Effect of different buried depth on the disintegration characteristic of red-bed soft rock and the evolution model of disintegration breakage under cyclic drying-wetting

The disintegration of red-bed soft rock exhibits a strong correlation with various geological disasters. However, the investigation into the evolutionary mechanisms underlying disintegration breakage has not yet received extensive exploration. In order to comprehensively examine the disintegration characteristics of red-bed soft rock, the slake durability tests were conducted to red-bed soft rocks of varying burial depths. Subsequently, an investigation was carried out to examine the disintegration characteristics and the evolution of disintegration parameters, including the coefficient of uniformity (Cu), coefficient of curvature (Cc), disintegration rate (DRE), disintegration ratio (Dr), and fractal dimension (D), throughout the disintegration process. Finally, employing the energy dissipation theory, an energy dissipation model was developed to predicate the disintegration process of samples at various burial depths. The findings demonstrate a decrease in the abundance of large particles and a concurrent increase in the abundance of small particles as the number of drying-wetting cycles increases. Furthermore, as the number of drying-wetting cycles increases, a significant alteration is observed in the content of particles larger than 10 mm, whereas the content of particles smaller than 10 mm undergoes only minor changes. The disintegration parameters, including the curvature coefficient, non-uniformity coefficient, disintegration rate, and fractal dimension, exhibit a positive correlation with the number of drying-wetting cycles. Conversely, the disintegration index demonstrates a decreasing trend with the increasing number of cycles. Nevertheless, as the burial depth increases, a notable trend emerges in the disintegration process, characterized by a gradual increase in the content of large particles alongside a progressive decrease in the content of small particles. Concurrently, the curvature coefficient, non-uniformity coefficient, disintegration rate, and fractal dimension exhibit a gradual decline, while the durability index experiences a gradual increase. In addition, based on the principle of energy dissipation, it is revealed that the surface energy increment of red-bed soft rock increases with the increase of the number of drying-wetting cycles, but decreases with the increase of burial depth. Ultimately, by leveraging the outcomes of energy dissipation analyses, a theoretical model is constructed to elucidate the correlation between surface energy and both the number of drying-wetting cycles and burial depth. This model serves as a theoretical reference for predicting the disintegration behavior of samples, offering valuable insights for future research endeavors.

Study on the Fractal Characteristics and Seepage Properties of Channels Filled by Coal Particles

Studying the seepage process in fracture channels (where coal particles are deposited) is of great significance for improving the performance of both on-site coal seam water injection and dust reduction technology. Through a self-developed simulation experiment of water-borne coal particle migration and accumulation and computer graphics, we investigated the influencing factors of particle accumulation in water injection and their influence law on seepage, discussed the interaction relationship between the fractal structure of coal and the characteristics of accumulated coal particles, and established a new fractal model of fracture permeability based on different particle accumulation states. The results show that the seepage velocity and the particle size jointly affect the migration and accumulation process of water-borne coal particles. When the coal particle size is constant and the seepage velocity increases, then the output of the coal powder increases, the deposition decreases, and the structure fractal dimension D3 of fractures decreases. At the same seepage velocity, with the increase of the coal particle size, the output of coal powder decreases, the deposition increases, and the structure fractal dimension D3 of fractures increases. In addition, the amount of coal powder produced in the intermittent water injection process is smaller than that produced in the continuous water injection process, more easily leading to accumulation. The variation law of the theoretical permeability with porosity remains consistent for different particle accumulation states: with the increase of porosity, the structure fractal dimension D3 of fractures decreases, while the theoretical permeability increases. The above research results can provide a theoretical basis for reducing the seepage damage of coal under the particle blocking effect.

