Self-Organized Cognitive Maps

This paper argues cognitive mapping is a learning process that can be simulated by a self-organizing neural network. The learning of city locations was considered in two studies. One study focused on the learning of city locations on four continents. Results indicated the neural network aligned the cities producing systematic errors similar to those in human cognitive maps. A second study had a neural network learn a biased sample of city locations in the United States. Results indicated a non-linear relationship between cognitive and physical distances. Self-organized cognitive maps naturally produce this non-linear relationship when information from more than one scale is mapped into one space.     

软岩饱水试验与软化临界现象研究

针对华南地区广为分布的“红层”软岩遇水软化问题,选择粉砂质泥岩、泥质粉砂岩等典型软岩为研究对象,在软岩饱水软化试验的基础上,采用“自组织临界性”理论深入分析了软化试验中的临界现象,结合软岩物理力学性质、微观结构以及水溶液离子浓度变化的试验结果,得出：在饱水3个月和6个月时,对应于所研究软岩软化的临界时间点,其物理、力学性质与水溶液离子浓度的变化在前3个月内变化幅度较大,3个月后较为平缓,并可能出现波动,6个月后开始趋于稳定;而其微观结构变化满足1～3个月变化较小,3～6个月自行调整而趋于有序,6个月之后结构类型完全改变。在此基础上,分析了软岩系统自组织临界现象中最显著的两个特征：自组织性和临界特性,并从系统演化的角度探讨了饱水软岩系统中一种具有一定稳定性的非平衡自组织有序结构的产生过程,给出了水作用下软岩工程特性变异达到稳定的临界时刻。     

Metallogenic Districts of Yangtze Cratonic Rim at the Edge of Chaos

Ｔｈｒｅｅｆｕｎｄａｍｅｎｔａｌｔｈｅｏｒｉｅｓａｒｅｒａｉｓｅｄｆｏｒ“ｃｏｍｐｌｅｘｉｔｙａｎｄｓｅｌｆ－ｏｒｇａｎｉｚｅｄｃｒｉｔｉｃａｌｉｔｙ（ＳＯＣ）ｏｆｍｅｔａｌｏｇｅｎｉｃｄｙｎａｍｉｃｓｙｓｔｅｍｓ”（Ｙｕ,１９９８）：（１）Ｎｏｎｌ...     

成矿动力系统在混沌边缘分形生长——一种新的成矿理论与方法论(下)

:“成矿动力系统在混沌边缘分形生长”理论是笔者将复杂性理论及非线性科学与矿床地质学相结合 ,对中国扬子古陆周缘六个矿集区的基本范式进行长期系统研究所取得的总结性成果。研究指出 ,成矿系统总体上是开放、远离平衡、时空延展的动力学系统。它们具有复杂性和自组织临界性的内禀基本属性 ,并且在混沌边缘分形生长。该理论以“地质作用与时 空结构是一切地质现象的本质与核心”的自然哲学理念作为根本立足点 ,建立起一种具有普适性的理论框架。然后进一步将其具体化为三大组成部分 ,即 ( 1)矿床的动力学属性 ,( 2 )矿床地质学场 ,( 3 )成矿系统的演化。体现了成矿作用 (其核心为成矿作用动力学 ) ,空间结构 (矿床地质学场 )和时间结构 (成矿系统的演化 )三位一体的整体耦合与交织 ,从而又使该理论具有包容性。在此基础上进而归纳出“成矿动力系统在混沌边缘分形生长”的 5项判定准则以及表征这些准则的 10项相应的动力学行为特征。最后笔者提出“矿质局部活化导致成矿的发生”的命题 ,拟定了“成矿的发生”的重要科学问题 ,以“元胞非线性网络”(CNN)作为复杂性的范式 ,定量揭示成矿的发生 ,并对矿床在混沌边缘作精确定位 ,对“成矿动力系统在混沌边缘”理论作进一步的延伸、深化与发展。该理论在?     

地震学中非线性预测方法的初步研究

介绍了近年来地震预测学中非线性理论和非线性方法的研究趋势和最新研究进展。在非线性数学模型的研究中，较为成功地将非线性门限模型，指数模型、具有长程关联自回归模型等应用于地震的中期预测上，在分形研究上，明确地取代了以往的一些经验结果，使对地震的活动的经验统计关系上升到分形的理论，在研究地震的动力学机制中，以多滑块－弹簧模型为代表，模拟地壳上地震断层运动机制和事实，建立了粘滑摩擦情况下的参数动力学方程。     

Complexity and Self-Organized Criticality of Solid Earth System(Ⅰ)

ＰＯＳＩＮＧＴＨＥＰＲＯＢＬＥＭ“ＣｏｍｐｌｅｘｉｔｙａｎｄＳｅｌｆ－ＯｒｇａｎｉｚｅｄＣｒｉｔｉｃａｌｉｔｙｏｆＳｏｌｉｄＥａｒｔｈＳｙｓｔｅｍ”ｉｓａｎｅｗｐｒｏｂｌｅｍａｓｗｅｌａｓａｎｅｗｐｒｏｐｏｓｉｔｉｏｎ．Ｔｈｅａｕｔｈｏｒｐｕｔｓｆｏ...     

Fractal Structures Driven by Self-gravity: Molecular Clouds and the Universe

In the interstellar medium, as well as in the Universe, large density fluctuations are observed, that obey power-law density distributions and correlation functions. These structures are hierarchical, chaotic, turbulent, but are also self-organizing. The apparent disorder is not random noise, but can be described by a fractal, with a deterministic fractal dimension. We present a new theory of the self-gravity thermodynamics, that could explain the existence of these fractal structures, and predict their fractal dimension. The media obeying scaling laws can be considered critical, as in second order phase transitions for instance. This revised version was published online in July 2006 with corrections to the Cover Date.     

The Role of Heterogeneities as a Tuning Parameter of Earthquake Dynamics

We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity (quasidynamic model). The model produces a brittle-ductile transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: (1) high stress drop barriers in near-vertical directions and (2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations.on leave from CNRS Rennes, France     

城市化:相变与自组织临界性

城市化的本质是一种自组织临界相变过程 ,在时间和空间上分别联系着自组织临界性(SOC)和空间复杂性。城市化过程作为SOC有 3个方面的标志 :时间方向的 1/ f涨落、空间方面的分形结构和等级方式的Zipf定律 ,其共性是无标度性。分形中心地景观和位序 -规模分布分别是城市化自组织临界过程在空间和等级两个领域的实证判据。在城市化的临界相变过程中 ,城市体系通常演化为无标度网络 ,而位序 -规模法则乃是空间领域的无标度性在等级领域的结构性“投影”。基于SOC思想研究城市化过程有助于理解自组织城市网络的复杂空间动力学 ,从而为发展城市演化的模拟实验方法提供理论思路     

带Hardy-Sobolev项的p-Laplace方程解的存在性

本文利用对称性临界点原理,在无界的柱形区域上,得到一类带Hardy-Sobolev项的p-Laplace方程的非平凡解的存在性。所得结果推广补充了已有的结论。