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Oscillatory properties of linear matrix differential system, applying generalization of polar coordinate transformation to certain systems of second order
High-performance spotlight Synthetic Aperture Radar (SAR) requires measurement of the radars motion during the synthetic aperture. A convenient coordinate frame for motion measurement is often not the convenient coordinate frame for motion compensation during the SAR data generation and image formation processing. A convenient frame for radar motion measurement is the Earth-Centered Earth-Fixed (ECEF) coordinate frame, whereas spotlight SAR processing typically require s polar coordinates from a selected Scene Reference Point (SRP). This report presents the conversion from ECEF coordinates to appropriate parameters for SAR processing.
We present the analysis of a coordinated set of observations from the POLAR Ultraviolet Imager (UVI), ground magnetometers, incoherent scatter radar, solar wind monitors, DMSP and GOES satellites, focused on a traveling convection vortex (TCV) event on 24th July 1996. Starting at approximately 10:48 UT, around magnetometers in Greenland and northern Canada observe pulsations consistent with the passing overhead of a series of alternating TCV filed-aligned current pairs. Azimuthal scans by the Sondrestrom incoherent scatter radar located near Kangerlussuaq (formerly Sondrestrom), Greenland, at this time show strong modulation in the strength and direction of ionospheric plasma flow. The magnetometer pulsations grow in magnitude over the next hour, peaking in intensity at 11:39 UT, at which time images form the UVI instrument show a localized intensification of auroral emissions over central and western Greenland. Subsequent images show the intensification grow in strength and propagate westward (tailward) until approximately 11:58 UT at which time the intensification fades. These observations are consistent with the westward passage of two pairs of moderately intense TCVs over central Greenland followed by a third very intense TCV pair. The intensification of auroral emissions at 11:39 UT is associated with the trailing vortex of the third TCV pair, thought to be the result of an upward field aligned current. The modulated flow observed by the radar is the result of the strong electric fields associated with the impulsive TCV related field aligned current systems as they pass through the field of view of the radar. Measurements of the solar wind from the V;IND and IMP-8 spacecraft suggest that a pressure change may be responsible for triggering the first two pairs of TCVS, and that a subsequent sudden change in the orientation of the interplanetary magnetic field may have produced the intensification of the third TCV pair and the associated auroral brightening. Magnetometer data from the GOES satellite located over the eastern United States at geostationary orbit is consistent with a series of field-aligned moving tailward past the satellite. DMSP particle data indicated that the TCVs occur on field lines which map to the boundary plasma sheet (BPS).
Series of plots must be made of antenna pattern on polar-coordinate sheet depicting vertical planes. Separate sheets are plotted depicting antenna patterns in vertical plane at azimuth positions. After all polar plots are drawn, they are labeled according to their azimuthal positions. Transparencies are then stiffened with regular wire, cardboard, or molded plastic.
Topics include: (1) polar coordinate transformations (M83); (2) multispectral ratios (M82); (3) maximum entropy restoration (M87); (4) automated computation of stellar magnitudes in nebulosity; (5) color and polarization; (6) aliasing.
Based on the analysis of the polar motion behavior, the possibility of predicting polar motion up to one year in advance was found. Comparing these predicted polar coordinates with the observed ones (smoothed), the root mean square (rms) of the differences is about 0.02 seconds. The differences of the relative polar motion are much smaller. For any time interval of 20 to 30 days throughout the whole year, the rms of the relative polar motion differences is about 0.01 second. Compared with the best available VLBI results (from 1977 to 1980), the rms of pred. to obs. is 0.013 seconds, and the relative rms (for time intervals less than two months) is 0.008 seconds (here the observed data is unsmoothed). It appears that 80 to 90% of the polar motion is composed of the stable, predictable Chandler and annual terms. The UT1-UTC has more complicated changes than polar motion making it difficult to find a satisfactory method of long term prediction. So far the rms prediction error is 0.0023 s for up to 30 days.
An estimate is made of the motion parameters, namely, linear and angular velocities, of a rigid body rotating and translating in three-space. The authors assume that the velocities are constant and that the motion is not completely observable. They consider two separate cases of partial observations corresponding to the orthogonal and the perspective projections, respectively. If (x, y, z) is the Cartesian coordinate of the three-space, the authors assume in the first case that the projection of the motion on the x-y plane is observed. If (r, theta, phi) is the polar coordinates of the three-space, they assume in the second case that the parameter vector (theta, phi) is observed. The use of both of these cases to estimate the motion parameters is discussed.
