In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-...In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme.An error estimate of accuracy O(τ^(4)+h^(n))is proved under the L^(2)-norm,specially O(τ^(4)+h^(n+1))can be obtained.Numerical exper-iments for transverse electric(TE)case and transverse magnetic(TM)case are demon-strated to verify the stability and the efficiency of the method in low and higher wave frequency.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
Model of an atom by analogy with the transmission line is derived using Maxwell’s equations and Lorentz’ theory of electrons. To be realistic such a model requires that the product of the structural coefficient of L...Model of an atom by analogy with the transmission line is derived using Maxwell’s equations and Lorentz’ theory of electrons. To be realistic such a model requires that the product of the structural coefficient of Lecher’s transmission lines σ and atomic number Z is constant. It was calculated that this electromechanical constant is 8.27756, and we call it structural constant. This constant builds the fine-structure constant 1/α = 137.036, and with permeability μ, permittivity ε and elementary charge e builds Plank’s constant h. This suggests the electromagnetic character of Planck’s constant. The relations of energy, frequency, wavelength and momentum of electromagnetic wave in an atom are also derived. Finally, an equation, similar to Schrodinger’s equation, was derived, with a clear meaning of the wave function, which represents the electric or magnetic field strength of the observed electromagnetic wave.展开更多
For many years, a Lorentz factor of L = 1/3 has been used to describe the local electric field in thin amorphous dielectrics. However, the exact meaning of thin has been unclear. The local electric field E<sub>l...For many years, a Lorentz factor of L = 1/3 has been used to describe the local electric field in thin amorphous dielectrics. However, the exact meaning of thin has been unclear. The local electric field E<sub>loc</sub> modeling presented in this work indicates that L = 1/3 is indeed valid for very thin solid dielectrics (t<sub>diel</sub> ≤ 20 monolayers) but significant deviations from L = 1/3 start to occur for thicker dielectrics. For example, L ≈ 2/3 for dielectric thicknesses of t<sub>diel</sub> = 50 monolayers and increases to L ≈ 1 for dielectric thicknesses t<sub>diel</sub> > 200 monolayers. The increase in L with t<sub>diel</sub> means that the local electric fields are significantly higher in thicker dielectrics and explains why the breakdown strength E<sub>bd</sub> of solid polar dielectrics generally reduces with dielectric thickness t<sub>diel</sub>. For example, E<sub>bd</sub> for SiO<sub>2</sub> reduces from approximately E<sub>bd</sub> ≈ 25 MV/cm at t<sub>diel</sub> = 2 nm to E<sub>bd</sub> ≈ 10 MV/cm at t<sub>diel</sub> = 50 nm. However, while E<sub>bd</sub> for SiO<sub>2</sub> reduces with t<sub>diel</sub>, all SiO<sub>2</sub> thicknesses are found to breakdown at approximately the same local electric field (E<sub>loc</sub>)<sub>bd</sub> ≈ 40 MV/cm. This corresponds to a coordination bond strength of 2.7 eV for the silicon-ion to transition from four-fold to three-fold coordination in the tetrahedral structure.展开更多
基金supported by NSFC.China(NOs.11201501,11571389)the Program for Innovation Research in Central University of Finance and Economics+1 种基金The second author is Supported by NSFC.China(Grant Nos.11471296,11101384)the third author is supported in part by Defense Industrial Technology Development Program(B1520133015).
文摘In this paper,Nodal discontinuous Galerkin method is presented to approxi-mate Time-domain Lorentz model equations in meta-materials.The upwind flux is cho-sen in spatial discrete scheme.Low-storage five-stage fourth-order explicit Runge-Kutta method is employed in time discrete scheme.An error estimate of accuracy O(τ^(4)+h^(n))is proved under the L^(2)-norm,specially O(τ^(4)+h^(n+1))can be obtained.Numerical exper-iments for transverse electric(TE)case and transverse magnetic(TM)case are demon-strated to verify the stability and the efficiency of the method in low and higher wave frequency.
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Model of an atom by analogy with the transmission line is derived using Maxwell’s equations and Lorentz’ theory of electrons. To be realistic such a model requires that the product of the structural coefficient of Lecher’s transmission lines σ and atomic number Z is constant. It was calculated that this electromechanical constant is 8.27756, and we call it structural constant. This constant builds the fine-structure constant 1/α = 137.036, and with permeability μ, permittivity ε and elementary charge e builds Plank’s constant h. This suggests the electromagnetic character of Planck’s constant. The relations of energy, frequency, wavelength and momentum of electromagnetic wave in an atom are also derived. Finally, an equation, similar to Schrodinger’s equation, was derived, with a clear meaning of the wave function, which represents the electric or magnetic field strength of the observed electromagnetic wave.
文摘For many years, a Lorentz factor of L = 1/3 has been used to describe the local electric field in thin amorphous dielectrics. However, the exact meaning of thin has been unclear. The local electric field E<sub>loc</sub> modeling presented in this work indicates that L = 1/3 is indeed valid for very thin solid dielectrics (t<sub>diel</sub> ≤ 20 monolayers) but significant deviations from L = 1/3 start to occur for thicker dielectrics. For example, L ≈ 2/3 for dielectric thicknesses of t<sub>diel</sub> = 50 monolayers and increases to L ≈ 1 for dielectric thicknesses t<sub>diel</sub> > 200 monolayers. The increase in L with t<sub>diel</sub> means that the local electric fields are significantly higher in thicker dielectrics and explains why the breakdown strength E<sub>bd</sub> of solid polar dielectrics generally reduces with dielectric thickness t<sub>diel</sub>. For example, E<sub>bd</sub> for SiO<sub>2</sub> reduces from approximately E<sub>bd</sub> ≈ 25 MV/cm at t<sub>diel</sub> = 2 nm to E<sub>bd</sub> ≈ 10 MV/cm at t<sub>diel</sub> = 50 nm. However, while E<sub>bd</sub> for SiO<sub>2</sub> reduces with t<sub>diel</sub>, all SiO<sub>2</sub> thicknesses are found to breakdown at approximately the same local electric field (E<sub>loc</sub>)<sub>bd</sub> ≈ 40 MV/cm. This corresponds to a coordination bond strength of 2.7 eV for the silicon-ion to transition from four-fold to three-fold coordination in the tetrahedral structure.
