30,524 research outputs found
Recent developments on fractal-based approaches to nanofluids and nanoparticle aggregation
This project was supported by the National Natural Science Foundation of China (Nos. 41572116, 51576114, â41630317), the Fundamental Research Funds for the Central Universities, China University of Geosciences (Wuhan) (No. CUG160602) and the Natural Science Foundation of Fujian Province of China (No. 2016J01254). The authors of the figures that used in presented review are also highly appreciated.Peer reviewedPostprin
Self-Assembly of 4-sided Fractals in the Two-handed Tile Assembly Model
We consider the self-assembly of fractals in one of the most well-studied
models of tile based self-assembling systems known as the Two-handed Tile
Assembly Model (2HAM). In particular, we focus our attention on a class of
fractals called discrete self-similar fractals (a class of fractals that
includes the discrete Sierpi\'nski carpet). We present a 2HAM system that
finitely self-assembles the discrete Sierpi\'nski carpet with scale factor 1.
Moreover, the 2HAM system that we give lends itself to being generalized and we
describe how this system can be modified to obtain a 2HAM system that finitely
self-assembles one of any fractal from an infinite set of fractals which we
call 4-sided fractals. The 2HAM systems we give in this paper are the first
examples of systems that finitely self-assemble discrete self-similar fractals
at scale factor 1 in a purely growth model of self-assembly. Finally, we show
that there exists a 3-sided fractal (which is not a tree fractal) that cannot
be finitely self-assembled by any 2HAM system
Multi-scale active shape description in medical imaging
Shape description in medical imaging has become an increasingly important research field in recent years. Fast and high-resolution image acquisition methods like Magnetic Resonance (MR) imaging produce very detailed cross-sectional images of the human body - shape description is then a post-processing operation which abstracts quantitative descriptions of anatomically relevant object shapes. This task is usually performed by clinicians and other experts by first segmenting the shapes of interest, and then making volumetric and other quantitative measurements. High demand on expert time and inter- and intra-observer variability impose a clinical need of automating this process. Furthermore, recent studies in clinical neurology on the correspondence between disease status and degree of shape deformations necessitate the use of more sophisticated, higher-level shape description techniques. In this work a new hierarchical tool for shape description has been developed, combining two recently developed and powerful techniques in image processing: differential invariants in scale-space, and active contour models. This tool enables quantitative and qualitative shape studies at multiple levels of image detail, exploring the extra image scale degree of freedom. Using scale-space continuity, the global object shape can be detected at a coarse level of image detail, and finer shape characteristics can be found at higher levels of detail or scales. New methods for active shape evolution and focusing have been developed for the extraction of shapes at a large set of scales using an active contour model whose energy function is regularized with respect to scale and geometric differential image invariants. The resulting set of shapes is formulated as a multiscale shape stack which is analysed and described for each scale level with a large set of shape descriptors to obtain and analyse shape changes across scales. This shape stack leads naturally to several questions in regard to variable sampling and appropriate levels of detail to investigate an image. The relationship between active contour sampling precision and scale-space is addressed. After a thorough review of modem shape description, multi-scale image processing and active contour model techniques, the novel framework for multi-scale active shape description is presented and tested on synthetic images and medical images. An interesting result is the recovery of the fractal dimension of a known fractal boundary using this framework. Medical applications addressed are grey-matter deformations occurring for patients with epilepsy, spinal cord atrophy for patients with Multiple Sclerosis, and cortical impairment for neonates. Extensions to non-linear scale-spaces, comparisons to binary curve and curvature evolution schemes as well as other hierarchical shape descriptors are discussed
Turbulence in the Solar Atmosphere: Manifestations and Diagnostics via Solar Image Processing
Intermittent magnetohydrodynamical turbulence is most likely at work in the
magnetized solar atmosphere. As a result, an array of scaling and multi-scaling
image-processing techniques can be used to measure the expected
self-organization of solar magnetic fields. While these techniques advance our
understanding of the physical system at work, it is unclear whether they can be
