Fractal Values Research Articles

Surface morphology of styrene-butadiene rubber vulcanizate filled with novel electron beam modified dual phase filler by atomic force microscopy

Topographic and phase imaging in tapping mode atomic force microscopy (TMAFM) has been performed to investigate the effect of unmodified and modified dual phase fillers on the morphology of and the microdispersion of the filler particles in the rubber matrix. The above fillers were modified using acrylate monomer (trimethylol propane triacrylate, TMPTA) or a silane coupling agent (triethoxysilylpropyltetrasulphide, Si-69) followed by electron beam modification at room temperature. Both unmodified and surface treated fillers were incorporated in a styrene-butadiene rubber. The phase images of the above composites show three levels of contrasts that correspond to matrix, filler aggregates, and bound rubber around the filler aggregates. Also, the images further elucidate the aggregated nature of the filler due to modification, which is more pronounced in the case of electron beam modified acrylated filler loaded rubber. The corresponding topographic images have been characterized by various statistical quantities like roughness parameters and one- and two-dimensional power spectral densities (1D-PSD and 2D-PSD). As compared to the control, significant increase in surface roughness is observed in the case of the modified dual phase filler loaded composites. The higher fractal value of these vulcanizates confirms the above fact. AFM study also suggests that the electron beam modification of the above fillers significantly increases the filler-filler and filler-polymer interactions.

Using fractal analysis to quantitatively characterize the shapes of volcanic particles

The shapes of volcanic particles reflect numerous eruptive parameters (e.g., magma viscosity, volatile content, and degree of interaction with water) and are useful for understanding fragmentation and transport processes associated with volcanic eruptions. However, quantitative analysis of volcanic particle shapes has proven difficult because of their morphological complexity and variability. Here a newly developed procedure for shape analysis based on fractal geometry is described and tested. Although volcanic particle shapes are not truly fractal, their complexity can be effectively characterized in terms of fractal values (pseudofractal dimensions) reflecting morphological invariance over discrete ranges of scale. Using fractal data produced by dilation of a particle's two‐dimensional boundary, a spectrum of fractal dimensions is calculated for each particle by taking the first derivative of the dilation data. Compared with fractal methods that express shape in terms of only one or two fractal dimensions, typically derived from the slope of data on a Richardson plot, this technique results in better discrimination between samples. In addition, use of multiple fractal values allows incorporation of multivariate statistical analysis, further strengthening the differentiating power of the technique. This fractal spectrum technique yields promising results for samples of sideromelane shards from Iceland and is likely to be effective at characterizing other kinds of volcanic particle shapes.

The Generalized Fractal Dimension of Seismic Records and its Application

AbstractBased on the fractal theory, we analyze the fractal dimension characters of seismic records with different noises. The signal part and noise background part in seismic records have different fractal dimensional ranges that depend on the measuring scales used in the calculation, and the fractal dimensional values are related with the measuring scales. Therefore a new concept of generalized fractal dimension can be used to calculate the fractal dimension of seismic records. The results of numerical calculation indicate that the algorithm of generalized fractal dimension shows a strong resistance to noise. Some effective examples to pick seismic first arrivals and continued signals are given.

Effects of nicardipine and diltiazem on fractal features of short-term heart rate variability--application of coarse graining spectral analysis.

This study was designed to investigate the effects of nicardipine and diltiazem on the fractal features of short-term heart rate variability (HRV), using coarse graining spectral analysis (CGSA). Eighteen healthy volunteers participated in this study; they were divided into two groups according to the drug administered. Five-minute electrocardiogram and arterial pressure recordings were made during stepwise infusions of either nicardipine (0.4, 0.8, 1.6, and 3.2 microg.kg(-1).min(-1)) or diltiazem (2, 4, 8, and 16 microg.kg(-1).min(-1)) under rate-controlled breathing at 0.25 Hz. CGSA broke down the total power of the time series into harmonic (low frequency [0.0-0.15 Hz; LF] and high frequency [0.15-0.5 Hz; HF]) and nonharmonic (fractal) components. Cardiac sympathetic nervous system (SNS) and parasympathetic nervous system (PNS) activity indicators were evaluated as the ratios LF/HF and HF/TP (total spectral power), respectively. Fractal components were evaluated as %fractal and the spectral exponent beta of 1/f(beta). Compared with control measurements, the maximum dose of nicardipine infusion caused a significant decrease in systolic arterial pressure, a significant increase in the mean heart rate, and a significant increase in plasma norepinephrine level, findings that were associated with significant increases in %fractal and beta values (54.2 +/- 13.3 vs 75.6 +/- 9.8, and 0.86 +/- 0.22 vs 1.32 +/- 0.46, respectively; P < 0.05). PNS and SNS indicators showed decreased and increased values, respectively. Diltiazem caused a reduction in arterial pressure; however, no other parameters, including the nonharmonic components of HRV, were affected by this drug. These findings strongly suggest that nicardipine suppresses vagal cardiac neural outflow and activate the SNS, an action which, subsequently, causes changes in the fractal features of HRV. Although diltiazem reduces arterial pressure, it preserves the basic neural balance of the autonomic nervous system in regard to heart rate control.

