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Symmetry, Volume 6, Issue 2 (June 2014) – 17 articles , Pages 164-472

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1632 KiB  
Review
Chiral Liquid Crystals: Structures, Phases, Effects
by Ingo Dierking
Symmetry 2014, 6(2), 444-472; https://doi.org/10.3390/sym6020444 - 16 Jun 2014
Cited by 161 | Viewed by 19879
Abstract
The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of [...] Read more.
The introduction of chirality, i.e., the lack of mirror symmetry, has a profound effect on liquid crystals, not only on the molecular scale but also on the supermolecular scale and phase. I review these effects, which are related to the formation of supermolecular helicity, the occurrence of novel thermodynamic phases, as well as electro-optic effects which can only be observed in chiral liquid crystalline materials. In particular, I will discuss the formation of helical superstructures in cholesteric, Twist Grain Boundary and ferroelectric phases. As examples for the occurrence of novel phases the Blue Phases and Twist Grain Boundary phases are introduced. Chirality related effects are demonstrated through the occurrence of ferroelectricity in both thermotropic as well as lyotropic liquid crystals. Lack of mirror symmetry is also discussed briefly for some biopolymers such as cellulose and DNA, together with its influence on liquid crystalline behavior. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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604 KiB  
Review
Symmetry Detection in Visual Impairment: Behavioral Evidence and Neural Correlates
by Zaira Cattaneo, Silvia Bona, Corinna Bauer, Juha Silvanto, Andrew M. Herbert, Tomaso Vecchi and Lotfi B. Merabet
Symmetry 2014, 6(2), 427-443; https://doi.org/10.3390/sym6020427 - 26 May 2014
Cited by 13 | Viewed by 9652
Abstract
Bilateral symmetry is an extremely salient feature for the human visual system. An interesting issue is whether the perceptual salience of symmetry is rooted in normal visual development. In this review, we discuss empirical work on visual and tactile symmetry detection in normally [...] Read more.
Bilateral symmetry is an extremely salient feature for the human visual system. An interesting issue is whether the perceptual salience of symmetry is rooted in normal visual development. In this review, we discuss empirical work on visual and tactile symmetry detection in normally sighted and visually impaired individuals. On the one hand, available evidence suggests that efficient visual symmetry detection may need normal binocular vision development. On the other hand, converging evidence suggests that symmetry can develop as a principle of haptic perceptual organization in individuals lacking visual experience. Certain features of visual symmetry detection, however, such as the higher salience of the patterns containing a vertical axis of symmetry, do not systematically apply to the haptic modality. The neural correlates (revealed with neuroimaging) associated with visual and haptic symmetry detection are also discussed. Full article
(This article belongs to the Special Issue Visual Symmetry)
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398 KiB  
Case Report
The Symmetric-Partitioning and Incremental-Relearning Classification and Back-Propagation-Network Tree Approach for Cycle Time Estimation in Wafer Fabrication
by Toly Chen
Symmetry 2014, 6(2), 409-426; https://doi.org/10.3390/sym6020409 - 23 May 2014
Cited by 3 | Viewed by 5298
Abstract
An innovative classification and back-propagation-network tree (CABPN tree) approach is proposed in this study to estimate the cycle time of a job in a wafer fabrication factory, which is one of the most important tasks in controlling the wafer fabrication factory. The CABPN [...] Read more.
An innovative classification and back-propagation-network tree (CABPN tree) approach is proposed in this study to estimate the cycle time of a job in a wafer fabrication factory, which is one of the most important tasks in controlling the wafer fabrication factory. The CABPN tree approach is an extension from the traditional classification and regression tree (CART) approach. In CART, the cycle times of jobs of the same branch are estimated with the same value, which is far from accurate. To tackle this problem, the CABPN tree approach replaces the constant estimate with variant estimates. To this end, the cycle times of jobs of the same branch are estimated with a BPN, and may be different. In this way, the estimation accuracy can be improved. In addition, to determine the optimal location of the splitting point on a node, the symmetric partition with incremental re-learning (SP-IR) algorithm is proposed and illustrated with an example. The applicability of the CABPN tree approach is shown with a real case. The experimental results supported its effectiveness over several existing methods. Full article
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258 KiB  
Article
Invisibility and PT Symmetry: A Simple Geometrical Viewpoint
by Luis L. Sánchez-Soto and Juan J. Monzón
Symmetry 2014, 6(2), 396-408; https://doi.org/10.3390/sym6020396 - 22 May 2014
Cited by 12 | Viewed by 6147
Abstract
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry [...] Read more.
