Narrow Results

Maxwell equations are not logical consistent. This problem is caused by the implication that the divergence and the curl of a vector are not related. Based on Chen's S-R decomposition of a rank-two tensor, this logical un-consistency is discarded and, as a consequence, the classical Maxwell equations are reformulated to deduce London equations. From boundary field point, the relations between Josephson current and outside magnetic field are established, which shows that the Josephson current is produced by vortices of boundary magnetic field. From local field point, the first London equation corresponds to the local average rotation of electric field and the second London equation corresponds to the local average rotation of magnetic field. The relation between the Josephson effects and vortices of electromagnetic fields is discussed.

In this paper, we have studied the Maxwell radiation from the electron orbiting the nucleus in an atom such as hydrogen atom. The orbiting electron is thought as two oscillating dipoles: one on $x$-axis and the other on $y$-axis with the same frequency. We have derived the electromagnetic wave and calculated powers of the radiation from these two oscillating dipoles, and then determined the time period it takes for the electron to change its energy levels from $E_2$ to $E_1$ due to the Maxwell radiation. Compared the time period due to the Maxwell radiation with the time period from the uncertainty principle, it is found that the two time periods are different from each other by about nine orders of magnitude. So, we are led to believe that the Maxwell theory could not be used in the quantum photo emission by the electron in an atom. Thus, we suggest that the quantum photo emission by the electron in an atom may be photon tunneling from the electron $t$ in an atom.

In this paper we study a coupled nonlinear Schrödinger–Maxwell system of equations. In this framework, we are concerned with the existence of semiclassical states. We use a perturbation scheme in a variational setting in order to study the concentration of the solutions when the Planck constant is supposed to be small enough.

In this paper we show how to describe the general theory of a linear metric compatible connection with the theory of Clifford valued differential forms. This is done by realizing that for each spacetime point the Lie algebra of Clifford bivectors is isomorphic to the Lie algebra of . In that way the pullback of the linear connection under a local trivialization of the bundle (i.e., a choice of gauge) is represented by a Clifford valued 1-form. That observation makes it possible to realize immediately that Einstein's gravitational theory can be formulated in a way which is similar to a gauge theory. Such a theory is compared with other interesting mathematical formulations of Einstein's theory, and particularly with a supposedly "unified" field theory of gravitation and electromagnetism proposed by M. Sachs. We show that his identification of Maxwell equations within his formalism is not a valid one. Also, taking profit of the mathematical methods introduced in the paper we investigate a very polemical issue in Einstein gravitational theory, namely the problem of the 'energy–momentum' conservation. We show that many statements appearing in the literature are confusing or even wrong.

The response of a long hollow cylindrical vessel made from a piezoelectric material is considered in the present investigation. The piezoelectric vessel is subjected to a thermal shock on one surface. The generalized piezo-thermo-elasticity formulation of Lord and Shulman is adopted which contains a single relaxation time to consider the finite speed of temperature wave propagation. The response of the cylinder is assumed to be axi-symmetric. Three coupled equations are established as the governing equations, which are the equation of motion, the energy equation and the Maxwell equation. These equations are transformed into the dimensionless ones. With the aid of the generalized differential quadrature method, these equations are discretized in the radial direction. After that, with the aid of the Newmark time marching scheme, the temporal evolutions of the thermo-electro-elastic parameters are obtained. Novel numerical results are presented to obtain the response of the cylinder subjected to a thermal shock using the Lord and Shulman theory of thermoelasticity.

We develop a formalism for efficient iterative solutions of scattering problems involving the Maxwell equations. The methods, borrowed from recent advancements in chemical reaction dynamics, represent the scattering wavefunctions on two grids; one used for the initial wave and is one-dimensional; the other is a small three-dimensional grid padded with absorbing-potentials on which the scattered function is represented. The formalism is automatically suitable for scattering studies of transmission, reflection and scattering components of a wave. The simulations can be done with time-dependent wavepackets or direct iterative solution for the Green's function, but the results are rigorous time-independent (frequency-dependent) scattering amplitudes. Model time-dependent simulations involving up to a 100×100×100 grid for the inner wavefunction were numerically done on a simple PC.

Maxwell equations are not logical consistent. This problem is caused by the implication that the divergence and the curl of a vector are not related. Based on Chen's S-R decomposition of a rank-two tensor, this logical un-consistency is discarded and, as a consequence, the classical Maxwell equations are reformulated to deduce London equations. From boundary field point, the relations between Josephson current and outside magnetic field are established, which shows that the Josephson current is produced by vortices of boundary magnetic field. From local field point, the first London equation corresponds to the local average rotation of electric field and the second London equation corresponds to the local average rotation of magnetic field. The relation between the Josephson effects and vortices of electromagnetic fields is discussed.

This note surveys how energy generation and strengthening has been used to prove Morawetz estimates for various field equations in Minkowski space, the exterior of the Schwarzschild spacetime, and the exterior of the Kerr spacetime. It briefly outlines an approach to proving a decay estimate for the Maxwell equation outside a Kerr black hole.