Comparing monofractal and multifractal analysis of corrosion damage evolution in reinforcing bars

Based on fractal theory and damage mechanics, the aim of this paper is to describe the monofractal and multifractal characteristics of corrosion morphology and develop a new approach to characterize the nonuniform corrosion degree of reinforcing bars. The relationship between fractal parameters and tensile strength of reinforcing bars are discussed. The results showed that corrosion mass loss ratio of a bar cannot accurately reflect the damage degree of the bar. The corrosion morphology of reinforcing bars exhibits both monofractal and multifractal features. The fractal dimension and the tensile strength of corroded steel bars exhibit a power function relationship, while the width of multifractal spectrum and tensile strength of corroded steel bars exhibit a linear relationship. By comparison, using width of multifractal spectrum as multifractal damage variable not only reflects the distribution of corrosion damage in reinforcing bars, but also reveals the influence of nonuniform corrosion on the mechanical properties of reinforcing bars. The present research provides a new approach for the establishment of corrosion damage constitutive models of reinforcing bars.     

分形理论及其在土壤空间变异研究中的应用

土壤具有不同程度的空间变异性,土壤空间变异研究对于土壤管理有重要意义.本文简要综述了分形理论及其在土壤空间变异研究中的应用,重点讨论了利用矩方法计算土壤属性分形维,多重分形分析土壤空间变异性及基于多重分形谱参数的土壤属性尺度转换.早期研究验证了分形理论在分析土壤空间变异中的有效性和应用潜力,国内外近期研究则报道了利用分形及多重分形理论分析土壤空间变异的最新进展.分形理论可以成为量化土壤属性空间变异性及尺度转换的重要工具.     

Multiplicative multi-fractal modeling of electromyography signals for discerning neuropathic conditions

In this paper, we present a new method for multi-scale analysis of electromyography signals based on an interesting fractal process known as multiplicative cascade multi-fractal. Using simulated needle electromyography signals, we show this method provides a means for discrimination of normal and neuropathic electromyography signals. We also present experimental results that show the new parameters, computed using multiplicative cascade multi-fractal modeling, are more robust than the conventional signal parameter, number of turns, in the presence of additive noise. Results of multiplicative cascade multi-fractal modeling are consistent with other multi-scale approaches; advantages and differences are high lighted.     

Fat fractal and multifractals for protein and enzyme surfaces.

The roughness and irregularity of the surfaces in the protein and enzyme are fractal features that may be characterized by fractal dimensions and mass exponents. The surface fractal dimensions calculated by the variation method are different from those obtained by other methods, since the former is applicable to the self-affine system. Thus the results reported here are reliable for the surfaces. However, the fat fractal and multifractal features of proteins and enzymes are studied by simulation. The surface mass exponents are regarded as another kind of scaling exponent, and the spectrum f(alpha) provides further detailed information about the surfaces of enzyme and protein. The applications of the spectrum f(alpha) to the enzymatic reactions is also discussed.     

Surface fractality as a guide for studying protein-protein interactions

The concept of fractal dimension is applied to protein surfaces. Satellite tobacco necrosis virus, prealhumin, retinol binding protein and lysozyme have been studied. A residue fractal index has been defined, which provides a suitable colour code when using computer graphics for visualizing surfaces. Some provisions are made that render the MS algorithm useful to calculate protein surface fractal dimensions. It has been found that a correlation exists between regions of high fractal dimension and those involved in protein-protein interactions. The usefulness of surface fractality in this context is demonstrated by a molecular docking experiment.     

