A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside...A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.展开更多
The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the...The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.展开更多
A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rota...A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements.The resulted solution is expressed in terms of two different sets of orbital elements.The first one is the classical orbital elements and the second one is the nonsingular orbital elements.Among of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most references.This specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic orbits.It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is constructed.Finally,the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.展开更多
Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level,either from the mesoscopic Boltzmann equation or some physical arguments,including(i)Burnett,Woods,super-Bur...Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level,either from the mesoscopic Boltzmann equation or some physical arguments,including(i)Burnett,Woods,super-Burnett,augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation,(ii)Grad 13,regularized 13/26 moment equations,rational extended thermodynamics equations,and generalized hydrodynamic equations,where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials,and(iii)bi-velocity equations and“thermo-mechanically consistent"Burnett equations based on the argument of“volume diffusion”.This paper is dedicated to assess the accuracy of these macroscopic equations.We first consider the RayleighBrillouin scattering,where light is scattered by the density fluctuation in gas.In this specific problem macroscopic equations can be linearized and solutions can always be obtained,no matter whether they are stable or not.Moreover,the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem.Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation.We find that(i)the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion,(ii)for the moment method,the more moments are included,the more accurate the results are,and(iii)macroscopic equations based on“volume diffusion"do not work well even when the Knudsen number is very small.Therefore,among about a dozen tested equations,the regularized 26 moment equations are the most accurate.However,for moderate and highly rarefied gas flows,huge number of moments should be included,as the convergence to true solutions is rather slow.The same conclusion is drawn from the problem of sound propagation between the transducer and receiver.This slow convergence of moment equations is due to the incapability of 展开更多
Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourie...Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourier-Laplace transform for model equations derived, the dispersion relations for both components are obtained.展开更多
由于电能和天然气能物理特性的天然互补性(电能易传输,天然气易存储)以及能源转换设备的技术支撑使得电-气综合能源系统(integrated electricity and gas system,IEGS)受到了国内外的普遍关注。为实现对IEGS的全面、实时和精确感知,需...由于电能和天然气能物理特性的天然互补性(电能易传输,天然气易存储)以及能源转换设备的技术支撑使得电-气综合能源系统(integrated electricity and gas system,IEGS)受到了国内外的普遍关注。为实现对IEGS的全面、实时和精确感知,需要构建面向IEGS的状态估计(state estimation for IEGS,IEGS-SE)。而现有的基于梯度法求解的IEGS-SE模型并未有效解决天然气系统的初值问题;此外现有的IEGS-SE研究不具有的良好抗差性能和较高的计算效率。基于已有电力系统的精确线性化量测方程,构建了天然气系统的精确线性化量测方程,并建立了线性化的压缩机模型和耦合元件模型,最后在此基础上提出了一种面向IEGS的基于加权最小绝对值(weighted least absolute value,WLAV)的双线性抗差状态估(bilinear robust state estimation based on weighted least absolute value,BWLAV)并给出了求解方法。该算法有效解决了天然气系统的初值问题,并通过仿真算例验证了该算法良好的抗差性能和较高的计算效率。展开更多
The flow-induced noise is simulated with a hybrid method.Firstly,a steady-state background flow field is given by solving Reynolds averaged Navier-Stokes(RANS)equations with finite volume(FV)method on structured grid....The flow-induced noise is simulated with a hybrid method.Firstly,a steady-state background flow field is given by solving Reynolds averaged Navier-Stokes(RANS)equations with finite volume(FV)method on structured grid.Then the linearized Euler equations(LEE)can be constructed based on the resulted background flow field,where the source term on the right hand side is computed using stochastic noise generation and radiation(SNGR)method.Finally,the unsteady acoustic field is obtained through solving LEE using high-order discontinuous Galerkin(DG)method on unstructured grid,where the parallel computing based on mesh partitioning and a″Quadrature-Free Implementation″method for high-order DG are employed to accelerate the computation.In order to demonstrate the sound propagation in detail,a visualization method for high-order schemes is also developed here.Moreover,in order to test the validation and the accuracy,a 3D cavity test in comparison with the experimental data is displayed first in this paper,then a 3D high-lift wing is also simulated to demonstrate its capability for very complex geometries.展开更多
