Academic literature on the topic 'Fractal mesh'
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Journal articles on the topic "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).
Dissertations / Theses on the topic "Fractal mesh"
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Pali, Esso-Passi. "Modélisation des phénomènes de coalescence des fissures sous pression associés au procédé Smart CutTM." Electronic Thesis or Diss., Lyon, INSA, 2023. http://www.theses.fr/2023ISAL0108.
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L'approche numérique X-FEM a été utilisée pour modéliser le phénomène de rupture par coalescence des fissures sous pression au sein du procédé Smart Cut.Le maillage fractal a été implémenté pour prendre en compte la différence d'échelle des échantillons représentatifs de substrats SOI modélisés. Ce type de maillage adaptatif permet de réduire le nombre d’éléments sur le maillage global tout en garantissant une bonne précision sur les champs mécaniques calculés au voisinage des fissures grâce à la finesse locale du maillage; en conséquence, un gain en temps de calcul CPU de plus de 90% a été obtenu avec ce maillage fractal par rapport à un maillage régulier équivalent. Une procédure a également été implémenté dans Cast3M pour générer ce type de maillage en boite noire. Afin d'extraire les facteurs d'intensité des contraintes (FICs) au front de la fissure sous pression interne, l'intégrale d’interaction a été modifiée pour prendre en compte le terme supplémentaire correspondant aux champs de pression appliqués sur les faces de la fissure; la procédure de calcul des FICs dans Cast3M a ainsi été adaptée et les résultats obtenus ont été validés par comparaison avec la solution analytique pour une fissure circulaire dans un massif infini. Une autre contribution de ce travail a concerné l'implémentation d'un algorithme prédictif de la pression dans une fissure 3D a cours de sa croissance. L'algorithme implémenté est basé sur la méthode implicite d'Euler à partir d'une loi de comportement en pression préalablement définie. La pression prédite par X-FEM a été validée par comparaison avec la solution analytique établie pour une fissure circulaire sous pression se propageant dans un milieu infini en mode I pur. La loi d'évolution en pression proposée a ensuite été appliquée à la propagation d'une fissure à front tortueux modélisée via les données expérimentale et une avancée préférentielle de la fissure dans les zones concaves a été remarquée. Le modèle de propagation a été étendu à deux fissures puis à leur coalescence. L'analyse des champs de contraintes a permis d'expliquer les phénomènes d'interactions entre les fissures. Une étude paramétrique de la coalescence de deux fissures circulaires n'échangeant pas de gaz a permis d'établir des critères de coalescence sous formes d'abaques pour des fissures coplanaires. Il en ressort que les interactions entre deux fissures favorisent la coalescence de ces fissures. Un modèle avec échange de gaz interne entre les fissures a été abordé mais nécessite d'être approfondi. Enfin,une étude prospective a été menée sur la rugosité dans le Smart Cut ainsi que quelques paramètres pouvant influencer cette rugosité, notamment la présence et l’épaisseur de la couche d'oxyde de silicium, le comportement hétérogène de la zone de silicium implantéeThe X-FEM approach has been used to model the rupture by coalescence of cracks under pressure in the Smart Cut process. The fractal mesh has been implemented to take into account the scale difference on the representative samples of the modeled SOI substrates. This makes it possible to reduce the number of finite elements on the global mesh while ensuring a good accuracy on the mechanical fields computed in the vicinity of the cracks due to the fineness of the local mesh. As result, more than 90% gain in computation time has been obtained using the proposed 3D fractal mesh compared to an equivalent regular mesh. A procedure has been developed in Cast3M to generate this type of mesh. In order to extract stress intensity factors (SIFs) at the front of a crack loaded by internal pressure, the interaction integral has been modified to take into account the additional term corresponding to the pressure fields applied on the crack faces. The results have been validated by comparison with the analytical solution of a penny-shaped crack in an infinite medium. Another contribution in this work concerns the implementation of an algorithm to predict the internal pressure of a 3D crack during propagation. The proposed algorithm is based on the Euler's implicit method and follows a predefined evolutive law in pressure. The numerical predicted pressure has been validated by comparison to the analytical solution established for a propagating penny-shaped crack in an infinite medium. The constitutive law proposed in pressure has also applied to the propagation of a single crack with