fractal geometry
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Author(s):  
Rajib Kumar Dash ◽  
Puspendu Bikash Saha ◽  
Dibyendu Ghoshal ◽  
Gopinath Palai

In this article two fractal geometry-based slotted patch antennas are designed to achieve wideband response with multiband characteristics and reduced cross polarized radiation in both E- and H-plane for all the resonating bands. The proposed antennas are fed with microstrip line feeding formed on a FR4 substrate of size 0.25𝜆0 × 0.25𝜆0 × 0.02𝜆0 mm3 and loaded with a partial ground plane at the bottom of the substrate. HFSS is used to design and simulate both the antennas. Wideband behavior and impedance matching of Antenna-1 are improved by optimizing the factor of iteration and length of the ground plane. Due to addition of 3 identical split ring resonators (SRR) with the antenna geometry leads to achieve multiband response in Antenna-2. The dimensions of the SRR connectors and feedline have been optimized through parametric analysis to match the impedance properly at all the three resonating bands. It has been found that simulated and measurement results of both the antennas are properly matched.


2022 ◽  
Vol 6 (1) ◽  
pp. 39
Author(s):  
Christoph Bandt ◽  
Dmitry Mekhontsev

Self-similar sets with the open set condition, the linear objects of fractal geometry, have been considered mainly for crystallographic data. Here we introduce new symmetry classes in the plane, based on rotation by irrational angles. Examples without characteristic directions, with strong connectedness and small complexity, were found in a computer-assisted search. They are surprising since the rotations are given by rational matrices, and the proof of the open set condition usually requires integer data. We develop a classification of self-similar sets by symmetry class and algebraic numbers. Examples are given for various quadratic number fields.


MAUSAM ◽  
2022 ◽  
Vol 46 (3) ◽  
pp. 297-302
Author(s):  
A. M. SELVAM ◽  
M. RADHAMANI

  Long-range spatio-temporal correlations manifested as the self-similar fractal geometry to the spatial pattern concomitant with inverse power law form for the power spectrum of temporal fluctuations are ubiquitous to real world dynamical systems and are recently identified as signatures of self-organized criticality Self-organised criticality in atmospheric flows is exhibited as the fractal geometry 10 the global cloud cover pattern and the inverse power law form for the atmospheric eddy energy spectrum, In this paper, a recently developed cell dynamical system model for  atmospheric flows is summarized. The model predicts inverse power law form of the statistical normal distribution for atmospheric eddy energy spectrum as a natural consequence of quantum-like mechanics governing atmospheric flows extending up to stratospheric levels and above, Model Predictions are in agreement with continuous periodogram analyses of atmospheric total ozone. Atmospheric total ozone variability (in days) exhibits the temporal signature of self-organized criticality, namely, inverse power law form for the power spectrum. Further, the long-range temporal correlations implicit to self-organized criticality can be quantified in terms of the universal characteristics  of the normal distribution. Therefore the total pattern of fluctuations of total ozone over a period of time is predictable.  


2021 ◽  
Vol 27 (6) ◽  
pp. 1397-1406
Author(s):  
Bo-Kyeong Kim ◽  
Eun-Mi Choi

With development of advanced technologies, the field of beauty is under strong pressure to try new approaches in line with the highly increasing interest in advance 3D printing based on 3D graphic design data. An increasing number of researches have been conducted to develop beauty and art design object using computer design programs. As part of this, three works were presented in this paper in which body painting designs and object were applied to mannequins by producing them with help of 3D printing techniques based on the motive of fractal that started from nature. This study examined how the generation principle of fractal geometry appears in the form of nature. The generation principle of fractal geometry models nature, fibonacci, and crystalline pattern by non-linearity, irregularity, and randomness around the iterative rule of self similarity. The present study is thought to be meaningful in that it suggests the possibility and practical value of a design method that can be technically and easily accessible to those majoring in beauty by means of its utility as a low-end 3D printing object.


2021 ◽  
Vol 13 (4) ◽  
pp. 427-434
Author(s):  
Andrey V. Smirnov ◽  
◽  
Alexander S. Fionov ◽  
Ilia A. Gorbachev ◽  
Elizaveta S. Shamsutdinova ◽  
...  