Numerical prediction of portal hypertension by a hydrodynamic blood flow model combing with the fractal theory

Portal hypertension (PH) can cause a series of complications, therefore, early prediction of PH is important. Traditional diagnostic methods are harmful to the human body, while other non-invasive methods are inaccurate and lack physical meaning. Combining various fractal theories and flow laws, we establish a complete portal system blood flow model from the Computed Tomography (CT) and angiography images. The portal vein pressure (PP) is obtained by the flow rate data from the Doppler ultrasound and the pressure-velocity relationship is established by the model. Three normal participants and 12 patients with portal hypertension were divided into three groups. For the three normal participants (Group A), their mean PP calculated by the model is 1752 Pa, falling into the normal range of PP. The mean PP of three patients with portal vein thrombosis (Group B) is 2357 Pa; and for the 9 patients with cirrhosis (Group C), their mean PP is 2915 Pa. These results validate the classification performance of the model. Moreover, the blood flow model can give early warning parameters of the corresponding portal vein trunk and portal vein microtubules for thrombosis and liver cirrhosis. This model presents the complete process of blood flow from sinusoids to the portal vein, adapts to the diagnosis of portal hypertension of thrombosis and liver cirrhosis, and provides a new method for noninvasive portal vein pressure detection from the perspective of biomechanics.

Kinetics of low radioactive wastewater imbibition and radionuclides sorption in partially saturated ternary-binder mortar

This study seeks to assess the imbibition kinetics of low radioactive wastewater (from the DayaBay nuclear power plant) into a partially saturated ternary-binder mortar, as well as the sorption kinetics of ⁶⁰Co and ¹³⁷Cs from the water. Mortar samples with the initial saturation degrees of 0, 0.4, 0.6, 0.8 and 1.0 were prepared for the wastewater treatment. Pore structure of the mortar was characterized using water vapor sorption isotherm and mercury intrusion porosimetry tests interpreted by the Guggenheim-Anderson-de Boer isothermal equilibrium, and volume- and energy-based fractal models. Results show that the mortar has consistent fractal pore structure between the models, and the liquid imbibitions follow the fractal imbibition kinetics, in which the parameters are non-linearly impacted by the initial saturation degrees. The sorption rate and retention capacity of ¹³⁷Cs are much lower than those of ⁶⁰Co, and both follow the Brouers-Sotolongo fractional kinetics. The findings uncover the complex liquid imbibition and radionuclides sorption kinetics in cement-based porous materials, and the in-situ data would contribute to the material designs and sorption controls for large scale in-situ treatments of wastewater from nuclear power plant.

A new fuzzy fractal control approach of non-linear dynamic systems: The case of controlling the COVID-19 pandemics

This article is presenting a first attempt on a proposed fuzzy fractal control method for efficiently controlling nonlinear dynamic systems. The main goal is to combine the main advantages of fractal theoretical concepts and fuzzy logic theory for achieving efficient control of nonlinear dynamic systems. The concept coming from Fractal theory, known as the fractal dimension, can be utilized to measure the complexity of the dynamic behavior of a non-linear plant. On the other hand, fuzzy logic theory can be used to represent and capture the expert knowledge in controlling a plant. In addition, fuzzy logic enables to manage the uncertainty involved in the decision-making process for achieving efficient control of a non-linear plant. We illustrate the proposed fuzzy fractal control method with the current worldwide situation that requires achieving an efficient control of the COVID-19 pandemics.

Fractal approach in expansive clay-based materials with special focus on compacted GMZ bentonite in nuclear waste disposal: a systematic review

Knowledge of the behavior of highly compacted expansive clays, as an engineered barrier, in disposal of high-level nuclear waste (HLW) systems to prevent the pollution due to migration of radionuclide is extremely essential. The prominent properties of globally and widely used bentonites have been extensively studied during past two decades. In China, GaoMiaoZi (GMZ) bentonite is the first choice as a buffer or backfill material for deep geological repositories. This review article presents the recent progresses of knowledge on water retention properties, hydromechanical behavior, and fractal characteristics of GMZ bentonite-based materials, by reviewing 217 internationally published research articles. Firstly, the current literature regarding hydrogeochemical and mechanical characteristics of GMZ bentonite influenced by various saline solutions are critically summarized and reviewed. Then, the role of osmotic suction π alongside the application of surface fractal dimension Ds is presented from the standpoint of fractal theory. Finally, the strength characteristics of GMZ bentonites using fractal approach have been discussed. Furthermore, this study sheds light on gaps, opportunities, and further research for understanding and analyzing the long-term hydromechanical characteristics of the designed backfill material, from the standpoint of surface fractality of bentonites, and implications of sustainable buffer materials in the field of geoenvironmental engineering.

