Explore the vast range of titles available.

We present a unified model for X-ray quasi-periodic oscillations (QPOs) seen in Narrow-line Seyfert 1 (NLSy1) galaxies, γ-ray and optical band QPOs that are seen in Blazars. The origin of these QPOs is attributed to the plasma motion in corona or jets of these AGN. In the case of X-ray QPOs, we applied the general relativistic precession model for the two simultaneous QPOs seen in NLSy1 1H 0707-945 and deduce orbital parameters, such the radius of the emission region, and spin parameter a for a circular orbit; we obtained the Carter’s constant Q, a, and the radius in the case of a spherical orbit solution. In other cases where only one X-ray QPO is seen, we localized the orbital parameters for NLSy1 galaxies REJ 1034+396, 2XMM J123103.2+110648, MS 2254.9-3712, Mrk 766, and MCG-06-30-15. By applying the lighthouse model, we found that a kinematic origin of the jet based γ-ray and optical QPOs, in a relativistic MHD framework, is possible. Based on the inbuilt Hamiltonian formulation with a power-law distribution in the orbital energy of the plasma consisting of only circular or spherical trajectories, we show that the resulting Fourier power spectral density (PSD) has a break corresponding to the energy at ISCO. Further, we derive connection formulae between the slopes in the PSD and that of the energy distribution. Overall, given the preliminary but promising results of these relativistic orbit models to match the observed QPO frequencies and PSD at diverse scales in the inner corona and the jet, it motivates us to build detailed models, including a transfer function for the energy spectrum in the corona and relativistic MHD jet models for plasma flow and its polarization properties.

This scientific literature survey aims to provide a detailed overview of Wave Active Filter (WAF), including sequential growth of the higher-order filter design using voltage mode and current mode design. This survey paper elaborates on a step-by-step procedure for the wave variable approach for filter design with mathematical analysis. In addition, this work specifically focuses on developing WAF designs using different active blocks. Higher-order WAF designs using modern active blocks are well recorded in this survey paper for better visualization. In literature, third-order and fourth-order WAF implementations are mainly enriched. Hence, an OTA-based WAF is designed for lower- to higher-order filters, demonstrating their efficacy for multifunctional applications such as Wave Active Low Pass Filter (WALPF), Wave Active High Pass Filter (WAHPF), and Wave Active Bandpass Filter (WABPF) using OTA. Besides the theoretical foundations, simulation, and experimental test results are also performed to validate the workability of the OTA-based WAF. The frequency responses of WALPF, WAHPF, and WABPF are demonstrated for the second to sixth orders. The functionality of the OTA-based WAF is verified through frequency spectrum analysis and Monte Carlo simulations. This paper ultimately offers an extensive review of the WAF design process, including mathematical analysis and practical realizations. It provides insights into WAF theory, its benefits, limitations, and potential for future advancements in high-order filters.

This paper presents a second and third-order wave active low pass filter (WALPF) using modern active block Voltage Differencing Differential Input Buffered Amplifier (VDDIBA) with a lower supply voltage of 1V. The wave-active approach is chosen for the filter designing to get a higher order, lower sensitivity, modular and stable filter structure. The design procedure of WALPF involves the implementation of wave-active equivalent for series inductor and shunt capacitor. And it needs to realize the subtractor block physically, and the lossy subtractor integrator block using VDDIBA gives a flavor of differencing voltage property. So, the physical implementation of the subtractor block and the lossy subtractor integrator block goes very smoothly using this block. It is considered a possible reason for reducing active blocks and passive components. Theoretical justification of the proposed WALPF is achieved by using the wave-equivalent concept of the wave-active approach. This method of WAF design consists of only one resistor and capacitor, making the filter structure less complex easy to use with a cut-off frequency of 10MHz. Finally, the workability test is examined with the PSPICE simulation that results in the WALPF frequency response using 180 nm TSMC CMOS technology parameter for VDDIBA.

The COVID-19 outbreak began in December 2019 and has affected people worldwide. It was declared a pandemic in 2020 by the World Health Organization. Developing rapid and reliable diagnostic techniques is crucial for identifying COVID-19 early and preventing the disease from becoming severe. In addition to conventional diagnostic techniques such as RT-PCR, computed tomography, serological assays, and sequencing methods, biosensors have become widely accepted for identifying and screening COVID-19 infection with high accuracy and sensitivity. Their low cost, high sensitivity, specificity, and portability make them ideal for diagnostics. The use of nanomaterials improves the performance of biosensors by increasing their sensitivities and limiting detection by several orders of magnitude. This manuscript briefly reviews the COVID-19 outbreak and its pathogenesis. Furthermore, it comprehensively discusses the currently available biosensors for SARS-CoV-2 detection, with a special emphasis on nanomaterials-based biosensors developed to detect this emerging virus and its variants efficiently.

