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