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Fractal Based Ultra-Wideband Antenna Design
Published in Praveen Kumar Malik, Planar Antennas, 2021
C. Muthu Ramya, R. Boopathi Rani
Figure 8.2. shows the constructional steps of Sierpinski carpet fractal structure. A square is used as a basic structure (initiator). In the step 1 iteration, nine squares scaled by a factor of three of the initiator are considered, and the central square is taken out from the initiator. This procedure is repeated on the eight left over small squares in the second step. The subsequent iterations can be done in this way. The self-similarity dimension for Sierpinski carpet fractal Ds is 1.89279 [21–23].
Fractal description of the roughness of rock joints
Published in Xie Heping, Fractals in Rock Mechanics, 2020
Noite et al. (1989) measured the contact area distribution of the core specimens labelled E30, E32, and E35 (stripe granite) by using the technique of injecting molten wooden metal into fractures which are initially evacuated. During the injection, stress was maintained on the fracture through a servo-controlled, stiff- testing machine. These contact area distributions are quite similar to the rock slit islands shown in Photo 14.1 and behave as fractals. Thus, a random Sierpinski carpet, shown in Figure 15.34, was chosen by Noite et al. (1989) to measure fractal dimensions of these experimentally obtained contact area distributions. A random Sierpinski carpet is constructed iteratively by successively removing small squares (or tremas) from the original black square (initiator). In the carpet shown, eight out of nine sub-squares, of scale b=13, remain at each level. This gives the approximate fractal dimension, D = log 8/log 3 = 1.89, of the carpet. In principle, the fractal dimension of a Sierpinski carpet can be measured by counting the number of tremas (corresponding to single areas of contact) with area, a larger than some set value, A. In practice, counting is carried out by superposing grids with successively smaller spacing and counting the number of grid squares at each level which are occluded more than 50% by a single trema. Thus, the fractal dimensions are derived from the slope of log(b2 − Ν) vs. log b, where b is the scale size of the grid, and Ν is the number of squares occluded for that scale b. The quantity (b2 − N) is the number of grid squares which remain uncut by tremas at this scale size. Table 15.14 gives the measuring results for the specimens E30 and E32 obtained by Noite et al. in which scale b = 1 corresponds to 32 mm. Since the contact area increases as the stress is increased, the fractal dimensions of the samples as a function of stress can be plotted as in Figure 15.35. The fractal dimensions clearly decrease with increasing stress and appear to approach a value near D = 1.95. This means that the roughness of joint surfaces is smoothed down as stress increases.
Symmetric circular-shaped multiband hybrid fractal antenna using TLBO approach: design and measurement
Published in International Journal of Electronics, 2022
Manpreet Kaur, Jagtar Singh Sivia, Navneet Kaur
In this paper, multiband circular-shaped hybrid fractal antenna is designed using TLBO approach. Similar circular-shaped fractal patterns are introduced onto the patch along with Sierpinski carpet fractal. Optimised value of ground dimension is used during designing. The prototype of antenna-B is experimentally tested to illustrate the multiband functionality of the proposed hybrid fractal technique. Measured results reveal that antenna-B supports six different operating bands i.e. (4.01–4.09 GHz), (6.49–7.00 GHz), (8.49–8.96 GHz), (10.87–11.32 GHz), (11.91–12.44 GHz) and (13.31–13.93 GHz). The reliability of the TLBO technique for the optimisation of ground plane dimension is illustrated. It is suggested that the designed hybrid fractal antenna exhibiting multiband behaviour is a suitable candidate. Such type of antennas can be embedded in several handhelds and modern communication devices. Moreover, performance regarding modifications in the designed structure is also examined.
On the Design and Analysis of I-Shaped Fractal Antenna for Emergency Management
Published in IETE Journal of Research, 2019
Sushil Kakkar, T. S. Kamal, A. P. Singh
The proposed configuration of fractal patch antenna for different iterations (first, second, and third) is shown in Figure 1. The geometry of the presented antenna has been inspired from Sierpinski carpet fractal structure. In order to obtain the generator of fractal geometry (first iteration), if instead of taking out the central square of Sierpinski carpet, the left and right squares are taken out, then it will form the shape of “I”. So far in literature, only a limited number of fractal structures have been used by antenna design engineers for emergency management. In an attempt in [22], the authors have perturbed the first iteration of the Sierpinski gasket structure and optimized it for the operation of antenna for emergency management. In another attempt in [24], the authors have used the Sierpinski carpet structure as defects in the ground plane and tuned it to work for emergency management application. In both of the mentioned cases, the structure of the antenna is comparably complex and analysed for limited iterations. In the presented work, the proposed geometry is very simple, easy to implement, flexible to match, and easy to fabricate.
Geometric limit of Julia set of a family of rational functions with odd degree
Published in Dynamical Systems, 2021
A. M. Alves, B. P. Silva e Silva, M. Salarinoghabi
As an example, the authors of [14] considered the family of cubic rational functions . Inspired by the works given in [14], for an odd integer number , in this paper we consider the family of rational functions which is a kind of generalization of the cubic family given in [14]. For a fixed integer d, it is easy to see that the family is linearly conjugate to the family of the McMullen maps with . Indeed, it is convenient to change the coordinates in by the linear map for some branch of the -th root, and consider the map in the new coordinates, i.e. the map The dynamic of the family is well understood by Hidalgo et al. in [10]. This family is regarded as a singular perturbation of the polynomial and exhibits very rich dynamical behaviour. These maps are known as McMullen maps, since McMullen (see [12]) first studied them. This family attracts many people for several reasons. The notable one is probably that the Julia set varies in several classic fractals. It can be homeomorphic to either a Cantor set, or a Cantor set of circles, or a Sierpinski carpet, see [6].