Fractal Surface Model Research Articles

МОДЕЛИРОВАНИЕ МИКРОРЕЛЬЕФА ПОВЕРХНОСТИ ПОЧВЕННОГО СЛОЯ ДЛЯ УТОЧНЕННЫХ РАСЧЕТОВ РАБОЧИХ ОРГАНОВ НА ПРОЧНОСТЬ

Issues of increasing the reliability of working parts of agricultural machines interacting with the soil surface are discussed in the article. A loading model based on taking into account microroughness of the surface soil layer using a fractal surface model constructed using the diamondsquare algorithm is proposed. It is shown that the parameters of microroughness of the soil surface, calculated using the proposed model, correspond to experimental data obtained by profiling the soil surface during pre-sowing treatment and during the preparation of flax. A comparative calculation of the loading of the needle harrow tooth and the tiller tooth was carried out in accordance with the model of a flat soil surface and a soil surface with a microrelief, modeled according to the proposed model. It is shown that the mechanical stresses in the working bodies interacting with the soil surface, loaded according to the proposed model, are 14% greater during pre-sowing treatment, and 25% greater when preparing flax trust, than when calculated using a model of a flat soil surface. The use of a microrelief model is optimal both when calculating soil tillage machines and when calculating other flax harvesting machines (pulling machines, flax sliver fluffers, balers and other units) that are not intended for direct tillage of the soil, but have contact with it during the technological process.

Numerical modeling on the deformation features of expansive soil slopes under moisture variations based on Fractal model

Expansive soils exhibit significant swelling-shrinkage characteristic under the cyclic moisture changes. The expansive soil slopes with high designing safety factor (gentle slope and low rainfall level) will also fail, which could not happen in an analysis ignoring expansive deformations. In this paper, the basic pore surface fractal model is derived and user-defined subroutines performing swelling-shrinkage deformation are developed to simulate the deformation features of expansive soil slopes under moisture variations. First, Fractal model is verified experimentally for accuracy in describing expansive soil issues. A hydro-mechanical coupling model based on the Fractal model in ABAQUS is then established to enable the numerical analysis of expansive soil slopes. In addition, the effects of swelling deformation, desiccation and slope ratio on deformation features are investigated. The results show that the consideration of swelling-shrinkage deformation causes the slope deformation features change, promotes larger additional displacements, and enhances water sensitivity. The simulated slopes can exhibit typical gentle sliding, shallow and progressive damage after several moisture cycling. This research provides a design reference for expansive soil slopes and expansive soil associated catastrophic issues.

Toward a Chemical Control of Colloidal YVO4 Nanoparticles Microstructure.

Rare-earth-doped oxides are a class of compounds that have been largely studied in the context of the development of luminescent nanocrystals for various applications including fluorescent labels for bioimaging, MRI contrast agents, luminescent nanocomposite coatings, etc. Elaboration of colloidal suspensions is usually achieved through coprecipitation. Particles exhibit emission properties that are similar to the bulk counterparts, although altered by crystalline defects or surface quenching species. Focusing on YVO4:Eu, one of the first reported systems, the aim of this work is to revisit the elaboration of nanoparticles obtained through a simple aqueous coprecipitation route. The objective is more precisely to get a better understanding of the parameters affecting the particles' internal microstructure, a feature that is poorly controlled and characterized. We show that the hydroxyl concentration in the precursor solution has a drastic effect on the particles' microstructure. Moreover, discrepancies in the reported particle structure are shown to possibly arise from the carbonation of the strongly basic orthovanadate precursor. For this study, SAXS/WAXS is shown to be a powerful tool to characterize the multiscale structure of the particles. It could be shown that playing on the precursor composition, it may be varied between almost monocrystalline nanocrystals to particles exhibiting a hierarchical microstructure well described by a surface fractal model. This work provides a new methodology for the characterization of nanoparticles microstructure and opens new directions for its optimization in view of applications.

