Quantum properties near the instability boundary in optomechanical system

The properties of the system near the instability boundary are very sensitive to external disturbances, which is important for amplifying some physical effects or improving the sensing accuracy. In this paper, the quantum properties near the instability boundary in a simple optomechanical system has been studied by numerical simulations. Calculations show that the transitional region connecting the Gaussian states and the Ring states when crossing the boundary is sometimes different from the region centered on the boundary line, but it is more essential. The change of the mechanical Wigner function in the transitional region directly reflects its bifurcation behavior in classical dynamics. Besides, quantum properties such as mechanical second-order coherence function and optomechanical entanglement, can be used to judge the corresponding bifurcation types and estimate the parameter width and position of the transitional region. The non-Gaussian transitional states exhibit strong entanglement robustness, and the transitional region as a boundary ribbon can be expected to replace the original classical instability boundary line in future applications.

Adaptive, locally linear models of complex dynamics

The dynamics of complex systems generally include high-dimensional, nonstationary, and nonlinear behavior, all of which pose fundamental challenges to quantitative understanding. To address these difficulties, we detail an approach based on local linear models within windows determined adaptively from data. While the dynamics within each window are simple, consisting of exponential decay, growth, and oscillations, the collection of local parameters across all windows provides a principled characterization of the full time series. To explore the resulting model space, we develop a likelihood-based hierarchical clustering, and we examine the eigenvalues of the linear dynamics. We demonstrate our analysis with the Lorenz system undergoing stable spiral dynamics and in the standard chaotic regime. Applied to the posture dynamics of the nematode Caenorhabditis elegans, our approach identifies fine-grained behavioral states and model dynamics which fluctuate about an instability boundary, and we detail a bifurcation in a transition from forward to backward crawling. We analyze whole-brain imaging in C. elegans and show that global brain dynamics is damped away from the instability boundary by a decrease in oxygen concentration. We provide additional evidence for such near-critical dynamics from the analysis of electrocorticography in monkey and the imaging of a neural population from mouse visual cortex at single-cell resolution.

Effect of Rolling Motion on Flow Instability of Parallel Rectangular Channels of Natural Circulation

In order to study the effect of rolling motion on flow instability of parallel rectangular channels of natural circulation, the natural circulation reactor simulation system is used for physical prototype. And theory analysis model of parallel rectangular channels of natural circulation system under rolling motion is established and coded by Fortran. The results of the program are verified to the experiments, and the results are in good agreement. The flow instability boundaries of different pressure under static and rolling motion are calculated respectively. The results show that: 1) under static condition, with the increase of the pressure, the instability boundary line changes, and the system becomes more stable; 2) under rolling conditions, the heating power of instability boundary decreases comparing to the stable conditions. The instability occurs earlier; 3) the stability of the system decreases with the increasing of rolling amplitude and frequency.

GLOBAL STABILITY FOR THERMAL CONVECTION IN A COUPLE-STRESS FLUID WITH TEMPERATURE AND PRESSURE DEPENDENT VISCOSITY

We show that the global nonlinear stability threshold for convection in a couple-stress fluid with temperature and pressure dependent viscosity is exactly the same as the linear instability boundary. This optimal result is important because it shows that linearized instability theory has captured completely the physics of the onset of convection. It has also been found that the couplestress fluid is more stable than the ordinary viscous fluid and then the effect of couple-stress parameter (F) and variable dependent viscosity (Γ) on the onset of convection is also analyzed.