Heart rate dynamics in refractory and well controlled temporal lobe epilepsy

Objectives: Disorders of cardiovascular and other autonomic nervous system functions are often found in patients with temporal lobe epilepsy (TLE). Cardiovascular dysregulation in TLE has previously been quantified assessing traditional...

PYRAMIDAL NEURONES IN MACAQUE VISUAL CORTEX: INTERAREAL PHENOTYPIC VARIATION OF DENDRITIC BRANCHING PATTERNS

The basal dendritic arbors of over 500-layer III pyramidal neurones of the macaque cortex were compared by fractal analyses, which provides a measure of the space filling (or branching pattern) of dendritic arbors. Fractal values (D) of individual cells were compared between the cytochrome oxidase (CO)-rich blobs and CO-poor interblobs of middle and upper layer III, and between sublaminae, in the primary visual area (V1). These data were compared with those in the CO compartments in the second visual area (V2), and seven other extrastriate cortical areas (V4, MT, LIP, 7a, TEO, TE and STP). There were significant differences in the fractal dimensions, and therefore the dendritic branching patterns, of cells in striate and extrastriate areas. Of the 55 possible pairwise comparisons of fractal dimension of neurones in different cortical areas (or CO compartments), 39 proved to be significantly different. The markedly different morphologies of pyramidal cells in the different cortical areas may be one of the features that determine the functional signatures of these cells by influencing the number of inputs received by, and propagation of potentials through, their dendritic arbors.

Fractal Characterization of Wear-Erosion Surfaces

Wear erosion is a complex phenomenon resulting in highly distorted and deformed surface morphologies. Most wear surface features have been described only qualitatively. In this study wear surfaces features were quantified using fractal analysis. The ability to assign numerical values to wear-erosion surfaces makes possible mathematical expressions that will enable wear mechanisms to be predicted and understood. Surface characterization came from wear-erosion experiments that included varying the erosive materials, the impact velocity, and the impact angle. Seven fractal analytical techniques were applied to micrograph images of wear-erosion surfaces. Fourier analysis was the most promising. Fractal values obtained were consistent with visual observations and provided a unique wear-erosion parameter unrelated to wear rate.

CT determination of bone mineral density and structural investigations on the axial skeleton for estimating the osteoporosis-related fracture risk by means of a risk score.

In addition to the pure measurement of bone mineral density (BMD) in osteodensitometry, the investigation of bone structure is becoming increasingly important for estimating fracture risk. In a clinical study, a risk score was proposed which separately assesses BMD and structural parameters for spongious and cortical bone and aggregates them into a single diagnostic parameter. In 120 lumbar vertebrae from 40 patients, BMD was determined separately for spongious and cortical bone by means of quantitative CT using a single energy procedure (SE-QCT/85 kV). In addition, structural parameters based on high resolution CT were calculated for the spongiosa and cortical bone. For all patients the number of osteoporosis-related fractures was determined on the entire skeletal system. According to WHO criteria, the patients were subdivided into four groups: 1, normal; 2, osteopenic; 3, osteoporotic without fractures; 4, severely osteoporotic. Weighting factors were determined by means of multivariate least-squares analysis and used to calculate a risk score of all parameters. The ability of the individual parameters and of the sum of discriminate between the individual groups was tested. If one considers the individual parameters (BMD and the fractal structural values for spongious and cortical bone), they allow a statistically significant separation of the four groups, although there is overlapping in the value ranges. In patients with fractures, there was a significant reduction in the cortical mineral density, accompanied by a deterioration in structural properties. The following individual values were obtained (minimum-mean-maximum): spongiosa BMD (mg ml-1), unfractured: 62-112-163, fractured: 9-48-77; cortical BMD (mg ml-1), unfractured: 190-287-405, fractured: 133-191-269; spongiosa structural parameter, unfractured: 0.35-0.73-1.01, fractured: 0.95-1.24-1.58; cortical structural parameter, unfractured: 18-31-65, fractured: 21-44-66. Above 77 mg ml-1 CaHA in the spongiosa and 270 mg ml-1 CaHA in cortical bone, no fractures were observed. By appropriately selecting the weighting factors, the score is free of overlapping between the groups with and without fractures (values: unfractured 1-9-15, fractured 16-21-29). With higher score values, the fracture risk is increasing.