Two-Way Parabolic Equation Method for Radio Propagation Over Rough Sea Surface

This article presents a two-way parabolic equation (2WPE) method based on the Pade(2,2) approximation form, which can model bidirectional electromagnetic wave (EW) propagation in a sea environment. Compared with other common approximation forms, the Pade(2,2) approximation has better convergence and accuracy. To accurately simulate the reflection and refraction effects of EW propagation near the sea surface, an improved fractal sea surface model is used to construct the geometric rough sea surface. The results of the Pade(2,2) approximation PE model are compared with those of the Miller–Brown model, and good agreement is observed. Numerous experiments prove that the 2WPE model is more accurate than the one-way parabolic equation model for predicting large-scale radio wave propagation in marine environments. Furthermore, we investigate the relationship between the backward-scattered EWs and the wind speed. The polynomial fitting method is adopted to process a large amount of sampled data for backward-scattered EWs with different wind speeds and frequencies. Through accurate judgment of the points of the polynomial fitting curve in a certain frequency range, the wind speed over the sea surface can be precisely determined. Thus, this article provides a novel theoretical method for marine remote sensing.

Fractal Dimension Estimation for Color Texture Images

As an important feature of image texture, fractal dimension is widely used to index, segment or classify texture images. Previously, many methods have been proposed to estimate fractal dimension. However, most of them are for binary and gray-scale images. Only a few of them are for color images. In this paper, by extending the differential box-counting approach to five-dimensional Euclidean hyper-space, we present a new robust and simple algorithm to estimate fractal dimension for color texture images. By the differential box-counting method, a real empty box not covering any pixel even with ideal resolution is also counted as a box having pixels, resulting in errors of computations. This problem is eliminated by our method based on fractal Brownian surface model. Our experiments demonstrate that our algorithm is able to capture the complexity of color natures, and outperforms other methods in terms of color texture complexity ranking and discrimination, robustness and computational complexity.

Adsorption pore structure and its fractal characteristics of coals by N2 adsorption/desorption and FESEM image analyses

The adsorption pore structure and its fractal characteristics of coals (0.69–2.79% Ro,m) were investigated by N2 adsorption/desorption and field emission scanning electron microscopy. First, organic matter (OM) pores and interparticle pores (InterP) with various shapes are distinguished in different rank coals. The OM pores present irregular shapes in low-/middle-rank bituminous coals, and circular, oval and slit shapes in high-rank bituminous coal and anthracite with width from 50 nm to 2 μm. In contrast, the InterP pores show polygonal/elongated shapes and exist between mineral grains or mineral and OM with width >100 nm. Second, the coals with H1 type hysteresis loop of N2 adsorption/desorption isotherms are favorable for gas adsorption due to large pore surface area, whereas coals with H2 and H3 types are conducive to gas desorption and diffusion because of open pores with good connectivity. Moreover, the fractal dimension of pore shape was obtained from FESEM images and ranges from 1.068 and 1.30, indicating the adsorption pore shape is relatively regular. The surface and volume fractal dimensions of micropores and mesopores were calculated from the N2 adsorption data on the basis of surface fractal model and FHH model, respectively. The fractal dimension of micropore and mesopore surface respectively ranges from 2.18 to 2.69 and 1.78 to 2.41, whereas that of micropore and mesopore volume respectively ranges from 2.18 to 2.67 and 2.29 to 2.79. The pore structure and coal composition during different coalification stages have specific effects on the fractal characteristics of pore shape, surface and volume.

Peak shear strength of compacted GMZ bentonites in saline solution

Knowledge of the peak shear strength of compacted bentonites is of fundamental importance to high-level nuclear waste repositories, as it forms the basis of the analysis of repository stability. The shear strength properties of GMZ bentonites are throughout investigated by undrained direct shear tests with different concentrations of NaCl solutions, and are explained in the light of the modified effective stress concept, which takes into consideration of the osmotic suction. The modified effective stress concept is expressed as p’ = p + π(p/π)Ds-2, incorporated with the normal stress (p) and osmotic suction (π) based on the bentonite surface fractal model. The peak shear strength behavior of GMZ bentonites in NaCl solutions appears to be explained satisfactorily by the modified effective stress. According to the Mohr-Coulomb criterion, the peak shear strength of bentonites saturated by distilled water and NaCl solutions is expressed by the same unique line in the τ-p’ plane. GMZ bentonite has the same values of the peak friction angle and the peak cohesion in distilled water and NaCl solutions of different concentrations.