A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretizatio...A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.展开更多
The Mach Effect Thruster (MET) is a propellant—less space drive which uses Mach’s principle to produce thrust in an accelerating material which is undergoing mass—energy fluctuations, [1]-[3]. Mach’s principle is ...The Mach Effect Thruster (MET) is a propellant—less space drive which uses Mach’s principle to produce thrust in an accelerating material which is undergoing mass—energy fluctuations, [1]-[3]. Mach’s principle is a statement that the inertia of a body is the result of the gravitational interaction of the body with the rest of the mass-energy in the universe. The MET device uses electric power of 100 - 200 Watts to operate. The thrust produced by these devices, at the present time, are small on the order of a few micro-Newtons. We give a physical description of the MET device and apparatus for measuring thrusts. Next we explain the basic theory behind the device which involves gravitation and advanced waves to incorporate instantaneous action at a distance. The advanced wave concept is a means to conserve momentum of the system with the universe. There is no momentun violation in this theory. We briefly review absorber theory by summarizing Dirac, Wheeler-Feynman and Hoyle-Narlikar (HN). We show how Woodward’s mass fluctuation formula can be derived from first principles using the HN-theory which is a fully Machian version of Einstein’s relativity. HN-theory reduces to Einstein’s field equations in the limit of smooth fluid distribution of matter and a simple coordinate transformation.展开更多
We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits per...We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits perpendicular to the incidence direction. As a main result of our calculation, we obtain in addition to the well-known alteration of the radial distance a time dependent correction term for the phase modifying the circular motion of the particle. A background of gravitational waves creates some kind of uncertainty.展开更多
In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients...In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion （the equivalence of the nonlinear stability, the linear stability and the spectral sta- bility of the standing pulse solutions） and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equa- tions. The Evans functions for the standing pulse solutions are constructed explicitly.展开更多
文摘A primordial field Self-interaction Principle, analyzed in Hestenes’ Geometric Calculus, leads to Heaviside’s equations of the gravitomagnetic field. When derived from Einstein’s nonlinear field equations Heaviside’s “linearized” equations are known as the “weak field approximation”. When derived from the primordial field equation, there is no mention of field strength;the assumption that the primordial field was predominant at the big bang rather suggests that ultra-strong fields are governed by the equations. This aspect has physical significance, so we explore the assumption by formulating the gauge field version of Heaviside’s theory. We compare with recent linearized gravity formulations and discuss the significance of differences.
文摘The paper is concerned with the problem of reduction of the general relativity theory to the Newton gravitation theory for a gravitation field with relatively low intensity. This problem is traditionally solved on the basis of linearized equations of general relativity which, being matched to the Newton theory equations, allow us to link the classical gravitation constant with the constant entering the general relativity equations. Analysis of the linearized general relativity equations shows that it can be done only for empty space in which the energy tensor is zero. In solids, the set of linearized general relativity equations is not consistent and is not reduced to the Newton theory equations. Specific features of the problem are demonstrated with the spherically symmetric static problem of general relativity which has the closed-form solution.
基金This work was supported by the National Natural Science Foundation of China(Grant No.61403416)the“The Hundred Talents Program”of Chinese Academy of Science.
