depends on two constants. Questions of superintegrability—i.e. the existence of further integrals—are discussed.

Accretion of a relativistic, collisionless kinetic gas into a Schwarzschild black hole

NASA Astrophysics Data System (ADS)

Rioseco, Paola; Sarbach, Olivier

2017-05-01

We provide a systematic study for the accretion of a collisionless, relativistic kinetic gas into a nonrotating black hole. To this end, we first solve the relativistic Liouville equation on a Schwarzschild background spacetime. The most general solution for the distribution function is given in terms of appropriate symplectic coordinates on the cotangent bundle, and the associated observables, including the particle current density and stress energy-momentum tensor, are determined. Next, we explore the case where the flow is steady-state and spherically symmetric. Assuming that in the asymptotic region the gas is described by an equilibrium distribution function, we determine the relevant parameters of the accretion flow as a function of the particle density and the temperature of the gas at infinity. In particular, we find that in the low temperature limit the tangential pressure at the horizon is about an order of magnitude larger than the radial one, showing explicitly that a collisionless gas, despite exerting kinetic pressure, behaves very differently than an isotropic perfect fluid, and providing a partial explanation for the known fact that the accretion rate is much lower than in the hydrodynamic case of Bondi-Michel accretion. Finally, we establish the asymptotic stability of the steady-state spherical flows by proving pointwise convergence results which show that a large class of (possibly nonstationary and nonspherical) initial conditions for the distribution function lead to solutions of the Liouville equation which relax in time to a steady-state, spherically symmetric configuration.

A multi-label learning based kernel automatic recommendation method for support vector machine.

PubMed

Zhang, Xueying; Song, Qinbao

2015-01-01

Choosing an appropriate kernel is very important and critical when classifying a new problem with Support Vector Machine. So far, more attention has been paid on constructing new kernels and choosing suitable parameter values for a specific kernel function, but less on kernel selection. Furthermore, most of current kernel selection methods focus on seeking a best kernel with the highest classification accuracy via cross-validation, they are time consuming and ignore the differences among the number of support vectors and the CPU time of SVM with different kernels. Considering the tradeoff between classification success ratio and CPU time, there may be multiple kernel functions performing equally well on the same classification problem. Aiming to automatically select those appropriate kernel functions for a given data set, we propose a multi-label learning based kernel recommendation method built on the data characteristics. For each data set, the meta-knowledge data base is first created by extracting the feature vector of data characteristics and identifying the corresponding applicable kernel set. Then the kernel recommendation model is constructed on the generated meta-knowledge data base with the multi-label classification method. Finally, the appropriate kernel functions are recommended to a new data set by the recommendation model according to the characteristics of the new data set. Extensive experiments over 132 UCI benchmark data sets, with five different types of data set characteristics, eleven typical kernels (Linear, Polynomial, Radial Basis Function, Sigmoidal function, Laplace, Multiquadric, Rational Quadratic, Spherical, Spline, Wave and Circular), and five multi-label classification methods demonstrate that, compared with the existing kernel selection methods and the most widely used RBF kernel function, SVM with the kernel function recommended by our proposed method achieved the highest classification performance.

A Multi-Label Learning Based Kernel Automatic Recommendation Method for Support Vector Machine

PubMed Central

Zhang, Xueying; Song, Qinbao

2015-01-01

Choosing an appropriate kernel is very important and critical when classifying a new problem with Support Vector Machine. So far, more attention has been paid on constructing new kernels and choosing suitable parameter values for a specific kernel function, but less on kernel selection. Furthermore, most of current kernel selection methods focus on seeking a best kernel with the highest classification accuracy via cross-validation, they are time consuming and ignore the differences among the number of support vectors and the CPU time of SVM with different kernels. Considering the tradeoff between classification success ratio and CPU time, there may be multiple kernel functions performing equally well on the same classification problem. Aiming to automatically select those appropriate kernel functions for a given data set, we propose a multi-label learning based kernel recommendation method built on the data characteristics. For each data set, the meta-knowledge data base is first created by extracting the feature vector of data characteristics and identifying the corresponding applicable kernel set. Then the kernel recommendation model is constructed on the generated meta-knowledge data base with the multi-label classification method. Finally, the appropriate kernel functions are recommended to a new data set by the recommendation model according to the characteristics of the new data set. Extensive experiments over 132 UCI benchmark data sets, with five different types of data set characteristics, eleven typical kernels (Linear, Polynomial, Radial Basis Function, Sigmoidal function, Laplace, Multiquadric, Rational Quadratic, Spherical, Spline, Wave and Circular), and five multi-label classification methods demonstrate that, compared with the existing kernel selection methods and the most widely used RBF kernel function, SVM with the kernel function recommended by our proposed method achieved the highest classification performance. PMID:25893896

Free-Energy Barrier of Filling a Spherical Cavity in the Presence of Line Tension: Implication to the Energy Barrier between the Cassie and Wenzel States on a Superhydrophobic Surface with Spherical Cavities.

PubMed

Iwamatsu, Masao

2016-09-20

The free-energy barrier of filling a spherical cavity having an inner wall of various wettabilities is studied. The morphology and free energy of a lens-shaped droplet are determined from the minimum of the free energy. The effect of line tension on the free energy is also studied. Then, the equilibrium contact angle of the droplet is determined from the generalized Young's equation. By increasing the droplet volume within the spherical cavity, the droplet morphology changes from spherical with an equilibrium contact angle of 180° to a lens with a convex meniscus, where the morphological complete drying transition occurs. By further increasing the droplet volume, the meniscus changes from convex to concave. Then, the lens-shaped droplet with concave meniscus spreads over the whole inner wall, resulting in an equilibrium contact angle of 0° to leave a spherical bubble, where the morphological complete wetting transition occurs. Finally, the whole cavity is filled with liquid. The free energy shows a barrier from complete drying to complete wetting as a function of droplet volume, which corresponds to the energy barrier between the Cassie and Wenzel states of the superhydrophobic surface with spherical cavities. The free-energy maximum occurs when the meniscus of the droplet becomes flat, and it is given by an analytic formula. The effect of line tension is expressed by the scaled line tension, and this effect is largest at the free-energy maximum. The positive line tension increases the free-energy maximum, which thus increases the stability of the Cassie superhydrophobic state, whereas the negative line tension destabilizes the superhydrophobic state.

State Transition Matrix for Perturbed Orbital Motion Using Modified Chebyshev Picard Iteration

NASA Astrophysics Data System (ADS)

Read, Julie L.; Younes, Ahmad Bani; Macomber, Brent; Turner, James; Junkins, John L.

2015-06-01

The Modified Chebyshev Picard Iteration (MCPI) method has recently proven to be highly efficient for a given accuracy compared to several commonly adopted numerical integration methods, as a means to solve for perturbed orbital motion. This method utilizes Picard iteration, which generates a sequence of path approximations, and Chebyshev Polynomials, which are orthogonal and also enable both efficient and accurate function approximation. The nodes consistent with discrete Chebyshev orthogonality are generated using cosine sampling; this strategy also reduces the Runge effect and as a consequence of orthogonality, there is no matrix inversion required to find the basis function coefficients. The MCPI algorithms considered herein are parallel-structured so that they are immediately well-suited for massively parallel implementation with additional speedup. MCPI has a wide range of applications beyond ephemeris propagation, including the propagation of the State Transition Matrix (STM) for perturbed two-body motion. A solution is achieved for a spherical harmonic series representation of earth gravity (EGM2008), although the methodology is suitable for application to any gravity model. Included in this representation the normalized, Associated Legendre Functions are given and verified numerically. Modifications of the classical algorithm techniques, such as rewriting the STM equations in a second-order cascade formulation, gives rise to additional speedup. Timing results for the baseline formulation and this second-order formulation are given.

Basis set study of classical rotor lattice dynamics.

PubMed

Witkoskie, James B; Wu, Jianlan; Cao, Jianshu

2004-03-22

The reorientational relaxation of molecular systems is important in many phenomenon and applications. In this paper, we explore the reorientational relaxation of a model Brownian rotor lattice system with short range interactions in both the high and low temperature regimes. In this study, we use a basis set expansion to capture collective motions of the system. The single particle basis set is used in the high temperature regime, while the spin wave basis is used in the low temperature regime. The equations of motion derived in this approach are analogous to the generalized Langevin equation, but the equations render flexibility by allowing nonequilibrium initial conditions. This calculation shows that the choice of projection operators in the generalized Langevin equation (GLE) approach corresponds to defining a specific inner-product space, and this inner-product space should be chosen to reveal the important physics of the problem. The basis set approach corresponds to an inner-product and projection operator that maintain the orthogonality of the spherical harmonics and provide a convenient platform for analyzing GLE expansions. The results compare favorably with numerical simulations, and the formalism is easily extended to more complex systems. (c) 2004 American Institute of Physics

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.

A study of nondiffracting Lommel beams propagating in a medium containing spherical scatterers

NASA Astrophysics Data System (ADS)

Belafhal, A.; Ez-zariy, L.; Hricha, Z.

2016-11-01

By means of the expansion of the nondiffracting beams on plane waves with help of the Whittaker integral, an exact analytical expression of the far-field form function of the scattering of the acoustic and optical nondiffracting Lommel beams propagating in a medium containing spherical particles, considered as rigid and single spheres, is investigated in this work. The form function of the scattering of the high order Bessel beam by a rigid and isolated sphere is deduced, from our finding, as a special case. The effects of the wave number-sphere radius product (ka) , the polar angle (φ) , the propagation half-cone angle (β) and the scattering angle (θ) on the far-field form function of the scattered wave have been analyzed and discussed numerically. The numerical results show that the illumination of a rigid sphere by Lommel beams produces asymmetrical scattering.

Encircling the dark: constraining dark energy via cosmic density in spheres

NASA Astrophysics Data System (ADS)

Codis, S.; Pichon, C.; Bernardeau, F.; Uhlemann, C.; Prunet, S.

2016-08-01

The recently published analytic probability density function for the mildly non-linear cosmic density field within spherical cells is used to build a simple but accurate maximum likelihood estimate for the redshift evolution of the variance of the density, which, as expected, is shown to have smaller relative error than the sample variance. This estimator provides a competitive probe for the equation of state of dark energy, reaching a few per cent accuracy on wp and wa for a Euclid-like survey. The corresponding likelihood function can take into account the configuration of the cells via their relative separations. A code to compute one-cell-density probability density functions for arbitrary initial power spectrum, top-hat smoothing and various spherical-collapse dynamics is made available online, so as to provide straightforward means of testing the effect of alternative dark energy models and initial power spectra on the low-redshift matter distribution.

Wave equations in conformal gravity

NASA Astrophysics Data System (ADS)

Du, Juan-Juan; Wang, Xue-Jing; He, You-Biao; Yang, Si-Jiang; Li, Zhong-Heng

2018-05-01

We study the wave equation governing massless fields of all spins (s = 0, 1 2, 1, 3 2 and 2) in the most general spherical symmetric metric of conformal gravity. The equation is separable, the solution of the angular part is a spin-weighted spherical harmonic, and the radial wave function may be expressed in terms of solutions of the Heun equation which has four regular singular points. We also consider various special cases of the metric and find that the angular wave functions are the same for all cases, the actual shape of the metric functions affects only the radial wave function. It is interesting to note that each radial equation can be transformed into a known ordinary differential equation (i.e. Heun equation, or confluent Heun equation, or hypergeometric equation). The results show that there are analytic solutions for all the wave equations of massless spin fields in the spacetimes of conformal gravity. This is amazing because exact solutions are few and far between for other spacetimes.

Stopped-flow kinetic studies of sphere-to-rod transitions of sodium alkyl sulfate micelles induced by hydrotropic salt.

PubMed

Zhang, Jingyan; Ge, Zhishen; Jiang, Xiaoze; Hassan, P A; Liu, Shiyong

2007-12-15

The kinetics and mechanism of sphere-to-rod transitions of sodium alkyl sulfate micelles induced by hydrotropic salt, p-toluidine hydrochloride (PTHC), were investigated by stopped-flow with light scattering detection. Spherical sodium dodecyl sulfate (SDS) micelles transform into short ellipsoidal shapes at low salt concentrations ([PTHC]/[SDS], chi(PTHC)=0.3 and 0.4). Upon stopped-flow mixing aqueous solutions of spherical SDS micelles with PTHC, the scattered light intensity gradually increases with time. Single exponential fitting of the dynamic traces leads to characteristic relaxation time, tau(g), for the growth process from spherical to ellipsoidal micelles, and it increases with increasing SDS concentrations. This suggests that ellipsoidal micelles might be produced by successive insertion of unimers into spherical micelles, similar to the case of formation of spherical micelles as suggested by Aniansson-Wall (A-W) theory. At chi(PTHC) > or = 0.5, rod-like micelles with much higher axial ratio form. The scattered light intensity exhibits an initially abrupt increase and then levels off. The dynamic curves can be well fitted with single exponential functions, and the obtained tau(g) decreases with increasing SDS concentration. Thus, the growth from spherical to rod-like micelles might proceed via fusion of spherical micelles, in agreement with mechanism proposed by Ikeda et al. At chi(PTHC)=0.3 and 0.6, the apparent activation energies obtained from temperature dependent kinetic studies for the micellar growth are 40.4 and 3.6 kJ/mol, respectively. The large differences between activation energies for the growth from spherical to ellipsoidal micelles at low chi(PTHC) and the sphere-to-rod transition at high chi(PTHC) further indicate that they should follow different mechanisms. Moreover, the sphere-to-rod transition kinetics of sodium alkyl sulfate with varying hydrophobic chain lengths (n=10, 12, 14, and 16) are also studied. The longer the carbon chain lengths, the slower the sphere-to-rod transition.

The moving-least-squares-particle hydrodynamics method (MLSPH)

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

Dilts, G.

1997-12-31

An enhancement of the smooth-particle hydrodynamics (SPH) method has been developed using the moving-least-squares (MLS) interpolants of Lancaster and Salkauskas which simultaneously relieves the method of several well-known undesirable behaviors, including spurious boundary effects, inaccurate strain and rotation rates, pressure spikes at impact boundaries, and the infamous tension instability. The classical SPH method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of motion for continua using as basis functions the SPH kernel function multiplied by the particle volume. This derivation is then modified by simply substituting the MLS interpolants for themore » SPH Galerkin basis, taking care to redefine the particle volume and mass appropriately. The familiar SPH kernel approximation is now equivalent to a colocation-Galerkin method. Both classical conservative and recent non-conservative formulations of SPH can be derived and emulated. The non-conservative forms can be made conservative by adding terms that are zero within the approximation at the expense of boundary-value considerations. The familiar Monaghan viscosity is used. Test calculations of uniformly expanding fluids, the Swegle example, spinning solid disks, impacting bars, and spherically symmetric flow illustrate the superiority of the technique over SPH. In all cases it is seen that the marvelous ability of the MLS interpolants to add up correctly everywhere civilizes the noisy, unpredictable nature of SPH. Being a relatively minor perturbation of the SPH method, it is easily retrofitted into existing SPH codes. On the down side, computational expense at this point is significant, the Monaghan viscosity undoes the contribution of the MLS interpolants, and one-point quadrature (colocation) is not accurate enough. Solutions to these difficulties are being pursued vigorously.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

DOE PAGES

Bunting, Gregory; Prakash, Arun; Walsh, Timothy; ...

2018-01-26

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Parallel Ellipsoidal Perfectly Matched Layers for Acoustic Helmholtz Problems on Exterior Domains

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

Bunting, Gregory; Prakash, Arun; Walsh, Timothy

Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and howmore » this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this study, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. Finally, this provides an additional advantage of PML over the infinite element approach.« less

Sarcoidosis: correlation of pulmonary parenchymal pattern at CT with results of pulmonary function tests

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

Bergin, C.J.; Bell, D.Y.; Coblentz, C.L.

1989-06-01

The appearances of the lungs on radiographs and computed tomographic (CT) scans were correlated with degree of uptake on gallium scans and results of pulmonary function tests (PFTs) in 27 patients with sarcoidosis. CT scans were evaluated both qualitatively and quantitatively. Patients were divided into five categories on the basis of the pattern of abnormality at CT: 1 = normal (n = 4); 2 = segmental air-space disease (n = 4); 3 = spherical (alveolar) masslike opacities (n = 4); 4 = multiple, discrete, small nodules (n = 6); and 5 = distortion of parenchymal structures (fibrotic end-stage sarcoidosis) (nmore » = 9). The percentage of the volume judged to be abnormal (CT grade) was correlated with PFT results for each CT and radiographic category. CT grades were also correlated with gallium scanning results and percentage of lymphocytes recovered from bronchoalveolar lavage (BAL). Patients in CT categories 1 and 2 had normal lung function, those in category 3 had mild functional impairment, and those in categories 4 and 5 showed moderate to severe dysfunction. The overall CT grade correlated well with PFT results expressed as a percentage of the predicted value. In five patients, CT scans showed extensive parenchymal disease not seen on radiographs. CT grades did not correlate with the results of gallium scanning or BAL lymphocytes. The authors conclude that patterns of parenchymal sarcoidosis seen at CT correlate with the PFT results and can be used to indicate respiratory impairment.« less

Scanning Electron Microscopy and Petrography of Glassy Particles Produced by Lava Fountain Eruptions. Ph.D. Thesis - Final Report

NASA Technical Reports Server (NTRS)

Ladle, G. H.

1978-01-01

A conceptual model of a lava fountain consists of a vent, spatter ramparts, fountain column, downwind plume and associated pumice deposits. Glassy particles produced by lava fountain eruptions consist primarily of sideromelane glass and minor to moderate amounts of vesicles and crystals. Particles are classified on the basis of morphology as: (1) spherical, (2) elongate, (3) glass-coated mineral grain, (4) shard, (5) reticulite, (6) composite particle, and (7) lithic fragment.

Properties of solid and gaseous hydrogen, based upon anisotropic pair interactions

NASA Technical Reports Server (NTRS)

Etters, R. D.; Danilowicz, R.; England, W.

1975-01-01

Properties of H2 are studied on the basis of an analytic anisotropic potential deduced from atomic orbital and perturbation calculations. The low-pressure solid results are based on a spherical average of the anisotropic potential. The ground state energy and the pressure-volume relation are calculated. The metal-insulator phase transition pressure is predicted. Second virial coefficients are calculated for H2 and D2, as is the difference in second virial coefficients between ortho and para H2 and D2.

Radiative transfer in molecular lines

NASA Astrophysics Data System (ADS)

Asensio Ramos, A.; Trujillo Bueno, J.; Cernicharo, J.

2001-07-01

The highly convergent iterative methods developed by Trujillo Bueno and Fabiani Bendicho (1995) for radiative transfer (RT) applications are generalized to spherical symmetry with velocity fields. These RT methods are based on Jacobi, Gauss-Seidel (GS), and SOR iteration and they form the basis of a new NLTE multilevel transfer code for atomic and molecular lines. The benchmark tests carried out so far are presented and discussed. The main aim is to develop a number of powerful RT tools for the theoretical interpretation of molecular spectra.

Analytical functions for beta and gamma absorbed fractions of iodine-131 in spherical and ellipsoidal volumes.