FRACTAL MODEL FOR THE CORRELATION RELATING TOTAL SUCTION TO WATER CONTENT OF BENTONITES

Great efforts have been made to determine total suction using elaborate laboratory tests, because there is no a specific correlation relating the total suction to the water content of bentonites. However, elaborate laboratory tests are difficult and time consuming to perform on bentonites. Thus, a theoretical equation is a necessary choice to correlate the total suction to the water content. A simple method is proposed to calculate the total suction from the water content based on the surface fractal model for bentonites. The correlation relating the total suction to the water content is expressed by a power-law function with the exponent of [Formula: see text] is the surface fractal dimension of bentonites. The surface fractal dimension can be determined using the nitrogen adsorption isotherm tests. The total suction of bentonites calculated from the proposed method is in satisfactory agreement with the experimental data found in the literature. In addition, the correlation of the total suction to the water content also offers another method to determine the surface fractal dimension of bentonites.

Effect of combined UV thermal and hydrolytic aging on micro-contact properties of silicone elastomer

Silicone elastomer seals are widely used in aerospace field due to the unique performance. However, aging and degradation problems still exist under the harsh working environment, such as ultraviolet radiation and high-low temperature. In this paper, combined UV thermal and hydrolytic aging tests have been carried out and the aging mechanism of silicone elastomer is studied by Nicolet 380 ATR-FTIR instrument. Then, fractal surface model of silicone elastomer seal is developed based on the surface topography, which is measured by optical digital microscope. Finally, finite element contact model of the fractal surface is developed to analyze the coupling aging effects on micro-contact characteristics of silicone elastomer. Results indicate that compression set and hardness of silicone elastomer increases when aging time increases; combined UV thermal and hydrolytic aging may lead to the increasement of hardness; contact pressure increases and the contact area decreases in the aging process. Finite element model based on fractal theory provides an effective method to study the micro-contact properties of rubber sealing.

Study on the optical performance of thin-film light-emitting diodes using fractal micro-roughness surface model

Although LEDs have been widely studied using optical simulations, there is no optical model considering the effect of micro-roughness surface (MRS) on the optical performance for packaged LEDs. In this work, we employ the finite-difference time-domain method and the direction-sensitive bidirectional scattering distribution function to characterize the optical properties of the MRS upon the n-GaN layer. The MRS is generated by the Weierstrass–Mandelbrot fractal function. Furthermore, thin-film LEDs (TFLEDs), blue TFLED devices, and white TFLED devices considering the MRS are investigated using the ray-tracing (RT) method. The results show that the MRS has different optical properties when the light propagates out and in the n-GaN layer. In turn, the difference in the scattering ability of various MRS causes a significant effect on the optical performance of packaged TFLEDs, including radiant efficacy, luminous efficacy, intensity pattern and spectrum, as well as the correlated color temperature.

Not just fractal surfaces, but surface fractal aggregates: Derivation of the expression for the structure factor and its applications

Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ⋅ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.

ГЕРМЕТИЧНОСТЬ МЕТАЛЛ-МЕТАЛЛИЧЕСКИХ УПЛОТНИТЕЛЬНЫХ УСТРОЙСТВ

A contact of machinery real engineering surfaces has a complex geometry and is defined by errors at machining, in particular, by macrodeviations, corrugation and roughness. This paper report the consideration carried out on a fluid consumption through an end axisymmetric sealing arrangement formed by a joint of metal surfaces. Sealed environment consumption is defined through a sum of leaks through a slit between surfaces conditioned on corrugation and dripping through a porous layer farmed by surface roughness on contact contour spots. The surface corrugation is modeled by splines according to initial parameters of a corrugation, and as a roughness a surface fractal model is used repeating a real roughness most accurate. On algorithms presented taking into account basic parameters of corrugation and roughness the 3D models of engineering surfaces are created and after their bringing in contact arises a possibility to obtain practically all parameters of contacting defining the impermeability of a sealing arrangement. The application of 3D models allows rendering processes passing in a contact of conjugate surfaces and obtaining some data, for instance, a tortuosity of leaking channels which earlier were chosen according to recommendations which no doubt increases computation accuracy.

