Peristaltic Pumping of Blood Through Small Vessels of Varying Cross-section

The paper is devoted to a study of the peristaltic motion of blood in the micro-circulatory system. The vessel is considered to be of varying cross-section. The progressive peristaltic waves are taken to be of sinusoidal nature. Blood is considered to be a Herschel-Bulkley fluid. Of particular concern here is to investigate the effects of amplitude ratio, mean pressure gradient, yield stress and the power law index on the velocity distribution, streamline pattern and wall shear stress. On the basis of the derived analytical expression, extensive numerical calculations have been made. The study reveals that velocity of blood and wall shear stress are appreciably affected due to the non-uniform geometry of blood vessels. They are also highly sensitive to the magnitude of the amplitude ratio and the value of the fluid index.Comment: Accepted for publication in ASME journal of Applied Mechanics. arXiv admin note: text overlap with arXiv:1108.1285v

Rational Orbits around Charged Black Holes

We show that all eccentric timelike orbits in Reissner-Nordstr\"{o}m spacetime can be classified using a taxonomy that draws upon an isomorphism between periodic orbits and the set of rational numbers. By virtue of the fact that the rationals are dense, the taxonomy can be used to approximate aperiodic orbits with periodic orbits. This may help reduce computational overhead for calculations in gravitational wave astronomy. Our dynamical systems approach enables us to study orbits for both charged and uncharged particles in spite of the fact that charged particle orbits around a charged black hole do not admit a simple one-dimensional effective potential description. Finally, we show that comparing periodic orbits in the RN and Schwarzschild geometries enables us to distinguish charged and uncharged spacetimes by looking only at the orbital dynamics.Comment: 16 pages, 21 figure

Comprehensive Spectral Analysis of Cyg X-1 using RXTE Data

We analyse a large number ($> 500$) pointed RXTE observations of Cyg X-1 and model the spectrum of each one. A subset of the observations for which there is simultaneous reliable measure of the hardness ratio by the All Sky Monitor, shows that the sample covers nearly all the spectral shapes of Cyg X-1. The relative strength, width of the Iron line and the reflection parameter are in general correlated with the high energy photon spectral index $\Gamma$. This is broadly consistent with a geometry where for the hard state (low $\Gamma \sim 1.7$) there is a hot inner Comptonizing region surrounded by a truncated cold disk. The inner edge of the disk moves inwards as the source becomes softer till finally in the soft state (high $\Gamma > 2.2$) the disk fills the inner region and active regions above the disk produce the Comptonized component. However, the reflection parameter shows non-monotonic behaviour near the transition region ($\Gamma \sim 2$), suggestive of a more complex geometry or physical state of the reflector. Additionally, the inner disk temperature, during the hard state, is on the average higher than in the soft one, albeit with large scatter. These inconsistencies could be due to limitations in the data and the empirical model used to fit them. The flux of each spectral component is well correlated with $\Gamma$ which shows that unlike some other black hole systems, Cyg X-1 does not show any hysteresis behaviour. In the soft state, the flux of the Comptonized component is always similar to the disk one, which confirms that the ultra-soft state (seen in other brighter black hole systems) is not exhibited by Cyg X-1. The rapid variation of the Compton Amplification factor with $\Gamma$, naturally explains the absence of spectra with $\Gamma < 1.6$, despite a large number having $\Gamma \sim 1.65$.Comment: 12 pages, 8 figures, accepted for publication in Research in Astronomy and Astrophysics (RAA