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Fractal Geometry (fractal + geometry)

Distribution by Scientific Domains

Engineering	41%
Polymers and Materials Science	16%
Life Sciences	16%

Selected Abstracts

Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry

EUROPEAN JOURNAL OF SOIL SCIENCE, Issue 3 2010
C. Fallico
Fractal geometry was deployed to analyse water retention curves (WRC). The three models used to estimate the curves were the general pore-solid fractal (PSF) model and two specific cases of the PSF model: the Tyler & Wheatcraft (TW) and the Rieu & Sposito (RS) models. The study was conducted on 30 undisturbed, sandy loam soil samples taken from a field and subjected to laboratory analysis. The fractal dimension, a non-variable scale factor characterizing each water retention model proposed, was estimated by direct scaling. The method for determining the fractal dimension proposed here entails limiting the analysis to the interval between an upper and lower pressure head cut-off on a log-log plot, and defining the dimension itself as the straight regression line that interpolates the points in the interval with the largest coefficient of determination, R2. The scale relative to the cut-off interval used to determine the fractal behaviour in each model used is presented. Furthermore, a second range of pressure head values was analysed to approximate the fractal dimension of the pore surface. The PSF model exhibited greater spatial variation than the TW or RS models for the parameter values typical of a sandy loam soil. An indication of the variability of the fractal dimension across the entire area studied is also provided. [source]

2D-Fractal Based Algorithms for Fine and Ultrafine Particulate Solids Systems Characterization

PARTICLE & PARTICLE SYSTEMS CHARACTERIZATION, Issue 4-5 2007
Giuseppe Bonifazi
Abstract Fractal geometry concerns the study of non-Euclidean geometrical figures generated by a recursive sequence of mathematical operations. The proposed 2D-fractal approach was applied to characterise the image structure and texture generated by fine and ultrafine particles when impacting on a flat surface. The work was developed with reference to particles usually produced in the ornamental stone sector during the different working phases carried out in dry conditions. Specific milling actions have been performed at a laboratoty scale on different ornamental stone products, in order to generate different particle populations to utilize in the study. The aim of the work was to develop a simple, reliable and low cost analytical set of procedures with the ability to establish correlations between particles detected by fractal characteristics and their classical attributes, e.g., i) size class distribution, ii) shape, iii) composition, etc. Such a logic should constitute the core of a control engine with the ability to optimize dust capture abatement strategies, according to produced dusts characteristics. [source]

Resonant properties of the Sierpinski-based fractal resonator and its application on low-loss miniaturized dual-mode bandpass filter

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 5 2009
Chang-Sin Ye
Abstract In this article, resonant characteristics of novel microstrip resonators based on the Sierpinski carpet fractal geometries are proposed in detail. With increasing the iteration order of the Sierpinski-based fractal resonators, the resonant frequency is decreased but the unloaded quality factor is slightly enhanced. The resonant properties are discussed using the RLC equivalent circuit. Additional, the design guide for bandpass filter using the nth order resonator is also developed. Using these fractal resonators, several dual-mode bandpass filters using different order resonators can be designed and fabricated to verify the advantages of the size and insertion loss reduction. It is also found good agreement between the simulation and measurement is achieved. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 1358,1361, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24321 [source]

Circular fractal monopole antenna based on descartes circle theorem for UWB application

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 6 2008
Salman Naeem Khan
Abstract An apollonian shaped ultra-wideband circular monopole antenna based on descartes circle theorem is presented. Different self similar geometries from DCT are analyzed and optimized for UWB applications. The proposed design is slightly modified to ensure an overall smooth current distribution limited by the junction point nature of the fractal geometries. The experimental results are compared with conventional circular disk monopole and annular monopole antenna. The measured return loss of the proposed design below ,10 dB is from 2.4 to over 40 GHz and its radiation pattern is omni-directional compared with circular disk and annular antennas in most of its impedance bandwidth. Moreover due to the fractal shape, the proposed design has less weight and wind loading effect. © 2008 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 1605,1608, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23437 [source]

Scaling analysis of water retention curves for unsaturated sandy loam soils by using fractal geometry

Effects of wildfire and permafrost on soil organic matter and soil climate in interior Alaska

GLOBAL CHANGE BIOLOGY, Issue 12 2006
JENNIFER W. HARDEN
Abstract The influence of discontinuous permafrost on ground-fuel storage, combustion losses, and postfire soil climates was examined after a wildfire near Delta Junction, AK in July 1999. At this site, we sampled soils from a four-way site comparison of burning (burned and unburned) and permafrost (permafrost and nonpermafrost). Soil organic layers (which comprise ground-fuel storage) were thicker in permafrost than nonpermafrost soils both in burned and unburned sites. While we expected fire severity to be greater in the drier site (without permafrost), combustion losses were not significantly different between the two burned sites. Overall, permafrost and burning had significant effects on physical soil variables. Most notably, unburned permafrost sites with the thickest organic mats consistently had the coldest temperatures and wettest mineral soil, while soils in the burned nonpermafrost sites were warmer and drier than the other soils. For every centimeter of organic mat thickness, temperature at 5 cm depth was about 0.5°C cooler during summer months. We propose that organic soil layers determine to a large extent the physical and thermal setting for variations in vegetation, decomposition, and carbon balance across these landscapes. In particular, the deep organic layers maintain the legacies of thermal and nutrient cycling governed by fire and revegetation. We further propose that the thermal influence of deep organic soil layers may be an underlying mechanism responsible for large regional patterns of burning and regrowth, detected in fractal analyses of burn frequency and area. Thus, fractal geometry can potentially be used to analyze changes in state of these fire prone systems. [source]

Scaling of geological discontinuity normal load,deformation response using fractal geometry

