9,041 research outputs found
Fractal Heterogeneous Media
A method is proposed for generating compact fractal disordered media, by
generalizing the random midpoint displacement algorithm. The obtained
structures are invasive stochastic fractals, with the Hurst exponent varying as
a continuous parameter, as opposed to lacunar deterministic fractals, such as
the Menger sponge. By employing the Detrending Moving Average algorithm [Phys.
Rev. E 76, 056703 (2007)], the Hurst exponent of the generated structure can be
subsequently checked. The fractality of such a structure is referred to a
property defined over a three dimensional topology rather than to the topology
itself. Consequently, in this framework, the Hurst exponent should be intended
as an estimator of compactness rather than of roughness. Applications can be
envisaged for simulating and quantifying complex systems characterized by
self-similar heterogeneity across space. For example, exploitation areas range
from the design and control of multifunctional self-assembled artificial nano
and micro structures, to the analysis and modelling of complex pattern
formation in biology, environmental sciences, geomorphological sciences, etc
The 3D nature of a real un-dismantled electrical contact interface
AbstractA 3D contact analysis and modeling suite of tools are developed and introduced in this work. The “3D Contact Map” of an electrical contact interface is presented demonstrating the 3D nature of the contact. It gives information on where the electrical contact spots in a 3D surface profile are located. An X-ray Computer Tomography (CT) technique is used to collect the 3D data to a resolution of around 5μm of a real un-dismantled contact interface for analysis. Previous work by Lalechos and Swingler presented “2D Contact Map” on a 2D contact profile from collected 3D data to a resolution of around 8μm. The main advantages of both 3D and 2D mapping techniques focus on the fact that they are non-destructive and there is no need to dismantle the component of interest. This current work focuses on the 3D mapping technique showing its advantages over the 2D mapping technique. For test purposes, a 16A rated AC single pole switch is scanned after two different current loading tests (0A and 16A). A comparison for the total mechanical area of contact, the number of contact spots and the total contact resistance is conducted using both the 2D and 3D mapping techniques to a resolution of around 5μm
Multifractal Analysis of Packed Swiss Cheese Cosmologies
The multifractal spectrum of various three-dimensional representations of
Packed Swiss Cheese cosmologies in open, closed, and flat spaces are measured,
and it is determined that the curvature of the space does not alter the
associated fractal structure. These results are compared to observational data
and simulated models of large scale galaxy clustering, to assess the viability
of the PSC as a candidate for such structure formation. It is found that the
PSC dimension spectra do not match those of observation, and possible solutions
to this discrepancy are offered, including accounting for potential luminosity
biasing effects. Various random and uniform sets are also analyzed to provide
insight into the meaning of the multifractal spectrum as it relates to the
observed scaling behaviors.Comment: 3 latex files, 18 ps figure
The influence of surface roughness on the adhesive interactions and phase behavior of suspensions of calcite nanoparticles
We investigate the impact of nanoparticle roughness on the phase behaviour of
suspensions in models of calcium carbonate nanoparticles. We use a Derjaguin
approach that incorporates roughness effects and interactions between the
nanoparticles modelled with a combination of DLVO forces and hydration forces,
derived using experimental data and atomistic molecular dynamics simulations,
respectively. Roughness effects, such as atomic steps or terraces appearing in
mineral surfaces result in very different effective inter-nanoparticle
potentials. Using stochastic Langevin Dynamics computer simulations and the
effective interparticle interactions we demonstrate that relatively small
changes in the roughness of the particles modify significantly the stability of
the suspensions. We propose that the sensitivity of the phase behavior to the
roughness is connected to the short length scale of the adhesive attraction
arising from the ordering of water layers confined between calcite surfaces.
Particles with smooth surfaces feature strong adhesive forces, and form gel
fractal structures, while small surface roughness, of the order of atomic steps
in mineral faces, stabilize the suspension. We believe that our work helps to
rationalize the contrasting experimental results that have been obtained
recently using nanoparticles or extended surfaces, which provide support for
the existence of adhesive or repulsive interactions, respectively. We further
use our model to analyze the synergistic effects of roughness, pH and ion
concentration on the phase behavior of suspensions, connecting with recent
experiments using calcium carbonate nanoparticles
Closed Contour Fractal Dimension Estimation by the Fourier Transform
This work proposes a novel technique for the numerical calculus of the
fractal dimension of fractal objects which can be represented as a closed
contour. The proposed method maps the fractal contour onto a complex signal and
calculates its fractal dimension using the Fourier transform. The Fourier power
spectrum is obtained and an exponential relation is verified between the power
and the frequency. From the parameter (exponent) of the relation, it is
obtained the fractal dimension. The method is compared to other classical
fractal dimension estimation methods in the literature, e. g.,
Bouligand-Minkowski, box-couting and classical Fourier. The comparison is
achieved by the calculus of the fractal dimension of fractal contours whose
dimensions are well-known analytically. The results showed the high precision
and robustness of the proposed technique
Genesis and Propagation of Fractal Structures During Photoelectrochemical Etching of n-Silicon
The genesis, propagation, and dimensions of fractal-etch patterns that form anodically on front- or back-illuminated n-Si(100) photoelectrodes in contact with 11.9 M NH₄F(aq) has been investigated during either linear-sweep voltammetry or when the electrode was held at a constant potential (E = +6.0 V versus Ag/AgCl). Optical images collected in situ during electrochemical experiments revealed the location and underlying mechanism of initiation and propagation of the structures on the surface. X-ray photoelectron spectroscopic (XPS) data collected for samples emersed from the electrolyte at varied times provided detailed information about the chemistry of the surface during fractal etching. The fractal structure was strongly influenced by the orientation of the crystalline Si sample. The etch patterns were initially generated at points along the circumference of bubbles that formed upon immersion of n-Si(100) samples in the electrolyte, most likely due to the electrochemical and electronic isolation of areas beneath bubbles. XPS data showed the presence of a tensile-stressed silicon surface throughout the etching process as well as the presence of SiO_xF_y on the surface. The two-dimensional fractal dimension D_(f,2D) of the patterns increased with etching time to a maximum observed value of D_(f,2D)=1.82. Promotion of fractal etching near etch masks that electrochemically and electronically isolated areas of the photoelectrode surface enabled the selective placement of highly branched structures at desired locations on an electrode surface
Colloidal stability of tannins: astringency, wine tasting and beyond
Tannin-tannin and tannin-protein interactions in water-ethanol solvent
mixtures are studied in the context of red wine tasting. While tannin
self-aggregation is relevant for visual aspect of wine tasting (limpidity and
related colloidal phenomena), tannin affinities for salivary proline-rich
proteins is fundamental for a wide spectrum of organoleptic properties related
to astringency. Tannin-tannin interactions are analyzed in water-ethanol
wine-like solvents and the precipitation map is constructed for a typical grape
tannin. The interaction between tannins and human salivary proline-rich
proteins (PRP) are investigated in the framework of the shell model for
micellization, known for describing tannin-induced aggregation of beta-casein.
Tannin-assisted micellization and compaction of proteins observed by SAXS are
described quantitatively and discussed in the case of astringency
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