This article reports fractal dimension analysis applied to soil CO2 fluxes measured in an Italian seismic area. The work was carried out with the use of a calibrated flux chamber unit. The fractal ...dimension (FD) from isotropic variograms was used as a method to understand related scale-dependent phenomena. The aim was to investigate the spatial variability of CO2 flux measurements in four directions (horizontal, vertical, 45° and 135° directions) related to different distances between the measuring points and from a fault. High fractal dimension values were found (2.5 ≤ FD ≤ 3.0). These imply strong anti-persistent behavior near to and far from the fault. Lower fractal dimensions were addressed at longer distances from the fault.
•Mineral powder can reduce the porosity of cement stone, reduce the average pore diameter and the maximum aperture of RAC.•SF has pozzolanic activity and some particles can react with the hydration ...product Ca(OH)2 of cement to form C-S-H gel.•Compared with ITZOM-NM, ITZOA-OM has higher porosity content, and the pores are mainly distributed on the surface of RA.•Mineral admixtures can increase the volume FD of RAC pores.
Recycled aggregate concrete (RAC) is an important form of construction waste resource utilization, but the existence of multiple interface transition zone (ITZ) leads to complex pore defects in RAC, which seriously weakens its mechanical properties and chloride ion permeability. In this paper, fly ash (FA), silica fume (SF) and mineral powder (SL) admixtures were incorporated into RAC for improving the pore structure of RAC. The effects of admixtures on the pore structure parameters and pore size distribution of RAC were detailly analyzed by means of back scattering electron imaging (BSE), mercury intrusion porosimetry (MIP) and fractal dimension theory (FDT). And the micro characteristics of porosity and pore structure in ITZ were quantitatively described. The results clearly show that the appropriate amount of admixture can reduce the porosity, average pore diameter and the maximum aperture of RAC. Furthermore, the macropores and capillary pores were significantly decreased and gradually changed into transition pores and gel pores. The refinement of pores increases the compactness of RAC, particularly the pozzolanic effect of SF. The newly generated CSH gel and the filling effect of SF greatly decrease the porosity of ITZ. In addition, the fractal dimension (FD) of pore volume exhibits a good positive linear relationship to the compressive strength and chloride ion permeability resistance of RAC.
Fractal dimension (FD) is a useful feature for texture segmentation, shape classification, and graphic analysis in many fields. The box-counting approach is one of the frequently used techniques to ...estimate the FD of an image. This paper presents an efficient box-counting-based method for the improvement of FD estimation accuracy. A new model is proposed to assign the smallest number of boxes to cover the entire image surface at each selected scale as required, thereby yielding more accurate estimates. The experiments using synthesized fractional Brownian motion images, real texture images, and remote sensing images demonstrate this new method can outperform the well-known differential boxing-counting (DBC) method.
In this paper, we study the long time behavior of the Kirchhoff type wave equation in the space H01(Ω)×L2(Ω). We prove the existence of the global attractor for the equation which covers the case of ...possible generation of the stiffness coefficient. We also consider the geometrical property of the global attractor. By means of the Z2 index, we provide, under suitable assumptions, the fractal dimension of the global attractor is infinite.
•A new numerical method to estimate the dimension of basin boundary is investigated.•The accuracy of the method is assessed using nine uniform artificial fractals.•The role of the box size used to ...cover the fractals is investigated.•It is shown that boxes with small resolution leads to systematic errors.•Accurate results can be obtained with a proposed criterion on box sizes.
The concept of basin entropy (Sb) was recently introduced as a means to characterize basins of attraction with regard to their complexity. It was also found a connection between Sb and the uncertainty exponent α. This connection allows the calculation of the fractal dimension d of the basin boundary between two basins of attraction. However, this method of calculation has not been explored in the literature. In this work we evaluate the performance of the method based upon the basin entropy in the calculation of the fractal dimension of basin boundaries. For that purpose, the method is applied to the calculation of d for several artificial uniform fractals, such as the Koch island and the Sierpinski Carpet, and the values obtained are compared with the exact dimensions obtained by analytical methods. It is concluded that excellent results are generally obtained if the boxes used in the calculation of Sb are chosen adequately, and a simple criterion for this choice is proposed. Numerical arguments are provided to justify the exclusion of small boxes with low resolution in the calculation of d. While the investigation is motivated by the calculation of d for basin boundaries, the method can be applied to any image containing two distinct regions with a boundary, whose dimension has to be determined.
High temperature can make the rock physical properties change significantly. In this study, the fractal dimension of cross-scale pores of the granite after high temperatures is first obtained. It is ...found that the fractal characteristics of mesopores and macropores are significant, while that of micropores are opposite. Secondly, the dual effects of high temperatures on the mechanical properties are studied, and the fractal dimension of cross-scale pores is closely related to the mechanical properties of rock. Then, it is found that when the rock is about to break, the abnormal changes in energy rate and frequency can be used as the rock failure precursor, but this method also has certain limitations. Finally, the correlation dimension is obtained based on acoustic emission (AE) time series. When the correlation dimension decreases to the local minimum after the fluctuation stage, it can effectively predict the imminent large-scale failure.
