scholarly journals Diffraction propagation of vortex diffractals

2021 ◽  
Vol 2091 (1) ◽  
pp. 012072
Author(s):  
P Korolenko ◽  
R Kubanov ◽  
N Pavlov ◽  
A Zotov
Keyword(s):  
Retrospective Analysis ◽  
Fractal Structure ◽  
Gaussian Beams ◽  
Computational Algorithms ◽  
Light Radiation ◽  
Two Dimensional ◽  
Propagation Medium ◽  
Weierstrass Functions ◽  
Diffraction Propagation ◽  
High Information

Abstract A brief retrospective analysis of studies of fractal light radiation is carried out. To assess the prospects of this scientific direction, new original results of studying the diffraction propagation of vortex wave beams with a fractal structure (vortex diffractals) are also presented. For this purpose, computational algorithms and related software have been developed. In calculating the amplitude-phase and scaling characteristics of diffractals two-dimensional Weierstrass functions and multistructures of Gaussian beams were used. The results indicate a high information capacity of vortex diffractals and explain their resistance to the influence of turbulence in the propagation medium.

scholarly journals Desain Buku Ajar Matematika Bilingual Materi Bangun Datar Menggunakan Pendekatan PMRI Berkonteks Kebudayaan Lokal

2018 ◽  
Vol 7 (3) ◽  
pp. 345-356
Author(s):  
Lisnani Lisnani ◽  
Sheilla Noveta Asmaruddin
Keyword(s):  
Retrospective Analysis ◽  
Cultural Context ◽  
Design Research ◽  
Design Experiment ◽  
Preliminary Design ◽  
Two Dimensional ◽  
Mathematics Textbook ◽  
Concept Understanding ◽  
Learning Mathematics ◽  
Textbook Design

AbstrakPembelajaran matematika merupakan pembelajaran dari sesuatu yang bersifat konkret menuju  abstrak. Hal ini sejalan dengan materi bangun datar yang cenderung abstrak. Namun, pada kenyataannya cara pemikiran siswa bersifat konkret. Maka dari itu, untuk menjembataninya diperlukan pendekatan yang mengutamakan pembelajaran yang bersifat konkret yaitu pendekatan PMRI (Pendidikan Matematika Realistik Indonesia). Pendekatan ini dilakukan dengan cara mendesain buku ajar bilingual berkonteks kebudayaan lokal melalui serangkaian aktivitas pembelajaran bangun datar menggunakan pendekatan PMRI. Penelitian ini merupakan penelitian design research yang terdiri dari tiga tahap yaitu preliminary design, the design experiment, dan retrospective analysis. Penelitian ini bertujuan menghasilkan lintasan belajar menggunakan buku ajar bilingual materi bangun datar. Pengumpulan data menggunakan lembar observasi, wawancara, dan lembar aktivitas siswa. Data dianalisis menggunakan lembar validasi dari ahli. Hasil analisis menunjukkan bahwa penggunaan buku ajar bilingual ini dapat meningkatkan pemahaman konsep siswa tentang bangun datar dari tahap informal ke tahap formal. Abstract (Bilingual Mathematics Textbook Design of Flat Building Topic Using Local Cultural Context PMRI Approach)Learning mathematics is a learning deriving from abstract towards concrete similarly to two-dimensional figure material. However, based on facts, the students’ thinking-process is concrete, which is abstract. Hence, to connect them, it is advisable to prioritize concrete learning. That is through Indonesia Realistic Mathematics Education (PMRI) approach by designing a bilingual Mathematics textbook based on local cultural context. This research is a design research consisting of three steps. There are preliminary design, the design experiment, and the retrospective analysis. The aim of the research produced a bilingual textbook in which the material focused on two-dimensional figure. Data collection by using observation sheet, interviews, and students’ worksheet. The data analysis by using validation sheet from the expert. The research is that the use of bilingual textbook using PMRI approach is able to improve the students’ concept understanding in two-dimensional figure from informal to formal step.

scholarly journals Fractal structure in two-dimensional quantum Regge calculus

1994 ◽  
Vol 338 (2-3) ◽  
pp. 187-196 ◽  
Author(s):  
Jun Nishimura ◽  
Masaki Oshikawa
Keyword(s):  
Fractal Structure ◽  
Two Dimensional ◽  
Regge Calculus

FRACTAL STRUCTURE OF TWO-DIMENSIONAL SUPERGRAVITY IN THE SUPERCONFORMAL GAUGE

1990 ◽  
Vol 05 (22) ◽  
pp. 4333-4339 ◽  
Author(s):  
S. A. APIKYAN
Keyword(s):  
Fractal Structure ◽  
Two Dimensional ◽  
Anomalous Dimensions ◽  
Arbitrary Genus

Two-dimensional induced quantum supergravity is analyzed. By the use of a superconformal gauge we derive the results of Polyakov and Zamolodchikov for the spectrum of anomalous dimensions of a conformal superfield. Their conjecture for the "string entropy exponent" γ for supergravity is proven and extended to an arbitrary genus surface.

