Characteristics Of Fractal Geometry Research Articles

Dynamic response characteristics and damage rule of graphite ore rock under different strain rates

In the process of mining graphite mine, rock mass is often subjected to dynamic loads such as blasting or mechanical crushing, which involves dynamic responses of different strain rates, and blasting and crushing effect are affected by the rock dynamic properties and damage specials. The dynamic response characteristics and damage rule of graphite ore rock under different strain rates are very important but rarely studied in the past. To study these issues and provide support for graphite ore rock mining, the dynamic compression tests of graphite ore rock under five kinds of impact pressures were designed and carried out by using the Split Hopkinson Pressure Bar (SHPB) test system, combining with the high-speed photography system and crushing screening tests. The dynamic characteristics, crushing process, crushing mode, crushing form and fragmentation distribution of the graphite ore rock under different strain rates were analyzed. The results show that the dynamic characteristics of the graphite ore rock have obvious strain rate effect. The hardening coefficient (DIF) is positively correlated with the cubic root of strain rate, and the softening factor (K) is negatively correlated with the cubic root of strain rate. Shear failure mainly occurs in the graphite ore rock under impact load, and the crushing process can be divided into five stages, they are compaction, crack initiation, crack expansion and penetration, fragmentation collision and fragmentation fall. In addition, the crushed blocks are mainly triangular pyramid (or cone-like) fine granular and powder. The broken fragments of the graphite ore rock are in accord with the fractal geometry characteristics. That is, the average broken particle size (dS) decreases linearly with the increase of strain rate, and the fractal dimension (Da) increases weakly with the increase of strain rate. Based on D-P fracture criterion and Weibull distribution model, the dynamic damage constitutive model of the graphite ore rock was established, and the correlation between strain rate and Weibull distribution parameters (m and F0) was used to reasonably modify the damage constitutive model. The modified damage constitutive model curve is in good agreement with the experimental curve, which can basically reflect the strain rate effect of the dynamic characteristics of the graphite ore rock and the evolution characteristics of the dynamic stress–strain curve at different stage.

High absorption and a tunable broadband absorption based on the fractal Technology of Infrared Metamaterial Broadband Absorber

This paper proposes a dual-band tunable broadband metamaterials absorber, achieved absorption in 3-5 μm mid-wavelength infrared (MWIR) and 8-12 μm long-wavelength infrared (LWIR). The absorber is composed of periodic units, and each unit is composed of a bottom ideal electric conductor-dielectric layer-graphene layer-metal fractal cross resonator in which a graphene layer-metal fractal cross is embedded. The metal structure uses the multi-scale self-similar characteristics of fractal geometry to create multiple resonances for the same element structure. Numerical simulations were carried out using the finite element method (FEM). The optimization results show that the designed single-layer 3-Level graphene-metal fractal cross absorber produces broadband absorption of 2.86 μm (absorption >90%) in the LWIR region and an average absorption rate of 92.1%. By adding the bottom layer 3 × 3 graphene-metal fractal cross array structure, a resonant absorption peak is generated in the MWIR region, and the broadband absorption of 0.38 μm (absorption >80%), and it achieves broadband absorption of 2.48 μm (absorption >90%) in the LWIR region. For the double-layer graphene-metal structure, the resonance bandwidth and absorptivity of the absorber can be tuned by adjusting the Fermi energy of each layer of graphene. Due to its broadband, polarization insensitivity, high absorption, flexible tunable, and other characteristics, the proposed metamaterials absorber is beneficial for fabricating nano-optoelectronic devices and can be applied in thermal imaging and infrared detection.

Comparative analysis of geometric forms and numerical calculation of fractals in Khayyam’s Mausoleum based on the Islamic architecture’s definitions and box-counting method

