Xu-Ming Wang

SIMULATING SEDIMENT TRANSPORT ON RIVER NETWORKS

The simulation of the variation of the erosion or sedimentation and the sediment-carrying capability of the water on the river segments, as it changes from the lower-water season to the higher-water season, is performed by a dynamical model of the sediment transport on a river network. The model is constructed by considering that the sediment-carrying capability of the water in one segment is modulated by the undergone state of it and that of its neighbor segments. The calculated results can simulate the relative variations occuring in the natural river when the water seasons alternate.

Statistical dynamics of regional populations and economies

A practical statistical analysis on the regional populations and GDPs of China is conducted. The result shows that the distribution of the populations and that of the GDPs obeys the shifted power law, respectively. To understand these characteristics, a generalized Langevin equation describing variation of population is proposed based on the correlation between population and GDP as well as the random fluctuations of the related factors. The equation is transformed into the Fokker-Plank equation, and the solution demonstrates a transform of population distribution from the normal Gaussian distribution to a shifted power law. It also suggests a critical point of time at which the transform occurs. The shifted power law distribution in the supercritical situation is qualitatively in accordance with the practical result. The distribution of the GDPs is derived based on the Cobb-Douglas production function, and presents a change from a shifted power law to the Gaussian distribution. This result indicates that the regional GDP distribution of our society will be the Gaussian distribution in the future. The analysis on the growth trend of economy suggests it will become a reality. These theoretical attempts may draw a historical picture of our world in the aspects of population and economy.

Towards Understanding What Contributes to Forming an Opinion

Opinion evolution mechanism can be captured by physical modeling. In this paper, a kinetic equation is established by defining a generalized displacement(cognitive level), a driving force and the related factors such as generalized potential, information quantity and attitude. It has been shown that the details of opinion evolution depend on the type of the driving force, self-dominated driving or environment-dominated driving. In the former case, the participants can have their attitudes changed in the process of competition between the self-driving force and environment-driving force. In the latter case, all of the participants are pulled by the environment. Some regularities behind the dynamics of opinion are also revealed, for instance, the information entropy decays with time in a special way, etc. The results may help us to get some deep understanding for the formation of a public opinion.

Dynamics of erosion-sedimentation in River networks

Based on the confluences of the different rank streams, a dynamical model of sediment transport in river network is proposed. A river can be divided into segments by the injection of branch streams of higher rank. Since there are no large fluctuations in stream flow and sediment concentration in a lower-water season, the real process in the river network can simulated by our model. With the model, the steady state indicates a scaling law that the quantity of erosion or sedimentation exponentially depends on the number of the segments along the reach of the channel. We also discuss the influence of the models parameters on steady scouring-deposition under larger impact factors. The result reveals abundant scouring- deposition phenomena which are coincident with natural river networks.

Sediment Transport Dynamics in River Networks Induced by Water Diversion

A river network is a typical completely open system formed by interconnected river channels. The interactions between the imports of a river (water and sediment) and the channel will cause the change of the channel patterns. This is actually a feedback between the erosion and the sedimentation states of the channel via an adjustment of the sedimentcarrying capability of the stream. This feedback mechanism indicates that river network is a self-organized system (Rodriguez-Iturbe, 1997), and some dynamical laws lead its evolution and some statistic laws dominate its steady state (Leopold, 1953; Leopold & Maddock, 1953; Dodds & Rothman, 2000). So, river networks have attracted, in decades past, a good much attention of physicists and geophysicists (Banavar, et al., 1997; Manna & Subramanian, 1996; Manna, 1998; Sinclair & Ball, 1996; Kramer & Marder, 1992; Takayasu & Inaoka, 1996; Maritan, et al., 1996; Caldarelli, et al., 1997; Giacometti, 2000; Somfai & Sander, 1997; Rinaldo, et al., 1996, and so on). They focused mainly on the distributions of river parameters or the scaling relations between them, as well as the evolutionary mechanism, that is, what creates the distributions and scaling relations? The pioneering field investigation executed by Leopold revealed that the slope, width and depth of a channel respectively depend on the discharge in power functions (Leopold & Maddock, 1953). From then, some other scaling relations, in power functions, between river parameters were found (Hack, 1957; Flint, 1974). The theoretical studies for the purpose of getting deeper understandings of the reasons why the nature has selected these laws were conducted by the dynamic modeling based on the local erosion rules (for instance, Banavar, et al. ,1997) or the other considerations, such as erosion process based on the minimum energy dissipation (Sun, 1994; Dhar, 2006), evolution of a quasi-random spanning tree (Manna, 1996), statistical physics method based on the self-similarity theory (Banavar, et al. ,1997), and so on. Our previous modeling studies were focused on another process, that is, sediment transport in river networks (Wang, et al. 2008; Hao, et al., 2008; Huo, et al., 2009). The core spirit of the models embodies the feedback mechanism between erosion and sedimentation via the adjustment of sediment-carrying capability (SCC) of runoff. A steady state shows scaling law that the quantity of erosion or sedimentation (QES) distributes exponentially along the channel in the downriver direction. The response of a river to the abrupt change of the input shows self-organized and self-adaptive behaviors. The former is represented by opposite variation of the SCC to the QES as the discharge changes, which shows that the response of the river trends to depress the increase of erosion as water flow increases and that of

SCALING BEHAVIOR OF SEDIMENT TRANSPORT INDUCED BY WATER DIVERSION IN RIVER NETWORKS

A sediment transport dynamic model, based on the consideration of streams confluence and/or diversion, is proposed to investigate the influence of water diversion on the mainstream. The simulated results accord qualitatively with the observed or experimental phenomenon in the Yellow River, that is, sedimentation will get more in the main channel as the water is diverted. Some interesting scaling laws describing the behavior of the erosion–sedimentation state in the process of sediment transport are observed, which may help us to get some understandings of sediment transport dynamics in a river network.