Two-dimensional axisymmetric simulations of binary neutron star (BNS) merger remnant are a cheap alternative to 3D simulations. To maintain realism for secular timescales, simulations must avoid accumulated errors from drifts in conserved quantities and artificial heating, and they must model turbulent transport in a way that remains plausible throughout the evolution. It is also crucial to avoid numerical artifacts due to the polar coordinate axis singularity. Methods that behave well near the axis often break flux-conservative form of the hydrodynamic equations, resulting in significant drifts in conserved quantities. We present a flux-conservative scheme that maintains smoothness near the axis without sacrificing conservative formulation of the equations or incurring drifts in conserved global quantities. We compare the numerical performance of different treatments of the hydrodynamic equations when evolving a hypermassive neutron star resembling the remnant of a BNS merger. These simulations demonstrate that the new scheme combines the axis smoothness of non-conservative methods with the mass and angular momentum conservation of other conservative methods on $\sim 10^2$ ms timescales of viscous and neutrino-driven evolution. Because fluid profiles remain smooth in the remnant interior, it is possible to remove artificial heating by evolving the entropy density. We show how physical heating and cooling terms can be easily calculated from source terms of the conservative evolution variables and demonstrate our implementation. Finally, we discuss and implement improvements to the effective viscosity scheme to better model the effect of magnetohydrodynamic instabilities as the remnant evolves.
Here, in this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.
Conventional ligands for CsPbBr 3 perovskite nanocrystals (NCs), composed of polar, coordinating head groups (e.g., ammonium or zwitterionic) and aliphatic tails, are instrumental in stabilizing the NCs against sintering and aggregation. Nonetheless, the aliphatic (insulating) nature of these ligands represents drawbacks with respect to objectives in optoelectronics, and yet removing these ligands typically leads to a loss of colloidal stability. Here, in this paper, we describe the preparation of CsPbBr 3 NCs in the presence of discrete conjugated oligomers that were prepared by an iterative synthetic approach and capped at their chain ends with sulfobetaine zwitterions for perovskite coordination. Notably, these zwitterionic oligofluorenes are compatible with the hot injection and ligand exchange conditions used to prepare CsPbBr 3 NCs, yielding stable NC dispersions with high photoluminescence quantum yields (PLQY, >90%) and spectral features representative of both the perovskite core and conjugated ligand shell. Controlling the chain length of these capping ligands effectively regulated inter-NC spacing and packing geometry when cast into solid films, with evidence derived from both transmission electron microscopy (TEM) and grazing incidence X-ray scattering measurements.
Magnetic field aligned filaments such as blobs and edge localized mode filaments carry significant amounts of heat and particles to the plasma facing components and they decrease their lifetime. The dynamics of these filaments determine at least a part of the heat and particle loads. These dynamics can be characterized by their translation and rotation. In this paper, we present an analysis method novel for fusion plasmas, which can estimate the angular velocity of the filaments on frame-by-frame time resolution. After pre-processing, the frames are two-dimensional (2D) Fourier-transformed, then the resulting 2D Fourier magnitude spectra are transformed to log-polar coordinates, and finally the 2D cross-correlation coefficient function (CCCF) is calculated between the consecutive frames. The displacement of the CCCF’s peak along the angular coordinate estimates the angle of rotation of the most intense structure in the frame. Further, the proposed angular velocity estimation method is tested and validated for its accuracy and robustness by applying it to rotating Gaussian-structures. The method is also applied to gas-puff imaging measurements of filaments in National Spherical Torus Experiment plasmas.
