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.
The present study focuses on the dynamical aspects of a discrete-time Leslie–Gower predator–prey model accompanied by a Holling type III functional response. Discretization is conducted by applying a piecewise constant argument method of differential equations. Moreover, boundedness, existence, uniqueness, and a local stability analysis of biologically feasible equilibria were investigated. By implementing the center manifold theorem and bifurcation theory, our study reveals that the given system undergoes period-doubling and Neimark–Sacker bifurcation around the interior equilibrium point. By contrast, chaotic attractors ensure chaos. To avoid these unpredictable situations, we establish a feedback-control strategy to control the chaos created under the influence of bifurcation. The fractal dimensions of the proposed model are calculated. The maximum Lyapunov exponents and phase portraits are depicted to further confirm the complexity and chaotic behavior. Finally, numerical simulations are presented to confirm the theoretical and analytical findings.
Fractal dimension can be used to the pore surface characterize. For pore structures in different sizes, the calculation models of fractal theory should be distinguished due to the different principles of the gas adsorption experiments. To further study the adaptability of the fractal model for gas adsorption experimental data, the author collected shale samples of Longmaxi formation from Well JY1, then CO2 and N2 adsorption provided the PSD curves. In addition, the fractal dimensions of micropore and mesopore were calculated by the Jaroniec fractal model and Frenkel–Halsey–Hill (FHH) fractal model respectively. The research shows that the Jaroniec model may be suitable to calculate CO2 adsorption data and could characterize the fractal dimension of micropore, while the FHH model may be suitable to calculate N2 adsorption data in the high relative pressure region. It suggests that the micropore and mesopore could have different dimensions and the evaluation of the structure in shale pores should consider both of them.
Fractal dimension of the chaotic attractor for earthquake sequence in Nurek dam based on 22.000 earthquakes detected during the period 1976-87 has been studied for this total period of observations as well as for the period from December 1977 to December 1987. The second period excluded increased seismic activity during second stage of filling the reservoir. Large fractal dimensions of the chaotic at tractor of 8.3 and 7.3 were found for the respective period which suggests the complexity of earthquake .dynamics in this region as compared to Koyna reservoir.
Alzheimer’s disease is a neurodegenerative cognitive, affective, and behavioral disorder aligned to the aging process and other coronary diseases. To contribute to the early diagnosis of the disease, a neuroimaging treatment is implemented through a preprocessing to subsequently calculate the fractal dimension associated with these images in order to propose an alternative to the one proposed in medical physics through positron emission tomography. In this work, a comparative analysis is made of a previous work using the Box Counting methodology versus the calculation of the fractal dimension by means of software developed by the researchers based on the same method. The differences between the fractal dimensions of the neuroimages of control patients and patients with the presence of the disease are maintained showing a lower value of fractal dimension in patients with the disease due to the physical deterioration of the brain.
Through direct shear tests, this paper aimed to research the effect of fine marble aggregate on the shear strength and fractal dimension of the interface between soil and concrete corroded by sulfuric acid. More realistic concrete rough surfaces than the artificially roughened surfaces were formed by immersing four concrete plates in plastic buckets filled with sulfuric acid for different periods of time. The sand was adopted to imitate the soil. 3D laser scanner was employed to obtain the digital shapes of concrete plates subjected to sulfuric acid, and the rough surfaces were evaluated by fractal dimension. Large direct shear experiments were performed to obtain the curves of the interface shear stress and shear displacement between sand and corroded concrete plate. The method of data fitting was adopted to calculate the parameters of shear strength (i.e., friction angle and the cohesive) and the parameters of the Clough–Duncan hyperbolic model. The results indicated that as the corrosion days increased, the surface of the concrete plate became rougher, the surface fractal dimensions of the concrete corroded by sulfuric acid became bigger, and the interface friction angle became greater. The friction angle of the interface and the fractal dimensions of the surface of the concrete plate containing crushed gravel and marble sand were smaller than that of the concrete plate containing crushed gravel and river sand.
The paper investigates the relationship between vibration acceleration of bearings with their operational state. To determine these dependencies, a testbench was built and 112 experiments were carried out with different bearings: 100 bearings that developed an internal defect during operation and 12bearings without a defect. From the obtained records, a dataset was formed, which was used to build classifiers. Dataset is freely available. A methodfor classifying new and used bearings was proposed, which consists in searching for dependencies and regularities of the signal using descriptive functions: statistical, entropy, fractal dimensions and others. In addition to processing the signal itself, the frequency domain of the bearing operationsignal was also used to complement the feature space. The paper considered the possibility of generalizing the classification for its application on thosesignals that were not obtained in the course of laboratory experiments. An extraneous dataset was found in the public domain. This dataset was used todetermine how accurate a classifier was when it was trained and tested on significantly different signals. Training and validation were carried out usingthe bootstrapping method to eradicate the effect of randomness, given the small amount of training data available. To estimate the quality of theclassifiers, the F1-measure was used as the main metric due to the imbalance of the data sets. The following supervised machine learning methodswere chosen as classifier models: logistic regression, support vector machine, random forest, and K nearest neighbors. The results are presented in theform of plots of density distribution and diagrams.