Teaching Point-Group Symmetry with Three-Dimensional Models
ERIC Educational Resources Information Center
Flint, Edward B.
2011-01-01
Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold…
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
DNA Cages with Icosahedral Symmetry in Bionanotechnology
NASA Astrophysics Data System (ADS)
Jonoska, Nataša; Taormina, Anne; Twarock, Reidun
Blueprints for polyhedral cages with icosahedral symmetry made of circular DNA molecules are provided. The basic rule is that every edge of the cage is met twice in opposite directions by the DNA strand(s), and vertex junctions are realized by a set of admissible junction types. As nanocontainers for cargo storage and delivery, the icosidodecahedral cages are of special interest because they have the largest volume per surface ratio of all cages discussed here.
ERIC Educational Resources Information Center
Fuchigami, Kei; Schrandt, Matthew; Miessler, Gary L.
2016-01-01
A hands-on symmetry project is proposed as an innovative way of teaching point groups to undergraduate chemistry students. Traditionally, courses teaching symmetry require students to identify the point group of a given object. This project asks the reverse: students are instructed to identify an object that matches each point group. Doing so…
Group Representations and Multinomial Combinatorics of the Icosahedral Symmetry
Balasubramanian, K
2004-02-02
The icosahedral symmetry is one of the most intriguing symmetries, as it not only presents challenge but it appears in many fullerenes and high energetic materials such as the dodecahedral N{sub 20}. We have considered the combinatorics of all irreducible representations of the icosahedral symmetry for a number of multinomial partitions for vertex, face and edge colorings in this work. We have constructed the combinatorial tables for all irreducible representations for various multinomial partitions of colorings for the vertices, edge and faces of the icosahedron. These techniques should have important applications to enumerations and spectroscopy of fullerenes and high-energy materials such as N{sub 20}.
Crystallography of decahedral and icosahedral particles. II - High symmetry orientations
NASA Technical Reports Server (NTRS)
Yang, C. Y.; Yacaman, M. J.; Heinemann, K.
1979-01-01
Based on the exact crystal structure of decahedral and icosahedral particles, high energy electron diffraction patterns and image profiles have been derived for various high symmetry orientations of the particles with respect to the incident beam. These results form a basis for the identification of small metal particle structures with advanced methods of transmission electron microscopy.
Virus templated plasmonic nanoclusters with icosahedral symmetry via directed assembly
NASA Astrophysics Data System (ADS)
Ratna, Banahalli; Fontana, Jake; Dressick, Walter; Phelps, Jamie; Johnson, John; Sampson, Travian; Rendell, Ronald; Soto, Carissa
2015-03-01
Controlling the spatial and orientational order of plasmonic nanoparticles may lead to structures with novel electromagnetic properties and applications such as sub-wavelength imaging and ultra-sensitive chemical sensors. Here we report the directed assembly of three-dimensional, icosahedral plasmonic nanoclusters with resonances at visible wavelengths. We show using transmission electron microcopy and in situ dynamic light scattering the nanoclusters consist of twelve gold nanospheres attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. We measured the bulk absorbance from aqueous suspensions of nanoclusters and reproduced the major features of the spectrum using finite-element simulations. Furthermore, because the viruses are easily produced in gram quantities the directed assembly approach is capable of high-throughput, providing a strategy to realize large quantities for applications. NRL summer intern under the HBCU/MI Summer Research Program.
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
ERIC Educational Resources Information Center
Casas, Lluís; Estop, Euge`nia
2015-01-01
Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
NASA Astrophysics Data System (ADS)
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-03-01
Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four students in a sophomore-level inorganic chemistry class at a small private university were divided by pre-selected lab groups into two groups, lecture and computer, for introductory information about point group symmetry. Both groups had low prior knowledge of symmetry elements although the lecture group had significantly higher knowledge than the computer group. After initial instruction, the lecture group scored significantly higher than the computer group on a point group assessment, even when prior knowledge was controlled. A second assessment, given after both groups had follow-up information from computer courseware, showed no significant difference between the groups. The computer group significantly improved between the two assessments, the lecture group did not. At the end-of-the semester post-test showed no significant difference between the two groups, although only 50% of the students in each group achieved mastery. Factors affecting the significant improvement of the low prior knowledge, computer group were examined and recommendations for future research provided.
Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections
ERIC Educational Resources Information Center
Chen, Lan; Sun, Hongwei; Lai, Chengming
2015-01-01
There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.
Bodner, Mark; Bourret, Emmanuel; Patera, Jiri; Szajewska, Marzena
2015-05-01
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120. This subgroup is noted by A1 × A1, because it is isomorphic to the Weyl group of the semi-simple Lie algebra A1 × A1. Thirteen of the A1 × A1 orbits are rectangles and four are line segments. The orbits form a stack of parallel layers centered on the axis of C60 passing through the centers of two opposite edges between two hexagons on the surface of C60. These two edges are the only two line segment layers to appear on the surface shell. Among the 24 convex polytopes with shell formed by hexagons and 12 pentagons, having 84 vertices [Fowler & Manolopoulos (1992). Nature (London), 355, 428-430; Fowler & Manolopoulos (2007). An Atlas of Fullerenes. Dover Publications Inc.; Zhang et al. (1993). J. Chem. Phys. 98, 3095-3102], there are only two that can be identified with breaking of the H3 symmetry to A1 × A1. The remaining ones are just convex shells formed by regular hexagons and 12 pentagons without the involvement of the icosahedral symmetry.
Kumar, Mohit
2013-01-01
Minor group human rhinoviruses bind low-density lipoprotein (LDL) receptors for endocytosis. Once they are inside endosomes, the acidic pH triggers their dissociation from the receptors and conversion into hydrophobic subviral A particles; these attach to the membrane and transfer their single-strand, positive-sense RNA genome into the cytosol. Here, we allowed human rhinovirus 2 (HRV2) A particles, produced in vitro by incubation at pH 5.4, to attach to liposomes; cryo-electron microscopy 3-dimensional single-particle image reconstruction revealed that they bind to the membrane around a 2-fold icosahedral symmetry axis. PMID:23946453
Köppl, Christoph; Werner, Hans-Joachim
2015-04-28
Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally do not transform according to irreducible representations of the underlying point group symmetry. Instead, groups of LMOs become symmetry-equivalent and this can be exploited to accelerate local calculations. We describe an implementation of such a symmetry treatment for density-fitted local Møller-Plesset perturbation theory, using various types of virtual orbitals: Projected atomic orbitals, orbital specific virtuals, and pair natural orbitals. The savings by the symmetry treatment are demonstrated by calculations for several large molecules having different point group symmetries. Benchmarks for the parallel execution efficiency of our method are also presented.
Mathivathanan, Logesh; Cruz, Raquel; Raptis, Raphael G.
2016-01-01
The trinuclear triangular cuprate anion of the title compound, tris[bis(triphenylphosphoranylidene)ammonium] tris(μ2-4-chloropyrazolato-κ2 N:N′)-μ3-oxido-tris[(nitrato-κ2 O,O′)cuprate(II)] nitrate monohydrate, (C36H30P2N)[Cu3(C3H2ClN2)3(NO3)3O]NO3·H2O, has point group symmetry 3., with the μ3-O atom located on the threefold rotation axis. The distorted square-pyramidal coordination sphere of the CuII atom is completed by two N atoms of trans-bridging pyrazolate groups and a chelating nitrate anion. The complex anion is slightly bent, with the nitrate and pyrazolate groups occupying positions above and below the Cu3 plane, respectively. In the crystal, weak O—H⋯O and C—H⋯O hydrogen bonds, as well as π–π interactions, are present. PMID:27375872
Symmetry-adapted digital modeling III. Coarse-grained icosahedral viruses.
Janner, A
2016-05-01
Considered is the coarse-grained modeling of icosahedral viruses in terms of a three-dimensional lattice (the digital modeling lattice) selected among the projected points in space of a six-dimensional icosahedral lattice. Backbone atomic positions (Cα's for the residues of the capsid and phosphorus atoms P for the genome nucleotides) are then indexed by their nearest lattice point. This leads to a fine-grained lattice point characterization of the full viral chains in the backbone approximation (denoted as digital modeling). Coarse-grained models then follow by a proper selection of the indexed backbone positions, where for each chain one can choose the desired coarseness. This approach is applied to three viruses, the Satellite tobacco mosaic virus, the bacteriophage MS2 and the Pariacoto virus, on the basis of structural data from the Brookhaven Protein Data Bank. In each case the various stages of the procedure are illustrated for a given coarse-grained model and the corresponding indexed positions are listed. Alternative coarse-grained models have been derived and compared. Comments on related results and approaches, found among the very large set of publications in this field, conclude this article. PMID:27126109
Continuous symmetry measures for complex symmetry group.
Dryzun, Chaim
2014-04-01
Symmetry is a fundamental property of nature, used extensively in physics, chemistry, and biology. The Continuous symmetry measures (CSM) is a method for estimating the deviation of a given system from having a certain perfect symmetry, which enables us to formulate quantitative relation between symmetry and other physical properties. Analytical procedures for calculating the CSM of all simple cyclic point groups are available for several years. Here, we present a methodology for calculating the CSM of any complex point group, including the dihedral, tetrahedral, octahedral, and icosahedral symmetry groups. We present the method and analyze its performances and errors. We also introduce an analytical method for calculating the CSM of the linear symmetry groups. As an example, we apply these methods for examining the symmetry of water, the symmetry maps of AB4 complexes, and the symmetry of several Lennard-Jones clusters.
Crystallography of decahedral and icosahedral particles. I - Geometry of twinning
NASA Technical Reports Server (NTRS)
Yang, C. Y.
1979-01-01
The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah
2014-01-01
Marine viruses play crucial roles in shaping the dynamics of oceanic microbial communities and in the carbon cycle on Earth. Here we report a 4.7-Å structure of a cyanobacterial virus, Syn5, by electron cryo-microscopy and modelling. A Cα backbone trace of the major capsid protein (gp39) reveals a classic phage protein fold. In addition, two knob-like proteins protruding from the capsid surface are also observed. Using bioinformatics and structure analysis tools, these proteins are identified to correspond to gp55 and gp58 (each with two copies per asymmetric unit). The non 1:1 stoichiometric distribution of gp55/58 to gp39 breaks all expected local symmetries and leads to non-quasi-equivalence of the capsid subunits, suggesting a role in capsid stabilization. Such a structural arrangement has not yet been observed in any known virus structures. PMID:24985522
Approximation of virus structure by icosahedral tilings.
Salthouse, D G; Indelicato, G; Cermelli, P; Keef, T; Twarock, R
2015-07-01
Viruses are remarkable examples of order at the nanoscale, exhibiting protein containers that in the vast majority of cases are organized with icosahedral symmetry. Janner used lattice theory to provide blueprints for the organization of material in viruses. An alternative approach is provided here in terms of icosahedral tilings, motivated by the fact that icosahedral symmetry is non-crystallographic in three dimensions. In particular, a numerical procedure is developed to approximate the capsid of icosahedral viruses by icosahedral tiles via projection of high-dimensional tiles based on the cut-and-project scheme for the construction of three-dimensional quasicrystals. The goodness of fit of our approximation is assessed using techniques related to the theory of polygonal approximation of curves. The approach is applied to a number of viral capsids and it is shown that detailed features of the capsid surface can indeed be satisfactorily described by icosahedral tilings. This work complements previous studies in which the geometry of the capsid is described by point sets generated as orbits of extensions of the icosahedral group, as such point sets are by construction related to the vertex sets of icosahedral tilings. The approximations of virus geometry derived here can serve as coarse-grained models of viral capsids as a basis for the study of virus assembly and structural transitions of viral capsids, and also provide a new perspective on the design of protein containers for nanotechnology applications. PMID:26131897
Highly symmetric Mn sites in icosahedral Ti-Mn
Jeong, E.; Holzer, J.C.; Carlsson, A.E.; Conradi, M.S.; Fedders, P.A.; Kelton, K.F. )
1990-01-15
We find that the {sup 55}Mn NMR linewidth and Knight shift of icosahedral Ti{sub 63}Mn{sub 37} ({ital i}-TiMn) are identical to those of the crystalline phases obtained upon annealing. Comparison of the linewidth in {ital i}-TiMn and a bcc Ti-Mn solid solution shows that the Mn sites in both phases have a nearly cubic or higher symmetry. These measurements and our analysis provide strong evidence for a large density of structurally ordered, highly symmetric sites in an icosahedral alloy and demonstrate that a high degree of structural disorder is not an intrinsic property of the icosahedral phase.
About the atomic structures of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Quiquandon, Marianne; Gratias, Denis
2014-01-01
This paper is a survey of the crystallographic methods that have been developed these last twenty five years to decipher the atomic structures of the icosahedral stable quasicrystals since their discovery in 1982 by D. Shechtman. After a brief recall of the notion of quasiperiodicity and the natural description of Z-modules in 3-dim as projection of regular lattices in N>3-dim spaces, we give the basic geometrical ingredients useful to describe icosahedral quasicrystals as irrational 3-dim cuts of ordinary crystals in 6-dim space. Atoms are described by atomic surfaces (ASs) that are bounded volumes in the internal (or perpendicular) 3-dim space and the intersections of which with the physical space are the actual atomic positions. The main part of the paper is devoted to finding the major properties of quasicrystalline icosahedral structures. As experimentally demonstrated, they can be described with a surprisingly few high symmetry ASs located at high symmetry special points in 6-dim space. The atomic structures are best described by aggregations and intersections of high symmetry compact interpenetrating atomic clusters. We show here that the experimentally relevant clusters are derived from one generic cluster made of two concentric triacontahedra scaled by τ and an external icosidodecahedron. Depending on which ones of the orbits of this cluster are eventually occupied by atoms, the actual atomic clusters are of type Bergman, Mackay, Tsai and others….
Classification of point-group-symmetric orientational ordering tensors
NASA Astrophysics Data System (ADS)
Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan; Wu, Kai; Zaanen, Jan
2016-08-01
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational-symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e., O(3), to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge-theoretical framework, to address the three-dimensional point-group-symmetric orientational orders on a general footing. This unified approach allows us to enlist order parameter tensors for all three-dimensional point groups. By construction, these tensor order parameters are the minimal set of simplest tensors allowed by the symmetries that uniquely characterize the orientational order. We explicitly give these for the point groups {Cn,Dn,T ,O ,I } ⊂SO(3 ) and {Cn v,S2 n,Cn h,Dn h,Dn d,Th,Td,Oh,Ih} ⊂O(3 ) for n ,2 n ∈{1 ,2 ,3 ,4 ,6 ,∞ } . This central result may be perceived as a road map for identifying exotic orientational orders that may become more and more in reach in view of rapid experimental progress in, e.g., nanocolloidal systems and novel magnets.
Classification of point-group-symmetric orientational ordering tensors.
Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan; Wu, Kai; Zaanen, Jan
2016-08-01
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational-symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e., O(3), to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge-theoretical framework, to address the three-dimensional point-group-symmetric orientational orders on a general footing. This unified approach allows us to enlist order parameter tensors for all three-dimensional point groups. By construction, these tensor order parameters are the minimal set of simplest tensors allowed by the symmetries that uniquely characterize the orientational order. We explicitly give these for the point groups {C_{n},D_{n},T,O,I}⊂SO(3) and {C_{nv},S_{2n},C_{nh},D_{nh},D_{nd},T_{h},T_{d},O_{h},I_{h}}⊂O(3) for n,2n∈{1,2,3,4,6,∞}. This central result may be perceived as a road map for identifying exotic orientational orders that may become more and more in reach in view of rapid experimental progress in, e.g., nanocolloidal systems and novel magnets. PMID:27627370
A crystallographic approach to structural transitions in icosahedral viruses.
Indelicato, Giuliana; Cermelli, Paolo; Salthouse, David G; Racca, Simone; Zanzotto, Giovanni; Twarock, Reidun
2012-04-01
Viruses with icosahedral capsids, which form the largest class of all viruses and contain a number of important human pathogens, can be modelled via suitable icosahedrally invariant finite subsets of icosahedral 3D quasicrystals. We combine concepts from the theory of 3D quasicrystals, and from the theory of structural phase transformations in crystalline solids, to give a framework for the study of the structural transitions occurring in icosahedral viral capsids during maturation or infection. As 3D quasicrystals are in a one-to-one correspondence with suitable subsets of 6D icosahedral Bravais lattices, we study systematically the 6D-analogs of the classical Bain deformations in 3D, characterized by minimal symmetry loss at intermediate configurations, and use this information to infer putative viral-capsid transition paths in 3D via the cut-and-project method used for the construction of quasicrystals. We apply our approach to the Cowpea Chlorotic Mottle virus (CCMV) and show that the putative transition path between the experimentally observed initial and final CCMV structures is most likely to preserve one threefold axis. Our procedure suggests a general method for the investigation and prediction of symmetry constraints on the capsids of icosahedral viruses during structural transitions, and thus provides insights into the mechanisms underlying structural transitions of these pathogens. PMID:21611828
Cubic Icosahedra? A Problem in Assigning Symmetry
ERIC Educational Resources Information Center
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays
NASA Astrophysics Data System (ADS)
Zappa, Emilio; Dykeman, Eric C.; Geraets, James A.; Twarock, Reidun
2016-04-01
In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally proposed by Kramer, to the case of aperiodic structures with icosahedral symmetry; these rotations induce a rotation of the physical and orthogonal spaces invariant under the icosahedral group, and hence, via the cut-and-project method, a continuous transformation of the corresponding model sets. We prove that this approach allows for a characterisation of such transitions in a purely group theoretical framework, and provide explicit computations and specific examples. Moreover, we prove that this approach can be used in the case of finite point sets with icosahedral symmetry, which have a wide range of applications in carbon chemistry (fullerenes) and biology (viral capsids).
Mechanical properties of icosahedral virus capsids
NASA Astrophysics Data System (ADS)
Vliegenthart, G. A.; Gompper, G.
2007-12-01
Virus capsids are self-assembled protein shells in the size range of 10 to 100 nanometers. The shells of DNA-viruses have to sustain large internal pressures while encapsulating and protecting the viral DNA. We employ computer simulations to study the mechanical properties of crystalline shells with icosahedral symmetry that serve as a model for virus capsids. The shells are positioned on a substrate and deformed by a uni-axial force excerted by a small bead. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number N of elementary building blocks (capsomers), and the Föppl-von Kármán number γ which characterizes the relative importance of shear and bending elasticity.
Icosahedral phase stabilities in Al-Cu-Ru alloys
Shield, J.E.; Hoppe, C.; McCallum, R.W.; Goldman, A.I. ); Kelton, K.F.; Gibbons, P.C. )
1992-02-01
By examining a wide region of the Al-Cu-Ru phase diagram, a thorough analysis of the compositional and thermal stability of the icosahedral phase has been completed. The primary solidification product of rapid solidification was a topologically and chemically disordered icosahedral phase with an extensive compositional region. Crystallization through exothermic events of the as-solidified materials produced crystalline phases, without the formation of the face-centered-icosahedral (FCI) phase. However, the FCI phase does form at higher temperatures through an endothermic reaction, indicating that it is a stable phase of the system, but only at elevated temperatures. Of the alloys studied, the FCI phase field was found to encompass Al{sub 65}Cu{sub 23}Ru{sub 12}, Al{sub 65}Cu{sub 20}Ru{sub 15}, Al{sub 70}Cu{sub 20}Ru{sub 10}, and Al{sub 70}Cu{sub 15}Ru{sub 15}. The transformation to the FCI phase involves an intermediate approximant phase that is very similar to the FCI structure. Also, a cubic approximant containing atomic arrangements with local icosahedral symmetry similar to {alpha}-Al Mn Si was determined to exist near the FCI phase field.
Atomic clusters and atomic surfaces in icosahedral quasicrystals.
Quiquandon, Marianne; Portier, Richard; Gratias, Denis
2014-05-01
This paper presents the basic tools commonly used to describe the atomic structures of quasicrystals with a specific focus on the icosahedral phases. After a brief recall of the main properties of quasiperiodic objects, two simple physical rules are discussed that lead one to eventually obtain a surprisingly small number of atomic structures as ideal quasiperiodic models for real quasicrystals. This is due to the fact that the atomic surfaces (ASs) used to describe all known icosahedral phases are located on high-symmetry special points in six-dimensional space. The first rule is maximizing the density using simple polyhedral ASs that leads to two possible sets of ASs according to the value of the six-dimensional lattice parameter A between 0.63 and 0.79 nm. The second rule is maximizing the number of complete orbits of high symmetry to construct as large as possible atomic clusters similar to those observed in complex intermetallic structures and approximant phases. The practical use of these two rules together is demonstrated on two typical examples of icosahedral phases, i-AlMnSi and i-CdRE (RE = Gd, Ho, Tm).
Icosahedral packing of B12 icosahedra in boron suboxide (B6O)
NASA Astrophysics Data System (ADS)
Hubert, Hervé; Devouard, Bertrand; Garvie, Laurence A. J.; O'Keeffe, Michael; Buseck, Peter R.; Petuskey, William T.; McMillan, Paul F.
1998-01-01
Objects with icosahedral symmetry (Ih) bear a special fascination; natural examples are rare, but include radiolaria and virus particles (virions). The discovery of C60, a molecule in the shape of a truncated icosahedron with Ih symmetry, has aroused widespread interest. In 1962, Mackay described a radiating packing of spheres in Ih symmetry, in which the centres of successive shells of spheres lie on the surfaces of icosahedra. There has been extensive investigation of the conditions under which such packing might be realized in assemblies of atoms or of molecules such as C60 (ref. 5). Here we report the preparation, at high temperatures and pressures, of boron suboxide (B6O) in which the preferred form of the material is as macroscopic, near-perfect, regular icosahedra, similar to the multiply-twinned particles observed in some cubic materials. A major difference is that B6O has a rhombohedral structure that nearly exactly fits the geometrical requirements needed to obtain icosahedral twins. These icosahedral particles have a structure that can be described as a Mackay packing of icosahedral B12 units, and thus has long-ranged order without translational symmetry.