Automatic segmentation for ultrasound image of carotid intimal-media based on improved superpixel generation algorithm and fractal theory

OBJECTIVE

Carotid atherosclerosis (CAS) is the main reason leading to cardiovascular conditions such as coronary heart disease and cerebrovascular diseases. In the carotid ultrasound images, the carotid intima-media structure can be observed in an annular narrow strip, which its inner contour corresponds to the carotid intima, and the outer contour corresponds to the carotid extima. With the development of carotid atherosclerosis, the carotid intima-media will gradually thicken. Therefore, doctors can observe the carotid intima-media so as to obtain the pathological changes of the internal structure of the patient's carotid arteries. However, due to the presence of artifacts and noises the quality of the ultrasound images are degraded, making it difficult to obtain accurate carotid intima-media structures. This article presents a novel self-adaptive method to enable obtaining the carotid intima-media through carotid intima/extima segmentation.

METHOD

After preprocessing the ultrasound images by homomorphic filtering and median filtering, we propose an improved superpixel generation algorithm that employs the fusion of gray-level and luminosity-based information to decompose the image into numerous superpixels and later presents the carotid intima. Meanwhile, based on the features of the carotid artery, the initial position of the carotid extima is located by the normalized cut algorithm and later the fractal theory is employed to segment the carotid extima.

RESULTS

The proposed method for segmenting carotid intima obtained mean values of the DICE true positive ratio (TPR), false positive ratio (FPR), precision scores of 97.797%, 99.126%, 0.540%, 97.202%, respectively. Further from the segmentation method of the carotid extima the performance measures such as mean DICE, TPR, accuracy, F-score obtained are 95.00%, 92.265%, 97.689%, 94.997%, respectively.

CONCLUSION

Comparing with traditional methods, the proposed method performed better. The experimental results indicated that the proposed method obtained the carotid intima-media both automatically and accurately thus effectively assist doctors in the diagnosis of CAS.

A fractal analysis of radon migration in discrete fracture network model

A novel model is proposed to simulate radon migration by combining the fractal theory and the discrete fracture network (DFN) model. In the model, a power-law distribution based on fractal theory is applied to fracture length and aperture and the fracture locations and orientations are modeled with the Poisson distribution and von Mises-Fisher distribution, respectively. The model was applied to produce a computer code that can calculate the radon concentration, flux, and diffusivity of the fractured media. The key issues related to the model were analyzed and the results reveal that: (1) the threshold value of the ratio of the minimum fracture length to the maximum decreases as the fractal dimension of the fracture lengths and the relation between them follows an exponential law; (2) As the fractal dimension of the fracture lengths increases, more connected fractures are generated, resulting in a linear increase of the mean efficient radon diffusivity. (3) The dip angle is the parameter that has the greatest influence on radon migration in determining fracture orientations. (4) The radon exhalation rate increases exponentially with increasing advection velocity. (5) Models with larger fractal dimension for fracture lengths have larger representative elementary volume (REV) size and follow an exponential law.

Anti-migraine effect of wine-processed Radix scutellariae: Pharmacodynamic verification in nitroglycerin-induced rats and correlation study between compounds dissolution and the fractal dimension

ETHNOPHARMACOLOGICAL RELEVANCE

Wine-processed Radix scutellariae (RS) is the processed product of RS, which is the dried root of Scutellaria baicalensis Georgi. It is recorded in Chinese traditional formula that wine-processed RS has the effect of anti-migraine, while the effect has not been confirmed and the possible mechanism remains unclear.

AIM OF THE STUDY

To verify the anti-migraine effect of wine-processed RS in nitroglycerin (NTG)-induced rats and explore the correlation between compounds dissolution and the pore structure based on fractal theory.

