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At least 1,171 records · Page 65

Structure and Rotation of the Solar Interior: Initial Results from the MDI Medium-L Program

The medium-l program of the Michelson Doppler Imager instrument on board SOHO provides continuous observations of oscillation modes of angular degree, l, from 0 to approximately 300. The data for the program are partly processed on board because only about 3% of MDI observations can be transmitted continuously to the ground. The on-board data processing, the main component of which is Gaussian-weighted binning, has been optimized to reduce the negative influence of spatial aliasing of the high-degree oscillation modes. The data processing is completed in a data analysis pipeline at the SOI Stanford Support Center to determine the mean multiplet frequencies and splitting coefficients. The initial results show that the noise in the medium-l oscillation power spectrum is substantially lower than in ground-based measurements. This enables us to detect lower amplitude modes and, thus, to extend the range of measured mode frequencies. This is important for inferring the Sun's internal structure and rotation. The MDI observations also reveal the asymmetry of oscillation spectral lines. The line asymmetries agree with the theory of mode excitation by acoustic sources localized in the upper convective boundary layer. The sound-speed profile inferred from the mean frequencies gives evidence for a sharp variation at the edge of the energy-generating core. The results also confirm the previous finding by the GONG (Gough et al., 1996) that, in a thin layer just beneath the convection zone, helium appears to be less abundant than predicted by theory. Inverting the multiplet frequency splittings from MDI, we detect significant rotational shear in this thin layer. This layer is likely to be the place where the solar dynamo operates. In order to understand how the Sun works, it is extremely important to observe the evolution of this transition layer throughout the 11-year activity cycle.

Kosovichev, A. G.↗

Diffusive dynamics of nanoparticles in ultra-confined media

Differential dynamic microscopy (DDM) was used to investigate the diffusive dynamics of nanoparticles of diameter 200 400 nm that were strongly confined in a periodic square array of cylindrical nanoposts. The minimum distance between posts was 1.3 5 times the diameter of the nanoparticles. The image structure functions obtained from the DDM analysis were isotropic and could be fit by a stretched exponential function. The relaxation time scaled diffusively across the range of wave vectors studied, and the corresponding scalar diffusivities decreased monotonically with increased confinement. The decrease in diffusivity could be described by models for hindered diffusion that accounted for steric restrictions and hydrodynamic interactions. The stretching exponent decreased linearly as the nanoparticles were increasingly confined by the posts. Altogether, these results are consistent with a picture in which strongly confined nanoparticles experience a heterogeneous spatial environment arising from hydrodynamics and volume exclusion on time scales comparable to cage escape, leading to multiple relaxation processes and Fickian but non-Gaussian diffusive dynamics.

36 MATERIALS SCIENCE↗

Selecting registration schemes in case of interstitial lung disease follow-up in CT

Purpose: Primary goal of this study is to select optimal registration schemes in the framework of interstitial lung disease (ILD) follow-up analysis in CT. Methods: A set of 128 multiresolution schemes composed of multiresolution nonrigid and combinations of rigid and nonrigid registration schemes are evaluated, utilizing ten artificially warped ILD follow-up volumes, originating from ten clinical volumetric CT scans of ILD affected patients, to select candidate optimal schemes. Specifically, all combinations of four transformation models (three rigid: rigid, similarity, affine and one nonrigid: third order B-spline), four cost functions (sum-of-square distances, normalized correlation coefficient, mutual information, and normalized mutual information), four gradient descent optimizers (standard, regular step, adaptive stochastic, and finite difference), and two types of pyramids (recursive and Gaussian-smoothing) were considered. The selection process involves two stages. The first stage involves identification of schemes with deformation field singularities, according to the determinant of the Jacobian matrix. In the second stage, evaluation methodology is based on distance between corresponding landmark points in both normal lung parenchyma (NLP) and ILD affected regions. Statistical analysis was performed in order to select near optimal registration schemes per evaluation metric. Performance of the candidate registration schemes was verified on a case sample of ten clinical follow-up CT scans to obtain the selected registration schemes. Results: By considering near optimal schemes common to all ranking lists, 16 out of 128 registration schemes were initially selected. These schemes obtained submillimeter registration accuracies in terms of average distance errors 0.18 ± 0.01 mm for NLP and 0.20 ± 0.01 mm for ILD, in case of artificially generated follow-up data. Registration accuracy in terms of average distance error in clinical follow-up data was in the range of 1.985–2.156 mm and 1.966–2.234 mm, for NLP and ILD affected regions, respectively, excluding schemes with statistically significant lower performance (Wilcoxon signed-ranks test, p < 0.05), resulting in 13 finally selected registration schemes. Conclusions: Selected registration schemes in case of ILD CT follow-up analysis indicate the significance of adaptive stochastic gradient descent optimizer, as well as the importance of combined rigid and nonrigid schemes providing high accuracy and time efficiency. The selected optimal deformable registration schemes are equivalent in terms of their accuracy and thus compatible in terms of their clinical outcome.