tortuous front modeled from experimental data. During the growth, the maximum stresses are located in the concave regions of the crack front, leading to the maximum K1 in these zones. This, according to the Griffith energy criterion, leads to a preferential advance of the crack in these concave regions and gives explanation of the phenomenon of crack recirculation experimentally observed in the Smart Cut. The propagation model has then been extended to the propagation of two cracks and the coalescence of two coplanar cracks under pressure in mode I has been modeled in 3D. The interactions between cracks are characterized by a local amplification of SIFs when the cracks are relatively close to each other. A parametric study has been carried out for two coplanar circular cracks under pressure. It appears that, interactions between two cracks are favorable to their coalescence and can be taken into account in the numerical X-FEM approach. Finally, a prospective study has been adressed on the roughness in the Smart Cut and some parameters that could influence the post-fracture roughness; for instance the presence and the thickness of the buried oxide layer, the material heterogenous behaviour of the implanted silicon region where cracks are located
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Chapalain, Marion. "Dynamique des matières en suspension en mer côtière : caractérisation, quantification et interactions sédiments/matière organique." Thesis, Brest, 2019. http://www.theses.fr/2019BRES0010/document.
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La connaissance de la dynamique des matières en suspension (MES) et des turbidités en milieu côtier est un élément clé pour comprendre les écosystèmes marins. Les processus de floculation/défloculation représentent des mécanismes essentiels contrôlant la dynamique des caractéristiques physiques des MES et, par conséquent, leur devenir dans l’environnement. Cette thèse a pour objectif de mieux comprendre la caractérisation des MES et leur variabilité de l’échelle tidale à l’échelle annuelle en mer côtière, en réponse aux différents forçages hydrodynamiques, hydrologiques et biologiques ayant lieu à l’interface entre estuaire et baie. À cette fin, des capteurs optiques et acoustiques ont été déployés in situ, lors de 6 campagnes en mer réalisées en 2016, en vue de caractériser et de quantifier les MES dans la colonne d’eau, à la sortie de l’embouchure de l’estuaire de Seine (France). Une analyse critique des mesures granulométriques issues du LISST-100X est proposée. Un travail de quantification des incertitudes de mesure associées à l’estimation de la concentration en MES a mis en avant le risqué lié à un rinçage insuffisant des filtres et a conduit à définir une masse minimum à filtrer, de l'ordre de 10 mg, quelle que soit la concentration. Ce travail a notamment permis de proposer une méthode d’estimation d’un volume optimal de filtration basée sur une mesure préalable de turbidité de référence. Les mesures à haute fréquence ont montré que la dynamique des caractéristiques physiques des MES en termes de concentration et de taille médiane sont contrôlées par le cycle advection-floculation-sédimentation-remise en suspension. Ces résultats ont permis de hiérarchiser les paramètres de contrôle des processus de floculation. La turbulence a été identifiée comme le principal paramètre de contrôle à l’échelle tidale et semi-lunaire, la taille médiane maximale des flocs étant inversement corrélée à l’intensité des courants. À l’échelle saisonnière, la variation des caractéristiques des MES (taille, densité, vitesse de chute) est liée à la variabilité du contenu en matière organique (MO), avec une floculation favorisée quand le taux de MO particulaire augmente. Ces flocs plus grands et moins denses sont également plus résistants à la fragmentation induite par cisaillement turbulent. Ces travaux ont également permis de discuter le concept de structuration fractale des flocs.La dynamique de la dimension fractale, déterminée en combinant des données in situ de concentration en MES et de distribution en classe de taille, peut traduire des variations de composition des MES, mais peut aussi résulter d'incertitudes de mesure associées aux instruments. Ces dernières sont discutées dans cette thèse. La variabilité saisonnière des caractéristiques des MES est plus prononcée au large que dans la zone sous influence de l’estuaire de Seine. À partir des observations ponctuelles en Baie de Seine et d’une série de mesure long terme dans la zone côtière belge acquise par le laboratoire RBINS, les méthodes acoustiques et optiques sont combinées. Ces dernières ont mis en avant une augmentation de la rétrodiffusion acoustique lorsque la densité moyenne des flocs diminueThe knowledge of suspended particulate matter (SPM) and turbidity dynamics in coastal waters is essential for studying marine ecosystems. Flocculation/deflocculation