9,896 research outputs found
All order covariant tubular expansion
We consider tubular neighborhood of an arbitrary submanifold embedded in a
(pseudo-)Riemannian manifold. This can be described by Fermi normal coordinates
(FNC) satisfying certain conditions as described by Florides and Synge in
\cite{FS}. By generalizing the work of Muller {\it et al} in \cite{muller} on
Riemann normal coordinate expansion, we derive all order FNC expansion of
vielbein in this neighborhood with closed form expressions for the curvature
expansion coefficients. Our result is shown to be consistent with certain
integral theorem for the metric proved in \cite{FS}.Comment: 27 pages. Corrected an error in a class of coefficients resulting
from a typo. Integral theorem and all other results remain unchange
The use of singular value gradients and optimization techniques to design robust controllers for multiloop systems
A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Analytical gradients of the singular values with respect to design variables in the controller are derived. A cumulative measure of the singular values and their gradients with respect to the design variables is used with a numerical optimization technique to increase the system's robustness. Both unconstrained and constrained optimization techniques are evaluated. Numerical results are presented for a two output drone flight control system
Application of matrix singular value properties for evaluating gain and phase margins of multiloop systems
For Abstract see A83-12457 (or A8312457/2
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
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