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This slide-show discusses the use of the Local Polynomial Approximation (LPA) to smooth signals from photonic Doppler velocimetry (PDV) applying a generalized Peano kernel theorem.
We investigate the exercise of locally extracting the real and imaginary parts of the four twist-2 Compton form factors (CFFs) {$\mathcal{H,E,\tilde H,\tilde E}$} which arise in the deeply virtual Compton scattering (DVCS) process e + p → e + p + y. Neglecting dynamical higher-twist contributions, we find that there are a sufficient number of DVCS observables and degrees of freedom to extract all 8 leading quantities model-independently, exploiting the azimuthal dependence of the absolute cross sections across all possible beam and target polarizations at a common kinematical point in {Q, t,x b , y}. As an example, for typical JLab lab-frame kinematics, we simplify the reduced DVCS observables to their dominant terms, providing a sufficient number of equations for local determination of the twist-2 CFFs. We demonstrate the feasibility using harmonic fitting to both cross sections and beam spin asymmetries with both real and pseudo-data.
Order contamination in soft x-ray beamline is a severe problem which poses difficulty in various analysis techniques. Generally grating analyzer is used to estimate the higher order contribution where poor knowledge of wall and land roughness contribution makes it difficult to get theoretical fit and so analysis gives qualitative estimation only. Here we demonstrate the application of multilayer mirror for accurate determination of order contamination in Toroidal grating monochromator (TGM) at reflectivity beamline of Indus-1. We used a Mo/Si multilayer of d{approx}100Aa period to quantify 2{sup nd} and 3{sup rd} order composition to identify order contamination below 0.5% or better.
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A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented.
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Frequency conversion theory with charge-storage diode, using Fourier harmonic analysis
Previously collected data on atmospheric pressure, density, temperature and winds between 25 and 200 km from sources including Meteorological Rocket Network data, ROBIN falling sphere data, grenade release and pitot tube data, meteor winds, chemical release winds, satellite data, and others were analyzed by a daily difference method and results on the distribution statistics, magnitude, and spatial structure of gravity wave and planetary wave atmospheric variations are presented. Time structure of the gravity wave variations were determined by the analysis of residuals from harmonic analysis of time series data. Planetary wave contributions in the 25-85 km range were discovered and found to have significant height and latitudinal variation. Long period planetary waves, and seasonal variations were also computed by harmonic analysis. Revised height variations of the gravity wave contributions in the 25 to 85 km height range were computed. An engineering method and design values for gravity wave magnitudes and wave lengths are given to be used for such tasks as evaluating the effects on the dynamical heating, stability and control of spacecraft such as the space shuttle vehicle in launch or reentry trajectories.
An advanced higher harmonic control (HHC) analysis has been developed and applied to investigate its effect on vibration reduction levels, blade and control system fatigue loads, rotor performance, and power requirements of servo-actuators. The analysis is based on a finite element method in space and time. A nonlinear time domain unsteady aerodynamic model, based on the indicial response formulation, is used to calculate the airloads. The rotor induced inflow is computed using a free wake model. The vehicle trim controls and blade steady responses are solved as one coupled solution using a modified Newton method. A linear frequency-domain quasi-steady transfer matrix is used to relate the harmonics of the vibratory hub loads to the harmonics of the HHC inputs. Optimal HHC is calculated from the minimization of the vibratory hub loads expressed in term of a quadratic performance index. Predicted vibratory hub shears are correlated with wind tunnel data. The fixed-gain HHC controller suppresses completely the vibratory hub shears for most of steady or quasi-steady flight conditions. HHC actuator amplitudes and power increase significantly at high forward speeds (above 100 knots). Due to the applied HHC, the blade torsional stresses and control loads are increased substantially. For flight conditions where the blades are stalled considerably, the HHC input-output model is quite nonlinear. For such cases, the adaptive-gain controller is effective in suppressing vibratory hub loads, even though HHC may actually increase stall areas on the rotor disk. The fixed-gain controller performs poorly for such flight conditions. Comparison study of different rotor systems indicates that a soft-inplane hingeless rotor requires less actuator power at high speeds (above 130 knots) than an articulated rotor, and a stiff-inplane hingeless rotor generally requires more actuator power than an articulated or a soft-inplane hingeless rotor. Parametric studies for a hingeless rotor operating in a transition flight regime and for an articulated rotor operating at the level-flight boundary (high speed and high thrust conditions) indicate that blade parameters including flap, lag, torsion stiffness distributions, linear pretwist, chordwise offset of center-of-mass from elastic axis and chordwise offset of elastic axis from aerodynamic center can be selected to minimize the actuator power requirements for HHC.
