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dynamics of fractal growth
相关语句
  分形生长动力学
     TWO NON-LINEAR MODELS IN DYNAMICS OF FRACTAL GROWTH
     分形生长动力学中的两种非线性模型
短句来源
     The onset and development of multiple hydraulic fracturing are a process of fractal dilatation, and its evolution complies with the spatio-temporal dynamics of fractal growth, similar to the Omori's well known law of aftershocks for earthquakes.
     多重水力断裂的发生和发展是一种分形扩张过程 ,其演化服从串级“崩塌间断平衡”的时空分形生长动力学 ,与地震的Omori余震律相类似。
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  相似匹配句对
     structural dynamics;
     ④结构动力学;
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     On Dynamics of Handwriting
     “笔迹动力学”探析
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     METALLOGENIC DYNAMICS
     成矿动力学刍议
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     On the Dynamics of Topic
     话题的动态性
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     FRACTAL AND PHYSICS
     FRACTAL与物理学
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As well known, the processes of fractal growth are a problem of moving boundaries. Two non-linear models in dynamics of fractal growth describing moving boundaries are given, and the solubility problems of the present two non-linear models are proved based on physical essence of moving boundaries.

分形生长过程是运动边界问题,文中给出了用运动边界条件描述的分形生长动力学的两种非线性模型,并依据运动边界的物理本质,给出了这两种非线性模型可解性定理的证明。

The author analyzed systematically the present status of the four research areas of self\|organized criticality, transient chaos, the edge of chaos and weak chaos in the science of complexity and concluded that, the four research areas are actually different approaches for probing into the essence of the same problem—the spatio\|temporal evolution of open, far\|from\|equilibrium, interacting, large, dissipative dynamical systems in nature. The author further summarized the interrelationships among the four areas...

The author analyzed systematically the present status of the four research areas of self\|organized criticality, transient chaos, the edge of chaos and weak chaos in the science of complexity and concluded that, the four research areas are actually different approaches for probing into the essence of the same problem—the spatio\|temporal evolution of open, far\|from\|equilibrium, interacting, large, dissipative dynamical systems in nature. The author further summarized the interrelationships among the four areas into an important proposition: the spatio\|temporal evolution of open, far\|from\|equilibrium, interacting, large, dissipative dynamical systems in nature complies to the \!dynamics of self\|organized critical processes\", and \!the systems grow fractally at the edge of chaos".Geosystems are both very important and complex open, far\|from\|equilibrium, interacting, large, dissipative dynamical systems in nature. they possess the innate, essential attribute of self\|organized criticality. Their spatio\|temporal behaviors obey the dynamics of self\|organized critical processes of geological processes. Geosystems are situated in the transitional spatio\|temporal domains between order and chaos, i.e., at the edge of chaos. They are in the weakly chaotic dynamic states, in which regular and chaotic motions coexist and mix up. And geosystems grow fractally at the edge of chaos.The author deduced and integrated these aspects into a theory of complexity in geosciences named \!Dynamics of self\|organized critical processes of geological processes—fractal growth of geosystems at the edge of chaos\", which is widely applicable to variable geosystems. The contents of this theory are divided into six parts, they are: (1) Self\|organized criticality, transient chaos, the edge of chaos and weak chaos; (2) The coupling and interactions as well as the coherence and cooperation of multicomponents;(3) The fractal dynamics of evolutionary processes;(4) The spatio\|temporal structures of processes;(5) The dynamics of fractal growth;(6) The theory of finite\|size scaling.