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible potentials appear as performing null rotations, which lead to the helicity-gauge symmetry of massless particles. In hyperbolic geometry, this can be interpreted, via Möbius transformations, as parallel displacements, a geometric action that has no Euclidean analogy. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
1359 KiB  
Review
Hydrodynamic Helical Orientations of Nanofibers in a Vortex
by Akihiko Tsuda
Symmetry 2014, 6(2), 383-395; https://doi.org/10.3390/sym6020383 - 20 May 2014
Cited by 8 | Viewed by 7625
Abstract
In this review article, I report our recent studies on spectroscopic visualizations of macroscopic helical alignments of nanofibers in vortex flows. Our designed supramolecular nanofibers, formed through self-assemblies of dye molecules, helically align in torsional flows of a vortex generated by mechanical rotary [...] Read more.
In this review article, I report our recent studies on spectroscopic visualizations of macroscopic helical alignments of nanofibers in vortex flows. Our designed supramolecular nanofibers, formed through self-assemblies of dye molecules, helically align in torsional flows of a vortex generated by mechanical rotary stirring of the sample solutions. The nanofiber, formed through bundling of linear supramolecular polymers, aligns equally in right- and left-handed vortex flows. However, in contrast, a one-handedly twisted nanofiber, formed through helical bundling of the supramolecular polymers, shows unequal helical alignments in these torsional flows. When the helical handedness of the nanofiber matches that of the vortex flow, the nanofiber aligns more efficiently in the flowing fluid. Such phenomena are observed not only with the artificial helical supramolecular nanofibers but also with biological nanofibers such as double-stranded DNA. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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290 KiB  
Article
Symmetry Perspectives on Some Auxetic Body-Bar Frameworks
by Patrick W. Fowler, Simon D. Guest and Tibor Tarnai
Symmetry 2014, 6(2), 368-382; https://doi.org/10.3390/sym6020368 - 15 May 2014
Cited by 8 | Viewed by 6500
Abstract
Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied [...] Read more.
Scalar mobility counting rules and their symmetry extensions are reviewed for finite frameworks and also for infinite periodic frameworks of the bar-and-joint, body-joint and body-bar types. A recently published symmetry criterion for the existence of equiauxetic character of an infinite framework is applied to two long known but apparently little studied hinged-hexagon frameworks, and is shown to detect auxetic behaviour in both. In contrast, for double-link frameworks based on triangular and square tessellations, other affine deformations can mix with the isotropic expansion mode. Full article
(This article belongs to the Special Issue Rigidity and Symmetry)
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2656 KiB  
Article
Dynamic Processes in Prochiral Solvating Agents (pro-CSAs) Studied by NMR Spectroscopy
by Jan Labuta, Shinsuke Ishihara, Katsuhiko Ariga and Jonathan P. Hill
Symmetry 2014, 6(2), 345-367; https://doi.org/10.3390/sym6020345 - 14 May 2014
Cited by 11 | Viewed by 6863
Abstract
Several dynamic processes, including tautomerism and macrocyclic inversion, in 1H-NMR prochiral solvating agents (pro-CSAs) are investigated. Various features of pro-CSA, including modes of interaction for complex formation, stoichiometry, binding strength and temperature effects were compared for three representative pro-CSA molecules. Structural effects [...] Read more.
Several dynamic processes, including tautomerism and macrocyclic inversion, in 1H-NMR prochiral solvating agents (pro-CSAs) are investigated. Various features of pro-CSA, including modes of interaction for complex formation, stoichiometry, binding strength and temperature effects were compared for three representative pro-CSA molecules. Structural effects of conjugated tetrapyrrole pro-CSA on the mechanism of enantiomeric excess determination are also discussed. Detailed analysis of species (complexes) and dynamic processes occurring in solution and their 1H-NMR spectral manifestations at various temperatures is presented. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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330 KiB  
Article
Closed-Form Expressions for the Matrix Exponential
by F. De Zela
Symmetry 2014, 6(2), 329-344; https://doi.org/10.3390/sym6020329 - 29 Apr 2014
Cited by 5 | Viewed by 9392
Abstract
We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to [...] Read more.
