12,307 research outputs found
Fractal extra dimension in Kaluza-Klein theory
Kaluza-Klein theory in which the geometry of an additional dimension is
fractal has been considered. In such a theory the mass of an elementary
electric charge appears to be many orders of magnitude smaller than the Planck
mass, and the "tower" of masses which correspond to higher integer charges
becomes aperiodic.Comment: 3 pages, accepted for publication in Phys.Rev.D (submitted on
3.28.2001
Minkowski dimension and explicit tube formulas for -adic fractal strings
The local theory of complex dimensions describes the oscillations in the
geometry (spectra and dynamics) of fractal strings. Such geometric oscillations
can be seen most clearly in the explicit volume formula for the tubular
neighborhoods of a -adic fractal string , expressed in terms
of the underlying complex dimensions. The general fractal tube formula obtained
in this paper is illustrated by several examples, including the nonarchimedean
Cantor and Euler strings. Moreover, we show that the Minkowski dimension of a
-adic fractal string coincides with the abscissa of convergence of the
geometric zeta function associated with the string, as well as with the
asymptotic growth rate of the corresponding geometric counting function. The
proof of this new result can be applied to both real and -adic fractal
strings and hence, yields a unifying explanation of a key result in the theory
of complex dimensions for fractal strings, even in the archimedean (or real)
case.Comment: 34 pages, 1 figure. arXiv admin note: substantial text overlap with
arXiv:1105.2966 This is the final version of an original research article on
the Minkowski dimension and explicit tube formulas for -adic fractal
strings. It is appeared in the open access journal Fractal Fractiona
The Fractal Geometry of the Cosmic Web and its Formation
The cosmic web structure is studied with the concepts and methods of fractal
geometry, employing the adhesion model of cosmological dynamics as a basic
reference. The structures of matter clusters and cosmic voids in cosmological
N-body simulations or the Sloan Digital Sky Survey are elucidated by means of
multifractal geometry. A non-lacunar multifractal geometry can encompass three
fundamental descriptions of the cosmic structure, namely, the web structure,
hierarchical clustering, and halo distributions. Furthermore, it explains our
present knowledge of cosmic voids. In this way, a unified theory of the
large-scale structure of the universe seems to emerge. The multifractal
spectrum that we obtain significantly differs from the one of the adhesion
model and conforms better to the laws of gravity. The formation of the cosmic
web is best modeled as a type of turbulent dynamics, generalizing the known
methods of Burgers turbulence.Comment: 35 pages, 8 figures; corrected typos, added references; further
discussion of cosmic voids; accepted by Advances in Astronom
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