Surface Changes in Mild Steel Coupons from the Action of Corrosion-Causing Bacteria

Changes which occur on the surface of mild steel coupons submerged in cultures of an Fe(III)-reducing bacterium, isolated from corroded pipe systems carrying crude oil, were studied microscopically to investigate the interaction between the corrosion-causing bacterium and the corroding mild steel coupon. Under micro-aerobic conditions and in the absence of the bacteria, a dense, crystalline, amorphous coat formed on the surface of the steel coupons. In the presence of bacteria the surface coat was extensively removed, exposing the bare metal to the environment. After about 2 weeks of exposure, the removal of the surface coating was followed by colonization of the metal surface by the bacteria. Colonization was mediated by fibrous, exopolysaccharidic material formed by the bacteria. Extension of studies to other bacteria isolated from crude oil and corroded pipes reveals that the formation of exopolysaccharide fibers and possession of adherent properties are common characteristics of bacteria from crude oil systems.     

Comparison of adhesion of the food spoilage bacterium Shewanella putrefaciens to stainless steel and silver surfaces

AIMS: To compare the number of attached Shewanella putrefaciens on stainless steel with different silver surfaces, thus evaluating whether silver surfaces could contribute to a higher hygienic status in the food industry. METHODS AND RESULTS: Bacterial adhesion to three types of silver surface (new silver, tarnished silver and sulphide-treated silver) was compared with adhesion to stainless steel (AISI 316) using the Malthus indirect conductance method to estimate the number of cfu cm(-2). The number of attached bacteria on new silver surfaces was lower than on steel for samples taken after 24 h. However, this was not statistically significant (P > 0.05). The numbers of attached bacteria were consistently lower when tarnished silver surfaces were compared with stainless steel and some, but not all, experiments showed statistical significance (P < 0.05). Treating new silver with sulphide to reproduce a tarnished silver surface did not result in a similar lowering of adhering cells when compared with steel (P > 0.05). CONCLUSIONS: New or tarnished silver surfaces caused a slight reduction in numbers of attached bacteria; however, the difference was only sometimes statistically significant. SIGNIFICANCE AND IMPACT OF THE STUDY: The lack of reproducibility in differences in numbers adhering to the different surfaces and lack of statistical significance between numbers of adhered viable bacteria do not indicate that the tested silver surfaces can be used to improve hygienic characteristics of surfaces in the food industry.     

长江源区高寒草原和高寒草甸土壤粒径分布特征

为探究长江源区主要下垫面土壤空间异质性与粒径分布(PSD)非均匀性,运用分形理论描述高寒草原和高寒草甸2种下垫面土壤粒径分布特征,分析了 2种下垫面土壤的分形维数特征差异及其与土壤颗粒组成的关系.结果表明:研究区土壤颗粒粒径主要分布于100-800 μm,高寒草原土壤单重分形维数(Dv)为2.429～2.508,高寒草...     

Self similarity of protein surfaces.

Scaling properties of the surfaces of 53 proteins are studied on the basis of experimentally determined 3-D structures of these biological macromolecules. It is found that the surfaces show self similarity within a yardstick range of 1.5 A less than epsilon less than 15 A. The self similarity is measured by the fractal dimension D of the surface. Two different algorithms for the determination of the fractal dimension are applied, both based on cubic yardstick particles. One is related to the contact surface (CS), which was first introduced by Connolly (17), while the other corresponds to the solvent accessible surface (SAS) of Richards (9). The fractal dimensions of both are different. While the CS type approach leads to relatively high values of D in the range 2.5 to 2.6 the SAS approach gives fractal dimensions of D approximately 2.     

Surface characterization of proteins using multi-fractal property of heat-denatured aggregates

Multi-fractal property of heat-denatured protein aggregates (HDPA) is characteristic of its individual form. The visual similarity between digitally generated microscopic images of HDPA with that of surface-image of its individual X-ray structures in protein databank (PDB) displayed using Visual Molecular Dynamics (VMD) viewer is the basis of the study. We deigned experiments to view the fractal nature of proteins at different aggregate scales. Intensity based multi-fractal dimensions (ILMFD) extracted from various planes of digital microscopic images of protein aggregates were used to characterize HDPA into different classes. Moreover, the ILMFD parameters extracted from aggregates show similar classification pattern to digital images of protein surface displayed by VMD viewer using PDB entry. We discuss the use of irregular patterns of heat-denatured aggregate proteins to understand various surface properties in native proteins.     

