Potential Landscape and Flux Framework of Nonequilibrium Networks: Robustness, Dissipation, and Coherence of Biochemical Oscillations

We established a theoretical framework for studying nonequilibrium networks with two distinct natures essential for characterizing the global probabilistic dynamics: the underlying potential landscape and the corresponding curl flux. We applied the idea to a biochemical oscillation network and found that the underlying potential landscape for the oscillation limit cycle has a distinct closed ring valley (Mexican hat-like) shape when the fluctuations are small. This global landscape structure leads to attractions of the system to the ring valley.

Estimation of suspended sediment concentrations using Pulse-coherent Acoustic Doppler Profiler (PCADP)

The objective of the study is to investigate the suitability of using Pulse-coherent Acoustic Doppler Profiler (PCADP) to estimate suspended sediment concentration (SSC). The acoustic backscatter intensity was corrected for spreading and absorption loss, then calibrated with OBS and finally converted to SSC. The results show that there is a good correlation between SSC and backscatter intensity with R value of 0.74. The mean relative error is 22.4%. Then the time span of little particle size variation was also analyzed to exclude the influence of size variation. The correlation coefficient increased to 0.81 and the error decreased to 18.9%. Our results suggest that the PCADP can meet the requirement of other professional instruments to estimate SSC with the errors between 20% and 50%, and can satisfy the need of dynamics study of suspended particles.

Mixed-layer water oscillations in tropical Pacific for ENSO cycle

The main modes of interannal variabilities of thermocline and sea surface wind stress in the tropical Pacific and their interactions are investigated, which show the following results. (1) The thermocline anomalies in the tropical Pacific have a zonal dipole pattern with 160 W as its axis and a meridional seesaw pattern with 6-8 degrees N as its transverse axis. The meridional oscillation has a phase lag of about 90 to the zonal oscillation, both oscillations get together to form the El Nino/La Nina cycle, which behaves as a mixed layer water oscillates anticlockwise within the tropical Pacific basin between equator and 12 degrees N. (2) There are two main patterns of wind stress anomalies in the tropical Pacific, of which the first component caused by trade wind anomaly is characterized by the zonal wind stress anomalies and its corresponding divergences field in the equatorial Pacific, and the abnormal cross- equatorial flow wind stress and its corresponding divergence field, which has a sign opposite to that of the equatorial region, in the off-equator of the tropical North Pacific, and the second component represents the wind stress anomalies and corresponding divergences caused by the ITCZ anomaly. (3) The trade winds anomaly plays a decisive role in the strength and phase transition of the ENSO cycle, which results in the sea level tilting, provides an initial potential energy to the mixed layer water oscillation, and causes the opposite thermocline displacement between the west side and east side of the equator and also between the equator and 12 degrees N of the North Pacific basin, therefore determines the amplitude and route for ENSO cycle. The ITCZ anomaly has some effects on the phase transition. (4) The thermal anomaly of the tropical western Pacific causes the wind stress anomaly and extends eastward along the equator accompanied with the mixed layer water oscillation in the equatorial Pacific, which causes the trade winds anomaly and produces the anomalous wind stress and the corresponding divergence in favor to conduce the oscillation, which in turn intensifies the oscillation. The coupled system of ocean-atmosphere interactions and the inertia gravity of the mixed layer water oscillation provide together a phase-switching mechanism and interannual memory for the ENSO cycle. In conclusion, the ENSO cycle essentially is an inertial oscillation of the mixed layer water induced by both the trade winds anomaly and the coupled ocean-atmosphere interaction in the tropical Pacific basin between the equator and 12 degrees N. When the force produced by the coupled ocean-atmosphere interaction is larger than or equal to the resistance caused by the mixed layer water oscillation, the oscillation will be stronger or maintain as it is, while when the force is less than the resistance, the oscillation will be weaker, even break.

特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.