PubMed

Mowlavi, Ali Asghar; Fornasier, Maria Rossa; Mirzaei, Mohammd; Bregant, Paola; de Denaro, Mario

2014-10-01

The beta and gamma absorbed fractions in organs and tissues are the important key factors of radionuclide internal dosimetry based on Medical Internal Radiation Dose (MIRD) approach. The aim of this study is to find suitable analytical functions for beta and gamma absorbed fractions in spherical and ellipsoidal volumes with a uniform distribution of iodine-131 radionuclide. MCNPX code has been used to calculate the energy absorption from beta and gamma rays of iodine-131 uniformly distributed inside different ellipsoids and spheres, and then the absorbed fractions have been evaluated. We have found the fit parameters of a suitable analytical function for the beta absorbed fraction, depending on a generalized radius for ellipsoid based on the radius of sphere, and a linear fit function for the gamma absorbed fraction. The analytical functions that we obtained from fitting process in Monte Carlo data can be used for obtaining the absorbed fractions of iodine-131 beta and gamma rays for any volume of the thyroid lobe. Moreover, our results for the spheres are in good agreement with the results of MIRD and other scientific literatures.

Phase function of a spherical particle when scattering an inhomogeneous electromagnetic plane wave.

PubMed

Frisvad, Jeppe Revall

2018-04-01

In absorbing media, electromagnetic plane waves are most often inhomogeneous. Existing solutions for the scattering of an inhomogeneous plane wave by a spherical particle provide no explicit expressions for the scattering components. In addition, current analytical solutions require evaluation of the complex hypergeometric function F 1 2 for every term of a series expansion. In this work, I develop a simpler solution based on associated Legendre functions with argument zero. It is similar to the solution for homogeneous plane waves but with new explicit expressions for the angular dependency of the far-field scattering components, that is, the phase function. I include recurrence formulas for practical evaluation and provide numerical examples to evaluate how well the new expressions match previous work in some limiting cases. The predicted difference in the scattering phase function due to inhomogeneity is not negligible for light entering an absorbing medium at an oblique angle. The presented theory could thus be useful for predicting scattering behavior in dye-based random lasing and in solar cell absorption enhancement.

Specifics of heat and mass transfer in spherical dimples under the effect of external factors

NASA Astrophysics Data System (ADS)

Shchukin, A. V.; Il'inkov, A. V.; Takmovtsev, V. V.; Khabibullin, I. I.

2017-06-01

The specifics are examined of heat transfer enhancement with spherical dimples under the effect of factors important for practice and characteristic of cooling systems of gas-turbine engines and power units. This experimental investigation deals with the effect of the following factors on the flow in a channel with hemispherical dimples: continuous air swirl in an annulus with dimples on its concave wall, dimples on the convex or concave wall of a curved rectangular channel, imposition of regular velocity fluctuations on the external flow in a straight rectangular channel, and adverse or favorable pressure gradient along the flow direction. The flow is turbulent. Reynolds numbers based on the channel hydraulic diameter are on the order of 104. Results of the investigation of a model of a two-cavity diffuser dimple proposed by the authors are presented. It has been found that results for channels with spherical dimples and for smooth channels differ not only quantitatively but also qualitatively. Thus, if the effect of centrifugal mass forces on convex and concave surfaces with hemispherical dimples and in a smooth channel is almost the same (quantitative and qualitative indicators are identical), the pressure gradient in the flow direction brings about the drastically opposite results. At the same time, the quantitative contribution to a change in heat transfer in hemispherical dimples is different and depends on the impact type. The results are discussed with the use of physical models created on the basis of the results of flow visualization studies and data on the turbulence intensity, pressure coefficient, etc. Results of the investigations suggest that application of spherical dimples under nonstandard conditions requires the calculated heat transfer to be corrected to account for one or another effect.

Investigating Aerosol Morphology Using Scattering Phase Functions Measured with a Laser Imaging Nephelometer

NASA Astrophysics Data System (ADS)

Manfred, K.; Adler, G. A.; Erdesz, F.; Franchin, A.; Lamb, K. D.; Schwarz, J. P.; Wagner, N.; Washenfelder, R. A.; Womack, C.; Murphy, D. M.

2017-12-01

Particle morphology has important implications for light scattering and radiative transfer, but can be difficult to measure. Biomass burning and other important aerosol sources can generate a mixture of both spherical and non-spherical particle morphologies, and it is necessary to represent these populations correctly in models. We describe a laser imaging nephelometer that measures the unpolarized scattering phase function of bulk aerosol at 375 and 405 nm using a wide-angle lens and CCD. We deployed this instrument to the Missoula Fire Sciences Laboratory to measure biomass burning aerosol morphology from controlled fires during the recent FIREX intensive laboratory study. Total integrated scattering signal agreed with that determined by a cavity ring-down photoacoustic spectrometer system and a traditional integrating nephelometer within instrument uncertainties. We compared measured scattering phase functions at 405 nm to theoretical models for spherical (Mie) and fractal (Rayleigh-Debye-Gans) particle morphologies based on the size distribution reported by an optical particle counter. We show that particle morphology can vary dramatically for different fuel types, and present results for two representative fires (pine tree vs arid shrub). We find that Mie theory is inadequate to describe the actual behavior of realistic aerosols from biomass burning in some situations. This study demonstrates the capabilities of the laser imaging nephelometer instrument to provide real-time, in situ information about dominant particle morphology that is vital for accurate radiative transfer calculations.

Radiation absorbed dose to bladder walls from positron emitters in the bladder content.

PubMed

Powell, G F; Chen, C T

1987-01-01

A method to calculate absorbed doses at depths in the walls of a static spherical bladder from a positron emitter in the bladder content has been developed. The beta ray dose component is calculated for a spherical model by employing the solutions to the integration of Loevinger and Bochkarev point source functions over line segments and a line segment source array technique. The gamma ray dose is determined using the specific gamma ray constant. As an example, absorbed radiation doses to the bladder walls from F-18 in the bladder content are presented for static spherical bladder models having radii of 2.0 and 3.5 cm, respectively. Experiments with ultra-thin thermoluminescent dosimeters (TLD's) were performed to verify the results of the calculations. Good agreement between TLD measurements and calculations was obtained.

ON THE UNIVERSALITY OF THE GLOBAL DENSITY SLOPE-ANISOTROPY INEQUALITY

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

Van Hese, Emmanuel; Baes, Maarten; Dejonghe, Herwig, E-mail: emmanuel.vanhese@gmail.com, E-mail: maarten.baes@ugent.be, E-mail: herwig.dejonghe@ugent.be

2011-01-10

Recently, some intriguing results have led to speculations whether the central density slope-velocity dispersion anisotropy inequality (An and Evans) actually holds at all radii for spherical dynamical systems. We extend these studies by providing a complete analysis of the global slope-anisotropy inequality for all spherical systems in which the augmented density is a separable function of radius and potential. We prove that these systems indeed satisfy the global inequality if their central anisotropy is {beta}{sub 0} {<=} 1/2. Furthermore, we present several systems with {beta}{sub 0}>1/2 for which the inequality does not hold, thus demonstrating that the global density slope-anisotropymore » inequality is not a universal property. This analysis is a significant step toward an understanding of the relation for general spherical systems.« less

Topological geons with self-gravitating phantom scalar field

NASA Astrophysics Data System (ADS)

Kratovitch, P. V.; Potashov, I. M.; Tchemarina, Ju V.; Tsirulev, A. N.

2017-12-01

A topological geon is the quotient manifold M/Z 2 where M is a static spherically symmetric wormhole having the reflection symmetry with respect to its throat. We distinguish such asymptotically at solutions of the Einstein equations according to the form of the time-time metric function by using the quadrature formulas of the so-called inverse problem for self-gravitating spherically symmetric scalar fields. We distinguish three types of geon spacetimes and illustrate them by simple examples. We also study possible observational effects associated with bounded geodesic motion near topological geons.

Dependence of Strain Distribution on In Content in InGaN/GaN Quantum Wires and Spherical Quantum Dots

NASA Astrophysics Data System (ADS)

Sharma, Akant Sagar; Dhar, S.

2018-02-01

The distribution of strain, developed in zero-dimensional quantum spherical dots and one-dimensional cylindrical quantum wires of an InGaN/GaN system is calculated as functions of radius of the structure and indium mole fraction. The strain shows strong dependence on indium mole fraction at small distances from the center. The strain associated with both the structures is found to decrease exponentially with the increase in dot or cylinder radius and increases linearly with indium content.

Magnetic rotational hysteresis study on spherical 85-160 nm Fe3O4 particles

NASA Astrophysics Data System (ADS)

Schmidbauer, E.

1988-05-01

Rotational hysteresis losses Wr were determined as a function of magnetic field H for dispensed spherical Fe3O4 particles of mean grain sizes 85 nm, 127 nm and 162 nm between 78 K and 294 K. The observed Wr-H curves are compared with theoretical curves for single domain particles. The analysed particles reveal centers of high magnetic anisotropy. Such centers can be of importance during the generation of a thermoremanent magnetization, as they may be the origin of enhanced magnetic stability.

Stabilizing liquid drops of arbitrary shape by the interfacial jamming of nanoparticles

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

Russell, Thomas P.; Cui, Mengmeng; Emrick, Todd

A stabilized assembly including a first liquid phase of non-spherical droplets in a second liquid phase, wherein the second liquid phase is immiscible with the first phase, and nanoparticle surfactants assembled at an interface of the non-spherical droplets and the second phase is disclosed. The nanoparticle surfactants include nanoparticles and end-functionalized polymers that can interact through ligand type interactions, and the first phase is stabilized by a disordered, jammed layer of nanoparticle surfactants. A method of preparing a stabilized assembly is also disclosed.

Potential Sources of Polarized Light from a Plant Canopy

NASA Technical Reports Server (NTRS)

Vanderbilt, Vern; Daughtry, Craig; Dahlgren, Robert

2016-01-01

Field measurements have demonstrated that sunlight polarized during a first surface reflection by shiny leaves dominates the optical polarization of the light reflected by shiny-leafed plant canopies having approximately spherical leaf angle probability density functions ("Leaf Angle Distributions" - LAD). Yet for other canopies - specifically those without shiny leaves and/or spherical LADs - potential sources of optically polarized light may not always be obvious. Here we identify possible sources of polarized light within those other canopies and speculate on the ecologically important information polarization measurements of those sources might contain.

A poloidal section neutron camera for MAST upgrade

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

Sangaroon, S.; Weiszflog, M.; Cecconello, M.

2014-08-21

The Mega Ampere Spherical Tokamak Upgrade (MAST Upgrade) is intended as a demonstration of the physics viability of the Spherical Tokamak (ST) concept and as a platform for contributing to ITER/DEMO physics. Concerning physics exploitation, MAST Upgrade plasma scenarios can contribute to the ITER Tokamak physics particularly in the field of fast particle behavior and current drive studies. At present, MAST is equipped with a prototype neutron camera (NC). On the basis of the experience and results from previous experimental campaigns using the NC, the conceptual design of a neutron camera upgrade (NC Upgrade) is being developed. As part ofmore » the MAST Upgrade, the NC Upgrade is considered a high priority diagnostic since it would allow studies in the field of fast ions and current drive with good temporal and spatial resolution. In this paper, we explore an optional design with the camera array viewing the poloidal section of the plasma from different directions.« less

Vaporization of irradiated droplets

NASA Astrophysics Data System (ADS)

Armstrong, R. L.; O'Rourke, P. J.; Zardecki, A.

1986-11-01

The vaporization of a spherically symmetric liquid droplet subject to a high-intensity laser flux is investigated on the basis of a hydrodynamic description of the system composed of the vapor and ambient gas. In the limit of the convective vaporization, the boundary conditions at the fluid-gas interface are formulated by using the notion of a Knudsen layer in which translational equilibrium is established. This leads to approximate jump conditions at the interface. For homogeneous energy deposition, the hydrodynamic equations are solved numerically with the aid of the CON1D computer code (``CON1D: A computer program for calculating spherically symmetric droplet combustion,'' Los Alamos National Laboratory Report No. LA-10269-MS, December, 1984), based on the implict continuous-fluid Eulerian (ICE) [J. Comput. Phys. 8, 197 (1971)] and arbitrary Lagrangian-Eulerian (ALE) [J. Comput. Phys. 14, 1227 (1974)] numerical mehtods. The solutions exhibit the existence of two shock waves propagating in opposite directions with respect to the contact discontinuity surface that separates the ambient gas and vapor.

Reconstructing the vibro-acoustic quantities on a highly non-spherical surface using the Helmholtz equation least squares method.

PubMed

Natarajan, Logesh Kumar; Wu, Sean F

2012-06-01

This paper presents helpful guidelines and strategies for reconstructing the vibro-acoustic quantities on a highly non-spherical surface by using the Helmholtz equation least squares (HELS). This study highlights that a computationally simple code based on the spherical wave functions can produce an accurate reconstruction of the acoustic pressure and normal surface velocity on planar surfaces. The key is to select the optimal origin of the coordinate system behind the planar surface, choose a target structural wavelength to be reconstructed, set an appropriate stand-off distance and microphone spacing, use a hybrid regularization scheme to determine the optimal number of the expansion functions, etc. The reconstructed vibro-acoustic quantities are validated rigorously via experiments by comparing the reconstructed normal surface velocity spectra and distributions with the benchmark data obtained by scanning a laser vibrometer over the plate surface. Results confirm that following the proposed guidelines and strategies can ensure the accuracy in reconstructing the normal surface velocity up to the target structural wavelength, and produce much more satisfactory results than a straight application of the original HELS formulations. Experiment validations on a baffled, square plate were conducted inside a fully anechoic chamber.

Mild Oxidation Promotes and Advanced Oxidation Impairs Remodeling of Human High-Density Lipoprotein in vitro

PubMed Central

Gao, Xuan; Jayaraman, Shobini; Gursky, Olga

2008-01-01

SUMMARY High-density lipoproteins (HDL) prevent atherosclerosis by removing cholesterol from macrophages and by exerting anti-oxidant and anti-inflammatory effects. Oxidation is thought to impair HDL functions, yet certain oxidative modifications may be advantageous; thus, mild oxidation reportedly enhances cell cholesterol uptake by HDL whereas extensive oxidation impairs it. To elucidate the underlying energetic and structural basis, we analyzed the effects of copper and hypochlorite (that preferentially oxidize lipids and proteins, respectively) on thermal stability of plasma spherical HDL. Circular dichroism, light scattering, calorimetry, gel electrophoresis and electron microscopy showed that mild oxidation destabilizes HDL and accelerates protein dissociation and lipoprotein fusion, while extensive oxidation inhibits these reactions; this inhibition correlates with massive protein cross-linking and lipolysis. We propose that mild oxidation lowers kinetic barriers for HDL remodeling due to diminished apolipoprotein affinity for lipids resulting from oxidation of methionine and aromatic residues in apolipoproteins A-I and A-II followed by protein cross-linking into dimers and/or trimers. In contrast, advanced oxidation inhibits protein dissociation and HDL fusion due to lipid re-distribution from core to surface upon lipolysis and to massive protein cross-linking. Our results help reconcile the apparent controversy in the studies of oxidized HDL and suggest that mild oxidation may benefit HDL functions. PMID:18190928

Polymer-coated surface enhanced Raman scattering (SERS) gold nanoparticles for multiplexed labeling of chronic lymphocytic leukemia cells

NASA Astrophysics Data System (ADS)

MacLaughlin, Christina M.; Parker, Edward P. K.; Walker, Gilbert C.; Wang, Chen

2012-01-01

The ease and flexibility of functionalization and inherent light scattering properties of plasmonic nanoparticles make them suitable contrast agents for measurement of cell surface markers. Immunophenotyping of lymphoproliferative disorders is traditionally undertaken using fluorescence detection methods which have a number of limitations. Herein, surface-enhanced Raman scattering (SERS) gold nanoparticles conjugated to monoclonal antibodies are used for the selective targeting of CD molecules on the surface of chronic lymphocytic leukemia (CLL) cells. Raman-active reporters were physisorbed on to the surface of 60 nm spherical Au nanoparticles, the particles were coated with 5kDa polyethylene glycol (PEG) including functionalities for conjugation to monoclonal IgG1 antibodies. A novel method for quantifying the number of antibodies bound to SERS probes on an individual basis as opposed to obtaining averages from solution was demonstrated using metal dots in transmission electron microscopy (TEM). The specificity of the interaction between SERS probes and surface CD molecules of CLL cells was assessed using Raman spectroscopy and dark field microscopy. An in-depth study of SERS probe targeting to B lymphocyte marker CD20 was undertaken, and proof-of-concept targeting using different SERS nanoparticle dyes specific for cell surface CD19, CD45 and CD5 demonstrated using SERS spectroscopy.

Global Dynamic Modeling of Space-Geodetic Data

NASA Technical Reports Server (NTRS)

Bird, Peter

1995-01-01

The proposal had outlined a year for program conversion, a year for testing and debugging, and two years for numerical experiments. We kept to that schedule. In first (partial) year, author designed a finite element for isostatic thin-shell deformation on a sphere, derived all of its algebraic and stiffness properties, and embedded it in a new finite element code which derives its basic solution strategy (and some critical subroutines) from earlier flat-Earth codes. Also designed and programmed a new fault element to represent faults along plate boundaries. Wrote a preliminary version of a spherical graphics program for the display of output. Tested this new code for accuracy on individual model plates. Made estimates of the computer-time/cost efficiency of the code for whole-earth grids, which were reasonable. Finally, converted an interactive graphical grid-designer program from Cartesian to spherical geometry to permit the beginning of serious modeling. For reasons of cost efficiency, models are isostatic, and do not consider the local effects of unsupported loads or bending stresses. The requirements are: (1) ability to represent rigid rotation on a sphere; (2) ability to represent a spatially uniform strain-rate tensor in the limit of small elements; and (3) continuity of velocity across all element boundaries. Author designed a 3-node triangle shell element which has two different sets of basis functions to represent (vector) velocity and all other (scalar) variables. Such elements can be shown to converge to the formulas for plane triangles in the limit of small size, but can also applied to cover any area smaller than a hemisphere. The difficult volume integrals involved in computing the stiffness of such elements are performed numerically using 7 Gauss integration points on the surface of the sphere, beneath each of which a vertical integral is performed using about 100 points.

Recovery of surface mass redistribution from a joint inversion of GPS and GRACE data - A methodology and results from the Australian and other continents

NASA Astrophysics Data System (ADS)

Han, S. C.; Tangdamrongsub, N.; Razeghi, S. M.

2017-12-01

We present a methodology to invert a regional set of vertical displacement data from Global Positioning System (GPS) to determine surface mass redistribution. It is assumed that GPS deformation is a result of the Earth's elastic response to the surface mass load of hydrology, atmosphere, and ocean. The identical assumption is made when global geopotential change data from Gravity Recovery And Climate Experiment (GRACE) are used to determine surface mass changes. We developed an algorithm to estimate the spectral information of displacements from "regional" GPS data through regional spherical (Slepian) basis functions and apply the load Love numbers to estimate the mass load. We rigorously examine all systematic errors caused by various truncations (spherical harmonic series and Slepian series) and the smoothing constraint applied to the GPS-only inversion. We demonstrate the technique by processing 16 years of daily vertical motions determined from 114 GPS stations in Australia. The GPS inverted surface mass changes are validated against GRACE data, atmosphere and ocean models, and a land surface model. Seasonal and inter-annual terrestrial mass variations from GPS are in good agreement with GRACE data and the water storage models. The GPS recovery compares better with the water storage model around the smaller coastal basins of Australia than two different GRACE solutions. The sub-monthly mass changes from GPS provide meaningful results agreeing with atmospheric mass changes in central Australia. Finally, we integrate GPS data from different continents with GRACE in the least-square normal equations and solve for the global surface mass changes by jointly inverting GPS and GRACE data. We present the results of surface mass changes from the GPS-only inversion and from the joint GPS-GRACE inversion.

