scholarly journals Direct Derivation of Liénard–Wiechert Potentials, Maxwell’s Equations and Lorentz Force from Coulomb’s Law

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 237
Author(s):  
Hrvoje Dodig
Keyword(s):  
Energy Conservation ◽  
Special Relativity ◽  
Lorentz Force ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Conservation Principle ◽  
Coulomb’S Law ◽  
The Moment ◽  
Coulomb's Law ◽  
Energy Conservation Principle

In this paper, the solution to long standing problem of deriving Maxwell’s equations and Lorentz force from first principles, i.e., from Coulomb’s law, is presented. This problem was studied by many authors throughout history but it was never satisfactorily solved, and it was never solved for charges in arbitrary motion. In this paper, relativistically correct Liénard–Wiechert potentials for charges in arbitrary motion and Maxwell equations are both derived directly from Coulomb’s law by careful mathematical analysis of the moment just before the charge in motion stops. In the second part of this paper, the electrodynamic energy conservation principle is derived directly from Coulomb’s law by using similar approach. From this energy conservation principle the Lorentz force is derived. To make these derivations possible, the generalized Helmholtz theorem was derived along with two novel vector identities. The special relativity was not used in our derivations, and the results show that electromagnetism as a whole is not the consequence of special relativity, but it is rather the consequence of time retardation.

scholarly journals Statistical energy conservation principle for inhomogeneous turbulent dynamical systems

2015 ◽  
Vol 112 (29) ◽  
pp. 8937-8941 ◽  
Author(s):  
Andrew J. Majda
Keyword(s):  
Dynamical Systems ◽  
Energy Conservation ◽  
Upper And Lower Bounds ◽  
Grand Challenge ◽  
Mean Flow ◽  
Turbulent Fluctuations ◽  
Conservation Principle ◽  
Wide Range ◽  
The Mean ◽  
Energy Conservation Principle

Understanding the complexity of anisotropic turbulent processes over a wide range of spatiotemporal scales in engineering shear turbulence as well as climate atmosphere ocean science is a grand challenge of contemporary science with important societal impact. In such inhomogeneous turbulent dynamical systems there is a large dimensional phase space with a large dimension of unstable directions where a large-scale ensemble mean and the turbulent fluctuations exchange energy and strongly influence each other. These complex features strongly impact practical prediction and uncertainty quantification. A systematic energy conservation principle is developed here in a Theorem that precisely accounts for the statistical energy exchange between the mean flow and the related turbulent fluctuations. This statistical energy is a sum of the energy in the mean and the trace of the covariance of the fluctuating turbulence. This result applies to general inhomogeneous turbulent dynamical systems including the above applications. The Theorem involves an assessment of statistical symmetries for the nonlinear interactions and a self-contained treatment is presented below. Corollary 1 and Corollary 2 illustrate the power of the method with general closed differential equalities for the statistical energy in time either exactly or with upper and lower bounds, provided that the negative symmetric dissipation matrix is diagonal in a suitable basis. Implications of the energy principle for low-order closure modeling and automatic estimates for the single point variance are discussed below.

scholarly journals Influence of the Metal–Semiconductor Interface Model on Power Conservation Principle in a Simulation of Bipolar Devices

Electronics ◽  
2021 ◽  
Vol 10 (24) ◽  
pp. 3120
Author(s):  
Janusz Wozny ◽  
Zbigniew Lisik ◽  
Jacek Podgorski
Keyword(s):  
Energy Conservation ◽  
Thermal Design ◽  
Drift Diffusion Model ◽  
Semiconductor Interface ◽  
Power Conservation ◽  
Power Semiconductor ◽  
Conservation Principle ◽  
Bipolar Devices ◽  
Energy Conservation Principle ◽  
Contact Metal

The purpose of the study is to present a proper approach that ensures the energy conservation principle during electrothermal simulations of bipolar devices. The simulations are done using Sentaurus TCAD software from Synopsys. We focus on the drift-diffusion model that is still widely used for power device simulations. We show that without a properly designed contact(metal)–semiconductor interface, the energy conservation is not obeyed when bipolar devices are considered. This should not be accepted for power semiconductor structures, where thermal design issues are the most important. The correct model of the interface is achieved by proper doping and mesh of the contact-semiconductor region or by applying a dedicated model. The discussion is illustrated by simulation results obtained for the GaN p–n structure; additionally, Si and SiC structures are also presented. The results are also supported by a theoretical analysis of interface physics.

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