MATERIALS AND METHODS

In the validation of pharmacodynamics, the effects of wine-processed RS on migraines were firstly evaluated by observing the number of head-scratching of rats, then investigated by determining the levels of nitric oxide (NO), calcitonin gene-related peptide (CGRP) and the expression of c-Fos in the brain of NTG-induced rat models using ELISA and immunohistochemical assessments. In the correlation study, the stir-frying time of RS was set to 5 min, 10 min and 15 min. The scanning electron microscope (SEM) and mercury intrusion method were used to explore the pore structure and main parameters of the pore structure including pore size distribution, pore volume, porosity, surface area and fractal dimension. The compounds dissolution of total flavonoids and five major components containing baicalein, baicalin, scutellarin, wogonin and wogonoside was determined by UV-Vis spectrophotometry and HPLC separately.

RESULTS

The animal experiments had shown that wine-processed RS could significantly reduce the head-scratching times of NTG-induced rat models (p < 0.01) and markedly decrease the levels of NO (p < 0.01), CGRP (p < 0.05) and the expression of c-Fos (p < 0.01) compared with model group. The data indicated that wine-processing would affect the dissolution of compounds by changing the pore structure of RS. The order of positive correlation between pore structure parameters and compounds' dissolution was total surface area > fractal dimension (r > 0) and the order of negative correlation was average pore size > total porosity > total volume (r < 0). Compared with the other sample groups (p < 0.05), the wine-processed RS stir-fried for 10 min had a pore structure which was more favorable for compounds dissolution.

CONCLUSIONS

Wine-processing could strengthen the anti-migraine effect of RS by changing the pore structure of RS, which is linked to the dissolution of compounds. The RS stir-fried for 10 min may be more effective in treating migraine.

Surface Morphology Analysis of Knit Structure-Based Triboelectric Nanogenerator for Enhancing the Transfer Charge

Harvesting waste biomechanical energy has provided a promising approach to improve the power supplement of wearable devices for extending usage life. Surface morphology is a significant factor for enhancing output performance of triboelectric nanogenerator; however, there is a limitation for evaluating the morphology of the surface and its impact on power generation. To evaluate the relationship between the surface morphology and transfer charge, there is a mathematical theory that is the fractal geometry theory that has been proposed to analyze the characteristic of irregular surface morphology. This theory provided a good understanding of the contact area and roughness of the surface. We have designed three categories of knit structures with cord appearance by using a flat knitting machine and analyzed their surface characteristics. Meanwhile, the geometric structures can be demonstrated through the fractal dimension for evaluating the generated output performance during contacting and separation. The present research exhibits that, with the increasing number of knitted units, the triboelectric power-generation performance continued to reduce due to the available contact area decreasing. After calculating the fractal dimension of different knit structures, the m*n rib structures show the high transfer charge when the fractal dimension is close to number one, especially the fractal dimension of the 1*1 rib structure that can reach 0.99. The fractal theory can be further used as an approach to evaluate the influence on the output performance of irregular surface morphology, unrelated to the uniform convex unit distraction. The result of this research also demonstrated the feasibility of a knitted-based triboelectric nanogenerator in scavenging biomechanical energy for powering portable electronics integrated into garments.

Complexity-based decoding of brain-skin relation in response to olfactory stimuli

BACKGROUND AND OBJECTIVE

Human body is covered with skin in different parts. In fact, skin reacts to different changes around human. For instance, when the surrounding temperature changes, human skin will react differently. It is known that the activity of skin is regulated by human brain. In this research, for the first time we investigate the relation between the activities of human skin and brain by mathematical analysis of Galvanic Skin Response (GSR) and Electroencephalography (EEG) signals.

METHOD

For this purpose, we employ fractal theory and analyze the variations of fractal dimension of GSR and EEG signals when subjects are exposed to different olfactory stimuli in the form of pleasant odors.

RESULTS

Based on the obtained results, the complexity of GSR signal changes with the complexity of EEG signal in case of different stimuli, where by increasing the molecular complexity of olfactory stimuli, the complexity of EEG and GSR signals increases. The results of statistical analysis showed the significant effect of stimulation on variations of complexity of GSR signal. In addition, based on effect size analysis, fourth odor with greatest molecular complexity had the greatest effect on variations of complexity of EEG and GSR signals.

