Time dependent intrinsic correlation analysis of temperature and dissolved oxygen time series using empirical mode decomposition

In the marine environment, many fields have fluctuations over a large range of different spatial and temporal scales. These quantities can be nonlinear \red{and} non-stationary, and often interact with each other. A good method to study the multiple scale dynamics of such time series, and their correlations, is needed. In this paper an application of an empirical mode decomposition based time dependent intrinsic correlation, \red{of} two coastal oceanic time series, temperature and dissolved oxygen (saturation percentage) is presented. The two time series are recorded every 20 minutes \red{for} 7 years, from 2004 to 2011. The application of the Empirical Mode Decomposition on such time series is illustrated, and the power spectra of the time series are estimated using the Hilbert transform (Hilbert spectral analysis). Power-law regimes are found with slopes of 1.33 for dissolved oxygen and 1.68 for temperature at high frequencies (between 1.2 and 12 hours) \red{with} both close to 1.9 for lower frequencies (time scales from 2 to 100 days). Moreover, the time evolution and scale dependence of cross correlations between both series are considered. The trends are perfectly anti-correlated. The modes of mean year 3 and 1 year have also negative correlation, whereas higher frequency modes have a much smaller correlation. The estimation of time-dependent intrinsic correlations helps to show patterns of correlations at different scales, for different modes.Comment: 35 pages with 22 figure

Optimized Double-well quantum interferometry with Gaussian squeezed-states

A Mach-Zender interferometer with a gaussian number-difference squeezed input state can exhibit sub-shot-noise phase resolution over a large phase-interval. We obtain the optimal level of squeezing for a given phase-interval $\Delta\theta_0$ and particle number $N$, with the resulting phase-estimation uncertainty smoothly approaching $3.5/N$ as $\Delta\theta_0$ approaches 10/N, achieved with highly squeezed states near the Fock regime. We then analyze an adaptive measurement scheme which allows any phase on $(-\pi/2,\pi/2)$ to be measured with a precision of $3.5/N$ requiring only a few measurements, even for very large $N$. We obtain an asymptotic scaling law of $\Delta\theta\approx (2.1+3.2\ln(\ln(N_{tot}\tan\Delta\theta_0)))/N_{tot}$, resulting in a final precision of $\approx 10/N_{tot}$. This scheme can be readily implemented in a double-well Bose-Einstein condensate system, as the optimal input states can be obtained by adiabatic manipulation of the double-well ground state.Comment: updated versio

A Generic Dynamical Model of Gamma-ray Burst Remnants

The conventional generic model is deemed to explain the dynamics of $\gamma$-ray burst remnants very well, no matter whether they are adiabatic or highly radiative. However, we find that for adiabatic expansion, the model could not reproduce the Sedov solution in the non-relativistic phase, thus the model needs to be revised. In the present paper, a new differential equation is derived. The generic model based on this equation has been shown to be correct for both radiative and adiabatic fireballs, and in both ultra-relativistic and non-relativistic phase.Comment: 10 pages, LaTeX, 4 postscript figures, accepted for publication in MNRA