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Symmetry, Volume 9, Issue 2

February 2017 - 9 articles

Cover Story: We introduced the class of Cyclotomic Aperiodic Substitution Tilings (CASTs) which covers a wide range of new and well known substitution tilings, e.g. those discovered by R. Penrose, R. Ammann, F.P.M. Beenker and L. Danzer. We investigated general properties, detailed substitution matrices and minimal inflation multipliers, as well as practical use cases to identify new specimens with individual dihedral symmetry Dn or D2n.
The figure shows an aperiodic rhomb substitution tiling (based on the substitution rules in Figure 14, example n = 6) with individual dihedral symmetry D12 and minimal inflation multiplier under the given boundary conditions. While for “odd n”, the identification of substitution rules is a rather straight forward exercise, the “even n” case tends to be more complex. View the paper
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Articles (9)

  • Article
  • Open Access
37 Citations
5,264 Views
11 Pages

Symmetry Analysis and Conservation Laws of the Zoomeron Equation

  • Tanki Motsepa,
  • Chaudry Masood Khalique and
  • Maria Luz Gandarias

21 February 2017

In this work, we study the (2 + 1)-dimensional Zoomeron equation which is an extension of the famous (1 + 1)-dimensional Zoomeron equation that has been studied extensively in the literature. Using classical Lie point symmetries admitted by the equat...

  • Article
  • Open Access
8 Citations
6,790 Views
13 Pages

A Symmetry Particle Method towards Implicit Non‐Newtonian Fluids

  • Yalan Zhang,
  • Xiaojuan Ban,
  • Xiaokun Wang and
  • Xing Liu

17 February 2017

In this paper, a symmetry particle method, the smoothed particle hydrodynamics (SPH) method, is extended to deal with non‐Newtonian fluids. First, the viscous liquid is modeled by a non‐Newtonian fluid flow and the variable viscosity under shear stre...

  • Article
  • Open Access
8 Citations
5,269 Views
15 Pages

10 February 2017

Sparse representations are widely used tools in image super-resolution (SR) tasks. In the sparsity-based SR methods, linear sparse representations are often used for image description. However, the non-linear data distributions in images might not be...

  • Article
  • Open Access
5 Citations
5,444 Views
18 Pages

Deformable Object Matching Algorithm Using Fast Agglomerative Binary Search Tree Clustering

  • Jaehyup Jeong,
  • Insu Won,
  • Hunjun Yang,
  • Bowon Lee and
  • Dongseok Jeong

10 February 2017

Deformable objects have changeable shapes and they require a different method of matching algorithm compared to rigid objects. This paper proposes a fast and robust deformable object matching algorithm. First, robust feature points are selected usi...

  • Article
  • Open Access
31 Citations
7,608 Views
17 Pages

5 February 2017

This study proposes gaze-based hand interaction, which is helpful for improving the user’s immersion in the production process of virtual reality content for the mobile platform, and analyzes efficiency through an experiment using a questionnaire. Fi...

  • Article
  • Open Access
5 Citations
8,772 Views
8 Pages

Aesthetic Patterns with Symmetries of the Regular Polyhedron

  • Peichang Ouyang,
  • Liying Wang,
  • Tao Yu and
  • Xuan Huang

3 February 2017

A fast algorithm is established to transform points of the unit sphere into fundamental region symmetrically. With the resulting algorithm, a flexible form of invariant mappings is achieved to generate aesthetic patterns with symmetries of the regula...

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Symmetry - ISSN 2073-8994Creative Common CC BY license