60 APPLIED LIFE SCIENCES↗

Some new results on the statistics of radio wave scintillation. I - Empirical evidence for Gaussian statistics

This paper presents an analysis of ionospheric scintillation data which shows that the underlying statistical structure of the signal can be accurately modeled by the additive complex Gaussian perturbation predicted by the Born approximation in conjunction with an application of the central limit theorem. By making use of this fact, it is possible to estimate the in-phase, phase quadrature, and cophased scattered power by curve fitting to measured intensity histograms. By using this procedure, it is found that typically more than 80% of the scattered power is in phase quadrature with the undeviated signal component. Thus, the signal is modeled by a Gaussian, but highly non-Rician process. From simultaneous UHF and VHF data, only a weak dependence of this statistical structure on changes in the Fresnel radius is deduced. The signal variance is found to have a nonquadratic wavelength dependence. It is hypothesized that this latter effect is a subtle manifestation of locally homogeneous irregularity structures, a mathematical model proposed by Kolmogorov (1941) in his early studies of incompressible fluid turbulence.

Rino, C. L.↗

Linear feedback rate bounds for regressive channels

Bounds for the linear feedback capacity of m-th order Gaussian autoregressive channels are derived. The upper bound is tighter than that found by Tiernan and Schalwijk (1974) for the feedback capacity of a first-order autoregressive Gaussian channel with not necessarily linear processing. The separation between the upper and lower bounds is small, and it is conjectured that the lower bound converges to the feedback capacity of the first-order channel as the number of signals tends to infinity.

Butman, S. A.↗

Statistical geometry of a small surface patch in a developed sea

The fractal and marginal fractal regimes in surface geometry are studied. The basic notions of fractal geometry are applied to a small surface patch in a developed sea, corresponding to the equilibrium wave number spectrum. Topothesy, outer and inner boundaries of the fractal range, and a cascade pattern in surface geometry are discussed. Theoretical predictions of whitecap and foam coverage are presented. A fractal decomposition for a surface patch is developed based on the Karhunen-Loeve expansion. The resulting series formalizes the cascade process of constructing realization of a Gaussian random patch. The implications of the research for microwave remote sensing signatures are considered.