笔者对复杂性科学中的自组织临界性、瞬态混沌、混沌边缘和弱混沌四大理论和研究领域就其发展现状和最近动态作系统和深入的剖析后得出结论 ,认为以上四者是对自然界中开放、远离平衡、相互作用的巨大耗散动力学系统的时空演化这个统一事物的本质的面面观。笔者进一步将四者的相互关系归纳成一个重要的命题 :自然界中开放、远离平衡、相互作用的巨大耗散动力学系统的时空演化服从“自组织临界过程动力学” ,并且系统“在混沌边缘分形生长”。地质系统是自然界中的一种既十分重要 ,又异常复杂的开放、远离平衡、相互作用的巨大耗散动力学系统。它具有自组织临界性的内禀基本属性。它的时空行为服从地质作用的自组织临界过程动力学。地质系统位于有序和混沌之间的过渡时空域 ,即混沌边缘 ,其中系统呈规则与混沌运动并存和混合的弱混沌动力学状态 ,并且地质系统在混沌边缘分形生长。将上述命题演绎和整合成一种广泛适用于地质系统的地球科学的复杂性理论 ,名之为 :“地质作用的自组织临界过程动力学———地质系统在混沌边缘分形生长” ,并将其内容归纳成 6部分 :(1)自组织临界性、瞬态混沌、混沌边缘和弱混沌 ,(2 )多组分的耦合与相互作用及其相干与协同 ,(3)演化过...

笔者对复杂性科学中的自组织临界性、瞬态混沌、混沌边缘和弱混沌四大理论和研究领域就其发展现状和最近动态作系统和深入的剖析后得出结论 ,认为以上四者是对自然界中开放、远离平衡、相互作用的巨大耗散动力学系统的时空演化这个统一事物的本质的面面观。笔者进一步将四者的相互关系归纳成一个重要的命题 :自然界中开放、远离平衡、相互作用的巨大耗散动力学系统的时空演化服从“自组织临界过程动力学” ,并且系统“在混沌边缘分形生长”。地质系统是自然界中的一种既十分重要 ,又异常复杂的开放、远离平衡、相互作用的巨大耗散动力学系统。它具有自组织临界性的内禀基本属性。它的时空行为服从地质作用的自组织临界过程动力学。地质系统位于有序和混沌之间的过渡时空域 ,即混沌边缘 ,其中系统呈规则与混沌运动并存和混合的弱混沌动力学状态 ,并且地质系统在混沌边缘分形生长。将上述命题演绎和整合成一种广泛适用于地质系统的地球科学的复杂性理论 ,名之为 :“地质作用的自组织临界过程动力学———地质系统在混沌边缘分形生长” ,并将其内容归纳成 6部分 :(1)自组织临界性、瞬态混沌、混沌边缘和弱混沌 ,(2 )多组分的耦合与相互作用及其相干与协同 ,(3)演化过程的分形动力学 ,(4 )作用的时空结构 ,(

The author applies the theory of complexity to studying the famous “five-storeyed type” morphological vertical zonality of the vein-type tungsten ore deposits in southern Jiangxi Province and obtains the following results:(1) The “five-storeyed type” morphological vertical zonality of the vein-type tungsten ore deposits is the consequence of “fractal dilatation of multiple hydraulic fracturing”. The ore-controlling multiple fractures of the vein-type tungsten ore deposits are heat-induced and fluid-driven fractures...

The author applies the theory of complexity to studying the famous “five-storeyed type” morphological vertical zonality of the vein-type tungsten ore deposits in southern Jiangxi Province and obtains the following results:(1) The “five-storeyed type” morphological vertical zonality of the vein-type tungsten ore deposits is the consequence of “fractal dilatation of multiple hydraulic fracturing”. The ore-controlling multiple fractures of the vein-type tungsten ore deposits are heat-induced and fluid-driven fractures dominated by hydraulic fracturing. The self-organized criticality of the vein-type tungsten ore deposits is the origin of multiple fractal dilatation, while the regions of the steepest gradients of hydrostatic stress field around the tip of mesoscopic cracks are the driven force of fractal dilatation. The onset and development of multiple hydraulic fracturing are a process of fractal dilatation, and its evolution complies with the spatio-temporal dynamics of fractal growth, similar to the Omori's well known law of aftershocks for earthquakes.(2) The “three rings-one cap type” geochemical zonality of ore formation for the vein-type tungsten ore deposits is an infiltration- dissolution- precipitation wave structure of multicomponent ore-forming solutions, and a target pattern formed by spatio-temporally synchronized propagation of chemical waves in ore-forming reaction-diffusion systems, as well as a radially symmetric, nested, spherically shaped, far-from-equilibrium localized dissipative structure, i.e. pulsating-type autosoliton formed by brief local excitation from external, succeeded by local breakdown of pulsation of structural, magmatic and ore-forming processes occurring in near-equilibrium geological media.(3) The vein-type tungsten ore deposits in Southern Jiangxi Province are far-from-equilibrium localized dissipative structures in near-equilibrium regional geological background. The tungsten metallogenic district of Southern Jiangxi Province is clusters of composite autosolitons, formed by propagation of magmatic and hydrothermal solitary waves of ore-forming materials for long distance under conditions of structural and magmatic pulsation of multiple stages. The ore-forming materials came from: ①“zone refining” from partial melting of source rocks of ore formation, ②transport-reaction of postmagmatic ore-forming hydrothermal solutions, and ③ infiltrative metasomatism of tungsten-containing strata.

