An anisotropic model of sandpile

An anisotropic model of sandpile has been proposed with different topping in different directions taken in consideration. Simulation results show that no significant differences exist between this anisotropic model and the isotropic one. Foundation item: Supported by the National Natural Science Foundation of China(104980113) Biography: Wang Xin(1978-), male, Master candidate, research direction: condense matter of physics.     

Influences of finite-size effects on the self-organized criticality of forest-fire model

The influences of finite-size effects on the self-organized criticality (SOC) of the traditional forest-fire model are investigated by means of a new method. The forest size is originally set to a value much greater than the correlation length of the forest. Finite-size effects are then studied by equally dividing the forest into more and more separate subsystems on condition that the forest size, igniting probability and planting probability are invariant. A new phenomenon, i.e. the finite-size effects with one-side frequency peak, is observed. The boundary between two neighboring subsystems can be regarded as a firebreak. The concept of 'separation ability' is introduced to represent the probability for the firebreak to block off the fire successfully. Restraining effects of separation ability on finite-size effects are analyzed. Finite-size effects and separation ability, as well as their relations are found to have practical importance to the actual forest-fire protection.     

多态概率元胞自动机森林火灾模型及应用

通过对概率元胞自动机模型的改进,分析了在既不能生长又不能燃烧的空地存在或森林砍伐形成的多态邻居条件下,森林中树木占有率的变化。模拟结果表明在适度留一些既不能生长又不能燃烧的空地或适度砍伐的条件下,不但不会减少森林中树木的比率反而有利于树木的生长。模拟结果与真实情况比较吻合。     

Sierpinski镂垫上具有三体自旋作用的Ising模型

应用实空间重整化群变换的方法,在Sierpinski镂垫上研究了外场作用下具有二体和三体自旋作用的Ising模型,求出了临界点和临界指数.与只有二体自旋作用的情况相比较,考虑三体自旋作用后,系统仍然只存在零温相变.     

Self-organized criticality of forest fires in China

Self-organized criticality (SOC) of forest fires in China from 1950 to 1989 is studied. The stability, scaleinvariant character of SOC and external effects on SOC of forest fires in China are analyzed in detail. Forest-fire cellular automata model is a typical model for the research of SOC. Based on the traditional forest-fire model, an improved model, in which effects of tree species, meteorological conditions and human efforts on forest fires are considered, is introduced. Actual forest fire data in China are compared with simulation results of the two models. It is shown that forest fire data in China have SOC behavior and simulation results of the improved model accord better with actual forest fire data than those of the traditional model.     

Self-organized criticality judgment and extreme statistics analysis of major urban fires

The spatial (economic loss) and temporal characteristics of urban fires were analyzed employing relevant statistical methods. A fractal structure in terms of the power-law relation between fire frequency and economic loss was found on a spatial scale, and an exponential relation between frequency and time interval was found on a temporal scale. Thus, urban fire does not meet the rigorous criteria of self-organized criticality. In addition, based on the spatial power-law distribution characteristics, a correlation model of the frequency and scale of loss due to urban fire was established using the extremum statistical method. This model was then applied to the case analysis of Hefei and the probability of major fire incidents in the future was predicted.     

地震强度递增沙堆模型响应机制的研究

针对汶川地震Ⅹ度和Ⅺ度烈度区崩塌滑坡面积与累计频率统计关系呈现不同分布规律的现象,开展了地震峰值加速度从0.075~0.450g的6组振动台沙堆模型实验.实验重现了随振动强度增加,落沙量与累计频率从幂律分布-对数正态分布-正态分布依次转变的现象.数学分析表明,变异系数的减小,是这3种概型依次转变的原因.根据实验观察,随扰动递增沙堆表面颗粒行为呈现不同响应模式:微振动时颗粒活动性消失的概率与活动性分叉的概率在总体上平衡,当颗粒间近邻的相互作用导致连锁反应时才能发生大规模落沙事件,具有最大的不确定性.强振动时大部分颗粒就能独立启动,大规模落沙成为必然事件.据此提出,落沙规模由自组织控制的颗粒链式反应过程,向外力控制的颗粒独立下落过程的转化是导致变异系数减小的物理机制.根据以上认识,随地震烈度增加,汶川地震触发的崩塌滑坡规模与累计频率依次服从幂律分布-对数正态分布的现象,可能是具有普适性意义的规律.     

