The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's th...The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.展开更多
We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in p...We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.展开更多
The Doppler effect can be defined as the frequency shift suffered by a wave phenomenon, when there is a difference in relative speed between the waves generated and their source. We know that it occurs in the case of ...The Doppler effect can be defined as the frequency shift suffered by a wave phenomenon, when there is a difference in relative speed between the waves generated and their source. We know that it occurs in the case of mechanical and electromagnetic waves. We propose to generalize the Doppler effect to the case of frequency changes of certain oscillatory variables in biology before and after puberty, starting from the basis that a metabolically accelerated system is equivalent to a mechanically accelerated system. We then established the following objectives: To verify if there is an average difference in heart and respiratory rates, before and after puberty. To verify the association of these frequency differences with the metabolic activity estimated as basal metabolic rate or BMR. We studied heart and respiratory rate data from healthy people of both sexes, verifying the frequency distribution before and after puberty. We also study the relationship of the frequency distribution with the evolution of the basal metabolic rate throughout life. Analysis of the results shows that the highest heart and respiratory rates occur before puberty, while the lowest rates occur after puberty. A high correlation of the evolution of the variables studied with the evolution of the metabolic acceleration of the system throughout life is also evident. Taking into account that a mechanically accelerated system is equivalent to a metabolically accelerated system, we can conclude that the frequency distribution found is the expression of a generalization of the Doppler effect in the case of biological physical systems.展开更多
文摘The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.
文摘We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.
文摘The Doppler effect can be defined as the frequency shift suffered by a wave phenomenon, when there is a difference in relative speed between the waves generated and their source. We know that it occurs in the case of mechanical and electromagnetic waves. We propose to generalize the Doppler effect to the case of frequency changes of certain oscillatory variables in biology before and after puberty, starting from the basis that a metabolically accelerated system is equivalent to a mechanically accelerated system. We then established the following objectives: To verify if there is an average difference in heart and respiratory rates, before and after puberty. To verify the association of these frequency differences with the metabolic activity estimated as basal metabolic rate or BMR. We studied heart and respiratory rate data from healthy people of both sexes, verifying the frequency distribution before and after puberty. We also study the relationship of the frequency distribution with the evolution of the basal metabolic rate throughout life. Analysis of the results shows that the highest heart and respiratory rates occur before puberty, while the lowest rates occur after puberty. A high correlation of the evolution of the variables studied with the evolution of the metabolic acceleration of the system throughout life is also evident. Taking into account that a mechanically accelerated system is equivalent to a metabolically accelerated system, we can conclude that the frequency distribution found is the expression of a generalization of the Doppler effect in the case of biological physical systems.
