Symmetry

256 KiB

Open AccessArticle

Symmetry Analysis and Conservation Laws of the Zoomeron Equation

by Tanki Motsepa, Chaudry Masood Khalique and Maria Luz Gandarias

Symmetry 2017, 9(2), 27; https://doi.org/10.3390/sym9020027 - 21 Feb 2017

Cited by 37 | Viewed by 4867

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 equation, for the ﬁrst [...] Read more.

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 equation, for the ﬁrst time we develop an optimal system of one-dimensional subalgebras. Based on this optimal system, we obtain symmetry reductions and new group-invariant solutions. Again for the ﬁrst time, we construct the conservation laws of the underlying equation using the multiplier method. Full article

(This article belongs to the Special Issue Lie and Conditional Symmetries and Their Applications for Solving Nonlinear Models)

1601 KiB

Open AccessArticle

A Symmetry Particle Method towards Implicit Non‐Newtonian Fluids

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

Symmetry 2017, 9(2), 26; https://doi.org/10.3390/sym9020026 - 17 Feb 2017

Cited by 8 | Viewed by 6249

Abstract

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 stress is determined by the Carreau‐Yasuda [...] Read more.

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 stress is determined by the Carreau‐Yasuda model. Then a pressure correction method is proposed, by correcting density error with individual stiffness parameters for each particle, to ensure the incompressibility of fluid. Finally, an implicit method is used to improve efficiency and stability. It is found that the nonNewtonian behavior can be well displayed in all cases, and the proposed SPH algorithm is stable and efficient. Full article

(This article belongs to the Special Issue Symmetry in Cooperative Applications II)

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3385 KiB

Open AccessArticle

Deformable Object Matching Algorithm Using Fast Agglomerative Binary Search Tree Clustering

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

Symmetry 2017, 9(2), 25; https://doi.org/10.3390/sym9020025 - 10 Feb 2017

Cited by 5 | Viewed by 5024

Abstract

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 using a statistical characteristic to obtain the feature [...] Read more.

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 using a statistical characteristic to obtain the feature points with the extraction method. Next, matching pairs are composed by the feature point matching of two images using the matching method. Rapid clustering is performed using the BST (Binary Search Tree) method by obtaining the geometric similarity between the matching pairs. Finally, the matching of the two images is determined after verifying the suitability of the composed cluster. An experiment with five different image sets with deformable objects confirmed the superior robustness and independence of the proposed algorithm while demonstrating up to 60 times faster matching speed compared to the conventional deformable object matching algorithms. Full article

(This article belongs to the Special Issue Symmetry in Complex Networks II)

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1308 KiB

Open AccessArticle

Single Image Super-Resolution by Non-Linear Sparse Representation and Support Vector Regression

by Yungang Zhang and Jieming Ma

Symmetry 2017, 9(2), 24; https://doi.org/10.3390/sym9020024 - 10 Feb 2017

Cited by 8 | Viewed by 4769

Abstract

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 well represented by linear sparse models. Moreover, many [...] Read more.

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 well represented by linear sparse models. Moreover, many sparsity-based SR methods require the image patch self-similarity assumption; however, the assumption may not always hold. In this paper, we propose a novel method for single image super-resolution (SISR). Unlike most prior sparsity-based SR methods, the proposed method uses non-linear sparse representation to enhance the description of the non-linear information in images, and the proposed framework does not need to assume the self-similarity of image patches. Based on the minimum reconstruction errors, support vector regression (SVR) is applied for predicting the SR image. The proposed method was evaluated on various benchmark images, and promising results were obtained. Full article

(This article belongs to the Special Issue Symmetry in Systems Design and Analysis)

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158 KiB

Open AccessErratum

Erratum: Rauh, A. Coherent States of Harmonic and Reversed Harmonic Oscillator. Symmetry, 2016, 8, 46

by Alexander Rauh

Symmetry 2017, 9(2), 23; https://doi.org/10.3390/sym9020023 - 9 Feb 2017

Viewed by 2833

Abstract

n/a Full article

20627 KiB

Open AccessArticle

A Study on Immersion of Hand Interaction for Mobile Platform Virtual Reality Contents

by Seunghun Han and Jinmo Kim

Symmetry 2017, 9(2), 22; https://doi.org/10.3390/sym9020022 - 5 Feb 2017

Cited by 30 | Viewed by 6921

Abstract

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. First, three-dimensional interactive content is produced for use [...] Read more.

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. First, three-dimensional interactive content is produced for use in the proposed interaction experiment while presenting an experiential environment that gives users a high sense of immersion in the mobile virtual reality environment. This is designed to induce the tension and concentration of users in line with the immersive virtual reality environment. Additionally, a hand interaction method based on gaze—which is mainly used for the entry of mobile virtual reality content—is proposed as a design method for immersive mobile virtual reality environment. The user satisfaction level of the immersive environment provided by the proposed gaze-based hand interaction is analyzed through experiments in comparison with the general method that uses gaze only. Furthermore, detailed analysis is conducted by dividing the effects of the proposed interaction method on user’s psychology into positive factors such as immersion and interest and negative factors such as virtual reality (VR) sickness and dizziness. In this process, a new direction is proposed for improving the immersion of users in the production of mobile platform virtual reality content. Full article

(This article belongs to the Special Issue Symmetry in Complex Networks II)

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2270 KiB

Open AccessArticle

Aesthetic Patterns with Symmetries of the Regular Polyhedron

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

Symmetry 2017, 9(2), 21; https://doi.org/10.3390/sym9020021 - 3 Feb 2017

Cited by 5 | Viewed by 8253

Abstract

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 regular polyhedra. Full article

(This article belongs to the Special Issue Polyhedral Structures)

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Graphical abstract

168 KiB

Open AccessEditorial

Acknowledgement to Reviewers of Symmetry in 2016

by Symmetry Editorial Office

Symmetry 2017, 9(2), 20; https://doi.org/10.3390/sym9020020 - 26 Jan 2017

Viewed by 3856

Abstract

The editors of Symmetry would like to express their sincere gratitude to the following reviewers for assessing manuscripts in 2016.[...] Full article

2984 KiB

Open AccessArticle

Cyclotomic Aperiodic Substitution Tilings

by Stefan Pautze

Symmetry 2017, 9(2), 19; https://doi.org/10.3390/sym9020019 - 25 Jan 2017

Cited by 6 | Viewed by 8615

Abstract

The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the

2 n

-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers [...] Read more.

The class of Cyclotomic Aperiodic Substitution Tilings (CASTs) is introduced. Its vertices are supported on the

2 n

-th cyclotomic field. It covers a wide range of known aperiodic substitution tilings of the plane with finite rotations. Substitution matrices and minimal inflation multipliers of CASTs are discussed as well as practical use cases to identify specimen with individual dihedral symmetry

D_{n}

or

D_{2 n}

, i.e., the tiling contains an infinite number of patches of any size with dihedral symmetry

D_{n}

or

D_{2 n}

only by iteration of substitution rules on a single tile. Full article

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Symmetry, Volume 9, Issue 2 (February 2017) – 9 articles

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