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Showing papers on "Fractal dimension published in 2014"


Journal ArticleDOI
01 Jan 2014-Fuel
TL;DR: In this paper, the impact of fractal dimension on adsorption capacity has been discussed based on the physical description of the fractal surfaces, and the authors showed that fractal geometries with fractal dimensions ranging from 2.68 to 2.83 were obtained from the nitrogen adsorptions data using the Frenkel-Halsey-Hill method.

493 citations


Journal ArticleDOI
TL;DR: In this article, a kinetic model of sand blasting is presented, which gives surface topographies and surface roughness power spectra in good agreement with experiments, showing that most natural surfaces and surfaces of engineering interest are self affine fractal over a wide range of length scales.
Abstract: Most natural surfaces and surfaces of engineering interest, e.g., polished or sand blasted surfaces, are self affine fractal over a wide range of length scales, with the fractal dimension \(D_\mathrm{f} = 2.15 \pm 0.15\). We give several examples which illustrate this and a simple argument, based on surface fragility, for why the fractal dimension usually is \(<\)2.3. A kinetic model of sand blasting is presented, which gives surface topographies and surface roughness power spectra in good agreement with experiments.

233 citations


Journal ArticleDOI
TL;DR: In this article, the fractal dimension of the pore surface was determined based on data of the specific surface area per unit pore volume (Spor), and a comparison of fractal dimensions determined by three different methods indicated a clear differentiation between the surface dimension and volume dimension.
Abstract: The geometry of pore structure of reservoir rock is described by the shape, size, distribution and connection of pores, and pore throats of rocks. Pore-space properties are important for the description and characterization of fluid storage and transport in reservoir rocks. We used the fractal concept to describe the geometric structure of the pores of 24 samples from an Eocene sandstone formation in China. The fractal behavior of pore volume distribution was investigated by capillary pressure curves and nuclear magnetic resonance (NMR). Additionally, the fractal dimension of the pore surface was determined based on data of the specific surface area per unit pore volume (Spor). The comparison of fractal dimensions determined by three different methods indicates a clear differentiation into the “surface dimension” and “volume dimension.” The fractal dimension resulting from longer transverse NMR relaxation times and lower capillary pressure reflects the volume dimension of larger pores. The fractal...

156 citations


Journal ArticleDOI
TL;DR: In this paper, the authors presented two new cubic covering methods, namely the differential cubic covering method (DCCM) and relative differential cubic cover method (RDCCM), to directly evaluate the fractal dimension of a rough surface according to the definition of box-counting dimension.

155 citations


Journal ArticleDOI
TL;DR: This article proposes an alternative, ht-index, to quantify the fractal or scaling structure of geographic features, and discusses 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.
Abstract: 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...

143 citations


Journal ArticleDOI
TL;DR: Based on the FHH model, the fractal characteristics of 58 coals from 14 mining areas in the eastern margin of the Ordos Basin, China are analyzed in this paper, and the results show that the DS ranges from 2.22 to 2.77 for the 58 coal, except for six samples with plots Type P4, for which correct DS could not be obtained.

134 citations


Journal ArticleDOI
TL;DR: An analysis of several methods of extraction of fractal parameters from the simulated, artificial surfaces and AFM images of the real, polycrystalline diamond films is presented in this paper, and the changes in the fractal dimension and the anisotropy ratio values observed over deposition time are also shown and discussed.

116 citations


Journal ArticleDOI
TL;DR: This article used digitized standard roughness profiles to determine roughness parameters such as statistical and 2D discontinuity roughness, and fractal dimensions, based on the relationship between the joint roughness coefficient (JRC) values and roughness parameter calculated using power law equations.
Abstract: This study used precisely digitized standard roughness profiles to determine roughness parameters such as statistical and 2D discontinuity roughness, and fractal dimensions. Our methods were based on the relationship between the joint roughness coefficient (JRC) values and roughness parameters calculated using power law equations. Statistical and 2D roughness parameters, and fractal dimensions correlated well with JRC values, and had correlation coefficients of over 0.96. However, all of these relationships have a 4th profile (JRC 6–8) that deviates by more than ±5 % from the JRC values given in the standard roughness profiles. This indicates that this profile is statistically different than the others. We suggest that fractal dimensions should be measured within the entire range of the divider, instead of merely measuring values within a suitable range. Normalized intercept values also correlated with the JRC values, similarly to the fractal dimension values discussed above. The root mean square first derivative values, roughness profile indexes, 2D roughness parameter, and fractal dimension values decreased as the sampling interval increased. However, the structure function values increased very rapidly with increasing sampling intervals. This indicates that the roughness parameters are not independent of the sampling interval, and that the different relationships between the JRC values and these roughness parameters are dependent on the sampling interval.

