Sedenionic formulation for the field equations of multifluid plasma

2020 ◽  
pp. 2150040
Author(s):  
Süleyman Demir ◽  
Damla Sümer ◽  
Murat Tanışlı
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
Maxwell Equations ◽  
Mathematical Tool ◽  
Source Terms ◽  
Classical Electromagnetism ◽  
Field Equations ◽  
Multifluid Plasma

In this paper, the multifluid equations of a plasma are reformulated in terms of conic sedenions in order to better reflect the analogies between multifluid plasma equations and Maxwell equations of classical electromagnetism. This formalism also provides us an efficient mathematical tool for unification of equations of fluid dynamics and electromagnetism in a compact and elegant way. Although the presented formulation enables us to express all of the field equations related to different disciplines, a set of Maxwell equations for multifluid plasma is combined into a single sedenionic equation. Moreover, the wave equation with source terms is generalized in a form similar to gravi-electromagnetism counterpart previously derived using this type sedenion.

Spacetime algebra for the reformulation of fluid field equations

2017 ◽  
Vol 14 (05) ◽  
pp. 1750075 ◽  
Author(s):  
Süleyman Demir ◽  
Murat Tanışlı
Keyword(s):  
Fluid Dynamics ◽  
Wave Equation ◽  
Compressible Fluids ◽  
Mathematical Tool ◽  
Field Equations ◽  
Fluid Field ◽  
Spacetime Algebra

In the light of the analogy between electromagnetism and fluid dynamics, the Maxwell-type equations of compressible fluids are reformulated on the basis of spacetime algebra. In this paper, it is proved that this algebra provides an efficient mathematical tool for describing fluid fields in a compact and elegant way. Moreover, the fluid wave equation in terms of potentials are derived in a form similar to electromagnetic and gravitational counterparts previously derived using spacetime algebra.

scholarly journals Quaternionic Approach to Dual Magnetohydrodynamics of Dyonic Cold Plasma

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
B. C. Chanyal ◽  
Mayank Pathak
Keyword(s):  
Wave Equation ◽  
Cold Plasma ◽  
Maxwell Equations ◽  
Magnetic Monopoles ◽  
Alfven Wave ◽  
Vorticity Field ◽  
Field Equations ◽  
Continuity Equations ◽  
Fields Equations ◽  
Quaternionic Formulation

The dual magnetohydrodynamics of dyonic plasma describes the study of electrodynamics equations along with the transport equations in the presence of electrons and magnetic monopoles. In this paper, we formulate the quaternionic dual fields equations, namely, the hydroelectric and hydromagnetic fields equations which are an analogous to the generalized Lamb vector field and vorticity field equations of dyonic cold plasma fluid. Further, we derive the quaternionic Dirac-Maxwell equations for dual magnetohydrodynamics of dyonic cold plasma. We also obtain the quaternionic dual continuity equations that describe the transport of dyonic fluid. Finally, we establish an analogy of Alfven wave equation which may generate from the flow of magnetic monopoles in the dyonic field of cold plasma. The present quaternionic formulation for dyonic cold plasma is well invariant under the duality, Lorentz, and CPT transformations.

scholarly journals GENERALIZED EINSTEIN–MAXWELL FIELD EQUATIONS IN THE PALATINI FORMALISM

2013 ◽  
Vol 22 (04) ◽  
pp. 1350017 ◽  
Author(s):  
GINÉS R. PÉREZ TERUEL
Keyword(s):  
Electromagnetic Field ◽  
Algebraic Equation ◽  
Ricci Tensor ◽  
Maxwell Equations ◽  
Natural Generalization ◽  
New Method ◽  
Maxwell Field ◽  
Field Equations ◽  
Palatini Formalism

We derive a new set of field equations within the framework of the Palatini formalism. These equations are a natural generalization of the Einstein–Maxwell equations which arise by adding a function [Formula: see text], with [Formula: see text] to the Palatini Lagrangian f(R, Q). The result we obtain can be viewed as the coupling of gravity with a nonlinear extension of the electromagnetic field. In addition, a new method is introduced to solve the algebraic equation associated to the Ricci tensor.

scholarly journals Relativistic equations for elementary particles

1948 ◽  
Vol 192 (1029) ◽  
pp. 195-218 ◽  
Keyword(s):  
Elementary Particle ◽  
Wave Equation ◽  
Equations Of Motion ◽  
Rest Mass ◽  
Wave Form ◽  
Total Charge ◽  
Field Equations ◽  
Relativistic Approximation ◽  
Special Cases ◽  
Linear Differential

From the general principles of quantum mechanics it is deduced that the wave equation of a particle can always be written as a linear differential equation of the first order with matrix coefficients. The principle of relativity and the elementary nature of the particle then impose certain restrictions on these coefficient matrices. A general theory for an elementary particle is set up under certain assumptions regarding these matrices. Besides, two physical assumptions concerning the particle are made, namely, (i) that it satisfies the usual second-order wave equation with a fixed value of the rest mass, and (ii) either the total charge or the total energy for the particle-field is positive definite. It is shown that in consequence of (ii) the theory can be quantized in the interaction free case. On introducing electromagnetic interaction it is found that the particle exhibits a pure magnetic moment in the non-relativistic approximation. The well-known equations for the electron and the meson are included as special cases in the present scheme. As a further illustration of the theory the coefficient matrices corresponding to a new elementary particle are constructed. This particle is shown to have states of spin both 3/2 and 1/2. In a certain sense it exhibits an inner structure in addition to the spin. In the non-relativistic approximation the behaviour of this particle in an electromagnetic field is the same as that of the Dirac electron. Finally, the transition from the particle to the wave form of the equations of motion is effected and the field equations are given in terms of tensors and spinors.

scholarly journals A Short Remark on Vortex as Fluid Particle from Neutrosophic Logic perspective (Towards “fluidicle” or “vorticle” model of QED.)

2020 ◽  
pp. 38-46
Author(s):  
Victor Christianto ◽  
◽  
◽  
Florentin Smarandache
Keyword(s):  
Fluid Dynamics ◽  
Maxwell Equations ◽  
Particle Dynamics ◽  
Fluid Particle ◽  
Alternative Approach ◽  
Neutrosophic Logic

In a previous paper in this journal (IJNS), it is mentioned about a possible approach to re-describe QED without renormalization route. As it is known that in literature, there are some attempts to reconcile vortex-based fluid dynamics and particle dynamics. Some attempts are not quite as fruitful as others. As a follow up to previous paper, the present paper will discuss two theorems for developing unification theories, and then point out some new proposals including by Simula (2020) on how to derive Maxwell equations in superfluid dynamics setting; this could be a new alternative approach towards “fluidicle” or “vorticle” model of QED. Further research is recommended in this new direction.

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