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
To improve heating uniformity and anthocyanin content of the blueberry pulp under microwave heating,the intermittent variable power microwave heating technology was introduced in the study.The effects of technology pa...To improve heating uniformity and anthocyanin content of the blueberry pulp under microwave heating,the intermittent variable power microwave heating technology was introduced in the study.The effects of technology parameters in terms of high microwave intensity heating time,intermittent time,low microwave intensity and low microwave intensity heating time on the blueberry pulp quality parameters(heating uniformity,average moisture content,the highest temperature and anthocyanin content)were investigated by using the response surface method.The results showed that the longer heating time under different microwave intensities resulted in the poorer heating uniformity.The intermittent stage promoted heat and mass transfer within the pulp and reduced the temperature difference and moisture gradient within the pulp,which enhanced desired uniformity of temperature and moisture distribution before entering the low microwave intensity heating stage.Therefore,the longer the intermittent time,the greater the heating uniformity.The optimal parameters were developed as high microwave intensity of 4 W·g^(-1),high microwave intensity heating time of 9.86 min,intermittent time of 10 min,low microwave intensity of 2.2 W·g^(-1)and low microwave intensity heating time of 6 min.This research might provide guidance for microwave heating berry fruits.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 National Natural Science Foundation of China(32072352)。
文摘To improve heating uniformity and anthocyanin content of the blueberry pulp under microwave heating,the intermittent variable power microwave heating technology was introduced in the study.The effects of technology parameters in terms of high microwave intensity heating time,intermittent time,low microwave intensity and low microwave intensity heating time on the blueberry pulp quality parameters(heating uniformity,average moisture content,the highest temperature and anthocyanin content)were investigated by using the response surface method.The results showed that the longer heating time under different microwave intensities resulted in the poorer heating uniformity.The intermittent stage promoted heat and mass transfer within the pulp and reduced the temperature difference and moisture gradient within the pulp,which enhanced desired uniformity of temperature and moisture distribution before entering the low microwave intensity heating stage.Therefore,the longer the intermittent time,the greater the heating uniformity.The optimal parameters were developed as high microwave intensity of 4 W·g^(-1),high microwave intensity heating time of 9.86 min,intermittent time of 10 min,low microwave intensity of 2.2 W·g^(-1)and low microwave intensity heating time of 6 min.This research might provide guidance for microwave heating berry fruits.
