Growing pseudo-eigenmodes and positive logarithmic norms in rotating shear flows

Rotating shear flows, when angular momentum increases and angular velocity decreases as functions of radiation coordinate, are hydrodynamically stable under linear perturbation. The Keplerian flow is an example of such systems which appears in astrophysical context. Although decaying eigenmodes exhibit large transient energy growth of perturbation which could govern nonlinearity into the system, the feedback of inherent instability to generate turbulence seems questionable. We show that such systems exhibiting growing pseudo-eigenmodes easily reach an upper bound of growth rate in terms of the logarithmic norm of the involved nonnormal operators, thus exhibiting feedback of inherent instability. This supports the existence of turbulence of hydrodynamic origin in the Keplerian accretion disc in astrophysics. Hence, this enlightens the mismatch between the linear theory and experimental/observed data and helps in resolving the outstanding question of origin of turbulence therein.Comment: 12 pages including 4 figures; to appear in New Journal of Physic

Neutrino-Antineutrino Asymmetry around Rotating Black Holes

Propagation of fermion in curved space-time generates gravitational interaction due to the coupling between spin of the fermion and space-time curvature. This gravitational interaction, which is an axial-vector appears as CPT violating term in the Lagrangian. It is seen that this space-time interaction can generate neutrino asymmetry in Universe. If the back-ground metric is spherically asymmetric, say, of a rotating black hole, this interaction is non-zero, thus the net difference to the number density of the neutrino and anti-neutrino is nonzero.Comment: 3 pages, pramana style; to appear in a special issue of Pramana -- J. Phys., as proceedings of IXth Particle-String-Cosmology (PASCOS), January 3-8, 2003, TIFR, Mumbai, Indi

Theory of Bank Lending with Monitoring and Application to Rural Banking in India 2002-2003

We present a model in Costly State Verification framework that relates capital raised in a firm to profitability. We explain how optimality of investment is affected by how the aggregate funding affects the expected outcomes of the project. Although we find underinvestment, the problem does not get severe with increasing dead weight costs.Strategic default, Underinvestment, CSV

Dynamics of electromagnetic waves in Kerr geometry

Here we are interested to study the spin-1 particle i.e., electro-magnetic wave in curved space-time, say around black hole. After separating the equations into radial and angular parts, writing them according to the black hole geometry, say, Kerr black hole we solve them analytically. Finally we produce complete solution of the spin-1 particles around a rotating black hole namely in Kerr geometry. Obviously there is coupling between spin of the electro-magnetic wave and that of black hole when particles propagate in that space-time. So the solution will be depending on that coupling strength. This solution may be useful to study different other problems where the analytical results are needed. Also the results may be useful in some astrophysical contexts.Comment: 15 Latex pages, 4 Figures; Accepted for publication in Classical and Quantum Gravit

Particle-Hole Symmetry and the Bose Glass to Superfluid Transition

The generic Hamiltonian describing the zero temperature transition between the insulating Bose glass phase and the superfluid phase lacks particle-hole symmetry, but a statistical version of this symmetry is believed to be restored at the critical point. We show that the renormalization group relevance of particle-hole asymmetry may be explored in a controlled fashion only for small time dimensions, ετ≪1, where we find a stable particle-hole asymmetric and an unstable particle-hole symmetric fixed point, but we provide evidence that the two merge for some finite ετ≈2/3, which tends to confirm symmetry restoration at the physical ετ = 1

Dynamical supersymmetry analysis of conformal invariance for superstrings in type IIB R-R plane-wave

In a previous work (arXiv:0902.3750 [hep-th]) we studied the world-sheet conformal invariance for superstrings in type IIB R-R plane-wave in semi-light-cone gauge. Here we give further justification to the results found in that work through alternative arguments using dynamical supersymmetries. We show that by using the susy algebra the same quantum definition of the energy-momentum (EM) tensor can be derived. Furthermore, using certain Jacobi identities we indirectly compute the Virasoro anomaly terms by calculating second order susy variation of the EM tensor. Certain integrated form of all such terms are shown to vanish. In order to deal with various divergences that appear in such computations we take a point-split definition of the same EM tensor. The final results are shown not to suffer from the ordering ambiguity as noticed in the previous work provided the coincidence limit is taken before sending the regularization parameter to zero at the end of the computation.Comment: 18 pages, Appendix B replaced by shorter argument in text (section 2.1), one reference adde