Possible potentials responsible for stable circular relativistic orbits

Bertrand's theorem in classical mechanics of the central force fields attracts us because of its predictive power. It categorically proves that there can only be two types of forces which can produce stable, circular orbits. In the present article an attempt has been made to generalize Bertrand's theorem to the central force problem of relativistic systems. The stability criterion for potentials which can produce stable, circular orbits in the relativistic central force problem has been deduced and a general solution of it is presented in the article. It is seen that the inverse square law passes the relativistic test but the kind of force required for simple harmonic motion does not. Special relativistic effects do not allow stable, circular orbits in presence of a force which is proportional to the negative of the displacement of the particle from the potential center.Comment: 11 pages, Latex fil

A general scheme for modeling gamma-ray burst prompt emission

We describe a general method for modeling gamma-ray burst prompt emission. We find that for the burst to be produced via the synchrotron process unphysical conditions are required -- the distance of the source from the center of the explosion ($R_\gamma$) must be larger than $\sim 10^{17}$cm and the source Lorentz factor \gta 10^3; for such a high Lorentz factor the deceleration radius ($R_d$) is less than $R_\gamma$ even if the number density of particles in the surrounding medium is as small as $\sim 0.1$ cm$^{-3}$. The result, $R_\gamma > R_d$, is in contradiction with the early x-ray and optical afterglow data. The synchrotron-self-Compton (SSC) process fares much better. There is a large solution space for a typical GRB prompt emission to be produced via the SSC process. The prompt optical emission accompanying the burst is found to be very bright (\lta 14 mag; for $z\sim2$) in the SSC model, which exceeds the observed flux (or upper limit) for most GRBs. Continuous acceleration of electrons can significantly reduce the optical flux and bring it down to the observed limits. (Abridged)Comment: Published in MNRAS Jan 2008, 56 page

Strongly Intensive Measures for Multiplicity Fluctuations

The recently proposed two families of strongly intensive measures of fluctuations and correlations are studied within Hadron-String-Dynamics (HSD) transport approach to nucleus-nucleus collisions. We consider the measures $\Delta^{K\pi}$ and $\Sigma^{K\pi}$ for kaon and pion multiplicities in Au+Au collisions in a wide range of collision energies and centralities. These strongly intensive measures appear to cancel the participant number fluctuations. This allows to enlarge the centrality window in the analysis of event-by-event fluctuations up to at least of 10% most central collisions. We also present a comparison of the HSD results with the data of NA49 and STAR collaborations. The HSD describes $\Sigma^{K\pi}$ reasonably well. However, the HSD results depend monotonously on collision energy and do not reproduce the bump-deep structure of $\Delta^{K\pi}$ observed from the NA49 data in the region of the center of mass energy of nucleon pair $\sqrt{s_{NN}}= 8\div 12$ GeV. This fact deserves further studies. The origin of this `structure' is not connected with simple geometrical or limited acceptance effects, as these effects are taken into account in the HSD simulations

AAV-mediated and pharmacological induction of Hsp70 expression stimulates survival of retinal ganglion cells following axonal injury.

We evaluated the effect of AAV2- and 17-AAG (17-N-allylamino-17-demethoxygeldanamycin)-mediated upregulation of Hsp70 expression on the survival of retinal ganglion cells (RGCs) injured by optic nerve crush (ONC). AAV2-Hsp70 expression in the retina was primarily observed in the ganglion cell layer. Approximately 75% of all transfected cells were RGCs. RGC survival in AAV2-Hsp70-injected animals was increased by an average of 110% 2 weeks after the axonal injury compared with the control. The increase in cell numbers was not even across the retinas with a maximum effect of approximately 306% observed in the inferior quadrant. 17-AAG-mediated induction of Hsp70 expression has been associated with cell protection in various models of neurodegenerative diseases. We show here that a single intravitreal injection of 17-AAG (0.2 ug ul(-1)) results in an increased survival of ONC-injured RGCs by approximately 49% compared with the vehicle-treated animals. Expression of Hsp70 in retinas of 17-AAG-treated animals was upregulated approximately by twofold compared with control animals. Our data support the idea that the upregulation of Hsp70 has a beneficial effect on the survival of injured RGCs, and the induction of this protein could be viewed as a potential neuroprotective strategy for optic neuropathies

Enhanced Transmission Through Disordered Potential Barrier

Effect of weak disorder on tunneling through a potential barrier is studied analytically. A diagrammatic approach based on the specific behavior of subbarrier wave functions is developed. The problem is shown to be equivalent to that of tunneling through rectangular barriers with Gaussian distributed heights. The distribution function for the transmission coefficient $T$ is derived, and statistical moments \left are calculated. The surprising result is that in average disorder increases both tunneling conductance and resistance.Comment: 10 pages, REVTeX 3.0, 2 figures available upon reques

Charge Lattices and Consistency of 6D Supergravity

We extend the known consistency conditions on the low-energy theory of six-dimensional N = 1 supergravity. We review some facts about the theory of two-form gauge fields and conclude that the charge lattice Gamma for such a theory has to be self-dual. The Green-Schwarz anomaly cancellation conditions in the supergravity theory determine a sublattice of Gamma. The condition that this sublattice can be extended to a self-dual lattice Gamma leads to a strong constraint on theories that otherwise appear to be self-consistent.Comment: 15 pages. v2: minor changes; references, additional example added; v3: minor corrections and clarifications added, JHEP versio

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