Group theory of icosahedral virus capsid vibrations: a top-down approach.
Peeters, Kasper; Taormina, Anne
2009-02-21
We explore the use of a top-down approach to analyse the dynamics of icosahedral virus capsids and complement the information obtained from bottom-up studies of viral vibrations available in the literature. A normal mode analysis based on protein association energies is used to study the frequency spectrum, in which we reveal a universal plateau of low-frequency modes shared by a large class of Caspar-Klug capsids. These modes break icosahedral symmetry and are potentially relevant to the genome release mechanism. We comment on the role of viral tiling theory in such dynamical considerations. PMID:19014954
Two-Dimensional Crystals of Icosahedral Viruses at Liquid interfaces
NASA Astrophysics Data System (ADS)
Fukuto, Masafumi; Yang, Lin; Checco, Antonio; Kuzmenko, Ivan; Nguyen, Quyen; Mank, Nick; Wang, Qian
2012-02-01
Two-dimensional (2D) assembly of turnip yellow mosaic virus (TYMV) on cationic lipid monolayers is investigated at the air-water interface. TYMV, an icosahedral virus with a diameter of 28 nm, exhibits well-defined roughness, charge distribution, and hydrophilic/hydrophobic patches on its surface. The electrostatic attraction to the lipid-coated aqueous interface provides means to impose a specific virus orientation and hence reduce the number of possible inter-particle interactions. The 2D geometry is particularly advantageous in dissecting the role of anisotropy in aqueous-media assembly, which involves various types of similarly weak interactions. We show that the assembly approach used not only facilitates crystallization but also provides insights on how complex anisotropic interactions can be exploited to generate long-range order. Specifically, we report an in situ x-ray scattering observation of novel 2D crystal forms of TYMV that reflect the virus' icosahedral symmetry. The symmetry, shape, and surface heterogeneities of TYMV suggest a mechanism by which these crystals are stabilized by a combination of hydrophobic, electrostatic, and steric interactions.
NASA Astrophysics Data System (ADS)
Blatov, V. A.; Ilyushin, G. D.
2012-12-01
A database of intermetallic compounds has been compiled using the TOPOS program package. This database includes 514 topological types, containing 12- and 13-atom icosahedral i clusters. An isolated group of 1649 i clusters is described by 14 point groups and their maximum symmetry D 3 d (bar 3 m) and T h ( m bar 3) is established, respectively, in 47 and 25 types of crystal structures. A structural analysis of the outer quasispherical shells showed that local 63-atom i configurations 1@12@50, which contain 50 atoms in the second layer, are implemented in 8 out of 19 cases. Examples of new topologically different types of 50-atom D50 deltahedra in the Samson phases ɛ-Mg23Al30 and β-Mg2Al3 are presented. Four topologically different sites with coordination numbers of 5, 6, 6, or 7 are established in the ɛ shell and seven sites with coordination numbers of 5, 5, 6, 6, 6, 6, or 7 are found in the β shell. The inner i clusters for the β-Mg2Al3 structure (with the symmetry bar 3 m) and the ɛ-Mg23Al30 structure (with the symmetry bar 3) have a similar chemical composition, i.e., Mg7Al6 and Mg6Al7, and their 50-atom shells are chemically identical to 18Mg + 32Al. The configurations found supplement the series of known two-layer icosahedral Bergman and Mackay clusters in the form of deltahedra with 32- and 42-atom shells.
Point Groups Based on Methane and Adamantane (Td) Skeletons.
ERIC Educational Resources Information Center
Fujita, Shinsaku
1986-01-01
Describes a procedure for constructing point groups based on the symmetric parent molecules of methane and adamantane. Intended for use in teaching concepts such as subgroups and cosets to beginners in group theory. (TW)
Exploring the symmetry and mechanism of virus capsid maturation via an ensemble of pathways.
May, Eric R; Feng, Jun; Brooks, Charles L
2012-02-01
Many icosahedral viruses undergo large-scale conformational transitions between icosahedrally symmetric conformations during their life cycles. However, whether icosahedral symmetry is maintained along the transition pathways for this process is unknown. By employing a simplified and directed structure-based potential we compute an ensemble of transition pathways for the maturation transition of bacteriophage HK97. We observe localized symmetry-breaking events, but find that the large-scale displacements are dominated by icosahedrally symmetric deformation modes. We find that all pathways obey a common mechanism characterized by formation of pentameric contacts early in the transition. PMID:22325284
Ideal structure of icosahedral Al-Cu-Li quasicrystals
NASA Astrophysics Data System (ADS)
Yamamoto, Akiji
1992-03-01
A structure model for the icosahedral Al-Cu-Li quasicrystal has been derived. This is described in six-dimensional space as a six-dimensional crystal, having four kinds of occupation domains with complicated polyhedral shape. A general structure-factor formula is derived for such polyhedral domains, and a simple description of the structure using the site symmetry is proposed. The model gives R factors of 0.076 and 0.085 for recent x-ray and neutron-single-crystal-diffraction data [Boissieu, Janot, Dubois, Audier, and Dubost, J. Phys. 3, 1 (1991)]. The structure consists of a large number of icosahedral clusters and linking atoms joining them. It leads to an ideal cubic R-Al-Cu-Li structure and a large number of other cubic crystals when appropriate phason strains are taken into account. Two structures, the ideal R-Al-Cu-Li structure and a fictitious structure with a period (1+ √5 )/2 times longer, are shown.
Surface structures of Al-Pd-Mn and Al-Cu-Fe icosahedral quasicrystals
Shen, Z.
1999-02-12
In this dissertation, the author reports on the surface structure of i-Al-Pd-Mn twofold, threefold, fivefold and i-Al-Cu-Fe fivefold surfaces. The LEED studies indicate the existence of two distinct stages in the regrowth of all four surfaces after Ar{sup +} sputtering. In the first stage, upon annealing at relatively low temperature: 500K--800K (depending on different surfaces), a cubic phase appears. The cubic LEED patterns transform irreversibly to unreconstructed quasicrystalline patterns upon annealing to higher temperatures, indicating that the cubic overlayers are metastable. Based upon the data for three chemically-identical, but symmetrically-inequivalent surfaces, a model is developed for the relation between the cubic overlayers and the quasicrystalline substrate. The model is based upon the related symmetries of cubic close-packed and icosahedral-packed materials. These results may be general among Al-rich, icosahedral materials. STM study of Al-Pd-Mn fivefold surface shows that terrace-step-kink structures start to form on the surface after annealing above 700K. Large, atomic ally-flat terraces were formed after annealing at 900K. Fine structures with fivefold icosahedral symmetry were found on those terraces. Data analysis and comparison of the STM images and structure model of icosahedral Al-Pd-Mn suggest that the fine structures in the STM images may be the pseudo Mackay (PMI) clusters which are the structure units of the structure model. Based upon his results, he can conclude that quasicrystalline structures are the stable structures of quasicrystal surfaces. In other words, quasicrystalline structures extend from the bulk to the surface. As a result of the effort reported in this dissertation, he believes that he has increased his understanding of the surface structure of icosahedral quasicrystals to a new level.
Radial vibrations of a sodium ion inside icosahedral C60
NASA Technical Reports Server (NTRS)
Ballester, J. L.; Dunlap, B. I.
1992-01-01
The very high symmetry of icosahedral C60 suggests that, as a first approximation, an atom trapped inside C60 would be subject to a potential that is radially symmetric about the center. All-electron local-density-functional calculations of the total energy of a sodium ion as a function of radial displacement from the center along the fivefold axis of C60 serve to refine such a radial potential. In particular, the calculations suggest studying potentials that have minima displaced from the center. An analytic functional form for a radial potential having a positive cusp at the origin is proposed, and the s-wave radial solutions of the corresponding Schroedinger equation are examined.
Beta cell device using icosahedral boride compounds
Aselage, Terrence L.; Emin, David
2002-01-01
A beta cell for converting beta-particle energies into electrical energy having a semiconductor junction that incorporates an icosahedral boride compound selected from B.sub.12 As.sub.2, B.sub.12 P.sub.2, elemental boron having an .alpha.-rhombohedral structure, elemental boron having a .beta.-rhombohedral structure, and boron carbides of the chemical formula B.sub.12-x C.sub.3-x, where 0.15
Experimental evidence of icosahedral and decahedral packing in one-dimensional nanostructures.
Velázquez-Salazar, J Jesús; Esparza, Rodrigo; Mejía-Rosales, Sergio Javier; Estrada-Salas, Rubén; Ponce, Arturo; Deepak, Francis Leonard; Castro-Guerrero, Carlos; José-Yacamán, Miguel
2011-08-23
The packing of spheres is a subject that has drawn the attention of mathematicians and philosophers for centuries and that currently attracts the interest of the scientific community in several fields. At the nanoscale, the packing of atoms affects the chemical and structural properties of the material and, hence, its potential applications. This report describes the experimental formation of 5-fold nanostructures by the packing of interpenetrated icosahedral and decahedral units. These nanowires, formed by the reaction of a mixture of metal salts (Au and Ag) in the presence of oleylamine, are obtained when the chemical composition is specifically Ag/Au = 3:1. The experimental images of the icosahedral nanowires have a high likelihood with simulated electron micrographs of structures formed by two or three Boerdijk-Coxeter-Bernal helices roped on a single structure, whereas for the decahedral wires, simulations using a model of adjacent decahedra match the experimental structures. To our knowledge, this is the first report of the synthesis of nanowires formed by the packing of structures with 5-fold symmetry. These icosahedral nanowire structures are similar to those of quasicrystals, which can only be formed if at least two atomic species are present and in which icosahedral and decahedral packing has been found for bulk crystals.
On the Characters and Representations of Continuous Point Groups.
ERIC Educational Resources Information Center
Flurry, R. L., Jr.
1979-01-01
Presents a method for carrying out the desired reduction which eliminates all ambiguities and trial-and-error. This method, which works with any properly constructed representation of any of the continuous points groups, is based upon the cosine form of the character for the arbitrary rotation operation. (HM)
Erickson, Jeremiah D; Mednikov, Evgueni G; Ivanov, Sergei A; Dahl, Lawrence F
2016-02-10
We present the first successful isolation and crystallographic characterization of a Mackay 55-metal-atom two-shell icosahedron, Pd55L12(μ3-CO)20 (L = PPr(i)3) (1). Its two-shell icosahedron of pseudo-Ih symmetry (without isopropyl substituents) enables a structural/bonding comparison with interior 55-metal-atom two-shell icosahedral geometries observed within the multi-shell capped 145-metal-atom three-shell Pd145(CO)72(PEt3)30 and 165-metal-atom four-shell Pt-centered (μ12-Pt)Pd164-xPtx(CO)72(PPh3)20 (x ≈ 7) nanoclusters, and within the recently reported four-shell Au133(SC6H4-p-Bu(t))52 nanocluster. DFT calculations carried out on a Pd55(CO)20(PH3)12 model analogue, with triisopropyl phosphine substituents replaced by H atoms, revealed a positive +0.84 e charge for the entire Pd55 core, with a highly positive second-shell Pd42 surface of +1.93 e.
Thermal stability of Al-Cu-Fe icosahedral alloys
NASA Astrophysics Data System (ADS)
Bessière, M.; Quivy, A.; Lefebvre, S.; Devaud-Rzepski, J.; Calvayrac, Y.
1991-12-01
A stable ideally quasiperiodic phase exists in a small range of concentration, close to the composition Al{62}Cu{25.5}Fe{12.5}. Reducing the iron content, or replacing small amounts of copper by aluminium, lead to icosahedral alloys which exhibit around 650 ^{circ}C structural transformations of unclear nature: in the X-ray powder diffraction pattern, the peak profiles become purely Lorentzian (Al{62.3}Cu{25.3}Fe{12.4}) or diffuse “side-bands” appear in the tails of the Bragg peaks (Al{63}Cu{24.5}Fe{12.5}). In the last case long annealing treatments eventually transform the Bragg peaks into diffuse peaks located at positions clearly off the ideal icosahedral symmetry. Small deviations from this composition range lead to Bragg peaks with shoulders whatever the heat-treatment may be; perfect icosahedral order is never obtained for these compositions (Al{63,25}Cu{24,5}Fe{12,25}, Al{64}Cu{24}Fe{12}, Al{63}Cu{25}Fe{12}). Une phase stable idéalement quasipériodique existe dans un petit domaine de concentration, au voisinage de la composition Al{62}Cu{25,5}Fe{12,5}. La diminution de la teneur en fer, ou le remplacement de faibles quantités de cuivre par de l'aluminium, conduisent à des alliages icosaédriques qui subissent vers 650 ^{circ}C des transformations structurales dont la nature n'est pas clairement identifiée: dans le diagramme de diffraction des rayons X sur poudre, les profils de raies deviennent purement Lorentziens (Al{62,3}Cu{25,3}Fe{12,4}) ou bien des raies diffuses apparaissent dans le pied des pics de Bragg (Al{63}Cu{24,5}Fe{12,5}). Dans ce dernier cas un long traitement de recuit transforme finalement les pics de Bragg en des pics diffus localisés à des positions clairement en dehors de celles correspondant à la symétrie icosaédrique idéale. De faibles écarts à ce domaine de compositions conduisent à des diagrammes de rayons X où les pics de Bragg sont épaulés quel que soit le traitement thermique ; l'ordre icosaédrique parfait n
Quantum transport through single and multilayer icosahedral fullerenes
NASA Astrophysics Data System (ADS)
Lovey, Daniel A.; Romero, Rodolfo H.
2013-10-01
We use a tight-binding Hamiltonian and Green functions methods to calculate the quantum transmission through single-wall fullerenes and bilayered and trilayered onions of icosahedral symmetry attached to metallic leads. The electronic structure of the onion-like fullerenes takes into account the curvature and finite size of the fullerenes layers as well as the strength of the intershell interactions depending on to the number of interacting atom pairs belonging to adjacent shells. Misalignment of the symmetry axes of the concentric iscosahedral shells produces breaking of the level degeneracies of the individual shells, giving rise some narrow quasi-continuum bands instead of the localized discrete peaks of the individual fullerenes. As a result, the transmission function for non symmetrical onions is rapidly varying functions of the Fermi energy. Furthermore, we found that most of the features of the transmission through the onions are due to the electronic structure of the outer shell with additional Fano-like antiresonances arising from coupling with or between the inner shells.
3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Vaid, Thomas P.
2014-01-01
Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching…
Three-Dimensional Icosahedral Phase Field Quasicrystal
NASA Astrophysics Data System (ADS)
Subramanian, P.; Archer, A. J.; Knobloch, E.; Rucklidge, A. M.
2016-08-01
We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation.
Symmetry in DIET phase transitions
NASA Astrophysics Data System (ADS)
Zhang, J. P.; Marks, L. D.
1989-11-01
Analysis of the route of the phase transitions in transition metal oxides driven by DIET of oxygen from the surfaces observed by high resolution electron microscopy indicates that there is a symmetry selection rule. The phase transitions are to a structure with a higher point group symmetry where the new phase with a lower oxygen content is either one with a supergroup symmetry with respect to the original phase, or is an amorphous intermediary. The final phase has the highest symmetry and is also a metallic conductor. If a possible lower oxygen content phase does not have the correct supergroup symmetry, it is not formed. It is also found that the point group is conserved during the phase transition if the oxide belongs to the highest groups O h or D 6h. This symmetry selection rule can therefore be used to predict the route of the phase transition. The symmetry rule operates when the phase transition is diffusional.
Three-Dimensional Icosahedral Phase Field Quasicrystal.
Subramanian, P; Archer, A J; Knobloch, E; Rucklidge, A M
2016-08-12
We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation. PMID:27563973
Topological Quantum Hashing with the Icosahedral Group
NASA Astrophysics Data System (ADS)
Burrello, Michele; Xu, Haitan; Mussardo, Giuseppe; Wan, Xin
2010-04-01
We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log2(1/ɛ)), we can approximate all SU(2) matrices to an average error ɛ with a cost of O(log(1/ɛ)) in time. The algorithm is applicable to generic quantum compiling.
3 nj-symbols and harmonic superposition coefficients: an icosahedral abacus
NASA Astrophysics Data System (ADS)
Aquilanti, Vincenzo; Coletti, Cecilia
2001-08-01
Angular momentum recoupling coefficients of angular momentum theory and matrix elements for basis set transformation of hyperspherical harmonics enjoy properties and sum rules crucial for applications but complicated without the guidance of graphical techniques. These coefficients being related to Racah's polynomials, the graphs also apply to polynomials of the hypergeometric family, their q-analogues and their `elliptic' extensions. A useful `abacus' exploiting the connections with presentations of icosahedral and related symmetries is introduced. Particular and limiting cases, such as those of the semiclassical type, allow a unified view of properties of angular and hyperangular momentum algebra, including relationships among vector coupling coefficients and rotation matrix elements.
Method of making an icosahedral boride structure
Hersee, Stephen D.; Wang, Ronghua; Zubia, David; Aselage, Terrance L.; Emin, David
2005-01-11
A method for fabricating thin films of an icosahedral boride on a silicon carbide (SiC) substrate is provided. Preferably the icosahedral boride layer is comprised of either boron phosphide (B.sub.12 P.sub.2) or boron arsenide (B.sub.12 As.sub.2). The provided method achieves improved film crystallinity and lowered impurity concentrations. In one aspect, an epitaxially grown layer of B.sub.12 P.sub.2 with a base layer or substrate of SiC is provided. In another aspect, an epitaxially grown layer of B.sub.12 As.sub.2 with a base layer or substrate of SiC is provided. In yet another aspect, thin films of B.sub.12 P.sub.2 or B.sub.12 As.sub.2 are formed on SiC using CVD or other vapor deposition means. If CVD techniques are employed, preferably the deposition temperature is above 1050.degree. C., more preferably in the range of 1100.degree. C. to 1400.degree. C., and still more preferably approximately 1150.degree. C.
Local growth of icosahedral quasicrystalline tilings
NASA Astrophysics Data System (ADS)
Hann, Connor T.; Socolar, Joshua E. S.; Steinhardt, Paul J.
2016-07-01
Icosahedral quasicrystals (IQCs) with extremely high degrees of translational order have been produced in the laboratory and found in naturally occurring minerals, yet questions remain about how IQCs form. In particular, the fundamental question of how locally determined additions to a growing cluster can lead to the intricate long-range correlations in IQCs remains open. In answer to this question, we have developed an algorithm that is capable of producing a perfectly ordered IQC yet relies exclusively on local rules for sequential, face-to-face addition of tiles to a cluster. When the algorithm is seeded with a special type of cluster containing a defect, we find that growth is forced to infinity with high probability and that the resultant IQC has a vanishing density of defects. The geometric features underlying this algorithm can inform analyses of experimental systems and numerical models that generate highly ordered quasicrystals.
Surface-reconstructed icosahedral structures for lead clusters
NASA Astrophysics Data System (ADS)
Hendy, Shaun C.; Doye, Jonathan P.
2002-12-01
We describe a family of icosahedral structures for lead clusters. In general, structures in this family contain a Mackay icosahedral core with a reconstructed two-shell outer-layer. This family includes the anti-Mackay icosahedra, which has a Mackay icosahedral core but with most of the surface atoms in hexagonal close-packed positions. Using a many-body glue potential for lead, we identify two icosahedral structures in this family which have the lowest energies of any known structure in the size range from 900 to 15 000 lead atoms. We show that these structures are stabilized by a feature of the many-body glue part of the interatomic potential.
Relaxed crystalline and icosahedral molecular clusters - CO2
NASA Astrophysics Data System (ADS)
van de Waal, B. W.
1987-05-01
The differences between the icosahedral arrangement and crystalline packing following the addition of more molecule shells are examined. The applicability of the Mackay (1962) procedure for constructing concentric icosahedra is evaluated. The relaxation of molecule crystal fragments by shifting molecular positions following deformation is studied. The relative energy difference between relaxed crystalline and icosahedral structure as a function of cluster size is calculated as ranging from 2.4 to 0.8 percent. The evolution of shells in the relaxed crystalline growth sequence reveals that the inner shells become crystalline when more shells are added; the icosahedral deformation is more prominent in the outer shell, but decreases with increasing cluster size. It is suggested that, when multilayer icosahedral structures are larger than critical size, they do not transform as a whole into a crystalline arrangement but develop a growing crystalline core.
Symmetry Engineering of Graphene Plasmonic Crystals.
Yeung, Kitty Y M; Chee, Jingyee; Song, Yi; Kong, Jing; Ham, Donhee
2015-08-12
The dispersion relation of plasmons in graphene with a periodic lattice of apertures takes a band structure. Light incident on this plasmonic crystal excites only particular plasmonic modes in select bands. The selection rule is not only frequency/wavevector matching but also symmetry matching, where the symmetry of plasmonic modes originates from the point group symmetry of the lattice. We demonstrate versatile manipulation of light-plasmon coupling behaviors by engineering the symmetry of the graphene plasmonic crystal.
