In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will sur...In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.展开更多
In this work, we study potential fluids, within which eddies exist and have quantum mechanical properties because according to Helmholtz, they are made up of an integer number of lines and their displacement in a pote...In this work, we study potential fluids, within which eddies exist and have quantum mechanical properties because according to Helmholtz, they are made up of an integer number of lines and their displacement in a potential medium is a function of a frequency. However, this system is Lorentz-invariant since Maxwell’s equations can be obtained from it, and this is what we demonstrate here. The considered hypothesis is that the electric charge arises naturally as the intensity of the eddy in the potential fluid, that is, the circulation of the velocity vector of the elements that constitute it, along that potential (it is not another parameter, whose experimental value must be added, as proposed by the standard model of elementary particles). Hence, the electric field appears as the rotational of the velocity field, at each point of the potential medium, and the magnetic field appears as the variation with respect to the velocity field of the potential medium, which is equivalent to the Biot and Savart law. From these considerations, Maxwell’s equations are reached, in particular his second equation which is the non-existence of magnetic monopoles, and the fourth equation which is Ampere’s law, both of which to date are obtained empirically demonstrated theoretically. The electromagnetic field propagation equation also arrives, thus this can be considered a demonstration that a potential medium in which eddies exists constitutes a Lorentz-invariant with quantum mechanical properties.展开更多
The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, ...The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.展开更多
The dynamics of atmosphere and ocean can be examined under different circumstances of shallow water waves like shallow water gravity waves,Kelvin waves,Rossby waves and inertio-gravity waves.The influences of these wa...The dynamics of atmosphere and ocean can be examined under different circumstances of shallow water waves like shallow water gravity waves,Kelvin waves,Rossby waves and inertio-gravity waves.The influences of these waves describe the climate change adaptation on marine environment and planet.Therefore,the present work aims to derive symmetry reductions of Broer-Kaup-Kupershmidt equation in shallow water of uniform depth and then a variety of exact solutions are constructed.It represents the propagation of nonlinear and dispersive long gravity waves in two horizontal directions in shallow water.The invariance of test equations under one parameter transformation leads to reduction of independent variable.Therefore,twice implementations of symmetry method result into equivalent system of ordinary differential equations.Eventually,the exact solutions of these ODEs are computed under parametric constraints.The derive results entail several arbitrary constants and functions,which make the findings more admirable.Based on the appropriate choice of existing parameters,these solutions are supplemented numerically and show parabolic nature,intensive and non-intensive behavior of solitons.展开更多
The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric an...The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.展开更多
We investigate a two-relaxation-time(TRT)lattice Boltzmann algorithm with the asymptotic analysis technique.The results are used to analyze invariance properties of the method.In particular,we focus on time dependent ...We investigate a two-relaxation-time(TRT)lattice Boltzmann algorithm with the asymptotic analysis technique.The results are used to analyze invariance properties of the method.In particular,we focus on time dependent Stokes and Navier-Stokes problems.展开更多
文摘In this paper we investigate the nearly small twist mappings with intersection property. With a certain non-degenerate condition, we proved that the most of invariant tori of the original small twist mappings will survive afer small perturtations. The persisted invariant tori are close to the unperturbed ones when the perturbation are small. The orbits reduced by those mappings are quasi-periodic in the invariant tori with the frequences closing to the original ones.
文摘In this work, we study potential fluids, within which eddies exist and have quantum mechanical properties because according to Helmholtz, they are made up of an integer number of lines and their displacement in a potential medium is a function of a frequency. However, this system is Lorentz-invariant since Maxwell’s equations can be obtained from it, and this is what we demonstrate here. The considered hypothesis is that the electric charge arises naturally as the intensity of the eddy in the potential fluid, that is, the circulation of the velocity vector of the elements that constitute it, along that potential (it is not another parameter, whose experimental value must be added, as proposed by the standard model of elementary particles). Hence, the electric field appears as the rotational of the velocity field, at each point of the potential medium, and the magnetic field appears as the variation with respect to the velocity field of the potential medium, which is equivalent to the Biot and Savart law. From these considerations, Maxwell’s equations are reached, in particular his second equation which is the non-existence of magnetic monopoles, and the fourth equation which is Ampere’s law, both of which to date are obtained empirically demonstrated theoretically. The electromagnetic field propagation equation also arrives, thus this can be considered a demonstration that a potential medium in which eddies exists constitutes a Lorentz-invariant with quantum mechanical properties.
