Journal articles: 'Fractal mesh'

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Hearst, R. J., and P. Lavoie. "Decay of turbulence generated by a square-fractal-element grid." Journal of Fluid Mechanics 741 (February 17, 2014): 567–84. http://dx.doi.org/10.1017/jfm.2013.684.

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AbstractA novel square-fractal-element grid was designed in order to increase the downstream measurement range of fractal grid experiments relative to the largest element of the grid. The grid consists of a series of square fractal elements mounted to a background mesh with spacing$L_0 = 100\, {\rm mm}$. Measurements were performed in the region$3.5 \le x/L_0 \le 48.5$, which represents a significant extension to the$x/L_0 < 20$of previously reported square fractal grid measurements. For the region$x/L_0 \gtrsim 24$it was found that a power-law decay region following$\langle {q}^2 \rangle \sim (x - x_0)^m$exists with decay exponents of$m = -1.39$and$-1.37$at$\mathit{Re}_{L_0} = 57\, 000$and$65\, 000$, respectively. This agrees with decay values previously measured for regular grids ($-1 \gtrsim m \gtrsim -1.4$). The turbulence in the near-grid region,$x/L_0 < 20$, is shown to be inhomogeneous and anisotropic, in apparent contrast with previous fractal grid measurements. Nonetheless, power-law fits to the decay of turbulent kinetic energy in this region result in$m = -2.79$, similar to$m \approx -2.5$recently reported by Valente & Vassilicos (J. Fluid Mech., vol. 687, 2011, pp. 300–340) for space-filling square fractals. It was also found that$C_\epsilon $is approximately constant for$x/L_0 \ge 25$, while it grows rapidly for$x/L_0 < 20$. These results reconcile previous fractal-generated turbulence measurements with classical grid turbulence measurements.

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Cui, Yan, Jimeng Wang, Chuan Cheng, Bo You, Yong Liu, and Ming Li. "Study on the Particle Surface Fractal Characteristics of Sulfide Ores." Applied Sciences 13, no. 16 (August 12, 2023): 9199. http://dx.doi.org/10.3390/app13169199.

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The fractal dimension is widely used in many fields as a parameter to characterize the geometric complexity and geometric distribution relationship of research objects. To study the surface characteristics of sulfide ore particles, the fractal theory was applied to quantitatively characterize the surface fractal dimension Ds of sulfide ore microparticles in three particle size ranges, 60–100 mesh, 100–140 mesh and >200 mesh, based on the area–perimeter method. Using an optical microscope, grain projection images of the particles were obtained. The grain shape and characteristics of sulfide ore particles were studied by means of an image processing system. The results demonstrate that the grain shape of sulfide ore particles can be expressed by fractal dimension, and the particle surface fractal dimension ranges from 2.4392 to 2.5492. It was found that the fractal properties begin to decrease due to the increasing of the particle size. The larger the fractal dimension, the finer the particles are. The fractal dimension of sulfide ore particles can be used as an important indicator of their particle shape distribution characteristics, which can provide important information for further study of the relevant physical and chemical properties of sulfide ore particles and provide a new theoretical method and basis for the adhesion and removal of sulfide ore dust. With the quantitative description of the fractal distribution of sulfide ore particles, a new way to study the adhesive force between particles is offered for further research.

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PRASAD, SRIJANANI ANURAG, and G. P. KAPOOR. "FRACTAL DIMENSION OF COALESCENCE HIDDEN-VARIABLE FRACTAL INTERPOLATION SURFACE." Fractals 19, no. 02 (June 2011): 195–201. http://dx.doi.org/10.1142/s0218348x11005336.

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In the present paper, the bounds on fractal dimension of Coalescence Hidden-variable Fractal Interpolation Surface (CHFIS) in ℝ3 on a equispaced mesh are found. These bounds determine the conditions on the free parameters for fractal dimension of the constructed CHFIS to become close to 3. The results derived here are tested on a tsunami wave surface by computing the lower and upper bounds of the fractal dimension of its CHFIS simulation.

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Jeng, J. ‐H, V. V. Varadan, and V. K. Varadan. "Fractal finite element mesh generation for vibration problems." Journal of the Acoustical Society of America 79, S1 (May 1986): S51. http://dx.doi.org/10.1121/1.2023267.

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Jeng, J. H., V. V. Varadan, and V. K. Varadan. "Fractal finite element mesh generation for vibration problems." Journal of the Acoustical Society of America 82, no. 5 (November 1987): 1829–33. http://dx.doi.org/10.1121/1.395801.

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Wang, Lei, and Hailong Wang. "Analysis of Uniaxial Compression Mechanical Properties of Rubber Powder Recycled Coarse Aggregate Concrete Based on Strain Energy Theory." Advances in Materials Science and Engineering 2022 (August 30, 2022): 1–19. http://dx.doi.org/10.1155/2022/6767428.

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In order to develop and make full use of waste construction concrete and waste tyre rubber powder, the experiment entirely used recycled coarse aggregate to replace natural crushed stone aggregate and investigated the effect of different mesh sizes of rubber powder (20 mesh, 60 mesh, and 100 mesh) on the uniaxial compressive mechanical properties, strain energy density, and pore structure of recycled coarse aggregate concrete at three curing ages (14 d, 28 d, and 90 d). Based on the strain energy theory, fractal theory, and grey correlation theory, the effects of the fractal dimension of the pore size of the rubber powder recycled concrete on the correlation of the strain energy parameters were investigated at different curing ages. The research results show that as the age period increases, the ability of the rubber powder recycled coarse aggregate concrete to absorb strain energy increases. Before the peak stress, the rubber powder recycled coarse aggregate concrete mainly carries out the storage of elastic strain energy. The incorporation of rubber powder can refine the pore structure of the rubber powder recycled coarse aggregate concrete so that the large pore size pores evolve towards the medium (50–200 μm) or small pores (<50 μm). The fractal dimension analysis revealed that the incorporation of 20 mesh and 60 mesh rubber powder enhances the inhomogeneity of the small pore (<50 μm) and the medium pore (40 μm–140 μm) in the recycled concrete. The grey correlation analysis revealed that the pore size factor with the greatest influence on the elastic energy density was the large pore size (>200 μm).

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Li, Tuanjie, Jie Jiang, Tingting Shen, and Zuowei Wang. "Analysis of mechanical properties of wire mesh for mesh reflectors by fractal mechanics." International Journal of Mechanical Sciences 92 (March 2015): 90–97. http://dx.doi.org/10.1016/j.ijmecsci.2014.11.023.

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Cai, Zhi-Jie, Xi-Qing Zheng, Hui-Qing Lan, Liu-Na Wang, Si-Wei Yang, and Rui Sheng. "Time-Varying Meshing Stiffness and Dynamic Parameter Model of Spiral Bevel Gears with Different Surface Roughness." Applied Sciences 14, no. 4 (February 14, 2024): 1533. http://dx.doi.org/10.3390/app14041533.