We study the bound orbit conditions for equatorial and eccentric orbits around a Kerr black hole both in the parameter space (\\(E\\), \\(L\\), \\(a\\)) representing the energy, angular momentum of the test particle, and spin of the black hole, and also (\\(e\\), \\(\\mu\\), \\(a\\)) space representing the eccentricity, inverse-latus rectum of the orbit, and spin. We apply these conditions and implement the relativistic precession (RP) model to M82X-1, which is an Intermediate-mass black hole (IMBH) system, where two high-frequency Quasi-Periodic Oscillations (HFQPOs) and a low-frequency QPO were simultaneously observed. Assuming that the QPO frequencies can also be generated by equatorial and eccentric trajectories, we calculate the probability distributions to infer \\(e\\), \\(a\\), and periastron distance, \\(r_p\\), of the orbit giving rise to simultaneous QPOs. We find that an eccentric orbit solution is possible in the region between innermost stable circular orbit (ISCO) and the marginally bound circular orbit (MBCO) for \\(e=0.2768^{+0.0657}_{-0.0451}\\), \\(a=0.2897 \\pm 0.0087\\), and \\(r_p=4.6164^{+0.0694}_{-0.1259}\\).

We derive the conditions for a non-equatorial eccentric bound orbit to exist around a Kerr black hole in two-parameter spaces: the energy, angular momentum of the test particle, spin of the black hole, and Carter's constant space (\\(E\\), \\(L\\), \\(a\\), \\(Q\\)), and eccentricity, inverse-latus rectum space (\\(e\\), \\(\\mu\\), \\(a\\), \\(Q\\)). These conditions distribute various kinds of bound orbits in different regions of the (\\(E\\), \\(L\\)) and (\\(e\\), \\(\\mu\\)) planes, depending on which pair of roots of the effective potential forms a bound orbit. We provide a prescription to select these parameters for bound orbits, which are useful inputs to study bound trajectory evolution in various astrophysical applications like simulations of gravitational wave emission from extreme-mass ratio inspirals, relativistic precession around black holes, and the study of gyroscope precession as a test of general relativity.

We expand the relativistic precession model to include nonequatorial and eccentric trajectories and apply it to quasi-periodic oscillations (QPOs) in black hole X-ray binaries (BHXRBs) and associate their frequencies with the fundamental frequencies of the general case of nonequatorial (with Carter's constant, \\(Q\\neq 0\\)) and eccentric (\\(e\\neq 0\\)) particle trajectories, around a Kerr black hole. We study cases with either two or three simultaneous QPOs and extract the parameters \\{\\(e\\), \\(r_p\\), \\(a\\), \\(Q\\)\\}, where \\(r_p\\) is the periastron distance of the orbit, and \\(a\\) is the spin of the black hole. We find that the orbits with \\(\\left[Q=0-4\\right]\\) should have \\(e\\lesssim 0.5\\) and \\(r_p \\sim 2-20\\) for the observed range of QPO frequencies, where \\(a \\in [0,1]\\), and that the spherical trajectories \\{\\(e=0\\), \\(Q \\neq0\\)\\} with \\(Q=2-4\\) should have \\(r_s \\sim 3-20\\). We find nonequatorial eccentric solutions for both M82 X-1 and GROJ 1655-40. We see that these trajectories, when taken together, span a torus region and give rise to a strong QPO signal. For two simultaneous QPO cases, we found equatorial eccentric orbit solutions for XTEJ 1550-564, 4U 1630-47, and GRS 1915+105, and spherical orbit solutions for BHXRBs M82 X-1 and XTEJ 1550-564. We also show that the eccentric orbit solution fits the Psaltis-Belloni-Klis correlation observed in BHXRB GROJ 1655-40. Our analysis of the fluid flow in the relativistic disk edge suggests that instabilities cause QPOs to originate in the torus region. We also present some useful formulae for trajectories and frequencies of spherical and equatorial eccentric orbits.