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

PubMed

Batke, Kilian; Eickerling, Georg

2013-11-14

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

Numerical Simulation of Dry Granular Flow Impacting a Rigid Wall Using the Discrete Element Method

PubMed Central

Wu, Fengyuan; Fan, Yunyun; Liang, Li; Wang, Chao

2016-01-01

This paper presents a clump model based on Discrete Element Method. The clump model was more close to the real particle than a spherical particle. Numerical simulations of several tests of dry granular flow impacting a rigid wall flowing in an inclined chute have been achieved. Five clump models with different sphericity have been used in the simulations. By comparing the simulation results with the experimental results of normal force on the rigid wall, a clump model with better sphericity was selected to complete the following numerical simulation analysis and discussion. The calculation results of normal force showed good agreement with the experimental results, which verify the effectiveness of the clump model. Then, total normal force and bending moment of the rigid wall and motion process of the granular flow were further analyzed. Finally, comparison analysis of the numerical simulations using the clump model with different grain composition was obtained. By observing normal force on the rigid wall and distribution of particle size at the front of the rigid wall at the final state, the effect of grain composition on the force of the rigid wall has been revealed. It mainly showed that, with the increase of the particle size, the peak force at the retaining wall also increase. The result can provide a basis for the research of relevant disaster and the design of protective structures. PMID:27513661

The carbohydrate deposits detected by histochemical methods in the molecular layer of the dentate gyrus in the hippocampal formation of patients with schizophrenia, Down's syndrome and dementia, and aged person.

PubMed

Nishimura, A; Ikemoto, K; Satoh, K; Yamamoto, Y; Rand, S; Brinkmann, B; Nishi, K

2000-11-01

Post-mortem brain tissue was obtained from 28 patients with brain disorders, of which 15 had clinically diagnosed schizophrenia, 6 Alzheimer type dementia, 5 dementia with tangles and 2 cases of Down's syndrome. The controls were 22 cases from autopsies without brain disorders or with no known episodes of brain disorder. The tissues were stained for the detection of carbohydrate deposits in the hippocampal formation, using lectin, immunohistochemical and conventional staining methods. The staining revealed the existence of spherical deposits in the inner and middle molecular layers of the dentate gyrus in the hippocampal formation which contained fucose, galactose, N-acetyl galactosamine, N-acetyl glucosamine, sialic acid, mannose and chondroitin sulfate. The number of the deposits was higher in patients with brain disorder such as schizophrenia, Alzheimer type dementia, dementia with tangles or Down's syndrome, and in some aged individuals, in comparison to those in younger individuals. No deposits were detected in a few younger or aged individuals. Spherical deposits 3-10 microm in diameter may be an immature form of the corpora amylacea, since they were similar in the histochemical characteristics with lectin, immunohistochemical and conventional staining methods. However, differing staining ability by hematoxylin, periodic acid Schiff's reagent and antibodies against the intracellular degraded proteins such as ubiquitin and tau-protein was observed. The antibodies against ubiquitin and tau-protein showed clear reactivity with the corpora amylacea and no reactivity with spherical deposits, indicating that the corpora amylacea has an intracellular origin and spherical deposits an extracellular matrix origin. The results obtained in this study indicate that not only neuronal degeneration but also unusual glycometabolism in neurons may disturb the neuronal function and cause brain disorders, and that spherical deposits may cause dysfunction of the neuronal network in the dentate gyrus of the hippocampus which is closely linked with recognition and memory functions.

OPTICS OF CONDUCTIVE KERATOPLASTY: IMPLICATIONS FOR PRESBYOPIA MANAGEMENT

PubMed Central

Hersh, Peter S

2005-01-01

Purpose To define the corneal optics of conductive keratoplasty (CK) and assess the clinical implications for hyperopia and presbyopia management. Methods Four analyses were done. (1) Multifocal effects: In a prospective study of CK, uncorrected visual acuity (UCVA) for a given refractive error in 72 postoperative eyes was compared to control eyes. (2) Surgically induced astigmatism (SIA): 203 eyes were analyzed for magnitude and axis of SIA. (3) Higher-order optical aberrations: Corneal higher-order optical aberrations were assessed for 36 eyes after CK and a similar patient population after hyperopic laser in situ keratomileusis (LASIK). (4) Presbyopia clinical trial: Visual acuity, refractive result, and patient questionnaires were analyzed for 150 subjects in a prospective, multicenter clinical trial of presbyopia management with CK. Results (1) 63% and 82% of eyes after CK had better UCVA at distance and near, respectively, than controls. (2) The mean SIA was 0.23 diopter (D) steepening at 175° (P < .001); mean magnitude was 0.66 D (SD, 0.43 D). (3) After CK, composite fourth- and sixth-order spherical aberration increased; change in (Z12) spherical aberration alone was not statistically significant. When compared to hyperopic LASIK, there was a statistically significant increase in composite fourth- and sixth-order spherical aberration (P < .01) and spherical aberration (Z12) alone (P < .02); spherical aberration change was more prolate after CK. (4) After the CK monovision procedure, 80% of patients had J3 or better binocular UCVA at near; 84% of patients were satisfied. Satisfaction was associated with near UCVA of J3 or better in the monovision eye (P = .001) and subjectively good postoperative depth perception (P = .038). Conclusions CK seems to produce functional corneal multifocality with definable introduction of SIA and higher-order optical aberrations, and development of a more prolate corneal contour. These optical factors may militate toward improved near vision function. PMID:17057812

Impact of contact lens zone geometry and ocular optics on bifocal retinal image quality

PubMed Central

Bradley, Arthur; Nam, Jayoung; Xu, Renfeng; Harman, Leslie; Thibos, Larry

2014-01-01

Purpose To examine the separate and combined influences of zone geometry, pupil size, diffraction, apodisation and spherical aberration on the optical performance of concentric zonal bifocals. Methods Zonal bifocal pupil functions representing eye + ophthalmic correction were defined by interleaving wavefronts from separate optical zones of the bifocal. A two-zone design (a central circular inner zone surrounded by an annular outer-zone which is bounded by the pupil) and a five-zone design (a central small circular zone surrounded by four concentric annuli) were configured with programmable zone geometry, wavefront phase and pupil transmission characteristics. Using computational methods, we examined the effects of diffraction, Stiles Crawford apodisation, pupil size and spherical aberration on optical transfer functions for different target distances. Results Apodisation alters the relative weighting of each zone, and thus the balance of near and distance optical quality. When spherical aberration is included, the effective distance correction, add power and image quality depend on zone-geometry and Stiles Crawford Effect apodisation. When the outer zone width is narrow, diffraction limits the available image contrast when focused, but as pupil dilates and outer zone width increases, aberrations will limit the best achievable image quality. With two-zone designs, balancing near and distance image quality is not achieved with equal area inner and outer zones. With significant levels of spherical aberration, multi-zone designs effectively become multifocals. Conclusion Wave optics and pupil varying ocular optics significantly affect the imaging capabilities of different optical zones of concentric bifocals. With two-zone bifocal designs, diffraction, pupil apodisation spherical aberration, and zone size influence both the effective add power and the pupil size required to balance near and distance image quality. Five-zone bifocal designs achieve a high degree of pupil size independence, and thus will provide more consistent performance as pupil size varies with light level and convergence amplitude. PMID:24588552

Finite basis representations with nondirect product basis functions having structure similar to that of spherical harmonics.

PubMed

Czakó, Gábor; Szalay, Viktor; Császár, Attila G

2006-01-07

The currently most efficient finite basis representation (FBR) method [Corey et al., in Numerical Grid Methods and Their Applications to Schrodinger Equation, NATO ASI Series C, edited by C. Cerjan (Kluwer Academic, New York, 1993), Vol. 412, p. 1; Bramley et al., J. Chem. Phys. 100, 6175 (1994)] designed specifically to deal with nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc., employs very special l-independent grids and results in a symmetric FBR. While highly efficient, this method is not general enough. For instance, it cannot deal with nondirect product bases of the above structure efficiently if the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are discrete variable representation (DVR) functions of the infinite type. The optimal-generalized FBR(DVR) method [V. Szalay, J. Chem. Phys. 105, 6940 (1996)] is designed to deal with general, i.e., direct and/or nondirect product, bases and grids. This robust method, however, is too general, and its direct application can result in inefficient computer codes [Czako et al., J. Chem. Phys. 122, 024101 (2005)]. It is shown here how the optimal-generalized FBR method can be simplified in the case of nondirect product bases of structures phi(n) (l)(s)f(l)(u), chi(m) (l)(t)phi(n) (l)(s)f(l)(u), etc. As a result the commonly used symmetric FBR is recovered and simplified nonsymmetric FBRs utilizing very special l-dependent grids are obtained. The nonsymmetric FBRs are more general than the symmetric FBR in that they can be employed efficiently even when the functions phi(n) (l)(s) [and/or chi(m) (l)(t)] are DVR functions of the infinite type. Arithmetic operation counts and a simple numerical example presented show unambiguously that setting up the Hamiltonian matrix requires significantly less computer time when using one of the proposed nonsymmetric FBRs than that in the symmetric FBR. Therefore, application of this nonsymmetric FBR is more efficient than that of the symmetric FBR when one wants to diagonalize the Hamiltonian matrix either by a direct or via a basis-set contraction method. Enormous decrease of computer time can be achieved, with respect to a direct application of the optimal-generalized FBR, by employing one of the simplified nonsymmetric FBRs as is demonstrated in noniterative calculations of the low-lying vibrational energy levels of the H3+ molecular ion. The arithmetic operation counts of the Hamiltonian matrix vector products and the properties of a recently developed diagonalization method [Andreozzi et al., J. Phys. A Math. Gen. 35, L61 (2002)] suggest that the nonsymmetric FBR applied along with this particular diagonalization method is suitable to large scale iterative calculations. Whether or not the nonsymmetric FBR is competitive with the symmetric FBR in large-scale iterative calculations still has to be investigated numerically.

Diagenetically altered fossil micrometeorites suggest cosmic dust is common in the geological record

NASA Astrophysics Data System (ADS)

Suttle, Martin D.; Genge, Matthew J.

2017-10-01

We report the discovery of fossil micrometeorites from Late Cretaceous chalk. Seventy-six cosmic spherules were recovered from Coniacian (87 ± 1 Ma) sediments of the White Chalk Supergroup. Particles vary from pristine silicate and iron-type spherules to pseudomorphic spherules consisting of either single-phase recrystallized magnetite or Fe-silicide. Pristine spherules are readily identified as micrometeorites on the basis of their characteristic mineralogies, textures and compositions. Both magnetite and silicide spherules contain dendritic crystals and spherical morphologies, testifying to rapid crystallisation of high temperature iron-rich metallic and oxide liquids. These particles also contain spherical cavities, representing weathering and removal of metal beads and irregular cavities, representing vesicles formed by trapped gas during crystallization; both features commonly found among modern Antarctic Iron-type (I-type) cosmic spherules. On the basis of textural analysis, the magnetite and Fe-silicide spherules are shown to be I-type cosmic spherules that have experienced complete secondary replacement during diagenesis (fossilization). Our results demonstrate that micrometeorites, preserved in sedimentary rocks, are affected by a suite of complex diagenetic processes, which can result in disparate replacement minerals, even within the same sequence of sedimentary beds. As a result, the identification of fossil micrometeorites requires careful observation of particle textures and comparisons with modern Antarctic collections. Replaced micrometeorites imply that geochemical signatures the extraterrestrial dust are subject to diagenetic remobilisation that limits their stratigraphic resolution. However, this study demonstrates that fossil, pseudomorphic micrometeorites can be recognised and are likely common within the geological record.

Predicting crystalline lens fall caused by accommodation from changes in wavefront error

PubMed Central

He, Lin; Applegate, Raymond A.

2011-01-01

PURPOSE To illustrate and develop a method for estimating crystalline lens decentration as a function of accommodative response using changes in wavefront error and show the method and limitations using previously published data (2004) from 2 iridectomized monkey eyes so that clinicians understand how spherical aberration can induce coma, in particular in intraocular lens surgery. SETTINGS College of Optometry, University of Houston, Houston, USA. DESIGN Evaluation of diagnostic test or technology. METHODS Lens decentration was estimated by displacing downward the wavefront error of the lens with respect to the limiting aperture (7.0 mm) and ocular first surface wavefront error for each accommodative response (0.00 to 11.00 diopters) until measured values of vertical coma matched previously published experimental data (2007). Lens decentration was also calculated using an approximation formula that only included spherical aberration and vertical coma. RESULTS The change in calculated vertical coma was consistent with downward lens decentration. Calculated downward lens decentration peaked at approximately 0.48 mm of vertical decentration in the right eye and approximately 0.31 mm of decentration in the left eye using all Zernike modes through the 7th radial order. Calculated lens decentration using only coma and spherical aberration formulas was peaked at approximately 0.45 mm in the right eye and approximately 0.23 mm in the left eye. CONCLUSIONS Lens fall as a function of accommodation was quantified noninvasively using changes in vertical coma driven principally by the accommodation-induced changes in spherical aberration. The newly developed method was valid for a large pupil only. PMID:21700108

A self-similar magnetohydrodynamic model for ball lightnings

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

Tsui, K. H.

2006-07-15

Ball lightning is modeled by magnetohydrodynamic (MHD) equations in two-dimensional spherical geometry with azimuthal symmetry. Dynamic evolutions in the radial direction are described by the self-similar evolution function y(t). The plasma pressure, mass density, and magnetic fields are solved in terms of the radial label {eta}. This model gives spherical MHD plasmoids with axisymmetric force-free magnetic field, and spherically symmetric plasma pressure and mass density, which self-consistently determine the polytropic index {gamma}. The spatially oscillating nature of the radial and meridional field structures indicate embedded regions of closed field lines. These regions are named secondary plasmoids, whereas the overall self-similarmore » spherical structure is named the primary plasmoid. According to this model, the time evolution function allows the primary plasmoid expand outward in two modes. The corresponding ejection of the embedded secondary plasmoids results in ball lightning offering an answer as how they come into being. The first is an accelerated expanding mode. This mode appears to fit plasmoids ejected from thundercloud tops with acceleration to ionosphere seen in high altitude atmospheric observations of sprites and blue jets. It also appears to account for midair high-speed ball lightning overtaking airplanes, and ground level high-speed energetic ball lightning. The second is a decelerated expanding mode, and it appears to be compatible to slowly moving ball lightning seen near ground level. The inverse of this second mode corresponds to an accelerated inward collapse, which could bring ball lightning to an end sometimes with a cracking sound.« less

DAMQT: A package for the analysis of electron density in molecules

NASA Astrophysics Data System (ADS)

López, Rafael; Rico, Jaime Fernández; Ramírez, Guillermo; Ema, Ignacio; Zorrilla, David

2009-09-01

DAMQT is a package for the analysis of the electron density in molecules and the fast computation of the density, density deformations, electrostatic potential and field, and Hellmann-Feynman forces. The method is based on the partition of the electron density into atomic fragments by means of a least deformation criterion. Each atomic fragment of the density is expanded in regular spherical harmonics times radial factors, which are piecewise represented in terms of analytical functions. This representation is used for the fast evaluation of the electrostatic potential and field generated by the electron density and nuclei, as well as for the computation of the Hellmann-Feynman forces on the nuclei. An analysis of the atomic and molecular deformations of the density can be also carried out, yielding a picture that connects with several concepts of the empirical structural chemistry. Program summaryProgram title: DAMQT1.0 Catalogue identifier: AEDL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEDL_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: GPLv3 No. of lines in distributed program, including test data, etc.: 278 356 No. of bytes in distributed program, including test data, etc.: 31 065 317 Distribution format: tar.gz Programming language: Fortran90 and C++ Computer: Any Operating system: Linux, Windows (Xp, Vista) RAM: 190 Mbytes Classification: 16.1 External routines: Trolltech's Qt (4.3 or higher) ( http://www.qtsoftware.com/products), OpenGL (1.1 or higher) ( http://www.opengl.org/), GLUT 3.7 ( http://www.opengl.org/resources/libraries/glut/). Nature of problem: Analysis of the molecular electron density and density deformations, including fast evaluation of electrostatic potential, electric field and Hellmann-Feynman forces on nuclei. Solution method: The method of Deformed Atoms in Molecules, reported elsewhere [1], is used for partitioning the molecular electron density into atomic fragments, which are further expanded in spherical harmonics times radial factors. The partition is used for defining molecular density deformations and for the fast calculation of several properties associated to density. Restrictions: The current version is limited to 120 atoms, 2000 contracted functions, and l=5 in basis functions. Density must come from a LCAO calculation (any level) with spherical (not Cartesian) Gaussian functions. Unusual features: The program contains an OPEN statement to binary files (stream) in file GOPENMOL.F90. This statement has not a standard syntax in Fortran 90. Two possibilities are considered in conditional compilation: Intel's ifort and Fortran2003 standard. This latter is applied to compilers other than ifort (gfortran uses this one, for instance). Additional comments: The distribution file for this program is over 30 Mbytes and therefore is not delivered directly when download or e-mail is requested. Instead a html file giving details of how the program can be obtained is sent. Running time: Largely dependent on the system size and the module run (from fractions of a second to hours). References: [1] J. Fernández Rico, R. López, I. Ema, G. Ramírez, J. Mol. Struct. (Theochem) 727 (2005) 115.

Spontaneously Assembled Nano-aggregates in Clear Green Tea Infusions from Camellia ptilophylla and Camellia sinensis.

PubMed

Lin, Xiaorong; Gao, Xiong; Chen, Zhongzheng; Zhang, Yuanyuan; Luo, Wei; Li, Xiaofei; Li, Bin

2017-05-10

Tea nano-aggregates spontaneously assembled in clear tea infusions are considered as the precursors of tea cream, although their molecular basis remains obscure. Here, we characterized nano-aggregates in green tea infusions from Camellia ptilophylla, a peculiar tea variety with 6.0% of theobromine, and Camellia sinensis as the control for comparative purpose. Numerous negatively charged spherical colloidal particles of 50-100 nm in diameter were primarily found in both green tea infusions. Catechins, proteins, and carbohydrates were confirmed as the dominant components in green tea nano-aggregates. In addition, iron, copper, nickel, proteins, and gallated catechins exhibited higher aggregating affinity than other components, whereas methylxanthines and calcium contributed to the transformation of nano-aggregates into tea cream. Green tea nano-aggregates were partly destroyed by simulated gastrointestinal digestion, and removing theses peculiar particles dramatically attenuated the bioaccessibility of methylxanthines, theanine, and some catechin monomers in green tea infusions. This study enhanced our knowledge of molecular interactions in the formation of green tea cream and provided insight into physicochemical profiles, phytochemical nature, and functional effects of green tea nano-aggregates.

A Robust and Fast Method to Compute Shallow States without Adjustable Parameters: Simulations for a Silicon-Based Qubit

NASA Astrophysics Data System (ADS)

Debernardi, Alberto; Fanciulli, Marco

Within the framework of the envelope function approximation we have computed - without adjustable parameters and with a reduced computational effort due to analytical expression of relevant Hamiltonian terms - the energy levels of the shallow P impurity in silicon and the hyperfine and superhyperfine splitting of the ground state. We have studied the dependence of these quantities on the applied external electric field along the [001] direction. Our results reproduce correctly the experimental splitting of the impurity ground states detected at zero electric field and provide reliable predictions for values of the field where experimental data are lacking. Further, we have studied the effect of confinement of a shallow state of a P atom at the center of a spherical Si-nanocrystal embedded in a SiO2 matrix. In our simulations the valley-orbit interaction of a realistically screened Coulomb potential and of the core potential are included exactly, within the numerical accuracy due to the use of a finite basis set, while band-anisotropy effects are taken into account within the effective-mass approximation.

