Transition from radiatively inefficient to cooling dominated phase in two temperature accretion discs around black holes

We investigate the transition of a radiatively inefficient phase of a viscous two temperature accreting flow to a cooling dominated phase and vice versa around black holes. Based on a global sub-Keplerian accretion disc model in steady state, including explicit cooling processes self-consistently, we show that general advective accretion flow passes through various phases during its infall towards a black hole. Bremsstrahlung, synchrotron and inverse Comptonization of soft photons are considered as possible cooling mechanisms. Hence the flow governs a much lower electron temperature ~10^8 - 10^{9.5}K compared to the hot protons of temperature ~10^{10.2} - 10^{11.8}K in the range of the accretion rate in Eddington units 0.01 - 100. Therefore, the solutions may potentially explain the hard X-rays and the gamma-rays emitted from AGNs and X-ray binaries. We finally compare the solutions for two different regimes of viscosity and conclude that a weakly viscous flow is expected to be cooling dominated compared to its highly viscous counterpart which is radiatively inefficient. The flow is successfully able to reproduce the observed luminosities of the under-fed AGNs and quasars (e.g. Sgr A*), ultra-luminous X-ray sources (e.g. SS433), as well as the highly luminous AGNs and ultra-luminous quasars (e.g. PKS 0743-67) at different combinations of the mass accretion rate and ratio of specific heats.Comment: 13 pages including 8 figures; couple of typos corrected; to appear in Research in Astronomy and Astrophysic

Liftable vector fields over corank one multigerms

In this paper, a systematic method is given to construct all liftable vector fields over an analytic multigerm $f: (\mathbb{K}^n, S)\to (\mathbb{K}^p,0)$ of corank at most one admitting a one-parameter stable unfolding.Comment: 34 pages. In ver. 2, several careless mistakes for calculations in Section 6 were correcte

Scattering states of a particle, with position-dependent mass, in a PT{\cal{PT}} symmetric heterojunction

The study of a particle with position-dependent effective mass (pdem), within a double heterojunction is extended into the complex domain --- when the region within the heterojunctions is described by a non Hermitian ${\cal{PT}}$ symmetric potential. After obtaining the exact analytical solutions, the reflection and transmission coefficients are calculated, and plotted as a function of the energy. It is observed that at least two of the characteristic features of non Hermitian ${\cal{PT}}$ symmetric systems --- viz., left / right asymmetry and anomalous behaviour at spectral singularity, are preserved even in the presence of pdem. The possibility of charge conservation is also discussed.Comment: 12 pages, including 6 figures; Journal of Physics A : Math. Theor. (2012

A 6-bit, 500-MS/s current-steering DAC in SiGe BiCMOS technology and considerations for SFDR performance

This paper presents a six-bit current-steering digital-to-analogue converter (DAC), which optimises the spurious free dynamic range (SFDR) performance of high-speed binary weighted architectures by lowering current switch distortion and reducing the clock feed-through effect. A novel current source cell is implemented that comprises heterojunction bipolar transistor current switches, negative-channel metal-oxide semiconductor (NMOS) cascode and NMOS current source to overcome distortion by specifically enhancing the SFDR for high-speed DACs. The DAC is implemented using silicon-germanium (SiGe) BiCMOS 130 nm technology and achieves a better than 21.96 dBc SFDR across the Nyquist band for a sampling rate of 500 MS/s with a core size of 0.1 mm2 and dissipates just 4 mW compared to other BiCMOS DACs that achieve similar SFDR performance with higher output voltages, resulting in a much larger power dissipation

Collective behavior of stock price movements in an emerging market

To investigate the universality of the structure of interactions in different markets, we analyze the cross-correlation matrix C of stock price fluctuations in the National Stock Exchange (NSE) of India. We find that this emerging market exhibits strong correlations in the movement of stock prices compared to developed markets, such as the New York Stock Exchange (NYSE). This is shown to be due to the dominant influence of a common market mode on the stock prices. By comparison, interactions between related stocks, e.g., those belonging to the same business sector, are much weaker. This lack of distinct sector identity in emerging markets is explicitly shown by reconstructing the network of mutually interacting stocks. Spectral analysis of C for NSE reveals that, the few largest eigenvalues deviate from the bulk of the spectrum predicted by random matrix theory, but they are far fewer in number compared to, e.g., NYSE. We show this to be due to the relative weakness of intra-sector interactions between stocks, compared to the market mode, by modeling stock price dynamics with a two-factor model. Our results suggest that the emergence of an internal structure comprising multiple groups of strongly coupled components is a signature of market development.Comment: 10 pages, 10 figure

Modular networks emerge from multiconstraint optimization

Modular structure is ubiquitous among complex networks. We note that most such systems are subject to multiple structural and functional constraints, e.g., minimizing the average path length and the total number of links, while maximizing robustness against perturbations in node activity. We show that the optimal networks satisfying these three constraints are characterized by the existence of multiple subnetworks (modules) sparsely connected to each other. In addition, these modules have distinct hubs, resulting in an overall heterogeneous degree distribution.Comment: 5 pages, 4 figures; Published versio

Study of underlying particle spectrum during huge X-ray flare of Mkn 421 in April 2013

Context: In April 2013, the nearby (z=0.031) TeV blazar, Mkn 421, showed one of the largest flares in X-rays since the past decade. Aim: To study all multiwavelength data available during MJD 56392 to 56403, with special emphasis on X-ray data, and understand the underlying particle energy distribution. Methods: We study the correlations between the UV and gamma bands with the X-ray band using the z-transformed discrete correlation function. We model the underlying particle spectrum with a single population of electrons emitting synchrotron radiation, and do a statistical fitting of the simultaneous, time-resolved data from the Swift-XRT and the NuSTAR. Results: There was rapid flux variability in the X-ray band, with a minimum doubling timescale of $1.69 \pm 0.13$ hrs. There were no corresponding flares in UV and gamma bands. The variability in UV and gamma rays are relatively modest with $\sim 8 \%$ and $\sim 16 \%$ respectively, and no significant correlation was found with the X-ray light curve. The observed X-ray spectrum shows clear curvature which can be fit by a log parabolic spectral form. This is best explained to originate from a log parabolic electron spectrum. However, a broken power law or a power law with an exponentially falling electron distribution cannot be ruled out either. Moreover, the excellent broadband spectrum from $0.3-79$ keV allows us to make predictions of the UV flux. We find that this prediction is compatible with the observed flux during the low state in X-rays. However, during the X-ray flares, the predicted flux is a factor of $2-50$ smaller than the observed one. This suggests that the X-ray flares are plausibly caused by a separate population which does not contribute significantly to the radiation at lower energies. Alternatively, the underlying particle spectrum can be much more complex than the ones explored in this work.Comment: 11 pages, 7 figures, Accepted in A&