Fungal fractal morphology of pellet formation in Aspergillus niger

Mycelial fractal values were compared to the conventional fungal morphological parameters: average total mycelial length, average number of tips and average growth unit. The fractal values were between 1.47 to 1.3 for the various submerged culture conditions of Aspergillus niger. The average pellet diameter was 1.4 mm at the fractal value of 1.47. The mycelia with fractal values close to 1 were less branched and slim.

Requirements for accurate quantification of self-affine roughness using the variogram method

Both stationary and non-stationary fractional Brownian profiles (self-affine profiles) with known values of fractal dimension, D, input standard deviation, σ, and data density, d, were generated. For different values of the input parameter of the variogram method (lag distance, h), D and another associated fractal parameter Kv were calculated for the aforementioned profiles. It was found that σ has no effect on calculated D. The estimated Kv was found to increase with D, σ and d according to the equation Kv = 2.0 × 10−5d0.35σ1.95D14.5. The parameter Kv seems to have potential to capture the scale effect of roughness profiles. Suitable ranges for h were estimated to obtain computed D within ±10% of the D used for the generation and also to satisfy a power functional relation between the variogram and h. Results indicated the importance of removal of non-stationarity of profiles to obtain accurate estimates for the fractal parameters. It was found that at least two parameters are required to quantify stationary roughness; the parameters D and Kv are suggested for use with the variogram method. In addition, one or more parameters should be used to quantify the non-stationary part of roughness, if it exists; at the basic level, the mean inclination/declination angle of the surface in the direction considered can be used to represent the non-stationarity. A new concept of feature size range of a roughness profile is introduced in this paper. The feature size range depends on d, D and σ. The suitable h range to use with the variogram method to produce accurate fractal parameter values for a roughness profile was found to depend on both d and D. It is shown that the feature size range of a roughness profile plays an important role in obtaining accurate roughness parameter values with both the divider and the variogram methods. The minimum suitable h was found to increase with decreasing d and increasing D. Procedures are given in this paper to estimate a suitable h range for a given natural rock joint profile to use with the variogram method to estimate D and Kv accurately for the profile.

456 The influence of psychotic states on the autonomic nervous system in schizophrenia

The analysis of heart rate variability (HRV) has proven to be useful in evaluating the neuroautonomic dysfunctions associated with various clinical conditions. The purpose of this study was to investigate the linear and non-linear dynamic measures of HRV, and to evaluate their relationship with the psychotic symptom severity, in clozapine-treated schizophrenic subjects. Fifty schizophrenic patients treated with clozapine as monotherapy and 50 normal control subjects were evaluated for HRV analysis. The HRV measurements were obtained from a 30-min resting electrocardiogram (ECG). The severity of psychotic symptoms was assessed using the Positive and Negative Syndrome Scale (PANSS). In the patient group, the complexity and symbolic dynamics measures as well as the time and frequency domain measures of HRV were significantly lower than in the control group (P<0.01). The intermediate-term fractal scaling component value was significantly higher in the patient group (P<0.01). The PANSS total score and the positive symptom subscale score had significant negative correlations with the sample entropy (SampEn) value (P<0.01). In conclusion, schizophrenic patients treated with clozapine had markedly different heart rate dynamics compared to normal control subjects. The severity of psychotic symptoms was associated with the SampEn value, suggesting that the non-linear complexity measure might be useful in assessing the neuroautonomic dysfunction in schizophrenia.

Developmental and morphological responses of mycelial systems of Stropharia caerulea and Phanerochaete velutina to soil nutrient enrichment