processes are crucial mechanisms controlling the dynamics of SPM physical characteristics and thus, the fate of these SPM in the environment. This PhD thesis focuses on the SPM characteristics and their dynamics in coastal waters, from tidal to annual scales, in response to hydrodynamic, hydrological and biological forcing that take place at the interface between estuaries and coastal seas. To this end, optical and acoustic sensors were deployed in situ through 6 field campaigns in 2016, in order to characterize and quantify SPM in the water column, near the mouth of the Seine estuary (France). A critical analysis of LISST-100X measurements in coastal waters is presented. The quantification of uncertainties on SPM concentration measurements is investigated: it highlights the crucial effect of salt retention, and the need for a minimum mass to filter, around 10 mg. A method for estimating an optimal filtration volume based on a reference turbidity measurement is proposed. High frequency measurements show that the dynamics of SPM and median diameter are controlled by the advection-flocculationsedimentation-resuspension cycle.These results allow to classify the factors controlling flocculation processes. Turbulence is identified as the main factor at the semi-diurnal and semi-lunar tidal scales, as the maximum median size of flocs decreases when the tidal currents intensify.At the seasonal scale, the variation of SPM characteristics (size, density, settling velocity) is correlated to the variability of the organic matter (OM) content: in particular, flocculation is enhanced by an increase of the particular OM fraction. The resulting larger and lesser dense flocs are also more resistant to the fragmentation induced by shear. This work also investigates the fractal approach applied to flocs. The fractal dimension variability, calculated by combining in situ data of SPM concentration and particle size distribution, can be associated to variations of the SPM composition, but can also result from uncertainties linked to instrument limitations. The latter are discussed in this PhD thesis. The seasonal variability of SPM characteristics is more pronounced offshore than at the mouth of the Seine estuary. From short-term observations in the Seine Bay and from long-term series in the Belgian coastal zone provided by the RBINS, optical turbidity and acoustic backscatter measurements are combined. They highlight an increase of the acoustic backscatter intensity when mean floc density
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Woo, Lily Lai Yam. "Performance Evaluation of a Wireless Protocol for Mesh Networking under the Influence of Broadband Electromagnetic Noise." 2010. http://hdl.handle.net/1993/3961.
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Migrating from a wired to a wireless implementation for communication system used in industrial applications is a logical move to avoid the many shortcomings associated with wires. When operated under harsh environments, those wires can break and could cause not only damage to the system but also endanger human lives. However, it is not well documented how well a wireless protocol can work under such harsh industrial environments. This thesis attempts to answer this research question in the point of view of gauging the performance of a wireless protocol under the influence of electromagnetic noise. More specifically, the type of noise signal that is the focus of this investigation is the random, pulsed type (e.g., discharges caused by sparking) that creates a hyperbolic broadband disturbance in the frequency domain. Consequently, a fractal noise model is used to study noise of this nature. The steps toward achieving this goal include: requirements gathering, wireless technology selection; noise modelling and synthesis; real noise capture and analysis to validate the chosen noise model; high-frequency fractal noise emulation in hardware; the use of a novel noise injection method for empirical work; and the conducting of a controlled synthetic noise-to-wireless node performance evaluation to obtain performance measure in the form of packet error rate (PER). Performance data in terms of PER versus signal-to-noise ratio (SNR) for various nodes separation have been collected. There were three significant findings: the obtained performance curves follow the standard 'S' trend; for a specific desired reliability (denoted by a certain PER), the SNR at the transmitter needs to be boosted as the correlation of the noise being present increases; and the maximum distance between nodes separation for a certain reliability to be achieved depends exponentially with the transmitter‟s SNR. The relationship in the third finding assists in placement of wireless nodes, which in turn can determine the minimum amount of wireless nodes required for an industrial system to reach the desired system reliability, thus boasting network cost saving.
