与激光聚变、自然灾害和深空探测等相关的非线性动力学斑图和轨道稳定性研究2013年度报告

王炜++王骏

摘 要：在激光聚变的稳定性分析和刻画方面，针对激光聚变中预热烧蚀RT不稳定性、界面流体不稳定性、激光-等离子体相互作用中的多种不稳定性现象开展全面的研究，对不稳定性导致的斑图演化定量规律、多种不稳定性的竞争以及多种因素对不稳定性的影响，开展了系统研究；并提出了若干控制和抑制相应不稳定性的方案。在大气海洋波动及固体灾变的研究方面，一方面围绕固体灾变，开展了局部化触发灾变破坏的理论模型研究，并针对多种脆性材料开展了实验观测，取得了阶段性的进展；另一方面，研究了一类带快震荡随机力的三维海洋原始方程组，证明了其不变测度的存在性和在分布意义下的收敛性；研究了无界区域中的带随机外力的二维准地转方程，克服了无界区域没有紧性的困难，证明了该随机方程随机吸引子的存在性。还针对地震波算子、不可压NS方程整体稳定性等问题开展了研究。这些都稳步推进了大气海洋方程波动的研究。在深空探测的轨道设计及相关基础理论方面，一方面在Arnold扩散的基础理论方面取得了关键性进展；另一方面针对平运动共振、小行星动力学特征等问题开展了系统的研究，为精细太阳系模型的发展开展了很多方法和计算上的准备，还围绕深空航天器轨道设计多个子课题开展了系统的研究，取得了突出的成果，形成了具有重要应用价值的程序库，为进一步研究奠定了基础。在生物信号转导动力学和调控机制的研究方面，围绕p53介导细胞命运抉择、转录终止子调控，小RNA对靶基因mRNA的调控等方面开展了系统的研究，并取得了阶段性的成果。我们还针对多种信号网络的同步、信号转导等过程开展了多角度的研究。CVTree3网络服务器新版本的编程已完整，正在内部试运行，很快即可发布。

关键词：激光聚变 灾变 深空探测 生物信号转导

Abstract： In this year， the ressearches of our project are carried out facing with four key scientific problems. All the participants worked actively， and the research plans are successfully archieved. Especially， some important results have been obtained. Presently， there are 58 scientific papers published in the high-tier journals， including Phys. Rev. Lett.， Phys. Plasma， Phys. Rev. E， EPL， PloS One and so on. Two monographs are published with the supports of this fund. These results includes. （1）the RT instability and interfacial fluid instability and various instabilities in laser-plasma interaction are widely studied. The quantitative characteristics of the pattern evolution， the comprtition between various instabilities as well as the effects of different environmental factors are systematically investigated. Some schemes to control or suppress these instabilies are proposed. （2）The theoretical model about how the localization induces the catastrophe is proposed， and the related experiments on the fragile materials are carried out. Some interim results are obtained. The primitive 3D ocean equation with fast oscillative stochastic forces are also studied. The existence and convergence under certain conditions are proved. Besides， some important studies on various kinds of nonliner partial differential equations are also carried out. （3）There are key progresses on the fundamental theory about Arnold diffusion. A series of characteristics about asteriods are carried out， which provides sufficient preparations for the further research on the precise model of solar system. There are also many valuable progresses on the design and control of deep-space vehicles. （4）There are systematical studies on the p53-centered network regulation， transcription terminator regulation， and the regulation on the mRNA of target genes by sRNA. Some important results are obtained. The coding of new-version CVTree3 is finished， and would be released. Besides， among all the students who participated into this project， there are 15 ones who received their doctorate degrees and 12 ones who received their master degrees. One participant received the National Science Fund for Distinguished Young Scholars.

Key Words： Laser fusion； Catastrophe； Deep-space voyage； Biological signal transduction

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