NASA Astrophysics Data System (ADS)
Harter, William G.; Li, Alvason Zhenhua
2013-06-01
Quantum revivals or "super-beats" are predicted to occur when angularly localized symmetric tops states are free to evolve. Similar types of dynamics are expected to involve spherical top superfine and superhyperfine level clusters that are labeled by induced representations of octahedral or tetrahedral symmetries for XY_4, XY_6, and related molecules. A considerably more complicated set of effects are expected for the icosahedral molecule C_ {60} and its related isotopomers. An important difference for icosahedral symmetry is that its superfine splitting ratios are most-irrational (Golden-ratio) fractions that preclude perfect Poincare recurrence of quantum phase while the octahedral splitting ratios are rational. William Harter and Justin Mitchell, International Journal of Molecular Science, 14, 714 (2013).
Symmetry, Equivalence and Self-Assembly
NASA Astrophysics Data System (ADS)
Douglas, Jack
2006-03-01
Molecular self-assembly at equilibrium is central to the formation of many biological structures and the emulation of this process through the creation of synthetic counterparts offers great promise for nanofabrication. The central problems in this field are an understanding of how the symmetry of the interacting particles encodes the geometrical structure of the organized structure and the nature of the thermodynamic transitions involved. Our approach is inspired by the self-assembly of actin, tubulin and icosahedral structures of plant and animal viruses. We observe chain, membrane,`nanotube' and hollow icosahedron structures using `equivalent' particles exhibiting an interplay between directional (dipolar and multi-polar) interactions and short-range (van der Waals) interactions. Specifically, a dipolar potential (continuous rotational symmetry) gives rise to chain formation, while potentials having discrete rotational symmetries (e.g., square quadrupole or triangular ring of dipoles) led to the self-organization of nanotube and icosahedral structures with some resemblance to tubulin and icosahedral viruses. The simulations are compared to theoretical models of molecular self-assembly, especially in the case of dipolar fluids where the corresponding analytic theory of equilibrium polymerization is well developed. These computations give insights into the design elements required for the development of synthetic systems exhibiting this type of organization.
The RNA of turnip yellow mosaic virus exhibits icosahedral order
Larson, Steven B.; Lucas, Robert W.; Greenwood, Aaron; McPherson, Alexander . E-mail: amcphers@uci.edu
2005-04-10
Difference electron density maps, based on structure factor amplitudes and experimental phases from crystals of wild-type turnip yellow mosaic virus and those of empty capsids prepared by freeze-thawing, show a large portion of the encapsidated RNA to have an icosahedral distribution. Four unique segments of base-paired, double-helical RNA, one to two turns in length, lie between 33-A and 101-A radius and are organized about either 2-fold or 5-fold icosahedral axes. In addition, single-stranded loops of RNA invade the pentameric and hexameric capsomeres where they contact the interior capsid surface. The remaining RNA, not seen in electron density maps, must serve as connecting links between these secondary structural elements and is likely icosahedrally disordered. The distribution of RNA observed crystallographically appears to be in agreement with models based on biochemical data and secondary structural analyses.
Symmetry relations of magnetic twin laws.
Schlessman, J; Litvin, D B
2001-11-01
Symmetry relationships between two simultaneously observed domain states (domain pair) are used to determine physical properties that can distinguish between the observed domains. Here the tabulation of these symmetry relationships is extended from non-magnetic cases to magnetic cases, in terms of magnetic point groups, i.e. all possible magnetic symmetry groups and magnetic twinning groups of domain pairs are determined and tabulated. PMID:11679705
TOPICAL REVIEW: Raman effect in icosahedral boron-rich solids
NASA Astrophysics Data System (ADS)
Werheit, Helmut; Filipov, Volodymyr; Kuhlmann, Udo; Schwarz, Ulrich; Armbrüster, Marc; Leithe-Jasper, Andreas; Tanaka, Takaho; Higashi, Iwami; Lundström, Torsten; Gurin, Vladimir N.; Korsukova, Maria M.
2010-04-01
We present Raman spectra of numerous icosahedral boron-rich solids having the structure of α-rhombohedral, β-rhombohedral, α-tetragonal, β-tetragonal, YB66, orthorhombic or amorphous boron. The spectra were newly measured and, in some cases, compared with reported data and discussed. We emphasize the importance of a high signal-to-noise ratio in the Raman spectra for detecting weak effects evoked by the modification of compounds, accommodation of interstitial atoms and other structural defects. Vibrations of the icosahedra, occurring in all the spectra, are interpreted using the description of modes in α-rhombohedral boron by Beckel et al. The Raman spectrum of boron carbide is largely clarified. Relative intra- and inter-icosahedral bonding forces are estimated for the different structural groups and for vanadium-doped β-rhombohedral boron. The validity of Badger's rule is demonstrated for the force constants of inter-icosahedral B-B bonds, whereas the agreement is less satisfactory for the intra-icosahedral B-B bonds.
Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles
Shevchenko, Vladimir Ya. Madison, Alexey E.; Mackay, Alan L.
2007-03-01
In icosahedral carbon nanoparticles, the diamond-like core can undergo a reversible topological transition into and coexist coherently with the onion shells. The general approach for describing and designing complex hierarchical icosahedral structures is discussed. Structural models of icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually identical to that in diamond are derived. It is shown that icosahedral diamond-like particles can be transformed into onion-like shell structures (and vice versa) by the consecutive smoothing (puckering) of atomic networks without disturbance of their topological integrity. The possibility of coherent coexistence of icosahedral diamond-like core with onion shells is shown.
Non-Hermitian Hamiltonians with unitary and antiunitary symmetries
Fernández, Francisco M. Garcia, Javier
2014-03-15
We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •PT-symmetric multidimensional oscillators appear to show PT phase transitions. •This transition was conjectured to be a high-energy phenomenon. •We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. •PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit.
Protruding Features of Viral Capsids Are Clustered on Icosahedral Great Circles.
Wilson, David P
2016-01-01
Spherical viruses are remarkably well characterized by the Triangulation (T) number developed by Casper and Klug. The T-number specifies how many viral capsid proteins are required to cover the virus, as well as how they are further subdivided into pentamer and hexamer subunits. The T-number however does not constrain the orientations of these proteins within the subunits or dictate where the proteins should place their protruding features. These protrusions often take the form of loops, spires and helices, and are significant because they aid in stability of the capsid as well as recognition by the host organism. Until now there has be no overall understanding of the placement of protrusions for spherical viruses, other than they have icosahedral symmetry. We constructed a set of gauge points based upon the work affine extensions of Keef and Twarock, which have fixed relative angular locations with which to measure the locations of these features. This work adds a new element to our understanding of the geometric arrangement of spherical viral capsid proteins; chiefly that the locations of protruding features are not found stochastically distributed in an icosahedral manner across the viral surface, but instead these features are found only in specific locations along the 15 icosahedral great circles. We have found that this result holds true as the T number and viral capsids size increases, suggesting an underlying geometric constraint on their locations. This is in spite of the fact that the constraints on the pentamers and hexamer orientations change as a function of T-number, as you need to accommodate more hexamers in the same solid angle between pentamers. The existence of this angular constraint of viral capsids suggests that there is a fitness or energetic benefit to the virus placing its protrusions in this manner. This discovery may have profound impacts on identifying and eliminating viral pathogens, understanding evolutionary constraints as well as
Protruding Features of Viral Capsids Are Clustered on Icosahedral Great Circles
Wilson, David P.
2016-01-01
Spherical viruses are remarkably well characterized by the Triangulation (T) number developed by Casper and Klug. The T-number specifies how many viral capsid proteins are required to cover the virus, as well as how they are further subdivided into pentamer and hexamer subunits. The T-number however does not constrain the orientations of these proteins within the subunits or dictate where the proteins should place their protruding features. These protrusions often take the form of loops, spires and helices, and are significant because they aid in stability of the capsid as well as recognition by the host organism. Until now there has be no overall understanding of the placement of protrusions for spherical viruses, other than they have icosahedral symmetry. We constructed a set of gauge points based upon the work affine extensions of Keef and Twarock, which have fixed relative angular locations with which to measure the locations of these features. This work adds a new element to our understanding of the geometric arrangement of spherical viral capsid proteins; chiefly that the locations of protruding features are not found stochastically distributed in an icosahedral manner across the viral surface, but instead these features are found only in specific locations along the 15 icosahedral great circles. We have found that this result holds true as the T number and viral capsids size increases, suggesting an underlying geometric constraint on their locations. This is in spite of the fact that the constraints on the pentamers and hexamer orientations change as a function of T-number, as you need to accommodate more hexamers in the same solid angle between pentamers. The existence of this angular constraint of viral capsids suggests that there is a fitness or energetic benefit to the virus placing its protrusions in this manner. This discovery may have profound impacts on identifying and eliminating viral pathogens, understanding evolutionary constraints as well as
Cardone, Giovanni; Yan, Xiaodong; Sinkovits, Robert S.; Tang, Jinghua; Baker, Timothy S.
2013-01-01
Single particle analysis is a valuable tool in cryo-electron microscopy for determining the structure of biological complexes. However, the conformational state and the preparation of the sample are factors that play a critical role in the ultimate attainable resolution. In some cases extensive analysis at the microscope of a sample under different conditions is required to derive the optimal acquisition conditions. Currently this analysis is limited to raw micrographs, thus conveying only limited information on the structure of the complex. We are developing a computing system that generates a three-dimensional reconstruction from a single micrograph acquired under cryogenic and low dose conditions, and containing particles with icosahedral symmetry. The system provides the microscopist with immediate structural information from a sample, while it is in the microscope and during the preliminary acquisition stage. The system is designed to run without user intervention on a multi-processor computing resource and integrates all the processing steps required for the analysis. Tests performed on experimental data sets show that the probability of obtaining a reliable reconstruction from one micrograph is primarily determined by the quality of the sample, with success rates close to 100% when sample conditions are optimal, and decreasing to about 60% when conditions are sub-optimal. The time required to generate a reconstruction depends significantly on the diameter of the particles, and in most instances takes about one minute. The proposed approach can provide valuable three-dimensional information, albeit at low resolution, on conformational states, epitope binding, and stoichiometry of icosahedral multi-protein complexes. PMID:23891839
Encapsulation of a polymer by an icosahedral virus
Elrad, Oren M.; Hagan, Michael F.
2011-01-01
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration, and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated to encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids. PMID:21149971
Electronic transport in polycrystalline samples of icosahedral phases
NASA Astrophysics Data System (ADS)
Vekilov, Yu. Kh.; Chernikov, M. A.; Dolinichek, Ya.
2016-01-01
The low-temperature electronic transport in polycrystals of quasicrystalline phases with an icosahedral structure has been analyzed within the model of the granular electronic system. In this model, the grains (drops) of a metallic icosahedral phase are surrounded by extended defects and grain boundaries, which create an insulating environment. The electron transport in this model is determined by the size quantization of electronic states inside metallic grains, by intergranular tunneling, and by electrostatic barriers. Depending on the temperature and structural state of the system, the hopping conductivity with variable lengths of jumps in the Efros-Shklovskii or Mott regime is observed with predominantly elastic cotunneling. In the case of strong intergranular coupling, the system passes into the metallic regime with the exponential temperature dependence of the electrical conductivity.
Monte Carlo simulations of icosahedral quasicrystal growth and melting
NASA Astrophysics Data System (ADS)
Dmitrienko, V. E.; Astaf'ev, S. B.; Kléman, M.
1999-01-01
Three-dimensional Monte Carlo simulations for atomic growth and melting of icosahedral quasicrystals are presented. It is supposed that the atoms can be locally ordered both icosahedrally and dodecahedrally, and the preferred ordering arises during the growth according to statistical and energetical criteria. All the waiting positions (where an atom could be in principle added) are generated on the cluster surface at every stage of the growth. The binding energies of all atoms and all waiting positions are computed with an oscillating Friedel potential. Then an object, chosen at random from the joined list of surface atoms and waiting positions, is treated according to the Metropolis criterion. The suggested growth process is completely local. It is found that the speed and sign of the process and the resulting structures depend strongly on the growth parameters. Most frequently, the main structural motif of grown clusters is the dodecahedral local ordering (DLO) whereas the icosahedral local ordering (ILO) is usually rare. However, the latter becomes dominant for rather exotic interatomic potentials or for high growth rates. The phenomenon of critical seed size is observed: for those parameters, for which large clusters grow, small enough seeds stop to grow and may even melt. The grown quasicrystals are faceted and their sizes in perpendicular space are rather close to those predicted theoretically and observed experimentally.
Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.
2006-07-31
Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.
Soft materials design via self assembly of functionalized icosahedral particles
NASA Astrophysics Data System (ADS)
Muthukumar, Vidyalakshmi Chockalingam
In this work we simulate self assembly of icosahedral building blocks using a coarse grained model of the icosahedral capsid of virus 1m1c. With significant advancements in site-directed functionalization of these macromolecules [1], we propose possible application of such self-assembled materials for drug delivery. While there have been some reports on organization of viral particles in solution through functionalization, exploiting this behaviour for obtaining well-ordered stoichiometric structures has not yet been explored. Our work is in well agreement with the earlier simulation studies of icosahedral gold nanocrystals, giving chain like patterns [5] and also broadly in agreement with the wet lab works of Finn, M.G. et al., who have shown small predominantly chain-like aggregates with mannose-decorated Cowpea Mosaic Virus (CPMV) [22] and small two dimensional aggregates with oligonucleotide functionalization on the CPMV capsid [1]. To quantify the results of our Coarse Grained Molecular Dynamics Simulations I developed analysis routines in MATLAB using which we found the most preferable nearest neighbour distances (from the radial distribution function (RDF) calculations) for different lengths of the functional groups and under different implicit solvent conditions, and the most frequent coordination number for a virus particle (histogram plots further using the information from RDF). Visual inspection suggests that our results most likely span the low temperature limits explored in the works of Finn, M.G. et al., and show a good degree of agreement with the experimental results in [1] at an annealing temperature of 4°C. Our work also reveals the possibility of novel stoichiometric N-mer type aggregates which could be synthesized using these capsids with appropriate functionalization and solvent conditions.
Dynamic and Kinetic Assembly Studies of an Icosahedral Virus Capsid
NASA Astrophysics Data System (ADS)
Lee, Kelly
2011-03-01
Hepatitis B virus has an icosahedrally symmetrical core particle (capsid), composed of either 90 or 120 copies of a dimeric protein building block. We are using time-resolved, solution small-angle X-ray scattering and single-molecule fluorescence microscopy to probe the core particle assembly reaction at the ensemble and individual assembly levels. Our experiments to date reveal the assembly process to be highly cooperative with minimal population of stable intermediate species. Solution conditions, particularly salt concentration, appears to influence the partitioning of assembly products into the two sizes of shells. Funding from NIH R00-GM080352 and University of Washington.
Melting of icosahedral gold nanoclusters from molecular dynamics simulations
NASA Astrophysics Data System (ADS)
Wang, Yanting; Teitel, S.; Dellago, Christoph
2005-06-01
Molecular dynamics simulations show that gold clusters with about 600-3000 atoms crystallize into a Mackay icosahedron upon cooling from the liquid. A detailed surface analysis shows that the facets on the surface of the Mackay icosahedral gold clusters soften but do not premelt below the bulk melting temperature. This softening is found to be due to the increasing mobility of vertex and edge atoms with temperature, which leads to inter-layer and intra-layer diffusion, and a shrinkage of the average facet size, so that the average shape of the cluster is nearly spherical at melting.
Magnetism in icosahedral quasicrystals: current status and open questions
Goldman, Alan I.
2014-07-02
Progress in our understanding of the magnetic properties of R-containing icosahedral quasicrystals (R = rare earth element) from over 20 years of experimental effort is reviewed. This includes the much studied R-Mg-Zn and R-Mg-Cd ternary systems, as well as several magnetic quasicrystals that have been discovered and investigated more recently including Sc-Fe-Zn, R-Ag-In, Yb-Au-Al, the recently synthesized R-Cd binary quasicrystals, and their periodic approximants. In many ways, the magnetic properties among these quasicrystals are very similar. However, differences are observed that suggest new experiments and promising directions for future research.
Melting of bcc Transition Metals and Icosahedral Clustering
Ross, M; Boehler, R; Japel, S
2006-05-26
In contrast to polyvalent metals, transition metals have low melting slopes(dT/dP) that are due to partially filled d-bands that allow for a lowering of liquid phase energy through s-d electron transfer and the formation of local structures. In the case of bcc transition metals we show the apparent discrepancy of DAC melting measurements with shock melting of Mo can be understood by reexamining the shock data for V and Ta and introducing the presence of an icosahedral short range order (ISRO) melt phase.
The symmetry of single-molecule conduction.
Solomon, Gemma C; Gagliardi, Alessio; Pecchia, Alessandro; Frauenheim, Thomas; Di Carlo, Aldo; Reimers, Jeffrey R; Hush, Noel S
2006-11-14
We introduce the conductance point group which defines the symmetry of single-molecule conduction within the nonequilibrium Green's function formalism. It is shown, either rigorously or to within a very good approximation, to correspond to a molecular-conductance point group defined purely in terms of the properties of the conducting molecule. This enables single-molecule conductivity to be described in terms of key qualitative chemical descriptors that are independent of the nature of the molecule-conductor interfaces. We apply this to demonstrate how symmetry controls the conduction through 1,4-benzenedithiol chemisorbed to gold electrodes as an example system, listing also the molecular-conductance point groups for a range of molecules commonly used in molecular electronics research.
Consistent polycyclic presentation of a Bieberbach group with a nonabelian point group
NASA Astrophysics Data System (ADS)
Mohammad, Siti Afiqah; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat
2016-02-01
Research on the nonabelian tensor square of a group is requisite on finding the other homological functors. One of the methods to explicate the nonabelian tensor square is to ensure the presentation of the group is polycyclic and to prove its consistency. In this research, the polycyclic presentation of a Bieberbach group with the quaternion point group of order eight is shown to be consistent.
Unusual properties of icosahedral boron-rich solids
NASA Astrophysics Data System (ADS)
Emin, David
2006-09-01
Icosahedral boron-rich solids are materials containing boron-rich units in which atoms reside at an icosahedron's 12 vertices. These materials are known for their exceptional bonding and the unusual structures that result. This article describes how the unusual bonding generates other distinctive and useful effects. In particular, radiation-induced atomic vacancies and interstitials spontaneously recombine to produce the "self-healing" that underlies these materials' extraordinary radiation tolerance. Furthermore, boron carbides, a group of icosahedral boron-rich solids, possess unusual electronic, magnetic and thermal properties. For example, the charge carriers, holes, localize as singlet pairs on icosahedra. The unusual origin of this localization is indicated by the absence of a concomitant photo-ionization. The thermally assisted hopping of singlet pairs between icosahedra produces Seebeck coefficients that are unexpectedly large and only weakly dependent on carrier concentration. These properties are exploited in devices: (1) long-lived high-power high-capacity beta-voltaic cells, (2) very high temperature thermoelectrics and (3) solid-state neutron detectors.
Shell and subshell periodic structures of icosahedral nickel nanoclusters
NASA Astrophysics Data System (ADS)
Zhang, Zhi; Hu, Wangyu; Xiao, Shifang
2005-06-01
Using the modified analytic embedded atom method and molecular dynamics, the binding energies and their second order finite differences (stability functions) of icosahedral Ni clusters with shell and subshell periodicity are studied in detail via atomic evolution. The results exhibit shell and subshell structures of the clusters with atoms from 147 to 250 000, and the atomic numbers corresponding to shell or subshell structures are in good agreement with the experimental magic numbers obtained in time-of-flight mass spectra of threshold photoionization, and Martin's theoretical proposition of progressive formation of atomic umbrellas. Clusters with size from 147 to 561 atoms are energetically investigated via one-by-one atomic evolution and their magic numbers are theoretically proved. For medium-size Ni clusters with 561 to 2057 atoms, the prediction of magic numbers with atomic numbers is performed on the basis of umbrellalike subshell growth in near face-edge-vertex order. The similarity of the energy curves makes it possible to extend the prediction to even larger Ni nanoclusters in hierarchical Mackay icosahedral configurations.
Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
NASA Astrophysics Data System (ADS)
Satoh, M.; Matsuno, T.; Tomita, H.; Miura, H.; Nasuno, T.; Iga, S.
2008-03-01
A new type of ultra-high resolution atmospheric global circulation model is developed. The new model is designed to perform "cloud resolving simulations" by directly calculating deep convection and meso-scale circulations, which play key roles not only in the tropical circulations but in the global circulations of the atmosphere. Since cores of deep convection have a few km in horizontal size, they have not directly been resolved by existing atmospheric general circulation models (AGCMs). In order to drastically enhance horizontal resolution, a new framework of a global atmospheric model is required; we adopted nonhydrostatic governing equations and icosahedral grids to the new model, and call it Nonhydrostatic ICosahedral Atmospheric Model (NICAM). In this article, we review governing equations and numerical techniques employed, and present the results from the unique 3.5-km mesh global experiments—with O(10 9) computational nodes—using realistic topography and land/ocean surface thermal forcing. The results show realistic behaviors of multi-scale convective systems in the tropics, which have not been captured by AGCMs. We also argue future perspective of the roles of the new model in the next generation atmospheric sciences.
Marzec, C J; Day, L A
1993-01-01
The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs
Moubayidin, Laila; Østergaard, Lars
2015-09-01
985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction.