Random close packing in protein cores

NASA Astrophysics Data System (ADS)

Ohern, Corey

Shortly after the determination of the first protein x-ray crystal structures, researchers analyzed their cores and reported packing fractions ϕ ~ 0 . 75 , a value that is similar to close packing equal-sized spheres. A limitation of these analyses was the use of `extended atom' models, rather than the more physically accurate `explicit hydrogen' model. The validity of using the explicit hydrogen model is proved by its ability to predict the side chain dihedral angle distributions observed in proteins. We employ the explicit hydrogen model to calculate the packing fraction of the cores of over 200 high resolution protein structures. We find that these protein cores have ϕ ~ 0 . 55 , which is comparable to random close-packing of non-spherical particles. This result provides a deeper understanding of the physical basis of protein structure that will enable predictions of the effects of amino acid mutations and design of new functional proteins. We gratefully acknowledge the support of the Raymond and Beverly Sackler Institute for Biological, Physical, and Engineering Sciences, National Library of Medicine training grant T15LM00705628 (J.C.G.), and National Science Foundation DMR-1307712 (L.R.).

Self-consistent nonlocal feedback theory for electrocatalytic swimmers with heterogeneous surface chemical kinetics

NASA Astrophysics Data System (ADS)

Nourhani, Amir; Crespi, Vincent H.; Lammert, Paul E.

2015-06-01

We present a self-consistent nonlocal feedback theory for the phoretic propulsion mechanisms of electrocatalytic micromotors or nanomotors. These swimmers, such as bimetallic platinum and gold rods catalyzing decomposition of hydrogen peroxide in aqueous solution, have received considerable theoretical attention. In contrast, the heterogeneous electrochemical processes with nonlocal feedback that are the actual "engines" of such motors are relatively neglected. We present a flexible approach to these processes using bias potential as a control parameter field and a locally-open-circuit reference state, carried through in detail for a spherical motor. While the phenomenological flavor makes meaningful contact with experiment easier, required inputs can also conceivably come from, e.g., Frumkin-Butler-Volmer kinetics. Previously obtained results are recovered in the weak-heterogeneity limit and improved small-basis approximations tailored to structural heterogeneity are presented. Under the assumption of weak inhomogeneity, a scaling form is deduced for motor speed as a function of fuel concentration and swimmer size. We argue that this form should be robust and demonstrate a good fit to experimental data.

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

PubMed Central

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

2012-01-01

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

Recognition of anions using urea and thiourea substituted calixarenes: A density functional theory study of non-covalent interactions

NASA Astrophysics Data System (ADS)

Athar, Mohd; Lone, Mohsin Y.; Jha, Prakash C.

2018-02-01

Designing of new calixarene receptors for the selective binding of anions is an age-old concept; even though expected outcomes from this field are at premature stage. Herein, we have performed quantum chemical calculations to provide structural basis of anion binding with urea and thiourea substituted calixarenes (1, 2, and 3). In particular, spherical halides (F-, Cl-, Br-) and linear anions (CN-, N3-, SCN-) were modelled for calculating binding energies with receptor 1, 2 and 3 followed by their marked IR vibrations; taking the available experimental information into account. We found that the thiourea substitutions have better capability to stabilize the anions. Results have suggested that the structural behaviour of macrocyclic motifs were responsible for displaying the anion binding potentials. Moreover, second order "charge transfer" interactions of n-σ∗NH and n-σ∗OH type along the H-bond axis played critical role in developing hydrogen bonds. The present work also examines the role of non-covalent interactions (NCI) and their effects on thermodynamic and chemical-reactivity descriptors.

Dynamic Multi-Coil Shimming of the Human Brain at 7 Tesla

PubMed Central

Juchem, Christoph; Nixon, Terence W.; McIntyre, Scott; Boer, Vincent O.; Rothman, Douglas L.; de Graaf, Robin A.

2011-01-01

High quality magnetic field homogenization of the human brain (i.e. shimming) for MR imaging and spectroscopy is a demanding task. The susceptibility differences between air and tissue are a longstanding problem as they induce complex field distortions in the prefrontal cortex and the temporal lobes. To date, the theoretical gains of high field MR have only been realized partially in the human brain due to limited magnetic field homogeneity. A novel shimming technique for the human brain is presented that is based on the combination of non-orthogonal basis fields from 48 individual, circular coils. Custom-built amplifier electronics enabled the dynamic application of the multi-coil shim fields in a slice-specific fashion. Dynamic multi-coil (DMC) shimming is shown to eliminate most of the magnetic field inhomogeneity apparent in the human brain at 7 Tesla and provided improved performance compared to state-of-the-art dynamic shim updating with zero through third order spherical harmonic functions. The novel technique paves the way for high field MR applications of the human brain for which excellent magnetic field homogeneity is a prerequisite. PMID:21824794

Numerical modeling of the Madison Dynamo Experiment.

NASA Astrophysics Data System (ADS)

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

2002-11-01

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

Scattering of clusters of spherical particles—Modeling and inverse problem solution in the Rayleigh-Gans approximation

NASA Astrophysics Data System (ADS)

Eliçabe, Guillermo E.

2013-09-01

In this work, an exact scattering model for a system of clusters of spherical particles, based on the Rayleigh-Gans approximation, has been parameterized in such a way that it can be solved in inverse form using Thikhonov Regularization to obtain the morphological parameters of the clusters. That is to say, the average number of particles per cluster, the size of the primary spherical units that form the cluster, and the Discrete Distance Distribution Function from which the z-average square radius of gyration of the system of clusters is obtained. The methodology is validated through a series of simulated and experimental examples of x-ray and light scattering that show that the proposed methodology works satisfactorily in unideal situations such as: presence of error in the measurements, presence of error in the model, and several types of unideallities present in the experimental cases.

Compton scattering study of electron momentum distribution in lithium fluoride using 662 keV gamma radiations

NASA Astrophysics Data System (ADS)

Vijayakumar, R.; Shivaramu; Ramamurthy, N.; Ford, M. J.

2008-12-01

Here we report the first ever 137Cs Compton spectroscopy study of lithium fluoride. The spherical average Compton profiles of lithium fluoride are deduced from Compton scattering measurements on poly crystalline sample at gamma ray energy of 662 keV. To compare the experimental data, we have computed the spherical average Compton profiles using self-consistent Hartree-Fock wave functions employed on linear combination of atomic orbital (HF-LCAO) approximation. The directional Compton profiles and their anisotropic effects are also calculated using the same HF-LCAO approximation. The experimental spherical average profiles are found to be in good agreement with the corresponding HF-LCAO calculations and in qualitative agreement with Hartree-Fock free atom values. The present experimental isotropic and calculated directional profiles are also compared with the available experimental isotropic and directional Compton profiles using 59.54 and 159 keV γ-rays.

Tensor Based Representation and Analysis of Diffusion-Weighted Magnetic Resonance Images

ERIC Educational Resources Information Center

Barmpoutis, Angelos

2009-01-01

Cartesian tensor bases have been widely used to model spherical functions. In medical imaging, tensors of various orders can approximate the diffusivity function at each voxel of a diffusion-weighted MRI data set. This approximation produces tensor-valued datasets that contain information about the underlying local structure of the scanned tissue.…

Approximating lens power.

PubMed

Kaye, Stephen B

2009-04-01

To provide a scalar measure of refractive error, based on geometric lens power through principal, orthogonal and oblique meridians, that is not limited to the paraxial and sag height approximations. A function is derived to model sections through the principal meridian of a lens, followed by rotation of the section through orthogonal and oblique meridians. Average focal length is determined using the definition for the average of a function. Average univariate power in the principal meridian (including spherical aberration), can be computed from the average of a function over the angle of incidence as determined by the parameters of the given lens, or adequately computed from an integrated series function. Average power through orthogonal and oblique meridians, can be similarly determined using the derived formulae. The widely used computation for measuring refractive error, the spherical equivalent, introduces non-constant approximations, leading to a systematic bias. The equations proposed provide a good univariate representation of average lens power and are not subject to a systematic bias. They are particularly useful for the analysis of aggregate data, correlating with biological treatment variables and for developing analyses, which require a scalar equivalent representation of refractive power.

Saccharide-derived microporous spherical biochar prepared from hydrothermal carbonization and different pyrolysis temperatures: synthesis, characterization, and application in water treatment.

PubMed

Tran, Hai Nguyen; Lee, Chung-Kung; Nguyen, Tien Vinh; Chao, Huan-Ping

2017-08-24

Three saccharides (glucose, sucrose, and xylose) were used as pure precursors for synthesizing spherical biochars (GB, SB, and XB), respectively. The two-stage synthesis process comprised: (1) the hydrothermal carbonization of saccharides to produce spherical hydrochar' and (2) pyrolysis of the hydrochar at different temperatures from 300°C to 1200°C. The results demonstrated that the pyrolysis temperatures insignificantly affected the spherical morphology and surface chemistry of biochar. The biochar' isoelectric point ranged from 2.64 to 3.90 (abundant oxygen-containing functionalities). The Brunauer-Emmett-Teller (BET)-specific surface areas (S BET ) and total pore volumes (V total ) of biochar increased with the increasing pyrolysis temperatures. The highest S BET and V total were obtained at a pyrolysis temperature of 900°C for GB (775 m 2 /g and 0.392 cm 3 /g), 500°C for SB (410 m 2 /g and 0.212 cm 3 /g), and 600°C for XB (426 m 2 /g and 0.225 cm 3 /g), respectively. The spherical biochar was a microporous material with approximately 71-98% micropore volume. X-ray diffraction results indicated that the biochar' structure was predominantly amorphous. The spherical biochar possessed the graphite structure when the pyrolysis temperature was higher than 600°C. The adsorption capacity of GB depended strongly on the pyrolysis temperature. The maximum Langmuir adsorption capacities ([Formula: see text]) of 900GB exhibited the following selective order: phenol (2.332 mmol/g) > Pb 2+ (1.052 mmol/g) > Cu 2+ (0.825 mmol/g) > methylene green 5 (0.426 mmol/g) > acid red 1 (0.076 mmol/g). This study provides a simple method to prepare spherical biochar - a new and potential adsorbent for adsorbing heavy metals and aromatic contaminants.

Elastic field of a spherical inclusion with non-uniform eigenfields in second strain gradient elasticity

NASA Astrophysics Data System (ADS)

Delfani, M. R.; Latifi Shahandashti, M.

2017-09-01

In this paper, within the complete form of Mindlin's second strain gradient theory, the elastic field of an isolated spherical inclusion embedded in an infinitely extended homogeneous isotropic medium due to a non-uniform distribution of eigenfields is determined. These eigenfields, in addition to eigenstrain, comprise eigen double and eigen triple strains. After the derivation of a closed-form expression for Green's function associated with the problem, two different cases of non-uniform distribution of the eigenfields are considered as follows: (i) radial distribution, i.e. the distributions of the eigenfields are functions of only the radial distance of points from the centre of inclusion, and (ii) polynomial distribution, i.e. the distributions of the eigenfields are polynomial functions in the Cartesian coordinates of points. While the obtained solution for the elastic field of the latter case takes the form of an infinite series, the solution to the former case is represented in a closed form. Moreover, Eshelby's tensors associated with the two mentioned cases are obtained.

Robust signal recovery using the prolate spherical wave functions and maximum correntropy criterion

NASA Astrophysics Data System (ADS)

Zou, Cuiming; Kou, Kit Ian

2018-05-01

Signal recovery is one of the most important problem in signal processing. This paper proposes a novel signal recovery method based on prolate spherical wave functions (PSWFs). PSWFs are a kind of special functions, which have been proved having good performance in signal recovery. However, the existing PSWFs based recovery methods used the mean square error (MSE) criterion, which depends on the Gaussianity assumption of the noise distributions. For the non-Gaussian noises, such as impulsive noise or outliers, the MSE criterion is sensitive, which may lead to large reconstruction error. Unlike the existing PSWFs based recovery methods, our proposed PSWFs based recovery method employs the maximum correntropy criterion (MCC), which is independent of the noise distribution. The proposed method can reduce the impact of the large and non-Gaussian noises. The experimental results on synthetic signals with various types of noises show that the proposed MCC based signal recovery method has better robust property against various noises compared to other existing methods.

The Application of Elliptic Cylindrical Phantom in Brachytherapy Dosimetric Study of HDR 192Ir Source

NASA Astrophysics Data System (ADS)

Ahn, Woo Sang; Park, Sung Ho; Jung, Sang Hoon; Choi, Wonsik; Do Ahn, Seung; Shin, Seong Soo

2014-06-01

The purpose of this study is to determine the radial dose function of HDR 192Ir source based on Monte Carlo simulation using elliptic cylindrical phantom, similar to realistic shape of pelvis, in brachytherapy dosimetric study. The elliptic phantom size and shape was determined by analysis of dimensions of pelvis on CT images of 20 patients treated with brachytherapy for cervical cancer. The radial dose function obtained using the elliptic cylindrical water phantom was compared with radial dose functions for different spherical phantom sizes, including the Williamsion's data loaded into conventional planning system. The differences in the radial dose function for the different spherical water phantoms increase with radial distance, r, and the largest differences in the radial dose function appear for the smallest phantom size. The radial dose function of the elliptic cylindrical phantom significantly decreased with radial distance in the vertical direction due to different scatter condition in comparison with the Williamson's data. Considering doses to ICRU rectum and bladder points, doses to reference points can be underestimated up to 1-2% at the distance from 3 to 6 cm. The radial dose function in this study could be used as realistic data for calculating the brachytherapy dosimetry for cervical cancer.

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.

Anomalous waterlike behavior in spherically-symmetric water models optimized with the relative entropy.

PubMed

Chaimovich, Aviel; Shell, M Scott

2009-03-28

Recent efforts have attempted to understand many of liquid water's anomalous properties in terms of effective spherically-symmetric pairwise molecular interactions entailing two characteristic length scales (so-called "core-softened" potentials). In this work, we examine the extent to which such simple descriptions of water are representative of the true underlying interactions by extracting coarse-grained potential functions that are optimized to reproduce the behavior of an all-atom model. To perform this optimization, we use a novel procedure based upon minimizing the relative entropy, a quantity that measures the extent to which a coarse-grained configurational ensemble overlaps with a reference all-atom one. We show that the optimized spherically-symmetric water models exhibit notable variations with the state conditions at which they were optimized, reflecting in particular the shifting accessibility of networked hydrogen bonding interactions. Moreover, we find that water's density and diffusivity anomalies are only reproduced when the effective coarse-grained potentials are allowed to vary with state. Our results therefore suggest that no state-independent spherically-symmetric potential can fully capture the interactions responsible for water's unique behavior; rather, the particular way in which the effective interactions vary with temperature and density contributes significantly to anomalous properties.

Characterization of Particle Size Standard NIST 1019b with SynchrotronX-ray Microtomography and Digital Data Extraction

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

Friedrich, Jon M.; Rivers, Mark L.; Perlowitz, Michael A.

We show that synchrotron x-ray microtomography ({mu}CT) followed by digital data extraction can be used to examine the size distribution and particle morphologies of the polydisperse (750 to 2450 {micro}m diameter) particle size standard NIST 1019b. Our size distribution results are within errors of certified values with data collected at 19.5 {micro}m/voxel. One of the advantages of using {mu}CT to investigate the particles examined here is that the morphology of the glass beads can be directly examined. We use the shape metrics aspect ratio and sphericity to examine of individual standard beads morphologies as a function of spherical equivalent diameters.more » We find that the majority of standard beads possess near-spherical aspect ratios and sphericities, but deviations are present at the lower end of the size range. The majority (> 98%) of particles also possess an equant form when examined using a common measure of equidimensionality. Although the NIST 1019b standard consists of loose particles, we point out that an advantage of {mu}CT is that coherent materials comprised of particles can be examined without disaggregation.« less

Empirical Relationships Between Optical Properties and Equivalent Diameters of Fractal Soot Aggregates at 550 Nm Wavelength.

NASA Technical Reports Server (NTRS)

Pandey, Apoorva; Chakrabarty, Rajan K.; Liu, Li; Mishchenko, Michael I.

2015-01-01

Soot aggregates (SAs)-fractal clusters of small, spherical carbonaceous monomers-modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension Df = 1.8) and aged (Df = 2.6) SAs at 550 nm wavelength using the numericallyexact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.

Development of discrete gas kinetic scheme for simulation of 3D viscous incompressible and compressible flows

NASA Astrophysics Data System (ADS)

Yang, L. M.; Shu, C.; Wang, Y.; Sun, Y.

2016-08-01

The sphere function-based gas kinetic scheme (GKS), which was presented by Shu and his coworkers [23] for simulation of inviscid compressible flows, is extended to simulate 3D viscous incompressible and compressible flows in this work. Firstly, we use certain discrete points to represent the spherical surface in the phase velocity space. Then, integrals along the spherical surface for conservation forms of moments, which are needed to recover 3D Navier-Stokes equations, are approximated by integral quadrature. The basic requirement is that these conservation forms of moments can be exactly satisfied by weighted summation of distribution functions at discrete points. It was found that the integral quadrature by eight discrete points on the spherical surface, which forms the D3Q8 discrete velocity model, can exactly match the integral. In this way, the conservative variables and numerical fluxes can be computed by weighted summation of distribution functions at eight discrete points. That is, the application of complicated formulations resultant from integrals can be replaced by a simple solution process. Several numerical examples including laminar flat plate boundary layer, 3D lid-driven cavity flow, steady flow through a 90° bending square duct, transonic flow around DPW-W1 wing and supersonic flow around NACA0012 airfoil are chosen to validate the proposed scheme. Numerical results demonstrate that the present scheme can provide reasonable numerical results for 3D viscous flows.

Dirac-Kähler particle in Riemann spherical space: boson interpretation

NASA Astrophysics Data System (ADS)

Ishkhanyan, A. M.; Florea, O.; Ovsiyuk, E. M.; Red'kov, V. M.

2015-11-01

In the context of the composite boson interpretation, we construct the exact general solution of the Dirac--K\\"ahler equation for the case of the spherical Riemann space of constant positive curvature, for which due to the geometry itself one may expect to have a discrete energy spectrum. In the case of the minimal value of the total angular momentum, $j=0$, the radial equations are reduced to second-order ordinary differential equations, which are straightforwardly solved in terms of the hypergeometric functions. For non-zero values of the total angular momentum, however, the radial equations are reduced to a pair of complicated fourth-order differential equations. Employing the factorization approach, we derive the general solution of these equations involving four independent fundamental solutions written in terms of combinations of the hypergeometric functions. The corresponding discrete energy spectrum is then determined via termination of the involved hypergeometric series, resulting in quasi-polynomial wave-functions. The constructed solutions lead to notable observations when compared with those for the ordinary Dirac particle. The energy spectrum for the Dirac-K\\"ahler particle in spherical space is much more complicated. Its structure substantially differs from that for the Dirac particle since it consists of two paralleled energy level series each of which is twofold degenerate. Besides, none of the two separate series coincides with the series for the Dirac particle. Thus, the Dirac--K\\"ahler field cannot be interpreted as a system of four Dirac fermions. Additional arguments supporting this conclusion are discussed.