used to predict solar eruptions, thus obtaining a practical significance for
space weather. We address part of this problem by focusing on solar active
regions and by investigating the usefulness of scaling and multi-scaling
image-processing techniques in solar flare prediction. Since solar flares
exhibit spatial and temporal intermittency, we suggest that they are the
products of instabilities subject to a critical threshold in a turbulent
magnetic configuration. The identification of this threshold in scaling and
multi-scaling spectra would then contribute meaningfully to the prediction of
solar flares. We find that the fractal dimension of solar magnetic fields and
their multi-fractal spectrum of generalized correlation dimensions do not have
significant predictive ability. The respective multi-fractal structure
functions and their inertial-range scaling exponents, however, probably provide
some statistical distinguishing features between flaring and non-flaring active
regions. More importantly, the temporal evolution of the above scaling
exponents in flaring active regions probably shows a distinct behavior starting
a few hours prior to a flare and therefore this temporal behavior may be
practically useful in flare prediction. The results of this study need to be
validated by more comprehensive works over a large number of solar active
regions.Comment: 26 pages, 7 figure
25 Years of Self-Organized Criticality: Solar and Astrophysics
Shortly after the seminal paper {\sl "Self-Organized Criticality: An
explanation of 1/f noise"} by Bak, Tang, and Wiesenfeld (1987), the idea has
been applied to solar physics, in {\sl "Avalanches and the Distribution of
Solar Flares"} by Lu and Hamilton (1991). In the following years, an inspiring
cross-fertilization from complexity theory to solar and astrophysics took
place, where the SOC concept was initially applied to solar flares, stellar
flares, and magnetospheric substorms, and later extended to the radiation belt,
the heliosphere, lunar craters, the asteroid belt, the Saturn ring, pulsar
glitches, soft X-ray repeaters, blazars, black-hole objects, cosmic rays, and
boson clouds. The application of SOC concepts has been performed by numerical
cellular automaton simulations, by analytical calculations of statistical
(powerlaw-like) distributions based on physical scaling laws, and by
observational tests of theoretically predicted size distributions and waiting
time distributions. Attempts have been undertaken to import physical models
into the numerical SOC toy models, such as the discretization of
magneto-hydrodynamics (MHD) processes. The novel applications stimulated also
vigorous debates about the discrimination between SOC models, SOC-like, and
non-SOC processes, such as phase transitions, turbulence, random-walk
diffusion, percolation, branching processes, network theory, chaos theory,
fractality, multi-scale, and other complexity phenomena. We review SOC studies
from the last 25 years and highlight new trends, open questions, and future
challenges, as discussed during two recent ISSI workshops on this theme.Comment: 139 pages, 28 figures, Review based on ISSI workshops "Self-Organized
Criticality and Turbulence" (2012, 2013, Bern, Switzerland
Reaction-controlled diffusion: Monte Carlo simulations
We study the coupled two-species non-equilibrium reaction-controlled
diffusion model introduced by Trimper et al. [Phys. Rev. E 62, 6071 (2000)] by
means of detailed Monte Carlo simulations in one and two dimensions. Particles
of type A may independently hop to an adjacent lattice site provided it is
occupied by at least one B particle. The B particle species undergoes
diffusion-limited reactions. In an active state with nonzero, essentially
homogeneous B particle saturation density, the A species displays normal
diffusion. In an inactive, absorbing phase with exponentially decaying B
density, the A particles become localized. In situations with algebraic decay
rho_B(t) ~ t^{-alpha_B}, as occuring either at a non-equilibrium continuous
phase transition separating active and absorbing states, or in a power-law
inactive phase, the A particles propagate subdiffusively with mean-square
displacement ~ t^{1-alpha_A}. We find that within the accuracy of
our simulation data, \alpha_A = \alpha_B as predicted by a simple mean-field
approach. This remains true even in the presence of strong spatio-temporal
fluctuations of the B density. However, in contrast with the mean-field
results, our data yield a distinctly non-Gaussian A particle displacement
distribution n_A(x,t) that obeys dynamic scaling and looks remarkably similar
for the different processes investigated here. Fluctuations of effective
diffusion rates cause a marked enhancement of n_A(x,t) at low displacements
|x|, indicating a considerable fraction of practically localized A particles,
as well as at large traversed distances.Comment: Revtex, 19 pages, 27 eps figures include
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