•Landscape metrics were used to identify urban phases reflecting distinct socioeconomic contexts.•The Attica’s urban spatial structure has rapidly changed following Athens’ expansion.•Patch ...fragmentation, dispersion and shape complexity continuously increased over time.•Athens’ spatial structure of the early 1990s was more sustainable than earlier and more recent morphologies.•Our results allow a better understanding of long-term form-function relationships in compact cities.
A multi-criteria approach based on descriptive, correlation and multivariate statistics and mathematical morphology was proposed to investigate long-term morphological changes in a metropolitan region (Attica, Greece) representative of the ‘Mediterranean compact city’ archetype. A total of 33 metrics measured at 6 time points (1948, 1975, 1990, 2000, 2006, 2012) from diachronic land-use maps were used to identify urban phases characterized by variable intensity of growth and reflecting distinct socioeconomic contexts at the local scale. The Attica's urban spatial structure has rapidly changed following Athens' expansion. Fragmentation, dispersion and shape complexity of built-up patches have been continuously increasing over time. Metrics' patterns differed significantly between two time intervals (1948–1990 and 1990–2012), with the highest spatial variability of landscape metrics being observed in the last two decades. Fractal indexes have reached the highest values in 2006 and 2012. Based on critical thresholds of per-capita land consumption, settlement dispersion and patch fragmentation, a Principal Component Analysis has indicated that the Athens' spatial structure of late 1980s and early 1990s was more sustainable than earlier and more recent urban morphologies. Results of this study contribute to a better understanding of long-term form-function relationships in compact and dispersed cities, offering an empirical base to identify sustainable urban forms.
To explore the evolution features of the pore–fracture structures and permeability behaviors of coal under high temperatures and nitrogen atmospheres, an infrared rapid heating apparatus was employed ...to heat coal samples up to 100–500 °C at intervals of 100 °C. The coal samples were then scanned using high-precision micro-CT, and a three-dimensional (3D) pore–fracture structure and equivalent pore network model of the coal samples were established. The changing laws of Ep, Cn, Et, and Lc that varied with the heating temperature were first quantitatively analyzed. The distribution of the surface area and volume of the pore fracture was then statistically characterized. The results showed that the number of pore fractures and throats reached a maximum at 200 °C. Pore and fracture structures in coal tend to develop more with increasing temperature. In addition, the variations in the fractal dimension, porosity, connectivity, and permeability of coal with temperature are discussed. The fractal dimension and porosity increased significantly with increasing temperature. Dc and φc are more linearly dependent on temperature than Df and. φf The interconnection between the pores and fissures caused by the temperature increase is responsible for the increase in connectivity and permeability. This study provides theoretical guidance for coal fire prevention and coalbed methane extraction.
•Variation laws for Ep, Cn, Et, and Lc of coal samples under different temperatures were obtained.•The effect of temperature on fractal dimension, porosity and connectivity was analyzed.•The liquid flow in pores and fractures of coal sample was visualized.•Permeability was well predicted by fractal dimension and porosity.
•Improved methodology for virtually reconstructing the 3D pore structures of OPC pastes was proposed.•A methodology to predict permeability on the basis of the reconstructed pore structures was ...proposed.•Pore structures were reconstructed by combining five BFU types per pore region.•The predicted permeability varied depending on the fractal dimensions.•The effects of two types of fractal dimensions on the permeability of each pore region were evaluated.
The permeability of cementitious materials is one of the crucial indicators in the quantitative evaluation of durability, and it is significantly affected by the characteristics of the internal pore structure of such materials. To predict the permeability of cementitious materials based on a clear analysis of their pore structure, we propose an improved methodology for virtually reconstructing the three-dimensional pore structures of ordinary Portland cement (OPC) pastes by using fractal theory. In addition, we propose a methodology to predict permeability on the basis of the reconstructed pore structure. The accuracy of pore structure reconstruction was found to be the highest when each pore region was reconstructed using five types of base fractal units (BFUs) based on the fractal dimensions of pore-size distribution and pore tortuousness. The permeability predictions generated using the proposed methodology indicated that when the volumetric parameter of the pore structure was the same, the permeability increased by up to four orders of magnitude as the geometric parameters varied. In addition, the fractal dimension of pore-size distribution had a more critical effect on the large capillary pores region, and the fractal dimension of pore tortuousness had a more critical effect on the gel & small capillary pores region. These results indicate that consideration of the geometric characteristics of the pore structure significantly influences the pore structure reconstruction and permeability prediction processes.