We discuss a method to obtain closed-form expressions of f(A), where f is an analytic function and A a square, diagonalizable matrix. The method exploits the Cayley–Hamilton theorem and has been previously reported using tools that are perhaps not sufficiently appealing to physicists. Here, we derive the results on which the method is based by using tools most commonly employed by physicists. We show the advantages of the method in comparison with standard approaches, especially when dealing with the exponential of low-dimensional matrices. In contrast to other approaches that require, e.g., solving differential equations, the present method only requires the construction of the inverse of the Vandermonde matrix. We show the advantages of the method by applying it to different cases, mostly restricting the calculational effort to the handling of two-by-two matrices. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
617 KiB  
Article
The Almost Periodic Rigidity of Crystallographic Bar-Joint Frameworks
by Ghada Badri, Derek Kitson and Stephen C. Power
Symmetry 2014, 6(2), 308-328; https://doi.org/10.3390/sym6020308 - 24 Apr 2014
Cited by 10 | Viewed by 6316
Abstract
A crystallographic bar-joint framework, C in Rd, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω (C), is a singleton. Moreover, the [...] Read more.
A crystallographic bar-joint framework, C in Rd, is shown to be almost periodically infinitesimally rigid if and only if it is strictly periodically infinitesimally rigid and the rigid unit mode (RUM) spectrum, Ω (C), is a singleton. Moreover, the almost periodic infinitesimal flexes of C are characterised in terms of a matrix-valued function, ΦC(z), on the d-torus, Td, determined by a full rank translation symmetry group and an associated motif of joints and bars. Full article
(This article belongs to the Special Issue Rigidity and Symmetry)
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179 KiB  
Article
Dynamical Relation between Quantum Squeezing and Entanglement in Coupled Harmonic Oscillator System
by Lock Yue Chew and Ning Ning Chung
Symmetry 2014, 6(2), 295-307; https://doi.org/10.3390/sym6020295 - 23 Apr 2014
Cited by 5 | Viewed by 6643
Abstract
In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in [...] Read more.
In this paper, we investigate into the numerical and analytical relationship between the dynamically generated quadrature squeezing and entanglement within a coupled harmonic oscillator system. The dynamical relation between these two quantum features is observed to vary monotically, such that an enhancement in entanglement is attained at a fixed squeezing for a larger coupling constant. Surprisingly, the maximum attainable values of these two quantum entities are found to consistently equal to the squeezing and entanglement of the system ground state. In addition, we demonstrate that the inclusion of a small anharmonic perturbation has the effect of modifying the squeezing versus entanglement relation into a nonunique form and also extending the maximum squeezing to a value beyond the system ground state. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
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1066 KiB  
Review
Supramolecular Chirality in Porphyrin Chemistry
by Victor Borovkov
Symmetry 2014, 6(2), 256-294; https://doi.org/10.3390/sym6020256 - 23 Apr 2014
Cited by 65 | Viewed by 11515
Abstract
Supramolecular chirality, being an intelligent combination of supramolecular chemistry and chiral science, plays a decisive role in the functioning of various natural assemblies and has attracted much attention from the scientific community, due to different applications in modern technologies, medicine, pharmacology, catalysis and [...] Read more.
Supramolecular chirality, being an intelligent combination of supramolecular chemistry and chiral science, plays a decisive role in the functioning of various natural assemblies and has attracted much attention from the scientific community, due to different applications in modern technologies, medicine, pharmacology, catalysis and biomimetic research. Porphyrin molecules are of particular interest to study this phenomenon owing to their unique spectral, physico-chemical and synthetic properties. This review highlights the most important types of chiral porphyrin structures by using the best-suited representative examples, which are frequently used in the area of supramolecular chirality. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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335 KiB  
Review
Quantum Local Symmetry of the D-Dimensional Non-Linear Sigma Model: A Functional Approach
by Andrea Quadri
Symmetry 2014, 6(2), 234-255; https://doi.org/10.3390/sym6020234 - 17 Apr 2014
Cited by 1 | Viewed by 5551
Abstract
We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transformations. The deformation of the [...] Read more.
We summarize recent progress on the symmetric subtraction of the Non-Linear Sigma Model in D dimensions, based on the validity of a certain Local Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure under local left transformations. The deformation of the classical non-linearly realized symmetry at the quantum level is analyzed by cohomological tools. It is shown that all the divergences of the one-particle irreducible (1-PI) amplitudes (both on-shell and off-shell) can be classified according to the solutions of the LFE. Applications to the non-linearly realized Yang-Mills theory and to the electroweak theory, which is directly relevant to the model-independent analysis of LHC data, are briefly addressed. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
3443 KiB  
Article
Domain Specificity in Human Symmetry Preferences: Symmetry is Most Pleasant When Looking at Human Faces
by Anthony C. Little
Symmetry 2014, 6(2), 222-233; https://doi.org/10.3390/sym6020222 - 17 Apr 2014
Cited by 31 | Viewed by 20066
Abstract
Visual symmetry has been found to be preferred to asymmetry in a variety of domains and across species. A number of theories propose to explain why symmetry is preferred. In this article, I compare a perceptual bias view, in which symmetry is preferred [...] Read more.
