Comparison of calculation methods of fractal dimension on agricultural soil surface roughness

Two-stage method for fractal dimension calculation of the mechanical equipment rough surface profile based on fractal theory

What is the matrix block size distribution of a fractured reservoir In order to answer this question and assess the potential of fractal geometry as a method of characterization of fracture networks, a pilot study has been done of the fractured chalk quarry in Laegerdorf. The fractures seen on the quarry walls were traced in the field for a total area of {approximately}200 {times} 45 m. The digitized pictures have been analyzed by a standard box-counting method. This analysis gave a fractal dimension of similarity varying from 1.33 for fractured areas between faults, to 1.43 for the fault zone, and 1.53 for the highly deformed fault gouge. The amplitude showed a similar trend. The fractal dimension for the whole system of fractures is {approximately}1.55. In other words, fracture networks in chalk have a nonlinear, fractal geometry, and so matrix block size is a scaling property of chalk reservoirs. In terms of rock mechanics, the authors interpret the variation of the fractal dimension as follows: A small fractal dimension and amplitude are associated with brittle deformation in the elastic regime, while a large fractal dimension and amplitude are associated with predominantly ductile, strain softening deformation in the plastic regime. The interactionmore » between the two regimes of deformation in the rock body is a key element of successful characterization and may be approached by seeing the rock as a non-Newtonian viscoelastic medium. The fractal dimension for the whole is close to a material independent limit that constrains the development of fractures.« less

The surface micro-topography of micro-WEDM is random, disordered and multi-scale and has been proved that it is fractal with the characteristic of self-affinity within a certain scale on the basic of the fractal geometry theory. According to the characterization of W-M fractal function, the principles of three evaluation methods about power spectrum method, structure function method and wavelet criterion have been described. The advantages and disadvantages of them evaluating the fractal property of the surface micro-topography of micro-WEDM have been compared in this paper. The experimental results indicate that the wavelet criterion is more stable and dependable than the other two methods, so the fractal dimension D of the surface micro-topography of micro-WEDM has been calculated using it. The result shows that the fractal dimension has the tendency of decrease with the increase of root mean square deviation (Sq) value while it is not absolutely monotonic, which can be used as a beneficial supplement to traditional evaluation parameters of surface roughness.

Surface roughness is an important characteristic in analyzing synthetic aperture radar images and three-dimensional (3-D) surfaces that influence the backscattering of electromagnetic waves. We propose an algorithm based on a fractal method for retrieving parameters of a surface. To estimate surface roughness parameters, 10,000 different 3-D surfaces with different rms-height and correlation length are simulated. 3-D simulation of surfaces is carried out based on fractal Brownian motion. The results show that the fractal method represents a good relationship between roughness parameters and fractal dimension. It can be seen that, in some cases, surfaces with different roughness have the same fractal dimension. Roughness index (RI) can be used as a complement to fractal dimension. We present empirical relationships among fractal dimension, roughness parameters, and RI. The method is implemented on L and C bands with HH and HV polarizations of AIRSAR data at different dates. The comparison between field measurement and estimated roughness showed that the accuracy of soil surface roughness estimation for band L with HH polarizations is better than bands L and C with polarizations HV and HH, respectively. The results of this method also are compared with the roughness estimates using the integral equation model (IEM). The analysis of outputs shows that the roughness estimation using the fractal and IEM is very similar in the low moisture at L band in HH polarization. The root mean square error of roughness for data at L band in HH polarization on July 1, 2002, is 0.54 and 0.53 cm for fractal and IEM, respectively.

A comparison of fractal dimension estimators based on multiple surface generation algorithms

The paper presents the results of a fractal analysis of the cross-sections of a porous mineral deposit consisting of spherical elements which formed a spatial system with varying porosity (0.4 to 0.95). The virtual deposit was generated using the Discrete Element Method in the YADE code by means of the so-called Radius Expansion Method. The fractal analysis was carried out using the structure function method, determining the fractal dimension (D), the topothesy (L) and the corner frequency (l) (MAINSAH et al. 2001). The conducted simulations have confirmed to a considerable extent the test results available in the literature involving the fractal analysis of mineral deposits with varying porosity. They clearly indicate that the fractal dimension does not change along with the porosity of the deposit, if the autocorrelation function or their transformations (e.g. structure function) methods are used. Moreover, based on the information available in the literature, it can be concluded that the value of the fractal dimension corresponds to mineral deposits with the specified geometric shapes of the elements which form them.

