fractal dimension
Recently Published Documents





2022 ◽  
Mahbubeh Bahreini ◽  
Ramin Barati ◽  
Abbas Kamaly

Abstract Early diagnosis is crucial in the treatment of heart diseases. Researchers have applied a variety of techniques for cardiovascular disease diagnosis, including the detection of heart sounds. It is an efficient and affordable diagnosis technique. Body organs, including the heart, generate several sounds. These sounds are different in different individuals. A number of methodologies have been recently proposed to detect and diagnose normal/abnormal sounds generated by the heart. The present study proposes a technique on the basis of the Mel-frequency cepstral coefficients, fractal dimension, and hidden Markov model. It uses the fractal dimension to identify sounds S1 and S2. Then, the Mel-frequency cepstral coefficients and the first- and second-order difference Mel-frequency cepstral coefficients are employed to extract the features of the signals. The adaptive Hemming window length is a major advantage of the methodology. The S1-S2 interval determines the adaptive length. Heart sounds are divided into normal and abnormal through the improved hidden Markov model and Baum-Welch and Viterbi algorithms. The proposed framework is evaluated using a number of datasets under various scenarios.

2022 ◽  
Vol 6 (1) ◽  
pp. 40
Lei Wang ◽  
Xiao Lu ◽  
Lisheng Liu ◽  
Jie Xiao ◽  
Ge Zhang ◽  

Currently, low heat Portland (LHP) cement is widely used in mass concrete structures. The magnesia expansion agent (MgO) can be adopted to reduce the shrinkage of conventional Portland cement-based materials, but very few studies can be found that investigate the influence of MgO on the properties of LHP cement-based materials. In this study, the influences of two types of MgO on the hydration, as well as the shrinkage behavior of LHP cement-based materials, were studied via pore structural and fractal analysis. The results indicate: (1) The addition of reactive MgO (with a reactivity of 50 s and shortened as M50 thereafter) not only extends the induction stage of LHP cement by about 1–2 h, but also slightly increases the hydration heat. In contrast, the addition of weak reactive MgO (with a reactivity of 300 s and shortened as M300 thereafter) could not prolong the induction stage of LHP cement. (2) The addition of 4 wt.%–8 wt.% MgO (by weight of binder) lowers the mechanical property of LHP concrete. Higher dosages of MgO and stronger reactivity lead to a larger reduction in mechanical properties at all of the hydration times studied. M300 favors the strength improvement of LHP concrete at later ages. (3) M50 effectively compensates the shrinkage of LHP concrete at a much earlier time than M300, whereas M300 compensates the long-term shrinkage more effectively than M50. Thus, M300 with an optimal dosage of 8 wt.% is suggested to be applied in mass LHP concrete structures. (4) The addition of M50 obviously refines the pore structures of LHP concrete at 7 days, whereas M300 starts to refine the pore structure at around 60 days. At 360 days, the concretes containing M300 exhibits much finer pore structures than those containing M50. (5) Fractal dimension is closely correlated with the pore structure of LHP concrete. Both pore structure and fractal dimension exhibit weak (or no) correlations with shrinkage of LHP concrete.

2022 ◽  
Vol 1 (15) ◽  
pp. 104-106
Egor Demidchenko ◽  
Aleksey Pudalov

The fractal dimension is considered on several examples; the method of its calculation is shown. The possibilities of using fractals in the study of complex signals are proposed

2022 ◽  
Vol 2022 ◽  
pp. 1-9
Jiawei Liu ◽  
Yingzhi Xia ◽  
Hui Li ◽  
Guoping Hu ◽  
Mingming Hu

