Dynamical interpretation of the wavefunction of the universe

In this paper, we study the physical meaning of the wavefunction of the universe. With the continuity equation derived from the Wheeler-DeWitt (WDW) equation in the minisuperspace model, we show that the quantity $\rho(a)=|\psi(a)|^2$ for the universe is inversely proportional to the Hubble parameter of the universe. Thus, $\rho(a)$ represents the probability density of the universe staying in the state $a$ during its evolution, which we call the dynamical interpretation of the wavefunction of the universe. We demonstrate that the dynamical interpretation can predict the evolution laws of the universe in the classical limit as those given by the Friedmann equation. Furthermore, we show that the value of the operator ordering factor $p$ in the WDW equation can be determined to be $p=-2$

IceCube Non-detection of GRBs: Constraints on the Fireball Properties

The increasingly deep limit on the neutrino emission from gamma-ray bursts (GRBs) with IceCube observations has reached the level that could put useful constraints on the fireball properties. We first present a revised analytic calculation of the neutrino flux, which predicts a flux an order of magnitude lower than that obtained by the IceCube collaboration. For benchmark model parameters (e.g. the bulk Lorentz factor is \Gamma=10^{2.5}, the observed variability time for long GRBs is t_v=0.01 s and the ratio between the energy in accelerated protons and in radiation is \eta_p=10 for every burst) in the standard internal shock scenario, the predicted neutrino flux from 215 bursts during the period of the 40-string and 59-string configurations is found to be a factor of ~3 below the IceCube sensitivity. However, if we accept the recently found inherent relation between the bulk Lorentz factor and burst energy, the expected neutrino flux increases significantly and the spectral peak shifts to lower energy. In this case, the non-detection then implies that the baryon loading ratio should be \eta_p<10 if the variability time of long GRBs is fixed to t_v=0.01 s. Instead, if we relax the standard internal shock scenario but keep to assume \eta_p=10, the non-detection constrains the dissipation radius to be R>4x10^{12} cm assuming the same dissipation radius for every burst and benchmark parameters for fireballs. We also calculate the diffuse neutrino flux from GRBs for different luminosity functions existing in the literature. The expected flux exceeds the current IceCube limit for some luminosity functions, and thus the non-detection constrains \eta_p<10 in such cases when the variability time of long GRBs is fixed to t_v=0.01 s.Comment: Accepted by ApJ, 14 pages, 5 figures, typos corrected, scheduled for the June 10, 2012, v752 - 1 issu

Observer-based networked control for continuous-time systems with random sensor delays

This is the post print version of the article. The official published version can be obtained from the link - Copyright 2009 Elsevier LtdThis paper is concerned with the networked control system design for continuous-time systems with random measurement, where the measurement channel is assumed to subject to random sensor delay. A design scheme for the observer-based output feedback controller is proposed to render the closed-loop networked system exponentially mean-square stable with H∞ performance requirement. The technique employed is based on appropriate delay systems approach combined with a matrix variable decoupling technique. The design method is fulfilled through solving linear matrix inequalities. A numerical example is used to verify the effectiveness and the merits of the present results.This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Associate Editor George Yin under the direction of Editor Ian R. Petersen. This work was supported in part by the Royal Society of the UK, the National Natural Science Foundation of China (60774047, 60674055) and the Taishan Scholar Programs Foundation of Shandong Province, China