Glazman, Roman E.↗

Efficient computer algebra algorithms for polynomial matrices in control design

The theory of polynomial matrices plays a key role in the design and analysis of multi-input multi-output control and communications systems using frequency domain methods. Examples include coprime factorizations of transfer functions, cannonical realizations from matrix fraction descriptions, and the transfer function design of feedback compensators. Typically, such problems abstract in a natural way to the need to solve systems of Diophantine equations or systems of linear equations over polynomials. These and other problems involving polynomial matrices can in turn be reduced to polynomial matrix triangularization procedures, a result which is not surprising given the importance of matrix triangularization techniques in numerical linear algebra. Matrices with entries from a field and Gaussian elimination play a fundamental role in understanding the triangularization process. In the case of polynomial matrices, matrices with entries from a ring for which Gaussian elimination is not defined and triangularization is accomplished by what is quite properly called Euclidean elimination. Unfortunately, the numerical stability and sensitivity issues which accompany floating point approaches to Euclidean elimination are not very well understood. New algorithms are presented which circumvent entirely such numerical issues through the use of exact, symbolic methods in computer algebra. The use of such error-free algorithms guarantees that the results are accurate to within the precision of the model data--the best that can be hoped for. Care must be taken in the design of such algorithms due to the phenomenon of intermediate expressions swell.

Baras, J. S.↗

Quantitative estimation of granitoid composition from thermal infrared multispectral scanner (TIMS) data, Desolation Wilderness, northern Sierra Nevada, California

We have produced images that quantitatively depict modal and chemical parameters of granitoids using an image processing algorithm called MINMAP that fits Gaussian curves to normalized emittance spectra recovered from thermal infrared multispectral scanner (TIMS) radiance data. We applied the algorithm to TIMS data from the Desolation Wilderness, an extensively glaciated area near the northern end of the Sierra Nevada batholith that is underlain by Jurassic and Cretaceous plutons that range from diorite and anorthosite to leucogranite. The wavelength corresponding to the calculated emittance minimum lambda(sub min) varies linearly with quartz content, SiO2, and other modal and chemical parameters. Thematic maps of quartz and silica content derived from lambda(sub min) values distinguish bodies of diorite from surrounding granite, identify outcrops of anorthosite, and separate felsic, intermediate, and mafic rocks.

Sabine, Charles↗

Improved Gaussian Beam-Scattering Algorithm

The localized model of the beam-shape coefficients for Gaussian beam-scattering theory by a spherical particle provides a great simplification in the numerical implementation of the theory. We derive an alternative form for the localized coefficients that is more convenient for computer computations and that provides physical insight into the details of the scattering process. We construct a FORTRAN program for Gaussian beam scattering with the localized model and compare its computer run time on a personal computer with that of a traditional Mie scattering program and with three other published methods for computing Gaussian beam scattering. We show that the analytical form of the beam-shape coefficients makes evident the fact that the excitation rate of morphology-dependent resonances is greatly enhanced for far off-axis incidence of the Gaussian beam.

Lock, James A.↗

General mechanism for producing scale-invariant perturbations and small non-Gaussianity in ekpyrotic models

We explore a new type of entropic mechanism for generating density perturbations in a contracting phase in which there are two scalar fields, but only one has a steep negative potential. This first field dominates the energy density and is the source of the ekpyrotic equation of state. The second field has a negligible potential, but its kinetic energy density is coupled to the first field with a non-linear sigma-model type interaction. We show that for any ekpyrotic equation of state it is possible to choose the potential and the kinetic coupling such that exactly scale-invariant (or nearly scale-invariant) entropy perturbations are produced. The corresponding background solutions are stable, and the bispectrum of the entropy perturbations vanishes as no non-Gaussianity is produced during the ekpyrotic phase. Finally, the only contribution to non-Gaussianity comes from the non-linearity of the conversion process during which entropic perturbations are turned into adiabatic ones, resulting in a local non-Gaussianity parameter f NL ~5.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Signal sequence detection given noisy, common background image sets.

The optimum processing (likelihood functional) is found for a set of M images, each the sum of a member of a signal sequence due to an object to be detected and its parameters estimated, a sample function of a noise field, and a sample function of a common background field. The noise fields are independent, zero mean, white Gaussian fields, all independent of the background field. The latter is assumed to be either (1) completely unknown or of known mean and covariance functions with (2) a certain fluctuation property or (3) Gaussian. Three equivalent forms of the optimum processing are found: (1) a summation of generalized matched filterings of the images, (2) a summation of matched filtering of certain generalized differences of the images, and (3) a summation of 'estimator-correlator' type filterings. The detection performance and optimum signal/image selection under the Neyman-Pearson criterion is given, and is shown that optimum processor and signal design can completely eliminate any effect of the background on detectability.