ERIC Educational Resources Information Center
Jittam, Piyachat; Ruenwongsa, Pintip; Panijpan, Bhinyo
2008-01-01
We have found it an effective way of teaching symmetry in the context of stereoselectivity, to use common everyday objects with the same point groups as the substrates involved. This has helped students to distinguish between those symmetry elements which allow for stereospecificity and those which preclude it. Two symmetry elements, the simple…
Point-group sensitive orientation mapping of non-centrosymmetric crystals
Winkelmann, Aimo; Nolze, Gert
2015-02-16
We demonstrate polarity-sensitive orientation mapping of non-centrosymmetric phases by Electron Backscatter Diffraction (EBSD). The method overcomes the restrictions of kinematic orientation determination by EBSD, which is limited to the centro-symmetric Laue-groups according to Friedel's rule. Using polycrystalline GaP as an example, we apply a quantitative pattern matching approach based on simulations using the dynamical theory of electron diffraction. This procedure results in a distinct assignment of the local orientation according to the non-centrosymmetric point group of the crystal structure under investigation.
Melting of icosahedral nickel clusters under hydrostatic pressure.
Fu, Bing; Chen, Li; Wang, Feifei; Xie, Yiqun; Ye, Xiang
2014-12-01
The thermal stabilities and melting behavior of icosahedral nickel clusters under hydrostatic pressure have been studied by constant-pressure molecular dynamics simulation. The potential energy and Lindemann index are calculated. The overall melting temperature exhibits a strong dependence on pressure. The Lindemann index of solid structure before melting varies slowly and is almost independent of pressure. However, after the clusters melt completely, the Lindemann index at the overall melting point strongly depends on pressure. The overall melting temperature is found to be increasing nonlinearly with increasing pressure, while the volume change during melting decreases linearly with increasing pressure. Under a high pressure and temperature environment, similar angular distributions were found between liquid and solid structures, indicating the existence of a converging local structure.
Many-molecule encapsulation by an icosahedral shell.
Perlmutter, Jason D; Mohajerani, Farzaneh; Hagan, Michael F
2016-01-01
We computationally study how an icosahedral shell assembles around hundreds of molecules. Such a process occurs during the formation of the carboxysome, a bacterial microcompartment that assembles around many copies of the enzymes ribulose 1,5-bisphosphate carboxylase/ oxygenase and carbonic anhydrase to facilitate carbon fixation in cyanobacteria. Our simulations identify two classes of assembly pathways leading to encapsulation of many-molecule cargoes. In one, shell assembly proceeds concomitantly with cargo condensation. In the other, the cargo first forms a dense globule; then, shell proteins assemble around and bud from the condensed cargo complex. Although the model is simplified, the simulations predict intermediates and closure mechanisms not accessible in experiments, and show how assembly can be tuned between these two pathways by modulating protein interactions. In addition to elucidating assembly pathways and critical control parameters for microcompartment assembly, our results may guide the reengineering of viruses as nanoreactors that self-assemble around their reactants. PMID:27166515
Dynamico, an Icosahedral Dynamical Core Designed for Consistency and Versatility
NASA Astrophysics Data System (ADS)
Dubos, T.
2014-12-01
The design of the icosahedral-hexagonal dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations (HPE) in a Lagrangian vertical coordinate, and the HPE in a hybrid mass-based vertical coordinate. In line with more general lines of thought known as physics-preserving discretizations and discrete differential geometry, kinematics and dynamics are separated as strictly as possible. This separation means that the transport of mass, scalars and potential temperature uses no information regarding the specific momentum equation being solved. This disregarded information includes the equation of state as well as any metric information, and is used only for certain terms of the momentum budget, written in Hamiltonian, vector-invariant form. The common Hamiltonian structure of the various equations of motion (Tort and Dubos, 2014 ; Dubos and Tort, 2014) is exploited to formulate energy-conserving spatial discretizations in a unified way. Furthermore most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. This design permits to consider several extensions in the near future, especially to deep-atmosphere, moist and non-hydrostatic equations. Representative academic three-dimensional benchmarks are run and analyzed, showing correctness of the model (Figure : time-zonal statistics from Held and Suarez (1994) simulations). Hopefully preliminary full-physics results will be presented as well. References : T. Dubos and M. Tort, "Equations of atmospheric motion in non-Eulerian vertical coordinates : vector-invariant form and Hamiltonian formulation", accepted by Mon. Wea. Rev. M. Tort and T. Dubos, "Usual approximations to the equations of atmospheric motion : a variational perspective" accepted by J. Atmos. Sci T. Dubos et al., "DYNAMICO
Difference in Icosahedral Short-Range Order in Early and Late Transition Metal Liquids
NASA Technical Reports Server (NTRS)
Lee, G. W.; Gangopadbyay, A. K.; Kelton, K. F.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.
2004-01-01
New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in-situ synchrotron x-ray diffraction measurements of electrostatically-levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid. although this has been predicted by theoretical studies on atomic clusters.
Difference in Icosahedral Short-Range Order in Early and Late Transition Metals Liquids
NASA Technical Reports Server (NTRS)
Lee, G. W.; Gangopadhyay, A. K.; Kelton, K. F.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.
2003-01-01
New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in-situ synchrotron x-ray diffraction measurements of electrostatically-levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid, although this has been predicted by theoretical studies on atomic clusters.
Jin, Renxi; Liu, Chong; Zhao, Shuo; Das, Anindita; Xing, Hongzhu; Gayathri, Chakicherla; Xing, Yan; Rosi, Nathaniel L; Gil, Roberto R; Jin, Rongchao
2015-08-25
The [Au37(PPh3)10(SR)10X2](+) nanocluster (where SR = thiolate and X = Cl/Br) was theoretically predicted in 2007, but since then, there has been no experimental success in the synthesis and structure determination. Herein, we report a kinetically controlled, selective synthesis of [Au37(PPh3)10(SC2H4Ph)10X2](+) (counterion: Cl(-) or Br(-)) with its crystal structure characterized by X-ray crystallography. This nanocluster shows a rod-like structure assembled from three icosahedral Au13 units in a linear fashion, consistent with the earlier prediction. The optical absorption and the electrochemical and catalytic properties are investigated. The successful synthesis of this new nanocluster allows us to gain insight into the size, structure, and property evolution of gold nanoclusters that are based upon the assembly of icosahedral units (i.e., cluster of clusters). Some interesting trends are identified in the evolution from the monoicosahedral [Au13(PPh3)10X2](3+) to the bi-icosahedral [Au25(PPh3)10(SC2H4Ph)5X2](2+) and to the tri-icosahedral [Au37(PPh3)10(SC2H4Ph)10X2](+) nanocluster, which also points to the possibility of achieving even longer rod nanoclusters based upon assembly of icosahedral building blocks. PMID:26214221
Demina, Tatiana A.; Pietilä, Maija K.; Svirskaitė, Julija; Ravantti, Janne J.; Atanasova, Nina S.; Bamford, Dennis H.
2016-01-01
ABSTRACT Despite their high genomic diversity, all known viruses are structurally constrained to a limited number of virion morphotypes. One morphotype of viruses infecting bacteria, archaea, and eukaryotes is the tailless icosahedral morphotype with an internal membrane. Although it is considered an abundant morphotype in extreme environments, only seven such archaeal viruses are known. Here, we introduce Haloarcula californiae icosahedral virus 1 (HCIV-1), a halophilic euryarchaeal virus originating from salt crystals. HCIV-1 also retains its infectivity under low-salinity conditions, showing that it is able to adapt to environmental changes. The release of progeny virions resulting from cell lysis was evidenced by reduced cellular oxygen consumption, leakage of intracellular ATP, and binding of an indicator ion to ruptured cell membranes. The virion contains at least 12 different protein species, lipids selectively acquired from the host cell membrane, and a 31,314-bp-long linear double-stranded DNA (dsDNA). The overall genome organization and sequence show high similarity to the genomes of archaeal viruses in the Sphaerolipoviridae family. Phylogenetic analysis based on the major conserved components needed for virion assembly—the major capsid proteins and the packaging ATPase—placed HCIV-1 along with the alphasphaerolipoviruses in a distinct, well-supported clade. On the basis of its virion morphology and sequence similarities, most notably, those of its core virion components, we propose that HCIV-1 is a member of the PRD1-adenovirus structure-based lineage together with other sphaerolipoviruses. This addition to the lineage reinforces the notion of the ancient evolutionary links observed between the viruses and further highlights the limits of the choices found in nature for formation of a virion. PMID:27435460
Metal-organic framework materials based on icosahedral boranes and carboranes
Mirkin, Chad A.; Hupp, Joseph T.; Farha, Omar K.; Spokoyny, Alexander M.; Mulfort, Karen L.
2010-11-02
Disclosed herein are metal-organic frameworks of metals and boron rich ligands, such as carboranes and icosahedral boranes. Methods of synthesizing and using these materials in gas uptake are disclosed.
Van Hove singularities of some icosahedral boron-rich solids by differential reflectivity spectra
NASA Astrophysics Data System (ADS)
Werheit, Helmut
2015-09-01
Differential reflectivity spectra of some icosahedral boron rich solids, β-rhombohedral boron, boron carbide and YB66-type crystals, were measured. The derivatives yield the van Hove singularities, which are compared with results obtained by other experimental methods.
Stable Icosahedral Hollow Cage Clusters: Stannapherene (Sn12 2-) and Plumbaspherene (Pb12 2-)
Cui, Lifeng; Wang, Lai S.
2008-01-01
One of the major objectives of cluster science is to discover stable atomic clusters, which may be used as building blocks for cluster-assembled nanomaterials. The discovery and bulk synthesis of the fullerenes have sprouted new research disciplines in chemistry and nanoscience and precipitated intense interests to search for other similar stable clusters. However, despite major research efforts, no other analogous gas-phase clusters have been found and yielded to bulk syntheses. In this article, we review our recent discoveries in cluster beam experiments of stannaspherene (Sn12 2–) and plumbaspherene (Pb12 2–), which are highly stable and symmetric cage clusters. The names for these two clusters derive from their icosahedral (Ih) symmetry and delocalized spherical π-bonding that are characteristics of buckminsterfullerene C60. Stannaspherene and plumbaspherene have diameters comparable to that of C60 and can be considered as inorganic analogs of the buckyball. The large internal space in Sn12 2– has been shown to be able to trap any transition metal atom to form new endohedral cage clusters, M@Sn12 –, analogous to endohedral fullerenes. The doped atom in M@Sn12 – keeps its quasi-atomic nature with large magnetic moments. These endohedral cages form a rich class of new building blocks for cluster-assembled materials with tunable magnetic, electronic, and chemical properties. During our attempt to synthesize endohedral stannaspherenes, we crystallized a new Pd2@Sn18 4– cluster, which can be viewed as the fusion of two Pd@Sn12 2– clusters. This result suggests that stannaspherene, plumbaspherene, and a large number of their endohedrally doped species can be synthesized in the bulk.
NASA Astrophysics Data System (ADS)
Cai, Tanhong
2001-07-01
We investigate the atomic structure of fivefold surface of icosahedral (i-) Al-Cu-Fe quasicrystal using scanning tunneling microscopy (STM) under ultra high vacuum (UHV). Annealing the sputtered surface at appropriate temperature produces a step-terrace structure on the surface. Our STM analysis indicates that the terraces are separated with primarily two stepheights in the ratio of t=5+1 /2 , a characteristic ratio in quasiperiodic structures. The measurements agree with the results from dynamical low energy electron diffraction (LEED) calculations. The spatial distribution of stepheights along the fivefold axis does not follow the quasiperiodic Fibonacci sequence. The existence of such stacking defects in the bulk structure is confirmed with the screw dislocations often observed in the STM scans. The first atomic resolution STM images on this type of material are obtained. The flat terraces are dominated with "ten-petal flower-like" motif, locally arranged with fivefold symmetry. Similar structural features can be identified in the atomically-dense planes generated from one of the available bulk structure models. Based on these results, we conclude that the fivefold i-AlCuFe surface corresponds to a two-dimensional cut of the bulk material. After examining the clean surface, we investigate the nucleation and growth of aluminium metallic thin films on the quasicrystalline i-Al-Cu-Fe fivefold surface. Upon deposition at room temperature, aluminium adatoms nucleate as pentagonal "starfish" with uniform size and in the same orientation. The same structure features are observed for different fluxes at low coverages. Based on the experimental results and the available bulk structure model, we identify the specific nucleation sites on the substrate and develop a model for the formation of the pentagonal starfish.
Schein, Stan; Gayed, James Maurice
2014-02-25
The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry--tetrahedral, octahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry.
NASA Astrophysics Data System (ADS)
Venderbos, J. W. F.
2016-03-01
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave-vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become "nonsymmorphic"-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M -point ordering vectors are worked out in detail. To show that our results generally apply to 2 D hexagonal lattices, we develop a general low-energy SU(3 ) theory of (spinless) saddle-point electrons.
A face-sharing bi-icosahedral model for Al₂₃⁻.
Koyasu, K; Tsukuda, T
2014-10-21
A face-sharing bi-icosahedral motif is proposed as a candidate structure of the magic cluster, Al23(-), on the basis of DFT calculations. The structure can be viewed as a quasi-molecule made of two Al13 (D3d) superatoms with an open electronic configuration via constructive overlap of 1F and 2P superatomic orbitals. A face-sharing tri-icosahedral motif is also predicted for Al33(-). PMID:25199061
Many-molecule encapsulation by an icosahedral shell
Perlmutter, Jason D; Mohajerani, Farzaneh; Hagan, Michael F
2016-01-01
We computationally study how an icosahedral shell assembles around hundreds of molecules. Such a process occurs during the formation of the carboxysome, a bacterial microcompartment that assembles around many copies of the enzymes ribulose 1,5-bisphosphate carboxylase/ oxygenase and carbonic anhydrase to facilitate carbon fixation in cyanobacteria. Our simulations identify two classes of assembly pathways leading to encapsulation of many-molecule cargoes. In one, shell assembly proceeds concomitantly with cargo condensation. In the other, the cargo first forms a dense globule; then, shell proteins assemble around and bud from the condensed cargo complex. Although the model is simplified, the simulations predict intermediates and closure mechanisms not accessible in experiments, and show how assembly can be tuned between these two pathways by modulating protein interactions. In addition to elucidating assembly pathways and critical control parameters for microcompartment assembly, our results may guide the reengineering of viruses as nanoreactors that self-assemble around their reactants. DOI: http://dx.doi.org/10.7554/eLife.14078.001 PMID:27166515
Multiple diffraction in an icosahedral Al-Cu-Fe quasicrystal
NASA Astrophysics Data System (ADS)
Fan, C. Z.; Weber, Th.; Deloudi, S.; Steurer, W.
2011-07-01
In order to reveal its influence on quasicrystal structure analysis, multiple diffraction (MD) effects in an icosahedral Al-Cu-Fe quasicrystal have been investigated in-house on an Oxford Diffraction four-circle diffractometer equipped with an Onyx™ CCD area detector and MoKα radiation. For that purpose, an automated approach for Renninger scans (ψ-scans) has been developed. Two weak reflections were chosen as the main reflections (called P) in the present measurements. As is well known for periodic crystals, it is also observed for this quasicrystal that the intensity of the main reflection may significantly increase if the simultaneous (H) and the coupling (P-H) reflections are both strong, while there is no obvious MD effect if one of them is weak. The occurrence of MD events during ψ-scans has been studied based on an ideal structure model and the kinematical MD theory. The reliability of the approach is revealed by the good agreement between simulation and experiment. It shows that the multiple diffraction effect is quite significant.
Hydrogen Characteristics of Ti-Based Icosahedral Quasicrystals
NASA Astrophysics Data System (ADS)
Viano, A. M.; Hanneken, J. W.; Kelton, K. F.; Gibbons, P. C.
1997-03-01
The ability of Ti-based icosahedral quasicrystals to store significant amounts of hydrogen is now well-known. Up to 64 atomic percent of hydrogen can be stored in Ti_45Zr_38Ni_17 with only a small fraction of the sample transforming to crystalline hydrides. The amount of crystalline phase present depends on both the method of hydrogenation and the surface preparation of the sample. The surface oxide layer, which has been characterized in air-exposed samples, greatly influences the absorption and desorption kinetics. To accurately determine the hydrogen characteristics, studies were performed on unoxidized, powdered quasicrystalline Ti_xZr_yNiz This was accomplished by gently ball-milling the as-quenched quasicrystalline ribbons in a stainless-steel vessel which was then connected directly to a modified Sieverts' apparatus. Absorption and desorption rates for the quasicrystal will be discussed and compared to those for other related alloys. The saturation limit of hydrogen in the quasicrystal, as measured from a determination of the pressure-composition isotherms, will also be presented.
Schottky effect in the i -Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant
NASA Astrophysics Data System (ADS)
Jazbec, S.; Kashimoto, S.; Koželj, P.; Vrtnik, S.; Jagodič, M.; Jagličić, Z.; Dolinšek, J.
2016-02-01
The analysis of low-temperature specific heat of rare-earth (RE)-containing quasicrystals and periodic approximants and consequent interpretation of their electronic properties in the T →0 limit is frequently hampered by the Schottky effect, where crystalline electric fields lift the degeneracy of the RE-ion Hund's rule ground state and introduce additional contribution to the specific heat. In this paper we study the low-temperature specific heat of a thulium-containing i -Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant, both being classified as "Schottky" systems. We have derived the crystal-field Hamiltonian for pentagonal symmetry of the crystalline electric field, pertinent to the class of Tsai-type icosahedral quasicrystals and their approximants, where the RE ions are located on fivefold axes of the icosahedral atomic cluster. Using the leading term of this Hamiltonian, we have calculated analytically the Schottky specific heat in the presence of an external magnetic field and made comparison to the experimental specific heat of the investigated quasicrystal and approximant. When the low-temperature specific heat C is analyzed in a C /T versus T2 scale (as it is customarily done for metallic specimens), the Schottky specific heat yields an upturn in the T →0 limit that cannot be easily distinguished from a similar upturn produced by the electron-electron interactions in exchange-enhanced systems and strongly correlated systems. Our results show that extraction of the electronic properties of RE-containing quasicrystals from their low-temperature specific heat may be uncertain in the presence of the Schottky effect.
ERIC Educational Resources Information Center
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
Geometrical symmetries of nuclear systems: {{ D }}_{3h} and {{ T }}_{d} symmetries in light nuclei
NASA Astrophysics Data System (ADS)
Bijker, Roelof
2016-07-01
The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with {{ D }}3h symmetry for 12C, and a tetrahedron with {{ T }}d symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
Design of Three-shell Icosahedral Matryoshka Clusters A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd, Mn)
Huang, Xiaoming; Zhao, Jijun; Su, Yan; Chen, Zhongfang; King, R. Bruce
2014-01-01
We propose a series of icosahedral matryoshka clusters of A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd), which possess large HOMO-LUMO gaps (1.29 to 1.54 eV) and low formation energies (0.06 to 0.21 eV/atom). A global minimum search using a genetic algorithm and density functional theory calculations confirms that such onion-like three-shell structures are the ground states for these A21B12 binary clusters. All of these icosahedral matryoshka clusters, including two previously found ones, i.e., [As@Ni12@As20]3− and [Sn@Cu12@Sn20]12−, follow the 108-electron rule, which originates from the high Ih symmetry and consequently the splitting of superatom orbitals of high angular momentum. More interestingly, two magnetic matryoshka clusters, i.e., Sn@Mn12@Sn20 and Pb@Mn12@Pb20, are designed, which combine a large magnetic moment of 28 µB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices. PMID:25376938
Comparative Study of Non-Enveloped Icosahedral Viruses Size
Nikitin, Nikolai; Trifonova, Ekaterina; Evtushenko, Evgeniy; Kirpichnikov, Mikhail; Atabekov, Joseph; Karpova, Olga
2015-01-01
Now, as before, transmission electron microscopy (TEM) is a widely used technique for the determination of virions size. In some studies, dynamic light scattering (DLS) has also been applied for this purpose. Data obtained by different authors and using different methods could vary significantly. The process of TEM sample preparation involves drying on the substrate, which can cause virions to undergo morphology changes. Therefore, other techniques should be used for measurements of virions size in liquid, (i.e. under conditions closer to native). DLS and nanoparticle tracking analysis (NTA) provide supplementary data about the virions hydrodynamic diameter and aggregation state in liquid. In contrast to DLS, NTA data have a higher resolution and also are less sensitive to minor admixtures. In the present work, the size of non-enveloped icosahedral viruses of different nature was analyzed by TEM, DLS and NTA: the viruses used were the encephalomyocarditis virus (animal virus), and cauliflower mosaic virus, brome mosaic virus and bean mild mosaic virus (plant viruses). The same, freshly purified, samples of each virus were used for analysis using the different techniques. The results were compared with earlier published data and description databases. DLS data about the hydrodynamic diameter of bean mild mosaic virus, and NTA data for all examined viruses, were obtained for the first time. For all virus samples, the values of size obtained by TEM were less than virions sizes determined by DLS and NTA. The contribution of the electrical double layer (EDL) in virions hydrodynamic diameter was evaluated. DLS and NTA data adjusted for EDL thickness were in better agreement with TEM results. PMID:26545232
Symmetry and equivalence restrictions in electronic structure calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Taylor, Peter R.
1988-01-01
A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.
NASA Technical Reports Server (NTRS)
Curreri, Peter A. (Technical Monitor); Kelton, K. F.; Gangopadhyay, A.; Lee, G. W.; Hyers, R. W.; Rathz, R. J.; Rogers, J.; Schenk, T.; Simonet, V.; Holland-Moritz, D.
2003-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si, for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.
NASA Technical Reports Server (NTRS)
Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.; Holland-Moritz, D.; Curreri, Peter A. (Technical Monitor)
2002-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si(3), for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron X-ray and high flux neutron facilities.
NASA Technical Reports Server (NTRS)
Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.
2003-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si[3], for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.