The interaction and balance between fractal components, which maintain to function in nature in perfect harmony with the highest efficiency, has been the source of inspiration for architects in different eras. Today, contemporary Iranian architecture needs a comprehensive study and familiarity with world issues, hence the Khayyam’s mausoleum was chosen. the main purpose of this article is to analyze the geometry and numerical calculation of the fractal size of the building and its semantic knowledge in the contemporary building, which leads to finding the architect’s goals of how to design these forms and common concepts with Islamic architecture. After achieving how to use Islamic elements in a contemporary monument, we come to the interrelationship between fractal geometry and architectural design.With the box-counting technique, the fractal dimension was calculated by checking the two-dimensional plates in 4 different scales from the largest to the smallest scale to prove its decimal dimension. Then, information was collected by descriptive-analytic method and after determining the common features between fractal forms with analytical and comparative process, the obtained quantitative data resulted in extracting similar cases from the building. Finally, the relationship between the characteristics of fractal geometry and the architecture of the tomb was proved and the obtained patterns were matched with the concepts of self-similarity, iteration (proportion and symmetry), micro scale and non-integer dimension. The elements used such as tiled ornaments, the Islamic star and Shamsa, domed-shaped roof, regular numerical pattern of geometric shapes with symbolism, unity in diversity, infinity and dynamism are reminiscent of Islamic architectural style. Furthermore, fractal has been used in three methods: conceptual, mathematical and intuitive, and has been manifested in both structural and aesthetic aspects.

Knitwear design with fractal formative characteristics

The purpose of this study is to develop a knitwear design with the potential for practical use through a combination of science and design by examining the concept and formative characteristics of fractal geometry and applying them to the development of 3D virtual clothing knitwear design. This study produced five main conclusions. First, the sub-concepts of “Repeatability,” “Scale variability,” and “complexity,” which are based on self-similarity, appear together with simple regularity in the fractal formative characteristics shown in fashion design. Second, fashion fields apply fractal geometry in three-dimensional surface textures and optical textile patterns as a method of expression. Third, it was confirmed that various expressions can be created with fractal patterns by using the SDS-ONE APEX 3-4 design system; moreover, fractal patterns are a suitable design source for the development of Jacquard knitwear patterns. Fourth, in the development of knitted jacquard fractal patterns, by arranging the patterns in perspective, the effect of emphasizing or reducing the human body by optical illusion was shown. Fifth, a knit Jacquard structure with a pattern that exhibits fractal modeling characteristics and applying it to a 3D virtual clothing sample design reduces the time required for sample production while expanding the knit design’s expression area and reducing costs. Thus, the clothing sample confirmed the effectiveness of practical knitwear design development.

A STUDY OF FRACTAL GEOMETRY IN WIRELESS SENSOR NETWORKS

Fractal geometry is a subject that studies non-integer dimensional figures. Most of the fractal geometry figures have a nested or recursive structure. This paper attempts to apply the nested or recursive structure characteristics of fractal geometry to wireless sensor networks. We selected two filling curves, Node-Gosper and Moore, as our research subjects. Node-Gosper Curve is a curve based on node-replacement with a fractal dimension of two. Its first-order graph consists of seven basic line segments. When the hierarchy becomes larger, it can be filled with a hexagonal-like shape. To allow the mobile anchor node of wireless sensor networks to walk along this curve, the number of levels of the Node-Gosper Curve can be adjusted according to parameters such as the sensing area and transmission range. Many space-filling curves have the common shortcoming that they cannot loop on their own, that is, the starting point and the end point are not close, which will cause the mobile anchor node to use extra paths from the end point back to the starting point. The Moore curve has a self-loop, i.e., the starting point and the ending point are almost at the same position. This paper applies Moore curve to the path planning of the mobile anchor node. We can use this path to traverse the entire sensing area and stay in the central point of each square cluster to collect the information of the nodes where the events occurred. The self-loop characteristic of the Moore curve is expected to reach each sensor to collect data faster than other space filling curves, that is, the transmission latency of the sensor traversal will be reduced

Organização compositiva e lumínica de uma fachada fractal

Este trabalho descreve o desenvolvimento e avaliação compositiva de um processo de projeto paramétrico que permite organizar elementos de fachada, com características da geometria fractal, conforme as necessidades do partido arquitetônico ou por meio do consequente comportamento da luz natural diurna. Para isso elementos de proteção baseados em fractais lineares foram criados, e por intermédio desses elementos é possível formar e controlar arranjos compositivos conforme a radiação solar incidente sob fachada. Os resultados desses arranjos são avaliados de modo quantitativo através de simulações dinâmicas da luz natural, e de modo qualitativo por intermédio de modelos renderizados e de uma maquete física, construída com o auxílio de uma cortadora a laser. Para se desenvolver o processo paramétrico uma sequência de ações foi elaborada dentro de um software de programação visual, sendo os principais módulos: a criação de um ambiente urbano; a formação de um elemento de fachada; e componentes de avaliação para o processo. Como conclusão foi possível identificar que os resultados e meios de avaliação disponibilizados pelo processo paramétrico possibilitam ampliar a tomada de decisão do projetista, podendo hierarquizar suas escolhas. Essas decisões ainda podem ser potencializadas com o auxílio de maquetes físicas, pois possibilitam identificar características pontuais que podem alterar as definições compositivas já identificadas em análises quantitativas e visualizações bidimensionais.