Patterns produced by foraging mycelial systems of decomposer fungi might be the visual evidence of strategies for obtaining differently distributed carbon sources. Mycelial systems might also be responsive to unevenly distributed mineral nutrients in the soil. The nature of the mycelial response might differ between species inhabiting eutrophicated disturbed sites, such as Stropharia caerulea (Kriesel), and inhabitants of more typical woodland soils, such as Phanerochaete velutina DC.: (Pers.) Parmasto. We examined the effect of enrichment of soil by addition of different concentrations of N, P and potassium on inoculum decay rate and on extension rate, biomass production and fractal dimension (determined by image analysis) of extra‐resource mycelia of S. caerulea and P. velutina extending from wood blocks across compacted non‐sterile soil in trays. S. caerulea was more responsive than P. velutina to both type and quantity of soil nutrient enrichment. P. velutina grew more rapidly, produced more biomass and decayed inocula more rapidly than S. caerulea under most conditions, rates of growth and resource decay of the former remaining stable over a range of soil nutrient enrichments. In contrast, morphology of S. caerulea altered on enriched soils compared to controls with greater and more pronounced fanning (divergence of separate hyphae) of the foraging mycelial front. These changes were reflected in fractal values. Extension rate and biomass production of S. caerulea was less than controls on N‐amended soil, but greater on P‐amended soils, with the greatest biomass produced on 0·13–0·27 mg P g−1 air‐dried soil. Decay rate of inocula was often positively related with mycelial production rates. These responses indicate extra‐resource mycelium of S. caerulea is able to respond rapidly to a range of soil nutrient enrichments, and this is discussed in terms of the different foraging strategies exhibited by the two fungi.

Resource acquisition by the mycelial-cord-former Stropharia caerulea: effect of resource quantity and quality

Saprotrophic mycelial-cord-forming basidiomycetes, which extend between organic substrata on the forest floor, exhibit remarkable patterns of reallocation of biomass and nutrients when encountering new resources. These have been equated with foraging strategies, and differ between species, resources quality and quantity. Stropharia caerulea occupies more disturbed sites than the fungi previously examined, and the responses of its mycelial foraging systems were investigated non-destructively by image analysis. Resource quantity and quality affected extension rate, extra-resource biomass production and distribution, as quantified by box-count fractal dimension. When mycelia grew from 0.5 cm 3 beech ( Fagus sylvatica) wood inocula across compressed, non-sterile soil to 0.06–4 cm 3 uncolonised sterile beech wood "baits" extension rate fell after contact with large wood baits but biomass production and mycelial distribution was unaffected. In contrast, extension rates of cord systems grown from 0.15 cm 3 U. dioica rhizome inocula to 0.1–1.2 cm 3 rhizome "baits" were unaffected after contact with equal or larger sized baits, but biomass production rates fell and mass fractal dimension increased. Mycelial morphology was affected by inoculum age; systems grown from 84 day old 0.5 cm 3 beech wood inocula took 10 days longer achieving the fractal values of systems developing from 22 day old inocula. Foraging strategies and resource relations of mycelial cord systems are discussed.

Diffusion Coefficients Calculated for Microporous Solids from Structural Parameters Evaluated by Fractal Geometry

This paper presents the examination of 14 microporous active carbons. The Dubinin−Astakhov equation for adsorption processes in micropores modified by a function F(z) for gamma distributed pore sizes was used for obtaining the micropore size distribution based on experimental data of benzene adsorption isotherms. This distribution can be used to determine the fractal cut-off values xmin and xmax. It is shown by means of fractal geometry how to get the structural parameters porosity ε and tortuosity τ. Both values are needed for the further calculation of diffusion coefficients according to the Knudsen diffusion equation. A comparison with experimental data shows a very good agreement between calculated and measured values.

アルカリ骨材反応による膨張ひびわれのフラクタル次元解析

Until now, crack property of concrete structure due to AAR have been estimated by means of number of cracks, crack width measured by a traverse method or an area method. However, the shape and the progress of crack, and the distribution are vaguely expressed and can't be quantified. This study applied a fractal analysis method to quantify the crack properties of concrete due to AAR. Condition of analysis, fractal characteristic value and appearance of crack were discussed. The damage degree due to AAR was quantitatively estimated. Both results of the analysis and the investigation on concrete structures were compared. The point of time of repairing the concrete structure was examined.

A fractal analysis of the influence of non-specific binding on antigen-antibody binding kinetics for biosensor applications

A fractal analysis of the influence of non-specific binding on the specific binding of antigen in solution to antibody immobilized on a biosensor surface is presented for first-, one and a half-, second, and other-order reactions occurring under external diffusion-limited conditions. Both single-step and dual-step binding of antigen in solution to antibody immobilized on the surface is considered. For a first-order reaction, an increase in the fractal parameter, b, leads to a decrease in the amount of antigen in solution bound specifically to the antibody on the surface when non-specific binding is either absent or present. The presence of non-specific binding leads to a decrease in the amount of antigen bound to the antibody on the surface. For a one and a half- and for second-order reactions and when non-specific binding is either absent or present to a small degree (α = 0·01), an increase in the fractal parameter, b, leads to a decrease in the amount of antigen bound specifically to the antibody immobilized on the biosensor surface is However, for an α value of 0·1, the maximum rate and the amount of antigen bound specifically to the antibody immobilized on the biosensor surface is obtained for fractal parameter values of 0·2 and 0·4, and 0·4 for the one and a half- and for second-order reactions, respectively. Apparently, some amount of heterogeneity is helpful in obtaining the optimum amount and rate of antigen in solution bound specifically to the antibody on the surface for reaction orders higher than one. The applicability of the approach to real antibody surfaces is demonstrated.

