scholarly journals Self-similar transformation and quasi-unit cell construction of quasi-periodic structure with twelve-fold rotational symmetry

2009 ◽  
Vol 58 (10) ◽  
pp. 7088
Author(s):  
Liao Long-Guang ◽  
Fu Hong ◽  
Fu Xiu-Jun
Keyword(s):  
Periodic Structure ◽  
Rotational Symmetry ◽  
Unit Cell ◽  
Similar Transformation ◽  
Self Similar ◽  
Cell Construction

Cubic Unit Cell Construction Kit

2000 ◽  
Vol 77 (5) ◽  
pp. 622 ◽  
Author(s):  
Bruce Mattson
Keyword(s):  
Unit Cell ◽  
Cell Construction ◽  
Construction Kit

Configurations and Self-similar Transformation of Octagonal Quasilattice

2008 ◽  
Vol 25 (12) ◽  
pp. 4336-4338 ◽  
Author(s):  
Liao Long-Guang ◽  
Fu Xiu-Jun ◽  
Hou Zhi-Lin
Keyword(s):  
Similar Transformation ◽  
Self Similar

scholarly journals is regular-closed

2018 ◽  
Vol 40 (1) ◽  
pp. 213-220 ◽  
Author(s):  
YUTARO HIMEKI ◽  
YUTAKA ISHII
Keyword(s):  
Rotational Symmetry ◽  
Iterated Function Systems ◽  
Geometric Proof ◽  
Contraction Ratio ◽  
Iterated Function ◽  
Mandelbrot Sets ◽  
Self Similar ◽  
Regular Closed

For each $n\geq 2$, we investigate a family of iterated function systems which is parameterized by a common contraction ratio $s\in \mathbb{D}^{\times }\equiv \{s\in \mathbb{C}:0<|s|<1\}$ and possesses a rotational symmetry of order $n$. Let ${\mathcal{M}}_{n}$ be the locus of contraction ratio $s$ for which the corresponding self-similar set is connected. The purpose of this paper is to show that ${\mathcal{M}}_{n}$ is regular-closed, that is, $\overline{\text{int}\,{\mathcal{M}}_{n}}={\mathcal{M}}_{n}$ holds for $n\geq 4$. This gives a new result for $n=4$ and a simple geometric proof of the previously known result by Bandt and Hung [Fractal $n$-gons and their Mandelbrot sets. Nonlinearity 21 (2008), 2653–2670] for $n\geq 5$.

VIBRATION CHARACTERISTICS OF PERIODIC STRUCTURE WITH MICRO OCTAGON-LIKE UNIT CELL

Mechanika ◽  
2012 ◽  
Vol 18 (1) ◽  
Author(s):  
Yulin Mei ◽  
Xiaoming Wang ◽  
Xiaofeng Wang ◽  
Peng Liu
Keyword(s):  
Periodic Structure ◽  
Vibration Characteristics ◽  
Unit Cell

scholarly journals An efficient method for indexing grazing-incidence X-ray diffraction data of epitaxially grown thin films

2020 ◽  
Vol 76 (3) ◽  
pp. 345-357 ◽  
Author(s):  
Josef Simbrunner ◽  
Benedikt Schrode ◽  
Jari Domke ◽  
Torsten Fritz ◽  
Ingo Salzmann ◽  
...  
Keyword(s):  
Rotational Symmetry ◽  
Grazing Incidence ◽  
Unit Cell ◽  
Structure Identification ◽  
X Ray Diffraction ◽  
Cell Parameters ◽  
Lattice Constants ◽  
The Matrix ◽  
Unit Cells ◽  
Complex Scenario

Crystal structure identification of thin organic films entails a number of technical and methodological challenges. In particular, if molecular crystals are epitaxially grown on single-crystalline substrates a complex scenario of multiple preferred orientations of the adsorbate, several symmetry-related in-plane alignments and the occurrence of unknown polymorphs is frequently observed. In theory, the parameters of the reduced unit cell and its orientation can simply be obtained from the matrix of three linearly independent reciprocal-space vectors. However, if the sample exhibits unit cells in various orientations and/or with different lattice parameters, it is necessary to assign all experimentally obtained reflections to their associated individual origin. In the present work, an effective algorithm is described to accomplish this task in order to determine the unit-cell parameters of complex systems comprising different orientations and polymorphs. This method is applied to a polycrystalline thin film of the conjugated organic material 6,13-pentacenequinone (PQ) epitaxially grown on an Ag(111) surface. All reciprocal vectors can be allocated to unit cells of the same lattice constants but grown in various orientations [sixfold rotational symmetry for the contact planes (102) and (102)]. The as-determined unit cell is identical to that reported in a previous study determined for a fibre-textured PQ film. Preliminary results further indicate that the algorithm is especially effective in analysing epitaxially grown crystallites not only for various orientations, but also if different polymorphs are present in the film.