Structure and property analysis for a fractal superhydrophobic surface model

Superhydrophobicity depends mainly on the microstructures of a surface. Although the superhydrophobic surfaces (SHS) have been fabricated, micro-mechanisms responsible for its contact angle hysteresis (CAH) and free energy barrier (FEB) still need to be deeply investigated. For this reason, we attempt to compare the superhydrophobicity of the different hierarchy for the SHS based on a three-dimensional (3-D) pillar model by a more practical thermodynamic method. Therefore, general relationships between the superhydrophobic property and the proposed surface microstructures are also established based on the CAH phenomena together with a transient equation for describing the relationships between advancing/receding CAs and the static apparent CAs. The simulation suggests that the superhydrophobicity of two-step/three-step surfaces is significantly/slightly improved in comparison with those of one-step/two-step surfaces respectively; therefore designing for a three-step surface is again unnecessary.

Study of the Electromagnetic Waves Propagation over the Improved Fractal Sea Surface Based on Parabolic Equation Method

An improved fractal sea surface model, which can describe the capillary waves very well, is introduced to simulate the one-dimension rough sea surface. In this model, the propagation of electromagnetic waves (EWs) is computed by the parabolic equation (PE) method using the finite-difference (FD) algorithm. The numerical simulation results of the introduced model are compared with those of the Miller-Brown model and the Elfouhaily spectrum inversion model. It has been shown that the effects of the fine structure of the sea surface on the EWs propagation in the introduced model are more apparent than those in the other two models.

Grazing-incidence small-angle X-ray scattering in a twofold rough-interface medium: a new theoretical approach using the q-eigenwave formalism.

Based on the rigorous Green function formalism to describe the grazing-incidence small-angle X-ray scattering (GISAXS) problem, a system of two linked integral equations is derived with respect to amplitudes of the reflected and transmitted plane q-eigenwaves (eigenstate functions) propagating through two homogeneous media separated from each other by a rough surface interface. To build up the coupled solutions of these basic equations beyond the perturbation theory constraint 2kσθ0 < 1, a simple iteration procedure is proposed as opposed to the self-consistent wave approach [Chukhovskii (2011). Acta Cryst. A67, 200-209; Chukhovski (2012). Acta Cryst. A68, 505-512]. Using the first-order iteration, analytical expressions for the averaged specular and non-specular scattering intensity distributions have been obtained. These expressions are further analysed in terms of the GISAXS parameters {k, θ, θ0} and surface finish ones {σ, l, h}, where θ and θ0 are the scattering and incidence angles of the X-rays, respectively, σ is the root-mean-square roughness, l is the correlation length, h is the fractal surface model index, k = 2π/λ, and λ is the X-ray wavelength. A direct way to determine the surface finish parameters from the experimental specular and diffuse scattering indicatrix scan data is discussed for an example of GISAXS measurements from rough surfaces of α-quartz and CdTe samples.

Numerical modelling of contact heat transfer problem with work hardened rough surfaces

A numerical model of heat conduction in vacuum through contact between two rough bodies made of commercial-purity AD1 aluminium is developed. To this end, the elastic–plastic contact deformation problem is solved accounting strain hardening. A method for consideration of surface initial cold work hardening and indentation size effect (ISE) is provided. Plastic characteristics of surface micro-volumes of material were taken from indentation results. Numerical realisation of the model in ANSYS finite element software is considered. Fractal surface models of two levels of roughness were used. Introduction of the second level roughness (microroughness) to the model was found to have considerable effect on the real contact area only when ISE is taken into account. An attempt to compare simulation results with data obtained with Shlykov’s semi-empirical model was made.

