An analogy between electromagnetic and internal waves

2019 ◽  
Vol 485 (4) ◽  
pp. 428-433
Author(s):  
V. G. Baydulov ◽  
P. A. Lesovskiy
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Internal Wave ◽  
Special Relativity ◽  
Internal Waves ◽  
Maxwell Equations ◽  
Wave Equations ◽  
Lagrange Function ◽  
Lorentz Transformations ◽  
Symmetry Transformations

For the symmetry group of internal-wave equations, the mechanical content of invariants and symmetry transformations is determined. The performed comparison makes it possible to construct expressions for analogs of momentum, angular momentum, energy, Lorentz transformations, and other characteristics of special relativity and electro-dynamics. The expressions for the Lagrange function are defined, and the conservation laws are derived. An analogy is drawn both in the case of the absence of sources and currents in the Maxwell equations and in their presence.

scholarly journals Elementary derivation of the expressions of momentum and energy in special relativity

2016 ◽  
Vol 38 (2) ◽  
Author(s):  
Luca Peliti
Keyword(s):  
Conservation Laws ◽  
Special Relativity ◽  
Newtonian Limit ◽  
Lorentz Transformations ◽  
Relativistic Dynamics ◽  
Elementary Derivation ◽  
Relativistic Mass ◽  
Basic Concepts

The derivation of the expressions of momentum and energy of a particle in special relativity is often less than satisfactory in elementary texts. In some, it is obtained by resorting to quantum or electrodynamic considerations, in others by introducing non-elementary concepts, like that of a four-vector, or even misleading ones, like “relativistic mass”. Nevertheless it is possible, following ideas described by Einstein in 1935, to obtain a fully elementary derivation of these expressions based only on the Lorentz transformations, on the conservation laws, and on the Newtonian limit. The resulting argument allows for a clearer and logically consistent introduction to the basic concepts of relativistic dynamics.

scholarly journals Can Lorentz transformations be determined by the null Michelson-Morley result?

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
J. A. S. Lima ◽  
Fernando D. Sasse
Keyword(s):  
Special Relativity ◽  
Maxwell Equations ◽  
Relativity Theory ◽  
Lorentz Transformations ◽  
Speed Of Light ◽  
Principle Of Relativity ◽  
General Coordinate Transformation ◽  
Special Relativity Theory ◽  
Lorentzian Form ◽  
Morley Experiment

The so-called principle of relativity is able to fix a general coordinate transformation which differs from the standard Lorentzian form only by an unknown speed which cannot in principle be identified with the light speed. Based on a reanalysis of the Michelson-Morley experiment using this extended transformation we show that such unknown speed is analytically determined regardless of the Maxwell equations and conceptual issues related to synchronization procedures, time and causality definitions. Such a result demonstrates in a pedagogical manner that the constancy of the speed of light does not need to be assumed as a basic postulate of the special relativity theory since it can be directly deduced from an optical experiment in combination with the principle of relativity. The approach presented here provides a simple and insightful derivation of the Lorentz transformations appropriated for an introductory special relativity theory course.

scholarly journals Exact conservation laws for gauge-free electromagnetic gyrokinetic equations

2021 ◽  
Vol 87 (3) ◽  
Author(s):  
Alain J. Brizard
Keyword(s):  
Angular Momentum ◽  
Conservation Laws ◽  
Electromagnetic Fields ◽  
Maxwell Equations ◽  
Low Frequency ◽  
Momentum Conservation ◽  
Magnetized Plasma ◽  
Angular Momentum Conservation ◽  
Symplectic Representations ◽  
Exact Energy

The exact energy and angular momentum conservation laws are derived by the Noether method for the Hamiltonian and symplectic representations of the gauge-free electromagnetic gyrokinetic Vlasov–Maxwell equations. These gyrokinetic equations, which are solely expressed in terms of electromagnetic fields, describe the low-frequency turbulent fluctuations that perturb a time-independent toroidally-axisymmetric magnetized plasma. The explicit proofs presented here provide a complete picture of the transfer of energy and angular momentum between the gyrocentres and the perturbed electromagnetic fields, in which the crucial roles played by gyrocentre polarization and magnetization effects are highlighted. In addition to yielding an exact angular momentum conservation law, the gyrokinetic Noether equation yields an exact momentum transport equation, which might be useful in more general equilibrium magnetic geometries.