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In order to explore the time-varying mesh stiffness and dynamic parameters of bevel gears with different surface roughness, the fractal dimension and characteristic scale coefficient are calculated to determine the fractal dimension of tooth surfaces of spiral bevel gears with rough features. Spiral bevel gears with distinct surface roughness are obtained by simulating the gear-cutting process, and after analysis, a dynamic differential equation for spiral bevel gears considering the surface roughness is proposed. By combining the differential equation with finite element analysis (FEA), the time-varying mesh stiffness of spiral bevel gears with various surface roughness is determined. FEA analysis yields the time-varying mesh stiffness under different surface roughness. The vibration velocity and acceleration of spiral bevel gears with different surface roughness are revealed by combining the time-varying mesh stiffness with the dynamic equation. The intricate relationship between gear surface microstructure and its mechanical behavior during engagement is thoroughly analyzed. A comprehensive dynamic parameter model is proposed to capture the influence of microtopological changes on gear dynamics. The results can offer valuable insights for the design and optimization of bevel gears, aiming to enhance their performance and durability.

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Leung, A. Y. T., G. R. Wu, and W. F. Zhong. "Exterior problems of acoustics by fractal finite element mesh." Journal of Sound and Vibration 272, no. 1-2 (April 2004): 125–35. http://dx.doi.org/10.1016/s0022-460x(03)00322-5.

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Lyu, Chengfu, Xinmao Zhou, Xuesong Lu, Ying Zhang, Chao Li, Qianshan Zhou, Zhaotong Sun, and Guojun Chen. "The Effect of Particle Size on the Interpretation of Pore Structure of Shale by N2 Adsorption." Geofluids 2021 (April 23, 2021): 1–9. http://dx.doi.org/10.1155/2021/8898142.

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Gas adsorption experiments are becoming one of the most common methods to quantify and analyze the pore structures of shale samples in the petroleum industry. In this regard, particle size of the specimen plays an important role in the results that could ultimately affect the pore structure interpretation. Hence, in this study, five shale samples at different thermal maturity levels are picked, and all are crushed into different groups of particle sizes: less than 40 mesh (<375 μm), less than 60 mesh (<250 μm), less than 80 mesh (<187.5 μm), and less than 100 mesh (<150 μm). Next, N2 adsorption is used to characterize the pore structures of the samples within different particle sizes. Furthermore, to interpret the data, several attributes such as the pore volume, surface area, fractal dimension (from the fractal analysis), and heterogeneity index (from the multifractal analysis), are studied and compared between the samples and particle size intervals to provide us with the effect that particle size could have on the pore structure analysis. The results showed that as the particle size varies, the pore structures of the shale samples could get affected. Based on the comparison of the results, it is recommended that a suitable particle size for the shale pore structure characterization in N2 adsorption experiments should be less than 60 mesh (<250 μm).

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TATLIER, MELKON. "FRACTAL GROWTH OF ZEOLITE COATINGS PREPARED BY THE SUBSTRATE HEATING METHOD." Fractals 11, no. 01 (March 2003): 77–85. http://dx.doi.org/10.1142/s0218348x03001501.

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The nature of the zeolite 4A coatings prepared by using the substrate heating method was investigated. It was determined that the fractal dimensions of the surfaces of the coatings varied between about 1.14 and 1.19 with respect to the coating thickness in a mesh size range of about 1.5 μm - 48.5 μm. The fractal dimension value increased to some extent for the thicker zeolite coatings. It is hypothesized that the significance of nucleation is relatively high in the substrate heating method when compared to conventional synthesis methods and this leads to zeolite coatings with fractal surfaces and intercrystal porosity.

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CHAND, A. K. B., and G. P. KAPOOR. "CUBIC SPLINE COALESCENCE FRACTAL INTERPOLATION THROUGH MOMENTS." Fractals 15, no. 01 (March 2007): 41–53. http://dx.doi.org/10.1142/s0218348x07003381.

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This paper generalizes the classical cubic spline with the construction of the cubic spline coalescence hidden variable fractal interpolation function (CHFIF) through its moments, i.e. its second derivative at the mesh points. The second derivative of a cubic spline CHFIF is a typical fractal function that is self-affine or non-self-affine depending on the parameters of the generalized iterated function system. The convergence results and effects of hidden variables are discussed for cubic spline CHFIFs.

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LEUNG, A. Y. T., G. R. WU, and W. F. ZHONG. "FRACTAL TWO-LEVEL FINITE ELEMENT MESH FOR ACOUSTIC SCATTERING PROBLEMS." Journal of Computational Acoustics 11, no. 01 (March 2003): 1–9. http://dx.doi.org/10.1142/s0218396x03001791.

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The problems of acoustic waves scattered by scatterer immersed in unbounded domain is an essential ingredient in the study of acoustic-structure interaction. In this paper the problems of acoustic scattering in an infinite exterior region are investigated by using a fractal two-level finite element mesh with self-similar layers in the media which encloses the conventional finite element mesh for the cavity. The similarity ratio is bigger than one so that the fractal mesh extends to infinity. Because of the self-similarity, the equivalent stiffness (mass) matrix of one layer is proportional to the others. By means of the Hankel functions automatically satisfying Sommerfeld's radiation conditions at infinity, the different unknown nodal pressures on different layers are transformed to some common unknowns of the Hankel coefficients. The set of infinite number of unknowns of nodal pressure is reduced to the set of finite number of Hankel's coefficients. All layers have the same matrix dimension after the transformation and the respective matrices of each layer are summed. Due to the proportionality, the infinite number of layers can be summed in closed form as the entries of each matrix are in geometric series. That is, processing one layer is enough to virtually represent a set of infinite number of layers covering an infinity domain. No new elements are created. Numerical examples show that this method is efficient and accurate in solving unbounded acoustic problems.

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14

Wainer, M. "Generating fractal-like surfaces on general purpose mesh-connected computers." IEEE Transactions on Computers 37, no. 7 (July 1988): 882–86. http://dx.doi.org/10.1109/12.2238.

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Bova, S. W., and G. F. Carey. "Mesh generation/refinement using fractal concepts and iterated function systems." International Journal for Numerical Methods in Engineering 33, no. 2 (January 30, 1992): 287–305. http://dx.doi.org/10.1002/nme.1620330205.

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Wang, Shu Ren, Paul Hagan, and Yan Cheng. "Fractal Characteristics of Sandstone Cutting Fracture under Mechanical Shock Loading Conditions." Applied Mechanics and Materials 226-228 (November 2012): 1789–94. http://dx.doi.org/10.4028/www.scientific.net/amm.226-228.1789.

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It is the key to guide rock-breaking design and engineering practice for how to obtain a reasonable test indicator to assess the cuttability of the rock. Some sandstone samples were tested by using the linear rock cutting machine in the school of mining engineering, University of New South Wales (UNSW), Australia. The curves characteristics for the weight percent of the broken debris with the mesh size distribution were obtained through the screening statistics. Furthermore, the fractal dimension of the specimen broken debris was derived through theoretical calculations and statistical analysis. The results showed that the rock cutting fragmentation is of significant fractal features under the mechanical shock loads. The broken debris fractal dimension of the structural integrity specimens is bigger, the range of the fractal dimension is smaller and the broken debris size distribution is more even than that of the poor structural integrity specimens. The fractal dimension is the ideal test indicator to assess and analysis the rock-breaking degree.