103 citations


Journal ArticleDOI
TL;DR: In this article, the effect of internal magnetic field gradients was most pronounced in rocks with larger pores and a high magnetic susceptibility contrast between the pore fluid and mineral grains, and quantified this behavior in terms of pore size and Carr-Purcell-Meiboom-Gill (CPMG) half-echo spacing through scaling arguments.
Abstract: Pore size distributions in rocks may be represented by fractal scaling, and fractal descriptions of pore systems may be used for prediction of petrophysical properties such as permeability, tortuosity, diffusivity, and electrical conductivity. Transverse relaxation time (T2) distributions determined by nuclear magnetic resonance (NMR) measurements may be used to determine the fractal scaling of the pore system, but the analysis is complicated when internal magnetic field gradients at the pore scale are sufficiently large. Through computations in ideal porous media and laboratory measurements of glass beads and sediment samples, we found that the effect of internal magnetic field gradients was most pronounced in rocks with larger pores and a high magnetic susceptibility contrast between the pore fluid and mineral grains. We quantified this behavior in terms of pore size and Carr-Purcell-Meiboom-Gill (CPMG) half-echo spacing through scaling arguments. We additionally found that the effects of intern...

95 citations


Journal ArticleDOI
TL;DR: In this paper, first-and second-order consensus algorithms in networks with stochastic disturbances are studied and the deviation from consensus is quantified using the notion of network coherence, which can be expressed as an $H 2 -norm.
Abstract: We consider first- and second-order consensus algorithms in networks with stochastic disturbances. We quantify the deviation from consensus using the notion of network coherence, which can be expressed as an $H_{2}$ norm of the stochastic system. We use the setting of fractal networks to investigate the question of whether a purely topological measure, such as the fractal dimension, can capture the asymptotics of coherence in the large system size limit. Our analysis for first-order systems is facilitated by connections between first-order stochastic consensus and the global mean first passage time of random walks. We then show how to apply similar techniques to analyze second-order stochastic consensus systems. Our analysis reveals that two networks with the same fractal dimension can exhibit different asymptotic scalings for network coherence. Thus, this topological characterization of the network does not uniquely determine coherence behavior. The question of whether the performance of stochastic consensus algorithms in large networks can be captured by purely topological measures, such as the spatial dimension, remains open.

83 citations


Journal ArticleDOI
15 Jan 2014-Wear
TL;DR: In this paper, a modified asperity contact model was proposed for fractal rough surfaces and the critical area of a single as perity was scale dependent and the plastic to elastic mode transition agreed with classical contact mechanics.

Journal ArticleDOI
TL;DR: In this article, an imaging method to assess the homogeneity of asphalt concrete using X-ray computed tomography, the improved OTSU image method, and fractal theory was presented.

Journal ArticleDOI
TL;DR: In this article, the authors present an overview of fractal media by continuum mechanics using the method of dimensional regularization and discuss wave equations in several settings (1d and 3d wave motions, fractal Timoshenko beam, and elastodynamics under finite strains).
Abstract: This paper presents an overview of modeling fractal media by continuum mechanics using the method of dimensional regularization. The basis of this method is to express the balance laws for fractal media in terms of fractional integrals and, then, convert them to integer-order integrals in conventional (Euclidean) space. Following an account of this method, we develop balance laws of fractal media (continuity, linear and angular momenta, energy, and second law) and discuss wave equations in several settings (1d and 3d wave motions, fractal Timoshenko beam, and elastodynamics under finite strains). We then discuss extremum and variational principles, fracture mechanics, and equations of turbulent flow in fractal media. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions and reduce to conventional forms for continuous media with Euclidean geometries upon setting the dimensions to integers. We also point out relations and potential extensions of dimensional regularization to other models of microscopically heterogeneous physical systems.

Journal ArticleDOI
TL;DR: In this article, an extended form of the Rayleigh-Debye-Gans theory for Fractal Aggregates (RDG-FA) is proposed in order to take into account the impact of multiple scattering (MS) within soot aggregates.
Abstract: The in situ optical characterization of smokes composed of soot particles relies on light extinction, angular static light scattering (SLS), or laser induced incandescence (LII). These measurements are usually interpreted by using the Rayleigh–Debye–Gans theory for Fractal Aggregates (RDG-FA). RDG-FA is simple to use but it completely neglects the impact of multiple scattering (MS) within soot aggregates. In this paper, based on a scaling approach that takes into account MS effects, an extended form of the RDG-FA theory is proposed in order to take into account these effects. The parameters of this extended theory and their dependency on the number of primary sphere inside the aggregate ( 1 N p 1006 ) and on the wavelength ( 266 nm λ 1064 nm ) are evaluated thanks to rigorous calculations based on discrete dipole approximation (DDA) and generalized multi-sphere Mie-solution (GMM) calculations. This study shows that size determination by SLS is not distorted by MS effect. On the contrary, it is shown that fractal dimension can be misinterpreted by light scattering experiments, especially at short wavelengths. MS effects should be taken into account for the interpretation of absorption measurements that are involved in LII or extinction measurements.