Embankment soil affected by saline can not only cause roadbed settlement, frosting, and road cracks but also cause corrosion and cracking of roadbed pipelines, which seriously affects the stability of the road. Water evaporation and dry cracking of the saline soil mainly cause soil swelling, poor water stability, and corrosive characteristics of the embankment soil. In this study, the evaporative cracking characteristics of soil with different saline concentrations were investigated. The results showed that the moisture content decreased linearly with the drying time in the early evaporation process, subsequently decreased slow down in the mid-term evaporation, and finally become got and remain a residual moisture content, which are 46.39%, 44.05%, 42.70%, and 40.27% with the increase of the saline concentration. The evaporation process with different saline concentrations in the soil can be divided into three stages: uniform evaporation stage, slow down evaporation stage, and equilibrium evaporation stage, which was consistent with the moisture content change. With the development of the drying time, the cracks gradually appeared on the soil surface, gradually deepened in the soil, and expanded the crack network. The development of cracks can be divided into three stages: the cracking preparation stage, the crack development stage, and the crack stable stage. The cracking began at high evaporation rate under high saline concentration, and the fractal dimension remained stable under similar saline concentration. The fractal dimension was gradually increased with the decrease of the moisture content and the increase of the saline concentration, respectively. The soil began to crack with larger moisture under high saline concentration. The drying cracks in the nature were consistent with the configuration of the cracks formed in the experimental results.

Anand Kumar S ◽  
Ajay Kushwaha ◽  
Nagesha B K ◽  
Sanjay Barad

Abstract The proposed work investigates the hybrid surface characterisation of intra thin-walled Ti6Al4V surfaces fabricated using laser powder bed fusion technology. The thin-walled samples were characterised using scanning electron microscopy and Opto-digital microscopy techniques. The fractal dimensional analysis was performed using ImageJ software integrated with an open-source MultiFrac plug-in. The surface microscopy analysis revealed satellites powder particles, partially melted powder particles, spherical balling, and pores on the thin-walled surface. The fractal dimension establishes a correlation between the surface roughness values. The surface areal surface parameters analysis suggested variation along the build direction of thin-walled Ti6Al4V sample. The development of sharp peaks and thus higher Ra, Sku and Ssk values were found along the build direction of the intra thin-walled samples. Therefore, the combination of areal surface topography analysis and fractal dimension approach can be a promising methodology towards surface characterisation of additively manufactured complex thin-walled surfaces.

2022 ◽  
Vol 12 (1) ◽  
Zaisheng Zhu ◽  
Zhenquan He ◽  
Guosheng Gai

AbstractPotassium-bearing shale is being developed as a potential alternative to potash for use in fertilisers. The first step in this process is to reduce its particle size by crushing. This paper explores whether roasting pre-cracked potassium-bearing shale can improve the quality of the resulting ultrafine product. Analysis of the particle size distribution of the ultrafine product and its fractal dimension found contradictory results: the minimum particle size distribution was obtained by roasting for 2.5 h, while the minimum fractal dimension was obtained by roasting for 1 h. Fuzzy comprehensive evaluation was conducted with three indicators—(1) the weight of the − 10 μm product, (2) the fractal dimension of the particle size distribution, and (3) d97—to obtain a unique combination of indicators that reflects the quality and quantity of the products. The weights of the three indicators were calculated by an analytic hierarchical process to be 0.69, 0.149 and 0.161, respectively. Roasting pre-cracked shale for 2–2.5 h was found to improve the mean values of the fuzzy comprehensive evaluation indicators by about 0.07. However, the cost increased from 2.82 RMB to ≥ 10.08 RMB, which is not feasible for widespread industrial implementation.

Biophysica ◽  
2022 ◽  
Vol 2 (1) ◽  
pp. 59-69
Liam Elkington ◽  
Prakash Adhikari ◽  
Prabhakar Pradhan

Fractal dimension, a measure of self-similarity in a structure, is a powerful physical parameter for the characterization of structural property of many partially filled disordered materials. Biological tissues are fractal in nature and reports show a change in self-similarity associated with the progress of cancer, resulting in changes in their fractal dimensions. Here, we report that fractal dimension measurement is a potential technique for the detection of different stages of cancer using transmission optical microscopy. Transmission optical microscopy of a thin tissue sample produces intensity distribution patterns proportional to its refractive index pattern, representing its mass density distribution. We measure fractal dimension detection of different cancer stages and find its universal feature. Many deadly cancers are difficult to detect in their early to different stages due to the hard-to-reach location of the organ and/or lack of symptoms until very late stages. To study these deadly cancers, tissue microarray (TMA) samples containing different stages of cancers are analyzed for pancreatic, breast, colon, and prostate cancers. The fractal dimension method correctly differentiates cancer stages in progressive cancer, raising possibilities for a physics-based accurate diagnosis method for cancer detection.

Sign in / Sign up

Export Citation Format

Share Document