與激光聚變、自然災害和深空探測等相關的非線性動力學斑圖和軌道穩定性研究2013年度報告

王煒++王駿

摘 要：在激光聚變的穩定性分析和刻畫方面，針對激光聚變中預熱燒蝕RT不穩定性、界面流體不穩定性、激光-等離子體相互作用中的多種不穩定性現象開展全面的研究，對不穩定性導致的斑圖演化定量規律、多種不穩定性的競爭以及多種因素對不穩定性的影響，開展了系統研究；并提出了若干控制和抑制相應不穩定性的方案。在大氣海洋波動及固體災變的研究方面，一方面圍繞固體災變，開展了局部化觸發災變破壞的理論模型研究，并針對多種脆性材料開展了實驗觀測，取得了階段性的進展；另一方面，研究了一類帶快震蕩隨機力的三維海洋原始方程組，證明了其不變測度的存在性和在分布意義下的收斂性；研究了無界區域中的帶隨機外力的二維準地轉方程，克服了無界區域沒有緊性的困難，證明了該隨機方程隨機吸引子的存在性。還針對地震波算子、不可壓NS方程整體穩定性等問題開展了研究。這些都穩步推進了大氣海洋方程波動的研究。在深空探測的軌道設計及相關基礎理論方面，一方面在Arnold擴散的基礎理論方面取得了關鍵性進展；另一方面針對平運動共振、小行星動力學特征等問題開展了系統的研究，為精細太陽系模型的發展開展了很多方法和計算上的準備，還圍繞深空航天器軌道設計多個子課題開展了系統的研究，取得了突出的成果，形成了具有重要應用價值的程序庫，為進一步研究奠定了基礎。在生物信號轉導動力學和調控機制的研究方面，圍繞p53介導細胞命運抉擇、轉錄終止子調控，小RNA對靶基因mRNA的調控等方面開展了系統的研究，并取得了階段性的成果。我們還針對多種信號網絡的同步、信號轉導等過程開展了多角度的研究。CVTree3網絡服務器新版本的編程已完整，正在內部試運行，很快即可發布。

關鍵詞：激光聚變 災變 深空探測 生物信號轉導

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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