•The pore structure of C10-C150 concrete is analyzed by Mercury intrusion porosimetry (MIP).•All fractal curves of concrete are divided into four segments according multi-fractal characteristic.•The ...scale of each fractal region in C10-C150 concrete is different.•Link of the most probable pore diameter and the pore specific surface area with fractal dimension is discussed.•A mathematical model between compressive strength and pore structure is addressed.•The mathematical model between fractal dimension and compressive strength is validated more accurately than other parameters.
Concrete is a heterogeneous, multiphase, and multilayer composite system with extremely intricate microscopic pore structure. The structural characteristics of microscopic pore of concrete are closely related to its mechanical properties and durability. The pore structure of concrete with various strength grades (C10-C150) was analyzed by Mercury intrusion porosimetry (MIP) from the aspects of pore diameter distribution, pore volume, pore specific surface area and fractal feature. The Menger sponge model was used to calculate the fractal dimension of different pore regions in each test group, and the most suitable pore fractal region was selected to establish the mathematical model between fractal dimension and compressive strength. The results showed that all fractal curves are divided into four segments according multi-fractal characteristic of concrete, namely Region I, Region II, Region III and Region IV. Region I is macropores fractal region (d = 10 μm ∼ 950 μm), representing the packing patterns of hydrated cement grains, while Region II - Region Ⅳ is micropores fractal region (d = 0.0064 μm ∼ 10 μm), reflecting mainly the microstructure of C-S-H hydrates. Region I and Region Ⅳ exhibit obvious fractal features and the fractal dimension D is between 2 and 3. However, the fractal dimension D > 3 in Region II and Region III, which are nonphysical from the point of view of surface geometry. The fractal dimension can clearly describe the internal pore characteristic, and it is a real good correlation with the most probable pore diameter and the pore specific surface area. Moreover, the mathematical model between the fractal dimension and the compressive strength both accords with the positive power exponential function in Region I and Region IV. The fractal dimension can be viewed as a comprehensive parameter of pore shape and spatial distribution of pore structure, which can more accurately represent the relationship between the microscopic pore structure features and compressive strength of concrete. In practical engineering, it serves to realize the damage detection of concrete on site.
Although geographic features, such as mountains and coastlines, are fractal, some studies have claimed that the fractal property is not universal. This claim, which is dubious, is mainly attributed ...to the strict definition of fractal dimension as a measure or index for characterizing the complexity of fractals. In this article, we propose an alternative, ht-index, to quantify the fractal or scaling structure of geographic features. A geographic feature has ht-index (h) if the pattern of far more small things than large ones recurs (h - 1) times at different scales. The higher the ht-index, the more complex the geographic feature. We conduct three case studies to illustrate how the computed ht-indexes capture the complexity of different geographic features. We further discuss how ht-index is complementary to fractal dimension and elaborate on a dynamic view behind ht-index that enables better understanding of geographic forms and processes.
This work studies the methods used to extract fractal dimensions from surface profiles and the applicability of fractals to measured surfaces. The work used generated surfaces to first evaluate these ...methods, and later applies the methods to measured surfaces. Two methods for generating surface profiles are used. The fractal dimension values of all generated profiles are calculated by four methods, then the results are compared. It is also found that self-similarity occurs at different fractal dimensions for the power spectrum and the Weierstrass-Mandelbrot generation methods. The analysis indicates that real measured rough surfaces are not easily represented as perfect fractals as researchers and engineers often assume.
•Effectiveness of various methods for extracting the fractal dimension is analyzed.•If fractals are effective at characterizing and describing measured surfaces is investigated.•Which fractal dimension extracted methods provide the ‘best’ prediction?
•OM displayed Type IV isotherm and mesopores stood out as the prevailing type of pores.•Total surface area and PV were less during AHP than HP revealing the role of water.•Pore diameter in AHP was ...larger while the diameter of pores increased with the progress of thermal advance in both.•Cascade forward neural network (CFNN) outperformed other models in predictions of N2 volume adsorbed/desorbed.