We present a unified model for X-ray quasi-periodic oscillations (QPOs) seen in Narrow-line Seyfert 1 (NLSy1) galaxies, \\(\\gamma\\)-ray and optical band QPOs that are seen in Blazars. The origin of these QPOs is attributed to the plasma motion in corona or jets of these AGN. In the case of X-ray QPOs, we applied the general relativistic precession model for the two simultaneous QPOs seen in NLSy1 1H 0707-945 and deduce orbital parameters, such the radius of the emission region, and spin parameter \\(a\\) for a circular orbit; we obtained the Carter's constant \\(Q\\), \\(a\\), and the radius in the case of a spherical orbit solution. In other cases where only one X-ray QPO is seen, we localized the orbital parameters for NLSy1 galaxies REJ 1034+396, 2XMM J123103.2+110648, MS 2254.9-3712, Mrk 766, and MCG-06-30-15. By applying the lighthouse model, we found that a kinematic origin of the jet based \\(\\gamma\\)-ray and optical QPOs, in a relativistic MHD framework, is possible. Based on the inbuilt Hamiltonian formulation with a power-law distribution in the orbital energy of the plasma consisting of only circular or spherical trajectories, we show that the resulting Fourier power spectral density (PSD) has a break corresponding to the energy at ISCO. Further, we derive connection formulae between the slopes in the PSD and that of the energy distribution. Overall, given the preliminary but promising results of these relativistic orbit models to match the observed QPO frequencies and PSD at diverse scales in the inner corona and the jet, it motivates us to build detailed models, including a transfer function for the energy spectrum in the corona and relativistic MHD jet models for plasma flow and its polarization properties.

We derive alternate and new closed-form analytic solutions for the non-equatorial eccentric bound trajectories, \\(\\{ \\phi \\left( r, \\theta \\right)\\), \\(\\ t \\left( r, \\theta \\right),\\ r \\left( \\theta \\right) \\}\\), around a Kerr black hole by using the transformation \\(1/r=\\mu \\left(1+ e \\cos \\chi \\right)\\). The application of the solutions is straightforward and numerically fast. We obtain and implement translation relations between energy and angular momentum of the particle, (\\(E\\), \\(L\\)), and eccentricity and inverse-latus rectum, (\\(e\\), \\(\\mu\\)), for a given spin, \\(a\\), and Carter's constant, \\(Q\\), to write the trajectory completely in the (\\(e\\), \\(\\mu\\), \\(a\\), \\(Q\\)) parameter space. The bound orbit conditions are obtained and implemented to select the allowed combination of parameters (\\(e\\), \\(\\mu\\), \\(a\\), \\(Q\\)). We also derive specialized formulae for spherical and separatrix orbits. A study of the non-equatorial analog of the previously studied equatorial separatrix orbits is carried out where a homoclinic orbit asymptotes to an energetically bound spherical orbit. Such orbits simultaneously represent an eccentric orbit and an unstable spherical orbit, both of which share the same \\(E\\) and \\(L\\) values. We present exact expressions for \\(e\\) and \\(\\mu\\) as functions of the radius of the corresponding unstable spherical orbit, \\(r_s\\), \\(a\\), and \\(Q\\), and their trajectories, for (\\(Q\\neq0\\)) separatrix orbits; they are shown to reduce to the equatorial case. These formulae have applications to study the gravitational waveforms from EMRIs besides relativistic precession and phase space explorations. We obtain closed-form expressions of the fundamental frequencies of non-equatorial eccentric trajectories that are equivalent to the previously obtained quadrature forms and also numerically match with the equivalent formulae previously derived. We sketch several orbits and discuss their astrophysical applications.

We present the results of customised single-pulsar noise analysis of 27 millisecond pulsars from the second data release of the Indian Pulsar Timing Array (InPTA-DR2). We model various stochastic noise sources present in the dataset using stationary Gaussian processes and estimate the noise budget of the InPTA-DR2 using Bayesian inference, involving model selection, Fourier harmonics selection, and parameter estimation for each pulsar. We check the efficacy of our noise characterisation by performing the Anderson-Darling test for Gaussianity on the noise-subtracted residuals. We find that all 11 pulsars with time baseline \\(\\lesssim2.5\\,\\text{yr}\\) show Gaussian residuals and do not have evidence for any red noise process in the optimal model, except for PSR J1944\\(+\\)0907, which shows presence of DM noise. PSRs J0437\\(-\\)4715, J1909\\(-\\)3744 and J1939\\(+\\)2134 show preference for the most complicated noise model, having achromatic and chromatic red noise processes. Only 4 out of 15 pulsars with time baseline \\(\\gtrsim2.5\\,\\text{yr}\\) show significant non-Gaussianity in noise-subtracted residuals. We suspect that this may require more advanced methods to model noise processes properly. A comparative study of six pulsars with data removed near solar conjunctions showed deviations from the parameter estimates obtained with the original dataset, indicating potential bias in red noise processes due to unmodeled solar-wind effects. The results presented in this work remain broadly consistent with the InPTA-DR1 noise budget, with better constraints obtained on noise processes for several pulsars and support for achromatic red noise in PSR J1012\\(+\\)5307 due to the extended time baseline.