CONCLUSION

Therefore, it can be said that human skin reaction changes with the variations in the activity of human brain. The result of analysis in this research can be further used to make a model between the activities of human skin and brain that will enable us to predict skin reaction to different stimuli.

Fractal morphology features and carbon component analysis of diesel particulates

External morphology and internal carbonaceous compositions are important characteristics for the source recognition of atmospheric particulate matter (PM). The fractal dimension of morphology and carbon components of diesel PM with different sizes both at high and low load were studied through fractal theory and thermal optical reflection method. It is revealed that small-size PM absorbs more soluble organic fractions and correspondingly has greater box dimension. Due to heavy aggregation, PM collected at low load has greater box dimension than that at high load because of heavy aggregation. OC1, which is the most volatile among organic carbons, is remarkably increased at low load or for small-size PM, absorbing more unburned hydrocarbons. At low load, a large amount of EC1 (char-EC) is generated and the ratio of OC/EC is more than 10, while, at high load, the EC is mainly composed of EC2 (soot-EC) and the ratio of OC/EC is less than 1. Apparently, the box dimension from the morphology of diesel PM presents a positive correlation with the ratio of OC/EC. Via above external and internal characteristics, particulates exhausted from motor vehicles in the atmosphere can be beneficially identified.

[Analysis of characteristics and influencing factors of fine particulate matters and submicron particulate matters in printing shop]

Objective: To analyze the physical characteristics of fine particulate matters (PM(2.5)) and submicron particulate matters (PM(1)), and investigate the factors influencing the emission peak of printer particles. Methods: A 12-hour particle concentration monitoring for PM(2.5) and PM(1) was conducted in a printing shop on January 5(th), 2018. PM(2.5) in the air was analyzed after the monitoring process to figure out morphological characteristics and element composition of printer particles. Besides, experiments were carried out in an enclosed space to detect the number concentration peaks of PM(1) during every printing process. Influencing factors investigated in this study were printer types, toner coverages and interval time between different printing processes. Results: The 12-hour particles concentration monitoring showed that the number concentration of PM(1) and the mass concentration of PM(2.5) were 7.510×10(4) pt/cm(3) and 96.85 μg/m(3). The diameter of most PM(2.5) was less than 100 nm, with a fractal dimension of 2.591. Most PM(2.5) appeared as regular spheres with typical agglomeration phenomenon, while some were in rhabditiform or irregular shapes. Element analysis showed that PM(2.5) was mainly composed of C, O, Si, Ca, with less metallic element. The PM(1) emission peak values of three printers were 3.60×10(4), 3.43×10(4), 0.31×10(4) pt/cm(3), respectively and the difference was not statistically significant (χ(2)=5.42, P>0.05). When the page coverage rate was 0%, 2.5%, 5%, 10%, 20% and 50%, the PM(1) emission peak value of printer A was 6.74×10(4), 4.62×10(4), 3.82×10(4), 2.82×10(4), 1.00×10(4) and 1.08×10(4) pt/cm(3), and the difference was also not statistically significant (χ(2)=7.01, P>0.05). The natural logarithm of PM(1) emission peak value in printing work was associated with the resting time before printing and the change value of heating roller temperature (r value was 0.83 and 0.89, respectively, all P values<0.05). Conclusion: PM(2.5) and PM(1) in the printing shop stayed at a high level. Particles appeared as various shapes and element compositions were complex. The temperature change of heating roller was one of most important factors that lead to the increased number concentration peak of PM(1).

A general pattern of the species abundance distribution

Since the 1970s, species abundance distributions (SADs) have been one of the most fundamental issues in ecology and have frequently been investigated and reviewed. However, there was surprisingly little consensus. This study focuses on three essential questions. (1) Is there a general pattern of SAD that no community can violate it? (2) If it exists, what does it look like? (3) Why is it like this? The frequency distributions of 19,833 SADs from eight datasets (including eleven taxonomic groups from terrestrial, aquatic, and marine ecosystems) suggest that a general pattern of SAD might exist. According to two hypotheses (the finiteness of the total energy and the causality from the entropy to the diversity), this study assumes that the general pattern of SAD is approximately consistent with Zipf's law, which means that Zipf's law might be more easily to observe when one investigates any SAD. In the future, this conjecture not only needs to be tested (or supported) by more and more datasets, but also depends on how well it is explained from different angles of theories.

