The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular po...The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind). 展开更多
Based on Hong's theory, previous random models, and a generalized expression suitable for FFT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simu...Based on Hong's theory, previous random models, and a generalized expression suitable for FFT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simulation demonstrate that the wave energy changes with the incidence angle and the distance from the wall. Particularly, the Mach effect and the combined wave spectrum characteristics are analyzed in detail, which are significant in both theory and practice.展开更多
The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the pisto...The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the piston are both sufficiently small, the author establishes the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength by employing a modified wave front tracking method.展开更多
We hypothesize that 100% of the energy of our cosmic system is held by a physically real Complex Tension Field (CTF). We are using an old methodology of thinking used by our forefather engineers long before the advent...We hypothesize that 100% of the energy of our cosmic system is held by a physically real Complex Tension Field (CTF). We are using an old methodology of thinking used by our forefather engineers long before the advent of modern scientific thinking. We call it Interaction Process Mapping Epistemology or IPM-E. We apply this IPM-E on to the prevailing Measurable Data Modeling Epistemology or MDM-E. This approach helped us analyze the “Measurement Problem”, recognized during the rise of quantum mechanics (QM), and helped us recover a universal property of all linear waves, that they do not interact, or interfere, with each other. This Non-Interaction of Waves, or the NIW-property, should be obvious through daily observations and through the Huygens-Fresnel diffraction integral and through critical evaluation of contradictory hypotheses we have been assigning to photons through ages. This implicates that the time-frequency Fourier theorem, although mathematically correct, and is used universally in all branches of science;does not map the real physical interaction processes for most optical phenomena. Accordingly, we present the necessary modifications for a few selected phenomena in classical and quantum optics to validate the NIW-property. In the process we find that accepting photons as non-interacting, but diffractively propagating linear wave packets crossing the entire cosmic space, requires CTF as a physical medium. Then we develop logical arguments in support of stable elementary particles as nonlinear but resonant vortex-like undulations of this same CTF. These vortex-like particles impose various secondary potential gradients around themselves giving rise to the four forces we know. Thus, CTF can serve as the cosmic substrate to develop a unified field theory without the need of dark matter and dark energy. In the process, we demonstrate a path to add ontologic thinking on our biologically successful epistemic thinking.展开更多
This article is devoted to the study of the propagations of the non- linear water waves on the shear flows. Assuming μ = kh is small and ε/μ~2 ～ 0 (1), and the base flow is uniformly sheared, the modified Boussine...This article is devoted to the study of the propagations of the non- linear water waves on the shear flows. Assuming μ = kh is small and ε/μ~2 ～ 0 (1), and the base flow is uniformly sheared, the modified Boussinesq equation is obtained. We calculate propagations of the single sohtary wave with vorticity Γ = 0, >0 and <0. The influences of the vorticity are manifested. At the end examples of the interactions of two solitary waves, moving in opposite and the same directions, are given. Besides the phase shift, there also occur second wavelets after head-on collision.展开更多
The large accelerations of plasma were observed early in type-Ⅰ comet tail. The accelerations can reach 300 cm/S^2. Recently, the direct measurements for comet G-Z show that the energy of particles reaches 2×10~...The large accelerations of plasma were observed early in type-Ⅰ comet tail. The accelerations can reach 300 cm/S^2. Recently, the direct measurements for comet G-Z show that the energy of particles reaches 2×10~5 eV. It is much higher than the initial展开更多
This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and pos...This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo（PLK） method is employed to derive the two-sided Korteweg–de Vries（KdV） equations with their corresponding phase shifts. The nonlinear Schrodinger equation（NLSE） is obtained from the modified Kd V（mKdV） equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.展开更多
In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four s...In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.展开更多
By means of the numerical method,the tropical air-sea interaction waves are studied.The results show that when the Kelvin waves are filtered out and only the equatorial Rossby waves are reserved both in the atmosphere...By means of the numerical method,the tropical air-sea interaction waves are studied.The results show that when the Kelvin waves are filtered out and only the equatorial Rossby waves are reserved both in the atmosphere and in the ocean,the disturbances can also propagate eastward because of the air-sea interaction.The critical wavelength of the eastward propagating waves is related to the intensity of the air-sea interaction.The stronger the air-sea interaction,the larger the eastward propagating components of the air-sea interaction waves.The results of the numerical experiments are in good agreement with those of the theoretical analysis(Chao and Zhang,1988).展开更多
文摘The Euler equations for two dimensional, steady, isentropic, and inviscid flow are considered. All the elementary waves are classified into incoming and outgoing waves under the assumption that there is a singular point in the configuration of the solution.The interactions of at most two incoming waves are dealt with in this paper, and all six kinds of configurations for the solutions are obtained. They are the Mach reflection (one kind), the shock wave S transmits contact discontinuity J (two kinds), the overtaking of two incoming shock waves (two kinds), and the collision of two incoming shock waves (one kind).
