THE BALANCE EQUATIONS OF ENERGY AND MOMENTUM IN CLASSICAL ELECTRODYNAMICS

1995 ◽  
pp. 464-495 ◽  
Author(s):  
J. L. Jiménez ◽  
I. Campos
Keyword(s):  
Classical Electrodynamics ◽  
Balance Equations ◽  
Energy And Momentum ◽  
Balance Equations Of Energy

Generation of Tunable Necklace-Pattern Solitons in Two-Dimensional Dissipative System

2013 ◽  
Vol 339 ◽  
pp. 645-650
Author(s):  
Bin Liu ◽  
Shu Jing Li ◽  
Lin Ting Ma
Keyword(s):  
Landau Equation ◽  
Dissipative System ◽  
Gaussian Pulse ◽  
Two Dimensional ◽  
Balance Equations ◽  
Ginzburg Landau ◽  
Quintic Nonlinearity ◽  
Elliptical Ring ◽  
Energy And Momentum ◽  
Triangular Ring

We obtain necklace-pattern solitons (NPSs) from the same-pattern initial Gaussian pulse modulated by alternating azimuthal phase sections (AAPSs) of out-phase based on the two-dimensional (2D) complex Ginzburg-Landau equation with the cubic-quintic nonlinearity. The initial radially symmetrical Gaussian pulse can evolves into general necklace-rings solitons (NRSs). The number and distribution of pearls is tunable by adjusting sections-number and sections-distribution of AAPSs. In addition, we study the linear increased relationship between size of initial pulses and ring-radii of NRSs. Moreover, we predict the number-threshold of pearls in theoretical analysis by using of balance equations for energy and momentum. Final, we extend the research results to obtain arbitrary NPSs, such as elliptical ring, triangular-ring, and pentagonal ring.

Process Analysis of Laser Beam Cladding

2000 ◽  
Vol 123 (4) ◽  
pp. 609-614 ◽  
Author(s):  
A. F. H. Kaplan ◽  
G. Groboth
Keyword(s):  
Laser Beam ◽  
Process Model ◽  
Process Analysis ◽  
Single Step ◽  
Balance Equations ◽  
Energy Redistribution ◽  
Geometrical Properties ◽  
Clad Layer ◽  
Powder Mass ◽  
Balance Equations Of Energy

The technology of laser beam cladding of metals by single-step powder delivery is analyzed with a process model which is based on balance equations of energy and mass. Effects like powder heating, clad layer formation, substrate dilution and overlapping of tracks are discussed in dependence of the process parameters. In particular, the powder catchment efficiency and the beam energy redistribution in the material can be optimized by the powder mass flow rate and by the geometrical properties of the beam and of the powder jet.

Distributed and Nonsteady-State Model of an Air Cooler Working with R22 and R410A

2016 ◽  
Vol 24 (02) ◽  
pp. 1650008 ◽  
Author(s):  
R. O. Nunes ◽  
L. F. N. Castro ◽  
L. Machado ◽  
R. N. N. Koury
Keyword(s):  
Theoretical Data ◽  
Step Change ◽  
Montreal Protocol ◽  
Momentum Balance ◽  
Mass Energy ◽  
Balance Equations ◽  
Model Simulations ◽  
Nonsteady State ◽  
Air Cooler ◽  
Energy And Momentum

The restrictions imposed by Montreal Protocol for use of CFCs fluids and Kyoto Protocol to HCFCs have motivated researchers and the industry to seek new alternatives. Within this context, R410A has emerged as one of the most likely replacement of R22. The purpose of this work is to develop a numerical model of an air cooler to simulate its behavior operating under dynamic conditions loaded with R22 or R410A refrigerant. The model divides the air cooler in volumes control in which mass, energy, and momentum balance equations are applied and solved. Theoretical data obtained by model simulations repeated tendencies observed in experimental data taken from literature. Model simulations have also shown that for a step change in the inlet refrigerant mass flow, the superheating response of air cooler is almost the same when it is working with R22 or R410A refrigerant.

Classical electrodynamics as a distribution theory. II

1958 ◽  
Vol 54 (2) ◽  
pp. 258-264 ◽  
Author(s):  
J. G. Taylor
Keyword(s):  
Electromagnetic Field ◽  
Total Energy ◽  
Distribution Theory ◽  
Classical Electrodynamics ◽  
Definition Of ◽  
Energy And Momentum

ABSTRACTIn a previous paper by the author (3) it was shown how the theory of distributions of L. Schwartz enables a mathematically consistent formalism to be given for a system composed of point charges interacting through their classical electromagnetic field. In the present paper a definition of the energy and momentum of the field lying in a space-like surface is given, and it is shown that from this four-vector it is possible to derive the usual equation of conservation of total energy and momentum.

scholarly journals Formulation of Time-Fractional Electrodynamics Based on Riemann-Silberstein Vector

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 987
Author(s):  
Tomasz P. Stefański ◽  
Jacek Gulgowski
Keyword(s):  
Wave Propagation ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Momentum Conservation ◽  
Point Of View ◽  
Classical Electrodynamics ◽  
Classical Solutions ◽  
Systems With Memory ◽  
Energy And Momentum ◽  
With Memory

In this paper, the formulation of time-fractional (TF) electrodynamics is derived based on the Riemann-Silberstein (RS) vector. With the use of this vector and fractional-order derivatives, one can write TF Maxwell’s equations in a compact form, which allows for modelling of energy dissipation and dynamics of electromagnetic systems with memory. Therefore, we formulate TF Maxwell’s equations using the RS vector and analyse their properties from the point of view of classical electrodynamics, i.e., energy and momentum conservation, reciprocity, causality. Afterwards, we derive classical solutions for wave-propagation problems, assuming helical, spherical, and cylindrical symmetries of solutions. The results are supported by numerical simulations and their analysis. Discussion of relations between the TF Schrödinger equation and TF electrodynamics is included as well.

scholarly journals Implications of Gauge-Free Extended Electrodynamics

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2110
Author(s):  
Donald Reed ◽  
Lee M. Hively
Keyword(s):  
Scalar Field ◽  
Eddy Currents ◽  
Skin Effect ◽  
New Technologies ◽  
Scalar Potential ◽  
Electrical Current ◽  
Classical Electrodynamics ◽  
Magnetic Vector Potential ◽  
Novel Concept ◽  
Energy And Momentum

Recent tests measured an irrotational (curl-free) magnetic vector potential (A) that is contrary to classical electrodynamics (CED). A (irrotational) arises in extended electrodynamics (EED) that is derivable from the Stueckelberg Lagrangian. A (irrotational) implies an irrotational (gradient-driven) electrical current density, J. Consequently, EED is gauge-free and provably unique. EED predicts a scalar field that equals the quantity usually set to zero as the Lorenz gauge, making A and the scalar potential () independent and physically-measureable fields. EED predicts a scalar-longitudinal wave (SLW) that has an electric field along the direction of propagation together with the scalar field, carrying both energy and momentum. EED also predicts the scalar wave (SW) that carries energy without momentum. EED predicts that the SLW and SW are unconstrained by the skin effect, because neither wave has a magnetic field that generates dissipative eddy currents in electrical conductors. The novel concept of a “gradient-driven” current is a key feature of US Patent 9,306,527 that disclosed antennas for SLW generation and reception. Preliminary experiments have validated the SLW’s no-skin-effect constraint as a potential harbinger of new technologies, a possible explanation for poorly understood laboratory and astrophysical phenomena, and a forerunner of paradigm revolutions.

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