Accurate design of megadalton-scale two-component icosahedral protein complexes.
Bale, Jacob B; Gonen, Shane; Liu, Yuxi; Sheffler, William; Ellis, Daniel; Thomas, Chantz; Cascio, Duilio; Yeates, Todd O; Gonen, Tamir; King, Neil P; Baker, David
2016-07-22
Nature provides many examples of self- and co-assembling protein-based molecular machines, including icosahedral protein cages that serve as scaffolds, enzymes, and compartments for essential biochemical reactions and icosahedral virus capsids, which encapsidate and protect viral genomes and mediate entry into host cells. Inspired by these natural materials, we report the computational design and experimental characterization of co-assembling, two-component, 120-subunit icosahedral protein nanostructures with molecular weights (1.8 to 2.8 megadaltons) and dimensions (24 to 40 nanometers in diameter) comparable to those of small viral capsids. Electron microscopy, small-angle x-ray scattering, and x-ray crystallography show that 10 designs spanning three distinct icosahedral architectures form materials closely matching the design models. In vitro assembly of icosahedral complexes from independently purified components occurs rapidly, at rates comparable to those of viral capsids, and enables controlled packaging of molecular cargo through charge complementarity. The ability to design megadalton-scale materials with atomic-level accuracy and controllable assembly opens the door to a new generation of genetically programmable protein-based molecular machines. PMID:27463675
None
2016-07-12
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ârenormalizableâ. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged âvectorâ particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of
2011-02-24
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of
Icosahedral quasiperiodic packing of fibres parallel to fivefold and threefold axes.
Audier, M; Duneau, M
2000-01-01
Building rules are examined for an icosahedral quasiperiodic packing of fibres with axes parallel to the ten threefold axes, first employing an experimental construction and afterwards a mathematical demonstration using the cut-and-project method applied in hyperspace. As a result of this latter approach, very simple two-dimensional (2D) building rules are proposed. Similar simple 2D rules have also been proposed for the case of an icosahedral quasiperiodic packing with fibre axes parallel to the six fivefold axes [Duneau & Audier (1999). Acta Cryst. A55, 746-754]. Finally, the construction of another icosahedral quasiperiodic packing resulting from a combination of two groups of fibres respectively parallel to six fivefold and ten threefold axes is reported. A brief discussion is given on different particular mechanical behaviours which might a priori be expected from the various enantiomorphic properties of these packings.
NASA Astrophysics Data System (ADS)
Kah, Cherno Baba; Yu, M.; Jayanthi, C. S.; Wu, S. Y.
2014-03-01
Our previous study on one-dimensional icosahedral B12 cluster (α-B12) based chain [Bulletin of APS Annual Meeting, p265 (2013)] and ring structures has prompted us to study the two-dimensional (2D) α-B12 based structures. Recently, we have carried out a systematic molecular dynamics study on the structural stabilities and electronic properties of the 2D α-B12 based structures using the SCED-LCAO method [PRB 74, 15540 (2006)]. We have considered several types of symmetry for these 2D structures such as δ3, δ4, δ6 (flat triangular), and α' types. We have found that the optimized structures are energetically in the order of δ6 < α' < δ3 < δ4 which is different from the energy order of α'< δ6 < δ4 < δ3 found in the 2D boron monolayer sheets [ACS Nano 6, 7443 (2012)]. A detailed discussion of this study will be presented. The first author acknowledges the McSweeny Fellowship for supporting his research in this work.
Dynamic Paper Constructions for Easier Visualization of Molecular Symmetry
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.
2010-01-01
A system for construction of simple poster-board models is described. The models dynamically demonstrate the symmetry operations of proper rotation, improper rotation, reflection, and inversion for the chemically important point groups D[subscript 3h], D[subscript 4h], D[subscript 5h], D[subscript 6h], T[subscript d], and O[subscript h]. The…
Web-Supported Chemistry Education: Design of an Online Tutorial for Learning Molecular Symmetry
ERIC Educational Resources Information Center
Korkmaz, Ali; Harwood, William S.
2004-01-01
This paper describes our use of the ADDIE protocol to design and develop an interactive tutorial for students learning molecular symmetry operations and point groups. The tutorial provides a 3-D environment where students can examine molecules, structures, and symmetry elements. Most such tutorials are connected to courses or instructors in…
Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
NASA Astrophysics Data System (ADS)
Cummings, F. R.; Muller, T. F. G.; Malgas, G. F.; Arendse, C. J.
2015-10-01
Potentiostatic anodization of commercially pure, 50 μm-thick titanium (Ti) foil was performed in aqueous, phosphate electrolytes at increasing experimental timeframes at a fixed applied potential for the synthesis of titania nanotube arrays (TNAs). High resolution scanning electron microscopy images, combined with energy dispersive spectroscopy and x-ray diffraction spectra reveal that anodization of the Ti foil in a 1 M NaF+0.5 M H3PO4 electrolyte for 4 h yields a titanate surface with pore diameters ranging between 100 and 500 nm. The presence of rods on the Ti foil surface with lengths exceeding 20 μm and containing high concentrations of phosphor on the exterior was also detected at these conditions, along with micro-sized coral reef-like titanate balls. We propose that the formation of these structures play a major role during the anodization process and impedes nanotube growth during the anodization process. High spatially resolved scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) performed along the length of a single anodized TiO2 nanotube reveals a gradual evolution of the nanotube crystallinity, from a rutile-rich bottom to a predominantly anatase TiO2 structure along its length.
Nucleation and Growth of Icosahedral Boron Suboxide Clusters at High Pressure
NASA Astrophysics Data System (ADS)
McMillan, Paul F.; Hubert, Hervé; Chizmeshya, Andrew; Petuskey, William T.; Garvie, Lawrence A. J.; Devouard, Bertrand
1999-10-01
The stoichiometry of boron suboxide (B6O1-δ) synthesized from mixtures of boron and boron oxide (B2O3) at high pressure lies closer to the nominal composition (δ=0) than materials obtained at atmospheric pressure. The materials obtained in the high pressure syntheses in the presence of molten B2O3 also have a higher degree of crystallinity than for sintered powders. For syntheses at temperatures of 1700-1800°C at pressures between 4 and approximately 5.5 GPa, the well-crystallized particles are dominated by icosahedral multiply-twinned particles up to approximately 40 μm in diameter. This unusual morphology is obtained by Mackay packing, i.e., by assembly of successive shells of icosahedral B12 units around a central icosahedral nucleus to give a multiply twinned particle in which each of the 20 elements has the Roverline3m space group of the rhombohedral α-B structure. We examine the thermodynamic and kinetic factors associated with the development of this morphology during high pressure growth and use ab initio calculations to investigate the energetic driving forces for initiation of the Mackay packing around the central icosahedral nucleus.
Technology Transfer Automated Retrieval System (TEKTRAN)
The inactivation mechanism of ultrashort pulsed laser irradiation at a wavelength of 425 nm has been studied using two different-sized, non-enveloped icosahedral viruses, murine norovirus-1 (MNV-1) and human papillomavirus-16 (HPV-16) pseudovirions. Our experimental results are consistent with a mo...
Projective symmetry of partons in Kitaev's honeycomb model
NASA Astrophysics Data System (ADS)
Mellado, Paula
2015-03-01
Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of Kitaev's honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities reflect not the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group. We acknowledge Fondecyt under Grant No. 11121397, Conicyt under Grant No. 79112004, and the Simons Foundation (P.M.); the Max Planck Society and the Alexander von Humboldt Foundation (O.P.); and the US DOE Grant No. DE-FG02-08ER46544 (O.T.).
Symmetry-protected entangling boundary zero modes in crystalline topological insulators
NASA Astrophysics Data System (ADS)
Chang, Po-Yao; Mudry, Christopher; Ryu, Shinsei
2014-09-01
Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.
Lowe, M.; McGrath, R.; Sharma, H. R.; Yadav, T. P.; Fournée, V.; Ledieu, J.
2015-03-07
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe{sub 3}O{sub 4} rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
NASA Astrophysics Data System (ADS)
Lowe, M.; Yadav, T. P.; Fournée, V.; Ledieu, J.; McGrath, R.; Sharma, H. R.
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
Dynamic stabilities of icosahedral-like clusters and their ability to form quasicrystals
NASA Astrophysics Data System (ADS)
Liang, Xiaogang; Hamid, Ilyar; Duan, Haiming
2016-06-01
The dynamic stabilities of the icosahedral-like clusters containing up to 2200 atoms are investigated for 15 metal elements. The clusters originate from five different initial structures (icosahedron, truncated decahedron, octahedron, closed-shell fragment of an HCP structure, and non-closed-shell fragment of an HCP structure). The obtained order of the dynamic stabilities of the icosahedral-like clusters can be assigned to three groups, from stronger to weaker, according to the size ranges involved: (Zr, Al, Ti) > (Cu, Fe, Co, Ni, Mg, Ag) > (Pb, Au, Pd, Pt, Rh, Ir), which correspond to the predicted formation ability of the quasicrystals. Thedifferences of the sequences can be explained by analyzing the parameters of the Gupta-type many-body inter-atomic potentials.
Adsorption sites on icosahedral quasicrystal surfaces: Dark stars and white flowers
Unal, B.; Jenks, C.J.; Thiel, P.A.
2009-01-12
From other work, two preferred sites have been suggested for metals and semimetals adsorbed on the fivefold surfaces of icosahedral, Al-based quasicrystals. Because of their appearance in scanning tunneling microscopy (STM) images, these sites are known as dark stars and white flowers. In this paper, we analyze four bulk structural models in physical space to determine the types, chemical decorations, and densities of the dark star - and, to a lesser extent, the white flower - adsorption sites for the fivefold planes of icosahedral Al-Pd-Mn. We find that the chemical decorations of these sites are heterogeneous, even within a single model. Both features are also structurally heterogeneous, according to STM measurements, and the structural variation is consistent with the bulk structure models. Finally, from the models, the density of dark stars in the planes correlates with the step height. This may explain previous experimental observations of different properties for different terraces.
Opening of an icosahedral boron framework: A combined infrared spectroscopic and computational study
NASA Astrophysics Data System (ADS)
Fagiani, Matias R.; Liu Zeonjuk, L.; Esser, Tim K.; Gabel, Detlef; Heine, Thomas; Asmis, Knut R.; Warneke, Jonas
2015-04-01
The opening of an icosahderal boron cage in the periodinated closo-dodecaborate B12I122- upon deiodination is studied using cryogenic ion trap vibrational spectroscopy combined with electronic structure calculations. Comparison of simulated vibrational spectra to the infrared photodissociation spectra of messenger-tagged B12I122- and B12In- (n = 7-9) formed by skimmer collision induced dissociation shows that the larger clusters absorb exclusively below 975 cm-1 and hence exhibit quasi-icosahedral B12-cage structures, while the higher energy absorptions in-between 1000 and 1300 cm-1 observed for n = 7 can only be recovered by considering a breakup of the icosahedral cage upon deiodination from n = 8 to n = 7.
Scanning Tunneling Microscopy Studies of Surface Structures of Icosahedral Al-Cu-Fe Quasicrystals
Tanhong Cai
2002-12-31
Three papers are included in this dissertation. The first paper: ''Structural aspects of the fivefold quasicrystalline Al-Cu-Fe surface from STM and dynamical LEED studies'', is in press with ''Surface Science''. The second paper: ''An STM study of the atomic structure of the icosahedral Al-Cu-Fe fivefold surface'' is submitted to ''Physical Review B, Rapid Communication''. The third paper: ''Pseudomorphic starfish: arrangement of extrinsic metal atoms on a quasicrystalline substrate'' is submitted to ''Nature''. Following the third paper are general conclusions and appendices that document the published paper ''Structural aspects of the three-fold surface of icosahedral Al-Pd-Mn'' (appearing in volume 461, issue 1-3 of ''Surface Science'' on page L521-L527, 2000), the design as well as the specifications of the aluminum evaporator used in the aluminum deposition study in this dissertation, an extended discussion of the aluminum deposition on the quasicrystalline surface, and the STM database.
Dual-phase glassy/nanoscale icosahedral phase materials in Cu–Zr–Ti–Pd system alloys
Louzguine-Luzgin, Dmitri V.; Churyumov, A.Yu.
2014-10-15
The present work is devoted to an investigation of the formation kinetics, stability and homogeneity area of the nanoscale icosahedral phase formed on heating in the dual-phase glassy/quasicrystalline phase Cu–Zr–Ti–Pd alloys. The data obtained indicate that the Cu–Zr–Ti–Pd icosahedral phase is not a Cu-rich part of the compositional homogeneity area of the Zr–Cu–Pd one. Moreover, Ti, as well as Pd, is found to be an important element stabilizing quasicrystalline phase in the Cu–Zr–Ti–Pd alloys. The formation criteria for Cu- and Zr/Hf-based icosahedral phases are discussed based on the quasilattice constant to average atomic diameter ratio. Deviation from a certain ratio leads to destabilization of the icosahedral phase. By using the isothermal calorimetry traces transformation kinetics above and below the glass-transition region was analyzed. Some difference in the transformation kinetics above and below the glass-transition region allows us to suggest that possible structure changes occur upon glass-transition. - Highlights: • Formation kinetics, stability and homogeneity area of nanoscale icosahedral phase • Cu–Zr–Ti–Pd icosahedral phase is not a Cu-rich part of Zr–Cu–Pd one. • Ti, as well as Pd, is an important element stabilizing quasicrystalline phase. • Difference in transformation kinetics above and below glass-transition region.
NASA Astrophysics Data System (ADS)
Dai, Mingxing; Wang, Renhui
1990-01-01
Higher-order Laue zone (HOLZ) line patterns of an Al 76Si 4Mn 20 quasi- crystalline icosahedral phase (I phase) have been obtained experimentally with a large angular range by connecting a series of conventional convergent-beam electron diffraction patterns. The computer simulated HOLZ line patterns covering the whole orientation triangle of the I phase, which were calculated by using cut and projection method and the simple quasilattice model, show principle agreement with the experimental ones.
Vibration isolation support system for a truncated icosahedral gravitational wave antenna
NASA Astrophysics Data System (ADS)
Velloso, W. F.; Melo, J. L.; Aguiar, O. D.
2000-06-01
We designed a mechanical isolation system for an icosahedral resonant gravitational wave detector we plan to construct in Brazil. We have used the NASTRAN finite element software to perform the numerical analysis. Our results show that the designed system could allow a damping factor better than -200 dB in the spectral range of interest, which is adequate to the sensibility level we want for the antenna.
Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole
NASA Astrophysics Data System (ADS)
Li, Lian-He
2013-11-01
The generalized 2D problem of icosahedral quasicrystals containing an elliptic hole is considered by using the extended Stroh formalism. The closed-form solutions for the displacements and stresses are obtained under general loading conditions. The solution of the Griffith crack problem as a special case of the results is also observed. The stress intensity factor and strain energy release rate are given. The effect of the phonon—phason coupling elastic constant on the mechanical behavior is also discussed.
NASA Astrophysics Data System (ADS)
Brien, Valérie; Dauscher, Anne; Machizaud, Francis
2006-08-01
The optical reflectivity of Al-based and Ti-based quasicrystalline and approximant samples were investigated versus the quality of their structural morphology using optical reflectometry, x-ray diffraction, and transmission electron microscopy. The different structural morphologies were obtained using three different preparation processes: sintering, pulsed laser deposition, and reactive cathodic magnetron sputtering. The work demonstrates that the canonical behavior of icosahedral state in specular reflectivity is extremely sensitive to different and very fine aspects of the microstructure: sizes of grains smaller than 50nm, slight local diffuse disorder, and shifts away from the icosahedral crystallographic structure (approximants). The work explains why the optical properties of the same kind of quasicrystals found in literature sometimes reveal a different behavior from one author to another. The study then confirms the work of some authors and definitely shows that the canonical behavior of icosahedral state in specular reflectivity over the 30000-50000cm-1 domain is characterized by a decreasing function made of steps. It also shows that this behavior can be interpreted thanks to the cluster hierarchy of the model of Janot [Phys. Rev. B 53, 181 (1996)].
The Icosahedral Ti-Zr-Ni Quasicrystal - A Ground State Quasicrystal?
NASA Astrophysics Data System (ADS)
Hennig, R. G.; Carlsson, A. E.; Kelton, K. F.; Henley, C. L.
2001-03-01
The icosahedral Ti-Zr-Ni quasicrystal is known to be thermodynamically stable [1]. Most stable quasicrystals form at high temperatures from the liquid phase. In contrast to those quasicrystals, however, the Ti-Zr-Ni quasicrystal forms at lower temperatures, near 570^circC, by a solid state transformation of crystal phases that are stable at higher temperatures. A decorated canonical cell tiling for the structure of this quasicrystal was determined by a refinement to x-ray and neutron diffraction data and results from ab initio calculations. The energetic stability of the icosahedral Ti-Zr-Ni quasicrystal was investigated by total energy calculations using the density-functional code VASP [2]. The ternary ground state phase diagram for Ti-Zr-Ni was determined. The energy of the structural model of the quasicrystal is found to be lower than the energy of any known competing phase. This result, coupled with the continued stability with long anneals at lower temperatures, strongly suggest that the icosahedral Ti-Zr-Ni quasicrystal is a ground state quasicrystal. [1] K. F. Kelton, W. J. Kim, and R. M. Stroud. Appl. Phys. Let. 70, 3230 (1997). [2] G. Kresse and J. Hafner, Phys. Rev. B47, RC 558 (1993); G. Kresse and J. Furthmüller, Phys. Rev. B54, 11169 (1996).
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2003-12-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Neutrinos and flavor symmetries
NASA Astrophysics Data System (ADS)
Tanimoto, Morimitsu
2015-07-01
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
NASA Astrophysics Data System (ADS)
Nakayama, Kei; Watanabe, Junya; Koyama, Yasumasa
2016-08-01
To understand the crystallographic relation between the Bergman-type icosahedral quasicrystal and its approximant-T structure, we have investigated the crystallographic features of prepared Zn-Mg-Al alloy samples, mainly by transmission electron microscopy. It was found that there existed three kinds of regions: that is, C14-Laves, approximant-T, and icosahedral-quasicrystal regions, in Zn-Mg-Al alloy samples with the composition of Zn-36at.%Mg-9at.%Al. Among these regions, in particular, we tried to determine an orientation relationship between neighboring icosahedral-quasicrystal and approximant-T regions. Based on the determined relationship, for instance, four threefold rotatory-inversion axes in the T structure were found to be parallel to four of ten threefold rotatory-inversion axes in the icosahedral quasicrystal. It was thus understood that the atomic arrangements of the Bergman-type icosahedral quasicrystal and its approximant-T structure are likely to resemble each other.
Icosahedral boron clusters: a perfect tool for the enhancement of polymer features.
Núñez, R; Romero, I; Teixidor, F; Viñas, C
2016-10-01
Boron clusters and organic molecules display manifestly different electronic, physical, chemical and geometrical characteristics. These differences highlight the complementarity of organic synthons and boron clusters, and therefore the feasibility of producing hybrid polymers incorporating both types of fragments. This review focuses on the development of hybrid organic-inorganic π conjugated, silane, siloxane and coordination polymers containing icosahedral boron clusters in the last few decades, which have received considerable academic and technological interest due to the combination of the electronic, optical and thermal properties of traditional inorganic materials with many of the desirable properties of organic plastics, including mechanical flexibility and low production costs.
Soft-x-ray, heat-capacity, and transport measurements on icosahedral and crystalline alloys
NASA Astrophysics Data System (ADS)
Bruhwiler, P. A.; Wagner, J. L.; Biggs, B. D.; Shen, Y.; Wong, K. M.; Schnatterly, S. E.; Poon, S. J.
1988-04-01
Soft-x-ray emission, heat-capacity, and resistivity measurements are reported for icosahedral and Frank-Kasper phases of Al-Cu-Li and Al-Cu-Mg. This is the first extensive comparison of electronic properties of periodic and quasiperiodic lattices generated by packing similar structural units. Results are compared with theories of quasicrystals and provide a guideline for the observability of Van Hove singularities in quasicrystals. The density of states N(0) is a factor of 3 less in Al-Cu-Li than in Al-Cu-Mg alloys; this is spectroscopically confirmed.
High Pressure X-ray Diffraction Study on Icosahedral Boron Arsenide (B12As2)
J Wu; H Zhu; D Hou; C Ji; C Whiteley; J Edgar; Y Ma
2011-12-31
The high pressure properties of icosahedral boron arsenide (B12As2) were studied by in situ X-ray diffraction measurements at pressures up to 25.5 GPa at room temperature. B12As2 retains its rhombohedral structure; no phase transition was observed in the pressure range. The bulk modulus was determined to be 216 GPa with the pressure derivative 2.2. Anisotropy was observed in the compressibility of B12As2-c-axis was 16.2% more compressible than a-axis. The boron icosahedron plays a dominant role in the compressibility of boron-rich compounds.
Neutron-diffraction approach to the atomic decoration of the Al-Mn icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Janot, Chr.; Pannetier, J.; Dubois, J. M.; de Boissieu, M.
1989-01-01
Neutron-diffraction data were obtained from single-phase icosahedral powder of the system Al74Si5Mn21 and its modification by isomorphous substitution on the Mn sites. Amplitudes and phase differences of partial structure factors were determined. Within a strip-projection approach, phases were reconstructed. Atomic densities calculated in the physical three-dimensional space show that Mackay (1981) icosahedra, the structural units usually invoked for quasi-crystal models, do not emerge as the basic ingredients of the atomic arrangements.