Visual symmetry has been found to be preferred to asymmetry in a variety of domains and across species. A number of theories propose to explain why symmetry is preferred. In this article, I compare a perceptual bias view, in which symmetry is preferred due to factors inherit to the visual system, and an evolutionary advantage view, in which symmetry is preferred due to selection pressures on partner preference. Preferences for symmetry in three stimulus types were determined by having symmetric and asymmetric versions of the same images rated for pleasantness: human female faces, macaque monkey faces, and abstract art. It was found that preferences for symmetry were strongest for human female faces and weakest for art. This finding builds on previous research suggesting that symmetry preferences for human faces are different from symmetry preferences in other domains and that simple perceptual bias explanations do not wholly explain human visual face symmetry preferences. While consistent with an evolutionary advantage view, these data are also potentially explainable via a perceptual bias view which accounts for experience of stimuli. The interplay between these two views is discussed in the context of the current study. Full article
(This article belongs to the Special Issue Visual Symmetry)
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256 KiB  
Review
Metalloporphyrin Symmetry in Chiral Recognition and Enantioselective Catalysis
by Gérard Simonneaux, Hassan Srour, Paul Le Maux, Soizic Chevance and Daniel Carrie
Symmetry 2014, 6(2), 210-221; https://doi.org/10.3390/sym6020210 - 10 Apr 2014
Cited by 15 | Viewed by 8234
Abstract
Symmetry plays a fundamental role in chiral recognition and enantioselective catalysis. Porphyrins possess a number of structural features that make them attractive for the stereocontrol of chiral recognition and metal-catalyzed asymmetric reactions. This article is a brief account of our studies on chiral [...] Read more.
Symmetry plays a fundamental role in chiral recognition and enantioselective catalysis. Porphyrins possess a number of structural features that make them attractive for the stereocontrol of chiral recognition and metal-catalyzed asymmetric reactions. This article is a brief account of our studies on chiral recognition and enantioselective catalysis by optically active metalloporphyrins. Some of the studies on chiral recognition and asymmetric catalysis by metalloporphyrins performed by others have also been included when useful. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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266 KiB  
Article
Topological Symmetry Groups of Small Complete Graphs
by Dwayne Chambers and Erica Flapan
Symmetry 2014, 6(2), 189-209; https://doi.org/10.3390/sym6020189 - 8 Apr 2014
Cited by 14 | Viewed by 5788
Abstract
Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R3. In this paper, we determine for each complete graph Kn with n [...] Read more.
Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R3. In this paper, we determine for each complete graph Kn with n ≤ 6, what groups can occur as topological symmetry groups or orientation preserving topological symmetry groups of some embedding of the graph in R3. Full article
(This article belongs to the Special Issue Supramolecular Chirality)
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493 KiB  
Article
Development of Symmetry Concepts for Aperiodic Crystals
by Ted Janssen
Symmetry 2014, 6(2), 171-188; https://doi.org/10.3390/sym6020171 - 31 Mar 2014
Cited by 1 | Viewed by 5523
Abstract
An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. [...] Read more.
An overview is given of the use of symmetry considerations for aperiodic crystals. Superspace groups were introduced in the seventies for the description of incommensurate modulated phases with one modulation vector. Later, these groups were also used for quasi-periodic crystals of arbitrary rank. Further extensions use time reversal and time translation operations on magnetic and electrodynamic systems. An alternative description of magnetic structures to that with symmetry groups, the Shubnikov groups, is using representations of space groups. The same can be done for aperiodic crystals. A discussion of the relation between the two approaches is given. Representations of space groups and superspace groups play a role in the study of physical properties. These, and generalizations of them, are discussed for aperiodic crystals. They are used, in particular, for the characterization of phase transitions between aperiodic crystal phases. Full article
(This article belongs to the Special Issue Crystal Symmetry and Structure)
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198 KiB  
Article
Spacetime Metrics from Gauge Potentials
by Ettore Minguzzi
Symmetry 2014, 6(2), 164-170; https://doi.org/10.3390/sym6020164 - 27 Mar 2014
Viewed by 5128
Abstract
I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the [...] Read more.
I present an approach to gravity in which the spacetime metric is constructed from a non-Abelian gauge potential with values in the Lie algebra of the group U(2) (or the Lie algebra of quaternions). If the curvature of this potential vanishes, the metric reduces to a canonical curved background form reminiscent of the Friedmann S3 cosmological metric. Full article
(This article belongs to the Special Issue Physics based on Two-by-two Matrices)
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