scholarly journals NUMERICAL ANALYSES ON PROPAGATION OF NONLINEAR INTERNAL WAVES

2011 ◽  
Vol 1 (32) ◽  
pp. 24
Author(s):  
Kei Yamashita ◽  
Taro Kakinuma ◽  
Keisuke Nakayama
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Wave Breaking ◽  
Wave Equations ◽  
Vertical Wall ◽  
Submerged Breakwater ◽  
Wave Trough ◽  
Water Region ◽  
Wave Nonlinearity ◽  
Sloping Beach

A set of nonlinear surface/internal-wave equations, which have been derived on the basis of the variational principle without any assumptions concerning wave nonlinearity and dispersion, is applied to compare numerical results with experimental data of surface/internal waves propagating through a shallow- or a deep-water region in a tank. Internal waves propagating over a submerged breakwater or a uniformly sloping beach are also simulated. The internal progressive wave shows remarkable shoaling when the interface reaches the critical level, after which physical variables including wave celerity become unstable near the wave-breaking point. In the case of the internal-wave trough reflecting at the vertical wall, the vertical velocities of water particles in the vicinity of the interface are different from that of the moving interface at the wall near the wave breaking, which means that the kinematic boundary condition on the interface of trough has been unsatisfied.

scholarly journals OPERA NEUTRINOS AND DEFORMED SPECIAL RELATIVITY

2012 ◽  
Vol 27 (10) ◽  
pp. 1250063 ◽  
Author(s):  
GIOVANNI AMELINO-CAMELIA ◽  
LAURENT FREIDEL ◽  
JERZY KOWALSKI-GLIKMAN ◽  
LEE SMOLIN
Keyword(s):  
Energy Range ◽  
Conservation Laws ◽  
Special Relativity ◽  
Lorentz Symmetry ◽  
Lorentz Transformations ◽  
Preferred Frame ◽  
Inertial Frames

In a recent study, Cohen and Glashow argue that superluminal neutrinos of the type recently reported by OPERA should be affected by anomalous Cherenkov-like processes. This causes them to lose much of their energy before reaching the OPERA detectors. Related concerns were reported also by Gonzalez-Mestres, Bi et al., and Cowsik et al., who argued that pions cannot decay to superluminal neutrinos over part of the energy range studied by OPERA. We observe here that these arguments are set within a framework in which Lorentz symmetry is broken, by the presence of a preferred frame. We further show that these anomalous processes are forbidden if Lorentz symmetry is instead "deformed", preserving the relativity of inertial frames. These deformations add nonlinear terms to energy–momentum relations, conservation laws and Lorentz transformations in a way that is consistent with the relativity of inertial observers.

Extended F-Expansion Method for Solving the modified Korteweg-de Vries (mKdV) Equation

2020 ◽  
Vol 11 (1) ◽  
pp. 93-100
Author(s):  
Vina Apriliani ◽  
Ikhsan Maulidi ◽  
Budi Azhari
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Internal Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Mkdv Equation ◽  
Innovative Methods ◽  
De Vries

One of the phenomenon in marine science that is often encountered is the phenomenon of water waves. Waves that occur below the surface of seawater are called internal waves. One of the mathematical models that can represent solitary internal waves is the modified Korteweg-de Vries (mKdV) equation. Many methods can be used to construct the solution of the mKdV wave equation, one of which is the extended F-expansion method. The purpose of this study is to determine the solution of the mKdV wave equation using the extended F-expansion method. The result of solving the mKdV wave equation is the exact solutions. The exact solutions of the mKdV wave equation are expressed in the Jacobi elliptic functions, trigonometric functions, and hyperbolic functions. From this research, it is expected to be able to add insight and knowledge about the implementation of the innovative methods for solving wave equations. 

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