Book chapters on the topic "Fractal mesh"
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Zhang, Jianjun, Zhenyu He, Yiu-ming Cheung, and Xinge You. "Writer Identification Using a Hybrid Method Combining Gabor Wavelet and Mesh Fractal Dimension." In Intelligent Data Engineering and Automated Learning - IDEAL 2009, 535–42. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-04394-9_65.
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Wnuk*, Michael P. "From Macro to Meso and Nano Material Failure. Quantized Cohesive Model for Fractal Cracks." In Security and Reliability of Damaged Structures and Defective Materials, 359–86. Dordrecht: Springer Netherlands, 2009. http://dx.doi.org/10.1007/978-90-481-2792-4_17.
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Osborne, A. R., and R. Caponio. "Theoretical Determination of the Fractal Dimension of Fluid Parcel Trajectories in Large and Meso-Scale Flows." In Ocean Variability & Acoustic Propagation, 407–16. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3312-8_31.
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Fernandes da Silva Junior, Paulo, Mauro Sérgio Pinto Silva Filho, Ewaldo Eder de Carvalho Santana, Paulo Henrique da Fonseca Silva, Elder Eldervitch Carneiro de Oliveira, Maciel Alves de Oliveira, Fabrício Ferreira Batista, et al. "Fractal and Polar Microstrip Antennas and Arrays for Wireless Communications." In Wireless Mesh Networks - Security, Architectures and Protocols. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.83401.
Full textConference papers on the topic "Fractal mesh"
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Yu, Bai, and Hong Fei. "Fractal Analysis of Traffic Flow Over Wireless Mesh Networks." In 2008 4th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM). IEEE, 2008. http://dx.doi.org/10.1109/wicom.2008.672.
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Gillen, Sean, and Katie Byl. "Mesh Based Analysis of Low Fractal Dimension Reinforcement Learning Policies." In 2021 IEEE International Conference on Robotics and Automation (ICRA). IEEE, 2021. http://dx.doi.org/10.1109/icra48506.2021.9561874.
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Макаренко, Константин, Konstantin Makarenko, Александр Никитин, and Alexander Nikitin. "Fractal Analysis of Morphological Parameters of the Structure Materials." In 29th International Conference on Computer Graphics, Image Processing and Computer Vision, Visualization Systems and the Virtual Environment GraphiCon'2019. Bryansk State Technical University, 2019. http://dx.doi.org/10.30987/graphicon-2019-2-240-243.
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It is proposed to use the methods of fractal analysis to determine the morphological characteristics of the structure of structural materials. The questions of fractal aggregation of particles in the process of crystallization of ductile iron are considered, an austenitic-graphite cell is used as an elementary particle. Based on the mesh method, images of the microstructure of ductile irons are analysed and conclusions are drawn about the similarity of the nature of the process of their crystallization and fractal aggregation of particles. Based on the calculated fractal dimensions, a theory is proposed to explain the features of the crystallization process of ductile irons.
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Treifi, Muhammad, Derek K. L. Tsang, and S. Olutunde Oyadiji. "Applications of the Fractal-Like Finite Element Method to Sharp Notched Plates." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35563.
