On the Material Invariant Formulation of Maxwell’s Displacement Current

@article{Christov2006OnTM,
  title={On the Material Invariant Formulation of Maxwell’s Displacement Current},
  author={Christo I. Christov},
  journal={Foundations of Physics},
  year={2006},
  volume={36},
  pages={1701-1717}
}
  • C. Christov
  • Published 14 November 2006
  • Physics
  • Foundations of Physics
Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic… 
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References

SHOWING 1-10 OF 49 REFERENCES
Dynamics of Patterns on Elastic Hypersurfaces. Part I. Shear Waves in the Middle Surface
The shear motions in an incompressible elastic continuum are considered and it is shown that, when linearized, the governing equations can be rendered into Maxwell’s form. The trace of the deviator
The Non-Linear Field Theories Of Mechanics
Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in
VIII. A dynamical theory of the electromagnetic field
  • J. Maxwell
  • Physics
    Philosophical Transactions of the Royal Society of London
  • 1865
(1) The most obvious mechanical phenomenon in electrical and magnetical experiments is the mutual action by which bodies in certain states set each other in motion while still at a sensible distance
Revisiting Stokes' first problem for Maxwell fluids
Stokes' first problem for Maxwell fluids is re-examined and new findings are presented. Specifically, the behaviour of the velocity field is examined with respect to vortex sheet and jump amplitude
Heat conduction paradox involving second-sound propagation in moving media.
TLDR
This Letter revisits the Maxwell-Cattaneo law of finite-speed heat conduction and shows that by using the material derivative of the thermal flux, in lieu of the local one, the paradox is completely resolved.
On the formulation of rheological equations of state
  • J. Oldroyd
  • Engineering
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1950
The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed. The right invariance properties can
DISCRETE OUT OF CONTINUOUS: DYNAMICS OF PHASE PATTERNS IN CONTINUA
A new paradigm is discussed in which the discrete facet of physical phenomenology is related to the existence of localized wave solutions (solitons) of a underlying metacontinuum (unified field,
The Soliton and Its History
We review the history of the soliton, since the first recorded observation of the ‘great solitary wave’ by Russell in 1834, as a means of developing the mathematical properties of a large class of
A Re-Examination of Maxwell's Electromagnetic Equations
It is pointed out that the usual derivation of the well-known Maxwell electromagnetic equations holds only for a medium at rest. A way in which the equations may be modified for the case when the
...
...