The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is ob...The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.展开更多
A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustica...A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.展开更多
Zipf＇s approach in linguistics is utilized to analyze the statistical features of frequency and correlation of 16 nearest neighboring nucleotides （AA, AC, AG, …, TT） in 12 human chro- mosomes （Y, 22, 21, 20, 19, ...Zipf＇s approach in linguistics is utilized to analyze the statistical features of frequency and correlation of 16 nearest neighboring nucleotides （AA, AC, AG, …, TT） in 12 human chro- mosomes （Y, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, and 12）. It is found that these statistical features of nearest neighboring nucleotides in human genome： （i） the frequency distribution is a linear function, and （ii） the correlation distribution is an inverse function. The coefficients of the linear function and inverse function depend on the GC content. It proposes the correlation distribution of nearest neighboring nucleotides for the first time and extends the descriptor about nearest neighboring nueleotides.展开更多
Recent progress on nuclear liquid gas phase transition (LGPT) has been reviewed, especially for the signals of LGPT in heavy ion collisions. These signals include the power-law charge distribution, cluster emission ra...Recent progress on nuclear liquid gas phase transition (LGPT) has been reviewed, especially for the signals of LGPT in heavy ion collisions. These signals include the power-law charge distribution, cluster emission rate, nuclear Zipf law, bimodality, the largest fluctuation of the fragments, Δ-scaling, caloric curve, phase coexis- tence diagram, critical temperature, critical exponent analysis, negative specific heat capacity and spinodal instability etc. The systematic works of the authors on experimental and theoretical LGPT are also introduced.展开更多
文摘The classical power law relaxation, i.e. relaxation of current with inverse of power of time for a step-voltage excitation to dielectric—as popularly known as Curie-von Schweidler law is empirically derived and is observed in several relaxation experiments on various dielectrics studies since late 19th Century. This relaxation law is also regarded as “universal-law” for dielectric relaxations;and is also termed as power law. This empirical Curie-von Schewidler relaxation law is then used to derive fractional differential equations describing constituent expression for capacitor. In this paper, we give simple mathematical treatment to derive the distribution of relaxation rates of this Curie-von Schweidler law, and show that the relaxation rate follows Zipf’s power law distribution. We also show the method developed here give Zipfian power law distribution for relaxing time constants. Then we will show however mathematically correct this may be, but physical interpretation from the obtained time constants distribution are contradictory to the Zipfian rate relaxation distribution. In this paper, we develop possible explanation that as to why Zipfian distribution of relaxation rates appears for Curie-von Schweidler Law, and relate this law to time variant rate of relaxation. In this paper, we derive appearance of fractional derivative while using Zipfian power law distribution that gives notion of scale dependent relaxation rate function for Curie-von Schweidler relaxation phenomena. This paper gives analytical approach to get insight of a non-Debye relaxation and gives a new treatment to especially much used empirical Curie-von Schweidler (universal) relaxation law.
基金supported by the Government of Perm Krai,Research Project No.C-26/628 dated 05/04/2021.
文摘A set of techniques for well treatment aimed to enhance oil recovery are considered in the present study.These are based on the application of elastic waves of various types(dilation-wave,vibro-wave,or other acoustically induced effects).In such a context,a new technique is proposed to predict the effectiveness of the elastic-wave well treatment using the rank distribution according to Zipf’s law.It is revealed that,when the results of elastic wave well treatments are analyzed,groups of wells exploiting various geological deposits can differ in terms of their slope coefficients and free members.As the slope coefficient increases,the average increase in the well oil production rate(after the well treatment)becomes larger.An equation is obtained accordingly for estimating the slope coefficient in the Zipf’s equation from the frequency of the elastic wave.The obtained results demonstrate the applicability of the Zipf’s law in the analysis of the technological efficiency of elastic-wave well treatment methods.
基金ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China （No.20173023 and No.90203012） and the Specialized Research Fund for the Doctoral Program of Higher Education of China
文摘Zipf＇s approach in linguistics is utilized to analyze the statistical features of frequency and correlation of 16 nearest neighboring nucleotides （AA, AC, AG, …, TT） in 12 human chro- mosomes （Y, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, and 12）. It is found that these statistical features of nearest neighboring nucleotides in human genome： （i） the frequency distribution is a linear function, and （ii） the correlation distribution is an inverse function. The coefficients of the linear function and inverse function depend on the GC content. It proposes the correlation distribution of nearest neighboring nucleotides for the first time and extends the descriptor about nearest neighboring nueleotides.
基金the National Natural Science Foundation of China for the Distinguished Young Scholar (No. 19725521) the National Natural Science Foundation of China (No. 19705012)+1 种基金 the Science and Technology Development Foundation of Shanghai (No.97QA14038)the Major State Basic Research Development Program of China (No. G200077400)
文摘Recent progress on nuclear liquid gas phase transition (LGPT) has been reviewed, especially for the signals of LGPT in heavy ion collisions. These signals include the power-law charge distribution, cluster emission rate, nuclear Zipf law, bimodality, the largest fluctuation of the fragments, Δ-scaling, caloric curve, phase coexis- tence diagram, critical temperature, critical exponent analysis, negative specific heat capacity and spinodal instability etc. The systematic works of the authors on experimental and theoretical LGPT are also introduced.