文摘A new formulation of the orbital element-based relative motion equations is developed for general Keplerian orbits.This new solution is derived by performing a Taylor expansion on the Cartesian coordinates in the rotating frame with respect to the orbital elements.The resulted solution is expressed in terms of two different sets of orbital elements.The first one is the classical orbital elements and the second one is the nonsingular orbital elements.Among of them,however,the semi-latus rectum and true anomaly are used due to their generality,rather than the semi-major axis and mean anomaly that are used in most references.This specific selection for orbital elements yields a new solution that is universally applicable to elliptic,parabolic and hyperbolic orbits.It is shown that the new orbital element-based relative motion equations are equivalent to the Tschauner–Hempel equations.A linear map between the initial orbital element differences and the integration constants associated with the solution of the Tschauner–Hempel equations is constructed.Finally,the presented solution is validated through comparison with a high-fidelity numerical orbit propagator.The numerical results demonstrate that the new solution is computationally effective;and the result is able to match the accuracy that is required for linear propagation of spacecraft relative motion over a broad range of Keplerian orbits.
文摘Many macroscopic equations are proposed to describe the rarefied gas dynamics beyond the Navier-Stokes level,either from the mesoscopic Boltzmann equation or some physical arguments,including(i)Burnett,Woods,super-Burnett,augmented Burnett equations derived from the Chapman-Enskog expansion of the Boltzmann equation,(ii)Grad 13,regularized 13/26 moment equations,rational extended thermodynamics equations,and generalized hydrodynamic equations,where the velocity distribution function is expressed in terms of low-order moments and Hermite polynomials,and(iii)bi-velocity equations and“thermo-mechanically consistent"Burnett equations based on the argument of“volume diffusion”.This paper is dedicated to assess the accuracy of these macroscopic equations.We first consider the RayleighBrillouin scattering,where light is scattered by the density fluctuation in gas.In this specific problem macroscopic equations can be linearized and solutions can always be obtained,no matter whether they are stable or not.Moreover,the accuracy assessment is not contaminated by the gas-wall boundary condition in this periodic problem.Rayleigh-Brillouin spectra of the scattered light are calculated by solving the linearized macroscopic equations and compared to those from the linearized Boltzmann equation.We find that(i)the accuracy of Chapman-Enskog expansion does not always increase with the order of expansion,(ii)for the moment method,the more moments are included,the more accurate the results are,and(iii)macroscopic equations based on“volume diffusion"do not work well even when the Knudsen number is very small.Therefore,among about a dozen tested equations,the regularized 26 moment equations are the most accurate.However,for moderate and highly rarefied gas flows,huge number of moments should be included,as the convergence to true solutions is rather slow.The same conclusion is drawn from the problem of sound propagation between the transducer and receiver.This slow convergence of moment equations is due to the incapability of
基金Supported by National Natural Science Foundation of China under Grant No.10861008the "211 Project" Innovative Talents Training Program of Inner Mongolia University and Grant-in-Aid for Scientific Research from Inner Mongolia University of Technology under Grant No.ZS201032
文摘Sound propagation and the initial value problems in gas mixtures of two components are investigated. By using the eigen theory of linearized Boltzmann equations, a model equations is formed, with the use of the Fourier-Laplace transform for model equations derived, the dispersion relations for both components are obtained.