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The fractal-like finite element method (FFEM) has been proved to be an accurate and efficient method to analyse the stress singularity of crack tips. The FFEM is a semi-analytical method. It divides the cracked body into singular and regular regions. Conventional finite elements are used to model both near field and far field regions. However, a very fine mesh of conventional finite elements is used within the singular regions. This mesh is generated layer by layer in a self-similar fractal process. The corresponding large number of degrees of freedom in the singular region is reduced extremely to a small set of global variables, called generalised co-ordinates, after performing a global transformation. The global transformation is performed using global interpolation functions. The Concept of these functions is similar to that of local interpolation functions (i.e. element shape functions.) The stress intensity factors are directly related to the generalised co-ordinates, and therefore no post-processing is necessary to extract them. In this paper, we apply this method to analyse the singularity problems of sharp notched plates. Following the work of Williams, the exact stress and displacement fields of a plate with a notch of general angle are derived for plane stress and plane strain conditions. These exact solutions which are eigenfunction expansion series are used as the global interpolation functions to perform the global transformation of the large number of local variables in the singular region around the notch tip to a few set of global co-ordinates and in the determination of the stress intensity factors. The numerical examples demonstrate the accuracy and efficiency of the FFEM for sharp notched problems.
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Jovanovic, Vojin T., and Kazem Kazerounian. "Using Chaos to Obtain Global Solutions in Computational Kinematics." In ASME 1996 Design Engineering Technical Conferences and Computers in Engineering Conference. American Society of Mechanical Engineers, 1996. http://dx.doi.org/10.1115/96-detc/mech-1193.
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Abstract In this paper we examine the sensitive dependence on the initial conditions of the Newton-Raphson search technique. It is demonstrated that this sensitivity has a fractal nature which can be effectively utilized to find all solutions to a nonlinear equation. The developed technique uses an important feature of fractals to preserve shape of basins of attraction on infinitely small scales.
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Reddy, R. M., and B. N. Rao. "Fractal Finite-Element Method for Evaluating Sensitivities of Fracture Parameters for Multiple Cracked Systems." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-66949.
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The sensitivities of fracture parameters in cracked structures provide useful information for the prediction of stability and arrest of a single crack, the growth pattern analysis of a system of interacting cracks, configurational stability analysis of evolving cracks, probabilistic fracture mechanics analysis and universal size effect model. In the case of multiple crack systems, for example, sensitivities of fracture parameters at one crack tip due to the growth of any other crack must be calculated to determine the strength of the interaction. In probabilistic fracture mechanics analysis of linear-elastic cracked structures, the first and second order reliability methods require accurate estimates of fracture parameters, their sensitivities. This paper presents a new fractal finite element method based continuum shape sensitivity analysis for evaluating sensitivities of fracture parameters in a homogeneous, isotropic, and two dimensional linear-elastic multiple cracked system subject to mixed-mode loading conditions. The method is based on the material derivative concept of continuum mechanics, and direct differentiation. Unlike virtual crack extension techniques, no mesh perturbation is needed in the proposed method to calculate the sensitivity of fracture parameters. Since the governing variational equation is differentiated prior to the process of discretization, the resulting sensitivity equations predict the first-order sensitivity of fracture parameters, more efficiently and accurately than the finite-difference method.
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Rajesh, K. N., and B. N. Rao. "Coupled EFGM and F2LFEM for Fracture Analysis of Cracks." In ASME 2009 Pressure Vessels and Piping Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/pvp2009-77190.
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This paper presents a coupling technique for integrating the element–free Galerkin method (EFGM) with fractal two-level finite element method (F2LFEM) for analyzing homogeneous, isotropic, and two dimensional linear–elastic cracked structures subjected to mixed–mode (modes I and II) loading conditions. F2LFEM is adopted for discretization of domain close to the crack tip and EFGM is adopted in the rest of the domain. In the transition region interface elements are employed. The shape functions within interface elements which comprises both the element–free Galerkin and the finite element shape functions, satisfies the consistency condition thus ensuring convergence of the proposed method. The proposed method combines the best features of EFGM and F2LFEM, in the sense that no structured mesh or special enriched basis functions are necessary and no post–processing (employing any path independent integrals) is needed to determine fracture parameters such as stress–intensity factors (SIFs) and T–stress. The numerical results show that SIFs and T–stress obtained using the proposed method are in excellent agreement with the reference solutions for the structural and crack geometries considered in this study. Also a parametric study is carried out to examine the effects of the similarity ratio, and the number of transformation terms on the quality of the numerical solutions.
