Modal analysis of gravitational instabilities in nearly Keplerian, counter-rotating collisionless discs

We present a modal analysis of instabilities of counter-rotating, self-gravitating collisionless stellar discs, using the recently introduced modified WKB formulation of spiral density waves for collisionless systems (Gulati \& Saini). The discs are assumed to be axisymmetric and in coplanar orbits around a massive object at the common center of the discs. The mass in both discs is assumed to be much smaller than the mass of the central object. For each disc, the disc particles are assumed to be in near circular orbits. The two discs are coupled to each other gravitationally. The perturbed dynamics of the discs evolves on the order of the precession time scale of the discs, which is much longer than the Keplerian time scale. We present results for the azimuthal wave number $m=1$ and $m=2$, for the full range of disc mass ratio between the prograde and retrograde discs. The eigenspectra are in general complex, therefore all eigenmodes are unstable. Eigenfunctions are radially more compact for $m = 1$ as compared to $m = 2$. Pattern speed of eigenmodes is always prograde with respect to the more massive disc. The growth rate of unstable modes increases with increasing mass fraction in the retrograde disc, and decreases with $m$; therefore $m=1$ instability is likely to play the dominant role in the dynamics of such systems.Comment: 24 pages, 8 figures, 1 tabl

Slow pressure modes in thin accretion discs

Thin accretion discs around massive compact objects can support slow pressure modes of oscillations in the linear regime that have azimuthal wavenumber $m=1$. We consider finite, flat discs composed of barotropic fluid for various surface density profiles and demonstrate--through WKB analysis and numerical solution of the eigenvalue problem--that these modes are stable and have spatial scales comparable to the size of the disc. We show that the eigenvalue equation can be mapped to a Schr\"odinger-like equation. Analysis of this equation shows that all eigenmodes have discrete spectra. We find that all the models we have considered support negative frequency eigenmodes; however, the positive eigenfrequency modes are only present in power law discs, albeit for physically uninteresting values of the power law index $\beta$ and barotropic index $\gamma$.Comment: 9 pages, 7 figures, 1 table, accepted in MNRAS for pulicatio

Change Detection from Remotely Sensed Images Based on Stationary Wavelet Transform

The major issue of concern in change detection process is the accuracy of the algorithm to recover changed and unchanged pixels. The fusion rules presented in the existing methods could not integrate the features accurately which results in more number of false alarms and speckle noise in the output image. This paper proposes an algorithm which fuses two multi-temporal images through proposed set of fusion rules in stationary wavelet transform. In the first step, the source images obtained from log ratio and mean ratio operators are decomposed into three high frequency sub-bands and one low frequency sub-band by stationary wavelet transform. Then, proposed fusion rules for low and high frequency sub-bands are applied on the coefficient maps to get the fused wavelet coefficients map. The fused image is recovered by applying the inverse stationary wavelet transform (ISWT) on the fused coefficient map. Finally, the changed and unchanged areas are classified using Fuzzy c means clustering. The performance of the algorithm is calculated in terms of percentage correct classification (PCC), overall error (OE) and Kappa coefficient (Kc). The qualitative and quantitative results prove that the proposed method offers least error, highest accuracy and Kappa value as compare to its preexistences

Enhance GPS Accuracy via Integration of Artificial Intelligence

GPS has improved navigation and location-based services, its precision is still affected by things like weather and building materials. The purpose of this research was to investigate the feasibility of using AI methods to enhance GPS precision. This research proves that GPS accuracy has increased significantly, making it suitable for use in increasingly important fields including driverless vehicles, precision agriculture, geospatial mapping, and more. These results highlight the revolutionary potential of incorporating AI to improve the accuracy and reliability of GPS technology, ushering in a new era of navigation and location-based applications. In this study, authors introduce an Artificial Intelligence technique, to increase the precision of GPS receivers. Interoperability of Sensors Mostly made out of a Three-Axis Accelerometer Once GPS signal is lost with any cause, this change in delta latitude and delta longitude will be computed by our trained artificial neural network, and then, based on this interpolation, artificial neural network calculates latitude and longitude. The 3-axis gyroscope is part of an inertial measurement unit (IMU) that is used in conjunction with AI to predict navigation parameters when GPS loses communication with a satellite

Congestion Aware WSN-IoT-Application Layer Protocols for Healthcare Services

In the healthcare industry, WSN-IoT networks can be used to gather patient data for statistical purposes. IoT-based application-level protocols do not take into account these facts while forwarding the data to the gateway or server, which may degrade the network performance if the data was collected from a patient with ordinary/critical health issues and the route was busy or congested. In this paper, we'll look at the performance of two application layer protocols (i.e. CoAP and MQTT) within the constraints of a scalable network by integrating a congestion-aware scheme with them

MATHCAD Geometrie Benutzerhandbuch

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