基金The project supported by the Natural Science Foundation of Zhejiang Province of China under Grant No. Y604036 and State Key Laboratory of 0il/Gas Reservoir Geology and Exploitation ＂PLN0402＂ The authors would like to thank Prof. Sen-Yue Lou for his help and discussion.
文摘The （3＋1）-dimensional Jimbo-Miwa （JM） equation is solved approximately by using the conformal invariant asymptotic expansion approach presented by Ruan. By solving the new （3＋1）-dimensional integrable models, which are conformal invariant and possess Painlevé property, the approximate solutions are obtained for the JM equation, containing not only one-soliton solutions but also periodic solutions and multi-soliton solutions. Some approximate solutions happen to be exact and some approximate solutions can become exact by choosing relations between the parameters properly.
文摘The dynamics of atmosphere and ocean can be examined under different circumstances of shallow water waves like shallow water gravity waves,Kelvin waves,Rossby waves and inertio-gravity waves.The influences of these waves describe the climate change adaptation on marine environment and planet.Therefore,the present work aims to derive symmetry reductions of Broer-Kaup-Kupershmidt equation in shallow water of uniform depth and then a variety of exact solutions are constructed.It represents the propagation of nonlinear and dispersive long gravity waves in two horizontal directions in shallow water.The invariance of test equations under one parameter transformation leads to reduction of independent variable.Therefore,twice implementations of symmetry method result into equivalent system of ordinary differential equations.Eventually,the exact solutions of these ODEs are computed under parametric constraints.The derive results entail several arbitrary constants and functions,which make the findings more admirable.Based on the appropriate choice of existing parameters,these solutions are supplemented numerically and show parabolic nature,intensive and non-intensive behavior of solitons.
文摘The wave/particle duality of particles in Physics is well known. Particles have properties that uniquely characterize them from one another, such as mass, charge and spin. Charged particles have associated Electric and Magnetic fields. Also, every moving particle has a De Broglie wavelength determined by its mass and velocity. This paper shows that all of these properties of a particle can be derived from a single wave function equation for that particle. Wave functions for the Electron and the Positron are presented and principles are provided that can be used to calculate the wave functions of all the fundamental particles in Physics. Fundamental particles such as electrons and positrons are considered to be point particles in the Standard Model of Physics and are not considered to have a structure. This paper demonstrates that they do indeed have structure and that this structure extends into the space around the particle’s center (in fact, they have infinite extent), but with rapidly diminishing energy density with the distance from that center. The particles are formed from Electromagnetic standing waves, which are stable solutions to the Schrödinger and Classical wave equations. This stable structure therefore accounts for both the wave and particle nature of these particles. In fact, all of their properties such as mass, spin and electric charge, can be accounted for from this structure. These particle properties appear to originate from a single point at the center of the wave function structure, in the same sort of way that the Shell theorem of gravity causes the gravity of a body to appear to all originate from a central point. This paper represents the first two fully characterized fundamental particles, with a complete description of their structure and properties, built up from the underlying Electromagnetic waves that comprise these and all fundamental particles.
文摘We investigate a two-relaxation-time(TRT)lattice Boltzmann algorithm with the asymptotic analysis technique.The results are used to analyze invariance properties of the method.In particular,we focus on time dependent Stokes and Navier-Stokes problems.
基金The National Natural Science Foundation of China under Grant No.60803014the National High-Tech Researchand Development Plan of China under Grant No.2006AA01Z160the National Research Foundationfor Doctoral Program of Higher Education of China under Grant No.200800011017~~