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Nedić, J., and S. Tavoularis. "Measurements of passive scalar diffusion downstream of regular and fractal grids." Journal of Fluid Mechanics 800 (July 7, 2016): 358–86. http://dx.doi.org/10.1017/jfm.2016.385.

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The diffusion of heat injected from a line source into turbulence generated by regular and fractal grids with the same solidity and inlet velocity was investigated experimentally with particular interest in the effects of grid geometry and relative location of the source on the width of the thermal plume and the mixing efficiency. These grids included one fractal square grid (FSG) and three regular square grids with mesh sizes that were comparable to the first (RG160), second (RG80) and fourth (RG18) iterations of the fractal grid. The heated line source was inserted on the centre plane of the grids, spanning the entire width of the wind tunnel at either of two downstream locations, an upstream location or a location nearly coincident with a grid. It was found that, in all cases examined, RG160 produced the strongest diffusion of the thermal plume and the highest level of scalar mixing. These observations were consistent with the evolution of the corresponding turbulent diffusivities, which, according to Taylor’s theory of diffusion, are the product of the transverse turbulence intensity and the integral length scale. We argue that to maximise scalar diffusion and mixing of a scalar released from a concentrated source inside a duct, one should prefer a regular grid over a fractal square grid; we also recommend the use of a grid with a mesh size roughly equal to half the height of the duct and placed at approximately one duct height upstream of the source.

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Comandini, Gianni, Valeska Ting, Mahdi Azarpeyvand, and Fabrizio Scarpa. "Experimental and Numerical Studies on the Hilbert Fractal Architecture as an Acoustic Metamaterial." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 265, no. 5 (February 1, 2023): 2358–61. http://dx.doi.org/10.3397/in_2022_0336.

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Experiments and numerical methods were used to investigate the key parameters which affect the transmission loss behaviour of Hilbert fractal acoustic metamaterials. The tests were conducted using a four-microphone impedance tube, and the numerical simulation was performed using COMSOL Multiphysics software. Fractal order and cavity slot widths on Hilbert fractal metamaterials were investigated. 3D printing manufacturing techniques were used to make polylactic acid specimens. The COMSOL model developed utilised thermo-viscous and lossless domains with boundary layer mesh in the fractal cavities. The tests and simulations' frequency range were 0.2 kHz to 3.0 kHz, with parametric gap widths ranging from 0.5 mm to 3.0 mm. There is a reasonable agreement between the numerical models and the experimental results; the second-order Hilbert fractal had the most significant effect on transmission loss, with an experimental peak of nearly 50 dB around 1600 Hz. Moreover, multiple transmission loss peaks were observed as a function of the gap width in the five Hilbert fractal orders studied. The gap width is one of the critical parameters for optimising the performance of the Hilbert fractal as an acoustic metamaterial.

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Chandler-Wilde, Simon N., David P. Hewett, Andrea Moiola, and Jeanne Besson. "Boundary element methods for acoustic scattering by fractal screens." Numerische Mathematik 147, no. 4 (February 24, 2021): 785–837. http://dx.doi.org/10.1007/s00211-021-01182-y.

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AbstractWe study boundary element methods for time-harmonic scattering in $${\mathbb {R}}^n$$ R n ($$n=2,3$$ n = 2 , 3 ) by a fractal planar screen, assumed to be a non-empty bounded subset $$\Gamma $$ Γ of the hyperplane $$\Gamma _\infty ={\mathbb {R}}^{n-1}\times \{0\}$$ Γ ∞ = R n - 1 × { 0 } . We consider two distinct cases: (i) $$\Gamma $$ Γ is a relatively open subset of $$\Gamma _\infty $$ Γ ∞ with fractal boundary (e.g. the interior of the Koch snowflake in the case $$n=3$$ n = 3 ); (ii) $$\Gamma $$ Γ is a compact fractal subset of $$\Gamma _\infty $$ Γ ∞ with empty interior (e.g. the Sierpinski triangle in the case $$n=3$$ n = 3 ). In both cases our numerical simulation strategy involves approximating the fractal screen $$\Gamma $$ Γ by a sequence of smoother “prefractal” screens, for which we compute the scattered field using boundary element methods that discretise the associated first kind boundary integral equations. We prove sufficient conditions on the mesh sizes guaranteeing convergence to the limiting fractal solution, using the framework of Mosco convergence. We also provide numerical examples illustrating our theoretical results.

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Topoliński, Tomasz, Adam Mazurkiewicz, Stanislaw Jung, Artur Cichański, and Krzysztof Nowicki. "Microarchitecture Parameters Describe Bone Structure and Its Strength Better Than BMD." Scientific World Journal 2012 (2012): 1–7. http://dx.doi.org/10.1100/2012/502781.

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Introduction and Hypothesis. Some papers have shown that bone mineral density (BMD) may not be accurate in predicting fracture risk. Recently microarchitecture parameters have been reported to give information on bone characteristics. The aim of this study was to find out if the values of volume, fractal dimension, and bone mineral density are correlated with bone strength.Methods. Forty-two human bone samples harvested during total hip replacement surgery were cut to cylindrical samples. The geometrical mesh of layers of bone mass obtained from microCT investigation and the volumes of each layer and fractal dimension were calculated. The finite element method was applied to calculate the compression forceFcausingε=0.8% strain.Results. There were stronger correlations for microarchitecture parameters with strength than those for bone mineral density. The values of determination coefficientR2for mean volume and force were 0.88 and 0.90 for mean fractal dimension and force, while for BMD and force the value was 0.53. The samples with bigger mean bone volume of layers and bigger mean fractal dimension of layers (more complex structure) presented higher strength.Conclusion. The volumetric and fractal dimension parameters better describe bone structure and strength than BMD.

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Laizet, S., and J. C. Vassilicos. "Stirring and scalar transfer by grid-generated turbulence in the presence of a mean scalar gradient." Journal of Fluid Mechanics 764 (December 23, 2014): 52–75. http://dx.doi.org/10.1017/jfm.2014.695.