Ultrarelativistic bound states in the spherical well

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

Żaba, Mariusz; Garbaczewski, Piotr

2016-07-15

We address an eigenvalue problem for the ultrarelativistic (Cauchy) operator (−Δ){sup 1/2}, whose action is restricted to functions that vanish beyond the interior of a unit sphere in three spatial dimensions. We provide high accuracy spectral data for lowest eigenvalues and eigenfunctions of this infinite spherical well problem. Our focus is on radial and orbital shapes of eigenfunctions. The spectrum consists of an ordered set of strictly positive eigenvalues which naturally splits into non-overlapping, orbitally labelled E{sub (k,l)} series. For each orbital label l = 0, 1, 2, …, the label k = 1, 2, … enumerates consecutive lth seriesmore » eigenvalues. Each of them is 2l + 1-degenerate. The l = 0 eigenvalues series E{sub (k,0)} are identical with the set of even labeled eigenvalues for the d = 1 Cauchy well: E{sub (k,0)}(d = 3) = E{sub 2k}(d = 1). Likewise, the eigenfunctions ψ{sub (k,0)}(d = 3) and ψ{sub 2k}(d = 1) show affinity. We have identified the generic functional form of eigenfunctions of the spherical well which appear to be composed of a product of a solid harmonic and of a suitable purely radial function. The method to evaluate (approximately) the latter has been found to follow the universal pattern which effectively allows to skip all, sometimes involved, intermediate calculations (those were in usage, while computing the eigenvalues for l ≤ 3).« less

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

Far-infrared response of spherical quantum dots: Dielectric effects and the generalized Kohn's theorem

NASA Astrophysics Data System (ADS)

Movilla, J. L.; Planelles, J.

2007-05-01

The influence of the dielectric environment on the far-infrared (FIR) absorption spectra of two-electron spherical quantum dots is theoretically studied. Effective mass and envelope function approaches with realistic steplike confining potentials are used. Special attention is paid to absorptions that are induced by the electron-electron interaction. High confining barriers make the FIR absorption coefficients almost independent of the quantum dot dielectric environment. Low barrier heights and strong dielectric mismatches preserve the strong fundamental (Kohn) mode but yield the cancellation of excited absorptions, thus monitoring dielectrically induced phase transitions from volume to surface states.

Amplitude-phase characteristics of electromagnetic fields diffracted by a hole in a thin film with realistic optical properties

NASA Astrophysics Data System (ADS)

Dorofeyev, Illarion

2009-03-01

Characteristics of a quasi-spherical wave front of an electromagnetic field diffracted by a subwavelength hole in a thin film with real optical properties are studied. Related diffraction problem is solved in general by use of the scalar and vector Green's theorems and related Green's function of a boundary-value problem. Local phase deviations of a diffracted wave front from an ideal spherical front are calculated. Diffracted patterns are calculated for the coherent incident fields in case of holes array in a screen of perfect conductivity.

-dimensional thin shell wormhole with deformed throat can be supported by normal matter

NASA Astrophysics Data System (ADS)

Mazharimousavi, S. Habib; Halilsoy, M.

2015-06-01

From the physics standpoint the exotic matter problem is a major difficulty in thin shell wormholes (TSWs) with spherical/cylindrical throat topologies. We aim to circumvent this handicap by considering angle dependent throats in dimensions. By considering the throat of the TSW to be deformed spherical, i.e., a function of and , we present general conditions which are to be satisfied by the shape of the throat in order to have the wormhole supported by matter with positive density in the static reference frame. We provide particular solutions/examples to the constraint conditions.

Spectra of confined positronium

NASA Astrophysics Data System (ADS)

Munjal, D.; Silotia, P.; Prasad, V.

2017-12-01

Positronium is studied under the effect of spherically confined plasma environment. Exponentially Cosine Screened Coulomb potential (ECSC) has been used to include the dense plasma screening effect on positronium. Time independent Schrodinger equation is solved numerically. Various physical parameters such as energy eigenvalues, radial matrix elements, oscillator strengths, and polarizability are well explored as a function of confinement parameters. Oscillator strength gets drastically modified under confinement. We have also obtained the results for Ps confined under spherically confined Debye potential and compared with results of ECSC potential. Also incidental degeneracy for different values of confinement parameters has been reported for the first time for positronium.

Polaronic effects on the off-center donor impurity in AlAs/GaAs/SiO2 spherical core/shell quantum dots

NASA Astrophysics Data System (ADS)

El Haouari, M.; Feddi, E.; Dujardin, F.; Restrepo, R. L.; Mora-Ramos, M. E.; Duque, C. A.

2017-11-01

The ground state of a conduction electron coupled to an off-center impurity donor in a AlAS/GaAs spherical core/shell quantum dot is investigated theoretically. The image-charge effect and the influence of the electron-polar-LO-phonon interaction are considered. The electron-impurity binding energy is calculated via a variational procedure and is reported both as a function of the shell width and of the radial position of the donor atom. The polaronic effects on this quantity are particularly discussed.

On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

NASA Astrophysics Data System (ADS)

Das, Tapas K.

2002-03-01

The equations governing general relativistic, spherically symmetric, hydrodynamic accretion of polytropic fluid on to black holes are solved in the Schwarzschild metric to investigate some of the transonic properties of the flow. Only stationary solutions are discussed. For such accretion, it has been shown that real physical sonic points may form even for flow with γ<4/3or γ>5/3. The behaviour of some flow variables in the close vicinity of the event horizon is studied as a function of specific energy and the polytropic index of the flow.

Generation of dynamo magnetic fields in protoplanetary and other astrophysical accretion disks

NASA Technical Reports Server (NTRS)

Stepinski, T. F.; Levy, E. H.

1988-01-01

A computational method for treating the generation of dynamo magnetic fields in astrophysical disks is presented. The numerical difficulty of handling the boundary condition at infinity in the cylindrical disk geometry is overcome by embedding the disk in a spherical computational space and matching the solutions to analytically tractable spherical functions in the surrounding space. The lowest lying dynamo normal modes for a 'thick' astrophysical disk are calculated. The generated modes found are all oscillatory and spatially localized. Tha potential implications of the results for the properties of dynamo magnetic fields in real astrophysical disks are discussed.

Inducing Lift on Spherical Particles by Traveling Magnetic Fields

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Grugel, Richard N.; Rose, M. Franklin (Technical Monitor)

2001-01-01

Gravity induced sedimentation of suspensions is a serious drawback to many materials and biotechnology processes, a factor that can, in principle, be overcome by utilizing an opposing Lorentz body force. In this work we demonstrate the utility of employing a traveling magnetic field (TMF) to induce a lifting force on particles dispersed in the fluid. Theoretically, a model has been developed to ascertain the net force, induced by TMF, acting on a spherical body as a function of the fluid medium's electrical conductivity and other parameters. Experimentally, the model is compared to optical observations of particle motion in the presence of TMF.

Inducing Lift on Spherical Particles by Traveling Magnetic Fields

NASA Technical Reports Server (NTRS)

Mazuruk, Konstantin; Grugel, Richard N.; Rose, M. Franklin (Technical Monitor)

2000-01-01

Gravity induced sedimentation of suspensions is a serious drawback to many materials and biotechnology processes, a factor that can, in principle, be overcome by utilizing an opposing Lorentz body force. In this work we demonstrate the utility of employing a traveling magnetic field (TMF) to induce a lifting force on particles dispersed in the fluid. Theoretically, a model has been developed to ascertain the net force, induced by TMF, acting on a spherical body as a function of the fluid medium's electrical conductivity and other parameters. Experimentally, the model is compared to optical observations of particle motion in the presence of TMF.

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.

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

PubMed

Michael, J Robert; Volkov, Anatoliy

2015-03-01

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

Ab initio Potential Energy Surface for H-H2

NASA Technical Reports Server (NTRS)

Partridge, Harry; Bauschlicher, Charles W., Jr.; Stallcop, James R.; Levin, Eugene

1993-01-01

Ab initio calculations employing large basis sets are performed to determine an accurate potential energy surface for H-H2 interactions for a broad range of separation distances. At large distances, the spherically averaged potential determined from the calculated energies agrees well with the corresponding results determined from dispersion coefficients; the van der Waals well depth is predicted to be 75 +/- (mu)E(sub h). Large basis sets have also been applied to reexamine the accuracy of theoretical repulsive potential energy surfaces. Multipolar expansions of the computed H-H2 potential energy surface are reported for four internuclear separation distances (1.2, 1.401, 1.449, and 1.7a(sub 0) of the hydrogen molecule. The differential elastic scattering cross section calculated from the present results is compared with the measurements from a crossed beam experiment.

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

NASA Astrophysics Data System (ADS)

Huang, Xiangdi

2017-02-01

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

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.

Self-propulsion of a spherical electric or magnetic microbot in a polar viscous fluid

NASA Astrophysics Data System (ADS)

Felderhof, B. U.

2015-02-01

The self-propulsion of a sphere immersed in a polar liquid or ferrofluid is studied on the basis of ferrohydrodynamics. In the electrical case an oscillating charge density located inside the sphere generates an electrical field that polarizes the fluid. The lag of polarization with respect to the electrical field due to relaxation generates a time-independent electrical torque density acting on the fluid, causing it to move. The resulting propulsion velocity of the sphere is calculated in perturbation theory to second order in powers of the charge density.

Linear and nonlinear properties of numerical methods for the rotating shallow water equations

NASA Astrophysics Data System (ADS)

Eldred, Chris

The shallow water equations provide a useful analogue of the fully compressible Euler equations since they have similar conservation laws, many of the same types of waves and a similar (quasi-) balanced state. It is desirable that numerical models posses similar properties, and the prototypical example of such a scheme is the 1981 Arakawa and Lamb (AL81) staggered (C-grid) total energy and potential enstrophy conserving scheme, based on the vector invariant form of the continuous equations. However, this scheme is restricted to a subset of logically square, orthogonal grids. The current work extends the AL81 scheme to arbitrary non-orthogonal polygonal grids, by combining Hamiltonian methods (work done by Salmon, Gassmann, Dubos and others) and Discrete Exterior Calculus (Thuburn, Cotter, Dubos, Ringler, Skamarock, Klemp and others). It is also possible to obtain these properties (along with arguably superior wave dispersion properties) through the use of a collocated (Z-grid) scheme based on the vorticity-divergence form of the continuous equations. Unfortunately, existing examples of these schemes in the literature for general, spherical grids either contain computational modes; or do not conserve total energy and potential enstrophy. This dissertation extends an existing scheme for planar grids to spherical grids, through the use of Nambu brackets (as pioneered by Rick Salmon). To compare these two schemes, the linear modes (balanced states, stationary modes and propagating modes; with and without dissipation) are examined on both uniform planar grids (square, hexagonal) and quasi-uniform spherical grids (geodesic, cubed-sphere). In addition to evaluating the linear modes, the results of the two schemes applied to a set of standard shallow water test cases and a recently developed forced-dissipative turbulence test case from John Thuburn (intended to evaluate the ability the suitability of schemes as the basis for a climate model) on both hexagonal-pentagonal icosahedral grids and cubed-sphere grids are presented. Finally, some remarks and thoughts about the suitability of these two schemes as the basis for atmospheric dynamical development are given.

Nuclear spin-spin coupling in a van der Waals-bonded system: xenon dimer.

PubMed

Vaara, Juha; Hanni, Matti; Jokisaari, Jukka

2013-03-14

Nuclear spin-spin coupling over van der Waals bond has recently been observed via the frequency shift of solute protons in a solution containing optically hyperpolarized (129)Xe nuclei. We carry out a first-principles computational study of the prototypic van der Waals-bonded xenon dimer, where the spin-spin coupling between two magnetically non-equivalent isotopes, J((129)Xe - (131)Xe), is observable. We use relativistic theory at the four-component Dirac-Hartree-Fock and Dirac-density-functional theory levels using novel completeness-optimized Gaussian basis sets and choosing the functional based on a comparison with correlated ab initio methods at the nonrelativistic level. J-coupling curves are provided at different levels of theory as functions of the internuclear distance in the xenon dimer, demonstrating cross-coupling effects between relativity and electron correlation for this property. Calculations on small Xe clusters are used to estimate the importance of many-atom effects on J((129)Xe - (131)Xe). Possibilities of observing J((129)Xe - (131)Xe) in liquid xenon are critically examined, based on molecular dynamics simulation. A simplistic spherical model is set up for the xenon dimer confined in a cavity, such as in microporous materials. It is shown that the on the average shorter internuclear distance enforced by the confinement increases the magnitude of the coupling as compared to the bulk liquid case, rendering J((129)Xe - (131)Xe) in a cavity a feasible target for experimental investigation.

Barn owls maximize head rotations by a combination of yawing and rolling in functionally diverse regions of the neck.

PubMed

Krings, Markus; Nyakatura, John A; Boumans, Mark L L M; Fischer, Martin S; Wagner, Hermann

2017-07-01

Owls are known for their outstanding neck mobility: these birds can rotate their heads more than 270°. The anatomical basis of this extraordinary neck rotation ability is not well understood. We used X-ray fluoroscopy of living owls as well as forced neck rotations in dead specimens and computer tomographic (CT) reconstructions to study how the individual cervical joints contribute to head rotation in barn owls (Tyto furcata pratincola). The X-ray data showed the natural posture of the neck, and the reconstructions of the CT-scans provided the shapes of the individual vertebrae. Joint mobility was analyzed in a spherical coordinate system. The rotational capability was described as rotation about the yaw and roll axes. The analyses suggest a functional division of the cervical spine into several regions. Most importantly, an upper region shows high rolling and yawing capabilities. The mobility of the lower, more horizontally oriented joints of the cervical spine is restricted mainly to the roll axis. These rolling movements lead to lateral bending, effectively resulting in a side shift of the head compared with the trunk during large rotations. The joints in the middle of the cervical spine proved to contribute less to head rotation. The analysis of joint mobility demonstrated how owls might maximize horizontal head rotation by a specific and variable combination of yawing and rolling in functionally diverse regions of the neck. © 2017 Anatomical Society.

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.

Support for the beam focusing hypothesis in the false killer whale.

PubMed

Kloepper, Laura N; Buck, John R; Smith, Adam B; Supin, Alexander Ya; Gaudette, Jason E; Nachtigall, Paul E

2015-08-01

The odontocete sound production system is complex and composed of tissues, air sacs and a fatty melon. Previous studies suggested that the emitted sonar beam might be actively focused, narrowing depending on target distance. In this study, we further tested this beam focusing hypothesis in a false killer whale. Using three linear arrays of hydrophones, we recorded the same emitted click at 2, 4 and 7 m distance and calculated the beamwidth, intensity, center frequency and bandwidth as recorded on each array at every distance. If the whale did not focus her beam, acoustics predicts the intensity would decay with range as a function of spherical spreading and the angular beamwidth would remain constant. On the contrary, our results show that as the distance from the whale to the array increases, the beamwidth is narrower and the received click intensity is higher than that predicted by a spherical spreading function. Each of these measurements is consistent with the animal focusing her beam on a target at a given range. These results support the hypothesis that the false killer whale is 'focusing' its sonar beam, producing a narrower and more intense signal than that predicted by spherical spreading. © 2015. Published by The Company of Biologists Ltd.

The virialization density of peaks with general density profiles under spherical collapse

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

Rubin, Douglas; Loeb, Abraham, E-mail: dsrubin@physics.harvard.edu, E-mail: aloeb@cfa.harvard.edu

2013-12-01

We calculate the non-linear virialization density, Δ{sub c}, of halos under spherical collapse from peaks with an arbitrary initial and final density profile. This is in contrast to the standard calculation of Δ{sub c} which assumes top-hat profiles. Given our formalism, the non-linear halo density can be calculated once the shape of the initial peak's density profile and the shape of the virialized halo's profile are provided. We solve for Δ{sub c} for halos in an Einstein de-Sitter and a ΛCDM universe. As examples, we consider power-law initial profiles as well as spherically averaged peak profiles calculated from the statisticsmore » of a Gaussian random field. We find that, depending on the profiles used, Δ{sub c} is smaller by a factor of a few to as much as a factor of 10 as compared to the density given by the standard calculation ( ≈ 200). Using our results, we show that, for halo finding algorithms that identify halos through an over-density threshold, the halo mass function measured from cosmological simulations can be enhanced at all halo masses by a factor of a few. This difference could be important when using numerical simulations to assess the validity of analytic models of the halo mass function.« less

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

NASA Astrophysics Data System (ADS)

Pace, Francesco; Meyer, Sven; Bartelmann, Matthias

2017-10-01

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

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

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

Pace, Francesco; Meyer, Sven; Bartelmann, Matthias, E-mail: francesco.pace@manchester.ac.uk, E-mail: sven.meyer@uni-heidelberg.de, E-mail: bartelmann@uni-heidelberg.de

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

Mean-square angle-of-arrival difference between two counter-propagating spherical waves in the presence of atmospheric turbulence.

PubMed

Chen, Chunyi; Yang, Huamin; Tong, Shoufeng; Lou, Yan

2015-09-21

The mean-square angle-of-arrival (AOA) difference between two counter-propagating spherical waves in atmospheric turbulence is theoretically formulated. Closed-form expressions for the path weighting functions are obtained. It is found that the diffraction and refraction effects of turbulent cells make negative and positive contributions to the mean-square AOA difference, respectively, and the turbulent cells located at the midpoint of the propagation path have no contributions to the mean-square AOA difference. If the mean-square AOA difference is separated into the refraction and diffraction parts, the refraction part always dominates the diffraction one, and the ratio of the diffraction part to the refraction one is never larger than 0.5 for any turbulence spectrum. Based on the expressions for the mean-square AOA difference, formulae for the correlation coefficient between the angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are derived. Numerical calculations are carried out by considering that the turbulence spectrum has no path dependence. It is shown that the mean-square AOA difference always approximates to the variance of AOA fluctuations. It is found that the correlation coefficient between the angles of arrival in the x or y direction of two counter-propagating spherical waves ranges from 0.46 to 0.5, implying that the instantaneous angles of arrival of two counter-propagating spherical waves in atmospheric turbulence are far from being perfectly correlated even when the turbulence spectrum does not vary along the path.

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.

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.

Huygens-Fresnel picture for electron-molecule elastic scattering★

NASA Astrophysics Data System (ADS)

Baltenkov, Arkadiy S.; Msezane, Alfred Z.

2017-11-01

The elastic scattering cross sections for a slow electron by C2 and H2 molecules have been calculated within the framework of the non-overlapping atomic potential model. For the amplitudes of the multiple electron scattering by a target the wave function of the molecular continuum is represented as a combination of a plane wave and two spherical waves generated by the centers of atomic spheres. This wave function obeys the Huygens-Fresnel principle according to which the electron wave scattering by a system of two centers is accompanied by generation of two spherical waves; their interaction creates a diffraction pattern far from the target. Each of the Huygens waves, in turn, is a superposition of the partial spherical waves with different orbital angular momenta l and their projections m. The amplitudes of these partial waves are defined by the corresponding phases of electron elastic scattering by an isolated atomic potential. In numerical calculations the s- and p-phase shifts are taken into account. So the number of interfering electron waves is equal to eight: two of which are the s-type waves and the remaining six waves are of the p-type with different m values. The calculation of the scattering amplitudes in closed form (rather than in the form of S-matrix expansion) is reduced to solving a system of eight inhomogeneous algebraic equations. The differential and total cross sections of electron scattering by fixed-in-space molecules and randomly oriented ones have been calculated as well. We conclude by discussing the special features of the S-matrix method for the case of arbitrary non-spherical potentials. Contribution to the Topical Issue "Low energy positron and electron interactions", edited by James Sullivan, Ron White, Michael Bromley, Ilya Fabrikant, and David Cassidy.

Profile of refractive errors in cerebral palsy: impact of severity of motor impairment (GMFCS) and CP subtype on refractive outcome.