Use of a quartz crystal microbalance to investigate the antiadhesive potential of N-acetyl-L-cysteine

The reduction of bacterial biofilm formation on stainless steel surfaces by N-acetyl-L-cysteine (NAC) is attributed to effects on bacterial growth and polysaccharide production, as well as an increase in the wettability of steel surfaces. In this report, we show that NAC-coated stainless steel and polystyrene surfaces affect both the initial adhesion of Bacillus cereus and Bacillus subtilis and the viscoelastic properties of the interaction between the adhered bacteria and the surface. A quartz crystal microbalance with dissipation was shown to be a powerful and sensitive technique for investigating changes in the applied NAC coating for initial cell surface interactions of bacteria. The kinetics of frequency and dissipation shifts were dependent on the bacteria, the life cycle stage of the bacteria, and the surface. We found that exponentially grown cells gave rise to a positive frequency shift as long as their cell surface hydrophobicity was zero. Furthermore, when the characteristics of binding between the cell and the surface for different growth phases were compared, the rigidity increased from exponentially grown cells to starved cells. There was a trend in which an increase in the viscoelastic properties of the interaction, caused by the NAC coating on stainless steel, resulted in a reduction in irreversibly adhered cells. Interestingly, for B. cereus that adhered to polystyrene, the viscoelastic properties decreased, while there was a reduction in adhered cells, regardless of the life cycle stage. Altogether, NAC coating on surfaces was often effective and could both decrease the initial adhesion and increase the detachment of adhered cells and spores. The most effective reduction was found for B. cereus spores, for which the decrease was caused by a combination of these two parameters.     

Fractal analysis of surface electromyography signals: A novel power spectrum-based method

This paper presents a novel power spectrum-based method for fractal analysis of surface electromyography signals. This method, named the bi-phase power spectrum method, provides a bi-phase power-law which represents a multi-scale statistically self-affine signal. This form of statistical self-affinity provides an accurate approximation for stochastic signals originating from a strong non-linear combination of a number of similar distributions, such as surface electromyography signals which are formed by the summation of a number of single muscle fiber action potentials. This power-law is characterized by a set of spectral indicators, which are related to distributional and geometrical characteristics of the electromyography signal’s interference pattern. These novel spectral indicators are capable of sensing the effects of motor units’ recruitment and shape separately by exploiting the geometry of the interference pattern. The bi-phase power spectrum method is compared to geometrical techniques and the 1/f^α approach for fractal analysis of electromyography signals. The extracted indicators using the bi-phase power spectrum method are evaluated in the context of force and joint angle and the results of a human study are presented. Results demonstrate that the bi-phase power spectrum method provides reliable information, consisting of components capable of sensing force and joint angle effects separately, which could be used as complementary information for confounded conventional measures.     

Development of a preclinical natural porcine knee simulation model for the tribological assessment of osteochondral grafts in vitro

In order to pre-clinically evaluate the performance and efficacy of novel osteochondral interventions, physiological and clinically relevant whole joint simulation models, capable of reproducing the complex loading and motions experienced in the natural knee environment are required. The aim of this study was to develop a method for the assessment of tribological performance of osteochondral grafts within an in vitro whole natural joint simulation model.The study assessed the effects of osteochondral allograft implantation (existing surgical intervention for the repair of osteochondral defects) on the wear, deformation and damage of the opposing articular surfaces. Tribological performance of osteochondral grafts was compared to the natural joint (negative control), an injury model (focal cartilage defects) and stainless steel pins (positive controls). A recently developed method using an optical profiler (Alicona Infinite Focus G5, Alicona Imaging GmbH, Austria) was used to quantify and characterise the wear, deformation and damage occurring on the opposing articular surfaces. Allografts inserted flush with the cartilage surface had the lowest levels of wear, deformation and damage following the 2 h test; increased levels of wear, deformation and damage were observed when allografts and stainless steel pins were inserted proud of the articular surface. The method developed will be applied in future studies to assess the tribological performance of novel early stage osteochondral interventions prior to in vivo studies, investigate variation in surgical precision and aid in the development of stratified interventions for the patient population.     