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AbstractThe stirring of a passive scalar by grid-generated turbulence in the presence of a mean scalar gradient is studied by direct numerical simulations (DNS) for six different grids: one fractal square grid with three fractal iterations, one fractal square grid with four fractal iterations, one fractal I grid and three different regular grids. Our results can be summarised as follows. (i) For all these grids, the turbulence intensity averaged over time and over a plane parallel to the grid takes its peak value when the streamwise position of this plane is between $0.75M_{eff}$ and $1.5M_{eff}$ where $M_{eff}$ is the effective mesh size introduced by Hurst & Vassilicos (Phys. Fluids, vol. 19, 2007, 035103). (ii) Downstream of the location of this peak, the turbulence intensity averaged in this way is greatly enhanced by the fractal grids relative to the regular grids even though the fractal grids have comparable or even lower blockage ratios. The novelty of this result lies in the fact that it concerns turbulence intensities averaged over lateral planes (as well as time). (iii) The pressure drop is about the same across grids of the same blockage ratio whether fractal or not, but the pressure recovery is longer for the fractal grids. (iv) Even so, the fractal grids enhance turbulent scalar fluxes by up to an order of magnitude in the region downstream of the aforementioned peak and they also greatly enhance the streamwise growth of the fluctuating scalar variance in that region. (v) We demonstrate on a simple planar model problem that the cause of this phenomenon lies in the fractality of the grids. (vi) The turbulence scalar flux coefficient is constant far enough downstream of all the present grids and is significantly dependent on the nature and details of the turbulence-generating grid.

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Liao, Renkuan, Shumei Ren, and Peiling Yang. "Quantitative Fractal Evaluation of Herbicide Effects on the Water-Absorbing Capacity of Superabsorbent Polymers." Journal of Nanomaterials 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/905630.

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The water absorption capacity of superabsorbent polymers (SAPs) is important for agricultural drought resistance. However, herbicides may leach into the soil and affect water absorption by damaging the SAP three-dimensional membrane structures. We used 100-mesh sieves, electron microscopy, and fractal theory to study swelling and water absorption in SAPs in the presence of three common herbicides (atrazine, alachlor, and tribenuron-methyl) at concentrations of 0.5, 1.0, and 2.0 mg/L. In the sieve experiments it was found that 2.0 mg/L atrazine reduces the capacity by 9.64–23.3% at different swelling points; no significant diminution was observed for the other herbicides or for lower atrazine concentrations. We found that the hydrogel membrane pore distributions have fractal characteristics in both deionized water and atrazine solution. The 2.0 mg/L atrazine destroyed the water-retaining polymer membrane pores and reduced the water-absorbing mass by modifying its three-dimensional membrane structure. A linear correlation was observed between the fractal analysis and the water-absorbing mass. Multifractal analysis characterized the membrane pore distribution by using the range of singularity indexes Δα(relative distinguishing range of 16.54–23.44%), which is superior to single-fractal analysis that uses the fractal dimensionD(relative distinguishing range of 2.5–4.0%).

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Zhu, Xuegui, Yi Wang, Jianming Zan, and Chuanbing Li. "Application of fractal theory in generation and refinement of finite element mesh." Applied Mathematics and Computation 175, no. 2 (April 2006): 1039–45. http://dx.doi.org/10.1016/j.amc.2005.08.017.

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Hiekel, Karl, Swetlana Jungblut, Maximilian Georgi, and Alexander Eychmüller. "Tailoring the Morphology and Fractal Dimension of 2D Mesh‐like Gold Gels." Angewandte Chemie 132, no. 29 (May 18, 2020): 12146–52. http://dx.doi.org/10.1002/ange.202002951.

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Hiekel, Karl, Swetlana Jungblut, Maximilian Georgi, and Alexander Eychmüller. "Tailoring the Morphology and Fractal Dimension of 2D Mesh‐like Gold Gels." Angewandte Chemie International Edition 59, no. 29 (May 18, 2020): 12048–54. http://dx.doi.org/10.1002/anie.202002951.

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Liu, Zhifeng, Tao Zhang, Yongsheng Zhao, and Shuxin Bi. "Time-varying stiffness model of spur gear considering the effect of surface morphology characteristics." Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering 233, no. 2 (May 12, 2018): 242–53. http://dx.doi.org/10.1177/0954408918775955.

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The nonuniform cantilever beam and Hertzian contact model have been widely used to derive the mesh stiffness of spur gear assuming that the contact surface is absolutely frictionless. However, studies have confirmed that machined surfaces are rough in microscale and can be simulated by the Weierstrass–Mandelbort function. In order to get a reasonable and precise mesh stiffness model, the M-B contact model and finite element method are combined to express the local contact stiffness Kh. Through the simulation and comparison, the analytical finite element method is proved to be consistent with the traditional models and introduces the roughness parameters of machined tooth surface into the meshing process. Furthermore, the results also show that it is advantageous to improve the total mesh stiffness by increasing the fractal dimension D and input torque T as well as decreasing the roughness parameter G. In this paper, a relationship is built between the total mesh stiffness of gear sets with tooth surface characters and input torque, which can be a guidance in the design of the tooth surface parameters and the choice of the processing method in the future.

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Huang, Li-jing, Meng Zhang, Zi-yan Wang, Shuai-yu Zhao, Hui Ji, and Bao-jia Li. "Fabrication of fractal Ag mesh/FTO transparent electrodes/heaters with enhanced electrical conductivity based on mesh hierarchy and shape optimization." Optics & Laser Technology 168 (January 2024): 109895. http://dx.doi.org/10.1016/j.optlastec.2023.109895.

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Feng, ZhiYong, ZhiQing Wei, QiXun Zhang, and Ping Zhang. "Fractal theory based dynamic mesh grouping scheme for efficient cognitive pilot channel design." Chinese Science Bulletin 57, no. 28-29 (September 28, 2012): 3684–90. http://dx.doi.org/10.1007/s11434-012-5369-7.

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Choi, Jinwoo, Daecheon Lim, and Sungjoon Lim. "Screen-Printed Metamaterial Absorber Using Fractal Metal Mesh for Optical Transparency and Flexibility." Fractal and Fractional 8, no. 5 (May 9, 2024): 284. http://dx.doi.org/10.3390/fractalfract8050284.

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In stealth applications, there is a growing emphasis on the development of radar-absorbing structures that are efficient, flexible, and optically transparent. This study proposes a screen-printed metamaterial absorber (MMA) on polyethylene terephthalate (PET) substrates using indium tin oxide (ITO) as the grounding layer, which achieves both optical transparency and flexibility. These materials and methods enhance the overall flexibility and transparency of MMA. To address the limited transparency caused by the silver nanoparticle ink for the top pattern, a metal mesh was incorporated to reduce the area ratio of the printed patterns, thereby enhancing transparency. By incrementing the fractal order of the structure, we optimized the operating frequency to target the X-band, which is most commonly used in radar detection. The proposed MMA demonstrates remarkable performance, with a measured absorption of 91.99% at 8.85 GHz and an average optical transmittance of 46.70% across the visible light spectrum (450 to 700 nm), indicating its potential for applications in transparent windows or drone stealth.

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Yue, Zhong Wen, Hui Zhang, Bo Yang Dou, and Peng Fei Han. "Experimental Study on Microcosmic and Microscopic Properties of C100 High-Strength Concrete." Advanced Materials Research 168-170 (December 2010): 2529–32. http://dx.doi.org/10.4028/www.scientific.net/amr.168-170.2529.