基于复杂系统理论的电网连锁故障研究

复杂系统理论是目前研究的一个热点,也是研究复杂电网连锁故障内在机理的最有力工具;该文首先介绍了电网连锁故障的研究历程及成果,然后根据对NERC15年数据进行的分析,说明电网大停电事故的长期关联性,并在此基础上分析了电网的自组织临界性及其对连锁故障的影响,最后简要地介绍了电网的小世界特性对连锁故障的影响。     

二维准流体的自组织临界性

在二维ＢＴＷ模型的基础上建立了准流体系统的计算机仿真模型．研究了临界点的存在性和系统的临界指数行为,建立了一个新的临界参量,确定了具体的算法和程序,得到了一些有意义的曲线．结果表明,二维准流体确实存在自组织临界性．     

带有临界Sobolev-Hardy指标椭圆问题的一个全局紧性结果

设Ω属于R^N是有界光滑区域，0∈Ω，N≥3，0≤s〈2，2＊（s）：=2（N-s）/N-2，2≤q〈2＊：=2＊（0）=2N/N-2，μ≥0，λ∈R．运用变分方法和分析技巧，证明了带有Dirichlet边界条件的奇异临界问题-△u-μu/｜x｜^2=｜u｜^2＊（s）-2/｜x｜^su＋λ｜u｜^q-2u的一个全局紧性结果．     

矸石山稳定性非线性破坏准则数值模拟分析

在探讨矸石山主要特征的基础上,基于Hoek-Brown非线性强度准则进行FLAC(fastlagrangian analysis of continua)数值模拟,分析矸石山稳定性随堆积高度的增加动态的变化过程.结果表明:随堆积高度增加,矸石山位移、变形程度增大,潜在滑移面逐渐形成,失稳破坏趋势渐增,且矸石山散粒层高度、面积增加,坡面出现局部滑塌几率增大;依据非线性强度准则计算得到的安全系数随矸石山高度增加而减小,符合矸石山堆积越高越不安全的实际情况.计算结果和理论分析表明采用文中方法分析矸石山稳定性具有合理性.     

Ising模型集团大小对重正化结果影响的分析

以二维三角晶格为例选取包含9个晶格的晶胞为Kadanoff集团,通过重正化变换求出其临界点和临界指数并与三角晶格[1]、六角晶格[2]的结果作比较,比较的结果表明:选取更大的集团可以提高其计算精度。     

Heisenberg群上具有临界指数的次椭圆方程解的存在性

本文将(1.1)推广到了Heisenberg群上并且讨论了(1.2)解的存在.     

Heisenberg群上具有临界指数的次椭圆方程解的不存在性

本文将（1．1）推广到了Heisenberg群上并且讨论了（1．2）解的不存在．     

用纤维方法研究一类带有Sobolev临界指数和Hardy项的半线性椭圆方程解的存在性问题

设Ω是R^n中的有界光滑区域，0∈Ω，N≥3，2＊：=2N/N-2是Sobolev临界指数，通过Pohozaev提出的纤维方法，证明了当参数λ和μ满足一定条件时，带有Dirichlet边界条件的椭圆问题-△u-μ/｜x｜^2u=｜u｜^2＊-2u＋λu解的存在性．     

带有临界Sobolev和Hardy项的半线性椭圆方程的解(Ⅰ)

设Ω( )RN是有界光滑区域,0∈Ω,N≥3,2*:=2N/N-2,0≤s＜2,2*(s):=2(N-s),2＜r＜2*(s).对于满足一定条件的参数λ和μ,证明了带Dirichlet边界条件的奇异椭圆问题-△u-μμ/|x|2=|u|2*-2u+λ|u|r-2/|x|su的一些重要性质.     

一类带Sobolev临界指数椭圆方程正解的存在性

研究了一类带Sobolev临界指数的椭圆方程.通过证明局部(P.S.)条件和能量泛函的估计,运用强极大值原理证明了这类方程正解的存在性.     

带有临界Sobolev-Hardy指标椭圆问题的径向解

设Ω(∪)RN是球心在原点半径为R的球形区域,N≥3,0≤s＜2,2*(s)=2(N-s)/N-2,μ≥0,λ＞0.运用变分方法和分析技巧,证明了带有Dirichlet边界条件的奇异临界问题-△u-μu/|x|2=|u|2*(s)-2/|x|s u+λu的无穷多个径向解的存在性.这些解都带有不同个数的节点.     

完全阻挫XY模型的Ising型相变

利用短时Monte Carlo方法研究正方点阵上铁磁键和反铁磁键按Z形排列和按列交错排列的完全阻挫（FF）XY模型的Ising型相变,计算这两种模型各自的临界温度Tc、静态指数2β／v,及v、动力学指数z。分析序参量（交错手征磁化强度Mx和交错磁化强度Mst）的选取对Ising型相变的影响,发现只有静态指数v的值明显依赖于序参量的选取。模拟结果表明,这2个FFXY模型的临界温度和临界指数基本相等,属同一个普适类。     

二维Ising模型重正化群方法集团不同大小划分结果的分析

基于二维三角晶格模型,分别选取包含7、9个格点自旋的集团为Kadanoff集团,通过实空间重正化群变换分析求解临界点及临界指数,对其结果对比分析表明:选取更大的自旋集团可以提高精度.