Aim To study the dIelectric breakdown phenomenon in the materials with quenched disorder. Methods Renormolization group methods were used. Results The percolation limit for breakdown pc , the breakdown field Ec～(Pc-...Aim To study the dIelectric breakdown phenomenon in the materials with quenched disorder. Methods Renormolization group methods were used. Results The percolation limit for breakdown pc , the breakdown field Ec～(Pc-p)v, and the fractal dimension of the structure of dielectric breakdown df were obtained. Conclusion The breakdown properties of the materials with quenched disorder are characterized by universal power laws, where the exponents are universal.展开更多
Ba<span style="font-family:Verdana;">sed on the urban resident population statistics from 2005 to 2018, thi</span><span style="font-family:Verdana;">s paper analyzes the distribut...Ba<span style="font-family:Verdana;">sed on the urban resident population statistics from 2005 to 2018, thi</span><span style="font-family:Verdana;">s paper analyzes the distribution and evolution of city scale in China by screening city samples according to the threshold criteria and using empirical research methods such as the City Primacy Index, the Rank-Scale Rule, the Gini coefficient of city scale, Kernel Density Estimation and Markov transfer matrix. The results show that: the most populous city in China has obvious advantages. The population distribution is concentrated in high order cities and in accordance with the law of order</span><span style="font-family:Verdana;">-</span><span style="font-family:""><span style="font-family:Verdana;">scale;the economic scale of cities is in a concentrated state, the gap between the economic development levels of different types of cities is large, and the megacities are more attractive, which to a certain extent limit the development of the scale of the rest of the cities;th</span><span style="font-family:Verdana;">e number of China’s city population is increasing, however, the ga</span><span style="font-family:Verdana;">p between the</span></span><span style="font-family:""> </span><span style="font-family:Verdana;">population scale of other cities and the most populous city continues to be large, and the structure of city population scale is not reasonable enough;megacities and megalopolises keep their original scale levels unchanged to a large extent, and the scale transition between the two types of cities is rather difficult. Finally, based on the explanatory framework of the dynamics of city scale evolution, policy recommendations are proposed to promote a more balanced distribution of city scale.</span>展开更多
文摘Aim To study the dIelectric breakdown phenomenon in the materials with quenched disorder. Methods Renormolization group methods were used. Results The percolation limit for breakdown pc , the breakdown field Ec～(Pc-p)v, and the fractal dimension of the structure of dielectric breakdown df were obtained. Conclusion The breakdown properties of the materials with quenched disorder are characterized by universal power laws, where the exponents are universal.
文摘Ba<span style="font-family:Verdana;">sed on the urban resident population statistics from 2005 to 2018, thi</span><span style="font-family:Verdana;">s paper analyzes the distribution and evolution of city scale in China by screening city samples according to the threshold criteria and using empirical research methods such as the City Primacy Index, the Rank-Scale Rule, the Gini coefficient of city scale, Kernel Density Estimation and Markov transfer matrix. The results show that: the most populous city in China has obvious advantages. The population distribution is concentrated in high order cities and in accordance with the law of order</span><span style="font-family:Verdana;">-</span><span style="font-family:""><span style="font-family:Verdana;">scale;the economic scale of cities is in a concentrated state, the gap between the economic development levels of different types of cities is large, and the megacities are more attractive, which to a certain extent limit the development of the scale of the rest of the cities;th</span><span style="font-family:Verdana;">e number of China’s city population is increasing, however, the ga</span><span style="font-family:Verdana;">p between the</span></span><span style="font-family:""> </span><span style="font-family:Verdana;">population scale of other cities and the most populous city continues to be large, and the structure of city population scale is not reasonable enough;megacities and megalopolises keep their original scale levels unchanged to a large extent, and the scale transition between the two types of cities is rather difficult. Finally, based on the explanatory framework of the dynamics of city scale evolution, policy recommendations are proposed to promote a more balanced distribution of city scale.</span>
