Normal gravity field in relativistic geodesy

Modern geodesy is subject to a dramatic change from the Newtonian paradigm to Einstein's theory of general relativity. This is motivated by the ongoing advance in development of quantum sensors for applications in geodesy including quantum gravimeters and gradientometers, atomic clocks and fiber optics for making ultra-precise measurements of the geoid and multipolar structure of the Earth's gravitational field. At the same time, VLBI, SLR, and GNSS have achieved an unprecedented level of accuracy in measuring coordinates of the reference points of the ITRF and the world height system. The main geodetic reference standard is a normal gravity field represented in the Newtonian gravity by the field of a Maclaurin ellipsoid. The present paper extends the concept of the normal gravity field to the realm of general relativity. We focus our attention on the calculation of the first post-Newtonian approximation of the normal field that is sufficient for applications. We show that in general relativity the level surface of the uniformly rotating fluid is no longer described by the Maclaurin ellipsoid but is an axisymmetric spheroid of the forth order. We parametrize the mass density distribution and derive the post-Newtonian normal gravity field of the rotating spheroid which is given in a closed form by a finite number of the ellipsoidal harmonics. We employ transformation from the ellipsoidal to spherical coordinates to deduce the post-Newtonian multipolar expansion of the metric tensor given in terms of scalar and vector gravitational potentials of the rotating spheroid. We compare these expansions with that of the normal gravity field generated by the Kerr metric and demonstrate that the Kerr metric has a fairly limited application in relativistic geodesy. Finally, we derive the post-Newtonian generalization of the Somigliana formula for the gravity field on the reference ellipsoid.Comment: 39 pages, no figures, accepted to Physical Review

Network monitoring in multicast networks using network coding

In this paper we show how information contained in robust network codes can be used for passive inference of possible locations of link failures or losses in a network. For distributed randomized network coding, we bound the probability of being able to distinguish among a given set of failure events, and give some experimental results for one and two link failures in randomly generated networks. We also bound the required field size and complexity for designing a robust network code that distinguishes among a given set of failure events

γγ→tcˉ+ctˉ\gamma\gamma \to t\bar{c}+c\bar{t} in a supersymmetric theory with an explicit R-parity violation

We studied the process $\gamma\gamma \to t\bar{c}+c\bar{t}$ in a $R_{p}$ violating supersymmetric Model with the effects from both B- and L-violating interactions. The calculation shows that it is possible to detect a $R_{p}$ violating signal at the Next Linear Collider. Information about the B-violating interaction in this model could be obtained under very clean background, if we take the present upper bounds for the parameters in the supersymmetric $\rlap/ R_{p}$ interactions. Even if we can not detect a signal of $\rlap/R_{p}$ in the experiment, we may get more stringent constraints on the heavy-flavor $\rlap/R_{p}$ couplings.Comment: 16 pages, 6 figure

Reliability Analysis of Components Life Based on Copula Model

It is the general character of most engineering systems that failure statistical correlation of elements exists in the fatigue happened process due to the twin loads．Based on randomized Basquin equation，the constitutive relations are established between element life and random variable including twin loads，initial strength,fatigue strength exponent．Product-moment correlation coefficients are derived and used to quantify the dependence of logarithm life of elements．Aim at fatigue life correlation of elements in structural systems, the computation model of the system reliability is preliminarily established by means of using copula function. The new model can express the dependence of elements fatigue life in structural systems, can be used probability prediction of structural systems under common stochastic cyclic load, which gives a new path for reliability-based design and probability assesment in equipment systems with multi-mode damage coupling

Feature Extraction of Composite Damage on Acoustic Emission Signals

 The aim of this study was to develop efficient methods to discriminate different damage mechanisms of composite. For this purpose, integration of Empirical Mode Decomposition (EMD) method and Hilbert-Huang Transform (HHT) was applied to define more relevant time-frequency descriptors. A complete methodology for the post-processing of the acoustic emission (AE) waveforms recorded during the quasi-static tension test of carbon fiber twill weave composite material was established in this work. AE signal is decomposed into several IMF components by means of EMD algorithm. The EMD can detach and extract all damage modes which consist in an AE signal. The HHT provide instantaneous frequencies in time-scale of an AE signal, which can be used as a new time-frequency descriptors of composite damage modes