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In order to study high strength and other characteristics of high strength concrete, scanning electron microscopy and mercury pressure method were used to analysis the surface morphology, organization, structure, composition and fractal features of C100 high strength concrete materials in terms of the microscopic mechanism, and the material strengthen mechanism and the causes of failure were revealed. The results shows that, as the adequate hydration and particle hydrates increase in C100 concrete, more gel-like mesh or wrinkles are generated, and there is a strong bonding effect between fine particles. As the use of mixing composites material in C100 high strength concrete, the density of the material is improved and the proportion of harmful hole is lowed, and its mechanical properties and durability are all improved. When concrete is damaged, cracks increase and coalescence show an increase of fractal value.

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Zhao, Zhifang, Yang Yang, Hongzheng Han, Hui Ma, Haixu Wang, and Zhanwei Li. "Meshing Characteristics of Spur Gears Considering Three-Dimensional Fractal Rough Surface under Elastohydrodynamic Lubrication." Machines 10, no. 8 (August 17, 2022): 705. http://dx.doi.org/10.3390/machines10080705.

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Taking the effect of actual surface topography under elastohydrodynamic lubrication (EHL) conditions on the contact state of gear pairs into consideration, a combination model with the analytical sliced method and two-dimensional (2D) EHL model is proposed to characterize the three-dimensional (3D) meshing characteristics of spur gears. Firstly, the surface topology of gears is tested by a surface profiler, which reflects that the topography of tooth surface accords with fractal characteristics. Thus, by adopting the Weierstrass–Mandelbrot (W-M) fractal function, the gear surface is characterized. Secondly, the numerical 2D EHL model with fractal roughness is established, and distributions of oil film pressure (OFP) and oil film thickness (OFT) at different meshing positions are obtained. Finally, considering the different topography distributions in the direction of face width, time-varying mesh stiffness (TVMS) is calculated based on the analytical sliced method. Thus, the influence of 3D surface topography can be considered. The Hertz contact stiffness is substituted by the time-varying lubricating oil film stiffness (OFS). The influences of tooth surface topography and lubricant film characteristics on meshing characteristics are investigated. The results show that the 3D rough tooth surface may be well characterized by a fractal function with random phase. Moreover, there is a great difference in the distribution of OFP and OFT between rough and smooth surfaces, which certainly influences the gear meshing characteristics.

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Jiang, Wei, Cuicui Ji, Hengjing Huang, Dandan Zhang, Yuntian Dai, and Daixi Feng. "Fractal Analysis of the Influence of Mesh Number of Sandpaper on Simulated Wear Process." IOP Conference Series: Materials Science and Engineering 439 (November 5, 2018): 032102. http://dx.doi.org/10.1088/1757-899x/439/3/032102.

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Buzzi, Rueter, Ghermandi, and Lasaponara. "The Extent of Infrastructure Causing Fragmentation in the Hydrocarbon Basin in the Arid and Semi-Arid Zones of Patagonia (Argentina)." Sustainability 11, no. 21 (October 25, 2019): 5956. http://dx.doi.org/10.3390/su11215956.

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Fragmentation is a disruption in the connectivity of landscapes. The aims of this paper are (i) to quantitatively assess the fragmentation rates in three landscape units located in a hydrocarbon basin, and (ii) to model their behavior between 2001 and 2013 using landscape metrics at different scales of resolution. The following metrics were selected using principal component analysis (PCA): The Clumpiness Index (CLUMPY), patch density (PD), perimeter-area fractal dimension (PAFRAC) and effective mesh size (MESH). Results from our investigations pointed out that hydrocarbon activity increased the fragmentation at the sites. In particular, the CLUMPY index increased in all three landscape units, the average of PD decreased from 60 to 14 patches per 100 hectares, whereas the mean of MESH was quite constant, however, due to oil production, it decreased mainly in the coastal valleys. Finally, the PAFRAC also decreased at sites with oil production, being more evident in the plateau and coastal canyons. As a whole, outputs from our analyses clearly pointed out that the monitoring of landscape fragmentation trends in arid and semi-arid zones can be successfully achieved using metrics derived from satellite spectral information.

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Qi, Hua Mei, Min Wu, and Zhi Gang Chen. "On Upper Bound of the Quality of Service Performance in the Gateway of Wireless Mesh Networks." Advanced Materials Research 403-408 (November 2011): 2697–703. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.2697.

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Motivated by the advantage of the gateway that acts as the performance bottleneck in wireless mesh networks (WMNs) while shaping the traffic with the greedy fractal shaper, a novel approach is proposed to derive the upper stochastic/statistical bound of the backlog, delay and delay jitter of the WMNs gateway quality of service (QoS) statistic bound model. By analyzing and evaluating the QoS performance of the present model based on network calculus theory with fair bandwidth distributed strategy, a number of useful curves are achieved. Simulation shows the performance of the present model.

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Bickel, David R., and Bruce J. West. "Multiplicative and Fractal Process in DNA Evolution." Fractals 06, no. 03 (September 1998): 211–17. http://dx.doi.org/10.1142/s0218348x98000262.

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Darwin's theory of evolution by natural selection revolutionized science in the nineteenth century. Not only did it provide a new paradigm for biology, the theory formed the basis for analogous interpretations of complex systems studied by other disciplines, such as sociology and psychology. With the subsequent linking of macroscopic phenomena to microscopic processes, the Darwinian interpretation was adopted to patterns observed in molecular evolution by assuming that natural selection operate fundamentally at the level of DNA. Thus, patterns of molecular evolution have important implications in many fields of science. Although the evolution rate of a given gene seems to be of approximately the same order of magnitude in all species, genes appear to differ in rate from one another by orders of magnitude, a fact which standard theory does not adequately explain. An understanding of the statistics of rates across different genes may shed light on this problem. The evolution rates of mammalian DNA, based on recent estimates of numbers of nonsynonymous substitutions in 49 genes of human, rodents, and artiodactyls, are studied. We find that the rate variations are better described by lognormal statistics, as would be the case for a multiplicative process, than by Gaussian statistics, which would correspond to a linear, additive process. Thus, we introduce a multiplicative evolution statistical hypothesis (MESH), in which the theoretical explanation of these statistics requires the evolution of different substitution rates in different genes to be a multiplicative process in that each rate results from the interaction of a number of interdependent contingency processes.

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Santos, Vanessa Cristina Dos, Mhamad El Hage, Laurent Polidori, and José Cândido Stevaux. "EFFECT OF DIGITAL ELEVATION MODEL MESH SIZE ON GEOMORPHIC INDICES: A CASE STUDY OF THE IVAÍ RIVER WATERSHED - STATE OF PARANÁ, BRAZIL." Boletim de Ciências Geodésicas 23, no. 4 (December 2017): 684–99. http://dx.doi.org/10.1590/s1982-21702017000400045.