Stability comparison of several icosahedral structure units of Al-Cr alloys
NASA Astrophysics Data System (ADS)
Liu, Da; Wang, Renhui; Ye, Yiying
1991-02-01
Total energies for three types of icosahedral structure units of Al-Cr alloys have been calculated based on the embedded-atom method. The results show that the most stable structure unit is the small icosahedron with a Cr atom at its center, and the hypothetical structures based on the Mackay icosahedron and Bergman rhombic triacontahedron possess higher energies compared with those of the face-centered-cubic-solid solutions and the mechanical mixtures of pure Al and Cr crystals. These results are found to be consistent with experiment.
2014-01-01
Background Low-power ultrashort pulsed (USP) lasers operating at wavelengths of 425 nm and near infrared region have been shown to effectively inactivate viruses such as human immunodeficiency virus (HIV), M13 bacteriophage, and murine cytomegalovirus (MCMV). It was shown previously that non-enveloped, helical viruses such as M13 bacteriophage, were inactivated by a USP laser through an impulsive stimulated Raman scattering (ISRS) process. Recently, enveloped virus like MCMV has been shown to be inactivated by a USP laser via protein aggregation induced by an ISRS process. However, the inactivation mechanism for a clinically important class of viruses – non-enveloped, icosahedral viruses remains unknown. Results and discussions We have ruled out the following four possible inactivation mechanisms for non-enveloped, icosahedral viruses, namely, (1) inactivation due to ultraviolet C (UVC) photons produced by non-linear optical process of the intense, fundamental laser beam at 425 nm; (2) inactivation caused by thermal heating generated by the direct laser absorption/heating of the virion; (3) inactivation resulting from a one-photon absorption process via chromophores such as porphyrin molecules, or indicator dyes, potentially producing reactive oxygen or other species; (4) inactivation by the USP lasers in which the extremely intense laser pulse produces shock wave-like vibrations upon impact with the viral particle. We present data which support that the inactivation mechanism for non-enveloped, icosahedral viruses is the impulsive stimulated Raman scattering process. Real-time PCR experiments show that, within the amplicon size of 273 bp tested, there is no damage on the genome of MNV-1 caused by the USP laser irradiation. Conclusion We conclude that our model non-enveloped virus, MNV-1, is inactivated by the ISRS process. These studies provide fundamental knowledge on photon-virus interactions on femtosecond time scales. From the analysis of the transmission
Dynamical x-ray diffraction from an icosahedral Al-Pd-Mn quasicrystal
Kycia, S.
1996-04-23
Primary extinction effects in diffraction from single grains of Al-Pd- Mn, and presumably many other FCI alloys, may be significant and should be corrected for prior to use of diffraction data in structural determinations. Probes based on dynamical diffraction effects, such as x-ray standing wave fluorescence, multiple beam interference, and x-ray transmission topographs, may now be used to study the bulk and surface structure of some quasicrystals. The observation of dynamical diffraction from icosahedral Al-Pd-Mn is a striking confirmation of the fact that quasicrystals can present a degree of structural perfection comparable to that found in the best periodic intermetallic crystals.
STM study of the atomic structure of the icosahedral Al-Cu-Fe fivefold surface
NASA Astrophysics Data System (ADS)
Cai, T.; Fournée, V.; Lograsso, T.; Ross, A.; Thiel, P. A.
2002-04-01
We use scanning tunneling microscopy (STM) to investigate the atomic structure of the icosahedral (i-) Al-Cu-Fe fivefold surface in ultra high vacuum (UHV). Studies show that large, atomically flat terraces feature many ten-petal ``flowers'' with internal structure. The observed flower patterns can be associated with features on Al rich dense atomic planes generated from two-dimensional cuts of bulk models based on x-ray and neutron diffraction experiments. The results confirm that the fivefold surface of i-Al-Cu-Fe corresponds to a bulk-terminated plane.
NASA Astrophysics Data System (ADS)
Zijlstra, E. S.; Kortus, J.; Krajčí, M.; Stadnik, Z. M.; Bose, S. K.
2004-03-01
We present a detailed analysis of electronic properties of the Cockayne model of icosahedral AlCuFe, both in its original form and after a structural relaxation using the ab initio density functional approach. The electronic density of states (DOS) and electric field gradients (EFG’s) of the Al and Fe atoms in the original and the relaxed Cockayne models were calculated and compared with available photoemission, Mössbauer, and nuclear quadrupole resonance spectroscopy data. The relaxed and the original models show significantly different electronic properties. Both models are deficient in describing the available experimental data. The DOS’s show two Fe-d peaks, where there is only one such peak in the photoemission spectroscopy data. These models also cannot account for the shape of the Mössbauer spectra. We show that the interchange between 12 Cu and 12 Fe atoms, each belonging to a single symmetry class, results in a smaller number of Cu-Fe nearest-neighbor pairs and a lowering of the total energy by an amount of ΔE˜50 meV/atom. This “modified” version of the Cockayne model was further relaxed for the final comparison between the calculation and experimental results. The modified model shows a considerable improvement: The DOS has only one Fe-d peak, in agreement with photoemission spectroscopy data, and the calculated EFG’s account very well for the experimental Mössbauer spectra.
NASA Technical Reports Server (NTRS)
Bleck, Rainer; Bao, Jian-Wen; Benjamin, Stanley G.; Brown, John M.; Fiorino, Michael; Henderson, Thomas B.; Lee, Jin-Luen; MacDonald, Alexander E.; Madden, Paul; Middlecoff, Jacques; Rosinski, James; Smirnova, Tanya G.; Sun, Shan; Wang, Ning
2015-01-01
A hydrostatic global weather prediction model based on an icosahedral horizontal grid and a hybrid terrain following/ isentropic vertical coordinate is described. The model is an extension to three spatial dimensions of a previously developed, icosahedral, shallow-water model featuring user-selectable horizontal resolution and employing indirect addressing techniques. The vertical grid is adaptive to maximize the portion of the atmosphere mapped into the isentropic coordinate subdomain. The model, best described as a stacked shallow-water model, is being tested extensively on real-time medium-range forecasts to ready it for possible inclusion in operational multimodel ensembles for medium-range to seasonal prediction.
Yamamoto, Akiji
2004-11-01
A section method for projected structures of icosahedral quasicrystals (IQCs) is given. A structure projected along a specified direction can be calculated directly from a six-dimensional periodic structure by this method. The method concludes that all peaks in high-resolution transmission electron-microscopy images of an IQC have different projected atom densities in general and leads to different chemical compositions and densities for all atom layers, suggesting that all surfaces of an IQC are different. Its application to icosahedral Al-Pd-Mn quasicrystals is shown.
Shen, Y.T.; Kim, T.H.; Gangopadhyay, A.K.; Kelton, K.F.
2009-06-05
One explanation for the glass transition is a geometrical frustration owing to the development of non-space-filling short-range order (icosahedral, tetrahedral). However, experimental demonstrations of this are lacking. Here, the first quantitative measurements of the time-dependent nucleation rate in a Zr59Ti3Cu20Ni8Al10 bulk metallic glass are combined with the first measurements of the evolution of the supercooled liquid structure to near the glass transition temperature to provide strong support for an icosahedral-order-based frustration model for the glass transition in Zr-based glasses.
Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
NASA Astrophysics Data System (ADS)
Gao, Zihao; Hua, Meng; Zhang, Haijun; Zhang, Xiao
2016-05-01
Three-dimensional (3D) Dirac and Weyl semimetals are novel states of quantum matter. We classify stable 3D Dirac and Weyl semimetals with reflection and rotational symmetry in the presence of time reversal symmetry and spin-orbit coupling, which belong to seventeen different point groups. They have two classes of reflection symmetry, with the mirror plane parallel and perpendicular to rotation axis. In both cases two types of Dirac points, existing through accidental band crossing (ABC) or at a time reversal invariant momentum (TBC), are determined by four different reflection symmetries. We classify those two types of Dirac points with a combination of different reflection and rotational symmetries. We further classify Dirac and Weyl line nodes to show in which types of mirror plane they can exist. Finally we discuss that Weyl line nodes and Dirac points can exist at the same time taking C4 v symmetry as an example.
Hierarchy of bond stiffnesses within icosahedral-based gold clusters protected by thiolates
Yamazoe, Seiji; Takano, Shinjiro; Kurashige, Wataru; Yokoyama, Toshihiko; Nitta, Kiyofumi; Negishi, Yuichi; Tsukuda, Tatsuya
2016-01-01
Unique thermal properties of metal clusters are believed to originate from the hierarchy of the bonding. However, an atomic-level understanding of how the bond stiffnesses are affected by the atomic packing of a metal cluster and the interfacial structure with the surrounding environment has not been attained to date. Here we elucidate the hierarchy in the bond stiffness in thiolate-protected, icosahedral-based gold clusters Au25(SC2H4Ph)18, Au38(SC2H4Ph)24 and Au144(SC2H4Ph)60 by analysing Au L3-edge extended X-ray absorption fine structure data. The Au–Au bonds have different stiffnesses depending on their lengths. The long Au–Au bonds, which are more flexible than those in the bulk metal, are located at the icosahedral-based gold core surface. The short Au–Au bonds, which are stiffer than those in the bulk metal, are mainly distributed along the radial direction and form a cyclic structural backbone with the rigid Au–SR oligomers. PMID:26778685
NASA Astrophysics Data System (ADS)
Majzoub, Eric Hish
Equilibrium phase formation is reported for ternary Ti-Zr-Ni alloys near the icosahedral phase (i-phase) forming composition. The i-phase forms over a small compositional range from a high-temperature equilibrium phase mixture of the Laves and alpha(Ti/Zr) solid solution phases. Additions of small amounts of Pb, 1--2 at. %, are demonstrated to substantially effect the equilibrium phase formation and extend the stability of the i-phase to nearly 700°C. An electrochemical method was used to hydrogenate Ti-based quasicrystals and their crystal approximants. This technique gives a consistently high hydrogen to metal atom ratio of 1.9, without crystal hydride formation in the quasicrystal. Nuclear Magnetic Resonance (NMR) measurements of the hydrogen dipole-dipole interaction were made using hydrided i-phase samples. Comparisons with simulations based on hydrogen filling of the approximant-phase tetrahedral interstitials reveals that any filling order is consistent with the experimental data. Studies of the atomic structure of hydrided and unhydrided i-TiZrNi quasicrystal and its approximant are reported. We construct constrained icosahedral glass models using Bergman and Mackay clusters to describe the i-phase in Ti-Zr-Ni and Ti-TM-Si-O. A comparison of simulated and experimental diffraction reveals that, the Bergman and Mackay clusters are the fundamental clusters in i-TiZrNi and i-TiMnSiO, respectively.
NASA Astrophysics Data System (ADS)
Bleck, Rainer; Sun, Shan; Li, Haiqin; Benjamin, Stan
2016-04-01
Current efforts to close the gap between weather prediction and climate models have led to the construction of a coupled ocean-atmosphere system consisting of two high-resolution component models, operating on matching icosahedral grids and utilizing adaptive, near-isentropic/isopycnic vertical coordinates. The two components models, FIM and HYCOM (the latter converted to an icosahedral mesh for this purpose), have been tested extensively in twice-daily global medium-range weather prediction (http://fim.noaa.gov) and in real-time ocean data assimilation (http://hycom.org), respectively. The use of matching horizontal grids, currently at resolutions of 15km, 30km and 60km, avoids coastline ambiguities and interpolation errors at the air-sea interface. The intended purpose of the coupled model being subseasonal-to-seasonal prediction, our focus is on mid-term precipitation biases and the statistical steadiness of the atmospheric circulation (blocking frequency, Rossby wave breaking, meridional heat transport, etc.), as well as on possible causes of ocean model drift. An attempt is made to isolate the weather model's role in modifying water mass properties and ocean circulations (including meridional overturning) by comparing coupled model results to ocean-only experiments forced by observed atmospheric boundary conditions. A multi-decadal run at 60km resolution is used to illustrate ENSO variability in the coupled system.
The Marine Algal Virus PpV01 Has an Icosahedral Capsid with T=219 Quasisymmetry
Yan, Xiaodong; Chipman, Paul R.; Castberg, Tonje; Bratbak, Gunnar; Baker, Timothy S.
2005-01-01
Phaeocystis pouchetii virus (PpV01) infects and lyses the haptophyte Phaeocystis pouchetii (Hariot) Lagerheim and was first isolated from Norwegian coastal waters. We have used electron cryomicroscopy and three-dimensional image reconstruction methods to examine the native morphology of PpV01 at a resolution of 3 nm. The icosahedral capsid of PpV01 has a maximum diameter of 220 nm and is composed of 2,192 capsomers arranged with T=219 quasisymmetry. One specific capsomer in each asymmetric unit contains a fiber-like protrusion. Density attributed to the presence of a lipid membrane appears just below (inside) the capsid. PpV01 is the largest icosahedral virus whose capsid structure has been determined in three dimensions from images of vitrified samples. Striking similarities in the structures of PpV01 and a number of other large double-stranded DNA viruses are consistent with a growing body of evidence that they share a common evolutionary origin. PMID:15994818
Baryogenesis from symmetry principle
NASA Astrophysics Data System (ADS)
Fong, Chee Sheng
2016-01-01
In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario and also to identify the different roles played by the symmetry. This formalism is then applied to the standard model and its supersymmetric extension, which constitute two important foundations for constructing models of baryogenesis.
NASA Astrophysics Data System (ADS)
Ilyushin, G. D.; Blatov, V. A.
2009-07-01
The mechanism of self-assembly of symmetrically and topologically different chains and microlayers (in the form of planar nets) from cyclic three-node clusters A 3 is considered in the model system. The obtained nets correspond to the uninodal Shubnikov nets N 3 12 12 and N 3 6 3 6 and the new binodal net N1 3 6 3 6 + N2 3 3 6 6 (1: 2). A complete three-dimensional reconstruction of the self-assembly of the icosahedral structure of the ZrZn22 compound ( cF184) is performed using computer methods (with the TOPOS program package) according to the following scheme: cluster precursor → primary chain → microlayer → microframework (supraprecursor) → ... → framework. It is revealed that the suprapolyhedral cluster precursor (nanocluster ˜12 Å in size) of the AB 2 composition is formed by three polyhedra shared by vertices in a cyclic manner: the A-ZrZn16 polyhedron (sixteen-vertex polyhedron with the point symmetry bar 4 3 m) and two B-ZrZn12 polyhedra (icosahedra with the point symmetry bar 3 m). The AB 2 cluster precursor in the structure retains the symmetry m. It is established that the structural mechanism of self-assembly of the two-dimensional layer in the ZrZn22 structure is described by the binodal net N1 3 6 3 6 + N2 3 3 6 6 (1: 2) constructed in the modeling.
Symmetry in Mathematics Learning.
ERIC Educational Resources Information Center
Dreyfus, Tommy; Eisenberg, Theodore
1989-01-01
Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)
ERIC Educational Resources Information Center
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
NASA Astrophysics Data System (ADS)
Kirihara, K.; Nagata, T.; Kimura, K.; Kato, K.; Takata, M.; Nishibori, E.; Sakata, M.
2003-07-01
X-ray charge densities of Al-based icosahedral quasicrystalline approximant crystals α-AlReSi, α-AlMnSi, and Al12Re were observed by a combination of the maximum entropy method with the Rietveld method. We successfully obtained the clear images of interatomic covalent bonds between Al and transition metals (Mn, Re) and those in the Al (or Si) icosahedron in Mackay icosahedral clusters of both α-AlReSi and α-AlMnSi approximant crystals. The bonding nature of the three kinds of glue atom sites connecting Mackay icosahedral clusters was also clarified. This covalent bonding nature should strongly relate with the enhancement of the electron density-of-states pseudogap near the Fermi level. In addition, the interatomic covalent bonds of α-AlReSi are stronger than those of α-AlMnSi. This fact leads to the low effective carrier density of α-AlReSi in comparison with that of α-AlMnSi. Unlike the covalent bonding nature of an icosahedron in α-AlReSi and α-AlMnSi crystals, the Al icosahedron with an Re center atom exhibits no Al-Al interatomic covalent bonds in the Al12Re crystal. The tendency for metallic-covalent bonding conversion in the Al icosahedron, which is related to the atom site occupancy of the icosahedral cluster center, is also strongly supported.
Symmetry Effects in Computation
NASA Astrophysics Data System (ADS)
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
Performance Analysis of high-order remap-type advection scheme on icosahedral-hexagonal grid
NASA Astrophysics Data System (ADS)
Mittal, Rashmi; Dubey, Sarvesh; Saxena, Vaibhav; Meurdesoif, Yann
2014-05-01
A comparative performance analysis on computational cost of second order advection schemes FF-CSLAM (Flux form conservative semi-Lagrangian multi-tracer transport scheme) and it's two simplifications on Icosahedral grid has been presented. Tracer transport is one of the main building blocks in atmospheric models and hence their performance greatly determines the overall performance of the model. FF-CSLAM falls in the category of arbitrary Lagrangian Eulerian (ALE) scheme. It exploits the finite volume formulation and therefore it is inherently conservative. Flux-area through edges are approximated with great circle arcs in an upwind fashion. Bi-quadratic sub-grid scale reconstructions using weighted least-squares method is employed to approximate trace field. Area integrals on the overlapped region of flux-area and static Eulerian meshes are evaluated via line-integrals. A brief description of implementation of FF-CSLAM on icosahedral -hexagonal meshes along with and its numerical accuracy in terms of standard test cases will be presented. A comparative analysis of the computational overhead is necessary to assess the suitability of FF-CSLAM for massively parallel and multi-threading computer architectures in comparison to other advection schemes implemented on icosahedral grids. The main focus of this work is to present the implementation of the shared memory parallelization and to describe the memory access pattern of the numerical scheme. FF-CSLAM is a remap-type advection scheme, thus extra calculation are done in comparison to the other advection schemes. The additional computations are associated with the search required to find the overlap area between the area swept through the edge and the underlining grid. But the experiments shows that the associated computational overhead is minimal for multi-tracer transport. It will be shown that for the Courant Number less than one, FF-CSLAM, the computations are not expensive. Since the grid cells are arranged in
The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, J. L.; MacDonald, A. E.
2014-12-01
A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP
NASA Astrophysics Data System (ADS)
Lee, Geun Woo
While lacking the long-range translationally periodic order of crystalline solids, liquids contain a significant amount of short-range order (SRO), which distinguishes them from gases. The local structure of a liquid is important to understand its chemical and physical properties. One of the remarkable phenomena related to the short-range order of liquids is undercooling. That is, liquids can be retained below their melting temperature for a long time without crystallization. Turnbull first demonstrated this for metallic liquids in 1952. To explain the surprising results, Frank hypothesized in 1952 that the local structure of liquid metals is icosahedral. This structure is quite different from those of crystal phases giving a large nucleation barrier and making the undercooling of liquids possible. However, a complete verification of Frank's hypothesis has not been possible thus far. In this dissertation, this goal has been achieved by demonstrating a direct connection between the nucleation barrier and the icosahedral SRO (ISRO) in Ti-Zr-Ni alloy liquids. Containerless environments and in-situ x-ray scattering experiments, essential for such studies, were possible because of the development of electrostatic levitation (ESL) and Beamline-ESL techniques. In addition, distorted icosahedral SRO in liquids will be shown, which has been expected but never observed. The other important topic related to the undercooled liquids is a liquid-liquid (L-L) transition. Since the undercooled liquids are essentially metastable, the L-L transition could be expected. However, L-L transitions in undercooled liquids have not been observed experimentally, although elemental liquids of P, C, and Si have shown first order transitions above the liquidus temperatures under high pressure. From specific heat measurements of a series of Ti-Zr-Ni alloys by the ESL technique, a maximum in the specific heat at constant pressure was observed in a few quasicrystal forming alloy compositions in
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-02-13
It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures-and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body-bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body-bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains.
Multiporous carbon allotropes transformed from symmetry-matched carbon nanotubes
NASA Astrophysics Data System (ADS)
Cai, Yingxiang; Wang, Hao; Xu, Shengliang; Hu, Yujie; Liu, Ning; Xu, Xuechun
2016-06-01
Carbon nanotubes (CNTs) with homogeneous diameters have been proven to transform into new carbon allotropes under pressure but no studies on the compression of inhomogeneous CNTs have been reported. In this study, we propose to build new carbon allotropes from the bottom-up by applying pressure on symmetry-matched inhomogeneous CNTs. We find that the (3,0) CNT with point group C3v and the (6,0) CNT with point group C6v form an all sp3 hybridized hexagonal 3060-Carbon crystal, but the (4,0) CNT with point group D4h and the (8,0) CNT with point group D8h polymerize into a sp2+sp3 hybridized tetragonal 4080-Carbon structure. Their thermodynamic, mechanical and dynamic stabilities show that they are potential carbon allotropes to be experimentally synthesized. The multiporous structures, excellently mechanical properties and special electronic structures (semiconductive 3060-Carbon and semimetallic 4080-Carbon) imply their many potential applications, such as gases purification, hydrogen storage and lightweight semiconductor devices. In addition, we simulate their feature XRD patterns which are helpful for identifying the two carbon crystals in future experimental studies.
Geometrical symmetries in atomic nuclei: From theory predictions to experimental verifications
NASA Astrophysics Data System (ADS)
Dudek, J.; Góźdź, A.; Molique, H.; Curien, D.
