【作者】 何越磊；

【导师】 姚令侃；

【作者基本信息】 西南交通大学 ， 道路与铁道工程， 2005， 博士

【摘要】 本文围绕着沙堆模型复杂性现象,展开了以自组织临界性理论为主的复杂性理论及应用的研究。在已有成果的基础上,具体工作如下: 1、我们先前的实验表明,散粒体呈现自组织临界性与系统的组构特征和组织原则有关,作为组织原则之一的颗粒非均匀性是影响因素。为进一步深入研究,探讨其它组构特征和组织原则以及其它外界因素对散粒体自组织临界性的影响,我们开展了如下实验: (1)人工碎石材料的均匀沙和非均匀沙单面坡沙堆实验。碎石材料的沙堆表现的规律属性与河沙材料的一致。散粒体颗粒的磨圆度虽然是散粒体的组构特征之一,但不是影响散粒体自组织临界性的因素。 (2)坡面插桩和增设坡脚平台的沙堆实验。这些人为对沙堆系统施加影响的办法会影响沙堆落沙的量值,但不能改变沙堆原有的规律属性。 (3)多尺度的米堆单面坡模型实验。表明颗粒形状对散粒体自组织临界性的影响不显著。 2、在实验基础上,开展沙堆模型复杂性理论专题研究: (1)在论述、分析自组织临界性理论特征和内涵的基础上,结合散粒体实验,探讨了沙堆模型的时空长程相关性,采用R/S分析法确定非均匀沙堆具有正的长程相关性,而均匀沙堆不具备。 (2)引入多重分形理论和方法,分析非均匀沙堆自组织临界状态的空间和时间上的多层次分形结构;建立简化的多重分形动力模型,分析了散粒体自组织临界状态的多重分形动力行为。进而,确定了散粒体自组织临界性的多重分形特征。表明非均匀沙堆比均匀沙堆具有更高的复杂性。 3、采用复杂性研究方法分析几类自然灾害的规律属性,探讨自组织临界性的普适性。 (1)斜坡灾害是沙堆模型直观表象的自然现象。在对滑坡、崩塌和泥石流的空间分布和时间序列分析时,证明这三种斜坡灾害幂率分布的共性和自组织临界性特征。 (2)临界状态下,许多差异很大的物理系统具有极大的相似性。基于此,分析洪水和沙尘暴的实测资料: a、介绍趋势消除波动分析法,分析实测最大洪峰流量时间序列,证明序列具有长程相关性。更多还原

【Abstract】 This paper focuses on complexity in sandpiles and studies the complexity theory and application of self-organized criticality. Base on the fruit had been taken the main work and conclusions are as follows:1、 By experiments we have discovered that self-organized criticality in granular mixtures is strongly influenced by the fabric characteristics and the organizing structure principle. The non-uniform degree of granular material, as an organizing structure principle, is a factor affecting SOC. For finding the other factor of the fabric characteristics and the organizing structure principle or others affecting SOC, we carried on the follow experiments:(1)Uniform and non-uniforn sandpiles of single slope experiments with the stuffs of artifical broken stone are done. The sandpiles of artifical broken stone have same law with the sandpiles of fluvial sand. The psephicity of granular is one of the fabric characteristics but is not a factor affecting SOC.(2)The experiment of pitching of pile on the slope of the sandpiles and the experiment of mountting a platform at toe of slope of the sandpiles are done. The means such as pitching of pile on the slope of the sandpiles and mountting a platform at toe of slope of the sandpiles can affect the quantity of falling sandpiles but these do not change the law of sandpiles.(3)Multi-scale single slope rice-piles experiments are done. The experiments indicate the effect to granular SOC of the shape is not marked.2、 Base on sandpiles experiments, we research granular complexity theory.(1)Discussing the characteristic and meaning of self-organization criticality theory and analyzing granular experiments, we research long range spatial-temporal correlation o f s andpiles. With the rescaled r ange analysis method, we ensure that non-uniform sandpiles has positive long range correlation but uniform sandpiles has not.(2)Multi-fractal theory and method is introduced. Multiple course of fractal structure of sliding size serial and sliding interval time serial are analyzed. And simplified multi-fractal dynamic model is set up, with which dynamic action of granular SOC is researched. Multi-fractal feature indicates non-uniform sandpilesis more complex than uniform.3 > The field data of some kinds of natural disaster are analyzed with different complexity analysis means. The universality of SOC is discussed.(1) The slope disaster is natural phenomenon that it is presentational by the sandpiles. Spatial and temporal distribution series of landslide, avalanche and debris flow are researched, it is proved that the three slope disasters have common property such as power distribution and the other characteristic of SOC.(2) In the critical state many very different physical systems are very similar. So we analyzed the field data of the flood and severe duststorm:a> Detrended fluctuation analysis method is introduced and used to analyze maximum-recorded flood peak time series. It is proved that the series has long range correlation.b .. Multi-fractal detrended fluctuation analysis method is introduced and used to analyze severe duststorm series. It is showed that the series has long range correlation and multi-fractal structure. Multi-fractal singularity exponent spectrum of the series is educed.c^ The methods study demonstrates the results with three kinds of means are comparable.Research discovers that flood, slope disaster and severe duststorm, which are three kinds of natural disaster systems of very different physical property and genesis, have some internal regularity.4> Fresh thinking and means for two kinds of complex disaster forecast having the attribute of SOC or quasiperiod are presented. Considering the reliability design for engineering, applying statistics of extremes directed by complexity theory is researched, and extreme value distribution of power distribution is deduced to graduating distribution of extremum type I. And an example is given. Direction of complexity theory such as SOC theory can provide fresh thinking for disaster forecast, project planning and design.5 , Considering interaction and compatibility between communication engineering and environment is a new task for road location design. The cellular automata is one of primary means for complexity research. The paper assumes generalized leading line location means and the cellular automata model for road location. The idea is a new means for road location design for compatibilitybetween communication engineering and environment.6>. At critical state, granular has the property both solid and fluid. We research the complex mechanism of granular in the two respects:(l)The paper researches the complex characteristics of granular including the cumulate texture, density and stress distribution. Moreover by means of the relative density of large-scale coarse grained soil test, we make know non-uniform sandpiles being banked has greater randomness, which makes for complexity of the structure space and the density. Researching exposure degree and intergranular acting at the slope of sandpiles, we conclude complexity of the fabric inside and surface of granular leads to complexity of critical activity. Non-uniform sandpiles is more complex than uniform inside and surface.(2)Under the thought of turbulence and laminar flow theory, we put forward turbulent motion layer and laminar motion layer hypothesis for granular critical fluid state. The hypothesis is used to explain the complex behavior mechanism and phenomena of granular SOC.更多还原