SURFACE FRACTAL DIMENSION OF BENTONITE AND ITS APPLICATION IN CALCULATION OF SWELLING DEFORMATION

The correlation between the void ratio of swelled montmorillonite and the vertical overburden pressure can be expressed as [Formula: see text]. The surface fractal dimension D s of five bentonites were estimated from the swelling deformation tests according to this fractal correlation. The reliability of surface fractal dimension obtained from the swelling deformation test was confirmed by nitrogen adsorption test, with identical values of surface fractal dimension obtained from both tests. The surface fractal dimension can also be used to estimate the swelling deformation of bentonite, after calculating the swelling coefficient K from the parameters of diffuse double layer (DDL) model in the osmotic swelling phase. Comparison of the model predictions with a number of experimental results on swelling deformation of both Na dominant and Ca dominant bentonites suggests that the surface fractal model works excellent in the cases tested.

Performance comparison of detection methods for weak target based on two-dimensional fractal sea surface

A detection method of the weak radar target is studied by applying fuzzy theory and multifractal correlation theory based on a two-dimensional fractal sea surface model. Firstly, a two-dimensional fractal sea surface model and its backscattering coefficient are introduced, the backscattering coefficient is a universal model affected by seawater permittivity, electromagnetic wave incidence angle, incident frequency, wind speed and wind direction factors. A novel two-dimensional wideband radar echo model, which is considered as a time-domain convolution of the stepped frequency signal radiated by airborne radar and the backscattering coefficient, is derived. Secondly, multifractal correlation theory is elaborated and a computation method of a membership degree of multifractal correlation spectrum is proposed, fuzzy theory and the AdaBoost algorithm are applied to the target detection. Finally, several target detection methods are compared with CA-CFAR and works of the predecessors. The results of the comparative study show its rationality of the two-dimensional wideband radar echo model and the superiority of wideband radars in detection performance, it is also seen that the multifractal correlation spectrum outperforms the multifractal spectrum in the probability of detection.

Formation of the magnetic fractal structure in CoSiO2 granular nanocomposite system at percolation threshold

AbstractMagnetic and structural properties of (Co)x(SiO2)1 − x nanocomposite systems have been investigated over a wide range of Co concentrations using small‐angle neutron scattering in combination with magnetic, magneto‐optic, and magneto‐transport characterization. It was found that in the region of structural percolation , the characteristics of magnetically correlated clusters are several times larger than the structural size of Co granules. Starting from the percolation point, the spatial distribution of magnetic nanoclusters can be described by the surface fractal model. With further growth of cobalt concentration x ≥ 0.67 the formation of three‐dimensional (3D) magnetic domains with typical sizes of 1.5 μm was observed.

INVESTIGATION ON THE SCATTERING FROM ONE-DIMENSIONAL NONLINEAR FRACTAL SEA SURFACE BY SECOND-ORDER SMALL-SLOPE APPROXIMATION

In this paper, a one-dimensional nonlinear fractal sea surface model has been established based on the narrow-band Lagrange model, which takes into account the vertical and horizontal skewnesses for the sea surface. By using the method of second-order small-slope approximation (SSA-II), the normalized radar cross section (NRCS) and Doppler spectrum of linear and nonlinear fractal sea surface are calculated. The calculated NRCS of the nonlinear fractal sea surface is larger than the linear surface for backscattering, especially for large incidence angles, which indicates the nonlinear surface has stronger scattering echoes. And the result of nonlinear fractal sea surface is also larger than the linear fractal sea surface for bistatic case, which is characterized as the discrepancies being small near specular direction, while the discrepancies becoming larger as the scattering angles departing from the specular direction. For the Doppler spectrum of sea surface, the nonlinearity of sea surface efiects greatly enhances the Doppler shift and the Doppler spectrum bandwidth at large incidence angles, which are attributed the fact that the nonlinear-wave components propagate faster than the linear-wave components and the nonlinear fractal sea surface corrects the phase velocities by adding the horizontal and vertical skewness. And also, all the results can indicate the validity of this nonlinear model.