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•Only mesopores and macropores have fractal characteristics.•The relationship between pores and mechanics properties of rock is studied.•AE parameters are used as the precursor information of rock failure.•Correlation dimension can be used to predict the imminent failure of granite.
Our understanding of Earth surface processes is rapidly advancing as new remote sensing technologies such as LiDAR and close-range digital photogrammetry become more accessible and affordable. A ...very-high spatial resolution digital terrain model (DTM) and orthophoto mosaic (mm scale) were produced using close-range digital photogrammetry based on ‘Structure-from-Motion’ (SfM) algorithms for a 250m transect along a shallow coral reef flat on Heron Reef, Great Barrier Reef. The precise terrain data were used to characterise surface roughness, a critical factor affecting ecological and physical processes on the reef. Three roughness parameters, namely the root mean square height, tortuosity (or rugosity) and fractal dimension, were derived and compared in order to asses which one better characterises reef flat roughness. The typical relief across the shallow reef flat was 0.1m with a maximum value of 0.42m. Coral reef terrain roughness, as characterised by the three chosen parameters, generally increased towards the middle of the transect where live coral covers most of the reef flat and decreases towards the edges of the transect. The fractal dimension (values ranging from 2.2 to 2.59) best characterised reef roughness, as evidenced by a closer agreement with the distribution of known coral benthic substrates. This is the first study quantifying scale-independent roughness of a coral reef at benthic and biotope/patch levels (cm-m). The readily available and cost-effective methods presented are highly appropriate for data collection, processing and analysis to generate very-high spatial resolution DTMs and orthophoto mosaics of shallow and energetic coral reefs.
•A very-high spatial resolution DTM was produced for an intertidal coral reef flat.•SfM is a cost-effective approach for mapping the terrain of shallow reef flats.•Methods presented are readily available and require minimum training.•Coral reef roughness was better characterised using the fractal dimension parameter.•This is the first study quantifying scale-independent roughness at cm resolution.
•The samples of single crack CGFB with different angles (15°, 45°, 75°) were prepared and the triaxial compression tests were carried out under seepage conditions.•The effects of seepage water ...pressure and crack defects on the seepage-stress coupling failure characteristics of CGFB were analyzed in depth.•The fracture morphology characteristics of CGFB after failure were quantitatively characterized, and the correlation between the fracture fractal dimension and its mechanical properties was studied.
In order to study the seepage-stress coupling failure characteristics and fracture fractal characteristics of cemented gangue-fly ash backfill (CGFB) with defects, the samples of single crack CGFB with different angles were prepared and the triaxial compression test under seepage conditions was carried out. The effects of seepage pressure and crack defects on the seepage-stress coupling failure characteristics of CGFB were analyzed. In addition, the box dimension method was introduced to calculate the fractal dimension, so as to quantitatively characterize the correlation between fracture morphology and mechanical properties. The results show that: 1) the permeability and acoustic emission change periodically with the stress-time curve during the deformation and failure of CGFB. With the increase of seepage pressure, the characteristic permeability of CGFB increases, and the characteristic permeability of CGFB with defects is higher than that of intact CGFB. 2) Under the seepage-stress coupling, there is no obvious corresponding relationship between the fractal dimension of fracture appearance and the compressive strength of CGFB: under the same seepage pressure, the higher the strength of CGFB with different angles, the greater the fractal dimension of fracture appearance; under the same crack angle, the greater the seepage pressure, the lower the strength and the larger the fracture fractal dimension. 3) Under the seepage-stress coupling, the fractal dimension of the failure fracture appearance has a good correlation with the dissipated energy, and the two increase linearly. This relative relationship is only related to the damage and fracture, and has nothing to do with the external conditions such as seepage pressure. The research results provide a theoretical basis for the stability analysis and instability prediction of artificial pillar containing joints, cracks and other geological defects under water-rich conditions in China.
The large-scale images and videos are one kind of the main source of big data. Dynamic texture (DT) is essential for understanding the video sequences with spatio-temporal similarities. This paper ...presents a powerful tool called dynamic fractal analysis to DT description and classification, which integrates rich description of DT with strong robustness to environmental changes. The proposed dynamic fractal spectrum (DFS) for DT sequences is composed of two components. The first one is a volumetric dynamic fractal spectrum component (V-DFS) that captures the stochastic self-similarities of DT sequences by treating them as 3D volumes; the second one is a multi-slice dynamic fractal spectrum component (S-DFS) that encodes fractal structures of repetitive DT patterns on 2D slices along different views of the 3D volume. To fully exploit various types of dynamic patterns in DT, five measurements of DT pixels are collected for the analysis on DT sequences from different perspectives. We evaluated our method on four publicly available benchmark datasets. All the experimental results have demonstrated the excellent performance of our method in comparison with state-of-the-art approaches.
•The dynamic multi-fractal analysis is developed for DT description.•Our method is very discriminative and robust to environmental changes.•A computational acceleration scheme is provided for the proposed descriptor.•Our method exhibits excellent performance on four benchmark datasets.
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