Gravitational radiations of generic isolated horizons and non-rotating dynamical horizons from asymptotic expansions

Instead of using a three dimensional analysis on quasi-local horizons, we adopt a four dimensional asymptotic expansion analysis to study the next order contributions from the nonlinearity of general relativity. From the similarity between null infinity and horizons, the proper reference frames are chosen from the compatible constant spinors for an observer to measure the energy-momentum and flux near quasi-local horizons. In particular, we focus on the similarity of Bondi-Sachs gravitational radiation for the quasi-local horizons and compare our results to Ashtekar-Kirshnan flux formular. The quasi-local energy momentum and flux of generic isolated horizons and non-rotating dynamical horizons are discussed in this paper.Comment: PRD, 15 page

Domain wall space-times with a cosmological constant

We solve vacuum Einstein's field equations with the cosmological constant in space-times admitting 3-parameter group of isometries with 2-dimensional space-like orbits. The general exact solutions, which are represented in the advanced and retarded null coordinates, have two arbitrary functions due to the freedom of choosing null coordinates. In the thin-wall approximation, the Israel's junction conditions yield one constraint equation on these two functions in spherical, planar, and hyperbolic domain wall space-times with reflection symmetry. The remain freedom of choosing coordinates are completely fixed by requiring that when surface energy density $\sigma_0$ of domain walls vanishes, the metric solutions will return to some well-known solutions. It leads us to find a planar domain wall solution, which is conformally flat, in the de Sitter universe.Comment: 9 pages. no figur

Adaptive RF Pigtail Probe Modeling for De-embedding of RF Measurements

This disclosure describes techniques for accurate estimation and de-embedding of the effects of pigtail probes in circuits. An adaptive pigtail model is developed and described that can accurately de-embed the effects of pigtail probes in digital circuits. Example parameters are identified that include pigtail length, tip length, pigtail tilt degree, ground distance, and solder amount. A pigtail simulation model is developed to model the soldered pigtail probe. The dependency of circuit impedance on the identified parameters is determined by experimentation which indicates that circuit performance can be boosted by short ground distance lengths, low tilt angles, thick support wires, short pin and cable lengths, and thick support wires. The pigtail model can be utilized to derive de-embedded results for different pigtail probe configurations without a need for explicitly measuring de-embedded results for those configurations