摘要 :
The exact integral expressions for the azimuthal magnetic field, H_φ(r/h, θ), and the polar electric field, E_θ(r/h, θ), produced at any polar-angle, θ, and at any distance, r, from the center of a Hertzian dipole of height h...
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The exact integral expressions for the azimuthal magnetic field, H_φ(r/h, θ), and the polar electric field, E_θ(r/h, θ), produced at any polar-angle, θ, and at any distance, r, from the center of a Hertzian dipole of height h were recently derived-reported in this journal (Knop, Microwave Opt Technol Lett 54 (2012), 1970-1975). Numerical computations-plots of these fields as a function of the polar angle θ with the distance parameter of r/h were there given for the case of a dipole of h/λ=0.10, where λ is the free space operating wavelength. These computations-plots are here extended to the cases of h/λ=0.05 and 0.01. Computations and plots of these fields as a function of r/h with θ as a parameter are also given. Critical comparisons to the h/λ=0.10 case are then made and generalizations formed for the fields' behavior as h/λ decreases. Approximate closed-form equations/formulas for the fields are also presented.
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Exact integral expressions for the electromagnetic fields produced at "any distance," from the center of a Hertzian dipole of height h are derived in this study (it is believed for the first time) by correct-analytical integration...
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Exact integral expressions for the electromagnetic fields produced at "any distance," from the center of a Hertzian dipole of height h are derived in this study (it is believed for the first time) by correct-analytical integration of its infinitesimal fields. Numerical integration of these expressions gives the amplitude and phase as a function of the polar angle, h, with the normalized distance, r/h, as a parameter for 0.05≤ r/h≤5, of both the azimuthal magnetic field, H_φ (r/h, θ), and the polar electric field, E_θ(r/h, θ), for a dipole of h/λ = 0.10, where k is the free-space operating wavelength. Plots of these results then reveal, in detail, the interesting rapid-transitional behavior of these fields for points in the sphere bounded by the dipole (r/h < 0.50) to those outside of it (r/h > 0.50). The latter outer fields approach a sinh behavior only as r/h approaches 5.0. Generalizations for any h/λ≤0.10 are discussed.
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We analyze the problem of an elastic sphere impacting on two spheres being in contact at rest for the case when adhesive forces act between the spheres. By use of the basic assumptions of Hertz's theory and Johnson's model of adhe...
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We analyze the problem of an elastic sphere impacting on two spheres being in contact at rest for the case when adhesive forces act between the spheres. By use of the basic assumptions of Hertz's theory and Johnson's model of adhesion between elastic bodies, the differential equations of the problem are derived. This approach ensures a sufficient number of equations that uniquely determine the velocities after impact.
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In contrast to the case of energy balance in systems of electromagnetic fields and ponderable matter, the discussion of the momentum balance is still ongoing. Surprisingly enough, the present day terminology 'Maxwell stress tensor...
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In contrast to the case of energy balance in systems of electromagnetic fields and ponderable matter, the discussion of the momentum balance is still ongoing. Surprisingly enough, the present day terminology 'Maxwell stress tensor' refers to the vacuum fields, while both Maxwell's seminal paper Physical Lines of Force and the Treatise did discuss the stress tensor within media. And in contrast to Hertz, Maxwell even allowed this tensor to be non-symmetric in anisotropic media. These core points of both works are excerpted here. The main result is that one should construct the stress tensor from the volume and area forces, rather than - conversely - derive the area and volume forces from the stress tensor. Thus, Maxwell's theory is more than Maxwell's equations, much more. In non-symmetric stress tensors [see Maxwell, Mansuripur], the field vectors are paired as E ? H, D ? B in agreement with their geometrical properties and boundary conditions.
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Augmented Lagrangian method is a well established tool for the solution of optimization problems with equality constraints. If combined with effective algorithms for the solution of bound constrained quadratic programming problems...
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Augmented Lagrangian method is a well established tool for the solution of optimization problems with equality constraints. If combined with effective algorithms for the solution of bound constrained quadratic programming problems, it can solve efficiently very large problems with bound and linear equality constraints. The point of this paper is to show that the performance of the algorithm can be essentially improved by enhancing the information on the free set of current iterates into the reorthogonalization of equality constraints. The improvement is demonstrated on the numerical solution of a large problem arising from the application of domain decomposition methods to the solution of discretized elliptic variational inequality describing a variant of Hertz's two-body contact problem. (C) 2021 Elsevier B.V. All rights reserved.
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In a recent paper on Hertz's Mechanics, Eisenthal claims that this mechanics is without mechanisms. He argues that the absence of mechanisms is a consequence of Hertz's philosophy of physics, presented in the introduction to this ...
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In a recent paper on Hertz's Mechanics, Eisenthal claims that this mechanics is without mechanisms. He argues that the absence of mechanisms is a consequence of Hertz's philosophy of physics, presented in the introduction to this book. In the present paper, I will show that Hertz created four mechanisms. These mechanisms play a fundamental role in the deduction of the equations of motion. Some physicists used these mechanisms to create Hertzian mechanical models or to apply Hertz's mechanics to phenomena.
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In order to describe physical reality a special (gravity-free) relativity is needed that is founded upon general non-uniform motions as they occur in our environment and hold for the non-inertial reference frame of our laboratory....
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In order to describe physical reality a special (gravity-free) relativity is needed that is founded upon general non-uniform motions as they occur in our environment and hold for the non-inertial reference frame of our laboratory. Such a generalized form of special relativity can be built upon an extension, at relativistic velocities, of Maxwell-hertz electrodynamics (MHE), which is valid for non-uniform motions, but At small velocities only. The new electromagnetic theory, called (in honor to Hertz) Hertz's Relativistic Electrodynamics (HRE), is completely independent and built-up In a completely different way as regards Einstein's Special Relativity (ESR).
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We consider an axially symmetric problem of the theory of elasticity for a nonuniform half space loaded by Hertz's pressure. The half space consists of a uniform base and a system of two periodically deposited elastic layers. The ...
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We consider an axially symmetric problem of the theory of elasticity for a nonuniform half space loaded by Hertz's pressure. The half space consists of a uniform base and a system of two periodically deposited elastic layers. The solution of the problem of the theory of elasticity for the nonuniform coating is compared with the solution of the problem in which this coating is simulated by a homogenized uniform layer.
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