Journal ArticleDOI
TL;DR: In this paper, the fractal geometry theory and method are used to simulate the rough surface topography, and the pressure gradients, friction factors and Poiseuille numbers for laminar flow through microchannels with roughened surfaces are derived.

Journal ArticleDOI
TL;DR: In this article, an approach based on the description of the microstructure of the voids using fractal geometry was used for the calculation of the permeability of porous materials.

Journal ArticleDOI
TL;DR: In this paper, the authors applied fractal and multifractal analysis on simulated pore structure of cement paste, where some hydration factors including the water to cement ratio and the degree of cement hydration are discussed in terms of the fractal dimension and the multifractual spectrum.

Journal ArticleDOI
TL;DR: A new definition in order to compute the fractal dimension of a subset respect to any fractal structure, which completes the theory of classical box-counting dimension and allows to classify and distinguish a much larger number of topological spaces than the classical definition.

Journal ArticleDOI
TL;DR: In this article, the pore structure in cement pastes is characterized using an innovative non-contact impedance measurement based on pore fractal theory, and the relationship between the cumulative pore volume and impedance response is revealed.

Journal ArticleDOI
TL;DR: In this article, the authors derived dimensionless and relative permeability of GDL in PEMFCs using fractal theory and showed that the dimensionless permeability decreases significantly with the increase of tortuosity fractal dimension.

Journal ArticleDOI
TL;DR: In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach, and analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient (TPG) is also obtained.
Abstract: In this paper, the mechanism for fluid flow at low velocity in a porous medium is analyzed based on plastic flow of oil in a reservoir and the fractal approach. The analytical expressions for flow rate and velocity of non-Newtonian fluid flow in the low permeability porous medium are derived, and the threshold pressure gradient (TPG) is also obtained. It is notable that the TPG (J) and permeability (K) of the porous medium analytically exhibit the scaling behavior J ~ K−DT/(1=DT), where DT is the fractal dimension for tortuous capillaries. The fractal characteristics of tortuosity for capillaries should be considered in analysis of non-Darcy flow in a low permeability porous medium. The model predictions of TPG show good agreement with those obtained by the available expression and experimental data. The proposed model may be conducible to a better understanding of the mechanism for nonlinear flow in the low permeability porous medium.

Journal ArticleDOI
TL;DR: In this article, a 3D dense point scanning technology and a new standard for evaluating the anti-skid performance of asphalt pavements was introduced, and four types of aggregates (A, B, C and D) under different states of grinding and abrasion have been measured, and their parameters, such as the fractal dimension and peak angle, have been calculated to evaluate the anti skid performance.

Journal ArticleDOI
TL;DR: The retinal vascular fractal dimension is a shared biomarker of diabetic microvasculopathy, thus indicating a possible common pathogenic pathway and Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes.
Abstract: Fractal analysis of the retinal vasculature provides a global measure of the complexity and density of retinal vessels summarised as a single variable: the fractal dimension. We investigated fractal dimensions as long-term predictors of microvasculopathy in type 1 diabetes. We included 180 patients with type 1 diabetes in a 16 year follow-up study. In baseline retinal photographs (from 1995), all vessels in a zone 0.5–2.0 disc diameters from the disc margin were traced using Singapore Institute Vessel Assessment-Fractal image analysis software. Artefacts were removed by a certified grader, and fractal dimensions were calculated using the box-counting method. At follow-up (in 2011), diabetic neuropathy, nephropathy and proliferative retinopathy were assessed and related to baseline fractal dimensions in multiple regressions adjusted for sex and baseline age, diabetes duration, HbA1c, BP, BMI, vibration perception threshold, albuminuria, retinopathy and vessel diameters. Mean baseline age and diabetes duration were 21.0 and 13.4 years, respectively, and of patients 50.0% were males. The mean fractal dimension was 1.3817. The 16 year incidences of neuropathy, nephropathy and proliferative retinopathy were 10.8%, 8.0% and 27.9%, respectively. Multiple regression analyses showed a lower fractal dimension to significantly predict incident neuropathy (OR 1.17 per 0.01 fractal dimension decrease [95% CI 1.01, 1.36]), nephropathy (OR 1.40 per 0.01 fractal dimension decrease [95% CI 1.10, 1.79]) and proliferative retinopathy (OR 1.22 per 0.01 fractal dimension decrease [95% CI 1.09, 1.37]). The retinal vascular fractal dimension is a shared biomarker of diabetic microvasculopathy, thus indicating a possible common pathogenic pathway. Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes.