红树植物木榄幼树斑块形状的分形分析

应用分形理论分析了山口国家级红树林自然保护区木榄幼树斑块形状的分形特征。木榄幼树斑块在整体水平上的分形维数为 1 .1 2 ,而单个斑块的分形维数介于 1 .1 7～ 1 .3 7之间。分形维数的大小与斑块形状的复杂程度密切相关。频谱法和周长 -面积法都适用于分析幼树斑块形状的分形特征。     

A mathematical analysis using fractals for binding interactions of nuclear estrogen receptors occurring on biosensor surfaces

A mathematical approach using fractal concepts is presented for modeling the binding and dissociation interactions between analytes and nuclear estrogen receptors (ER) occurring on surface plasmon resonance biosensor chip surfaces. A kinetic knowledge of the binding interactions mediated by ER would help in better understanding the carcinogenicity of these steroidogenic compounds and assist in modulating these reactions. The fractal approach is applied to analyte-ER interaction data obtained from literature. Numerical values obtained for the binding and dissociation rate coefficients are linked to the degree of roughness or heterogeneity (fractal dimension, D(f)) present on the biosensor surface. For example, a single-fractal analysis is used to describe the binding and dissociation phases for the binding of estradiol and ERalpha in solution to clone 31 protein immobilized on a biosensor chip (C-S. Suen et al., 1998, J. Biol. Chem. 273(42), 27645-27653). The binding and the dissociation rate coefficients are 27.57 and 8.813, respectively, and the corresponding fractal dimensions are 1.986 and 2.268, respectively. In some examples dual-fractal models were employed to obtain a better fit of either the association or the dissociation phases or for both. Predictive relationships are developed for (a) the binding and the dissociation rate coefficients as a function of their respective fractal dimensions and (b) the ratio K(A) (= k/k(d)) as a function of the ratio of the fractal dimensions (D(f)/D(fd)). The analysis should provide further physical insights into the ER-mediated interactions occurring on biosensor and other surfaces.     

Cleanability in relation to bacterial retention on unused and abraded domestic sink materials

The relative cleanability of stainless steel, enamelled steel, mineral resin and polycarbonate domestic sink materials was assessed by comparing the number of organisms remaining on surfaces after cleaning. In unused condition all materials, other than one enamelled steel, were equally cleanable. Stainless steel, abraded artificially or impact damaged to a similar degree as stainless steel subjected to domestic wear, retained approximately one log order less bacteria after cleaning than the other materials subjected to the same treatments. Little difference in cleanability was recorded between the abraded surfaces of the other materials although enamelled steel surfaces were less cleanable than mineral resin or polycarbonate after impact damage, because of the greater susceptibility of enamelled steel to damage by this treatment. When cleaning time was extended beyond 10 s for the abraded and impact damaged materials, their cleanability was not enhanced as compared with stainless steel. Changes in surface finish after abrasion were assessed by surface roughness measurement and scanning electron microscopy. Surfaces with poor cleanability before and after abrasion were characterized by pitting, crevices or jags. These surfaces are likely to retain more bacteria because of increased numbers of attachment sites, a larger bacterial/material surface contact area and topographical areas in which applied cleaning shear forces are reduced. Materials that resist surface changes, e.g. stainless steel, will remain more hygienic when subjected to natural wear than materials which become more readily damaged.     

