In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the sa...In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.展开更多
The 10 920 stress indicators collected so far by the WSM (World Stress Map) project represent the observed ori-entations of the maximum horizontal principal stress (sHmax) in a certain region. Assuming that the long-w...The 10 920 stress indicators collected so far by the WSM (World Stress Map) project represent the observed ori-entations of the maximum horizontal principal stress (sHmax) in a certain region. Assuming that the long-wave component of sHmax is expressed by the absolute direction of plate motions, we can get the relative orientation and the magnitude of the short-wave component resulted from the local tectonic process or other factors with vector analytical technique. The global surface was divided into basic element bins by 2.52.5 dimensions and the WSM indicators were statistically analyzed for each element by weight coefficient method in order to determine the mean orientation of the stress. We calculated the long-wave component of the global stress field using HS2-NUVEL1 model. The relative magnitude or the direction limitation of short-wave component, which reflect the local contribution to the observed stresses, was determined by the angle between the mean sHmax and the orien-tation of the long-wave component. The results of this paper show that the contribution of either the long-wave component or the short-wave component is approximately equal to most of the global plates on the basis of the mean effect of the observed stresses. For some of continental regions, the local active tectonics plays an important role in the observed stresses and controls the generation and occurrence of earthquakes.展开更多
A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behave...A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.展开更多
A new method for solving electromagnetic field boundary value problem is given.Byusing this method,the boundary value problem of the vector wave equation can be transformedinto the independent boundary value problem o...A new method for solving electromagnetic field boundary value problem is given.Byusing this method,the boundary value problem of the vector wave equation can be transformedinto the independent boundary value problem of scalar wave equations and the two additionalvector differential operations.All the dyadic Green’s functions got by eigenfunction expansionof the dyadic Green’s function can be got by this method easily and some of the dyadic Green’sfunctions for complex systems which are very difficult to get by the ordinary method have beengot by this new method.The dyadic Green’s function for a dielectric loaded cavity is one of thegiven examples.展开更多
In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichart...In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal展开更多
The velocity of the electromagnetic radiation in a perfect dielectric, containing no charges and no conduction currents, is explored and determined on making use of the Lorentz transformations. Besides the idealised b...The velocity of the electromagnetic radiation in a perfect dielectric, containing no charges and no conduction currents, is explored and determined on making use of the Lorentz transformations. Besides the idealised blackbody radiation, whose vacuum propagation velocity is the universal constant c, being this value independent of the observer, there is another behaviour of electromagnetic radiation, we call inertial radiation, which is characterized by an electromagnetic inertial density , and therefore, it happens to be described by a time-like Poynting four-vector field which propagates with velocity . is found to be a relativistic invariant expressible in terms of the relativistic invariants of the electromagnetic field. It is shown that there is a rest frame, where the Poynting vector is equal to zero. Both phase and group velocities of the electromagnetic radiation are evaluated. The wave and eikonal equations for the dynamics of the radiation field are formulated.展开更多
In nature, there are two fundamentally different types of motion of the electric and magnetic fields: dynamic and kinematic. A typical manifestation of the first type of motion takes place in a plane harmonic EM-wave....In nature, there are two fundamentally different types of motion of the electric and magnetic fields: dynamic and kinematic. A typical manifestation of the first type of motion takes place in a plane harmonic EM-wave. For already more than a century the question about the ratio of the phases of the electric and magnetic fields, oscillating in such a wave, remains open. From time to time in this regard, fierce disputes arise. The point is that far from any phase difference turns out to be compatible with the full system of Maxwellian equations. Maxwell’s classical theory as applied to such a wave leads to the conclusion that the electric and magnetic vectors in it oscillate harmoniously with zero phase shift. In the framework of this theory, a rigorous mathematical proof is given.展开更多
文摘In two previous papers <a href="#ref1">[1]</a> and <a href="#ref2">[2]</a>, a structure for vector products in <em>n</em> dimensions was presented, and at the same time it was possible to propose the existence of a vector analogous to the curl of a vector field, for a space of four dimensions. In continuation of these works, the objective is to develop, through dimensional analogy, the idea of a hypothetical vector field, associated with the classical electromagnetic wave. This hypothetical field has a possible mathematical existence only when considering a space of four dimensions. The properties of the electromagnetic wave are preserved and equations with mathematical forms analogous to those of Maxwell’s equations are presented.
