Weber electrodynamics,part II unipolar induction,Z-antenna

Weber electrodynamics predicts the localized unipolar induction observed by Müller and Kennard; whereas the Maxwell theory, based upon closed current loops and the flux rule, fails. The Weber theory for high frequency fields predicts a zero self torque on the Pappas-Vaughan Z-antenna, as observed. In contrast, the Maxwell theory predicts a sizeable self torque which is not observed.     

An experimental confirmation of longitudinal electrodynamic forces

According to the conventional views of electromagnetic theory, as these are expressed in the Lorentz force law, all the forces which act on a current carrying metallic conductor are perpendicular to the current streamlines. However, over the years, from Ampère through Maxwell until the present day, there have been persistent claims that when current flows in a metallic conductor, there are mechanical forces acting along current streamlines which subject the conductor to tensile stress, and which are therefore capable of performing work in the direction of current flow. The problem of substantiating these claims has always lain in the difficulty of designing an experiment in which the effects are unambiguously demonstrated. The present paper describes an experiment which to a large extent removes these ambiguities, and which provides a compelling novel demonstration of forces acting along current streamlines. A force calculation based on Ampère's original electrodynamic force law is found to be consistent with the observed behaviour. Received 15 November 2000 and Received in final form 12 March 2001     

The Ampere-Neumann Electrodynamics of Metallic Conductors

This is a review of the old electrodynamics which prevailed during the first half of the 165-year history of electromagnetism. Amperes principal achievement was the deduction of his empirical force law from experiments with several current balances. Faraday then discovered electro-magnetic induction. This prompted F. E. Neumann to work out a quantitative explanation of induction based on Amperes force law. It involved the concept of the electrodynamic potential which, as we know now, is the same entity as magnetic energy. With the newtonian principle of virtual work, Neumann found his potential yielded the correct mechanical forces on metallic current circuits. Neumanns theory contains a physical quantity which today is called the magnetic vector potential and treated as a mathematical contrivance. Neumanns mutual inductance formula has become a powerful tool of inductance calculations. Maxwell made a major contribution to the Ampere-Neumann electrodynamics by developing the mean-geometric-distance method for calculating the inductance of conductors of finite cross-sections. This became particularly useful after Sommerfeld solved Neumanns double integral for parallel, straight wires. Maxwell built all of Neumanns mathematical theory into his field equations but the lingo changed. Electrodynamic potential became kinetic energy of the field; conductor element interactions became flux linkage; and so on. Maxwells equations do not contain a magnetic force law. He believed both Amperes law and the law currently in use, which was first suggested by Grassmann in 1845, were compatible with field theory. Lorentz later found that the motion of charges in vacuum obeyed only Grassmanns law and not Amperes. From then onward the old electrodynamics fell into disuse and field theory has reigned supremely ever since. Recent developments have shown the conflict between Amperes and Grassmanns law to be related to the nature, of the electric current. Conduction currents in metals obey Amperes law and convection currents in vacuum obey Grassmanns law. Both laws agree on the reaction forces between closed metallic circuits, because the relativistic contribution from the Grassmann law then integrates to zero. This fact appears to have mislead Lorentz in believing that the drifting electron in vacuum is magnetically equivalent to the current element of metals. An examination of the long debate concerning the validity of Newtons third law of motion in electromagnetism proves the Ampere-Neumann electro-dynamics to be valid for metallic circuits while the theory of special relativity and field momentum conservation are required for convecting charges in vacuum. This conclusion is strongly supported by experimental evidence. It demands a change in the concept of the metallic current element.     

Covariant hysteretic constitutive theory for Maxwell’s equations: application to axially rotating media

This paper explores a class of non-linear constitutive relations for materials with memory in the framework of covariant macroscopic Maxwell theory. Based on earlier models for the response of hysteretic ferromagnetic materials to prescribed slowly varying magnetic background fields, generalized models are explored that are applicable to accelerating hysteretic magneto-electric substances coupled self-consistently to Maxwell fields. Using a parameterized model consistent with experimental data for a particular material that exhibits purely ferroelectric hysteresis when at rest in a slowly varying electric field, a constitutive model is constructed that permits a numerical analysis of its response to a driven harmonic electromagnetic field in a rectangular cavity. This response is then contrasted with its predicted response when set in uniform rotary motion in the cavity.     

The ultimate speed implied by theories of Weber's type

As in the last few years there has been a renewed interest in the laws of Ampère for the force between current elements and of Weber for the force between charges, we analyze the limiting velocity which appears in Weber's law. Then we make the same analysis for Phipps' potential and for generalizations of it. Comparing the results with the relativistic calculation, we obtain that these theories can yieldc for the ultimate speed of the charges or for the ultimate relative speed between the charges but not for both simultaneously, as in the case in the special theory of relativity.     