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Abstract: Geomorphometry is the science of quantitative description of land surface morphology by the mean of geomorphic indices extracted from Digital Elevation Models (DEMs). The analysis of these indices is the first and most common procedure performed in several geoscience-related subjects. This study aims to assess the impact of mesh size degradation on different local and regional geomorphic indices extracted for GDEM and TOPODATA DEMs. Thus, these DEMs, having a mesh size of 30 m, were subsampled to 60, 120 and 240 m and then geomorphic indices were calculated using the full resolution DEM and the subsampled ones. Depending on their behavior, these indices are then classified into stable and unstable. The results show that the most affected indices are slope and hydrographic indices such as Strahler order, stream sinuosity and fractal dimension and watershed perimeter, whereas elevation remains stable. It also shows that the effect depends on the presence of the canopy and geological structures in the studied area.

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Koňas, Petr. "3D visualization and finite element mesh formation from wood anatomy samples, Part II – Algorithm approach." Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis 57, no. 1 (2009): 79–88. http://dx.doi.org/10.11118/actaun200957010079.

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Paper presents new original application WOOD3D in form of program code assembling. The work extends the previous article “Part I – Theoretical approach” in detail description of implemented C++ classes of utilized projects Visualization Toolkit (VTK), Insight Toolkit (ITK) and MIMX. Code is written in CMake style and it is available as multiplatform application. Currently GNU Linux (32/64b) and MS Windows (32/64b) platforms were released. Article discusses various filter classes for image filtering. Mainly Otsu and Binary threshold filters are classified for anatomy wood samples thresholding. Registration of images series is emphasized for difference of colour spaces compensation is included. Resulted work flow of image analysis is new methodological approach for images processing through the composition, visualization, filtering, registration and finite element mesh formation. Application generates script in ANSYS parametric design language (APDL) which is fully compatible with ANSYS finite element solver and designer environment. The script includes the whole definition of unstructured finite element mesh formed by individual elements and nodes. Due to simple notation, the same script can be used for generation of geometrical entities in element positions. Such formed volumetric entities are prepared for further geometry approximation (e.g. by boolean or more advanced methods). Hexahedral and tetrahedral types of mesh elements are formed on user request with specified mesh options. Hexahedral meshes are formed both with uniform element size and with anisotropic character. Modified octree method for hexahedral mesh with anisotropic character was declared in application. Multicore CPUs in the application are supported for fast image analysis realization. Visualization of image series and consequent 3D image are realized in VTK format sufficiently known and public format, visualized in GPL application Paraview. Future work based on mesh improvement through mesh error statistic, image acquisition and thresholding improvement by more sophisticated filters together with code optimization for fast image analysis is discussed. Also fractal characteristics classification on microscopic scale level is taken into account for further work.

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Li, Wei, and Xin Gong. "Generation of Digital Art Composition Using a Multilabel Learning Algorithm." Mathematical Problems in Engineering 2021 (September 9, 2021): 1–8. http://dx.doi.org/10.1155/2021/3462846.

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The traditional methods for generating digital art composition have the disadvantage of capturing incomplete geometric information, which leads to obvious defects in the generation results. Therefore, a digital art composition generation method based on the multilabel learning algorithm is proposed in this research. Firstly, a preset series of grids are prepared to generate sampling and fractal pixels on the drawing base. Then, the preset grid construction is constructed by the interactive program of the preset grid library. After the stroke is drawn by the user, the actual motion trajectory of the pen is sampled by the digital panel, and the stroke information in the motion trajectory is obtained by the multilabel learning algorithm. Next, the steps of generating art composition are designed, including generating the skeleton of art composition, generating the geometric network structure of the skeleton, generating the sampling pixel and connecting the fractal pixel, and initializing other attributes of the mesh. Experimental results show that the proposed method has higher sampling rate and geometric information capture rate and has better application performance and prospect.

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Sun, Jianlei, and David Schechter. "Optimization-Based Unstructured Meshing Algorithms for Simulation of Hydraulically and Naturally Fractured Reservoirs With Variable Distribution of Fracture Aperture, Spacing, Length, and Strike." SPE Reservoir Evaluation & Engineering 18, no. 04 (November 25, 2015): 463–80. http://dx.doi.org/10.2118/170703-pa.

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Summary Multistage hydraulically fractured wells are applied widely to produce unconventional resource plays. In naturally fractured reservoirs, hydraulic-fracture treatments may induce complex-fracture geometries that one cannot model accurately and efficiently with Cartesian and corner-point grid systems or standard dual-porosity approaches. The interaction of hydraulic and naturally occurring fractures almost certainly plays a role in ultimate well and reservoir performance. Current simulation models are unable to capture the complexity of this interaction. Generally speaking, our ability to detect and characterize fracture systems is far beyond our capability of modeling complex natural-fracture systems. To evaluate production performance in these complex settings with numerical simulation, fracture networks require advanced meshing and domain-discretization techniques. This paper investigates these issues by developing natural-fracture networks with fractal-based techniques. After a fracture network is developed, we demonstrate the feasibility of gridding complex natural-fracture behavior with optimization-based unstructured meshing algorithms. Then we can demonstrate that one can simulate natural-fracture complexities such as variable aperture, spacing, length, and strike. This new approach is a significant step beyond the current method of dual-porosity simulation that essentially negates the sophisticated level of fracture characterization pursued by many operators. We use currently established code for fractal discrete-fracture-network (FDFN) models to build realizations of naturally fractured reservoirs in terms of stochastic fracture networks. From outcrop, image-log, and core analysis, it is possible to extract fracture fractal parameters pertaining to aperture, spacing, and length distribution, including center distribution as well as a fracture strike. Then these parameters are used as input variables for the FDFN code to generate multiple realizations of fracture networks mimicking fracture clustering and randomly distributed natural fractures. After incorporating hydraulic fractures, complex-fracture networks are obtained for further reservoir-domain discretization. To discretize the complex-fracture networks, a new mesh-generation approach is developed to conform to nonorthogonal and low-angle intersections of extensively clustered discrete-fracture networks with nonuniform aperture distribution. Optimization algorithms are adopted to reduce highly skewed cells, and to ensure good mesh quality around fracture tips, intersections, and regions of extensive fracture clustering. Moreover, local grid refinement is implemented with a predefined distance function to control cell sizes and shapes around and far away from fractures. Natural-fracture spacing, length, strike, and aperture distribution are explicitly gridded, thus introducing a new simulation approach that is far superior to dual-porosity simulation. Finally, initial sensitivity studies are performed to demonstrate both the capability of the optimization-based unstructured meshing algorithms, and the effect of aforementioned natural-fracture parameters on well performance. This study demonstrates how to incorporate a fractal-based characterization approach into the current work flow for simulating unconventional reservoirs, and most importantly solves several issues such as nonorthogonal intersections, extensive clustering, and nonuniform aperture distribution associated with domain discretization with unstructured grids for complex-fracture networks. The proposed meshing techniques for complex fracture networks can be easily implemented in existing preprocessing, unstructured mesh generators. The sensitivity study and the simulation runs demonstrate the importance of fracture characterization as well as uncertainties associated with naturally fractured reservoirs on well-production performance.