In this study, to clarify the role of water during thermal maturation on organic porosity evolution, pore structure characteristics of the Qingshankou shale (type I kerogen) were studied during anhydrous and hydrous pyrolysis (AHP and HP) over wide a range of temperature (300–450 °C). Following each step of thermal maturation, geochemical properties, and pore structure were analyzed with Rock Eval and low-pressure N2 adsorption, respectively. Furthermore, the deconvolution technique was applied to the pore size distribution curves to investigate different pore families and their complexity was assessed using fractal dimension analysis. Next, the volume of N2 adsorbed/desorbed was modeled using several intelligent models. It was found that organic matter displayed Type IV isotherm with hysteresis loops and mesopores stood out as the prevailing type of pores within the samples. Moreover, total surface area and pore volume were found less for AHP samples than the HP samples at all temperatures, which revealed the role of water in the evolution of organic porosity. Pore diameter in AHP samples was larger compared to HP ones, while the diameter of pores increased with the progress of thermal advance in both scenarios. The original sample exhibited five mesopore and two macropore families, while with rising temperature pore families with smaller average pore widths were decreased, and pore families with larger average pore widths were created and expanded. Furthermore, heterogeneity of the pores with maturation was more evident in AHP samples due to the decrease in the number of pores with smaller pore widths. The role of water in the creation of fractures within pyrobitumen was remarkable since it caused a substantial increase in the total pore volume of the organic matter during the gas window. Finally, modeling outcomes showed that cascade forward neural network (CFNN) outperformed other models in predictions of N2 volume adsorbed/desorbed with an average absolute percent relative error (AAPRE) of 2.48 %. It was understood that relative pressure followed by pyrolysis method (AHP or HP) were the most important variables in the estimation of N2 adsorbed/desorbed volumes based on sensitivity analysis. Collectively, the role of water on organic porosity evolution was confirmed based on distinct discrepancies in the two groups of samples pore structure details.
•The performance of three kinds of foamed concrete for railway subgrade was tested.•Pore size distribution in materials was characterized quantitatively by X-CT.•The pore morphology characteristics ...of different sphericity were analyzed.•The influence of pore parameters on the performance of foamed concrete was analyzed.
The uneven settlement of weak roadbed will lead to road subsidence, which will reduce driving comfort and even cause traffic accidents. In the treatment of weak road base, foamed concrete has become an excellent subgrade replacement material because of its light weight and high strength. In order to study the pore structure characteristics of foamed concrete used in the railway roadbed replacement project, three kinds of foamed concrete with different density made in construction site were analyzed based on X-ray computed tomography (X-CT) technology. The results showed that the porosity of the three kinds of foamed concrete was different, the pore size distribution was also different, and the sphericity of pores was closely related to the pore size. Finally, the basic mechanical properties of foamed concrete were analyzed from the point of view of pore parameters.
A convection-diffusion equation for E reaction arising in rotating disk electrodes is discussed and solved by Taylor series method and Pade approximation. A fractional modification is suggested to ...deal with the porous property of the electrodes, the effect of the porous structure on the convection-diffusion process is elucidated.
•A convection-diffusion equation arising in rotating disk electrodes is studied.•Taylor series method is used to solve the equation.•Pade technology is used to accelerate the convergence rate.•A fractal modification of convection-diffusion equation is suggested considering the porous structure of the electrodes.
Surface texture of an image plays an imperative role in understanding objects such as aggregates, woods, grains, soils, trees, and houses. Fractal dimension (FD) helps to characterise these objects ...by quantifying their complex texture patterns. Differential box counting (DBC) is one of the popularly used methods to measure FD of a gray-scale image. However, it suffers from several limitations. So, this study introduces three improved DBC methods using three box heights based on eigenvalue, kurtosis, and skewness of an image respectively. These methods also use a new xy-plane shifting mechanism and a modified formula for computing nr. Moreover, weighted least squares (WLS) regression is adopted, where a trapezoidal membership function (TMF) based rule is proposed for assigning weights to each grid size. The image surface exhibits multifractal nature, hence two multifractal analysis methods are also analysed and included in the experiments. All the experiments are performed on three gray-scale image databases viz., the synthesized Fractal Brownian motion (FBM) images, natural texture images of Brodatz database, and images of Outex database that are captured at different rotations. Experimental results show that the proposed methods outperform some of the state-of-the-art methods.
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•Surface texture analysis of an image is done based on fractal dimension (FD).•FD is computed using an improved differential box counting method.•This work addresses the over-counting problem along z-direction.•The under-counting problem along xy-directionis is also solved using a xy-plane shiftiting mechanism.•Weighted least squares regression is utilized to obtain a better fitted line.
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