Proceedings ArticleDOI
04 Dec 2014
TL;DR: A real-time Electroencephalogram (EEG)-based emotion recognition algorithm using Higuchi Fractal Dimension (FD) Spectrum is proposed and results show that using FD spectrum features it is possible to improve classification accuracy.
Abstract: In this paper, a real-time Electroencephalogram (EEG)-based emotion recognition algorithm using Higuchi Fractal Dimension (FD) Spectrum is proposed. As EEG is a nonlinear and multi-fractal signal, its FD spectrum can give a better understanding of the nonlinear property of EEG. Three values are selected from the whole spectrum and are combined with the other features such as statistical and Higher Order Crossings ones. The Support Vector Machine is used as the classifier. The proposed algorithm is validated on both benchmark database DEAP with video stimuli and our own dataset which used visual stimuli to evoke emotions. Up to 8 emotions can be recognized with only 4 channels. The experiment analysis results show that using FD spectrum features it is possible to improve classification accuracy.

Journal ArticleDOI
TL;DR: In this article, the joint distribution of relative velocities and separations of identical inertial particles suspended in randomly mixing and turbulent flows is computed by matching asymptotic forms of the distribution.
Abstract: We compute the joint distribution of relative velocities and separations of identical inertial particles suspended in randomly mixing and turbulent flows. Our results are obtained by matching asymptotic forms of the distribution. The method takes into account spatial clustering of the suspended particles as well as singularities in their motion (so-called ‘caustics’). It thus takes proper account of the fractal properties of phase space and the distribution is characterised in terms of the corresponding phase-space fractal dimension D2. The method clearly exhibits universal aspects of the distribution (independent of the statistical properties of the flow): at small particle separations R and not too large radial relative speeds |VR|, the distribution of radial relative velocities exhibits a universal power-law form , provided that D2 ≤ d + 1 and that the Stokes number St is large enough for caustics to form. The range in VR over which this power law is valid depends on R, on the Stokes number and upon th...

Journal ArticleDOI
TL;DR: In this paper, the authors showed that the fractal dimension of large fluidized agglomerates can be up to two orders of magnitude larger than one, which is due to the multidimensional nature of fluidized nanoparticles.

Journal ArticleDOI
TL;DR: In this paper, an active grid consisting of Sierpinski triangle, space-filling squares, and Apollonian gasket type fractal shapes was used to generate turbulent flow.
Abstract: The study of decaying isotropic turbulent flow is an important point of reference for turbulence theories and numerical simulations. For the past several decades, most experimental results appear to favor power-law decay with exponents between −1.2 and −1.4, approximately. More recently, studies of fractal-generated turbulence with multi-scale passive grids have shown increased Reynolds numbers and exponential or very fast power-law decays following an increase of kinetic energy close to the grid. Other recent studies have confirmed that such non-classical decay is limited to the region near the grid. In order to generate turbulence with multi-scale injection of kinetic energy at more elevated Reynolds numbers and with more spatially homogeneous distributions than available in prior experiments, we use an active-grid consisting of winglets with fractal shapes. We consider various types of fractal winglets, namely, Sierpinski triangle, space-filling squares, and Apollonian gasket type fractal shapes. Regular non-fractal winglets are also considered. Passive fractal grids are studied by keeping the winglets locked in place. Data are acquired using X-wire thermal anemometry and the decay is analyzed between 15 < x/M < 50 (M is the mesh-size). Results exhibit power-law decay with decay exponent approximately between −1.0 and −1.3. The precise values of the decay exponent and the coefficient Ce=el/urms3 depend on the geometry of the initial condition, although it is not possible to discern systematic or monotonic trends with respect to Reλ, component anisotropy, grid fractal dimension, or blockage ratio.

Journal ArticleDOI
TL;DR: The results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.

Journal ArticleDOI
TL;DR: In this paper, a physically-based model for describing the temporal evolution of porosity, saturated and relative permeabilities, retention curve and diffusion coefficient during rock dissolution by reactive fluids is presented.

Journal ArticleDOI
TL;DR: In this article, a fractal model was proposed to describe the pore structure of the lithology of a reservoir and the relationship among the structural parameters of similar lithological porous media and saturation as well as the dimensionless capillary pressure function J(SW).