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 8 2001
Michael E. Plesha
Abstract The mechanical behaviour of discontinuities in rock, such as joints, is known to be size-dependent. It is also suspected that the behaviour of larger size features, such as faults, is also size-dependent. This size dependence has serious implications for performing numerical response simulations of geological media. In this paper, we develop a new mathematical theory for scaling of one particular discontinuity property, namely the interface normal stiffness. To accomplish this, we idealize an interface to have fractal geometry, and we develop analytical relations which show that the interface normal stiffness, which is commonly thought to be a size-independent property, is in fact a size-dependent property and has fractal characteristics that may be exploited to develop a fundamental theory for scaling. Copyright © 2001 John Wiley & Sons, Ltd. [source]

CURRENT VARIABILITY SHAPES MORPHOLOGICAL COMPLEXITY IN COLONIAL STREAM DIATOMS

JOURNAL OF PHYCOLOGY, Issue 2001
Article first published online: 24 SEP 200
Passy, S. I.1,2 & Freehafer, D.2 1Department of Biology, Rensselaer Polytechnic Institute, Troy, NY 12180; 2US Geological Survey, 425 Jordan Rd., Troy, NY 12180-8349 USA On August 27, 1999 diatoms were sampled, and current velocity was measured at 81 locations on a regular square sampling grid in an unshaded, cobble-bottom reach of White Creek, NY. The grid had an extent of 16 m2, interval, the distance between neighboring sampling points, of 0.5 m, and grain size, the size of the elementary sampling unit, of 0.01 m2. Six of the seven dominant benthic diatoms were colonial forms, including Diatoma vulgaris, Fragilaria capucina, F. crotonensis, Gomphoneis minuta, Melosira varians, and Synedra ulna. Their morphology and distribution were investigated from the perspective of fractal geometry and stream ecology, respectively. Fractal dimension of diatom colonies, indicative of their shape complexity, ranged from 1.06 to 1.54, demonstrating vast morphological variation from simple geometric shapes to complex outlines. The relative abundance of the six diatoms was regressed against current regime, which ranged from 0.03 to 0.66 m, s -1. All regression models were significant at P < 0.05 and explained between 55% and 94% of the variation in diatom distribution. The diatom niche breadth, i.e. the amount of environmental variability a species can tolerate, was defined from these models and showed substantial variation, from 5 to 14. The regression model of fractal dimension against niche breadth was significant and explained 76% of colonial shape variation, revealing a strong relationship between diatom colonial complexity and habitat variability. This finding suggests that environmental variability could create highly complex colonial morphologies in benthic diatoms as an evo-lutionary strategy for survival in unpredictable environments. [source]

Systematic review: hepatic fibrosis , regression with therapy

ALIMENTARY PHARMACOLOGY & THERAPEUTICS, Issue 10 2008
C. D. ZOIS
Summary Background, Hepatic fibrosis occurs in response to chronic liver injury, regardless of the cause. An impressive amount of knowledge concerning the pathogenesis and treatment of liver fibrosis has emerged over the past few years. The hallmark of this event is the activation of the hepatic stellate cell. The latter event causes accumulation of extracellular matrix and formation of scar, leading to deterioration in hepatic function. Aim, To assess chronic liver injury, many invasive and non-invasive methods have been suggested. Methods, Although transient elastography, image analysis of fractal geometry and fibrotest with actitest have been used in clinical practice, liver biopsy remains the recommended choice, especially when histological staging of fibrosis or response to treatment is needed. Conclusions, The recent advances in anti-viral therapy have resulted in many reports on fibrosis and even on cirrhosis regression, especially early and in young people. A number of new agents have been suggested for the treatment of fibrosis, with promising results in animals; however, their efficacy in humans remains to be elucidated. The investigation of heterogeneity and plasticity of hepatic stellate cells is a topic of scientific interest and may result in improvements in patient management. [source]

Fractal-shaped microstrip dual-mode bandpass filter with asymmetrical sinuous spurlines

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 3 2009
Fu Tong
Abstract In this article, miniaturized dual-mode bandpass filters using Koch fractal-shaped slots and sinuous spurlines are proposed. Because of the space-filling property of the fractal geometry, the transmission characteristics of this filter can be adjusted by the iteration order of the Koch fractal curve. Moreover, asymmetrical sinuous spurlines are adopted to tune the degenerate modes. Compared with the conventional square-patch filters, fractal slots and sinuous spurlines can also provide more current distribution distortions which improve the electrical length and realize a compact design. Experimental data in agreement with theoretical data verify the design methodology. © 2009 Wiley Periodicals, Inc. Microwave Opt Technol Lett 51: 745,747, 2009; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.24167 [source]

Interlaminar contact development during thermoplastic fusion bonding

POLYMER ENGINEERING & SCIENCE, Issue 2 2002
F. Yang
Fabrication of layered thermoplastics and thermoplastic-matrix composites using processes such as tow placement, tape laying, and resistance welding is fundamentally based on the principle of fusion bonding, which involves applying heat and pressure to contacting thermoplastic surfaces. One of the important processing steps,intimate contact development,is considered in this paper. Interlaminar intimate contact development has a strong dependency on the thermoplastic surface geometry. Profilometric measurements of common thermoplastic prepreg tows, such as AS4/PEEK and IM7/PIXA, show that surface roughness features appear at several length scales and that the surfaces have fractal asperity structures. In this paper, principles of fractal geometry are used to describe prepreg surfaces. Based on this description, a microscale fluid flow model is developed to relate a degree of intimate contact to the process parameters (pressure, temperature, and time) and the fractal parameters of the surface. The model development and comparisons with experimental data are presented and discussed. [source]