The paper presents the results of a study of the frequency dependence of the S11 parameters of antenna samples with fractal geometry, created using 3D printing technology, followed by the deposition of a conductive copper coating by galvanization. It is shown that changing the dimension of the fractal at different iterations, shifting and dividing the resonant frequencies, it is possible to flexibly form the working bands of antennas in any frequency range and any width. The developed designs can be used to create broadband rectennas.


Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2391
Author(s):  
Nikolay Anatolyevich Torkhov ◽  
Maxim Pavlovich Evstigneev ◽  
Andrey Alexandrocivh Kokolov ◽  
Leonid Ivanovich Babak

This paper investigates the relation between the geometry of metric space of a TiAlNiAu thin film metal system and the geometry of normed functional space of its sheet resistances (functionals), which are elements of the functional space. The investigation provides a means to describe a lateral size effect that involves a dependency in local approximation of sheet resistance Rsq of TiAlNiAu metal film on its lateral linear dimensions (in (x,y) plane). This dependency is defined by fractal geometry of dendrites, or, more specifically, it is a power-law dependency on fractal dimension Df value. The revealed relation has not only fundamental but also a great practical importance both for a precise calculation of thin film metal system Rsq values in designing discreet devices and ICs, and for controlling results at micro- and nanoscale in producing workflow for thin metal films and systems based on them.


Author(s):  
Даниил Васильевич Раков ◽  
Татьяна Геннадьевна Стоцкая

Статья посвящена анализу предпосылок образования синергетики и фрактальной геометрии с точки зрения историко-философского подхода. Авторы предпринимают попытку обоснования новых способов описания процессов, лежащих в основе положений синергетики путем применения фрактальной геометрии. Особое внимание уделяется рассмотрению перспектив использования основных положений синергетики и фрактальной геометрии к решению широкого спектра вопросов. Результаты анализа основных концепций теорий диссипативных систем, самоорганизации систем и фрактальной геометрии выявляют их согласованность в рамках постнеклассического научного познания. Теоретическая и / или практическая значимость исследования заключается в возможных перспективах в области моделирования поведения широкого ряда процессов различной природы с вероятным выявлением некоторых внесистемных механизмов функционирования, общих на своем начальном уровне для процессов любой природы. The article is devoted to the analysis of the prerequisites for the formation of synergetics and fractal geometry from the point of view of the historical and philosophical approach. The authors attempt to substantiate new ways of describing the processes underlying the provisions of synergetics by applying fractal geometry. Particular attention is paid to the prospects of using the main provisions of synergetics and fractal geometry to solve a wide range of issues. The results of the analysis of the main concepts of the theory of dissipative systems, self-organization of systems and fractal geometry reveal their consistency within the framework of post-non-classical scientific knowledge. Theoretical and / or Practical Implications the purpose of this study is to identify possible prospects in the field of modeling the behavior of a wide range of processes of various nature with the likely identification of some non-systemic mechanisms of functioning that are common at their initial level for processes of any nature.


2021 ◽  
Vol 87 (12) ◽  
pp. 1013-1019
Author(s):  
Ryosuke YAMADA ◽  
Ryota SUZUKI ◽  
Akio NAKAMURA ◽  
Hirokatsu KATAOKA
Keyword(s):  

MAUSAM ◽  
2021 ◽  
Vol 61 (1) ◽  
pp. 35-38
Author(s):  
R. SAMUEL SELVARAJ ◽  
S. TAMILSELVI ◽  
R. GAYATHRI

The annual rainfall data of Chennai is analyzed using the Fractal Construction Technique. According to Mandelbrot the dimension of any line including nautical lines may not be Euclidean but Fractional, Mandelbrot, 1982. This fractional dimension leads to a repetitive appearance of any pattern. Climate which is usually periodic by nature can be analyzed through this technique. Efforts are on to search the fractal geometry of climate and to predict its periodicity on different temporal scales. This paper estimates the various parameters like Lyapunov exponent, Maximum Lyapunov characteristic exponent, Lyapunov time, Kaplan-Yorke dimension for the annual rainfall of Chennai.


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