26,193 research outputs found
Measurement of the electromagnetic field backscattered by a fractal surface for the verification of electromagnetic scattering models
Fractal geometry is widely accepted as an efficient theory for the characterization of natural surfaces; the opportunity of describing irregularity of natural surfaces in terms of few fractal parameters makes its use in direct and inverse electromagnetic (EM) scattering theories highly desirable. In this paper, we present an innovative procedure for manufacturing fractal surfaces and for measuring their scattering properties.
A cardboardâaluminum fractal surface was built as a representation of a WeiestrassâMandelbrot fractal process; the EM field scattered from it was measured in an anechoic chamber. A monostatic radarlike configuration was employed. Measurement results were compared to Kirchhoff approximation and small perturbation method closed-form results that were analytically obtained by employing the fractional Brownian motion to model the surface shape. Matching and discrepancies between theories andmeasurements are then discussed. Finally, fractal and classical surface models are compared as far as their use in the EM scattering is concerned.Postprint (published version
The 10 micron amorphous silicate feature of fractal aggregates and compact particles with complex shapes
We model the 10 micron absorption spectra of nonspherical particles composed
of amorphous silicate. We consider two classes of particles, compact ones and
fractal aggregates composed of homogeneous spheres. For the compact particles
we consider Gaussian random spheres with various degrees of non-sphericity. For
the fractal aggregates we compute the absorption spectra for various fractal
dimensions. The 10 micron spectra are computed for ensembles of these particles
in random orientation using the well-known Discrete Dipole Approximation. We
compare our results to spectra obtained when using volume equivalent
homogeneous spheres and to those computed using a porous sphere approximation.
We conclude that, in general, nonspherical particles show a spectral signature
that is similar to that of homogeneous spheres with a smaller material volume.
This effect is overestimated when approximating the particles by porous spheres
with the same volume filling fraction. For aggregates with fractal dimensions
typically predicted for cosmic dust, we show that the spectral signature
characteristic of very small homogeneous spheres (with a volume equivalent
radius r_V<0.5 micron) can be detected even in very large particles. We
conclude that particle sizes are underestimated when using homogeneous spheres
to model the emission spectra of astronomical sources. In contrast, the
particle sizes are severely overestimated when using equivalent porous spheres
to fit observations of 10 micron silicate emission.Comment: Accepted for publication in A&
Two Sets of Simple Formulae to Estimating Fractal Dimension of Irregular Boundaries
Irregular boundary lines can be characterized by fractal dimension, which
provides important information for spatial analysis of complex geographical
phenomena such as cities. However, it is difficult to calculate fractal
dimension of boundaries systematically when image data is limited. An
approximation estimation formulae of boundary dimension based on square is
widely applied in urban and ecological studies. However, the boundary dimension
is sometimes overestimated. This paper is devoted to developing a series of
practicable formulae for boundary dimension estimation using ideas from
fractals. A number of regular figures are employed as reference shapes, from
which the corresponding geometric measure relations are constructed; from these
measure relations, two sets of fractal dimension estimation formulae are
derived for describing fractal-like boundaries. Correspondingly, a group of
shape indexes can be defined. A finding is that different formulae have
different merits and spheres of application, and the second set of boundary
dimensions is a function of the shape indexes. Under condition of data
shortage, these formulae can be utilized to estimate boundary dimension values
rapidly. Moreover, the relationships between boundary dimension and shape
indexes are instructive to understand the association and differences between
characteristic scales and scaling. The formulae may be useful for the
pre-fractal studies in geography, geomorphology, ecology, landscape science,
and especially, urban science.Comment: 28 pages, 2 figures, 9 table
Deterministic diffusion in flower shape billiards
We propose a flower shape billiard in order to study the irregular parameter
dependence of chaotic normal diffusion. Our model is an open system consisting
of periodically distributed obstacles of flower shape, and it is strongly
chaotic for almost all parameter values. We compute the parameter dependent
diffusion coefficient of this model from computer simulations and analyze its
functional form by different schemes all generalizing the simple random walk
approximation of Machta and Zwanzig. The improved methods we use are based
either on heuristic higher-order corrections to the simple random walk model,
on lattice gas simulation methods, or they start from a suitable Green-Kubo
formula for diffusion. We show that dynamical correlations, or memory effects,
are of crucial importance to reproduce the precise parameter dependence of the
diffusion coefficent.Comment: 8 pages (revtex) with 9 figures (encapsulated postscript
Fractal analysis of the effect of particle aggregation distribution on thermal conductivity of nanofluids
This project was supported by the National Natural Science Foundation of China (No. 41572116), the Fundamental Research Funds for the Central Universities, China University of Geosciences, Wuhan) (No. CUG160602).Peer reviewedPostprin
Dynamical Symmetry Breaking in Fractal Space
We formulate field theories in fractal space and show the phase diagrams of
the coupling versus the fractal dimension for the dynamical symmetry breaking.
We first consider the 4-dimensional Gross-Neveu (GN) model in the
(4-d)-dimensional randomized Cantor space where the fermions are restricted to
a fractal space by the high potential barrier of Cantor fractal shape. By the
statistical treatment of this potential, we obtain an effective action
depending on the fractal dimension. Solving the 1/N leading Schwinger-Dyson
(SD) equation, we get the phase diagram of dynamical symmetry breaking with a
critical line similar to that of the d-dimensional (2<d<4) GN model except for
the system-size dependence. We also consider QED4 with only the fermions
formally compactified to d dimensions. Solving the ladder SD equation, we
obtain the phase diagram of dynamical chiral symmetry breaking with a linear
critical line, which is consistent with the known results for d=4 (the
Maskawa-Nakajima case) and d=2 (the case with the external magnetic field).Comment: 28 pages, 5 figures, LaTeX with epsf macr
Multiple light scattering and near-field effects in a fractal tree-like ensamble of dielectric nanoparticles
We numerically study light scattering and absorption in self-similar
aggregates of dielectric nanoparticles, as generated by simulated ballistic
deposition upon a surface starting from a single seed particle. The resulting
structure exhibits a complex tree-like shape, intended to mimic the morphologic
properties of building blocks of real nanostructured thin films produced by
means of fine controlled physical deposition processes employed in
nanotechnology. The relationship of scattering and absorption cross sections to
morphology is investigated within a computational scheme which thoroughly takes
into account both multiple scattering and near-field effects. Numerical results
are compared with a pre-existing single scattering limited analytical treatment
of light scattering in fractal aggregates of small dielectric particles.Comment: 10 pages, 9 figures. Accepted for publication in Physical Review
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