This study proposes the analysis and evaluation method of time series ultrasonic signal using the chaotic feature extraction for ultrasonic pattern recognition. Features extracted from time series data using the chaotic time series signal analysis quantitatively welding defects. For this purpose analysis objective in this study is fractal dimension and Lyapunov exponent. Trajectory changes in the strange attractor indicated that even same type of defects carried substantial difference in chaoticity resulting from distance shills such as 0.5 and 1.0 skip distance. Such differences in chaoticity enables the evaluation of unique features of defects in the weld zone. In experiment fractal(correlation) dimension and Lyapunov exponent extracted from 6dB ultrasonic defect signals of weld zone showed chaoticity. In quantitative chaotic feature extraction, feature values(mean values) of 4.2690 and 0.0907 in the case of porosity and 4.2432 and 0.0888 in the case of incomplete penetration were proposed on the basis of fractal dimension and Lyapunov exponent. Proposed chaotic feature extraction in this study enhances ultrasonic pattern recognition results from defect signals of weld zone such as vertical hole.

Water jet drilling (WJD) technology is a highly efficient method to extract coalbed methane from reservoirs with low permeability. It is crucial to efficiently remove the coal fragments while drilling. In this study, to disclose coal fragmentation features and size distributions under water jet impact in drilling, the image processing method was utilized to obtain the geometric dimensions of coal fragments. The size distributions, morphologies and fractal characteristics of coal fragmentation were studied based on generalized extreme value distribution and fractal theory. The effects of the jet impact velocity and coal strength on the fragmentation features were analyzed. The results show that fine particles dominate the coal fragments in WJD for coal seams with various strengths. In experiments conducted at the Fengchun coal mine, owing to the higher coal strength of the M7 coal seam, the fragmentation degree of coal subjected to water jets during WJD is lower in the M7 coal steam than in the M8 coal seam, which results in a large dominant fragment size and small fractal dimension under the same impact energy. It was found that the higher the jet impact velocity is, the higher the quantity of fragments generated from WJD and the smaller the particle size. The NUM-based cumulative probability distribution curves of coal fragments are more intensive in the range of relatively small particle sizes and then become sparser with the increase in particle size. When the impact velocity increases, (i) the size distribution curves move toward smaller particle sizes, and the dominant fragment size decreases; (ii) the shape (major axis/minor axis) of coal fragments move toward the upper left, and the curve shape for a high impact velocity attains unity more quickly; and (iii) the fractal dimension value increases linearly. In addition, the fractal dimensions are obviously affected by the dominant fragment size; they increase with the decrease in the dominant fragment size. This study can provide a basis for further research on coal fragment transportation in WJD and parameter selection for discharging coal fragments during drilling for CBM development.

Floating Properties of Agglomerated Inclusion in Liquid Steel

The formation of WEDM surface is a complicated process. There are many factors which make machined surface topography have the characteristics of complex and irregular, and impact using performance of parts. The work investigated microscopic features of the WEDM surface topography based on power spectral density and fractal theory, and proposed power spectral density evaluation method of the WEDM surface. The fractal dimension of the WEDM surface was calculated by structure function method. The physical meaning of the fractal dimension of the WEDM surface was described. The result shows that topography of the WEDM surface exhibits strong fractal characteristics within a certain scale. The processing parameters and pulse power performance will affect the fractal dimension D. The fractal dimension D has a certain relationship with the surface roughness Ra. It is more reasonable to use the fractal dimension D as well as the surface roughness Ra together to evaluate WEDM surface quality.

Relationship between fractal microphase separation and permselectivity of block copolymer membranes containing poly(dimethylsiloxane)

