At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynam...At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.展开更多
We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory.By introducing a fractal approach to describe the chaotic dynamical behavio...We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory.By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization,we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons,and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy.We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons.Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field,and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms.It is shown that,besides the electric and magnetic fields,core scattering is a primary factor in the fractal dynamics.展开更多
The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entrop...The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entropy (ME) as well as the features of the information and fractal dimensions within the Isospin Quantum Molecular Dynamical Model compensated by the lattice methods. Results demonstrate from various views that the existence of deterministic chaos in the dynamical process of reaction.展开更多
This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different ...This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.展开更多
Newton's method and generalized Newton's methods are efficient and convenient tools for constructing chaotic fractal images ,and have been widely investigated in recent years. This paper gives a class generali...Newton's method and generalized Newton's methods are efficient and convenient tools for constructing chaotic fractal images ,and have been widely investigated in recent years. This paper gives a class generalized Newton's methods that come from Secant method ,and constructs their chaotic fractal images to support the analyses of their algorithm.展开更多
文摘At its most basic level physics starts with space-time topology and geometry. On the other hand topology’s and geometry’s simplest and most basic elements are random Cantor sets. It follows then that nonlinear dynamics i.e. deterministic chaos and fractal geometry is the best mathematical theory to apply to the problems of high energy particle physics and cosmology. In the present work we give a short survey of some recent achievements of applying nonlinear dynamics to notoriously difficult subjects such as quantum entanglement as well as the origin and true nature of dark energy, negative absolute temperature and the fractal meaning of the constancy of the speed of light.
基金Supported by the Natural Science Foundation of Zhejiang Province under Grant Nos.Y604106, Y606128the Scientific Research Fund of Zhejiang Provincial Education Department of China under Grant No.20070568the Natural Science Foundation of Zhejiang Lishui University under Grant No.KY08003
基金Project supported by the Natural Science Foundation of Shandong Province,China(Grant No.ZR2014AM030)
文摘We study the ionization of helium Rydberg atoms in an electric field above the classical ionization threshold within the semiclassical theory.By introducing a fractal approach to describe the chaotic dynamical behavior of the ionization,we identify the fractal self-similarity structure of the escape time versus the distribution of the initial launch angles of electrons,and find that the self-similarity region shifts toward larger initial launch angles with a decrease in the scaled energy.We connect the fractal structure of the escape time plot to the escape dynamics of ionized electrons.Of particular note is that the fractal dimensions are sensitively controlled by the scaled energy and magnetic field,and exhibit excellent agreement with the chaotic extent of the ionization systems for both helium and hydrogen Rydberg atoms.It is shown that,besides the electric and magnetic fields,core scattering is a primary factor in the fractal dynamics.
文摘The characteristics of the nonlinear dynamics in the Heavy Ion Collision (HIC) at intermediate energies have been studied by evaluating the productions of the Generalized Entropy (GE) and the Multifragmentation Entropy (ME) as well as the features of the information and fractal dimensions within the Isospin Quantum Molecular Dynamical Model compensated by the lattice methods. Results demonstrate from various views that the existence of deterministic chaos in the dynamical process of reaction.
文摘This paper introduced a new three-dimensional continuous quadratic autonomous chaotic system, modified from the Lorenz system, in which each equation contains a single quadratic cross-product term, which is different from the Lorenz system and other existing systems. Basic properties of the new system are analyzed by means of Lyapunov exponent spectrum, Poincaré mapping, fractal dimension, power spectrum and chaotic behaviors. Furthermore, the forming mechanism of its compound structure obtained by merging together two simple attractors after performing one mirror operation has been investigated by detailed nu-merical as well as theoretical analysis. Analysis results show that this system has complex dynamics with some interesting characteristics.
文摘Newton's method and generalized Newton's methods are efficient and convenient tools for constructing chaotic fractal images ,and have been widely investigated in recent years. This paper gives a class generalized Newton's methods that come from Secant method ,and constructs their chaotic fractal images to support the analyses of their algorithm.