Effects of AlN hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross using response surface methodology

The effects of aluminium nitride (AlN) hydrolysis on fractal geometry characteristics of residue from secondary aluminium dross were studied using response surface methodology. The results show that the fractal dimensions of the residue can be significantly influenced by the AlN hydrolysis from secondary aluminium dross. The hydrolysis of AlN in the dross was spontaneous under temperatures of 303–373 K. The actual fractal dimensions of residue were significantly affected by the liquid–solid ratio (p<0.05) and changed from 1.16 to 1.80, which accurately aligned with those from the calculations. Moreover, the fractal dimensions of residue were significantly affected by the interactions between hydrolysis temperature and hydrolysis time, liquid–solid ratio and hydrolysis time, respectively (p<0.01). The minimum fractal dimensions of the residue reached 1.15 under the optimized conditions, which included a hydrolysis temperature of 30 °C, liquid–solid ratio of 5 mL/g and hydrolysis time of 10 min. The results suggest that response surface methodology can guide in optimizing the conditions of AlN hydrolysis in order to obtain the minimum fractal dimensions of residue for improving the reutilization of the dross.

프랙탈 아트 프린트를 활용한 패션 디자인 특성 분석

Fractal geometry is a scientific theory that explains the complexity of nature by systematizing chaos phenomena into a mathematical model. With the development of digital technology, various images obtained through fractal geometry can now be applied in fashion design. The study is examined with reference to the characteristics of fractal geometry and, through a case study of collections from 2007 to 2016, analyzes how those characteristics are reflected in art prints on fashion design. The three main characteristics of fractal art prints used in fashion design are as follows. The first is

Study on vibration characteristics of damping blade with snubber and shroud based on fractal theory

Snubber and shroud have been widely adopted in steam turbine last stage blades to decrease the vibration stress. The contact surfaces between snubber and shroud own obviously fractal geometry characteristics. Based on fractal geometry theory and finite element nonlinear vibration theory, the fractal friction model that describes friction damping contact could be accurately established. In this paper, the contact fractal elements are set up and the nonlinear vibration response characteristics of a long steam turbine last stage blade with snubber and shroud are calculated. The results show that, with the increase of shroud normal force, the resonant amplitude of the blade experiences a decreasing period followed by an increasing period while the modal damping ratio increases first and then decreases when there is only shroud contact. The regulations are similar when there are both shroud and snubber contacts. The resonant frequency increases until the normal contact forces increase to some degree.

The Structural and Spatial Analysing of Fractal Geometry in Organizing of Iranian Traditional Architecture

Geometry as one of the most influential elements has played effective roles in various structural, spatial and decorative (ornamental) systems in Iranian architecture. In this regard, three attributes of similarity, iteration and change in scale as the basic features of such geometry are clearly visible and assessable in the whole range of Iranian architecture. On the other hand, the mentioned three-fold features are the main characteristics of fractal geometry. Therefore, assuming the existence of fractal patterns in Iranian architecture is a probable and realizable issue and it deserves research and analysis. Therefore, the current article seeks to realize the premise of the existence of the fractal geometry in three scales of macro (city), medium (neighbourhood) and micro (building and motifs) in Iranian architecture specially, in cities of Isfahan and Yazd.

A Study on Diverse Expression in Modern Fashion through the Principle of Fractal Geometry

The objective of the study is to analyze expressions of modern fashion in relation to design principle of a science theory, fractal geometry, in order to identify various and multi-layered expressions of fashion. As for methodology, the study interprets principle and characteristics of fractal geometry based on literature review in areas of linguistic, philosophy, sociology and science. The research identifies expressive characteristics of fractal through empirical studies, and applies them to fashion in order to analyze how fractal design principles are reflected in modern fashion in terms of form and significance. Fractal aesthetics pursue order, balance, diversity and openness among disorder and insecurity. They are closely related to the function of modern fashion that works as a multi-layered code, instead of being confined to conventional idea about fashion that functions as wear.