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maxwell’s Equations as the Basis for Model of Atoms

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Journal of Applied Mathematics and Physics 2014年第5期2卷 235-251页

作者： Milan Perkovac The First Technical school TEsLA Klaiceva 7 Zagreb Croatia

A century ago the classical physics couldn’t explain many atomic physical phenomena. Now the situation has changed. It’s because within the framework of classical physics with the help of maxwell’s equations we can derive schrödinger’s equation, which is the foundation of quantum physics. The equations for energy, momentum, frequency and wavelength of the electromagnetic wave in the atom are derived using the model of atom by analogy with the transmission line. The action constant A0 = (μ0/ε0)1/2s02e2 is a key term in the above mentioned equations. Besides the other well-known constants, the only unknown constant in the last expression is a structural constant of the atom s0. We have found that the value of this constant is 8.277 56 and that it shows up as a link between macroscopic and atomic world. After calculating this constant we get the theory of atoms based on maxwell’s and Lorentz equations only. This theory does not require knowledge of Planck’s constant h, which is replaced with theoretically derived action constant A0, while the replacement for the fine structure constant α-1 is theoretically derived expression 2s02 = 137.036. so, the structural constant s0 replaces both constants h and α. This paper also defines the stationary states of atoms and shows that the maximal atomic number is equal to Zmax = 137. The presented model of the atoms covers three of the four fundamental interactions, namely the electromagnetic, weak and strong interactions.

关键词： Action Constant Fine structure Constant Lecher’s Line maxwell’s Equations New Elements Phase Velocity Planck’s Constant stability of Atoms standing Waves stationary states synchronized states system of the Elements structural Coefficient structural Constant Transmission Line Undiscovered Elements

Re-Thinking Biology—I. maxwell’s Demon and the spontaneous Origin of Life

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Advances in Biological Chemistry 2017年第5期7卷 170-181页

作者： Christopher Busby Charles Vyvyan Howard Environmental Research sIA 1117 Latvian Academy of Sciences Riga Latvia Centre for Molecular Biosciences University of Ulster Coleraine UK

A hypothesis is advanced in which life began from a Darwinian selection among a diversification of molecular species containing the phosphate moiety which broke the constraints implicit in the second Law of Thermodynamics, discussed famously by schrodinger, by obtaining energy from specific infrared frequencies located in the phosphorus-oxygen vibration at a frequency around 1000 cm-1. We propose the source of this energy was from the internal conversion of solar broadband energy by the phosphate mineral Apatite, present at the bottom of a primitive biogenesis pond. In this scenario, life is re-defined as being hotter than its environment and as using its excess energy, supplied by infra-red conversion, to react with its molecular environment and pump itself up the “entropy slope” thereby;replication is through breakages of increasingly large phosphate containing biopolymers. The idea has implications for modern explanations of living systems.

关键词： Abiogenesis Evolution Infra-Red Radiation Thermodynamics 2nd Law maxwell’s Demon Phosphate

Derivation of maxwell’s Equations via the Covariance Requirements of the special Theory of Relativity, starting with Newton’s Laws

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Journal of Applied Mathematics and Physics 2019年第9期7卷 2052-2073页

作者： Allan D. Pierce East sandwich Massachusetts USA

The purpose of this paper is to establish a connection between maxwell’s equations, Newton’s laws, and the special theory of relativity. This is done with a derivation that begins with Newton’s verbal enunciation of his first two laws. Derived equations are required to be covariant, and a simplicity criterion requires that the four-vector force on a charged particle be linearly related to the four-vector velocity. The connecting tensor has derivable symmetry properties and contains the electric and magnetic field vectors. The Lorentz force law emerges, and maxwell’s equations for free space emerge with the assumption that the tensor and its dual must both satisfy first-order partial differential equations. The inhomogeneous extension yields a charge density and a current density as being the source of the field, and yields the law of conservation of charge. Newton’s third law is reinterpreted as a reciprocity statement, which requires that the charge in the source term can be taken as the same physical entity as that of the test particle and that both can be assigned the same units. Requiring covariance under either spatial inversions or time reversals precludes magnetic charge being a source of electromagnetic fields that exert forces on electric charges.

关键词： Relativity maxwell’s Equations Newton’s Laws Covariance

A Fresh View for maxwell’s Equations and Electromagnetic Wave Propagation

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Journal of Modern Physics 2015年第7期6卷 921-926页

作者： Narahari V. Joshi Department of Physics University of Los Andes Merida Venezuela

Equations related with wave propagation are reexamined as in certain circumstances law of conservation of energy is not fulfilled even though it is cautiously clarified with the help of Heisenberg’s uncertainty principle. Recently, attempt has also been made to understand certain discrepancies in optical phenomena like diffraction or interference. The purpose of the present investigation, therefore, is to overcome some discrepancies by introducing constants of integration in maxwell’s Equation. It turns out that the presence of vibrating strings (or store energy) in the medium becomes essential to understand several details of the wave propagation.

