16,716 research outputs found
Stochastic Self-Similar and Fractal Universe
The structures formation of the Universe appears as if it were a classically
self-similar random process at all astrophysical scales. An agreement is
demonstrated for the present hypotheses of segregation with a size of
astrophysical structures by using a comparison between quantum quantities and
astrophysical ones. We present the observed segregated Universe as the result
of a fundamental self-similar law, which generalizes the Compton wavelength
relation. It appears that the Universe has a memory of its quantum origin as
suggested by R.Penrose with respect to quasi-crystal. A more accurate analysis
shows that the present theory can be extended from the astrophysical to the
nuclear scale by using generalized (stochastically) self-similar random
process. This transition is connected to the relevant presence of the
electromagnetic and nuclear interactions inside the matter. In this sense, the
presented rule is correct from a subatomic scale to an astrophysical one. We
discuss the near full agreement at organic cell scale and human scale too.
Consequently the Universe, with its structures at all scales (atomic nucleus,
organic cell, human, planet, solar system, galaxy, clusters of galaxy, super
clusters of galaxy), could have a fundamental quantum reason. In conclusion, we
analyze the spatial dimensions of the objects in the Universe as well as
spacetime dimensions. The result is that it seems we live in an El Naschie's E
infinity Cantorian spacetime; so we must seriously start considering fractal
geometry as the geometry of nature, a type of arena where the laws of physics
appear at each scale in a self--similar way as advocated long ago by the
Swedish school of astrophysics.Comment: 17 pages, 3 figures, accepted by Chaos, Solitons & Fractla
Structure of interacting aggregates of silica nanoparticles in a polymer matrix: Small-angle scattering and Reverse Monte-Carlo simulations
Reinforcement of elastomers by colloidal nanoparticles is an important
application where microstructure needs to be understood - and if possible
controlled - if one wishes to tune macroscopic mechanical properties. Here the
three-dimensional structure of big aggregates of nanometric silica particles
embedded in a soft polymeric matrix is determined by Small Angle Neutron
Scattering. Experimentally, the crowded environment leading to strong
reinforcement induces a strong interaction between aggregates, which generates
a prominent interaction peak in the scattering. We propose to analyze the total
signal by means of a decomposition in a classical colloidal structure factor
describing aggregate interaction and an aggregate form factor determined by a
Reverse Monte Carlo technique. The result gives new insights in the shape of
aggregates and their complex interaction in elastomers. For comparison, fractal
models for aggregate scattering are also discussed
Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures
A correct statistical model of soil pore structure can be critical for understanding flow and transport processes in soils, and creating synthetic soil pore spaces for hypothetical and model testing, and evaluating similarity of pore spaces of different soils. Advanced visualization techniques such as X-ray computed tomography (CT) offer new opportunities of exploring heterogeneity of soil properties at horizon or aggregate scales. Simple fractal models such as fractional Brownian motion that have been proposed to capture the complex behavior of soil spatial variation at field scale rarely simulate irregularity patterns displayed by spatial series of soil properties. The objective of this work was to use CT data to test the hypothesis that soil pore structure at the horizon scale may be represented by multifractal models. X-ray CT scans of twelve, water-saturated, 20-cm long soil columns with diameters of 7.5 cm were analyzed. A reconstruction algorithm was applied to convert the X-ray CT data into a stack of 1480 grayscale digital images with a voxel resolution of 110 microns and a cross-sectional size of 690 × 690 pixels. The images were binarized and the spatial series of the percentage of void space vs. depth was analyzed to evaluate the applicability of the multifractal model. The series of depth-dependent macroporosity values exhibited a well-defined multifractal structure that was revealed by singularity and Rényi spectra. The long-range dependencies in these series were parameterized by the Hurst exponent. Values of the Hurst exponent close to one were observed indicating the strong persistence in variations of porosity with depth. The multifractal modeling of soil macropore structure can be an efficient method for parameterizing and simulating the vertical spatial heterogeneity of soil pore space
Residual Multiparticle Entropy for a Fractal Fluid of Hard Spheres
The residual multiparticle entropy (RMPE) of a fluid is defined as the
difference, , between the excess entropy per particle (relative to an
ideal gas with the same temperature and density), , and the
pair-correlation contribution, . Thus, the RMPE represents the net
contribution to due to spatial correlations involving three,
four, or more particles. A heuristic `ordering' criterion identifies the
vanishing of the RMPE as an underlying signature of an impending structural or
thermodynamic transition of the system from a less ordered to a more spatially
organized condition (freezing is a typical example). Regardless of this, the
knowledge of the RMPE is important to assess the impact of non-pair
multiparticle correlations on the entropy of the fluid. Recently, an accurate
and simple proposal for the thermodynamic and structural properties of a
hard-sphere fluid in fractional dimension has been proposed [Santos,
A.; L\'opez de Haro, M. \emph{Phys. Rev. E} \textbf{2016}, \emph{93}, 062126].
The aim of this work is to use this approach to evaluate the RMPE as a function
of both and the packing fraction . It is observed that, for any given
dimensionality , the RMPE takes negative values for small densities, reaches
a negative minimum at a packing fraction
, and then rapidly increases, becoming positive beyond a
certain packing fraction . Interestingly, while both
and monotonically decrease as dimensionality
increases, the value of exhibits a nonmonotonic
behavior, reaching an absolute minimum at a fractional dimensionality . A plot of the scaled RMPE shows a
quasiuniversal behavior in the region .Comment: 10 pages, 3 figures; v2: minor change
Multifractal concentrations of inertial particles in smooth random flows
Collisionless suspensions of inertial particles (finite-size impurities) are
studied in 2D and 3D spatially smooth flows. Tools borrowed from the study of
random dynamical systems are used to identify and to characterise in full
generality the mechanisms leading to the formation of strong inhomogeneities in
the particle concentration.
Phenomenological arguments are used to show that in 2D, heavy particles form
dynamical fractal clusters when their Stokes number (non-dimensional viscous
friction time) is below some critical value. Numerical simulations provide
strong evidence for this threshold in both 2D and 3D and for particles not only
heavier but also lighter than the carrier fluid. In 2D, light particles are
found to cluster at discrete (time-dependent) positions and velocities in some
range of the dynamical parameters (the Stokes number and the mass density ratio
between fluid and particles). This regime is absent in 3D, where evidence is
that the Hausdorff dimension of clusters in phase space (position-velocity)
remains always above two.
After relaxation of transients, the phase-space density of particles becomes
a singular random measure with non-trivial multiscaling properties. Theoretical
results about the projection of fractal sets are used to relate the
distribution in phase space to the distribution of the particle positions.
Multifractality in phase space implies also multiscaling of the spatial
distribution of the mass of particles. Two-dimensional simulations, using
simple random flows and heavy particles, allow the accurate determination of
the scaling exponents: anomalous deviations from self-similar scaling are
already observed for Stokes numbers as small as .Comment: 21 pages, 13 figure
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