基金MOST contract of 2001BA601B02 and State Natural Science Foundation of China (49804006).
文摘The 10 920 stress indicators collected so far by the WSM (World Stress Map) project represent the observed ori-entations of the maximum horizontal principal stress (sHmax) in a certain region. Assuming that the long-wave component of sHmax is expressed by the absolute direction of plate motions, we can get the relative orientation and the magnitude of the short-wave component resulted from the local tectonic process or other factors with vector analytical technique. The global surface was divided into basic element bins by 2.52.5 dimensions and the WSM indicators were statistically analyzed for each element by weight coefficient method in order to determine the mean orientation of the stress. We calculated the long-wave component of the global stress field using HS2-NUVEL1 model. The relative magnitude or the direction limitation of short-wave component, which reflect the local contribution to the observed stresses, was determined by the angle between the mean sHmax and the orien-tation of the long-wave component. The results of this paper show that the contribution of either the long-wave component or the short-wave component is approximately equal to most of the global plates on the basis of the mean effect of the observed stresses. For some of continental regions, the local active tectonics plays an important role in the observed stresses and controls the generation and occurrence of earthquakes.
文摘A photon structure is advanced based on the experimental evidence and the vector potential quantization at a single photon level. It is shown that the photon is neither a point particle nor an infinite wave but behaves rather like a local “wave-corpuscle” extended over a wavelength, occupying a minimum quantization volume and guided by a non-local vector potential real wave function. The quantized vector potential oscillates over a wavelength with circular left or right polarization giving birth to orthogonal magnetic and electric fields whose amplitudes are proportional to the square of the frequency. The energy and momentum are carried by the local wave-corpuscle guided by the non-local vector potential wave function suitably normalized.
基金This project is supported by the National Science Fundation of China
文摘A new method for solving electromagnetic field boundary value problem is given.Byusing this method,the boundary value problem of the vector wave equation can be transformedinto the independent boundary value problem of scalar wave equations and the two additionalvector differential operations.All the dyadic Green’s functions got by eigenfunction expansionof the dyadic Green’s function can be got by this method easily and some of the dyadic Green’sfunctions for complex systems which are very difficult to get by the ordinary method have beengot by this new method.The dyadic Green’s function for a dielectric loaded cavity is one of thegiven examples.
基金Supported by the National Natural Science Foundation of China the Doctoral Foundation of NEM of China
文摘In this note, we are concerned with the global singularity structures of weak solutions to 4 - D semilinear dispersive wave equations whose initial data are chosen to be singular at a single point, Combining Strichartz＇s inequality with the commutator argument techniques, we show that the weak solutions stay globally conormal if the Cauchy data are conormal
文摘The velocity of the electromagnetic radiation in a perfect dielectric, containing no charges and no conduction currents, is explored and determined on making use of the Lorentz transformations. Besides the idealised blackbody radiation, whose vacuum propagation velocity is the universal constant c, being this value independent of the observer, there is another behaviour of electromagnetic radiation, we call inertial radiation, which is characterized by an electromagnetic inertial density , and therefore, it happens to be described by a time-like Poynting four-vector field which propagates with velocity . is found to be a relativistic invariant expressible in terms of the relativistic invariants of the electromagnetic field. It is shown that there is a rest frame, where the Poynting vector is equal to zero. Both phase and group velocities of the electromagnetic radiation are evaluated. The wave and eikonal equations for the dynamics of the radiation field are formulated.
文摘In nature, there are two fundamentally different types of motion of the electric and magnetic fields: dynamic and kinematic. A typical manifestation of the first type of motion takes place in a plane harmonic EM-wave. For already more than a century the question about the ratio of the phases of the electric and magnetic fields, oscillating in such a wave, remains open. From time to time in this regard, fierce disputes arise. The point is that far from any phase difference turns out to be compatible with the full system of Maxwellian equations. Maxwell’s classical theory as applied to such a wave leads to the conclusion that the electric and magnetic vectors in it oscillate harmoniously with zero phase shift. In the framework of this theory, a rigorous mathematical proof is given.