关键词： maxwell’s Equations Wave Propagations string Theory

A New Formulation of maxwell’s Equations in Clifford Algebra

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Journal of Applied Mathematics and Physics 2017年第8期5卷 1575-1588页

作者： Pirooz Mohazzabi Norbert J. Wielenberg Gary Clark Alexander Department of Mathematics and Physics University of Wisconsin-Parkside Kenosha WI USA Department of Mathematical sciences DePaul University Chicago IL USA

A new unification of the maxwell equations is given in the domain of Clifford algebras with in a fashion similar to those obtained with Pauli and Dirac algebras. It is shown that the new electromagnetic field multivector can be obtained from a potential function that is closely related to the scalar and the vector potentials of classical electromagnetics. Additionally it is shown that the gauge transformations of the new multivector and its potential function and the Lagrangian density of the electromagnetic field are in agreement with the transformation rules of the second-rank antisymmetric electromagnetic field tensor, in contrast to the results obtained by applying other versions of Clifford algebras.

关键词： Clifford Algebra maxwell’s Equations Electromagnetism Vector Potential

Analysis of maxwell’s Equations. Cosmic Magnetism

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Journal of High Energy Physics, Gravitation and Cosmology 2018年第1期4卷 1-7页

作者： Vladimir s. Netchitailo Biolase Inc. Irvine CA USA

According to Hypersphere World-Universe Model, dark matter particles DIRACs are magnetic dipoles consisting of two Dirac’s monopoles. We conclude that DIRACs are the subject of maxwell’s equations. so-called “auxiliary” magnetic field intensity H is indeed current density of magnetic dipoles. The developed approach to magnetic field can explain a wealth of discovered phenomena in Cosmic Magnetism: a dark magnetic field, the large-scale structure of the Milky Way’s magnetic field, and other magnetic phenomena which are only partly related to objects visible in other spectral ranges.

关键词： Hypersphere World-Universe Model maxwell’s Equations Dirac’s Monopole Magnetic Dipole Magnetic Field Intensity Magnetic Dipoles Current Density Cosmic Magnetism Dark Magnetic Field

The Dynamic Gravitation of Photons from the Perspective of maxwell’s Wave Equations

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Journal of Modern Physics 2014年第12期5卷 1094-1096页

作者： Guido Zbiral Private Retired scientist Klosterneuburg Austria

Although the gravitational constant (G) does not explicitly occur in the maxwell Wave Equations, this paper will show that G is indeed implicitly contained in them. The logical consequence hereby is that electromagnetic radiation is associated with dynamic gravitation and not—as assumed in Einstein’s special Theory of Relativity—with “static” gravitation, dynamic gravitation being at the time unknown. According to the maxwell Wave Equations, gravitation experiences the same dynamic (speed of light c) as electromagnetic radiation and must therefore also be of a quantum nature. There must exist an equal number of gravitational quanta as there are photons. since photons do not possess a baryonic rest mass but only a relativistic mass, this mass must be nonbaryonic in nature—precisely as their dynamic gravitation.

关键词： Photon Dynamic Gravitation Gravitational Quanta maxwell’s Wave Equations

solution of maxwell’s Equations for Cylindrical symmetry Waveguides

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Journal of Applied Mathematics and Physics 2020年第5期8卷 753-765页

作者： N. V. selina Kuban state Technological University Krasnodar Russia

The solution of maxwell’s equations for a piecewise homogeneous medium of cylindrical symmetry has been obtained. The parameters of the cylindrical waveguide modes have been calculated on its basis. The conclusions are confirmed by numerical calculation of the first four modes of a hollow metal waveguide operating as a mode convector.

关键词： maxwell’s Equations Circular Waveguide Modes of the Waveguide

stability analysis of FDTD to UPML for time dependent maxwell equations

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science China Mathematics 2009年第4期52卷 794-816页

作者： FANG Nengsheng YING Lung-An school of Finance Southwestern University of Finance and EconomicsChengdu 610074China school of Mathematical sciences Xiamen UniversityXiamen 361005China school of Mathematical sciences Peking UniversityBeijing 100871China

We study an finite-difference time-domain (FDTD) system of uniaxial perfectly matched layer (UPML) method for electromagnetic scattering problems. Particularly we analyze the discrete initial-boundary value problems of the transverse magnetic mode (TM) to maxwell's equations with Yee's algorithm. An exterior domain in two spacial dimension is truncated by a square with a perfectly matched layer filled by a certain artificial medium. Besides, an artificial boundary condition is imposed on the outer boundary of the UPML. Using energy method, we obtain the stability of this FDTD system on the truncated domain. Numerical experiments are designed to approve the theoretical analysis.

关键词： maxwell’s equations uniaxial perfectly matched layer initial-boundary value problem stability FDTD