文摘Based on Hong's theory, previous random models, and a generalized expression suitable for FFT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simulation demonstrate that the wave energy changes with the incidence angle and the distance from the wall. Particularly, the Mach effect and the combined wave spectrum characteristics are analyzed in detail, which are significant in both theory and practice.
基金supported by the National Natural Science Foundation of China(Nos.11626176,11701435)the Fundamental Research Funds for the Central Universities of China(Nos.2018IB015,2018IVB013)
文摘The 1-D piston problem for the pressure gradient equations arising from the flux-splitting of the compressible Euler equations is considered. When the total variations of the initial data and the velocity of the piston are both sufficiently small, the author establishes the global existence of entropy solutions including a strong rarefaction wave without restriction on the strength by employing a modified wave front tracking method.
文摘We hypothesize that 100% of the energy of our cosmic system is held by a physically real Complex Tension Field (CTF). We are using an old methodology of thinking used by our forefather engineers long before the advent of modern scientific thinking. We call it Interaction Process Mapping Epistemology or IPM-E. We apply this IPM-E on to the prevailing Measurable Data Modeling Epistemology or MDM-E. This approach helped us analyze the “Measurement Problem”, recognized during the rise of quantum mechanics (QM), and helped us recover a universal property of all linear waves, that they do not interact, or interfere, with each other. This Non-Interaction of Waves, or the NIW-property, should be obvious through daily observations and through the Huygens-Fresnel diffraction integral and through critical evaluation of contradictory hypotheses we have been assigning to photons through ages. This implicates that the time-frequency Fourier theorem, although mathematically correct, and is used universally in all branches of science;does not map the real physical interaction processes for most optical phenomena. Accordingly, we present the necessary modifications for a few selected phenomena in classical and quantum optics to validate the NIW-property. In the process we find that accepting photons as non-interacting, but diffractively propagating linear wave packets crossing the entire cosmic space, requires CTF as a physical medium. Then we develop logical arguments in support of stable elementary particles as nonlinear but resonant vortex-like undulations of this same CTF. These vortex-like particles impose various secondary potential gradients around themselves giving rise to the four forces we know. Thus, CTF can serve as the cosmic substrate to develop a unified field theory without the need of dark matter and dark energy. In the process, we demonstrate a path to add ontologic thinking on our biologically successful epistemic thinking.
基金The project supported by the National Natural Science Foundation of China
文摘This article is devoted to the study of the propagations of the non- linear water waves on the shear flows. Assuming μ = kh is small and ε/μ~2 ～ 0 (1), and the base flow is uniformly sheared, the modified Boussinesq equation is obtained. We calculate propagations of the single sohtary wave with vorticity Γ = 0, >0 and <0. The influences of the vorticity are manifested. At the end examples of the interactions of two solitary waves, moving in opposite and the same directions, are given. Besides the phase shift, there also occur second wavelets after head-on collision.
基金Project supported by the National Natural Science Foundation of China.
文摘The large accelerations of plasma were observed early in type-Ⅰ comet tail. The accelerations can reach 300 cm/S^2. Recently, the direct measurements for comet G-Z show that the energy of particles reaches 2×10~5 eV. It is much higher than the initial
文摘This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo（PLK） method is employed to derive the two-sided Korteweg–de Vries（KdV） equations with their corresponding phase shifts. The nonlinear Schrodinger equation（NLSE） is obtained from the modified Kd V（mKdV） equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.
基金supported by 973 Key program and the Key Program from Beijing Educational Commission with No. KZ200910028002Program for New Century Excellent Talents in University (NCET)+4 种基金Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality (PHR-IHLB)The research of Sheng partially supported by NSFC (10671120)Shanghai Leading Academic Discipline Project: J50101The research of Zhang partially supported by NSFC (10671120)The research of Zheng partially supported by NSF-DMS-0603859
文摘In this paper we survey the authors＇ and related work on two-dimensional Riemann problems for hyperbolic conservation laws, mainly those related to the compressible Euler equations in gas dynamics. It contains four sections： 1. Historical review. 2. Scalar conservation laws. 3. Euler equations. 4. Simplified models.
文摘By means of the numerical method,the tropical air-sea interaction waves are studied.The results show that when the Kelvin waves are filtered out and only the equatorial Rossby waves are reserved both in the atmosphere and in the ocean,the disturbances can also propagate eastward because of the air-sea interaction.The critical wavelength of the eastward propagating waves is related to the intensity of the air-sea interaction.The stronger the air-sea interaction,the larger the eastward propagating components of the air-sea interaction waves.The results of the numerical experiments are in good agreement with those of the theoretical analysis(Chao and Zhang,1988).