Comparative Studies on the Sampling and Investigation of Microbial Contamination of Surfaces by the Contact Plate and Swab Methods

In this study a comparison was made of recovering bacteria from stainless steel, plastic, wood, agar and meat surfaces. Sampling was performed using the agar contact and swab methods. The results indicated that for a flat, firm surface the contact plate method was more suitable, considering both recovery and repeatability. Swabbing was, by contrast, better for flexible and uneven surfaces and for heavily contaminated surfaces. Bacteriological guidelines are suggested for the hygienic evaluation of surface contamination of meat carcasses and for working surfaces in meat processing plates.     

Statistical method for surface pattern-matching between dissimilar molecules: electrostatic potentials and accessible surfaces

This paper outlines a statistical method for patternmatching between surfaces and is applicable to structural and energetic patterns found on molecular surfaces. Correlation coefficients generated for the pattern match are scale invariant. Regression analysis applied to the patterns reveals the scaling and displacement relationships. The method for measuring the similarities between molecular surfaces of two dissimilar molecules held infixed orientations is given explicitly. Implicit in this procedure is a method for studying the inverse phenomenon, namely complementarity between surface parameters at a binding site and its ligand. The method has been used to assess surface differences in structural similarities generated by computer fitting and by visual comparison. Various pitfalls likely to be encountered in evaluating molecular structural similarities are noted.     

遗传算法支持下土地利用空间分形特征尺度域的识别

针对土地利用空间分形特征只存在于有限尺度域的现象,采用无标度区内离散点拟合的离差平方和平均值最小作为目标函数,提出了一种基于遗传算法的土地利用空间分形特征尺度域的识别方法,用于准确计算分形维数的有效区间范围。以武汉市武昌区水域空间分形特征为例,利用Quickbird多光谱遥感影像提取土地利用空间信息,重点讨论了基于遗传算法识别土地利用空间分形特征尺度域范围的总体思路、适应度函数和遗传算子等环节;然后分别从测定系数、标准差和无标度区间3个角度,将其同人工判断法、相关系数法以及强化系数法进行对比讨论;并结合研究区域实际的水域空间分布格局,分析不同方法计算所得半径维数的合理性。结果表明,土地利用分形特征尺度域的范围对分形维数计算结果有较大影响;相对于传统计算方法来说,遗传算法在尺度无标度区间识别上具有更高的精度,可以为土地利用空间格局分形特征的研究提供客观指导意见。     

Detection of glucose and related analytes by biosensors: a fractal analysis

A fractal analysis is used to model the binding and dissociation kinetics of connective tissue interstitial glucose, adipose tissue interstitial glucose, insulin, and other related analytes on biosensor surfaces. The analysis provides insights into diffusion-limited analyte-receptor reactions occurring on heterogeneous biosensor surfaces. Numerical values obtained for the binding and the dissociation rate coefficients are linked to the degree of heterogeneity or roughness (fractal dimension, Df) present on the biosensor chip surface. The binding and dissociation rate coefficients are sensitive to the degree of heterogeneity on the surface. For example, for the binding of plasma insulin, as the fractal dimension value increases by a factor of 2.47 from Df1 equal to 0.6827 to Df2 equal to 1.6852, the binding rate coefficient increases by a factor of 4.92 from k1 equal to 1.0232 to k2 equal to 5.0388. An increase in the degree of heterogeneity on the probe surface leads to an increase in the binding rate coefficient. A dual-fractal analysis is required to fit the binding kinetics in most of the cases presented. A single fractal analysis is adequate to describe the dissociation kinetics. Affinity (ratio of the binding to the dissociation rate coefficient) values are also presented. Interferents for glucose such as uric acid and ascorbic acid were also detected using glucose biosensors based on carbon nanotube (CNT) nanoelectrode ensembles (NEEs) (29) (Lin, Y.; Lu, F.; Tu, Y.; Ren, Z. Nano Lett. 2004, 4 (2), 191-195). Attempts are made to standardize biosensor properties in terms of diffusion characteristics on in vivo responsiveness.