PubMed

Saunders, Kathryn J; Little, Julie-Anne; McClelland, Julie F; Jackson, A Jonathan

2010-06-01

To describe refractive status in children and young adults with cerebral palsy (CP) and relate refractive error to standardized measures of type and severity of CP impairment and to ocular dimensions. A population-based sample of 118 participants aged 4 to 23 years with CP (mean 11.64 +/- 4.06) and an age-appropriate control group (n = 128; age, 4-16 years; mean, 9.33 +/- 3.52) were recruited. Motor impairment was described with the Gross Motor Function Classification Scale (GMFCS), and subtype was allocated with the Surveillance of Cerebral Palsy in Europe (SCPE). Measures of refractive error were obtained from all participants and ocular biometry from a subgroup with CP. A significantly higher prevalence and magnitude of refractive error was found in the CP group compared to the control group. Axial length and spherical refractive error were strongly related. This relation did not improve with inclusion of corneal data. There was no relation between the presence or magnitude of spherical refractive errors in CP and the level of motor impairment, intellectual impairment, or the presence of communication difficulties. Higher spherical refractive errors were significantly associated with the nonspastic CP subtype. The presence and magnitude of astigmatism were greater when intellectual impairment was more severe, and astigmatic errors were explained by corneal dimensions. Conclusions. High refractive errors are common in CP, pointing to impairment of the emmetropization process. Biometric data support this In contrast to other functional vision measures, spherical refractive error is unrelated to CP severity, but those with nonspastic CP tend to demonstrate the most extreme errors in refraction.

Retinal sensitivity and choroidal thickness in high myopia.

PubMed

Zaben, Ahmad; Zapata, Miguel Á; Garcia-Arumi, Jose

2015-03-01

To estimate the association between choroidal thickness in the macular area and retinal sensitivity in eyes with high myopia. This investigation was a transversal study of patients with high myopia, all of whom had their retinal sensitivity measured with macular integrity assessment microperimetry. The choroidal thicknesses in the macular area were then measured by optical coherence tomography, and statistical correlations between their functionality and the anatomical structuralism, as assessed by both types of measurements, were analyzed. Ninety-six eyes from 77 patients with high myopia were studied. The patients had a mean age ± standard deviation of 38.9 ± 13.2 years, with spherical equivalent values ranging from -6.00 diopter to -20.00 diopter (8.74 ± 2.73 diopter). The mean central choroidal thickness was 159.00 ± 50.57. The mean choroidal thickness was directly correlated with sensitivity (r = 0.306; P = 0.004) and visual acuity but indirectly correlated with the spherical equivalent values and patient age. The mean sensitivity was not significantly correlated with the macular foveal thickness (r = -0.174; P = 0.101) or with the overall macular thickness (r = 0.103; P = 0.334); furthermore, the mean sensitivity was significantly correlated with visual acuity (r = 0.431; P < 0.001) and the spherical equivalent values (r = -0.306; P = 0.003). Retinal sensitivity in highly myopic eyes is directly correlated with choroidal thickness and does not seem to be associated with retinal thickness. Thus, in patients with high myopia, accurate measurements of choroidal thickness may provide more accurate information about this pathologic condition because choroidal thickness correlates to a greater degree with the functional parameters, patient age, and spherical equivalent values.

[Clinical results of the aspheric intraocular lens FY-60AD (Hoya) with particular respect to decentration and tilt].

PubMed

Mester, U; Heinen, S; Kaymak, H

2010-09-01

Aspheric intraocular lenses (IOLs) aim to improve visual function and particularly contrast vision by neutralizing spherical aberration. One drawback of such IOLs is the enhanced sensitivity to decentration and tilt, which can deteriorate image quality. A total of 30 patients who received bilateral phacoemulsification before implantation of the aspheric lens FY-60AD (Hoya) were included in a prospective study. In 25 of the patients (50 eyes) the following parameters could be assessed 3 months after surgery: visual acuity, refraction, contrast sensitivity, pupil size, wavefront errors and decentration and tilt using a newly developed device. The functional results were very satisfying and comparable to results gained with other aspheric IOLs. The mean refraction was sph + 0.1 D (±0.7 D) and cyl 0.6 D (±0.8 D). The spherical equivalent was −0.2 D (±0.6 D). Wavefront measurements revealed a good compensation of the corneal spherical aberration but vertical and horizontal coma also showed opposing values in the cornea and IOL. The assessment of the lens position using the Purkinje meter demonstrated uncritical amounts of decentration and tilt. The mean amount of decentration was 0.2 mm±0.2 mm in the horizontal and vertical directions. The mean amount of tilt was 4.0±2.1° in horizontal and 3.0±2.5° in vertical directions. In a normal dioptric power range the aspheric IOL FY-60AD compensates the corneal spherical aberration very well with only minimal decentration. The slight tilt is symmetrical in both eyes and corresponds to the position of the crystalline lens in young eyes. This may contribute to our findings of compensated corneal coma.

Description of an α-cluster tail in 8Be and 20Ne: Delocalization of the α cluster by quantum penetration

NASA Astrophysics Data System (ADS)

Kanada-En'yo, Yoshiko

2014-10-01

We analyze the α-cluster wave functions in cluster states of ^8Be and ^{20}Ne by comparing the exact relative wave function obtained by the generator coordinate method (GCM) with various types of trial functions. For the trial functions, we adopt the fixed range shifted Gaussian of the Brink-Bloch (BB) wave function, the spherical Gaussian with the adjustable range parameter of the spherical Tohsaki-Horiuchi-Schuck-Röpke (sTHSR), the deformed Gaussian of the deformed THSR (dTHSR), and a function with the Yukawa tail (YT). The quality of the description of the exact wave function with a trial function is judged by the squared overlap between the trial function and the GCM wave function. A better result is obtained with the sTHSR wave function than the BB wave function, and further improvement can be made with the dTHSR wave function because these wave functions can describe the outer tail better. The YT wave function gives almost an equal quality to or even better quality than the dTHSR wave function, indicating that the outer tail of α-cluster states is characterized by the Yukawa-like tail rather than the Gaussian tail. In weakly bound α-cluster states with small α separation energy and the low centrifugal and Coulomb barriers, the outer tail part is the slowly damping function described well by the quantum penetration through the effective barrier. This outer tail characterizes the almost zero-energy free α gas behavior, i.e., the delocalization of the cluster.

A Primer on Elliptic Functions with Applications in Classical Mechanics

ERIC Educational Resources Information Center

Brizard, Alain J.

2009-01-01

The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…

Recursive formulas for determining perturbing accelerations in intermediate satellite motion

NASA Astrophysics Data System (ADS)

Stoianov, L.

Recursive formulas for Legendre polynomials and associated Legendre functions are used to obtain recursive relationships for determining acceleration components which perturb intermediate satellite motion. The formulas are applicable in all cases when the perturbation force function is presented as a series in spherical functions (gravitational, tidal, thermal, geomagnetic, and other perturbations of intermediate motion). These formulas can be used to determine the order of perturbing accelerations.

Controlling Particle Morphologies at Fluid Interfaces: Macro- and Micro- approaches

NASA Astrophysics Data System (ADS)

Beesabathuni, Shilpa Naidu

The controlled generation of varying shaped particles is important for many applications: consumer goods, biomedical diagnostics, food processing, adsorbents and pharmaceuticals which can benefit from the availability of geometrically complex and chemically inhomogeneous particles. This thesis presents two approaches to spherical and non-spherical particle synthesis using macro and microfluidics. In the first approach, a droplet microfluidic technique is explored to fabricate spherical conducting polymer, polyaniline, particles with precise control over morphology and functionality. Microfluidics has recently emerged as an important alternate to the synthesis of complex particles. The conducting polymer, polyaniline, is widely used and known for its stability, high conductivity, and favorable redox properties. In this approach, monodisperse micron-sized polyaniline spherical particles were synthesized using two-phase droplet microfluidics from Aniline and Ammonium persulfate oxidative polymerization in an oil-based continuous phase. The morphology of the polymerized particles is porous in nature which can be used for encapsulation as well as controlled release applications. Encapsulation of an enzyme, glucose oxidase, was also performed using the technique to synthesize microspheres for glucose sensing. The polymer microspheres were characterized using SEM, UV-Vis and EDX to understand the relationship between their microstructure and stability. In the second approach, molten drop impact in a cooling aqueous medium to generate non-spherical particles was explored. Viscoelastic wax based materials are widely used in many applications and their performance and application depends on the particle morphology and size. The deformation of millimeter size molten wax drops as they impacted an immiscible liquid interface was investigated. Spherical molten wax drops impinged on a cooling water bath, then deformed and as a result of solidification were arrested into various shapes such as ellipsoids, mushrooms, spherulites and discs. The final morphology of the wax particles is governed by the interfacial, inertial, viscous and thermal effects, which can be studied over a range of Weber, Capillary, Reynolds and Stefan numbers. A simplified Stefan problem for a spherical drop was solved. The time required to initiate a phase transition at the interface of the molten wax and water after impact was estimated and correlated with the drop deformation history and final wax particle shape to develop a capability to predict the shape. While the microfluidic synthesis approach offers precise control over morphology and functionality, large particle throughput is a limitation. The drop impact in a liquid medium emulsion approach is limited to crosslinking or heat sensitive materials but can be extended to large scale production for industrial applications. Both approaches are simple, robust and cost effective making them viable and attractive solutions for complex particle synthesis. The choice of the approach is dependent on considerations such as particle material, size, shape, throughput and end application.

The Exponential Function, XI: The New Flat Earth Society.

ERIC Educational Resources Information Center

Bartlett, Albert A.

1996-01-01

Discusses issues related to perpetual population growth. Argues that if we believe that there are no limits to growth, we will have to abandon the concept of a spherical Earth which puts limits to growth. (JRH)

Fusion yield: Guderley model and Tsallis statistics

NASA Astrophysics Data System (ADS)

Haubold, H. J.; Kumar, D.

2011-02-01

The reaction rate probability integral is extended from Maxwell-Boltzmann approach to a more general approach by using the pathway model introduced by Mathai in 2005 (A pathway to matrix-variate gamma and normal densities. Linear Algebr. Appl. 396, 317-328). The extended thermonuclear reaction rate is obtained in the closed form via a Meijer's G-function and the so-obtained G-function is represented as a solution of a homogeneous linear differential equation. A physical model for the hydrodynamical process in a fusion plasma-compressed and laser-driven spherical shock wave is used for evaluating the fusion energy integral by integrating the extended thermonuclear reaction rate integral over the temperature. The result obtained is compared with the standard fusion yield obtained by Haubold and John in 1981 (Analytical representation of the thermonuclear reaction rate and fusion energy production in a spherical plasma shock wave. Plasma Phys. 23, 399-411). An interpretation for the pathway parameter is also given.

On the stability of soliton and hairy black hole solutions of 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant

NASA Astrophysics Data System (ADS)

Baxter, J. Erik; Winstanley, Elizabeth

2016-02-01

We investigate the stability of spherically symmetric, purely magnetic, soliton and black hole solutions of four-dimensional 𝔰𝔲(N) Einstein-Yang-Mills theory with a negative cosmological constant Λ. These solutions are described by N - 1 magnetic gauge field functions ωj. We consider linear, spherically symmetric, perturbations of these solutions. The perturbations decouple into two sectors, known as the sphaleronic and gravitational sectors. For any N, there are no instabilities in the sphaleronic sector if all the magnetic gauge field functions ωj have no zeros and satisfy a set of N - 1 inequalities. In the gravitational sector, we prove that there are solutions which have no instabilities in a neighbourhood of stable embedded 𝔰𝔲(2) solutions, provided the magnitude of the cosmological constant |" separators=" Λ | is sufficiently large.

Characteristic investigation of Golay9 multiple mirror telescope with a spherical primary mirror

NASA Astrophysics Data System (ADS)

Wu, Feng; Wu, Quanying; Zhu, Xifang; Xiang, Ruxi; Qian, Lin

2017-10-01

The sparse aperture provides a novel solution to the manufacturing difficulties of modern super large telescopes. Golay configurations are optimal in the sparse aperture family. Characteristics of the Golay9 multiple mirror telescope having a spherical primary mirror are investigated. The arrangement of the nine sub-mirrors is discussed after the planar Golay9 configuration is analyzed. The characteristics of the entrance pupil are derived by analyzing the sub-aperture shapes with different relative apertures and sub-mirror sizes. Formulas about the fill factor and the overlay factor are deduced. Their maximal values are presented based on the derived tangency condition. Formulas for the point spread function (PSF) and the modulation transfer function (MTF) of the Golay9 MMT are also deduced. Two Golay9 MMT have been developed by Zemax simulation. Their PSF, MTF, fill factors, and overlay factors prove that our theoretical results are consistent with the practical simulation ones.

Spherical Hecke algebra in the Nekrasov-Shatashvili limit

NASA Astrophysics Data System (ADS)

Bourgine, Jean-Emile

2015-01-01

The Spherical Hecke central (SHc) algebra has been shown to act on the Nekrasov instanton partition functions of gauge theories. Its presence accounts for both integrability and AGT correspondence. On the other hand, a specific limit of the Omega background, introduced by Nekrasov and Shatashvili (NS), leads to the appearance of TBA and Bethe like equations. To unify these two points of view, we study the NS limit of the SHc algebra. We provide an expression of the instanton partition function in terms of Bethe roots, and define a set of operators that generates infinitesimal variations of the roots. These operators obey the commutation relations defining the SHc algebra at first order in the equivariant parameter ɛ 2. Furthermore, their action on the bifundamental contributions reproduces the Kanno-Matsuo-Zhang transformation. We also discuss the connections with the Mayer cluster expansion approach that leads to TBA-like equations.

Hierarchical nanoparticle assemblies formed by decorating breath figures.

PubMed

Böker, Alexander; Lin, Yao; Chiapperini, Kristen; Horowitz, Reina; Thompson, Mike; Carreon, Vincent; Xu, Ting; Abetz, Clarissa; Skaff, Habib; Dinsmore, A D; Emrick, Todd; Russell, Thomas P

2004-05-01

The combination of two self-assembly processes on different length scales leads to the formation of hierarchically structured nanoparticle arrays. Here, the formation of spherical cavities, or 'breath figures'-made by the condensation of micrometre-sized water droplets on the surface of a polymer solution-that self-assemble into a well-ordered hexagonal array, is combined with the self-assembly of CdSe nanoparticles at the polymer solution-water droplet interface. Complete evaporation of the solvent and water confines the particle assembly to an array of spherical cavities and allows for ex situ investigation. Fluorescence confocal, transmission electron and scanning electron microscope images show the preferential segregation of the CdSe nanoparticles to the polymer solution-water interface where they form a 5-7-nm-thick layer, thus functionalizing the walls of the holes. This process opens a new route to fabricating highly functionalized ordered microarrays of nanoparticles, potentially useful in sensory, separation membrane or catalytic applications.

Literature Review of Spherical Resorcinol-Formaldehyde for Cesium Ion Exchange

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

Brown, Garrett N.

2014-09-30

The current report summarizes work performed throughout the scientific community and DOE complex as reported in the open literature and DOE-sponsored reports to evaluate the Cs+ ion exchange (CIX) characteristics of SRF resin. King (2007) completed a similar literature review in support of material selection for the Small Column Ion Exchange (SCIX) project. Josephson et al. (2010) and Sams et al. (2009) provided a similar brief review of SRF CIX for the near-tank Cs+ removal (NTCR) project. Thorson (2008a) documented the basis for recommending SRF over SuperLigTM 644 as the primary CIX resin in the WTP. The current review expandsmore » on previous work, summarizes additional work completed to date, and provides a broad view of the literature without focusing on a specific column system. Although the focus of the current review is the SRF resin, many cited references include multiple materials such as the non-spherical GGRF and SuperLigTM 644 organic resins and crystalline silicotitanate (CST) IONSIVTM IE-911, a non-elutable inorganic material. This report summarizes relevant information provided in the literature.« less

Phosphorescence Kinetics of Singlet Oxygen Produced by Photosensitization in Spherical Nanoparticles. Part I. Theory.

PubMed

Hovan, Andrej; Datta, Shubhashis; Kruglik, Sergei G; Jancura, Daniel; Miskovsky, Pavol; Bánó, Gregor

2018-05-24

The singlet oxygen produced by energy transfer between an excited photosensitizer (pts) and ground-state oxygen molecules plays a key role in photodynamic therapy. Different nanocarrier systems are extensively studied to promote targeted pts delivery in a host body. The phosphorescence kinetics of the singlet oxygen produced by the short laser pulse photosensitization of pts inside nanoparticles is influenced by singlet oxygen diffusion from the particles to the surrounding medium. Two theoretical models are presented in this work: a more complex numerical one and a simple analytical one. Both the models predict the time course of singlet oxygen concentration inside and outside of the spherical particles following short-pulse excitation of pts. On the basis of the comparison of the numerical and analytical results, a semiempirical analytical formula is derived to calculate the characteristic diffusion time of singlet oxygen from the nanoparticles to the surrounding solvent. The phosphorescence intensity of singlet oxygen produced in pts-loaded nanocarrier systems can be calculated as a linear combination of the two concentrations (inside and outside the particles), taking the different phosphorescence emission rate constants into account.

Extension of geometrical-optics approximation to on-axis Gaussian beam scattering. II. By a spheroidal particle with end-on incidence.

PubMed

Xu, Feng; Ren, Kuan Fang; Cai, Xiaoshu; Shen, Jianqi

2006-07-10

On the basis of our previous work on the extension of the geometrical-optics approximation to Gaussian beam scattering by a spherical particle, we present a further extension of the method to the scattering of a transparent or absorbing spheroidal particle with the same symmetric axis as the incident beam. As was done for the spherical particle, the phase shifts of the emerging rays due to focal lines, optical path, and total reflection are carefully considered. The angular position of the geometric rainbow of primary order is theoretically predicted. Compared with our results, the Möbius prediction of the rainbow angle has a discrepancy of less than 0.5 degrees for a spheroidal droplet of aspect radio kappa within 0.95 and 1.05 and less than 2 degrees for kappa within 0.89 and 1.11. The flux ratio index F, which qualitatively indicates the effect of a surface wave, is also studied and found to be dependent on the size, refractive index, and surface curvature of the particle.

Thermodynamic Theory of Spherically Trapped Coulomb Clusters

NASA Astrophysics Data System (ADS)

Wrighton, Jeffrey; Dufty, James; Bonitz, Michael; K"{A}Hlert, Hanno

2009-11-01

The radial density profile of a finite number of identical charged particles confined in a harmonic trap is computed over a wide ranges of temperatures (Coulomb coupling) and particle numbers. At low temperatures these systems form a Coulomb crystal with spherical shell structure which has been observed in ultracold trapped ions and in dusty plasmas. The shell structure is readily reproduced in simulations. However, analytical theories which used a mean field approachfootnotetext[1]C. Henning et al., Phys. Rev. E 74, 056403 (2006) or a local density approximationfootnotetext[2]C. Henning et al., Phys. Rev. E 76, 036404 (2007) have, so far, only been able to reproduce the average density profile. Here we present an approach to Coulomb correlations based on the hypernetted chain approximation with additional bridge diagrams. It is demonstrated that this model reproduces the correct shell structure within a few percent and provides the basis for a thermodynamic theory of Coulomb clusters in the strongly coupled fluid state.footnotetext[3]J. Wrighton, J.W. Dufty, H. K"ahlert and M. Bonitz, J. Phys. A 42, 214052 (2009) and Phys. Rev. E (2009) (to be submitted)

Real-Time Motion Tracking for Indoor Moving Sphere Objects with a LiDAR Sensor.