Comparison of Fractal Dimension Calculation Methods for Channel Bed Profiles

Objective To evaluated the quality of life of maintenance hemodialysis (MHD) and CAPD patients and to discuss the influence factors of quality of life of MHD and CAPD patients. Methods The objects' clinical and questionnaire data were obtained from the Department of Nephrology and Blood Purification Center, the First Affiliated Hospital of Zhengzhou University, from July to September 2016, which inclued 118 MHD patients and 76 CAPD patients.The quality of life of MHD and CAPD patients was evaluated through the application of KDQOL-SFTM 1.3 version. At the meantime, related indexes reflecting nutrition and the adequecy of hemodialysis of MHD and CAPD patients were screened. Results The KDTA score of MHD patients was (62.4±11.3), SF-36 score was (58.3±17.9), significantly lower than the general population(P<0.05). In KDTA and SF-36, the score of 11 fractal dimensions was slightly higher than the United States, and the scores of 6 fractal dimensions was slightly higher than Spain.Compared with the survey data in Guangzhou, scores of all fractal dimensions were obviously improved and the same as survey data of Shenyang and Hefei.The KDTA score of CAPD patients was (71.4±8.9), SF-36 score was (61.6±16.3), significantly lower than the general population(P<0.05). In KDTA and SF-36, the score of 7 fractal dimensions was significantly higher than Hongkong, and the rest of which were all relatively low than Hongkong.Compared with the survey data in Guangzhou, scores of all fractal dimensions were obviously improved and the same as survey data of Shenyang and Hefei.The KDTA and SF-36 overall scores of MHD patients were significantly lower than the CAPD patients(P<0.05). In 11 fractal dimensions, the scores of all fractal dimensions of CAPD patients were higher than MHD patients and showed significant differences in EKD, BKD, WS, CF, QSI, SexF, SoS and PS(P<0.05). In 8 fractal dimensions’ scores of SF-36, besides PF, SF and Energy, the other fractal dimensions’ scores of CAPD patients were all higher than MHD patients and showed significant differences in PF, RP, BP, EWB, RE and SF(P<0.05). The general data for the MHD patients showed that the quality of life existed differences (P<0.05) among the sex, literacy, annual household income, the conditions of health insurance, the primary diseases and the dialysis age, and also had a correlation (P<0.05) with the scores of SAG, ALB, HB, Kt/V, iPTH, Ca×P. Multiple-factor analysis showed that dialysis age, sex (female), the primary disease (DN), iPTH, Kt/V, the score of SGA was the independent risk factors for the quality of life of the MHD patients, of which dialysis age was a long-time effect factor. The general data for the CAPD patients showed that professional conditions, the conditions of health insurance, the causes of primary diseased and the dialysis age existed differences (P<0.05), and also had a correlation (P<0.05) with the score of SAG, ALB, HB, Kt/V, multiple-factor analysis showed that the primary disease(DN), Kt/V, ALB, the score of SGA were the independent risk factors for the quality of life of the CAPD patients. Conclusions MHD and CAPD patients have a low quality of life, there are differences between developing and developed country.Diabetic Nephropathy, Kt/V, SGA are the common independent risk factors for the quality of life of the MHD and CAPD patients. Key words: Maintenance hemodialysis; CAPD; Quality of life

Fractal dimension is a very important parameter in fractal theory. Usually fractal dimension is determined by the slop of log(Nr) versus log(1/r). In this paper, we focus on the effect of different data post processing method on fractal dimension. From original data of the fractal dimension determination, it can be seen that log(Nr) is positively related to log(1/r). For the low values of log(1/r), the slow change in log(Nr) in some small intervals is due to the slow change in the number of boxes covering every grid. Both the low scale and the high scale data have a significant effect on the fractal dimension, and the former contributes to a large fractal dimension while the latter contributes to a small one. To obtain an accurate fractal dimension, different data post processing methods are studied. Using the second power sample step is tried, which gives a uniform sample step in log(Nr) versus log(1/r) coordinate system, and weakens the effect of the low scale data. But the reserved points are too few to obtain an accurate fractal dimension, which is a statistic quantity. At last, the three-line fitting is tried, the fractal dimension is determined by the slope of middle line, which eliminates the effect of low and high scale data, and gives a reasonable and optimization result.

In this study, the optical refractive constants of the (5, 5) SWBNNT and (5, 5) SWCNT systems were calculated in both parallel and perpendicular directions of the tube axis by using Quantum ESPRESSO and YAMBO code. It also extended the optical behaviors of (5, 5) SWCNT and (5, 5) SWBNNT to both perpendicular and parallel directions instead of the parallel directions reported in the literature. It also looked at the effects of the diameter of the nanotube on the optical properties instead of chiral angles. From our results, the best optical reflection was found for (5, 5) SWBNNT, while the best optical refraction was found with (5, 5) SWCNT. It was observed that the SWCNT demonstrates refraction in both parallel and perpendicular directions, while (5, 5) SWBNNT shows perfect absorption in perpendicular direction. These new features that appeared for both nanotubes in perpendicular directions were due to new optical band gaps, which appear in the perpendicular directions to both nanotubes’ axis. The electron energy loss (EEL) spectrum of SWBNNT revealed the prominent π- and π + δ- Plasmon peaks, which demonstrates themselves in the reflectivity spectrum. Furthermore, little effect of diameter was observed for the perpendicular direction to both nanotubes’ axis; as such, the combined properties of (5, 5) SWBNNT and (5, 5) SWCNT materials/systems for transmitting light offer great potential for applications in mobile phone touch screens and mobile network antennas. In addition, the studies of optical properties in the perpendicular axis will help bring ultra-small nanotubes such as SWCNT and SWBNNT to the applications of next-generation nanotechnology.