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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

Hierarchical Expansion Method in the Solution of the Navier-Stokes equations for Incompressible Fluids in Laminar Two-Dimensional Flow

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Energy and Power Engineering 2018年第1期10卷 1-9页

作者： Gaianê Sabundjian Thadeu das Neves Conti Eduardo Lobo Lustosa Cabral Reactor Department Nuclear Energy Research Institutes S&atilde o Paulo Brazil

Among the several methods used to solve the Navier-Stokes equations Hierarchical Expansion Method has demonstrated satisfactory results. This work aimed to apply the expansion of the variables in hierarchical functions for the solution of the Navier-Stokes equations for incompressible fluids in two dimensions in laminar flow. This method is based on the finite element method. The expansion functions in this study were based on Legendre polynomials, adjusted in the rectangular elements in such a way that corner, side and area functions were defined. The order of the expansion functions associated with the sides and with the area of the elements is adjusted to the necessary or desired degree. This method is denominated by Hierarchical Expansion Method. In order to validate the proposed numeric method three well-known problems of the literature in two dimensions were analyzed;however, for this paper only one problem was presented. The results demonstrated that method was able to provide precise results. From the results obtained in this paper it is possible to conclude that the hierarchical expansion method can be effective for the solution of fluid dynamic problems that involve incompressible fluids.

关键词： Finite Element Petrov-Galerkin Formulation Navier-Stokes equations Hierarchical Expansion Functions Incompressible Fluid

The two independent equations of circuits in integral form of field theory:The fundamental law of circuits

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Science China(Physics,Mechanics & Astronomy) 2005年第3期48卷 300-318页

作者： CHEN Shennian Department of Electronic Engineering Huaqiao University Quanzhou 362011 China

Circuit theory is an extremely important basic theory in electrical and electronic sciences and technologies. Over more than a century, researchers have come to the conclusion that a fundamental law of circuits needs to satisfy the following three conditions: (1) Independency. It must be able to solve independently the basic problems of general solutions to the distribution of current and voltage in circuits. (2) Fundamentality. It cannot be derived from circuit theory and it must be the starting point for the establishment of circuit theory; it deduces the problem relevant to circuit theory by using purely logical inference, and establishes circuit theory into an independent deductive system. (3) Applicability. It must be widely applicable to all spheres of circuits, which includes sinusoidal steady-state linear and nonlinear networks, non-sinusoidal steady-state linear and nonlinear networks, transient-state processes, etc. From all networks to which the fundamental law of circuits applies, sinusoidal steady-state linear network is chosen as the most basic one to demonstrate that the two independent equations of circuits in integral form derived from Maxwell equations are able to meet these three conditions. Consequently, it is believed to be the fundamental law of circuits newly recognized today. This paper also makes the initiative to establish a circuit theory by which the basic rules of electromagnetic field govern the circuits, and the unity of electromagnetic fields and circuits is achieved.

关键词： circuit and system, fundamental law, network field theory, two independent equations of circuits in integral form.

Cordial Volterra Integral equations with Vanishing Delays

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Journal of Applied Mathematics and Physics 2017年第2期5卷 294-302页

作者： Hongjiu Wang Zhanwen Yang Melusi Khumalo College of Science Heilongjiang University of Science and Technology Harbin China Department of Pure and Applied Mathematics University of Johannesburg Auckland Park Johannesburg South Africa Science Research Center The Academy of Fundamental and Interdisciplinary Science Harbin Institute of Technology Har-bin China

Cordial Volterra integral equations (CVIEs) from some applications models associated with a noncompact cordial Volterra integral operator are discussed in the recent years. A lot of real problems are effected by a delayed history information. In this paper we investigate some properties of cordial Volterra integral operators influenced by a vanishing delay. It is shown that to replicate all eigenfunctions , or , the vanishing delay must be a proportional delay. For such a linear delay, the spectrum, eigenvalues and eigenfunctions of the operators and the existence, uniqueness and solution spaces of solutions are presented. For a nonlinear vanishing delay, we show a necessary and sufficient condition such that the operator is compact, which also yields the existence and uniqueness of solutions to CVIEs with the vanishing delay.