Neutrino-driven convection plays a crucial role in the development of core-collapse supernova (CCSN) explosions. However, the complex mechanism that triggers the shock revival and the subsequent explosion has remained inscrutable for many decades. Multidimensional simulations suggest that the growth of fluid instabilities, especially development of convection, will determine the morphology of the explosion. We have performed 3D simulations using spherical-polar coordinates covering a reduced angular extent (90° computational domain), and with angular resolutions of 2°, 1°, 1/2°, and 1/4°, to study the development of turbulent-like flows in core-collapse supernova explosions on a time scale of order 100 ms. We have employed the multi-physics Chimera code that includes detailed nuclear physics and spectral neutrino transport. Coarse resolution models do not develop an inertial range, presumably due to the bottleneck effect, such that the energy is prevented from cascading down to small scales and tends to accumulate at large scales. High-resolution models instead, start to recover the k −5/3 scaling of Kolmogorov's theory. Stochasticity and few simulation samples limit our ability to predict the development of explosions. Over the simulated time period, our models show no clear trend in improving (or diminishing) conditions for explosion as the angular resolution is increased. However, we find that disordered flow provides an effective pressure, as characterized by the Reynolds stress, behind the shock. This contribution, ~40%–50% of the thermal pressure, aids shock revival and thus the development of the explosion. Finally, we show that the kinetic energy power spectrum of reduced angular extent and full 4π models are consistent, thus indicating that a 90° computational domain is an adequate configuration to study the character of turbulence in CCSNe.
Mirror-centered, closed-form expressions for hyperbolic surfaces used in X-ray beamlines have been derived. Hyperbolic mirrors create a virtual focus or source point and can be used to lengthen or shorten the effective focal distance of a compound optical system. The derivations here express off-axis segments of a hyperbolic surface in terms of the real and virtual focal distances and the incident glancing angle at the center of the mirror. Conventional mathematical expressions of hyperbolic shapes describe the surfaces in Cartesian or polar coordinates centered on an axis of symmetry, necessitating cumbersome rotation and translation to mirror-centered coordinates. The representation presented here, with zero slope and the origin at the central point, is most convenient for modeling, metrology, aberration correction, and general surface analysis of off-axis configurations. The direct derivation avoids the need for nested coordinate transforms. A series expansion provides a helpful approximation; the coefficients of the implicit equation are also provided.
The emerging multimodal active energy resource units make it necessary to introduce constant voltage amplitude buses (PV bus) in the operation of modern distribution systems. To enable the analysis of PV bus using linear power flow models, this letter proposes a relaxed PV bus model for solving power flow related problems using an indirect modeling approach. The developed PV bus model can be applied to linear power flow models in both rectangular and polar coordinates. Besides, the approximation error of the relaxed PV bus model can also be controlled and quantified. Lastly, the proposed relaxed PV bus model is validated using different test systems. According to the numerical studies, the maximum error on the PV bus approximation in all case studies is only 0.61%, and the maximum error of the supporting power at the PV buses is 6.5%.
In addition to fixing the color-coding legend, the new figures plot Fourier phase in a more easily recognizable format: polar coordinates rather than Cartesian coordinates. The same phase data is displayed—indicating the position of the first ridge to the east of the prime meridian—but the new plots avoid unphysical jumps, e.g. from +180° to -180° as longitude increases across the International Dateline. A slight disadvantage of the new format is that each hemisphere requires a separate plot. The wavenumber-1 Northern Hemisphere phase plots give, in effect, a view from above the North Pole, with Eurasia at the top and North America at the bottom. Wavenumber-1 Southern Hemisphere plots give an analogous view from the South Pole. Plots for higher wavenumbers, however, wrap around at fractions of 360° (180°, 120°, ...) and cannot be interpreted as a geographical view.
TTU-X1 (South Site) raw data in polar coordinates including the ZT, DZ, VR, SW, and SQ moments.
TTU-X2 (North Site) raw data in polar coordinates including the ZT, DZ, VR, SW, and SQ moments.
Detection and timely identification of power system disturbances are essential for situation awareness and reliable electricity grid operation. Because records of actual events in the system are limited, ensemble simulation-based events are needed to provide adequate data for building event-detection models through deep learning; e.g., a convolutional neural network (CNN). An ensemble numerical simulation-based training data set have been generated through dynamic simulations performed on the Polish system with various types of faults in different locations. Such data augmentation is proven to be able to provide adequate data for deep learning. The synchronous generators’ frequency signals are used and encoded into images for developing and evaluating CNN models for classification of fault types and locations. With a time-domain stacked image set as the benchmark, two different time-series encoding approaches, i.e., wavelet decomposition-based frequency-domain stacking and polar coordinate system-based Gramian Angular Field (GAF) stacking, are also adopted to evaluate and compare the CNN model performance and applicability. The various encoding approaches are suitable for different fault types and spatial zonation. With optimized settings of the developed CNN models, the classification and localization accuracies can go beyond 84 and 91%, respectively.