Empirically correct electrodynamics

The electrodynamics that predicts all known relevant observations is based upon the force F=(qq ′R/R³) [1 − 2v·v′/c² + 3(v·R) (v′·R)/c²R² + (a — a′)·R/c²] on charge q at r with the absolute velocity v and acceleration a due to charge q′ at r′ with absolute velocity v′ and acceleration a′, where R=r − r′. This force yields Ampere’s original empirical law for the force between current elements, which predicts the many effects due to Ampere tension between colinear current elements. It yields Faraday induction as well as Müller’s localized unipolar induction. The force on an accelerating charge due to a stationary charge yields Lenz’s law for the induced back emf; and, when applied to gravitation, qq′ being replaced by — Gmm′, it yields the inertial force ma, confirming Mach’s priniciple. For charge velocities approaching the velocity of light c it predicts the results of the Kaufmann-Bucherer experiments and the Bertozzi experiment, assuming neomechanics, or mass change with velocity. It is readily written as a field theory. Introducing time retardation, it yields waves and radiation. It predicts the observed zero self-torque on the Pappas-Vaughan Z-shaped antenna. Energy is conserved. The Weber electrodynamic theory is shown to fail.     

A Two-Layer Model for Superposed Electrified Maxwell Fluids in Presence of Heat Transfer

Based on a modified-Darcy-Maxwell model, two-dimensional, incompressible and heat transfer flow of two bounded layers, through electrified Maxwell fluids in porous media is performed. The driving force for the instability under an electric field, is an electrostatic force exerted on the free charges accumulated at the dividing interface. Normal mode analysis is considered to study the linear stability of the disturbances layers. The solutions of thelinearized equations of motion with the boundary conditions lead to an implicit dispersion relation between the growth rate and wave number. These equations are parameterized by Weber number, Reynolds number, Marangoni number, dimensionless conductivities, and dimensionless electric potentials. The case of long waves interfacial stability has been studied. The stability criteria are performed theoretically in which stability diagrams are obtained. Inthe limiting cases, some previously published results can be considered as particular cases of our results. It is found that the Reynolds number plays a destabilizing role in the stability criteria, while the damping influence is observed for the increasing of Marangoni number and Maxwell relaxation time.     

Determination of the Electromagnetic Lagrangian from a System of Poisson Brackets

The Lagrangian and Hamiltonian formulations of electromagnetism are reviewed and the Maxwell equations are obtained from the Hamiltonian for a system of many electric charges. It is shown that three of the equations which were obtained from the Hamiltonian, namely the Lorentz force law and two Maxwell equations, can be obtained as well from a set of postulated Poisson brackets. It is shown how the results derived from these brackets can be used to reconstruct the original Lagrangian for the theory aided by some reasoning based on physical concepts.     

Effects of trapped electrons on off-axis lower hybrid current drive in tokamaks

The effects of trapped electrons on off-axis lower hybrid current drive （LHCD） in tokamaks are studied, A computer code for solving the Fokker-Planck equation in a toroidal geometry is developed and employed. The code is suitable for various auxiliary heating and current drive schemes in tokamak plasmas. The influence of the resonance regime on the current drive efficiency as well as the influence of trapped particle fraction on the current drive efficiency are emphasized. It is shown that, as an electrostatic force, the lower hybrid wave causes some of the trapped electrons to be untrapped and lose their energy, which can cut the LHCD efficiency by about 30%. The ITER scaling law is also used to estimate the trapped electron effects.[第一段]     

A Theory of the Self-Consistent and Space-Charge Effect in Hybrid-Magnicon Amplifier

A novel axially modulated, annular electron beam cusp-injected, slowly varied section opened cavity, hybrid-magnicon amplifier had been proposed I once. The hybrid-magnicon has wavelength up to millimeter wave bend. The while its non-self-consistent non-space-charge nonlinear numerical calculation method was discussed. But due to bunch effect is changing uniform distribution state of the annular electron beam in the driver cavity, and then dynamic force balances of the beam is changing. Therefore, besides the interaction force between electron beam and the rotating TM_n10 mode electromagnetic field also must consider the electromagnetic force of current density and the action force between the space-charges and the action force of the charge density grade, et al. effect. For some problems of theory, this report try discuss from Maxwell Equations.     

Slowly varying fully nonlinear wavetrains in the Ginzburg-Landau equation

Following the ideas of Howard and Kopell [9] a perturbation theory is developed for slowly varying fully nonlinear wavetrains (i.e. solutions which appear locally as travelling waves, but with frequencies and wavelengths which may vary widely on long length and time scales). This perturbation theory is applied to the Ginzburg-Landau equation. The motion and stability of slowly varying wavetrains is shown to be governed by a simple wave equation which can develop shocks corresponding to rapid changes in wavenumber. Numerical results supporting this theory are presented. A shock structure is proposed and numerically verified. These results together with a winding invariant valid in the limit of slow variation suggest that over a large range of parameters many initial conditions relax to uniform wavetrains. The evolution of a marginally diffusively stable wavetrain is also examined; it is argued that the evolution is governed by a perturbed Korteweg-de Vries equation.     

