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
Quantum physics can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of soli...Quantum physics can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria (SDC) electrolytes in SOFCs lowers the open-circuit voltage (OCV) below the Nernst voltage (Vth). The low OCV is calculated with Wagner’s equation, included in the Nernst-Planck equation, which is based on the first and second thermodynamic laws. Experimental and theoretical limitations of Wagner’s equation have been discovered. Considering the separation of the Boltzmann distribution and Maxwell’s Demon, only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants in the definitions of the chemical and electrical potentials. This means that an additional thermodynamic law is needed. Furthermore, quantum physics can be explained by the additional thermodynamic law.展开更多
Bell’s non-locality theorem can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the...Bell’s non-locality theorem can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria electrolytes in SOFCs lowers the open-circuit voltage (OCV) to less than the Nernst voltage. This low OCV has been explained by Wagner’s equation, which is based on chemical equilibrium theory. However, Wagner’s equation is insufficient to explain the low OCV, which should be explained by fluctuation and dissipation theorems. Considering the separation of the Boltzmann distribution and Maxwell’s demon, only carrier species with sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants into the definitions of the chemical and electrical potentials. Then, an energy loss equal to the activation energy will occur because of the interactions between ions and electrons. This energy loss means that an additional thermodynamic law based on an advanced model of Maxwell’s demon is needed. In this report, the zero-point energy can be explained by this additional ther-modynamic law, as can Bell’s non-locality theorem.展开更多
The fine-structure constant of 1/137 is puzzling and has never been fully explained. When the interaction coefficient is 1/137, the transference number should be 136/137. With the transference number concept, we notic...The fine-structure constant of 1/137 is puzzling and has never been fully explained. When the interaction coefficient is 1/137, the transference number should be 136/137. With the transference number concept, we noticed that we must examine the constant of 1/136 instead of 1/137 to discover an empirical relationship in which the fine-structure constant is related to the mass ratio of electrons and quarks. Then, the physical meaning of this empirical relationship is discussed.展开更多
For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergenc...For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE（max1≤k≤n｜Sk｜^1/q-∈bn^1/qp）^＋〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 （log n） ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.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.
文摘Quantum physics can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria (SDC) electrolytes in SOFCs lowers the open-circuit voltage (OCV) below the Nernst voltage (Vth). The low OCV is calculated with Wagner’s equation, included in the Nernst-Planck equation, which is based on the first and second thermodynamic laws. Experimental and theoretical limitations of Wagner’s equation have been discovered. Considering the separation of the Boltzmann distribution and Maxwell’s Demon, only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants in the definitions of the chemical and electrical potentials. This means that an additional thermodynamic law is needed. Furthermore, quantum physics can be explained by the additional thermodynamic law.
文摘Bell’s non-locality theorem can be understood in terms of classical thermodynamics, which is already considered to be a complete field. However, inconsistencies in classical thermodynamics have been discovered in the area of solid-oxide fuel cells (SOFCs). The use of samarium-doped ceria electrolytes in SOFCs lowers the open-circuit voltage (OCV) to less than the Nernst voltage. This low OCV has been explained by Wagner’s equation, which is based on chemical equilibrium theory. However, Wagner’s equation is insufficient to explain the low OCV, which should be explained by fluctuation and dissipation theorems. Considering the separation of the Boltzmann distribution and Maxwell’s demon, only carrier species with sufficient energy to overcome the activation energy can contribute to current conduction, as determined by incorporating different constants into the definitions of the chemical and electrical potentials. Then, an energy loss equal to the activation energy will occur because of the interactions between ions and electrons. This energy loss means that an additional thermodynamic law based on an advanced model of Maxwell’s demon is needed. In this report, the zero-point energy can be explained by this additional ther-modynamic law, as can Bell’s non-locality theorem.
文摘The fine-structure constant of 1/137 is puzzling and has never been fully explained. When the interaction coefficient is 1/137, the transference number should be 136/137. With the transference number concept, we noticed that we must examine the constant of 1/136 instead of 1/137 to discover an empirical relationship in which the fine-structure constant is related to the mass ratio of electrons and quarks. Then, the physical meaning of this empirical relationship is discussed.
基金supported by National Natural Science Foundation of China (Grant No. 10871146)supported by Natural Sciences and Engineering Research Council of Canada
文摘For a sequence of identically distributed negatively associated random variables {Xn; n ≥ 1} with partial sums Sn = ∑i=1^n Xi, n ≥ 1, refinements are presented of the classical Baum-Katz and Lai complete convergence theorems. More specifically, necessary and sufficient moment conditions are provided for complete moment convergence of the form ∑n≥n0 n^r-2-1/pq anE（max1≤k≤n｜Sk｜^1/q-∈bn^1/qp）^＋〈∞to hold where r 〉 1, q 〉 0 and either n0 = 1,0 〈 p 〈 2, an = 1,bn = n or n0 = 3,p = 2, an = 1 （log n） ^1/2q, bn=n log n. These results extend results of Chow and of Li and Spataru from the indepen- dent and identically distributed case to the identically distributed negatively associated setting. The complete moment convergence is also shown to be equivalent to a form of complete integral convergence.
