Strings of interconnected hollow carbon nanoparticles with porous shells prepared using simple solid-phase synthesis

Strings of interconnected hollow carbon nanoparticles with porous shells were prepared by simple heat-treatments of a mixture of resorcinol-formaldehyde gel and transition-metal salts. The sample was characterized by scanning electron microscopy, transmission electron microscopy, X-ray diffraction and nitrogen adsorption. Results show that the sample consisted of relatively uniform hollow particles with sizes ranging from 70 to 80 nm forming a strings-of-pearls-like nanostructure. The material with porous shells possessed well-developed graphitic structure with an interlayer (d(002)) spacing of 0.3369 nm and the stack height of the graphite crystallites of 9 nm.

Development of nanodomain and fractal morphologies in solvent annealed block copolymer thin films

We have systematically studied the thin film morphologies of asymmetric polystyrene-block-poly(ethylene oxide) (PS-b-PEO) diblock copolymer subjected to solvent vapors of varying selectivity for the constituent blocks. Upon a short treatment in neutral or PS-selective vapor, the film exhibited a highly ordered array of hexagonally packed, cylindrical microdomains. In the case of PEO selective vapor annealing, such ordered cylindrical microdomains were not obtained. instead, fractal patterns on the microscale were observed and their growth processes investigated. Furthermore, hierarchical structures could be obtained if the fractal pattern was exposed to neutral or PS selective vapor.

SAXS measurements of the interface in polyacrylate and epoxy interpenetrating networks with fractal geometry

The interface thickness in two-component interpenetrating polymer networks (IPN) system based on polyacrylate and epoxy were determined using small-angle X-ray scattering (SAXS) in terms of the theory proposed by Ruland. The thickness was found to be nonexistent for the samples at various compositions and synthesized at variable conditions-temperature and initiator concentration. By viewing the system as a two-phase system with a sharp boundary, the roughness of the interface was described by fractal dimension, D, which slightly varies with composition and synthesis condition. Length scales in which surface fractals are proved to be correct exist for each sample and range from 0.02 to 0.4 Angstrom(-1). The interface in the present IPN system was treated as fractal, which reasonably explained the differences between Pored's law and experimental data, and gained an insight into the interaction between different segments on the interface. (C) 1997 Elsevier Science Ltd.

Fractal roughness characterization of super-ground Mn-Zn ferrite single crystals

The surface of superground Mn-Zn ferrite single crystal may be identified as a self-affine fractal in the stochastic sense. The rms roughness increased as a power of the scale from 10(2) nm to 10(6) nm with the roughness exponent alpha = 0.17 +/- 0.04, and 0.11 +/- 0.06, for grinding feed rate of 15 and 10 mu m/rev, respectively. The scaling behavior coincided with the theory prediction well used for growing self-affine surfaces in the interested region for magnetic heads performance. The rms roughnesses increased with increase in the feed rate, implying that the feed rate is a crucial grinding parameter affecting the supersmooth surface roughness in the machining process.

SMALL-ANGLE X-RAY-SCATTERING STUDY ON THE INTERFACE IN BLOCK-COPOLYMERS WITH FRACTAL PROPERTIES

The interface thickness in two triblock copolymers were determined using small-angle x-ray scattering in the context of the theory proposed by Ruland. The thickness was found to be nonexistent for the samples at three different temperatures. By viewing th

DYNAMIC SCALING AND FRACTAL BEHAVIOR OF SPINODAL PHASE-SEPARATION IN POLYMER MIXTURES OF POLY(METHYL METHACRYLATE) WITH POLY(STYRENE-CO-ACRYLONITRILE)

Dynamic scaling and fractal behaviour of spinodal phase separation is studied in a binary polymer mixture of poly(methyl methacrylate) (PMMA) and poly(styrene-co-acrylonitrile) (SAN). In the later stages of spinodal phase separation, a simple dynamic scaling law was found for the scattering function S(q,t):S(q,t) approximately q(m)-3S approximately (q/q(m)). The possibility of using fractal theory to describe the complex morphology of spinodal phase separation is discussed. In phase separation, morphology exhibits strong self-similarity. The two-dimensional image obtained by optical microscopy can be analysed within the framework of fractal concepts. The results give a fractal dimension of 1.64. This implies that the fractal structure may be the reason for the dynamic scaling behaviour of the structure function.

