@article{uoadl:3146491,
    volume = "82",
    number = "1",
    journal = "Physica Scripta",
    issn = "0031-8949, 1402-4896",
    BIBTEX_ENTRY = "article",
    year = "2010",
    author = "Agop, M. and Munceleanu, G. V. and Niculescu, O. and Dandu-Bibire, T.",
    abstract = "Considering that the motions of the particles take place on ‘arbitrary’
fractals, an extended hydrodynamic model of the scale relativity is
built. In this approach, static (particle in a box) and time-dependent
(free particle) systems are analyzed. The particle in a box can be
associated with a fractal fluid: the zero value of the real
(differentiable) part of the complex speed field specifies the
coherence, while the non-zero value of the imaginary (non-differentiable
or fractal) part implies, through a quantization relation, a Reynolds
criterion. For a minimal value of the Reynolds number, a Heisenberg’s
‘egalitarian’ relationship results, whereas for big Reynolds numbers,
the flow regime of the fractal fluid becomes turbulent. In such a
context, the microscopic-macroscopic scale transition could be
associated with an evolution scenario towards chaos. The free
time-dependent particle can be associated with an incoherent fractal
fluid: the differentiable and fractal components of the complex speed
field are inhomogeneous in fractal coordinates due to the action of a
fractal potential. There exists a momentum transfer on both speed
components and the ‘observable’ in the form of a uniform motion is
generated through a specific mechanism of ‘vacuum’ polarization induced
by the same fractal potential.",
    title = "Static and free time-dependent fractal systems through an extended
hydrodynamic model of the scale relativity theory",
    doi = "10.1088/0031-8949/82/01/015010"
}