PubMed

Huang, Lvwen; Chen, Siyuan; Zhang, Jianfeng; Cheng, Bang; Liu, Mingqing

2017-08-23

Object tracking is a crucial research subfield in computer vision and it has wide applications in navigation, robotics and military applications and so on. In this paper, the real-time visualization of 3D point clouds data based on the VLP-16 3D Light Detection and Ranging (LiDAR) sensor is achieved, and on the basis of preprocessing, fast ground segmentation, Euclidean clustering segmentation for outliers, View Feature Histogram (VFH) feature extraction, establishing object models and searching matching a moving spherical target, the Kalman filter and adaptive particle filter are used to estimate in real-time the position of a moving spherical target. The experimental results show that the Kalman filter has the advantages of high efficiency while adaptive particle filter has the advantages of high robustness and high precision when tested and validated on three kinds of scenes under the condition of target partial occlusion and interference, different moving speed and different trajectories. The research can be applied in the natural environment of fruit identification and tracking, robot navigation and control and other fields.

Real-Time Motion Tracking for Indoor Moving Sphere Objects with a LiDAR Sensor

PubMed Central

Chen, Siyuan; Zhang, Jianfeng; Cheng, Bang; Liu, Mingqing

2017-01-01

Object tracking is a crucial research subfield in computer vision and it has wide applications in navigation, robotics and military applications and so on. In this paper, the real-time visualization of 3D point clouds data based on the VLP-16 3D Light Detection and Ranging (LiDAR) sensor is achieved, and on the basis of preprocessing, fast ground segmentation, Euclidean clustering segmentation for outliers, View Feature Histogram (VFH) feature extraction, establishing object models and searching matching a moving spherical target, the Kalman filter and adaptive particle filter are used to estimate in real-time the position of a moving spherical target. The experimental results show that the Kalman filter has the advantages of high efficiency while adaptive particle filter has the advantages of high robustness and high precision when tested and validated on three kinds of scenes under the condition of target partial occlusion and interference, different moving speed and different trajectories. The research can be applied in the natural environment of fruit identification and tracking, robot navigation and control and other fields. PMID:28832520

Quantum Dynamics with Short-Time Trajectories and Minimal Adaptive Basis Sets.

PubMed

Saller, Maximilian A C; Habershon, Scott

2017-07-11

Methods for solving the time-dependent Schrödinger equation via basis set expansion of the wave function can generally be categorized as having either static (time-independent) or dynamic (time-dependent) basis functions. We have recently introduced an alternative simulation approach which represents a middle road between these two extremes, employing dynamic (classical-like) trajectories to create a static basis set of Gaussian wavepackets in regions of phase-space relevant to future propagation of the wave function [J. Chem. Theory Comput., 11, 8 (2015)]. Here, we propose and test a modification of our methodology which aims to reduce the size of basis sets generated in our original scheme. In particular, we employ short-time classical trajectories to continuously generate new basis functions for short-time quantum propagation of the wave function; to avoid the continued growth of the basis set describing the time-dependent wave function, we employ Matching Pursuit to periodically minimize the number of basis functions required to accurately describe the wave function. Overall, this approach generates a basis set which is adapted to evolution of the wave function while also being as small as possible. In applications to challenging benchmark problems, namely a 4-dimensional model of photoexcited pyrazine and three different double-well tunnelling problems, we find that our new scheme enables accurate wave function propagation with basis sets which are around an order-of-magnitude smaller than our original trajectory-guided basis set methodology, highlighting the benefits of adaptive strategies for wave function propagation.

A mean spherical model for soft potentials: The hard core revealed as a perturbation

NASA Technical Reports Server (NTRS)

Rosenfeld, Y.; Ashcroft, N. W.

1978-01-01

The mean spherical approximation for fluids is extended to treat the case of dense systems interacting via soft-potentials. The extension takes the form of a generalized statement concerning the behavior of the direct correlation function c(r) and radial distribution g(r). From a detailed analysis that views the hard core portion of a potential as a perturbation on the whole, a specific model is proposed which possesses analytic solutions for both Coulomb and Yukawa potentials, in addition to certain other remarkable properties. A variational principle for the model leads to a relatively simple method for obtaining numerical solutions.

Properties of plate-like carbonyl iron particle for magnetorheological fluid

NASA Astrophysics Data System (ADS)

Shilan, S. T.; Mazlan, S. A.; Khairi, M. H. A.; Ubaidillah

2016-11-01

This work experimentally discussed the characterization, magnetic, and rheological properties of plate-like carbonyl iron particle (CIP) in comparison with conventional spherical CIP. Plate-like CIP was produced by using ball milling method. The effect of plate-like shape on the magnetic behavior of CIP was firstly investigated by vibrating sample magnetometer (VSM). The results indicated that the plate-like CIP obtained higher saturation magnetization (about 8%) than that of the spherical particles. In addition, the field-dependent rheological properties such as yield stress were investigated and the results are compared between two particles as a function of the magnetic field intensity.

Coulomb matrix elements in multi-orbital Hubbard models.

PubMed

Bünemann, Jörg; Gebhard, Florian

2017-04-26

Coulomb matrix elements are needed in all studies in solid-state theory that are based on Hubbard-type multi-orbital models. Due to symmetries, the matrix elements are not independent. We determine a set of independent Coulomb parameters for a d-shell and an f-shell and all point groups with up to 16 elements (O h , O, T d , T h , D 6h , and D 4h ). Furthermore, we express all other matrix elements as a function of the independent Coulomb parameters. Apart from the solution of the general point-group problem we investigate in detail the spherical approximation and first-order corrections to the spherical approximation.

An investigation of the forward scattering theorem

NASA Technical Reports Server (NTRS)

Karam, M. A.; Fung, A. K.

1987-01-01

The calculation of an EM wave's extinction loss during propagation within an inhomogeneous medium, as in active and passive remote sensing modeling, can be undertaken either through the summation of the scattering and absorption losses or through the use of the forward scattering theorem. Attention is presently given to the similarities and differences of these two approaches as a function of dielectric properties of a spherical scatterer and the incident frequency. Scattering loss is obtainable by integrating the magnitude-squared of the scattered field over a spherical surface surrounding the scatterer; the scattered field and the field within the scatterer are computed according to Mie theory.

A two-dimensional phase separation on the spherical surface of the metallic glass Au55Pb22.5Sb22.5

NASA Technical Reports Server (NTRS)

Lee, M. C.; Johnson, W. L.

1982-01-01

Recent experiments indicate that a phase separation in a spherical sample of the metallic glass Au55Pb22.5Sb22.5 occurs near the surface of the sphere. This strongly suggests either a contribution of surface-free energy to the decomposition process or a possible influence of near surface impurities absorbed during synthesis of the sphere. The surface phase separation has been studied as a function of cooling rate of the sphere. At high cooling rates (small sphere sizes), the surface separation disappears altogether suggesting that the surface of the parent liquid droplet is initially homogeneous.

Absolute Equation-of-State Measurement for Polystyrene from 25 - 60 Mbar Using a Spherically Converging Shock Wave

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

Glenzer, Siegfried

We have developed an experimental platform for the National Ignition Facility (NIF) that uses spherically converging shock waves for absolute equation of state (EOS) measurements along the principal Hugoniot. In this Letter we present radiographic compression measurements for polystyrene that were taken at shock pressures reaching 60 Mbar (6 TPa). This significantly exceeds previously published results obtained on the Nova laser [Cauble et al., Phys. Rev. Lett. 80, 1248 (1998)] at strongly improved precision, allowing to discriminate between different EOS models. We find excellent agreement with Kohn-Sham Density Functional Theory based molecular dynamics simulations.

Application of the dual-kinetic-balance sets in the relativistic many-body problem of atomic structure

NASA Astrophysics Data System (ADS)

Beloy, Kyle; Derevianko, Andrei

2008-05-01

The dual-kinetic-balance (DKB) finite basis set method for solving the Dirac equation for hydrogen-like ions [V. M. Shabaev et al., Phys. Rev. Lett. 93, 130405 (2004)] is extended to problems with a non-local spherically-symmetric Dirac-Hartree-Fock potential. We implement the DKB method using B-spline basis sets and compare its performance with the widely- employed approach of Notre Dame (ND) group [W.R. Johnson, S.A. Blundell, J. Sapirstein, Phys. Rev. A 37, 307-15 (1988)]. We compare the performance of the ND and DKB methods by computing various properties of Cs atom: energies, hyperfine integrals, the parity-non-conserving amplitude of the 6s1/2-7s1/2 transition, and the second-order many-body correction to the removal energy of the valence electrons. We find that for a comparable size of the basis set the accuracy of both methods is similar for matrix elements accumulated far from the nuclear region. However, for atomic properties determined by small distances, the DKB method outperforms the ND approach.

Transport-reaction model for defect and carrier behavior within displacement cascades in gallium arsenide

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

Wampler, William R.; Myers, Samuel M.

2014-02-01

A model is presented for recombination of charge carriers at displacement damage in gallium arsenide, which includes clustering of the defects in atomic displacement cascades produced by neutron or ion irradiation. The carrier recombination model is based on an atomistic description of capture and emission of carriers by the defects with time evolution resulting from the migration and reaction of the defects. The physics and equations on which the model is based are presented, along with details of the numerical methods used for their solution. The model uses a continuum description of diffusion, field-drift and reaction of carriers and defectsmore » within a representative spherically symmetric cluster. The initial radial defect profiles within the cluster were chosen through pair-correlation-function analysis of the spatial distribution of defects obtained from the binary-collision code MARLOWE, using recoil energies for fission neutrons. Charging of the defects can produce high electric fields within the cluster which may influence transport and reaction of carriers and defects, and which may enhance carrier recombination through band-to-trap tunneling. Properties of the defects are discussed and values for their parameters are given, many of which were obtained from density functional theory. The model provides a basis for predicting the transient response of III-V heterojunction bipolar transistors to pulsed neutron irradiation.« less

PDQ-8 reference manual (LWBR development program)

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

Pfiefer, C J; Spitz, C J

1978-05-01

The PDQ-8 program is designed to solve the neutron diffusion, depletion problem in one, two, or three dimensions on the CDC-6600 and CDC-7600 computers. The three dimensional spatial calculation may be either explicit or discontinuous trial function synthesis. Up to five lethargy groups are permitted. The fast group treatment may be simplified P(3), and the thermal neutrons may be represented by a single group or a pair of overlapping groups. Adjoint, fixed source, one iteration, additive fixed source, eigenvalue, and boundary value calculations may be performed. The HARMONY system is used for cross section variation and generalized depletion chain solutions.more » The depletion is a combination gross block depletion for all nuclides as well as a fine block depletion for a specified subset of the nuclides. The geometries available include rectangular, cylindrical, spherical, hexagonal, and a very general quadrilateral geometry with diagonal interfaces. All geometries allow variable mesh in all dimensions. Various control searches as well as temperature and xenon feedbacks are provided. The synthesis spatial solution time is dependent on the number of trial functions used and the number of gross blocks. The PDQ-8 program is used at Bettis on a production basis for solving diffusion--depletion problems. The report describes the various features of the program and then separately describes the input required to utilize these features.« less

Electron Transport Coefficients and Effective Ionization Coefficients in SF6-O2 and SF6-Air Mixtures Using Boltzmann Analysis

NASA Astrophysics Data System (ADS)

Wei, Linsheng; Xu, Min; Yuan, Dingkun; Zhang, Yafang; Hu, Zhaoji; Tan, Zhihong

2014-10-01

The electron drift velocity, electron energy distribution function (EEDF), density-normalized effective ionization coefficient and density-normalized longitudinal diffusion velocity are calculated in SF6-O2 and SF6-Air mixtures. The experimental results from a pulsed Townsend discharge are plotted for comparison with the numerical results. The reduced field strength varies from 40 Td to 500 Td (1 Townsend=10-17 V·cm2) and the SF6 concentration ranges from 10% to 100%. A Boltzmann equation associated with the two-term spherical harmonic expansion approximation is utilized to gain the swarm parameters in steady-state Townsend. Results show that the accuracy of the Boltzmann solution with a two-term expansion in calculating the electron drift velocity, electron energy distribution function, and density-normalized effective ionization coefficient is acceptable. The effective ionization coefficient presents a distinct relationship with the SF6 content in the mixtures. Moreover, the E/Ncr values in SF6-Air mixtures are higher than those in SF6-O2 mixtures and the calculated value E/Ncr in SF6-O2 and SF6-Air mixtures is lower than the measured value in SF6-N2. Parametric studies conducted on these parameters using the Boltzmann analysis offer substantial insight into the plasma physics, as well as a basis to explore the ozone generation process.

The dynamics of magnetic nanoparticles exposed to non-heating alternating magnetic field in biochemical applications: theoretical study

NASA Astrophysics Data System (ADS)

Golovin, Yuri I.; Gribanovsky, Sergey L.; Golovin, Dmitry Y.; Zhigachev, Alexander O.; Klyachko, Natalia L.; Majouga, Alexander G.; Sokolsky, Marina; Kabanov, Alexander V.

2017-02-01

In the past decade, magneto-nanomechanical approach to biochemical systems stimulation has been studied intensively. This method involves macromolecule structure local deformation via mechanical actuation of functionalized magnetic nanoparticles (f-MNPs) by non-heating low frequency (LF) alternating magnetic field (AMF). Specificity at cellular or molecular level and spatial locality in nanometer scale are its key advantages as compared to magnetic fluid hyperthermia. However, current experimental studies have weak theoretical basis. Several models of magneto-nanomechanical actuation of macromolecules and cells in non-heating uniform LF AMF are presented in the article. Single core-shell spherical, rod-like, and Janus MNPs, as well as dimers consisting of two f-MNPs with macromolecules immobilized on their surfaces are considered. AMF-induced rotational oscillations of MNPs can affect properties and functioning of macromolecules or cellular membranes attached to them via periodic deformations in nanometer scale. This could be widely used in therapy, in particular for targeted drug delivery, controlled drug release, and cancer cell killing. An aggregate composed of MNPs can affect associated macromolecules by force up to several hundreds of piconewton in the case of MNPs of tens of nanometers in diameter and LF AMF below 1 T. AMF parameters and MNP design requirements for effective in vitro and in vivo magneto-nanomechanical treatment are presented.

Curvature dependence of the effect of ionic functionalization on the attraction among nanoparticles in dispersion

NASA Astrophysics Data System (ADS)

Jabes, B. Shadrack; Bratko, Dusan; Luzar, Alenka

2018-06-01

Solubilization of nanoparticles facilitates nanomaterial processing and enables new applications. An effective method to improve dispersibility in water is provided by ionic functionalization. We explore how the necessary extent of functionalization depends on the particle geometry. Using molecular dynamics/umbrella sampling simulations, we determine the effect of the solute curvature on solvent-averaged interactions among ionizing graphitic nanoparticles in aqueous dispersion. We tune the hydrophilicity of molecular-brush coated fullerenes, carbon nanotubes, and graphane platelets by gradually replacing a fraction of the methyl end groups of the alkyl coating by the ionizing -COOK or -NH3Cl groups. To assess the change in nanoparticles' dispersibility in water, we determine the potential-of-mean-force profiles at varied degrees of ionization. When the coating comprises only propyl groups, the attraction between the hydrophobic particles intensifies from spherical to cylindrical to planar geometry. This is explained by the increasing fraction of surface groups that can be brought into contact and the reduced access to water molecules, both following the above sequence. When ionic groups are added, however, the dispersibility increases in the opposite order, with the biggest effect in the planar geometry and the smallest in the spherical geometry. These results highlight the important role of geometry in nanoparticle solubilization by ionic functionalities, with about twice higher threshold surface charge necessary to stabilize a dispersion of spherical than planar particles. At 25%-50% ionization, the potential of mean force reaches a plateau because of the counterion condensation and saturated brush hydration. Moreover, the increase in the fraction of ionic groups can weaken the repulsion through counterion correlations between adjacent nanoparticles. High degrees of ionization and concomitant ionic screening gradually reduce the differences among surface interactions in distinct geometries until an essentially curvature-independent dispersion environment is created. Insights into tuning nanoparticle interactions can guide the synthesis of a broad class of nonpolar nanoparticles, where solubility is achieved by ionic functionalization.

Staircase polymetalsilicon nanocomplexes - Polymetalphenyl siloxanes: Structure and properties

NASA Astrophysics Data System (ADS)

Shapkin, N. P.; Balanov, M. I.; Razov, V. I.; Gardionov, S. V.; Mayorov, V. Yu; Tokar, E. A.; Papynov, E. K.; Korochentsev, V. V.; Leont'ev, L. B.; Slobodyuk, A. B.; Modin, E. B.

2018-03-01

Polyphenyl siloxanes containing chromium, iron, and aluminum in the backbone chain have been synthesized. The structure of the obtained staircase nano-metal complexes has been studied by the methods of XRD analysis and IR, 29Si and 27Al NMR, and XPS spectroscopy and scanning electron microscopy. Physical-chemical characteristics of these compounds have been investigated by the positron annihilation spectroscopy (PAS) and low-temperature nitrogen adsorption. The data of X-ray diffraction analysis (XRD) enabled us to calculate the size and volume of coherent scattering regions (CSR) and the cross-section area of the polymer chains. By means of the PAS method, the specific volumes of positron (Ve+) and positronium (Vps) "traps" have been calculated. The data of 29Si NMR spectroscopy have shown the presence of T2 and T3 fragments in the structure. As was shown on the basis of the data of 27Al NMR and XPS spectroscopy, tetrahedral (66%) and octahedral surroundings of the metal atom were realized in the backbone chain. The obtained data were used to describe a spatial layered structure of phenyl siloxanes containing trivalent metals. The electron microscopy of nanocomplexes revealed the presence of spherical particles, whose size changes in cases of chromium, iron, and aluminum. Using the data of low-temperature nitrogen adsorption, it was assumed that the specific surface area was filled with a layer of compacted spherical particles, whereas the layer thickness was determined, in its turn, by the specific polarizing potential (SPP) calculated as a ratio of the polarizing potential (PP) to the volume of voids between coherent scattering regions. Similar dependence is observed between the layer thickness and the specific polarizing potential calculated as a ratio of the polarizing potential to the positronium "trap" volume. A direct dependence between the thickness of the spherical particles layer and the specific polarizing potential has been demonstrated. The assumption on a fractal structure of spherical particles was made. Tribotechnical properties of the motor oil with metal siloxane additives have been studied.

One-dimensional MHD simulations of MTF systems with compact toroid targets and spherical liners

NASA Astrophysics Data System (ADS)

Khalzov, Ivan; Zindler, Ryan; Barsky, Sandra; Delage, Michael; Laberge, Michel

2017-10-01

One-dimensional (1D) MHD code is developed in General Fusion (GF) for coupled plasma-liner simulations in magnetized target fusion (MTF) systems. The main goal of these simulations is to search for optimal parameters of MTF reactor, in which spherical liquid metal liner compresses compact toroid plasma. The code uses Lagrangian description for both liner and plasma. The liner is represented as a set of spherical shells with fixed masses while plasma is discretized as a set of nested tori with circular cross sections and fixed number of particles between them. All physical fields are 1D functions of either spherical (liner) or small toroidal (plasma) radius. Motion of liner and plasma shells is calculated self-consistently based on applied forces and equations of state. Magnetic field is determined by 1D profiles of poloidal and toroidal fluxes - they are advected with shells and diffuse according to local resistivity, this also accounts for flux leakage into the liner. Different plasma transport models are implemented, this allows for comparison with ongoing GF experiments. Fusion power calculation is included into the code. We performed a series of parameter scans in order to establish the underlying dependencies of the MTF system and find the optimal reactor design point.