FRACTAL BEHAVIOR OF SPINODAL DECOMPOSITION IN POLYMER BLENDS

Fractal behaviour of ramified domains in the late stage of spinodal phase separation in a binary polymer blend of poly(vinyl acetate) with poly(methyl methacrylate) was investigated by optical microscopic method. In the late stage of the spinodal decomposition, the fractal dimension D is about 1.64. It implies that some anomalous properties of irregular structure probably may be explained by fractal concepts.

Uso da geometria fractal na avaliação da variabilidade espacial de parâmetros de agregação do solo em São Paulo - Brasil.

O objetivo deste estudo foi explorar a aplicabilidade da teoria de fractais no estudo da variabilidade espacial em agregação de solo. A dimensão fractal D junto com RL que é o parâmetro que estima o tamanho do maior agregado foram usados como descritores de fragmentação. Estes valores estimados em diferentes locais na área experimental, foram interpolados usando krigagem ordinária e mapas de isolinhas construídos.

Optical determination of fractal dimensions using Fourier transforms

R. Zwiggelaar and C.R. Bull, 'Optical determination of fractal dimensions using Fourier transforms', Optical Engineering 34 (5), 1325-1332 (1995)

On the Fractal Nature of WWW and Its Application to Cache Modeling

The World Wide Web (WWW or Web) is growing rapidly on the Internet. Web users want fast response time and easy access to a enormous variety of information across the world. Thus, performance is becoming a main issue in the Web. Fractals have been used to study fluctuating phenomena in many different disciplines, from the distribution of galaxies in astronomy to complex physiological control systems. The Web is also a complex, irregular, and random system. In this paper, we look at the document reference pattern at Internet Web servers and use fractal-based models to understand aspects (e.g. caching schemes) that affect the Web performance.

Using fractal downscaling of satellite precipitation products for hydrometeorological applications

The objective of spatial downscaling strategies is to increase the information content of coarse datasets at smaller scales. In the case of quantitative precipitation estimation (QPE) for hydrological applications, the goal is to close the scale gap between the spatial resolution of coarse datasets (e.g., gridded satellite precipitation products at resolution L × L) and the high resolution (l × l; L»l) necessary to capture the spatial features that determine spatial variability of water flows and water stores in the landscape. In essence, the downscaling process consists of weaving subgrid-scale heterogeneity over a desired range of wavelengths in the original field. The defining question is, which properties, statistical and otherwise, of the target field (the known observable at the desired spatial resolution) should be matched, with the caveat that downscaling methods be as a general as possible and therefore ideally without case-specific constraints and/or calibration requirements? Here, the attention is focused on two simple fractal downscaling methods using iterated functions systems (IFS) and fractal Brownian surfaces (FBS) that meet this requirement. The two methods were applied to disaggregate spatially 27 summertime convective storms in the central United States during 2007 at three consecutive times (1800, 2100, and 0000 UTC, thus 81 fields overall) from the Tropical Rainfall Measuring Mission (TRMM) version 6 (V6) 3B42 precipitation product (~25-km grid spacing) to the same resolution as the NCEP stage IV products (~4-km grid spacing). Results from bilinear interpolation are used as the control. A fundamental distinction between IFS and FBS is that the latter implies a distribution of downscaled fields and thus an ensemble solution, whereas the former provides a single solution. The downscaling effectiveness is assessed using fractal measures (the spectral exponent β, fractal dimension D, Hurst coefficient H, and roughness amplitude R) and traditional operational scores statistics scores [false alarm rate (FR), probability of detection (PD), threat score (TS), and Heidke skill score (HSS)], as well as bias and the root-mean-square error (RMSE). The results show that both IFS and FBS fractal interpolation perform well with regard to operational skill scores, and they meet the additional requirement of generating structurally consistent fields. Furthermore, confidence intervals can be directly generated from the FBS ensemble. The results were used to diagnose errors relevant for hydrometeorological applications, in particular a spatial displacement with characteristic length of at least 50 km (2500 km2) in the location of peak rainfall intensities for the cases studied. © 2010 American Meteorological Society.