文摘由于电能和天然气能物理特性的天然互补性(电能易传输,天然气易存储)以及能源转换设备的技术支撑使得电-气综合能源系统(integrated electricity and gas system,IEGS)受到了国内外的普遍关注。为实现对IEGS的全面、实时和精确感知,需要构建面向IEGS的状态估计(state estimation for IEGS,IEGS-SE)。而现有的基于梯度法求解的IEGS-SE模型并未有效解决天然气系统的初值问题;此外现有的IEGS-SE研究不具有的良好抗差性能和较高的计算效率。基于已有电力系统的精确线性化量测方程,构建了天然气系统的精确线性化量测方程,并建立了线性化的压缩机模型和耦合元件模型,最后在此基础上提出了一种面向IEGS的基于加权最小绝对值(weighted least absolute value,WLAV)的双线性抗差状态估(bilinear robust state estimation based on weighted least absolute value,BWLAV)并给出了求解方法。该算法有效解决了天然气系统的初值问题,并通过仿真算例验证了该算法良好的抗差性能和较高的计算效率。
基金Supported by the Aeronautical Science Foundation of China(20101552018)the National Natural Science Foundation of China(11272152)
文摘The flow-induced noise is simulated with a hybrid method.Firstly,a steady-state background flow field is given by solving Reynolds averaged Navier-Stokes(RANS)equations with finite volume(FV)method on structured grid.Then the linearized Euler equations(LEE)can be constructed based on the resulted background flow field,where the source term on the right hand side is computed using stochastic noise generation and radiation(SNGR)method.Finally,the unsteady acoustic field is obtained through solving LEE using high-order discontinuous Galerkin(DG)method on unstructured grid,where the parallel computing based on mesh partitioning and a″Quadrature-Free Implementation″method for high-order DG are employed to accelerate the computation.In order to demonstrate the sound propagation in detail,a visualization method for high-order schemes is also developed here.Moreover,in order to test the validation and the accuracy,a 3D cavity test in comparison with the experimental data is displayed first in this paper,then a 3D high-lift wing is also simulated to demonstrate its capability for very complex geometries.
基金supported by the National Natural Science Foundation of China(No.10771150)the National Basic Research Program of China(No.2005CB321701)+1 种基金the Program for New Century Excellent Talents in University(No.NCET-07-0584)the Natural Science Foundation of Sichuan Province(No.07ZB087)
文摘A nonconforming finite element method of finite difference streamline diffusion type is proposed to solve the time-dependent linearized Navier-Stokes equations. The backward Euler scheme is used for time discretization. Crouzeix-Raviart nonconforming finite element approximation, namely, nonconforming （P1）2 - P0 element, is used for the velocity and pressure fields with the streamline diffusion technique to cope with usual instabilities caused by the convection and time terms. Stability and error estimates are derived with suitable norms.
文摘The Mach Effect Thruster (MET) is a propellant—less space drive which uses Mach’s principle to produce thrust in an accelerating material which is undergoing mass—energy fluctuations, [1]-[3]. Mach’s principle is a statement that the inertia of a body is the result of the gravitational interaction of the body with the rest of the mass-energy in the universe. The MET device uses electric power of 100 - 200 Watts to operate. The thrust produced by these devices, at the present time, are small on the order of a few micro-Newtons. We give a physical description of the MET device and apparatus for measuring thrusts. Next we explain the basic theory behind the device which involves gravitation and advanced waves to incorporate instantaneous action at a distance. The advanced wave concept is a means to conserve momentum of the system with the universe. There is no momentun violation in this theory. We briefly review absorber theory by summarizing Dirac, Wheeler-Feynman and Hoyle-Narlikar (HN). We show how Woodward’s mass fluctuation formula can be derived from first principles using the HN-theory which is a fully Machian version of Einstein’s relativity. HN-theory reduces to Einstein’s field equations in the limit of smooth fluid distribution of matter and a simple coordinate transformation.
文摘We investigate the influence of a gravitational wave background on particles in circular motion. We are especially interested in waves leading to stationary orbits. This consideration is limited to circular orbits perpendicular to the incidence direction. As a main result of our calculation, we obtain in addition to the well-known alteration of the radial distance a time dependent correction term for the phase modifying the circular motion of the particle. A background of gravitational waves creates some kind of uncertainty.
基金supported by a Faculty Research Grant of Lehigh University
文摘In this paper, we consider a nonlinear system of reaction diffusion equa- tions arising from mathematical neuroscience and two nonlinear scalar reaction diffusion equations under some assumptions on their coefficients. The main purpose is to couple together linearized stability criterion （the equivalence of the nonlinear stability, the linear stability and the spectral sta- bility of the standing pulse solutions） and Evans functions to accomplish the existence and instability of standing pulse solutions of the nonlinear system of reaction diffusion equations and the nonlinear scalar reaction diffusion equa- tions. The Evans functions for the standing pulse solutions are constructed explicitly.