Harger, R. O.↗

Lattice thermal conductivity of filled skutterudites: An anharmonicity perspective

We report a phenomenological model to calculate the high-temperature lattice thermal conductivity of filled skutterudite antimonides. The model needs no phonon resonant scattering terms. Instead, we assume that umklapp processes dominate the high-temperature phonon scattering. In order to represent the anharmonicity introduced by the filling atom, we introduce a Gaussian term into the relaxation time of the umklapp process. The developed model agrees remarkably well with the experimental results of RE{sub f}Co{sub 4}Sb{sub 12} and RE{sub f}Fe{sub 4}Sb{sub 12} (RE = Yb, Ba, and Ca) alloys. To further test the validity of our model, we calculate the lattice thermal conductivity of nanostructured or multi-filled skutterudites. The calculation results are also in good agreement with experiment, increasing our confidence in the developed anharmonicity model.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Spatiotemporal dynamics of Gaussian laser pulse in a multi ions plasma

Spatiotemporal evolutions of Gaussian laser pulse propagating through a plasma with multiple charged ions are studied, taking into account the ponderomotive nonlinearity. Coupled differential equations for beam width and pulse length parameters are established and numerically solved using paraxial ray approximation. In one-dimensional geometry, effects of laser and plasma parameters such as laser intensity, plasma density, and temperature on the longitudinal pulse compression and the laser intensity distribution are analyzed for plasmas with singly and doubly charged ions. The results demonstrate that self-compression occurs in a laser intensity range with a turning point intensity in which the self-compression process has its strongest extent. The results also show that the multiply ionized ions have different effect on the pulse compression above and below turning point intensity. Finally, three-dimensional geometry is used to analyze the simultaneous evolution of both self-focusing and self-compression of Gaussian laser pulse in such plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Discrete Approximations of Determinantal Point Processes on Continuous Spaces: Tree Representations and Tail Triviality

We prove tail triviality of determinantal point processes μ on continuous spaces. Tail triviality has been proved for such processes only on discrete spaces, and hence we have generalized the result to continuous spaces. To do this, we construct tree representations, that is, discrete approximations of determinantal point processes enjoying a determinantal structure. There are many interesting examples of determinantal point processes on continuous spaces such as zero points of the hyperbolic Gaussian analytic function with Bergman kernel, and the thermodynamic limit of eigenvalues of Gaussian random matrices for Sine{sub 2},Airy{sub 2},Bessel{sub 2}, and Ginibre point processes. Our main theorem proves all these point processes are tail trivial.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An unsupervised machine-learning checkpoint-restart algorithm using Gaussian mixtures for particle-in-cell simulations

We propose an unsupervised machine-learning checkpoint-restart (CR) algorithm for particle-in-cell (PIC) algorithms using Gaussian mixtures (GM). The algorithm compresses the particle population per spatial cell by constructing a velocity distribution function using GM. Particles are reconstructed at restart time by local resampling of the Gaussians. To guarantee fidelity of the CR process, we ensure the exact preservation of invariants such as charge, momentum, and energy for both compression and reconstruction stages, everywhere on the mesh. We also ensure the preservation of Gauss' law after particle reconstruction by exactly matching the density profile at restart time. As a result, the GM CR algorithm is shown to provide a clean, conservative restart capability while potentially affording orders of magnitude savings in input/output requirements. Here, we demonstrate the algorithm using a recently developed exactly energy- and charge-conserving PIC algorithm using both electrostatic and electromagnetic tests. The tests demonstrate not only a high-fidelity CR capability, but also its potential for enhancing the fidelity of the PIC solution for a given particle resolution.

97 MATHEMATICS AND COMPUTING↗