scholarly journals SELF-SIMILAR STRUCTURES IN BIOMECHANICS. HUMAN VIBRORECEPTORS

2021 ◽  
Vol 161 ◽  
pp. 10-19
Author(s):  
L.Ya. Banakh
Keyword(s):  
Periodic Structure ◽  
Mechanical Model ◽  
Dynamic Properties ◽  
Incoming Signal ◽  
Inertial Parameters ◽  
Self Similar ◽  
Pacini Corpuscle

The concept of dynamic-fractal self-similar structures (dynamic fractal) is introduced. This concept consists in scaling the dynamic, i.e. elastic-inertial parameters of the forming cells. It is shown that a dynamic fractal decreasing in length amplifies the incoming signal along the structure. A dynamic fractal that increases in length, on the contrary, has the good vibroisolation properties, the attenuation intensity in which is higher than in the periodic structure. The dynamic properties of the Pacini corpuscle, which is a human vibration detector, are investigated. Its mechanical model is constructed. It is shown that the vibroreceptor is a dynamic fractal with parameters decreasing in length. Therefore the vibroreceptor amplifies the incoming signal, which makes it possible to detect even weak vibration effects on a person

Fractal Models and the Structure of Materials

MRS Bulletin ◽  
1988 ◽  
Vol 13 (2) ◽  
pp. 22-27 ◽  
Author(s):  
Dale W. Schaefer
Keyword(s):  
Fractal Geometry ◽  
Materials Science ◽  
Rotational Symmetry ◽  
Disordered Materials ◽  
Growth Processes ◽  
Fractal Models ◽  
Kinetic Growth ◽  
Fractal Properties ◽  
New Ideas ◽  
Self Similar

Science often advances through the introdction of new ideas which simplify the understanding of complex problems. Materials science is no exception to this rule. Concepts such as nucleation in crystal growth and spinodal decomposition, for example, have played essential roles in the modern understanding of the structure of materials. More recently, fractal geometry has emerged as an essential idea for understanding the kinetic growth of disordered materials. This review will introduce the concept of fractal geometry and demonstrate its application to the understanding of the structure of materials.Fractal geometry is a natural concept used to describe random or disordered objects ranging from branched polymers to the earth's surface. Disordered materials seldom display translational or rotational symmetry so conventional crystallographic classification is of no value. These materials, however, often display “dilation symmetry,” which means they look geometrically self-similar under transformation of scale such as changing the magnification of a microscope. Surprisingly, most kinetic growth processes produce objects with self-similar fractal properties. It is now becoming clear that the origin of dilation symmetry is found in disorderly kinetic growth processes present in the formation of these materials.

Broadband Seismic Isolation of Periodic Ladder Frame Structure

2020 ◽  
Vol 143 (1) ◽  
Author(s):  
Rajan Prasad ◽  
Abhijit Sarkar
Keyword(s):  
Periodic Structure ◽  
Seismic Isolation ◽  
Periodic Structures ◽  
Stop Band ◽  
Design Guidelines ◽  
Unit Cell ◽  
Frame Structure ◽  
Design Parameters ◽  
Pictorial Presentation ◽  
Selection Of

Abstract Ladder frame structures are used as models for multistorey buildings. These periodic structures exhibit alternating propagating and attenuating frequency bands. Of the six different wave modes of propagation, two modes strongly attenuate at all frequencies. The other four modes have nonoverlapping stop band characteristics. Thus, it is challenging to isolate such structures when subjected to broadband, multimodal base excitation. In this study, we seek to synthesize a periodic ladder frame structure that has attenuation characteristics over the maximal range of frequencies for all the modes of wave propagation. We synthesize a unit cell of the periodic structure, which comprises two distinct regions having different inertial, stiffness, and geometric properties. The eigenvalues of the transfer matrix of the unit cell determines the attenuating or the nonattenuating characteristics of the structure. A novel pictorial presentation in the form of eigenvalue map is developed. This is used to synthesize the optimal unit cell. Also, design guidelines for suitable selection of the design parameters are presented. It is shown that a large finite periodic structure comprising a unit cell synthesized using the present approach has significantly better isolation characteristics in comparison to the homogeneous or any other arbitrarily chosen periodic structure.

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