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Eichler, Jan, Pavel Hazdra, Miloslav Capek, and Milos Mazanek. "Modal Resonant Frequencies and Radiation Quality Factors of Microstrip Antennas." International Journal of Antennas and Propagation 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/490327.

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The chosen rectangular and fractal microstrip patch antennas above an infinite ground plane are analyzed by the theory of characteristic modes. The resonant frequencies and radiationQare evaluated. A novel method by Vandenbosch for rigorous evaluation of the radiationQis employed for modal currents on a Rao-Wilton-Glisson (RWG) mesh. It is found that the resonant frequency of a rectangular patch antenna with a dominant mode presents quite complicated behaviour including having a minimum at a specific height. Similarly, as predicted from the simple wire model, the radiationQexhibits a minimum too. It is observed that the presence of out-of-phase currents flowing along the patch antenna leads to a significant increase of theQfactor.

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Lehane, James R., and A. A. Ekdale. "Analytical tools for quantifying the morphology of invertebrate trace fossils." Journal of Paleontology 88, no. 4 (July 2014): 747–59. http://dx.doi.org/10.1666/13-080.

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The analysis of trace fossils usually is performed qualitatively, which makes comparing trace fossils from different units less objective than quantitative approaches. Quantifying the shape of trace fossils enables scientists to compare trace fossils described by different people with greater precision and accuracy. This paper describes several methods for quantifying invertebrate trace fossils, including morphology dependent methods (motility index, mesh size, topology, tortuosity, branching angle, and the number of cell sides) and morphology independent methods (fractal analysis, burrow area shape, and occupied space percentage (OSP)). These tools were performed on a select group of graphoglyptid trace fossils, highlighting the benefits and flaws of each analytical approach. Combined together, these methods allow for more objective comparisons between different trace fossils.

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Valente, P. C., and J. C. Vassilicos. "The decay of turbulence generated by a class of multiscale grids." Journal of Fluid Mechanics 687 (October 12, 2011): 300–340. http://dx.doi.org/10.1017/jfm.2011.353.

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AbstractA new experimental investigation of decaying turbulence generated by a low-blockage space-filling fractal square grid is presented. We find agreement with previous works by Seoud & Vassilicos (Phys. Fluids, vol. 19, 2007, 105108) and Mazellier & Vassilicos (Phys. Fluids, vol. 22, 2010, 075101) but also extend the length of the assessed decay region and consolidate the results by repeating the experiments with different probes of increased spatial resolution. It is confirmed that this moderately high Reynolds number${\mathit{Re}}_{\lambda } $turbulence (up to${\mathit{Re}}_{\lambda } \simeq 350$here) does not follow the classical high Reynolds number scaling of the dissipation rate$\varepsilon \ensuremath{\sim} {u{}^{\ensuremath{\prime} } }^{3} / L$and does not obey the equivalent proportionality between the Taylor-based Reynolds number${\mathit{Re}}_{\lambda } $and the ratio of integral scale$L$to the Taylor microscale$\lambda $. Instead we observe an approximate proportionality between$L$and$\lambda $during decay. This non-classical behaviour is investigated by studying how the energy spectra evolve during decay and examining how well they can be described by self-preserving single-length-scale forms. A detailed study of homogeneity and isotropy is also presented which reveals the presence of transverse energy transport and pressure transport in the part of the turbulence decay region where we take data (even though previous studies found mean flow and turbulence intensity profiles to be approximately homogeneous in much of the decay region). The exceptionally fast turbulence decay observed in the part of the decay region where we take data is consistent with the non-classical behaviour of the dissipation rate. Measurements with a regular square mesh grid as well as comparisons with active-grid experiments by Mydlarski & Warhaft (J. Fluid Mech., vol. 320, 1996, pp. 331–368) and Kang, Chester & Meveneau (J. Fluid Mech., vol. 480, 2003, pp. 129–160) are also presented to highlight the similarities and differences between these turbulent flows and the turbulence generated by our fractal square grid.

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Davis, Kristofer, and Yaoguo Li. "Efficient 3D inversion of magnetic data via octree-mesh discretization, space-filling curves, and wavelets." GEOPHYSICS 78, no. 5 (September 1, 2013): J61—J73. http://dx.doi.org/10.1190/geo2012-0192.1.

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Airborne magnetic survey data sets can contain from hundreds of thousands to millions of observations and typically cover large areas. The large number of measurements combined with a model mesh to accommodate the survey extent can render an inversion of these data intractable. Faced with this challenge, we have developed a three-step procedure to locally optimize the degree of model discretization and to compress the corresponding sensitivity matrix for the inversion of magnetic data. The mesh optimization is achieved through the use of adaptive octree discretization. The compression is achieved by first reordering the model cells using the Hilbert space filling curve and then applying the one-dimensional wavelet transform to the corresponding sensitivities. The fractal property of the Hilbert curve groups the spatially adjacent cells into algebraically adjacent positions in the reordered model mesh and thereby maximizes the number of zero or near-zero coefficients in the one-dimensional wavelet transform. Winnowing these insignificant coefficients finally leads to a highly sparse representation of the sensitivity matrix, which dramatically reduces the required memory and CPU time in the inversion. As a result, the proposed algorithm is capable of inverting huge data sets ([Formula: see text] measurements) with commensurate model sizes in a short time on a single desktop computer. As a test, we inverted an entire magnetic data set with 170,000 observations from a large uranium exploration program and achieved a reduction in computational cost exceeding 10,000 times.

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Pratiwi, Indah, and Edy Sanwani. "Studi pengaruh penggilingan kondisi kering dan basah terhadap kinetika dan karakteristik distribusi ukuran butir bijih sulfida kompleks galena sfalerit – Uji pendahuluan." Jurnal Teknologi Mineral dan Batubara 19, no. 2 (2023): 125–39. http://dx.doi.org/10.30556/jtmb.vol19.no2.2023.1452.

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Grinding is generally carried out in wet conditions, but issues regarding water conservation and high-water treatment costs encourage the application of grinding in dry conditions. Both produce products with certain characteristics that affect the success of the next process. Grinding of P100 6 mesh (3.36 mm) ore was performed using steel ball media with dry and wet grinding with 33.33% solids for 5, 10, 15, 20, 25, and 30 minutes. Particle size distribution of the grinding product was obtained from the wet sieving process and the -200 mesh (-75µm) ore particles were analyzed using a laser diffraction particle size analyzer. The Alyavdin grinding kinetics equation model was used to study the kinetics of ore grinding behavior and the particle size distribution and its characteristics consisting of uniformity index, size modulus and fractal dimension were studied using the logistic, Rosin-Rammler (RR) and Gates-Gaudin-Schuhmann (GGS) equation model. Equivalent particle size (EPS) and specific surface area (SSA) observations were carried out on the -200 mesh (-75µm) grinding product. Grinding in dry condition is more effective in reducing the size of complex galena-sphalerite sulphide ore, indicated by high grinding rate with the highest K value of 0,135/minute, high cummulative % undersize, low size modulus, high uniformity index, high fine particle and high SSA compared to wet grinding. Alyavdin's kinetics model can describe the grinding kinetics of galena sphalerite complex sulfide ore, while the particle size distribution follows the logistic equation model.

