From the mesoscopic point of view,a definition of soft point is introduced by considering the attributes of geometric profile and mass distribution.After that,this concept is used to develop the soft matching techniqu...From the mesoscopic point of view,a definition of soft point is introduced by considering the attributes of geometric profile and mass distribution.After that,this concept is used to develop the soft matching technique to simulate the chaotic behaviors of the equations.Especially,a tennis model with deformation factor a(t)is proposed to derive a generalized Newton-Stokes equation v′(t)=λ(v T-a(t)v(t)).Furthermore,a concept of duality of deformation factor a(t)and velocity v(t)with respect to the generalized NewtonStokes equation is established.To solve this equation,two data-driven models of a(t)are provided,one is based on the concept of soft matching,while the other is by using the amplitude modulation.Finally,the related iterative algorithm is developed to simulate the motion of the falling body via the duality of a(t)and v(t).Numerical examples successfully demonstrate the phenomenon of chaos,which consists of the continual random oscillations and sudden accelerations.Moreover,the algorithm is tested by using larger coefficients corresponding to the terminal velocity and shows more satisfactory results.It may enable us to characterize the total energy of the dynamical system more accurately.展开更多
The central dogma of molecular biology describes the flow of genetic information from DNA via RNA to protein and duplication from ancestral to descendent DNA（Crick,1958）.However,the genetic information could not be ...The central dogma of molecular biology describes the flow of genetic information from DNA via RNA to protein and duplication from ancestral to descendent DNA（Crick,1958）.However,the genetic information could not be quantified and mathematically modeled.So it differs from the“information”formulated by Shannon and used in information and coding theories（Shannon,1949）.展开更多
基金supported by the National Natural Science Foundation of China(Nos.12061160462,11631015)。
文摘From the mesoscopic point of view,a definition of soft point is introduced by considering the attributes of geometric profile and mass distribution.After that,this concept is used to develop the soft matching technique to simulate the chaotic behaviors of the equations.Especially,a tennis model with deformation factor a(t)is proposed to derive a generalized Newton-Stokes equation v′(t)=λ(v T-a(t)v(t)).Furthermore,a concept of duality of deformation factor a(t)and velocity v(t)with respect to the generalized NewtonStokes equation is established.To solve this equation,two data-driven models of a(t)are provided,one is based on the concept of soft matching,while the other is by using the amplitude modulation.Finally,the related iterative algorithm is developed to simulate the motion of the falling body via the duality of a(t)and v(t).Numerical examples successfully demonstrate the phenomenon of chaos,which consists of the continual random oscillations and sudden accelerations.Moreover,the algorithm is tested by using larger coefficients corresponding to the terminal velocity and shows more satisfactory results.It may enable us to characterize the total energy of the dynamical system more accurately.
基金supported by the National Natural Science Foundation of China (31372222)the Key Research Project of the National Natural Science Foundation of China (91531302)
文摘The central dogma of molecular biology describes the flow of genetic information from DNA via RNA to protein and duplication from ancestral to descendent DNA（Crick,1958）.However,the genetic information could not be quantified and mathematically modeled.So it differs from the“information”formulated by Shannon and used in information and coding theories（Shannon,1949）.
