Physics:Metafluid dynamics

Metafluid dynamics is a closely related concept to metamaterial dynamics in physics.

Background

Metafluid dynamics was an effort to connect the ephemeral and statistical nature of quantum mechanical objects with the temporary and statistical, but yet stable, nature of "structures" in turbulent flows; that work was published as a research thesis (Marmanis 1993).

The works that influenced its conception were Albert Einstein's insistence on a causal interpretation of quantum mechanics, De Broglie's mechanical models, and related work along these lines. The literature on the subject of aether models was discovered by the author upon completion of the theory's core ideas during the academic years 1994 and 1995.

History

The term "metafluid dynamics" appeared for the first time in a conference talk delivered in the "International Symposium on Theoretical and Computational Fluid Dynamics" at Florida State University on November 7, 1996.

Initial publications

The theory was published, in the [1] Physics of Fluids under the title Analogy between the Navier-Stokes and Maxwell's equations: Application to Turbulence (Marmanis 1998).

A year later, the theory was presented in more detail in the thesis entitled Analogy between the Electromagnetic and Hydrodynamic Equations: Application to Turbulence (Marmanis 1999). This paper attempted to introduce an ontological connection between turbulent motion as described by the Navier–Stokes equations and dynamics of the electromagnetic field as described by Maxwell's equations. The paper observed that the electromagnetic field is non-linear when expressed in terms of the electromagnetic potentials—yet Maxwell's equations are linear due to the original modeling of charge and current. It should be stressed that this ontological interpretation was never previously published, although several fluid models have been presented as early as 1890, for the same purpose.

The last article by the same author, namely, "Turbulence, electromagnetism, and quantum mechanics: A common perspective" was published in the book Photon: Old problems in light of new ideas (Dvoeglazov 2000).

The metafluid dynamics was not created by trial-and-error of mechanical models of aether and is not an analogy that was revived; a juxtaposition of the fields that are involved in earlier models and those that are involved in the metafluid dynamics suffices as a proof. For historical references, see, the comprehensive book by Whittaker (1951).

Later publications

Since that time there have been several other publications that relate directly or indirectly to the metafluid dynamics:

• In 1999, R.M. Kirby, H. Marmanis and D.H. Laidlaw presented the first visualizations of turbulent charge—the analog of the electric charge in electromagnetism—in a conference paper entitled "Visualizing Multivalued Data from 2D Incompressible Flows Using Concepts from Painting".
• In 2000, A. C. R. Mendes, W. Oliveira and F.I. Takakura presented hydrodynamic turbulence as a constrained system from the point of view of metafluid dynamics in "Turbulence as a constrained system". This is the first Lagrangian description of metafluid dynamics that the author is aware of.
• In 2001, G. Rousseaux discussed the question of completeness for Maxwell's equations in Les équations de Maxwell sont-elles incomplètes? and the position of the metafluid dynamics on that matter.
• In 2002, G. Rousseaux and É. Guyon presented a review of the metafluid dynamics in the paper "À propos d’une analogie entre la mécanique des fluides et l’électromagnétisme".
• In 2003, A. C. R. Mendes, C. Neves, W. Oliveira and F.I. Takakura presented the metafluid dynamics as a gauge field theory.
• In 2003, L. Saul presented a kinetic theory of a space-time model that is endowed with spin. In that context, by following the analogy that forms the core of metafluid dynamics, the author shows how to derive (to first order) Maxwell's equations of electromagnetism and Schrödinger's equation for the electron.
• In 2004, D. Bǎleanu presented the metafluid dynamics as a constrained system within fractional Riemann-Liouville derivatives.
• In 2005, A. C. R. Mendes, C. Neves, W. Oliveira and F.I. Takakura applied the Dirac quantization condition to the metafluid dynamics on NC spaces.
• In 2005, D. Bǎleanu published the Metafluid dynamics and Hamilton-Jacobi formalism and the existence of the hidden gauge symmetry was analyzed. The main point of this work is that the obtained results are in agreement with those of the Faddeev-Jackiw approach.
• In 2005, Z. Akdeniz, P. Vignolo and M.P. Tosi published the paper "Shell structure in the density profile of a rotating gas of spin-polarized fermions". The authors of that paper study a Fermi gas of spin-polarized charged particles in a uniform magnetic field, under conditions such that the Coulomb interactions can be neglected, can be mapped into a rotating Fermi gas of neutral atomic particles in a state of complete spin polarization, where the atom–atom interactions are negligible on account of the Pauli principle suppressing s-wave scattering. The interesting part here is that the authors invoke the metafluid dynamics correspondence to establish the map.

References

• Bǎleanu D. Czechoslovak Journal of Physics,Vol. 54, No. 11 (2004) pp. 1165-1170
• Bǎleanu D. Czechoslovak Journal of Physics,Vol. 55, No. 4 (2005) pp. 473 - 478
• Debnath L. Internat. J. Math. & Math. Sci., Vol. 22, No. 4 (1999) pp. 667–688
• Marmanis H. On the nature of turbulence in the equilibrium range, Technical Report, Institute de Mecanique des Fluides de Toulouse (IMFT), France, (1993)
• Marmanis, H. Phys. Fluids Vol. 10, No. 6, pp. 1428-1437
• Marmanis H. Analogy between the Electromagnetic and Hydrodynamic Equations: Application to Turbulence, Ph.D. Thesis, Brown University (1999)
• Marmanis, H. Photons: Old problems in light of new ideas, Ed. V.V. Dvoeglazov, Nova Science Publications (2000)
• Mendes A.C.R., Oliveira W. and Takakura F.I. (2000) [2]
• Mendes A.C.R., Neves C., Oliveira W. and Takakura F.I. Braz. J. Phys. Vol.33, No. 2 (2003)
• Mendes A.C.R., Neves C., Oliveira W. and Takakura F.I. (2005) [3]
• Saul, L. "Spin Waves as Metric in a Kinetic Space-Time" Physics Letters A 314 (2003) pp. 472–478