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Chipizubov, V. V., P. N. Sukhonin, and V. V. Petrash. "Prospects for the use of porous composite materials in products for respiratory protection from viral and bacterial infections." Bulletin of the Medical Institute "REAVIZ" (REHABILITATION, DOCTOR AND HEALTH), no. 1 (April 13, 2021): 11–16. http://dx.doi.org/10.20340/vmi-rvz.2021.1.covid.2.

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The effectiveness of cleaning the air flow from the droplet and dispersed phases of liquids, which are the main medium for transporting most respiratory viruses from the carrier to the infected person, was assessed. Samples of Cribrol, polymer composite with a three-dimensional fractal mesh structure of through and non-through pores from 5 to 150 μm, were examined. The experiments showed high hygroscopic properties of this material, providing moisture absorption of more than 700 % of the dry weight of the test sample. It has been found that Cribrol can undergo thermal decontamination in heating devices and can be used repeatedly. This material has been concluded to be promising for use in PPE, and its structure can easily be adapted to various respiratory personal protective equipment (PPE).

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Jin, Ming Sheng, Shi Ming Ji, Li Zhang, Xian Zhang, and Ya Qi Shen. "Effect of Free Abrasive Particle in Gasbag Polishing Technique." Advanced Materials Research 69-70 (May 2009): 83–87. http://dx.doi.org/10.4028/www.scientific.net/amr.69-70.83.

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Free abrasive particle plays a crucial role in material removal and quality improvement of curved surface mould. In order to observe and investigate the general distribution state, fractal dimension and movement characteristic of abrasive particle in gasbag polishing process better, an abrasive particle stroboscopic photography system is established and polishing experiment is carried out. The abrasive particle contacts with not only the rubber gasbag enwrapped by polishing cloth full of mesh-like structures, but also the mould surface. Contact analysis of abrasive particle including the discussions of contact state, material removal mechanism and advantage of precession polishing is helpful to hold the optimal polishing process parameters combination and establish ideal abrasive particle field for higher polishing efficiency and more well-proportioned surface quality.

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Chen, Yufeng, Zhengtao Xiang, Yabo Dong, and Dongming Lu. "Multi-Fractal Characteristics of Mobile Node’s Traffic in Wireless Mesh Network with AODV and DSDV Routing Protocols." Wireless Personal Communications 58, no. 4 (December 25, 2009): 741–57. http://dx.doi.org/10.1007/s11277-009-9904-z.

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Scholz, Christopher H. "A further note on earthquake size distributions." Bulletin of the Seismological Society of America 88, no. 5 (October 1, 1998): 1325–26. http://dx.doi.org/10.1785/bssa0880051325.

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Abstract At the scale range of 1 to 10 km, faults are not continuous surfaces but are tabular bodies composed of a mesh of subparallel unconnected strands, or subfaults. The cumulative length distribution of these subfaults is observed to be a power law with an approximate exponent of −2 and an upper fractal limit at W*, the seismogenic width. If it is assumed that small earthquakes, with lengths L ≤ W*, represent the rupture of these subfaults, this offers a physical explanation for small earthquakes having their observed power-law distribution with exponent −2/3. This further implies that any earthquake will be composed of a population of subevents involving the rupture of this population of subfaults: precisely what was proposed by Frankel (1991) to explain the ω−2 high-frequency falloff of earthquake displacement spectra.

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Moroz, L. I., and A. G. Maslovskaya. "Fractional-Differential Model of Heat Conductivity Process in Ferroelectrics under the Intensive Heating Conditions." Mathematics and Mathematical Modeling, no. 2 (July 20, 2019): 29–47. http://dx.doi.org/10.24108/mathm.0219.0000185.

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Ferroelectrics, due a number of characteristics, behave as hereditary materials with fractal structure. To model mathematically the systems with so-called memory effects one can use the fractional time-derivatives. The pyro-electric properties of ferroelectrics arouse interest in developing the fractional-differential approach to simulating heat conductivity process.The present study deals with development and numerical implementation of fractal heat conductivity model for hereditary materials using the concepts of fractional-differential calculus applied to the simulation of intensive heating processes in ferroelectrics.The paper proposes a mathematical model governed through mixed initial-boundary value problem for partial differential equation containing a fractional time-derivative as well as nonlinear temperature dependence on the heat capacity. To solve the problem the computational algorithm was designed which is based on an analog of the Crank – Nicolson finite difference scheme combining with the Grunwald – Letnikov formula for fractional time-derivative approximation. The approximation of Neumann boundary condition is included into the finite difference problem statement using scheme of fictitious mesh points. The total system of linear algebraic equations is solved by sweep method.The designed application program allows one to perform the computer simulation of heat conductivity process in hereditary materials. The model verification was performed for numerical solving test problem with known analytical solution. The results of computational experiments are demonstrated for the example of estimating heat distribution in a typical ferroelectric crystal of TGS (triglycine sulfate) near the temperature of phase transition. The fractional derivative order was approximately evaluated to be ~0.7 at variation of this parameter. We applied the comparison of fractal model implementation results with experimental data related to the time when the ferroelectric crystal is heated to Curie temperature. These findings demonstrate that one needs to use the modified models at the analysis of the field effects arising in hereditary materials.

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Li, Rong, Xin Xiong, Jun Ma, and Mengting Zou. "Effects of Macro-Pitting Fault on Dynamic Characteristics of Planetary Gear Train Considering Surface Roughness." Actuators 13, no. 1 (December 19, 2023): 1. http://dx.doi.org/10.3390/act13010001.

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The planetary gearbox plays a vital role in a wide range of mechanical power transmission systems, including high-speed trains, wind turbines, vehicles, and aircraft. At the same time, the planetary gear train inside the gearbox is regarded as the most susceptible to failure in the entire transmission system. To analyze the influence of surface roughness on the dynamic characteristics of the planetary gear train, a dynamic modeling method based on fractal theory is proposed. Firstly, the tooth surface contact model was established based on the W-M fractal function, and the time-varying mesh stiffness (TVMS) of the planetary gear train was calculated under healthy and tooth macro-pitting. Then, the lumped-parameter method is introduced to construct a planetary gear train translation-torsion dynamic model that comprehensively considers TVMS and tooth backlash. The vibration acceleration signals of the planetary gear train under different macro-pitting states and surface roughness are simulated and calculated, allowing a quantificative analysis of the influence of surface roughness on system vibration response. Finally, the correctness of the model for the planetary gear train is verified by experiments. The results show that compared with the planetary gear train modeling method based on Hertz contact theory, the root mean squared error of the vibration signal of this work under a macro-pitting fault state is reduced by 8.7%, further improving the reliability of the model.

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Journal articles on the topic 'Fractal mesh'

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