关键词： Cordial Volterra Integral equations Vanishing Delay Propositional Delay Compactness Existence and Uniqueness

Numerical Solution of Differential equations by Direct Taylor Expansion

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Journal of Applied Mathematics and Physics 2017年第3期5卷 623-630页

作者： Pirooz Mohazzabi Jennifer L. Becker Department of Mathematics and Physics University of Wisconsin-Parkside Kenosha WI USA

A variation of the direct Taylor expansion algorithm is suggested and applied to several linear and nonlinear differential equations of interest in physics and engineering, and the results are compared with those obtained from other algorithms. It is shown that the suggested algorithm competes strongly with other existing algorithms, both in accuracy and ease of application, while demanding a shorter computation time.

关键词： Taylor Series Expansion Algorithm Numerical Solution Differential equations

Limit Treatment of Space-Time Foam Calculations If Non Pathological Big Bang Singularity Is Accessible to Modified Einstein equations

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Journal of High Energy Physics, Gravitation and Cosmology 2017年第3期3卷 438-453页

作者： Andrew Beckwith Physics Department College of Physics Chongqing University Chongqing China

When initial radius if Stoica actually derived Einstein equations in a formalism which removes the big bang singularity pathology, then the reason for Planck length no longer holds. We follow what Ng derived as limit calculations as to a space time length factor Without the drop off of the vacuum energy as given by is at least the value of . We review the work by Ng as to quantum foam as to how that affects a general expression as to energy when , with determined at least approximately by arguments he presented in 2008 in the Dark side of the universe conference. Well before certain effects make themselves apparent, in ways which are illustrated in the manuscript. Having at a point singularity would remove expansion by the scale factor, so that the extreme version of Stoica’s treatment in an isolated 4-dimensional universe would be no expansion at all.

关键词： Fjortoft Theorem Thermodynamic Potential Matter Creation Vacuum Energy Mach’s Theorem Non-Pathological Singularity Affecting Einstein equations Planck Length. Brane Worlds

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

Augmented Lagrangian Methods for Numerical Solutions to Higher Order Differential equations

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Journal of Applied Mathematics and Physics 2017年第2期5卷 239-251页

作者： Xuefeng Li Department of Mathematical Sciences Loyola University New Orleans LA USA

A large number of problems in engineering can be formulated as the optimization of certain functionals. In this paper, we present an algorithm that uses the augmented Lagrangian methods for finding numerical solutions to engineering problems. These engineering problems are described by differential equations with boundary values and are formulated as optimization of some functionals. The algorithm achieves its simplicity and versatility by choosing linear equality relations recursively for the augmented Lagrangian associated with an optimization problem. We demonstrate the formulation of an optimization functional for a 4th order nonlinear differential equation with boundary values. We also derive the associated augmented Lagrangian for this 4th order differential equation. Numerical test results are included that match up with well-established experimental outcomes. These numerical results indicate that the new algorithm is fully capable of producing accurate and stable solutions to differential equations.

关键词： Augmented Lagrangian Methods Method of Multipliers Finite Element Solutions Differential equations

A Second Order Characteristic Mixed Finite Element Method for Convection Diffusion Reaction equations

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Journal of Applied Mathematics and Physics 2017年第6期5卷 1301-1319页

作者： Tongjun Sun School of Mathematics Shandong University Jinan China

A combined approximate scheme is defined for convection-diffusion-reaction equations. This scheme is constructed by two methods. Standard mixed finite element method is used for diffusion term. A second order characteristic finite element method is presented to handle the material derivative term, that is, the time derivative term plus the convection term. The stability is proved and the L2-norm error estimates are derived for both the scalar unknown variable and its flux. The scheme is of second order accuracy in time increment, symmetric, and unconditionally stable.

关键词： Mixed Finite Element Method Characteristic Method Second Order Accuracy Convection Diffusion Reaction equations