SL(n+1,R)/S(GL(1,R)×GL(n,R))上线丛的一个超几何方程

本文研究了伪黎曼对称空间SL（n+1,R）/S（GL（1,R）×GL（n,R））线丛上的微分方程.利用李代数方法,即Casimir算子得到这个微分算子.这个微分算子是一个超几何方程,这个结论推广了文献[1,3,5]中的微分方程.     

脉冲激光沉积动力学研究进展

脉冲激光沉积技术是现代常用的先进薄膜材料制备技术之一.文章在简要介绍脉冲激光沉积技术及其进展的基础上,较全面地介绍了脉冲激光沉积动力学的基本物理图像和动力学构架,深入地探讨了激光烧蚀靶材过程、等离子体膨胀过程和薄膜沉积过程的动力学规律,阐述了我国学者在脉冲激光沉积动力学研究方面的贡献,例如包括脉冲激光沉积三个工艺过程自洽的统一模型,等离子体膨胀的冲击波模型,基于局域能量动量守恒定律的新等离子体演化动力学模型,包括热源项、蒸发项、等离子体屏蔽效应和动态物性参数的烧蚀热传导模型,考虑电子碰撞效应和能带结构变化的修正双温模型,能统一描写从纳秒级到飞秒级脉冲激光烧蚀规律的统一双温模型等.     

镓填充二氧化硅纳米管的电子束诱导的反常膨胀

研究了镓填充二氧化硅纳米管的电子束诱导的膨胀现象, 确认微球系统中镓液体在电子束辐照下存在反常膨胀现象. 首先分析了相关的实验过程和现象, 指出此膨胀过程可以视为准静态过程; 然后根据傅里叶热传导定律, 在准静态热力学的框架下定量讨论了该系统在电子束辐 照下微球中镓液体相对体积随温度变化规律, 进一步确定系统的相对膨胀率和系统的膨胀系数, 发现反常膨胀系数是正常热膨胀系数的5-9倍. 最后指出这种反常膨胀是由系统的电离效应和残存效应共同引起的, 两者造成系统的粒子数密度急剧增加, 从而导致系统的内部压强急剧增加, 产生体积反常膨胀.     

Sandpile Dynamics Driven by Degree on Scale-Free Networks

We introduce a sandpile model driven by degree on scale-free networks, where the perturbation is triggered at nodes with the same degree. We numerically investigate the avalanche behaviour of sandpile driven by different degrees on scale-free networks. It is observed that the avalanche area has the same behaviour with avalanche size. When the sandpile is driven at nodes with the minimal degree, the avalanches of our model behave similarly to those of the original Bak-Tang-Wiesenfeld （BTW） model on scale-free networks. As the degree of driven nodes increases from the minimal value to the maximal value, the avalanche distribution gradually changes from a clean power law, then a mixture of Poissonian and power laws, finally to a Poisson-like distribution. The average avalanche area is found to increase with the degree of driven nodes so that perturbation triggered on higher-degree nodes will result in broader spreading of avalanche propagation.     

Criticality of Epidemic Spreading in Mobile Individuals Mediated by Environment

We investigate the critical behaviour of an epidemical model in a diffusive population mediated by a static vector environment on a 2D network. It is found that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behaviour near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.     

Spatiotemporal Characteristic of Epidemic Spreading in Mobile Individuals

We numerical simulate the propagation behaviour and people distribution trait of epidemic spreading in mobile individuals by using cellular automaton method. The simulation results show that there exists a critical value of infected rate fluctuating amplitude, above which the epidemic can spread in whole population. Moreover, with the value of infected rate fluctuating amplitude increasing, the spatial distribution of infected population exhibits the spontaneous formation of irregular spiral waves and convergence phenomena, at the same time, the density of different populations will oscillate automatically with time. What is more, the traits of dynamic grow clearly and stably when the time and the value of infected rate fluctuating amplitude increasing. It is also found that the maximal proportion of infected individuals is independent of the value of fluctuating amplitude rate, but increases linearly with the population density.     

基于无标度网络拓扑结构变化的舆论演化模型

基于BA无标度网络,构建了舆论和网络结构相互影响的自适应舆论演化模型.舆论的演化不仅受制于网络拓扑结构,而且也导致拓扑结构的变化.研究表明,演化达到稳态后,网络结构不再是初始的无标度网络而呈现泊松分布,而且随着时间的推移,系统中的舆论演化表现出很强的趋同效应,原来初始状态的几十个舆论,在长时间的演化后,大部分舆论灭亡,只有少数的舆论存留,且发展壮大.这种趋向与社会上的舆论、意见、信仰的演化大体上是符合的.     

Multiple Partial Attacks on Complex Networks

We numerically investigate the effect of four kinds of partial attacks of multiple targets on the Barabási Albert （BA） scale-free network and the Erdos-Rényi （ER） random network. Comparing with the effect of single target complete knockout we find that partial attacks of multiple targets may produce an effect higher than the complete knockout of a single target on both BA scale-free network and ER random network. We also find that the BA scale-free network seems to be more susceptible to multi-target partial attacks than the ER random network.     

外场和惯性双重影响下的无标度网络上舆论传播动力学

本文在考虑恒定外场φ0和节点惯性eγkh的影响下,提出了网络结构和舆论演化相互适应的舆论演化模型.研究发现,在外场和节点惯性作用下,系统中的度分布经过时间演化后逐渐偏离典型的幂率分布;同时随着时间的演化,舆论分布会出现明显的趋同现象,这种现象的产生不仅与外场本身的强度有关,而且还取决于该节点本身惯性因子;研究还表明通过调节惯性因子和外场大小可以控制舆论总数的变化,甚至于还可以控制变化的快慢.