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Islam, Tanveer ul, and Prasanna S. Gandhi. "Spontaneous Fabrication of Three Dimensional Multi-Scale Fractal Structures Using Hele Shaw Cell." In ASME 2016 11th International Manufacturing Science and Engineering Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/msec2016-8755.
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Several bio-systems such as leaf veins, respiratory system, blood circulation, some plant xylem etc., involving multi-scale fractal topologies are being mimic for their inherent natural optimization. 3D fractal structures spanning multiple scales are difficult to fabricate. In this paper we demonstrate a new method to fabricate structures spanning meso and micro-scale in a relatively easy and inexpensive manner. A well known Saffman-Taylor instability is exploited for the same in a lifted Hele-Shaw cell. In this cell a thin layer of liquid is squeezed between two plates being lifted angularly leaving behind the fractal rearrangement of fluid which is proposed to be solidified later. We demonstrate and characterize fractal structures fabricated using two different fluids and corresponding methods of solidification. The first one is ceramic suspension in a photo-polymer and another is polystyrene solution with photo-polymerization and solvent vaporization as methods of solidification respectively. The fabrication process is completed in period of a few seconds.
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Jovanovic, Vojin, and Kazem Kazerounian. "Optimal Design Using Chaotic Descent Method." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5853.
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Abstract This paper presents a novel method for locating global minima in design optimization problems. The method is applicable to any general nonlinear function. It is based on utilizing sensitive fractal areas to locate all of the solutions along one direction in variable space. The search begins from an arbitrary chosen point in the space and descends towards a better design along a randomly chosen direction. Descent depends on finding points that belong to Julia set from which all of the solutions along that direction can be located. The process is repeated until optimal design is obtained. To examine the behavior of the algorithm appropriate examples were selected and results discussed.
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Gravelle, Andrew, and Alejandro Marangoni. "Incorporating heterogeneous stress translation in a fractal structural-mechanical theory of particle-filled colloidal networks." In 2022 AOCS Annual Meeting & Expo. American Oil Chemists' Society (AOCS), 2022. http://dx.doi.org/10.21748/igey1339.
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The fractal nature of colloidal aggregate gels has been well established, and the mechanical and rheological properties of these systems have frequently been interpreted using fractal scaling theory. However, many foods also contain a dispersed particulate phase, such as emulsified fat droplets. The goal of this work was to extend the fractal formalism to interpret the effect of such filler particles on the observed mechanical response of aggregated colloidal networks. To this end, we address the impact of rigid inclusions on the elastic modulus of particle-filled colloidal networks. Our approach acknowledges the heterogeneous nature of stress distribution at length scales beyond the colloidal aggregates, while maintaining structural information at the level of individual clusters. This was achieved by introducing an additional scaling factor to account for system heterogeneity which contains intrinsic information about the network’s capacity to form load-bearing links. In this model, rigid fillers bound to the network induce stress concentration, but additionally serve as junction zones which introduce additional load-bearing pathways. This gives rise to the commonly observed positive correlation between the modulus and filler volume fraction. The proposed relationship between the load-bearing network connectivity and scaling behavior may have additional implications on the fractal dimension determined by rheological methods. The modified fractal model thus provides an alternative view of how fillers contribute to the small- and large-deformation behavior of filled colloidal gels. Further, this model accommodates an experimentally observed negative correlation between the scaling behavior of the modulus resulting from (i) the addition of fillers and (ii) that arising from increasing structurant concentration. Incorporating heterogeneity at the meso-scale provides an intuitive explanation for these findings, which cannot be explained using the traditional approach.
Reports on the topic "Fractal mesh"
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Derikx, P. J. L., H. Heskamp, M. Alewijn, and B. van de Kooi. Nabij-infrarood spectroscopie (NIRS) voor de hygiënisatie bepaling van de dikke fractie mest na mestscheiding. Wageningen: Wageningen Food Safety Research, 2020. http://dx.doi.org/10.18174/543113.
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