The Two-Dimensional Flow Analysis of Continuous Spiral Reamer Bionic Structure on the Basis of ANSYS

2011 ◽  
Vol 236-238 ◽  
pp. 1576-1580
Author(s):  
Bai Qing Zhang ◽  
Hua Zhu ◽  
Mei Ying Liu
Keyword(s):  
Fractal Structure ◽  
Flow Analysis ◽  
Two Dimensional ◽  
Ansys Software ◽  
Dimensional Flow ◽  
Shape Structure ◽  
Two Dimensional Flow ◽  
Bionic Structure ◽  
Clay Materials

In order to improve the stratification of clay materials in the spiral reamer, we use "bionics method" to modify the structure of the spiral reamer, namely, to add corrugated shape structure to the cutter and hub. Through the analysis of ANSYS software, it is found that corrugated fractal structure can both improve the stratification of clay materials, and increase the yield as well.

FRACTAL STRUCTURE OF TWO DIMENSIONAL SUPERGRAVITY

1988 ◽  
Vol 03 (12) ◽  
pp. 1213-1219 ◽  
Author(s):  
A.M. POLYAKOV ◽  
A.B. ZAMOLODCHIKOV
Keyword(s):  
Fractal Structure ◽  
Two Dimensional ◽  
Anomalous Dimensions ◽  
Dimensional Gravity

We extend our formulae for anomalous dimensions of usual two dimensional gravity to the cases of supergravity.

scholarly journals Development of algorithms for constructing two-dimensional optimal boundary-adaptive grids and their software implementation

2021 ◽  
Vol 21 (3) ◽  
pp. 222-230
Author(s):  
A. E. Chistyakov ◽  
V. V. Sidoryakina ◽  
S. V. Protsenko
Keyword(s):  
Test Problem ◽  
Complex Geometry ◽  
Adaptive Grid ◽  
Software Implementation ◽  
Computational Algorithms ◽  
Computational Domain ◽  
Two Dimensional ◽  
Adaptive Grids ◽  
Qualitative Properties ◽  
Optimal Boundary

Introduction. It is noted that the use of adaptive grids in calculations makes it possible to improve the accuracy and efficiency of computational algorithms without increasing the number of nodes. This approach is especially efficient when calculating nonstationary problems. The objective of this study is the development, construction and software implementation of methods for constructing computational two-dimensional optimal boundary-adaptive grids for complex configuration regions while maintaining the specified features of the shape and boundary of the region. The application of such methods contributes to improving the accuracy, efficiency, and cost-effectiveness of computational algorithms.Materials and Methods. The problem of automatic construction of an optimal boundary-adaptive grid in a simply connected region of arbitrary geometry, topologically equivalent to a rectangle, is considered. A solution is obtained for the minimum set of input information: the boundary of the region in the physical plane and the number of points on it are given. The creation of an algorithm and a mesh generation program is based on a model of particle dynamics. This provides determining the trajectories of individual particles and studying the dynamics of their pair interaction in the system under consideration. The interior and border nodes of the grid are separated through using the mask tool, and this makes it possible to determine the speed of movement of nodes, taking into account the specifics of the problem being solved.Results. The developed methods for constructing an optimal boundary-adaptive grid of a complex geometry region provides solving the problem on automatic grid construction in two-dimensional regions of any configuration. To evaluate the results of the algorithm research, a test problem was solved, and the solution stages were visualized. The computational domain of the test problem and the operation of the function for calculating the speed of movement of interior nodes are shown in the form of figures. Visualization confirms the advantage of this meshing method, which separates the border and interior nodes.Discussion and Conclusions. The theoretical and numerical studies results are important both for the investigation of the grids qualitative properties and for the computational grid methods that provide solving numerical modeling problems efficiently and with high accuracy.

FRACTAL ANALYSIS OF SOIL PORE VARIABILITY WITH TWO DIMENSIONAL BINARY IMAGES

Fractals ◽  
2011 ◽  
Vol 19 (04) ◽  
pp. 401-406 ◽  
Author(s):  
R. UTHAYAKUMAR ◽  
G. AROCKIA PRABAKAR ◽  
S. ABDUL AZIS
Keyword(s):  
Image Analysis ◽  
Plant Growth ◽  
Fractal Structure ◽  
Pore Space ◽  
Pore Surface ◽  
Two Dimensional ◽  
Fractal Scaling ◽  
Binary Images ◽  
Pyroligneous Acid ◽  
Surface Dimension

The manure which we are using for plant growth does not help to increase the porosity of the soil. We use pyroligneous acid to treat the soil as softener, nutrient and porosity increaser. This helps to the soil to remove unwanted carbonates and separate the soil particles. In this way, we can increase 30% porosity of the soil. When we pour pyroligneous acid into soil, the soil increase the carbon content. We consider changes of pore space of a soil by image analysis and also assess the applicability of fractal scaling of pore surfaces. The calculated pore surface dimension showing that the surface exhibit fractal structure. Lacunarity shows the size distribution of holes. If Lacunarity increases, then the value become decreases. This study demonstrates that applicability of fractal scaling for evaluating pore surface of the soil images.

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