应用复杂性理论对于赣南脉钨矿床的著名“五层楼”式形态垂直分带进行研究 ,获得如下结果。 (1 )赣南脉钨矿床的“五层楼”式形态垂直分带是“多重水力断裂分形扩张”的结果。脉钨矿床的控矿多重断裂是一种以水力断裂为主导的热致与流体驱动断裂构造。脉钨矿床的自组织临界性是多重分形扩张之源 ,而中观破裂尖端周围流体静力学应力场梯度最大区则是分形扩张的驱动力。多重水力断裂的发生和发展是一种分形扩张过程 ,其演化服从串级“崩塌间断平衡”的时空分形生长动力学 ,与地震的Omori余震律相类似。 (2 )脉钨矿床“三环一帽”式的成矿地球化学分带是一种多组分成矿溶液的渗滤、溶解沉淀波结构 ,是成矿反应扩散系统中化学波的时空同步化传播而形成的目标斑图 ,是近平衡地质介质内 ,通过外界的“短暂局部激发”、继之以构造、岩浆和成矿脉动作用等“局部中断”而形成的径向对称、嵌套球状、远离平衡的局域化耗散结构 ,即脉动型自孤子。 (3)赣南脉钨矿床是近平衡区域地质背景中远离平衡的局域化耗散结构。赣南钨矿集区是复合自孤子的群集体。它们是在构造、岩浆多期次脉动条件下 ,来自①矿源层部分熔融的“区域提纯”、②岩浆期后成矿热液输运反应和③含钨地层、岩石...

应用复杂性理论对于赣南脉钨矿床的著名“五层楼”式形态垂直分带进行研究 ,获得如下结果。 (1 )赣南脉钨矿床的“五层楼”式形态垂直分带是“多重水力断裂分形扩张”的结果。脉钨矿床的控矿多重断裂是一种以水力断裂为主导的热致与流体驱动断裂构造。脉钨矿床的自组织临界性是多重分形扩张之源 ,而中观破裂尖端周围流体静力学应力场梯度最大区则是分形扩张的驱动力。多重水力断裂的发生和发展是一种分形扩张过程 ,其演化服从串级“崩塌间断平衡”的时空分形生长动力学 ,与地震的Omori余震律相类似。 (2 )脉钨矿床“三环一帽”式的成矿地球化学分带是一种多组分成矿溶液的渗滤、溶解沉淀波结构 ,是成矿反应扩散系统中化学波的时空同步化传播而形成的目标斑图 ,是近平衡地质介质内 ,通过外界的“短暂局部激发”、继之以构造、岩浆和成矿脉动作用等“局部中断”而形成的径向对称、嵌套球状、远离平衡的局域化耗散结构 ,即脉动型自孤子。 (3)赣南脉钨矿床是近平衡区域地质背景中远离平衡的局域化耗散结构。赣南钨矿集区是复合自孤子的群集体。它们是在构造、岩浆多期次脉动条件下 ,来自①矿源层部分熔融的“区域提纯”、②岩浆期后成矿热液输运反应和③含钨地层、岩石淋滤交代的成矿物质 ,通过岩浆和热液孤

 
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