Characterizing Multispectral Images of Tumorous, Bruised, Skin-torn, and Wholesome Poultry Carcasses

A multispectral imaging system which provides image information of poultry carcasses in the spatial and the frequency domains was developed. This article discusses the spectral image characterization of poultry carcasses for separating tumorous, bruised and skin-torn carcasses from the normal carcasses based on the gray-scale intensity, Fourier power spectrum, and fractal analyses of the spectral images. Tumorous, bruised, and other damaged carcasses were scanned by an intensified multispectral camera with various wavelength filters (542-847 nm). The results showed that the spectral images scanned at the optical wavelengths of 542 and 700 nm were useful for separating the tumorous from the normal carcasses in the spatial domain. Fractal dimension, roughness and slope were calculated from the Fourier spectra of each carcass. The mean fractal dimension of the normal carcasses scanned at 542 nm wavelength was larger than that of tumorous carcasses (P < 0.005) and skin-torn carcasses (P < 0.1). Fractal dimension of tumor (542 nm) was smaller than that of bruised carcasses of 542 nm spectral images (P < 0.01). The fractal slope mean values of the normal carcasses were larger than the tumor (P < 0.005) and the bruise (P < 0.05). Whereas, the slope of bruised carcass scanned at 542 nm was much smaller than the slope of bruise scanned at 700 nm (P < 0.005). Neural network classifier performed with 91.4% accuracy for the separation of tumorous carcasses from normals based on the spectral images scanned at both 542 and 700 nm wavelengths.

Temporal behaviour of pressure in solar coronal loops

The temporal evolution of pressure in solar coronal loops is studied using the ideal theory of magnetohydrodynamic turbulence in cylindrical geometry. The velocity and the magnetic fields are expanded in terms of the Chandrasekhar-Kendall (C-K) functions. The three-mode representation of the velocity and the magnetic fields submits to the investigation of chaos. When the initial values of the velocity and the magnetic field coefficients are very nearly equal, the system shows periodicities. For randomly chosen initial values of these parameters, the evolution of the velocity and the magnetic fields is nonlinear and chaotic. The consequent plasma pressure is determined in the linear and nonlinear regimes. The evidence for the existence of chaos is established by evaluating the invariant correlation dimension of the attractorD 2, a fractal value of which indicates the existence of deterministic chaos.

Pattern of prolactin diurnal secretion in normal humans: evidence for nonlinear dynamics.

Prolactin (PRL) circadian profiles were analyzed using methods of nonlinear dynamics, directly from the experimental data, by combining in a single time-series (432 measurements), six individual 24-hour PRL profiles (72 measurements per profile, sampling interval = 20 min), obtained from young healthy human volunteers (4 males, 2 females), under basal conditions. Significant autocorrelation exists between any given point of the time series and a limited number of its successors. Fourier analysis showed a dominant frequency of 1 cycle/24 h, without sub-24-hour harmonics. Poincaré section indicated the presence of a fractal attractor and a sketch of the attractor revealed a highly convoluted geometric structure with a conical contour. The box-counting dimension (D0), information dimension (D1) and correlation dimension (D2) of the attractor had low, fractal values, did not differ significantly from each other, and exhibited saturation at an embedding dimension of 2. The evidence taken together suggests that, under basal conditions, the daily changes in the peripheral blood levels of PRL are governed by nonlinear deterministic dynamics, with a dominant rhythm of 1 cycle/day mixed with a higher-frequency, low-amplitude signal.

Fractal Characterization of Seismic Networks in Taiwan

The fractal dimension is calculated for the geometrical distributions of the seismic stations of three networks (the old CWB seismic network, the TTSN and the CWBSN) in Taiwan based on the correlation integral algorithm proposed by Hirata et al. (1987). Results show that the distribution of the data points of correlation integral for the old CWB seismic network distribute very irregularly and cannot be approximated by a fractal set point. The fractal dimesion value for the TTSN (1.18±0.02) is less than that for the CWBSN (1.56±0.01). This indicates that the dimension resolution and the detectability of sparse phenomena are lower for the former than the latter.