Experimental results indicate that propagation paths of cracks in geomaterials are often irregular. producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propaga...Experimental results indicate that propagation paths of cracks in geomaterials are often irregular. producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propagation in geomaterials. The formula correlates the dynamic and static fracture toughnesses with crack velocity, crack length and a microstructural parameter, and allows the fractal dimension to be obtained. From the equations for estimating crack velocity and fractal dimension it can be shown that the measured crack ve1ocity, Vo, should be much smaller than the fractal crack velocity, V. It can also be shown that the fractal dimension of the crack propagation path can be calculated directly from Vo and from the fracture toughness.展开更多
Traffic network is an importance asp ect of researching controllable parameters of an urban spatial morpholo-gy.Based on GIS,traffic network str ucture complexity can be understood by using fractal geometry in which t...Traffic network is an importance asp ect of researching controllable parameters of an urban spatial morpholo-gy.Based on GIS,traffic network str ucture complexity can be understood by using fractal geometry in which th e length-radius dimension describes change of network density,and ramification-radius dimension describes complexity and accessibility of urban network.It i s propitious to analyze urban traffic network and to understand dynamic c hange process of traffic network using expanding f ractal-dimension quantification.Meanwhile the length-radius dimension and ramifica-tion-radius dimension could be rega rd as reference factor of quantitative describing urban traffic network.展开更多
文摘Experimental results indicate that propagation paths of cracks in geomaterials are often irregular. producing rough fracture surfaces which are fractal. A formula is derived for the fractal kinematics of crack propagation in geomaterials. The formula correlates the dynamic and static fracture toughnesses with crack velocity, crack length and a microstructural parameter, and allows the fractal dimension to be obtained. From the equations for estimating crack velocity and fractal dimension it can be shown that the measured crack ve1ocity, Vo, should be much smaller than the fractal crack velocity, V. It can also be shown that the fractal dimension of the crack propagation path can be calculated directly from Vo and from the fracture toughness.
文摘Traffic network is an importance asp ect of researching controllable parameters of an urban spatial morpholo-gy.Based on GIS,traffic network str ucture complexity can be understood by using fractal geometry in which th e length-radius dimension describes change of network density,and ramification-radius dimension describes complexity and accessibility of urban network.It i s propitious to analyze urban traffic network and to understand dynamic c hange process of traffic network using expanding f ractal-dimension quantification.Meanwhile the length-radius dimension and ramifica-tion-radius dimension could be rega rd as reference factor of quantitative describing urban traffic network.