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.

Probing crustal structures from neutron star compactness

NASA Astrophysics Data System (ADS)

Sotani, Hajime; Iida, Kei; Oyamatsu, Kazuhiro

2017-10-01

With various sets of the parameters that characterize the equation of state (EOS) of nuclear matter, we systematically examine the thickness of a neutron star crust and of the pasta phases contained therein. Then, with respect to the thickness of the phase of spherical nuclei, the thickness of the cylindrical phase and the crust thickness, we successfully derive fitting formulas that express the ratio of each thickness to the star's radius as a function of the star's compactness, the incompressibility of symmetric nuclear matter and the density dependence of the symmetry energy. In particular, we find that the thickness of the phase of spherical nuclei has such a strong dependence on the stellar compactness as the crust thickness, but both of them show a much weaker dependence on the EOS parameters. Thus, via determination of the compactness, the thickness of the phase of spherical nuclei as well as the crust thickness can be constrained reasonably, even if the EOS parameters remain to be well-determined.

Wrinkling Non-Spherical Particles and Its Application in Cell Attachment Promotion

NASA Astrophysics Data System (ADS)

Li, Minggan; Joung, Dehi; Hughes, Bethany; Waldman, Stephen D.; Kozinski, Janusz A.; Hwang, Dae Kun

2016-07-01

Surface wrinkled particles are ubiquitous in nature and present in different sizes and shapes, such as plant pollens and peppercorn seeds. These natural wrinkles provide the particles with advanced functions to survive and thrive in nature. In this work, by combining flow lithography and plasma treatment, we have developed a simple method that can rapidly create wrinkled non-spherical particles, mimicking the surface textures in nature. Due to the oxygen inhibition in flow lithography, the non-spherical particles synthesized in a microfluidic channel are covered by a partially cured polymer (PCP) layer. When exposed to plasma treatment, this PCP layer rapidly buckles, forming surface-wrinkled particles. We designed and fabricated various particles with desired shapes and sizes. The surfaces of these shapes were tuned to created wrinkle morphologies by controlling UV exposure time and the washing process. We further demonstrated that wrinkles on the particles significantly promoted cell attachment without any chemical modification, potentially providing a new route for cell attachment for various biomedical applications.

Inviscid dynamics of a wet foam drop with monodisperse bubble size distribution

NASA Astrophysics Data System (ADS)

McDaniel, J. Gregory; Akhatov, Iskander; Holt, R. Glynn

2002-06-01

Motivated by recent experiments involving the acoustic levitation of foam drops, we develop a model for nonlinear oscillations of a spherical drop composed of monodisperse aqueous foam with void fraction below 0.1. The model conceptually divides a foam drop into many cells, each cell consisting of a spherical volume of liquid with a bubble at its center. By treating the liquid as incompressible and inviscid, a nonlinear equation is obtained for bubble motion due to a pressure applied at the outer radius of the liquid sphere. Upon linearizing this equation and connecting the cells at their outer radii, a wave equation is obtained with a dispersion relation for the sound waves in a bubbly liquid. For the spherical drop, this equation is solved by a normal mode expansion that yields the natural frequencies as functions of standard foam parameters. Numerical examples illustrate how the analysis may be used to extract foam parameters, such as void fraction and bubble radius, from the experimentally measured natural frequencies of a foam drop.

Variational extension of the mean spherical approximation to arbitrary dimensions

NASA Astrophysics Data System (ADS)

Velázquez, Esov S.; Blum, Lesser; Frisch, Harry L.

1997-10-01

We generalize a variational principle for the mean spherical approximation for a system of charged hard spheres in 3D to arbitrary dimensions. We first construct a free energy variational trial function from the Debye-Hückel excess charging internal energy at a finite concentration and an entropy obtained at the zero-concentration limit by thermodynamic integration. In three dimensions the minimization of this expression with respect to the screening parameter leads to the mean spherical approximation, usually obtained by solution of the Ornstein-Zernike equation. This procedure, which interpolates naturally between the zero concentration/coupling limit and the high-concentration/ coupling limit, is extended to arbitrary dimensions. We conjecture that this result is also equivalent to the MSA as originally defined, although a technical proof of this point is left for the future. The Onsager limit T ΔS MSA / ΔE MSA → 0 for infinite concentration/coupling is satisfied for all d ≠ 2, while for d=2 this limit is 1.

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.

Wigner functions for nonclassical states of a collection of two-level atoms

NASA Technical Reports Server (NTRS)

Agarwal, G. S.; Dowling, Jonathan P.; Schleich, Wolfgang P.

1993-01-01

The general theory of atomic angular momentum states is used to derive the Wigner distribution function for atomic angular momentum number states, coherent states, and squeezed states. These Wigner functions W(theta,phi) are represented as a pseudo-probability distribution in spherical coordinates theta and phi on the surface of a sphere of radius the square root of j(j +1) where j is the total angular momentum.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-07-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in a closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2017a) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Spectroscopic studies on some fluorescent mixed-ligand titanium(IV) complexes.

PubMed

Baranwal, Balram Prasad; Singh, Alok Kumar; Varma, Anand

2011-12-15

A novel route to synthesize some titanium(IV) complexes containing acetylacetone, straight chain carboxylic acid and hydroxycarboxylic acid ligands has been investigated. Complexes with the general formula [Ti(acac)Cl(2-n)(OOCR*)(n)(OOCC(15)H(31))] (where Hacac=acetylacetone, R*COOH=hydroxycarboxylic acids and n=1 or 2) have been isolated and characterized. Molecular weight determinations indicated mononuclear nature of the complexes. LMCT bands were observed in the electronic spectra. Infrared spectra suggested bidentate nature of the ligands. Fluorescent behaviour of the complexes was noticed on the basis of fluorescence spectra. Powder XRD indicated them to be semi-crystalline having the crystallite size in 136-185 nm range. Transmission electron microscopy (TEM) indicated spherical particles of ~ 200 nm diameter. On the basis of physico-chemical studies, it is suggested that titanium is having coordination number 7 or 8 in these complexes. Copyright © 2011 Elsevier B.V. All rights reserved.

A two-parameter family of double-power-law biorthonormal potential-density expansions

NASA Astrophysics Data System (ADS)

Lilley, Edward J.; Sanders, Jason L.; Evans, N. Wyn

2018-05-01

We present a two-parameter family of biorthonormal double-power-law potential-density expansions. Both the potential and density are given in closed analytic form and may be rapidly computed via recurrence relations. We show that this family encompasses all the known analytic biorthonormal expansions: the Zhao expansions (themselves generalizations of ones found earlier by Hernquist & Ostriker and by Clutton-Brock) and the recently discovered Lilley et al. (2018b) expansion. Our new two-parameter family includes expansions based around many familiar spherical density profiles as zeroth-order models, including the γ models and the Jaffe model. It also contains a basis expansion that reproduces the famous Navarro-Frenk-White (NFW) profile at zeroth order. The new basis expansions have been found via a systematic methodology which has wide applications in finding other new expansions. In the process, we also uncovered a novel integral transform solution to Poisson's equation.

Lattice-free prediction of three-dimensional structure of programmed DNA assemblies

PubMed Central

Pan, Keyao; Kim, Do-Nyun; Zhang, Fei; Adendorff, Matthew R.; Yan, Hao; Bathe, Mark

2014-01-01

DNA can be programmed to self-assemble into high molecular weight 3D assemblies with precise nanometer-scale structural features. Although numerous sequence design strategies exist to realize these assemblies in solution, there is currently no computational framework to predict their 3D structures on the basis of programmed underlying multi-way junction topologies constrained by DNA duplexes. Here, we introduce such an approach and apply it to assemblies designed using the canonical immobile four-way junction. The procedure is used to predict the 3D structure of high molecular weight planar and spherical ring-like origami objects, a tile-based sheet-like ribbon, and a 3D crystalline tensegrity motif, in quantitative agreement with experiments. Our framework provides a new approach to predict programmed nucleic acid 3D structure on the basis of prescribed secondary structure motifs, with possible application to the design of such assemblies for use in biomolecular and materials science. PMID:25470497

Screening of the chemical reactivity of three different graphite sources using the formation of reductively alkylated graphene as a model reaction.

PubMed

Knirsch, Kathrin C; Englert, Jan M; Dotzer, Christoph; Hauke, Frank; Hirsch, Andreas

2013-11-28

Reductive alkylation of three graphite starting materials G(flake), G(powder), and G(spherical) reveals pronounced differences in the obtained covalently functionalized graphene with respect to the degree of functionalization, exfoliation efficiency and product homogeneity, as demonstrated by statistical Raman microscopy (SRM), TGA/MS, IR-spectroscopy and solubility behavior.

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…

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

Karbanovski, V. V., E-mail: Karbanovski_V_V@mail.ru; Sorokin, O. M.; Nesterova, M. I.

The system of the spherical-symmetric vacuum equations of the General Relativity Theory is considered. The general solution to a problem representing two classes of line elements with arbitrary functions g{sub 00} and g{sub 22} is obtained. The properties of the found solutions are analyzed.

Impact-generated dust clouds around planetary satellites: asymmetry effects

NASA Astrophysics Data System (ADS)

Sremčević, Miodrag; Krivov, Alexander V.; Spahn, Frank

2003-06-01

In a companion paper (Krivov et al., Impact-generated dust clouds around planetary satellites: spherically symmetric case, Planet. Space. Sci. 2003, 51, 251-269) an analytic model of an impact-generated, steady-state, spherically symmetric dust cloud around an atmosphereless planetary satellite (or planet - Mercury, Pluto) has been developed. This paper lifts the assumption of spherical symmetry and focuses on the asymmetry effects that result from the motion of the parent body through an isotropic field of impactors. As in the spherically symmetric case, we first consider the dust production from the surface and then derive a general phase-space distribution function of the ensemble of ejected dust motes. All quantities of interest, such as particle number densities and fluxes, can be obtained by integrating this phase-space distribution function. As an example, we calculate an asymmetric distribution of dust number density in a cloud. It is found that the deviation from the symmetric case can be accurately described by a cosine function of the colatitude measured from the apex of the satellite motion. This property of the asymmetry is rather robust. It is shown that even an extremely asymmetric dust production at the surface, when nearly all dust is ejected from the leading hemisphere, turns rapidly into the cosine modulation of the number density at distances larger than a few satellite radii. The amplitude of the modulation depends on the ratio of the moon orbital velocity to the speed of impactors and on the initial angular distribution of the ejecta. Furthermore, regardless of the functional form of the initial angular distribution, the number density distribution of the dust cloud is only sensitive to the mean ejecta angle. When the mean angle is small - ejection close to the normal of the surface - the initial dust production asymmetry remains persistent even far from the satellite, but when this angle is larger than about 45°, the asymmetry coefficient drops very rapidly with the increasing distance. The dependence of the asymmetric number density on other parameters is very weak. On the whole, our results provide necessary theoretical guidelines for a dedicated quest of asymmetries in the dust detector data, both those obtained by the Galileo dust detector around the Galilean satellites of Jupiter and those expected from the Cassini dust experiment around outer Saturnian moons.

Biomimetic shoulder complex based on 3-PSS/S spherical parallel mechanism

NASA Astrophysics Data System (ADS)

Hou, Yulei; Hu, Xinzhe; Zeng, Daxing; Zhou, Yulin

2015-01-01

The application of the parallel mechanism is still limited in the humanoid robot fields, and the existing parallel humanoid robot joint has not yet been reflected the characteristics of the parallel mechanism completely, also failed to solve the problem, such as small workspace, effectively. From the structural and functional bionic point of view, a three degrees of freedom(DOFs) spherical parallel mechanism for the shoulder complex of the humanoid robot is presented. According to the structure and kinetic characteristics analysis of the human shoulder complex, 3-PSS/S(P for prismatic pair, S for spherical pair) is chosen as the original configuration for the shouder complex. Using genetic algorithm, the optimization of the 3-PSS/S spherical parallel mechanism is performed, and the orientation workspace of the prototype mechanism is enlarged obviously. Combining the practical structure characteristics of the human shouder complex, an offset output mode, which means the output rod of the mechanism turn to any direction at the point a certain distance from the rotation center of the mechanism, is put forward, which provide possibility for the consistent of the workspace of the mechanism and the actual motion space of the human body shoulder joint. The relationship of the attitude angles between different coordinate system is derived, which establishs the foundation for the motion descriptions under different conditions and control development. The 3-PSS/S spherical parallel mechanism is proposed for the shoulder complex, and the consistence of the workspace of the mechanism and the human shoulder complex is realized by the stuctural parameter optimization and the offset output design.

In vitro comparative optical bench analysis of a spherical and aspheric optic design of the same IOL model.

PubMed

Tandogan, Tamer; Auffarth, Gerd U; Choi, Chul Y; Liebing, Stephanie; Mayer, Christian; Khoramnia, Ramin

2017-02-08

To analyse objective optical properties of the spherical and aspheric design of the same intraocular lens (IOL) model using optical bench analysis. This study entailed a comparative analysis of 10 spherical C-flex 570 C and 10 aspheric C-flex 970 C IOLs (Rayner Intraocular Lenses Ltd., Hove, UK) of 26 diopters [D] using an optical bench (OptiSpheric, Trioptics, Germany). In all lenses, we evaluated the modulation transfer function (MTF) at 50 lp/mm and 100 lp/mm and the Strehl Ratio using a 3-mm (photopic) and 4.5-mm (mesopic) aperture. At 50 lp/mm, the MTF values were 0.713/0.805 (C-flex 570 C/C-flex 970 C) for a 3-mm aperture and 0.294/0.591 for a 4.5-mm aperture. At 100 lp/mm, the MTF values were 0.524/0.634 for a 3-mm aperture and 0.198/0.344 for a 4.5-mm aperture. The Strehl Ratio was 0.806/0.925 and 0.237/0.479 for a 3-mm and 4.5-mm aperture respectively. A Mann-Whitney U test revealed all intergroup differences to be statistically significant (p < 0.01). The aspheric IOL design achieved higher MTF values than the spherical design of the same IOL for both apertures. Moreover, the differences between the two designs of the IOL were more prominent for larger apertures. This suggests that the evaluated IOL provides enhanced optical quality to patients with larger pupils or working under mesopic conditions.

Contact lens design with slope-constrained Q-type aspheres for myopia correction

NASA Astrophysics Data System (ADS)

Peng, Wei-Jei; Cheng, Yuan-Chieh; Hsu, Wei-Yao; Yu, Zong-Ru; Ho, Cheng-Fang; Abou-El-Hossein, Khaled

2017-08-01

The design of the rigid contact lens (CL) with slope-constrained Q-type aspheres for myopia correction is presented in this paper. The spherical CL is the most common type for myopia correction, however the spherical aberration (SA) caused from the pupil dilation in dark leads to the degradation of visual acuity which cannot be corrected by spherical surface. The spherical and aspheric CLs are designed respectively based on Liou's schematic eye model, and the criterion is the modulation transfer function (MTF) at the frequency of 100 line pair per mm, which corresponds to the normal vision of one arc-minute. After optimization, the MTF of the aspheric design is superior to that of the spherical design, because the aspheric surface corrects the SA for improving the visual acuity in dark. For avoiding the scratch caused from the contact profilometer, the aspheric surface is designed to match the measurability of the interferometer. The Q-type aspheric surface is employed to constrain the root-mean-square (rms) slope of the departure from a best-fit sphere directly, because the fringe density is limited by the interferometer. The maximum sag departure from a best-fit sphere is also controlled according to the measurability of the aspheric stitching interferometer (ASI). The inflection point is removed during optimization for measurability and appearance. In this study, the aspheric CL is successfully designed with Q-type aspheres for the measurability of the interferometer. It not only corrects the myopia but also eliminates the SA for improving the visual acuity in dark based on the schematic eye model.

Dynamical density functional theory for arbitrary-shape colloidal fluids including inertia and hydrodynamic interactions

NASA Astrophysics Data System (ADS)

Duran-Olivencia, Miguel A.; Goddard, Ben; Kalliadasis, Serafim

2015-11-01

Over the last few decades the classical density-functional theory (DFT) and its dynamic extensions (DDFTs) have become a remarkably powerful tool in the study of colloidal fluids. Recently there has been extensive research to generalise all previous DDFTs finally yielding a general DDFT equation (for spherical particles) which takes into account both inertia and hydrodynamic interactions (HI) which strongly influence non-equilibrium properties. The present work will be devoted to a further generalisation of such a framework to systems of anisotropic particles. To this end, the kinetic equation for the Brownian particle distribution function is derived starting from the Liouville equation and making use of Zwanzig's projection-operator techniques. By averaging over all but one particle, a DDFT equation is finally obtained with some similarities to that for spherical colloids. However, there is now an inevitable translational-rotational coupling which affects the diffusivity of asymmetric particles. Lastly, in the overdamped (high friction) limit the theory is notably simplified leading to a DDFT equation which agrees with previous derivations. We acknowledge financial support from European Research Council via Advanced Grant No. 247031.

Collapsing shells and black holes: a quantum analysis

NASA Astrophysics Data System (ADS)

Leal, P.; Bernardini, A. E.; Bertolami, O.

2018-06-01

The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. This shell is considered to be inside a black hole event horizon. The encountered properties are investigated making use of the Israel junction conditions on the shell, considering that it is the boundary between two spherically symmetric spacetimes. Using this method, and considering two different Kantowski–Sachs spacetimes as a representation for the Schwarzschild spacetime, the relevant quantities on the shell are computed, such as its stress-energy tensor and the action for the whole spacetime. From the obtained action, the Wheeler–deWitt equation is deduced in order to provide the quantum framework for the system. Solutions for the wave function of the system are found on both the commutative and NC scenarios. It is shown that, on the commutative version, the wave function has a purely oscillatory behavior in the interior of the shell. In the NC setting, it is shown that the wave function vanishes at the singularity, as well as, at the event horizon of the black hole.

Determination of many-electron basis functions for a quantum Hall ground state using Schur polynomials

NASA Astrophysics Data System (ADS)

Mandal, Sudhansu S.; Mukherjee, Sutirtha; Ray, Koushik

2018-03-01

A method for determining the ground state of a planar interacting many-electron system in a magnetic field perpendicular to the plane is described. The ground state wave-function is expressed as a linear combination of a set of basis functions. Given only the flux and the number of electrons describing an incompressible state, we use the combinatorics of partitioning the flux among the electrons to derive the basis wave-functions as linear combinations of Schur polynomials. The procedure ensures that the basis wave-functions form representations of the angular momentum algebra. We exemplify the method by deriving the basis functions for the 5/2 quantum Hall state with a few particles. We find that one of the basis functions is precisely the Moore-Read Pfaffian wave function.

Meshless Local Petrov-Galerkin Euler-Bernoulli Beam Problems: A Radial Basis Function Approach

NASA Technical Reports Server (NTRS)

Raju, I. S.; Phillips, D. R.; Krishnamurthy, T.

2003-01-01

A radial basis function implementation of the meshless local Petrov-Galerkin (MLPG) method is presented to study Euler-Bernoulli beam problems. Radial basis functions, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as in the conventional MLPG method. Compactly and noncompactly supported radial basis functions are considered. The non-compactly supported cubic radial basis function is found to perform very well. Results obtained from the radial basis MLPG method are comparable to those obtained using the conventional MLPG method for mixed boundary value problems and problems with discontinuous loading conditions.