We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on...We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.展开更多
To investigate whether and how manual acupuncture（MA） modulates brain activities,we design an experiment where acupuncture at acupoint ST36 of the right leg is used to obtain electroencephalograph（EEG） signals in ...To investigate whether and how manual acupuncture（MA） modulates brain activities,we design an experiment where acupuncture at acupoint ST36 of the right leg is used to obtain electroencephalograph（EEG） signals in healthy subjects.We adopt the autoregressive（AR） Burg method to estimate the power spectrum of EEG signals and analyze the relative powers in delta（0 Hz-4 Hz）,theta（4 Hz-8 Hz）,alpha（8 Hz-13 Hz）,and beta（13 Hz-30 Hz） bands.Our results show that MA at ST36 can significantly increase the EEG slow wave relative power（delta band） and reduce the fast wave relative powers（alpha and beta bands）,while there are no statistical differences in theta band relative power between different acupuncture states.In order to quantify the ratio of slow to fast wave EEG activity,we compute the power ratio index.It is found that the MA can significantly increase the power ratio index,especially in frontal and central lobes.All the results highlight the modulation of brain activities with MA and may provide potential help for the clinical use of acupuncture.The proposed quantitative method of acupuncture signals may be further used to make MA more standardized.展开更多
文摘We study the nonlinear parabolic equations for travelling wave solutions of Burger’s equations. The purpose of the present work is to study various types of Burger’s equations describing waves and those are based on nonlinear equations. We focus on to describe the analytic solution in the special pattern of travelling wave solutions using tan-cot function method. We discuss about inviscid and viscous version of Burger’s equation for fluid flow and investigate the effects of internal friction of a fluid via Reynolds number. By changing the velocity amplitude, the nature of flows with shock wave and disturbance are observed. For numerical solutions, the Crank-Nicolson scheme is introduced to establish the wave solutions.
基金Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 50537030)the National Natural Science Foundation of China (Grant Nos. 61072012 and 61172009)+1 种基金the Young Scientists Fund of the National Natural Science Foundation of China (Grant Nos. 61104032 and 60901035)the Tianjin Municipal Natural Science Foundation (Grant No. 12JCZDJC21100)
文摘To investigate whether and how manual acupuncture（MA） modulates brain activities,we design an experiment where acupuncture at acupoint ST36 of the right leg is used to obtain electroencephalograph（EEG） signals in healthy subjects.We adopt the autoregressive（AR） Burg method to estimate the power spectrum of EEG signals and analyze the relative powers in delta（0 Hz-4 Hz）,theta（4 Hz-8 Hz）,alpha（8 Hz-13 Hz）,and beta（13 Hz-30 Hz） bands.Our results show that MA at ST36 can significantly increase the EEG slow wave relative power（delta band） and reduce the fast wave relative powers（alpha and beta bands）,while there are no statistical differences in theta band relative power between different acupuncture states.In order to quantify the ratio of slow to fast wave EEG activity,we compute the power ratio index.It is found that the MA can significantly increase the power ratio index,especially in frontal and central lobes.All the results highlight the modulation of brain activities with MA and may provide potential help for the clinical use of acupuncture.The proposed quantitative method of acupuncture signals may be further used to make MA more standardized.
