Geometric approach for the modified second generation time delay interferometry

Time-delay interferometry for LISA

LISA ~Laser Interferometer Space Antenna! is a mission to detect and study low-frequency cosmic gravitational radiation through its influence on the phases or frequencies of laser beams exchanged between three remote spacecraft. We previously showed how, with lasers of identical frequencies on stationary spacecraft, the measurement of twelve time series of Doppler shifts could be combined to ca...

Time-Delay Interferometry

Equal-arm interferometric detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower lev...

The second geometric-arithmetic index for trees and unicyclic graphs

Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...

Collinear phase matching for second harmonic generation using conoscopic interferometry

Time Delay Interferometry and LISA Optimal Sensitivity

The sensitivity of LISA depends on the suppression of several noise sources; dominant one is laser frequency noise. It has been shown that the six Doppler data streams obtained from three space-crafts can be appropriately time delayed and optimally combined to cancel this laser frequency noise. We show that the optimal data combinations when operated in a network mode improves the sensitivity o...