2013-02-01
In the lectures delivered at the 2012 Predeal School an overview has been presented of the contemporary theory of the nuclear geometrical (shape) symmetries. The formalism combines two most powerful theory tools applicable in the context: The group- and group-representation theory together with the modern realistic mean-field theory. We suggest that all point-groups of symmetry of the mean-field Hamiltonian, sufficiently rich in symmetry elements (as discussed in the text) may lead to the magic numbers that characterise such a group in analogy with the spherical magic gaps characterising nuclear sphericity. We discuss in simple terms the mathematical and physical arguments for the presence of such symmetries in nuclei. In our opinion: It is not so much the question of Whether? - but rather: Where in the Nuclear Chart several of the point group-symmetries will be seen? We focus our presentation on the tetrahedral symmetry with the magic numbers calculated to be 32, 40, 56, 64, 70, 90 and 136, and discuss qualitatively the problem of the formulation of the experimental criteria which would allow for the final discovery of the tetrahedral symmetry in subatomic physics.
Thermal Conductivity and Seebeck Coefficients of Icosahedral Boron Arsenide Films on Silicon Carbide
Y Gong; Y Zhang; M Dudley; Y Zhang; J Edgar; P Heard; M Kuball
2011-12-31
The thermal conductivity of icosahedral boron arsenide (B{sub 12}As{sub 2}) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3{omega} technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 {micro}V/K and 136 {micro}V/K for samples grown at 1350 C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Terrace-dependent nucleation of small Ag clusters on a five-fold icosahedral quasicrystal surface
Unal, B.; Evans, J.W.; Lograsso, T.A.; Ross, A.R.; Jenks, C.J.; Thiel, P.A.
2007-07-21
Nucleation of Ag islands on the five-fold surface of icosahedral Al-Pd-Mn is influenced strongly by trap sites. Submonolayers of Ag prepared by deposition at 365 K and with a flux of 1 x 10{sup -3} monolayers/s exhibit a variation in Ag island densities across different terraces. Comparisons with previous work and with rate equation analysis indicate that trap sites are not saturated under these experimental conditions and that the difference in island densities is not necessarily due to variation in trap densities. While it could have a number of different origins, our results point to a terrace-dependent value of the effective diffusion barrier for Ag adatoms.
Reinterpretation of the zero-temperature conductivity in icosahedral AlPdRe
NASA Astrophysics Data System (ADS)
Rapp, Ö.
2016-07-01
The zero-temperature conductivity σ (0 ) of icosahedral (i )-AlPdRe has been found to be simply related to the resistance ratio R =ρ4.2 K/ρ295 K by a power law, σ (0 ) ˜R-1.74 , over four orders of magnitude in σ (0 ) . This relation includes metallic single grain samples, and polygrain samples of different morphologies which are metallic for small R values, and insulatinglike at large R . Electronic transport properties of single grain i -AlPdRe samples are thus found to be on common ground with polygrain i -AlPdRe. The relation between R and σ (0 ) can be qualitatively understood from published band-structure calculations on quasicrystalline approximants.
Defining criteria for oligomannose immunogens for HIV using icosahedral virus capsid scaffolds.
Astronomo, Rena D; Kaltgrad, Eiton; Udit, Andrew K; Wang, Sheng-Kai; Doores, Katie J; Huang, Cheng-Yuan; Pantophlet, Ralph; Paulson, James C; Wong, Chi-Huey; Finn, M G; Burton, Dennis R
2010-04-23
The broadly neutralizing antibody 2G12 recognizes a conserved cluster of high-mannose glycans on the surface envelope spike of HIV, suggesting that the "glycan shield" defense of the virus can be breached and may, under the right circumstances, serve as a vaccine target. In an attempt to recreate features of the glycan shield semisynthetically, oligomannosides were coupled to surface lysines on the icosahedral capsids of bacteriophage Q beta and cowpea mosaic virus (CPMV). The Q beta glycoconjugates, but not CPMV, presented oligomannose clusters that bind the antibody 2G12 with high affinity. However, antibodies against these 2G12 epitopes were not detected in immunized rabbits. Rather, alternative oligomannose epitopes on the conjugates were immunodominant and elicited high titers of anti-mannose antibodies that do not crossreact with the HIV envelope. The results presented reveal important design considerations for a carbohydrate-based vaccine component for HIV. PMID:20416507
Defining criteria for oligomannose immunogens for HIV using icosahedral virus capsid scaffolds.
Astronomo, Rena D; Kaltgrad, Eiton; Udit, Andrew K; Wang, Sheng-Kai; Doores, Katie J; Huang, Cheng-Yuan; Pantophlet, Ralph; Paulson, James C; Wong, Chi-Huey; Finn, M G; Burton, Dennis R
2010-04-23
The broadly neutralizing antibody 2G12 recognizes a conserved cluster of high-mannose glycans on the surface envelope spike of HIV, suggesting that the "glycan shield" defense of the virus can be breached and may, under the right circumstances, serve as a vaccine target. In an attempt to recreate features of the glycan shield semisynthetically, oligomannosides were coupled to surface lysines on the icosahedral capsids of bacteriophage Q beta and cowpea mosaic virus (CPMV). The Q beta glycoconjugates, but not CPMV, presented oligomannose clusters that bind the antibody 2G12 with high affinity. However, antibodies against these 2G12 epitopes were not detected in immunized rabbits. Rather, alternative oligomannose epitopes on the conjugates were immunodominant and elicited high titers of anti-mannose antibodies that do not crossreact with the HIV envelope. The results presented reveal important design considerations for a carbohydrate-based vaccine component for HIV.
Yan, Xiaodong; Cardone, Giovanni; Zhang, Xing; Zhou, Z Hong; Baker, Timothy S
2014-04-01
In cryo-electron microscopy and single particle analysis, data acquisition and image processing are generally carried out in sequential steps and computation of a three-dimensional reconstruction only begins once all the micrographs have been acquired. We are developing an integrated system for processing images of icosahedral particles during microscopy to provide reconstructed density maps in real-time at the highest possible resolution. The system is designed as a combination of pipelines to run in parallel on a computer cluster and analyzes micrographs as they are acquired, handling automatically all the processing steps from defocus estimation and particle picking to origin/orientation determination. An ab initio model is determined independently from the first micrographs collected, and new models are generated as more particles become available. As a proof of concept, we simulated data acquisition sessions using three sets of micrographs of good to excellent quality that were previously recorded from different icosahedral viruses. Results show that the processing of single micrographs can keep pace with an acquisition rate of about two images per minute. The reconstructed density map improves steadily during the image acquisition phase and its quality at the end of data collection is only moderately inferior to that obtained by expert users who processed semi-automatically all the micrographs after the acquisition. The current prototype demonstrates the advantages of integrating three-dimensional image processing with microscopy, which include an ability to monitor acquisition in terms of the final structure and to predict how much data and microscope resources are needed to achieve a desired resolution.
Zhang, Xing; Zhou, Z. Hong; Baker, Timothy S.
2014-01-01
In cryo-electron microscopy and single particle analysis, data acquisition and image processing are generally carried out in sequential steps and computation of a three-dimensional reconstruction only begins once all the micrographs have been acquired. We are developing an integrated system for processing images of icosahedral particles during microscopy to provide reconstructed density maps in real-time at the highest possible resolution. The system is designed as a combination of pipelines to run in parallel on a computer cluster and analyzes micrographs as they are acquired, handling automatically all the processing steps from defocus estimation and particle picking to origin/orientation determination. An ab-initio model is determined independently from the first micrographs collected, and new models are generated as more particles become available. As a proof of concept, we simulated data acquisition sessions using three sets of micrographs of good to excellent quality that were previously recorded from different icosahedral viruses. Results show that the processing of single micrographs can keep pace with an acquisition rate of about two images per minute. The reconstructed density map improves steadily during the image acquisition phase and its quality at the end of data collection is only moderately inferior to that obtained by expert users who processed semi-automatically all the micrographs after the acquisition. The current prototype demonstrates the advantages of integrating three-dimensional image processing with microscopy, which include an ability to monitor acquisition in terms of the final structure and to predict how much data and microscope resources are needed to achieve a desired resolution. PMID:24613762
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-01-01
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine–thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine–cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-03-18
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine-thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine-cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
A universal symmetry detection algorithm.
Maurer, Peter M
2015-01-01
Research on symmetry detection focuses on identifying and detecting new types of symmetry. The paper presents an algorithm that is capable of detecting any type of permutation-based symmetry, including many types for which there are no existing algorithms. General symmetry detection is library-based, but symmetries that can be parameterized, (i.e. total, partial, rotational, and dihedral symmetry), can be detected without using libraries. In many cases it is faster than existing techniques. Furthermore, it is simpler than most existing techniques, and can easily be incorporated into existing software. The algorithm can also be used with virtually any type of matrix-based symmetry, including conjugate symmetry.
Pseudo-fivefold diffraction symmetries in tetrahedral packing.
Lee, Stephen; Henderson, Ryan; Kaminsky, Corey; Nelson, Zachary; Nguyen, Jeffers; Settje, Nick F; Schmidt, Joshua Teal; Feng, Ji
2013-07-29
We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo-fivefold rotational diffraction symmetry. A unified geometric model involving the 600-cell is presented: the model accounts for the observed pseudo-fivefold symmetries among the different Bravais lattice types. The model accounts for vertex-, edge-, polygon-, and cell-centered fused-icosahedral clusters. Vertex-centered and edge-centered types correspond to the well-known pseudo-fivefold symmetries in Ih and D5h quasicrystalline approximants. The concept of a tetrahedrally-packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused-icosahedrally-packed crystals. This reciprocal-space cluster is a direct result of the pseudosymmetry and, just as the real-space clusters, can be rationalized by the 600-cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally-packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry-based Jones model are shown to accord with the observed electron counts for a variety of Group 10-12 tetrahedrally-packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu2, Cd3Cu4, Cu5Cd8, and Cu3Cd10. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn11Au15Cd23, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10-12 elements is presented. This compound crystallizes in Im3 (space group no. 204) with a = 13.842(2) Å. The structure was solved with R1 = 3.53 %, I > 2σ; = 5.33 %, all data with 1282/0/38 data/restraints/parameters.
NASA Astrophysics Data System (ADS)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
Sekhar Chivukula
2016-07-12
The symmetries of a quantum field theory can be realized in a variety of ways. Symmetries can be realized explicitly, approximately, through spontaneous symmetry breaking or, via an anomaly, quantum effects can dynamically eliminate a symmetry of the theory that was presentÂ at the classical level. Â Quantum Chromodynamics (QCD),Â the modern theoryÂ of the strong interactions, exemplify each ofÂ these possibilities.Â The interplayÂ of these effects determine theÂ spectrum of particles that we observeÂ and, ultimately, account forÂ 99% of the mass of ordinary matter.Â
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
NASA Astrophysics Data System (ADS)
Castaños, Octavio
2010-09-01
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
NASA Technical Reports Server (NTRS)
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.
NASA Astrophysics Data System (ADS)
Miceli, P. F.; Youngquist, S. E.; Neumann, D. A.; Zabel, H.; Rush, J. J.; Rowe, J. M.
1986-12-01
We present an inelastic neutron scattering study of the vibrational density of states, g¯(E), for the icosahedral and crystalline phases of Al0.80Mn0.20. At low energy transfers we find nearly identical g¯(E)~E2 dependences indicating that the two materials are elastically similar. In the intermediate energy range, 20-35 meV, the crystalline g¯(E) shows weak structure while that of the icosahedral phase remains smooth. Above 40 meV there is an excess of the icosahedral g¯(E) compared to that of the crystalline material. These results provide a direct test for models of the interatomic forces and dynamics of the icosahedral phase.
Pauling, L. )
1988-07-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, noise) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals.
Structural determination of a 1/1 rational approximant to the icosahedral phase in Ti-Cr-Si alloys
NASA Astrophysics Data System (ADS)
Libbert, J. L.; Kelton, K. F.; Goldman, A. I.; Yelon, W. B.
1994-05-01
We report the discovery and structural refinement of a large unit cell bcc crystalline phase in a Ti-Cr-Si alloy that is a 1/1 rational approximant to the icosahedral phase in that system. The crystal structure was determined from a Rietveld analysis of x-ray and neutron powder diffraction data. Our results demonstrate that this phase is closely related to the α(Al-Mn-Si) phase, which in turn, is closely related to the structure of the icosahedral phase in the Al-transition-metal alloys. The neutron data indicate that the structure contains a significant amount of oxygen located in the Mackay clusters. Partial ordering of this oxygen may provide an explanation for the localized diffuse scattering often observed in the i phase and related crystalline phases in Ti-transitional-metal alloys.
Chern, I-Liang
1994-08-01
Two versions of a control volume method on a symmetrized icosahedral grid are proposed for solving the shallow-water equations on a sphere. One version expresses of the equations in the 3-D Cartersian coordinate system, while the other expresses the equations in the northern/southern polar sterographic coordinate systems. The pole problem is avoided because of these expressions in both versions and the quasi-homogenity of the icosahedral grid. Truncation errors and convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence test for a steady zonal flow is demonstrated. Several simulations of Rossby-Haurwitz waves with various numbers are also performed.
Structural determination of a 1/1 rational approximant to the icosahedral phase in Ti-Cr-Si alloys
Libbert, J.L.; Kelton, K.F. ); Goldman, A.I. ); Yelon, W.B. )
1994-05-01
We report the discovery and structural refinement of a large unit cell bcc crystalline phase in a Ti-Cr-Si alloy that is a 1/1 rational approximant to the icosahedral phase in that system. The crystal structure was determined from a Rietveld analysis of x-ray and neutron powder diffraction data. Our results demonstrate that this phase is closely related to the [alpha](Al-Mn-Si) phase, which in turn, is closely related to the structure of the icosahedral phase in the Al-transition-metal alloys. The neutron data indicate that the structure contains a significant amount of oxygen located in the Mackay clusters. Partial ordering of this oxygen may provide an explanation for the localized diffuse scattering often observed in the [ital i] phase and related crystalline phases in Ti-transitional-metal alloys.
Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals
NASA Astrophysics Data System (ADS)
Hennig, R. G.; Carlsson, A. E.; Kelton, K. F.; Henley, C. L.
2005-04-01
The ab initio phase diagram determines the energetic stability of the icosahedral TiZrNi quasicrystal. The complete ab initio zero-temperature ternary phase diagram is constructed from the calculated energies of the elemental, binary and ternary Ti-Zr-Ni phases. For this, the icosahedral i -TiZrNi quasicrystal is approximated by periodic structures of up to 123 atoms/unit cell, based on a decorated-tiling model [R. G. Hennig, K. F. Kelton, A. E. Carlsson, and C. L. Henley, Phys. Rev. B 67, 134202 (2003)]. The approximant structures containing the 45-atom Bergman cluster are nearly degenerate in energy, and are all energetically stable against the competing phases. It is concluded that i -TiZrNi is a ground-state quasicrystal, as it is experimentally the low-temperature phase for its composition.
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang–Mills theory in four dimensions.
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang-Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross-Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang-Mills theory in four dimensions.
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment. PMID:11223922
Symmetry in context: salience of mirror symmetry in natural patterns.
Cohen, Elias H; Zaidi, Qasim
2013-05-31
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits.
Symmetry in context: Salience of mirror symmetry in natural patterns
Cohen, Elias H.; Zaidi, Qasim
2013-01-01
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773
Stagno, Vincenzo; Bindi, Luca; Shibazaki, Yuki; Tange, Yoshinori; Higo, Yuji; Mao, H-K; Steinhardt, Paul J; Fei, Yingwei
2014-01-01
The first natural-occurring quasicrystal, icosahedrite, was recently discovered in the Khatyrka meteorite, a new CV3 carbonaceous chondrite. Its finding raised fundamental questions regarding the effects of pressure and temperature on the kinetic and thermodynamic stability of the quasicrystal structure relative to possible isochemical crystalline or amorphous phases. Although several studies showed the stability at ambient temperature of synthetic icosahedral AlCuFe up to ~35 GPa, the simultaneous effect of temperature and pressure relevant for the formation of icosahedrite has been never investigated so far. Here we present in situ synchrotron X-ray diffraction experiments on synthetic icosahedral AlCuFe using multianvil device to explore possible temperature-induced phase transformations at pressures of 5 GPa and temperature up to 1773 K. Results show the structural stability of i-AlCuFe phase with a negligible effect of pressure on the volumetric thermal expansion properties. In addition, the structural analysis of the recovered sample excludes the transformation of AlCuFe quasicrystalline phase to possible approximant phases, which is in contrast with previous predictions at ambient pressure. Results from this study extend our knowledge on the stability of icosahedral AlCuFe at higher temperature and pressure than previously examined, and provide a new constraint on the stability of icosahedrite. PMID:25070248
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo E-mail: luca.santoni@sns.it E-mail: filippo.vernizzi@cea.fr
2015-09-01
Effective theories of a scalar φ invariant under the internal galileon symmetry φ→φ+b{sub μ} x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon's quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
BOOK REVIEW: Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ryder, L. H.
2005-11-01
One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would
Symmetry constraint for foreground extraction.
Fu, Huazhu; Cao, Xiaochun; Tu, Zhuowen; Lin, Dongdai
2014-05-01
Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties.
NASA Astrophysics Data System (ADS)
Dykeman, Eric C.; Sankey, Otto F.
2010-02-01
We describe a technique for calculating the low-frequency mechanical modes and frequencies of a large symmetric biological molecule where the eigenvectors of the Hessian matrix are determined with full atomic detail. The method, which follows order N methods used in electronic structure theory, determines the subset of lowest-frequency modes while using group theory to reduce the complexity of the problem. We apply the method to three icosahedral viruses of various T numbers and sizes; the human viruses polio and hepatitis B, and the cowpea chlorotic mottle virus, a plant virus. From the normal-mode eigenvectors, we use a bond polarizability model to predict a low-frequency Raman scattering profile for the viruses. The full atomic detail in the displacement patterns combined with an empirical potential-energy model allows a comparison of the fully atomic normal modes with elastic network models and normal-mode analysis with only dihedral degrees of freedom. We find that coarse-graining normal-mode analysis (particularly the elastic network model) can predict the displacement patterns for the first few (˜10) low-frequency modes that are global and cooperative.
Scanning tunneling microscopy of cleaved AlPdMn icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Urban, K.
1997-03-01
Quasicrystal surfaces produced by in-situ cleavage in ultra-high vacuum have been investigated by scanning tunneling microscopy. Twofold and fivefold surfaces of icosahedral AlPdMn single-quasicrystals have been studied. The surfaces were found to be rough. Their structure is determined by cluster aggregates of various sizes formed on the basis of an elementary cluster whose contrast behavior and diameter of about 1 nm point to the Mackay-type cluster [1]. The surface of these elementary clusters exhibits a smooth density of electronic states. These observations agree with the predictions of recent models on the quasicrystal structure and electronic properties in which the Mackay-type clusters play a dominant role [2]. In particular, these clusters are believed to act as deep potential wells leading to electron states primarily bound to these. Crack propagation during cleavage occurs along zones of lower strength between the clusters indicating that these act as rigid entities. This corroborates the assumption made in modern treatments of quasicrystal plasticity that the Mackay-type clusters control the mechanical properties [3,4]. [1] Ph. Ebert, M. Feuerbacher, N. Tamura, M. Wollgarten, and K. Urban, Phys. Rev. Lett. 77, 3827 (1996). [2] C. Janot, Phys. Rev. B 53, 181 (1996). [3] M. Feuerbacher, B. Baufeld, R. Rosenfeld, M. Bartsch, G. Hanke, M. Beyss, M. Wollgarten, and K. Urban, Philos. Mag. Lett. 71, 91 (1995). [4] F. Krul, R. Mikulla, P. Gumbsch, and H.-R. Trebin (to be published).
Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal.
Yamada, Tsunetomo; Takakura, Hiroyuki; Euchner, Holger; Pay Gómez, Cesar; Bosak, Alexei; Fertey, Pierre; de Boissieu, Marc
2016-07-01
The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = -0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye-Waller factor, which explains the vanishing of 'high-Q perp' reflections. PMID:27437112
Speculation of equilibrium pressure of Ti36Zr40Ni20Pd4 icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Huang, Huogen; Chen, Liang
2015-08-01
Ti-Zr-Ni quasicrystals have been demonstrated to store a large number of hydrogen atoms, which implies strong potential application in hydrogen energy field for them. However, the desorption of hydrogen atoms in the quasicrystals is quite difficult, with the indication of high desorption temperature and slow desorption rate. The shortage limits their use in the field to a large extent. But this kind of quasicrystals might be used in nuclear fusion energy field, because tritium as a coral fuel for nuclear fusion needs tight storage. However, equilibrium pressure at room temperature of Ti-Zr-Ni quasicrystals, important for their application in fusion energy field, has not been clear yet. In this work, we designed a gas-solid reaction system with the pressure resolution of 10-8Pa and carried out hydrogen desorption investigation at different temperatures on Ti36Zr40Ni20Pd4 icosahedral quasicrystal. Based on three Pressure-Composition-Temperature desorption curves, we speculate according to Van't Hoff theory about hydrogen storage that its equilibrium pressure at room temperature could be at the magnitude of 10-6Pa, displaying good stability of hydrogen in the quasicrystal and also implying application prospects in fusion energy field for quasicrystals of this type.
Atomic structure and phason modes of the Sc-Zn icosahedral quasicrystal.
Yamada, Tsunetomo; Takakura, Hiroyuki; Euchner, Holger; Pay Gómez, Cesar; Bosak, Alexei; Fertey, Pierre; de Boissieu, Marc
2016-07-01
The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = -0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye-Waller factor, which explains the vanishing of 'high-Q perp' reflections.