Monaural and interaural intensity discrimination: level effects and the "binaural advantage"

This study examined whether the level effects seen in monaural intensity discrimination (Weber's law and the "near miss") in a two-interval task are also observed in discrimination of interaural intensity differences (IIDs) in a single-interval task. Both tasks were performed for various standard levels of 4-kHz pure tones and broadband noise. The Weber functions (10 log deltaI/I versus I in dB) in the monaural and binaural conditions were parallel. For noise, the Weber functions had slopes close to zero (Weber's law) while the Weber functions for the tones had a mean slope of -0.089 (near miss). The near miss for the monaural and binaural tasks with tones was eliminated when a high-pass masker was gated with the listening intervals. The near-miss was also observed for 250- and 1000-Hz tones in the binaural task despite overall decreased sensitivity to changes in IID at 1000 Hz. The binaural thresholds showed a small (about 2-dB) advantage over monaural thresholds only in the broadband noise conditions. More important, however, is the fact that the level effects seen monaurally are also seen binaurally. This suggests that the basic mechanisms responsible for Weber's law and the near miss are common to monaural and binaural processing.     

Connections Between the Riemann and the Lorentz Force Laws

It is known that for the magnetic force due to a closed circuit, the Weber force law can be identical to the Lorentz force law. In this investigation it is shown that for both the electric and the magnetic force of the quasi-static case, the Riemann force law can be identical to the Lorentz force law, while the former is based on a potential energy depending on a relative speed and is in accord with Newton's law of action and reaction.     

Direct scattering, trapping, and desorption in atom-surface collisions

Maxwell is credited as the first to invoke the assumption that an impinging gas beam scatters from a surface with a direct contribution exhibiting little change in state and a trapping-desorption fraction that desorbs in equilibrium [J. C. Maxwell, Phil. Trans. R. Soc. London 170, 231 (1879)]. Here a classical mechanical scattering theory is developed to describe direct scattering, trapping, and subsequent desorption of the incident beam. This theory allows a rigorous test of the Maxwell assumption and determines the conditions under which it is valid. The theory also gives quantitative explanations of important new experimental measurements [K. D. Gibson, N. Isa, and S. J. Sibener, J. Chem. Phys. 119, 13 083 (2003)] for direct and trapping-desorption scattering of Ar atoms by a self-assembled layer of 1-decanethiol on Au(111).     

Maxwell’s demon and the second law of thermodynamics

An idealized, two-dimensional Maxwell demon is described which incorporates an irreversible process. The vertex of the device acts as a purely mechanical ‘trap door’. This idealized mechanism is found to generate a violation of the second law of thermodynamics. These results indicate that the second law of thermodynamics is not valid in general for idealized, irreversible systems.     

On Mach's principle

We propose the postulate that the resultant force acting on any body is zero. With this postulate and with a Weber force law for gravitation, we obtain equations of motion and conclude that all inertial forces are due to gravitational interaction with other bodies in the universe, as suggested by Mach. We then obtain the same value for the advance of the perhelion of the planets as is given by general relativity. All this is accomplished in a strictly relational theory. Finally, we relate these points to topical questions of electrodynamics raised by the experimental studies of Graneau and Pappas.     

On the Material Invariant Formulation of Maxwell’s Displacement Current

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum.     

The variational theory of adiabatic motions,and its applications to linear and non-linear oscillators

This paper presents a variational derivation of the adiabatic periodic motion theorems and related time-integral-of-energy results, including the virial theorem, and some of their applications to linear and non-linear oscillators. Specifically, (i) first, the Maupertuis-Euler-Langrange (MEL) action principle is formulated for the most general (scleronomic and holonomic) system; in the derivation the time-dependent system parameters are treated just like additional generalized co-ordinates and subjected to similar variations; (ii) next, combination of MEL's principle with the first law of thermodynamics yields the adiabatic theorem; subsequent specializations of it lead to additional energetic equations; (iii) the theory is then applied to the one d.o.f. linear and non-linear oscillator; the effects of linear friction and of a harmonic external force are also discussed; useful relations for the adiabatically varying system parameters are thus obtained.     

Multi-layer flows of immiscible fractional Maxwell fluids in a cylindrical domain

Laminar unsteady multilayer axial flows of fractional immiscible Maxwell fluids in a circular cylinder are investigated. The flow of fluids is generated by a time-dependent pressure gradient in the axial direction and by the translational motion of a cylinder along his axis. The considered mathematical model is based on the fractional constitutive equation of Maxwell fluids with Caputo time-fractional derivatives. Analytical solutions for the fractional differential equations of the velocity fields with boundary and interfaces conditions have been determined by using the Laplace transform coupled with the Hankel transform of order zero and the Weber transform of order zero. The influence of the memory effects on the motion of the fluid has been investigated for the particular case of three fractional Maxwell fluids. It is found that for increasing values of the fractional parameter the fluid velocity is decreasing. The memory effects have a stronger influence on the velocity of the second layer.