A relationship between species richness and evenness that depends on specific relative abundance distribution

Although many ecologists focus on the relationship between species richness (S) and evenness (E), conflicts between observation and theory are difficult to reconcile. Empirical S–E relationships were not consistent, while relationships show strong correlation between S and E. Since E essentially depended on the relative abundance distribution (RAD), the hypothesis of this paper was that the S–E relationship should be determined by RAD. Theoretical S–E relationships for various RADs have already been reported, but they were rarely assessed by the raw data. This study constructed S–E relationships for a specific RAD, which indicated that if the community had a fractal distribution of rank abundance, E would decrease with S, and the S–E relationship would be unique for a given RAD. Such theoretical expectations were supported by three datasets with 82 samples, which suggested that the S–E relationship were controlled by RAD and inconsistent S–E relationships in statistical analyses could be accounted for by the variation of underlying RAD model between communities. From the perspective of RAD, it could be too early to split the diversity into S and E only based on the S–E relationship in statistical analyses.

Membrane fouling in a submerged membrane bioreactor: An unified approach to construct topography and to evaluate interaction energy between two randomly rough surfaces

Quantitatively evaluating interaction energy between two randomly rough surfaces is the prerequisite to quantitatively understand and control membrane fouling in membrane bioreactors (MBRs). In this study, a new unified approach to construct rough topographies and to quantify interaction energy between a randomly rough particle and a randomly rough membrane was proposed. It was found that, natural rough topographies of both foulants and membrane could be well constructed by a modified two-variable Weierstrass-Mandelbrot (WM) function included in fractal theory. Spatial differential relationships between two constructed surfaces were accordingly established. Thereafter, a new approach combining these relationships, surface element integration (SEI) approach and composite Simpson's rule was deduced to calculate the interaction energy between two randomly rough surfaces in a submerged MBR. The obtained results indicate the profound effects of surface morphology on interaction energy and membrane fouling. This study provided a basic approach to investigate membrane fouling and interface behaviors.

The enhancement mechanism of wine-processed Radix Scutellaria on NTG-induced migraine rats

To elucidate the increasing dissolution and enhancement mechanism of wine-processed Radix Scutellaria (RS) by fractal theory in nitroglycerin (NTG)-induced migraine rats. We prepared three RS from the process with 10% (S1), 15% (S2), 20% (S3) (v/m) rice wine. Mercury intrusion porosimetry and scanning electron microscope were employed to explore the internal structure of RS and the components dissolution of RS was analyzed by HPLC. Rats were randomly allocated into following groups and orally given different solutions for 10days: normal group (NOR, normal saline), model group (MOD, normal saline), Tianshu capsule group (TSC, 0.425mg/kg), ibuprofen group (IBU, 0.0821mg/kg), crude RS group (CRU, 1.04mg/kg) and wine-processed RS group (WP, 1.04mg/kg) followed by bolus subcutaneously injection of NTG (10mg/kg) to induce migraine model except NOR. Biochemical indexes (nitric oxide-NO, calcitonin-gene-related peptide-CGRP, and endothelin-ET) and c-fos positive cells were measured with commercial kits and immunohistochemical method, separately. Total surface area significantly increased in wine-processed RS (p<0.05) while fractal dimension markedly decreased (p<0.05) compared with crude RS. Additionally, S3 owned the highest increase of dissolution including the percentage increase of total extract, total flavonoids and main compounds (all p<0.05 vs S1 and S2). Pharmacodynamic data showed c-fos positive cells significantly decreased (p<0.05) in WP compared with MOD and the level of NO, CGRP, ET in WP was better than that of CRU. Wine-processed RS could be a promising candidate medicine for migraine treatment due to its increased component dissolution.

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory

Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.