An optimum truncation level, N, in a spherical-harmonic analysis of the geomagnetic main field at the core-mantle boundary is determined by harmonic-spline analysis. Specifically, that value of N is found at which the two analyses are closest in a well defined sense and, for that value of N, the 'closeness' of two models is determined. Depending slightly on the definition of closeness, optimum N is found to be either 10 or 11. For those values the two analyses give remarkably similar results, showing that the conveniences of spherical harmonics can be retained with little penalty.
Purpose: To first demonstrate the viability of applying an image processing technique for tracking regions on low-contrast cine-MR images acquired during image-guided radiation therapy, and then outline a scheme that uses tracking data for optimizing gating results in a patient-specific manner. Methods: A first-generation MR-IGRT system—treating patients since January 2014—integrates a 0.35 T MR scanner into an annular gantry consisting of three independent Co-60 sources. Obtaining adequate frame rates for capturing relevant patient motion across large fields-of-view currently requires coarse in-plane spatial resolution. This study initially (1) investigate the feasibility of rapidly tracking dense pixel correspondences across single, sagittal plane images (with both moderate signal-to-noise and spatial resolution) using a matching objective for highly descriptive vectors called scale-invariant feature transform (SIFT) descriptors associated to all pixels that describe intensity gradients in local regions around each pixel. To more accurately track features, (2) harmonic analysis was then applied to all pixel trajectories within a region-of-interest across a short training period. In particular, the procedure adjusts the motion of outlying trajectories whose relative spectral power within a frequency bandwidth consistent with respiration (or another form of periodic motion) does not exceed a threshold value that is manually specified following the training period. To evaluate the tracking reliability after applying this correction, conventional metrics—including Dice similarity coefficients (DSCs), mean tracking errors (MTEs), and Hausdorff distances (HD)—were used to compare target segmentations obtained via tracking to manually delineated segmentations. Upon confirming the viability of this descriptor-based procedure for reliably tracking features, the study (3) outlines a scheme for optimizing gating parameters—including relative target position and a tolerable margin about this position—derived from a probability density function that is constructed using tracking results obtained just prior to treatment. Results: The feasibility of applying the matching objective for SIFT descriptors toward pixel-by-pixel tracking on cine-MR acquisitions was first retrospectively demonstrated for 19 treatments (spanning various sites). Both with and without motion correction based on harmonic analysis, sub-pixel MTEs were obtained. A mean DSC value spanning all patients of 0.916 ± 0.001 was obtained without motion correction, with DSC values exceeding 0.85 for all patients considered. While most patients show accurate tracking without motion correction, harmonic analysis does yield substantial gain in accuracy (defined using HDs) for three particularly challenging subjects. An application of tracking toward a gating optimization procedure was then demonstrated that should allow a physician to balance beam-on time and tissue sparing in a patient-specific manner by tuning several intuitive parameters. Conclusions: Tracking results show high fidelity in assessing intrafractional motion observed on cine-MR acquisitions. Incorporating harmonic analysis during a training period improves the robustness of the tracking for challenging targets. The concomitant gating optimization procedure should allow for physicians to quantitatively assess gating effectiveness quickly just prior to treatment in a patient-specific manner.