Atomic structure and phason modes of the Sc–Zn icosahedral quasicrystal
Yamada, Tsunetomo; Takakura, Hiroyuki; Euchner, Holger; Pay Gómez, Cesar; Bosak, Alexei; Fertey, Pierre; de Boissieu, Marc
2016-01-01
The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = −0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye–Waller factor, which explains the vanishing of ‘high-Q perp’ reflections. PMID:27437112
The icosahedral RNA virus as a grotto: organizing the genome into stalagmites and stalactites.
Harvey, Stephen C; Zeng, Yingying; Heitsch, Christine E
2013-03-01
There are two important problems in the assembly of small, icosahedral RNA viruses. First, how does the capsid protein select the viral RNA for packaging, when there are so many other candidate RNA molecules available? Second, what is the mechanism of assembly? With regard to the first question, there are a number of cases where a particular RNA sequence or structure--often one or more stem-loops--either promotes assembly or is required for assembly, but there are others where specific packaging signals are apparently not required. With regard to the assembly pathway, in those cases where stem-loops are involved, the first step is generally believed to be binding of the capsid proteins to these "fingers" of the RNA secondary structure. In the mature virus, the core of the RNA would then occupy the center of the viral particle, and the stem-loops would reach outward, towards the capsid, like stalagmites reaching up from the floor of a grotto towards the ceiling. Those viruses whose assembly does not depend on protein binding to stem-loops could have a different structure, with the core of the RNA lying just under the capsid, and the fingers reaching down into the interior of the virus, like stalactites. We review the literature on these alternative structures, focusing on RNA selectivity and the assembly mechanism, and we propose experiments aimed at determining, in a given virus, which of the two structures actually occurs.
Nász, István; Adám, Eva
2006-01-01
The icosahedral adenovirus capsid has three rotational axes of different types. The six five-fold, ten three-fold and the fifteen two-fold axes have two superficial points each, altogether 62. The axes determine the number and location of the identical rotational facet groups and that during the different rotational phases which other regular facets and with what multiplicity shall be covered by them. The number of rotational facets of the five-, three- and two-fold rotational symmetry axes is 4, 6.66 and 10, respectively. In all the three cases, there are two kinds of possible arrangements of the facets. During the rotation - when the facets of the facet group placed on one by one to the neighbouring identical facet groups - at the five-fold axes, the facets of the rotational facet group get into cover position 12 times with all the 20 regular capsid facets, 20 times at the three-fold axes, and 30 times at the two-fold axes in a way that a different facet combination (facet hit) falls to every facet, and the original symmetry is not disturbed. After all, this means 240, 400 and 600 facet combinations, i.e. multiplicity in case of five-, three- and two-fold symmetry axes respectively, and these numbers correspond with that of the theoretically possible variations. The same results can be calculated by multiplying the number of real rotations of the capsid bringing the body into itself i.e. the number 60 with the number of facets contributing to the five-, three- and two-fold rotational phases. The other way of the determination of multiplicity takes into account that all the facet groups of the capsid rotate simultaneously during all the rotational phases, and this multiplies the number of multiplicity with the number of the rotational types five-, three- and two-fold which result in one and the same multiplicity number in the case of five-, three- and two-fold symmetry, alike 1200. Perpendicular to the five-fold symmetry axes with the line of intersection drawn
NASA Astrophysics Data System (ADS)
Obaid, R.; Leibscher, M.
2015-02-01
We present a molecular symmetry analysis of electronic states and transition dipole moments for molecules which undergo large amplitude intramolecular torsions. The method is based on the correlation between the point group of the molecule at highly symmetric configurations and the molecular symmetry group. As an example, we determine the global irreducible representations of the electronic states and transition dipole moments for the quinodimethane derivative 2-[4-(cyclopenta-2,4-dien-1-ylidene)cyclohexa-2,5-dien-1-ylidene]-2H-1,3-dioxole for which two torsional degrees of freedom can be activated upon photo-excitation and construct the resulting symmetry adapted transition dipole functions.
Obaid, R.; Leibscher, M.
2015-02-14
We present a molecular symmetry analysis of electronic states and transition dipole moments for molecules which undergo large amplitude intramolecular torsions. The method is based on the correlation between the point group of the molecule at highly symmetric configurations and the molecular symmetry group. As an example, we determine the global irreducible representations of the electronic states and transition dipole moments for the quinodimethane derivative 2-[4-(cyclopenta-2,4-dien-1-ylidene)cyclohexa-2,5-dien-1-ylidene]-2H-1, 3-dioxole for which two torsional degrees of freedom can be activated upon photo-excitation and construct the resulting symmetry adapted transition dipole functions.
ERIC Educational Resources Information Center
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
Reflections on Symmetry and Proof
ERIC Educational Resources Information Center
Merrotsy, Peter
2008-01-01
The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…
Dynamical Symmetries in Classical Mechanics
ERIC Educational Resources Information Center
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
Hexagonal projected symmetries.
Oliveira, Juliane F; Castro, Sofia B S D; Labouriau, Isabel S
2015-09-01
In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern. PMID:26317198
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
Chiral symmetry and pentaquarks
Dmitri Diakonov
2004-07-01
Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.
NASA Astrophysics Data System (ADS)
Christodoulides, Demetrios
2015-03-01
Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.
Pauling, L. )
1988-11-01
A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals.
Symmetries in laminated composite plates
NASA Technical Reports Server (NTRS)
Noor, A. K.
1976-01-01
The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.
Atomic structure of icosahedral B4C boron carbide from a first principles analysis of NMR spectra.
Mauri, F; Vast, N; Pickard, C J
2001-08-20
Density functional theory is demonstrated to reproduce the 13C and 11B NMR chemical shifts of icosahedral boron carbides with sufficient accuracy to extract previously unresolved structural information from experimental NMR spectra. B4C can be viewed as an arrangement of 3-atom linear chains and 12-atom icosahedra. According to our results, all the chains have a CBC structure. Most of the icosahedra have a B11C structure with the C atom placed in a polar site, and a few percent have a B (12) structure or a B10C2 structure with the two C atoms placed in two antipodal polar sites.
Plasticity of single-grain icosahedral Al-Pd-Mn quasi-crystals deformed at room temperature
Mompiou, F.; Caillard, D
2004-07-12
Transmission electron microscopy observations have been performed on icosahedral Al-Pd-Mn quasi-crystal samples deformed at 20 deg. C under a high confining pressure. They reveal a large density of wavy walls from which several climbing dislocations are emitted. Near-screw dislocations have been found at the wall terminations with a Burgers vector contained in the wall plane. Careful plane determinations and dislocation analyses are not consistent with a glide and cross-slip mechanism. The results can be better interpreted as a deformation by cracks in mode III followed by a re-healing process.
Tai, K. P.; Gao, N.; Dai, X. D.; Li, J. H.; Lai, W. S.; Liu, B. X.
2006-08-28
Metallic glasses are obtained in an immiscible Nb-Ag system by ion beam mixing and an atomic configuration in the amorphous structure is discovered, i.e., an icositetrahedral ordering, which, together with an icosahedral ordering also observed in the Nb-Ag metallic glasses and in some previously reported systems, helps in formulating a structural spectrum of the amorphous solids. The experimental characterization and atomistic modeling with an ab initio derived Nb-Ag potential demonstrate the significance of structural heredity, i.e., the crystalline structures of the constituent metals play a decisive role in determining the atomic structure of the metallic glasses in the system.
NASA Astrophysics Data System (ADS)
Takeuchi, Tsunehiro
2015-03-01
The bulk thermal rectifiers usable at high temperature were developed using the unusual increase of electron thermal conductivity of icosahedral quasicrystals (ICQ's) at high temperature. Our previously performed analyses in terms of linear response theory suggested that the unusual increase of electron thermal conductivity of ICQ was brought about by the synergy effect of quasiperiodicity and narrow pseudogap at the Fermi level. Since the linear response theory suggests that the unusual increase of electron thermal conductivity is coupled with the small magnitude of Seebeck coefficient, the composition of Al-Cu-Fe ICQ, where the thermal conductivity shows the most significant increase with increasing temperature, was determined with a great help of Seebeck coefficient measurements. Consequently obtained Al61.5Cu26.5Fe12.0 ICQ, which was characterized by the small magnitude of Seebeck coefficient, possessed 9 times larger value of thermal conductivity at 1000 K than that observed at 300 K. The increasing tendency of electron thermal conductivity with increasing temperature was further enhanced by means of small amount of Re substitution for Fe. This substitution definitely reduced the lattice thermal conductivity while the electron thermal conductivity was kept unchanged. The lattice thermal conductivity was reduced by 35 % under the presence of 0.5 at.% Re, and the thermal conductivity at 1000 K consequently became about 11 times larger than that at 300 K. The thermal rectifiers were constructed using our newly developed ICQ (Al61.5Cu26.5Fe12.0 or Al61.0Si0.5Cu26.5Fe11.5Re0.5) together with one of the selected materials (Si, Al2O3, CuGeTe2 or Ag2Te) that possess thermal conductivity decreasing with increasing temperature. The heat current flowing in the rectifiers was confirmed to show significant direction dependence. The consequently obtained TRR =|
Structure of icosahedral quasicrystals and density-matrix functional theory for correlation effects
NASA Astrophysics Data System (ADS)
Hennig, Richard Georg
In the first part of this work, the atomic and electronic structure as well as the energetics of the icosahedral TiZrNi quasicrystal and the 1/1 approximant W-TiZrNi were determined. An atomic decoration model for the quasicrystal was developed invoking similarities to the structure of the 1/1 approximant. The structure of the quasicrystal was refined using a combined approach of diffraction refinement and ab initio calculations. The ternary ground state phase diagram was calculated using density-functional calculations. It was found that the TiZrNi quasicrystal is lower in energy than the competing phases indicating that it is a ground state quasicrystal. The electronic density of states of the quasicrystals shows a pseudogap. The hydrogen site energy distribution of the approximant was calculated and it was shown that a determination of the distribution by chemical potential measurements is impossible due to its complexity and the strong temperature and concentration dependent hydrogen-hydrogen interactions. In the second part of this work a density-matrix functional for isolated impurities was developed. The density-matrix functional for the electron interaction energy, was based on two theorems proved in this work. It was shown that the second-moment approximation yields the exact ground state for a dimer molecule with arbitrary on-site and inter-site Coulomb interactions. The second-moment approximation is implemented as a variational method. By comparison to results from exact diagonalization and the Hartree-Fock method it was shown that the functional was accurate in the case of isolated impurities. The combined effect of disorder and electron interactions for the model of an Anderson impurity in a random alloy were investigated and unexpected crossover behavior in the effects of disorder and electron interactions on the spin fluctuations was found. As a first application of the second-moment approximation, the electronic structure of dangling-bond defects
NASA Astrophysics Data System (ADS)
Strocchi, Franco
One of the most powerful ideas of modern theoretical physics is the mechanism of spontaneous symmetry breaking. It is at the basis of most of the recent achievements in the description of phase transitions in Statistical Mechanics as well as of collective phenomena in solid state physics. It has also made possible the unification of weak, electromagnetic and strong interactions in elementary particle physics. Philosophically, the idea is very deep and subtle (this is probably why its exploitation is a rather recent achievement) and the popular accounts do not fully do justice to it.
NASA Astrophysics Data System (ADS)
Houtz, Rachel; Colwell, Kitran; Terning, John
2016-09-01
We explore a new class of natural models which ensure the one-loop divergences in the Higgs mass are cancelled. The top-partners that cancel the top loop are new gauge bosons, and the symmetry relation that ensures the cancellation arises at an infrared fixed point. Such a cancellation mechanism can, a la Little Higgs models, push the scale of new physics that completely solves the hierarchy problem up to 5-10 TeV. When embedded in a supersymmetric model, the stop and gaugino masses provide the cutoffs for the loops, and the mechanism ensures a cancellation between the stop and gaugino mass dependence of the Higgs mass parameter.
Surface defects and symmetries
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph
2015-04-01
In quantum field theory, defects of various codimensions are natural ingredients and carry a lot of interesting information. In this contribution we concentrate on topological quantum field theories in three dimensions, with a particular focus on Dijkgraaf-Witten theories with abelian gauge group. Surface defects in Dijkgraaf-Witten theories have applications in solid state physics, topological quantum computing and conformal field theory. We explain that symmetries in these topological field theories are naturally defined in terms of invertible topological surface defects and are thus Brauer-Picard groups.
Critical scaling of icosahedral medium-range order in CuZr metallic glass-forming liquids
Wu, Z. W.; Li, F. X.; Huo, C. W.; Li, M. Z.; Wang, W. H.; Liu, K. X.
2016-01-01
The temperature evolution of icosahedral medium-range order formed by interpenetrating icosahedra in CuZr metallic glassforming liquids was investigated via molecular dynamics simulations. Scaling analysis based on percolation theory was employed, and it is found that the size distribution of clusters formed by the central atoms of icosahedra at various temperatures follows a very good scaling law with the cluster number density scaled by S−τ and the cluster size S scaled by |1 − Tc/T|−1/σ, respectively. Here Tc is scaling crossover-temperature. τ and σ are scaling exponents. The critical scaling behaviour suggests that there would be a structural phase transition manifested by percolation of locally favoured structures underlying the glass transition, if the liquid could be cooled slowly enough but without crystallization intervening. Furthermore, it is revealed that when icosahedral short-range order (ISRO) extends to medium-range length scale by connection, the atomic configurations of ISROs will be optimized from distorted ones towards more regular ones gradually, which significantly lowers the energies of ISROs and introduces geometric frustration simultaneously. Both factors make key impacts on the drastic dynamic slow-down of supercooled liquids. Our findings provide direct structure-property relationship for understanding the nature of glass transition. PMID:27779239
Baker, T. S.; Olson, N. H.; Fuller, S. D.
1999-01-01
Viruses are cellular parasites. The linkage between viral and host functions makes the study of a viral life cycle an important key to cellular functions. A deeper understanding of many aspects of viral life cycles has emerged from coordinated molecular and structural studies carried out with a wide range of viral pathogens. Structural studies of viruses by means of cryo-electron microscopy and three-dimensional image reconstruction methods have grown explosively in the last decade. Here we review the use of cryo-electron microscopy for the determination of the structures of a number of icosahedral viruses. These studies span more than 20 virus families. Representative examples illustrate the use of moderate- to low-resolution (7- to 35-Å) structural analyses to illuminate functional aspects of viral life cycles including host recognition, viral attachment, entry, genome release, viral transcription, translation, proassembly, maturation, release, and transmission, as well as mechanisms of host defense. The success of cryo-electron microscopy in combination with three-dimensional image reconstruction for icosahedral viruses provides a firm foundation for future explorations of more-complex viral pathogens, including the vast number that are nonspherical or nonsymmetrical. PMID:10585969
Larson, Eric T.; Reiter, Dirk; Young, Mark; Lawrence, C. Martin
2006-01-01
Sulfolobus turreted icosahedral virus (STIV) was the first icosahedral virus characterized from an archaeal host. It infects Sulfolobus species that thrive in the acidic hot springs (pH 2.9 to 3.9 and 72 to 92°C) of Yellowstone National Park. The overall capsid architecture and the structure of its major capsid protein are very similar to those of the bacteriophage PRD1 and eukaryotic viruses Paramecium bursaria Chlorella virus 1 and adenovirus, suggesting a viral lineage that predates the three domains of life. The 17,663-base-pair, circular, double-stranded DNA genome contains 36 potential open reading frames, whose sequences generally show little similarity to other genes in the sequence databases. However, functional and evolutionary information may be suggested by a protein's three-dimensional structure. To this end, we have undertaken structural studies of the STIV proteome. Here we report our work on A197, the product of an STIV open reading frame. The structure of A197 reveals a GT-A fold that is common to many members of the glycosyltransferase superfamily. A197 possesses a canonical DXD motif and a putative catalytic base that are hallmarks of this family of enzymes, strongly suggesting a glycosyltransferase activity for A197. Potential roles for the putative glycosyltransferase activity of A197 and their evolutionary implications are discussed. PMID:16840342
NASA Technical Reports Server (NTRS)
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
NASA Astrophysics Data System (ADS)
Tsurumaru, Toyohiro
2010-01-01
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of “rank two” can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
Tsurumaru, Toyohiro
2010-01-15
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C{sub 4}, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of 'rank two' can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
Improved Statistics for Determining the Patterson Symmetry fromUnmerged Diffraction Intensities
Sauter, Nicholas K.; Grosse-Kunstleve, Ralf W.; Adams, Paul D.
2006-01-09
We examine procedures for detecting the point-group symmetryof macromolecular datasets and propose enhancements. To validate apoint-group, it is sufficient to compare pairs of Bragg reflections thatare related by each of the group's component symmetry operators.Correlation is commonly expressed in the form of a single statisticalquantity (such as Rmerge) that incorporates information from all of theobserved reflections. However, the usual practice of weighting all pairsof symmetry-related intensities equally can obscure the fact that thevarious symmetry operators of the point-group contribute differingfractions of the total set. In some cases where particular symmetryelements are significantly under-represented, statistics calculatedglobally over all observations do not permit conclusions about thepoint-group and Patterson symmetry. The problem can be avoided byrepartitioning the data in a way that explicitly takes note of individualoperators. The new analysis methods, incorporated into the programLABELIT (cci.lbl.gov/labelit), can be performed early enough during dataacquisition, and are quick enough, that it is feasible to pause tooptimize the data collection strategy.
Dynamical Symmetries in atomic nuclei
Jolie, J.
2010-04-26
We review the use of dynamical symmetries and supersymmetries in nuclear physics using the interacting boson approximation. Special emphasis will be put on the experimental techniques used and the influence of symmetry on experimental observables. We illustrate this by a detailed study on mixed symmetry states in {sup 94}Mo. We present also experiments performed to test predictions of dynamical supersymmetries in the Pt-Au region.
Wilczek, Frank
2005-01-20
Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence for these bold ideas is indirect. But soon the theory will undergo a critical test depending on whether the quanta of this symmetry-breaking field, the so-called Higgs particles, are produced at the Large Hadron Collider (due to begin operation in 2007).
Lo, Pok Man; Swanson, Eric S.
2011-03-15
Schwinger-Dyson equations are used to study spontaneous chiral and parity symmetry breaking of three-dimensional quantum electrodynamics with two-component fermions. This theory admits a topological photon mass that explicitly breaks parity symmetry and generates a fermion mass. We show for the first time that it is possible to spontaneously break both parity and chiral symmetry. We also find that chiral symmetry is restored at a critical number of fermion flavors in our truncation scheme. Finally, the Coleman-Hill theorem is used to demonstrate that the results are reasonably accurate.
Leptogenesis and residual CP symmetry
NASA Astrophysics Data System (ADS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-03-01
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z 2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S 4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Unified Symmetry of Hamilton Systems
NASA Astrophysics Data System (ADS)
Xu, Xue-Jun; Qin, Mao-Chang; Mei, Feng-Xiang
2005-11-01
The definition and the criterion of a unified symmetry for a Hamilton system are presented. The sufficient condition under which the Noether symmetry is a unified symmetry for the system is given. A new conserved quantity, as well as the Noether conserved quantity and the Hojman conserved quantity, deduced from the unified symmetry, is obtained. An example is finally given to illustrate the application of the results. The project supported by National Natural Science Foundation of China under Grant No. 10272021 and the Doctoral Program Foundation of Institution of Higher Education of China under Grant No. 20040007022
Givental Graphs and Inversion Symmetry
NASA Astrophysics Data System (ADS)
Dunin-Barkowski, Petr; Shadrin, Sergey; Spitz, Loek
2013-05-01
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Tricas, Hugo; Colon, Marta; Ellis, David; Macgregor, Stuart A; McKay, David; Rosair, Georgina M; Welch, Alan J; Glukhov, Ivan V; Rossi, Fulvio; Laschi, Franco; Zanello, Piero
2011-04-28
The icosahedral carboranes 1-C(6)F(5)-2-Ph-1,2-closo-C(2)B(10)H(10) (1), 1-(4'-F(3)CC(6)H(4))-2-Ph-1,2-closo-C(2)B(10)H(10) (2), 1,2-(4'-F(3)CC(6)H(4))(2)-1,2-closo-C(2)B(10)H(10) (3), 1-(4'-H(3)CC(6)F(4))-2-Ph-1,2-closo-C(2)B(10)H(10) (4), 1-(4'-F(3)CC(6)F(4))-2-Ph-1,2-closo-C(2)B(10)H(10) (5), 1,2-(4'-F(3)CC(6)F(4))(2)-1,2-closo-C(2)B(10)H(10) (6), 1,7-(4'-F(3)CC(6)F(4))(2)-1,7-closo-C(2)B(10)H(10) (7) and 1,12-(4'-F(3)CC(6)F(4))(2)-1,12-closo-C(2)B(10)H(10) (8), with fluorinated aryl substituents on cage carbon atoms, have been prepared in good to high yields and characterised by microanalysis, (1)H, (11)B and (19)F NMR spectroscopies, mass spectrometry, single-crystal X-ray diffraction and (spectro)electrochemistry. By analysis of <δ(11)B>, the weighted average (11)B chemical shift, a ranking order for the ortho carboranes 1-6 is established based on the combined electron-withdrawing properties of the C-substituents, and is in perfect agreement with that established independently by electrochemical study. In a parallel computational study the effects of a wide range of different substituents on the redox properties of carboranes have been probed by comparison of ΔE values, where ΔE is the energy gap between the DFT-optimised [7,9-R(2)-7,9-nido-C(2)B(10)](2-) anion and its DFT-optimised basket-shaped first oxidation product. The overall conclusion from the NMR spectroscopic, electrochemical and computational studies is that strongly electron withdrawing substituents significantly stabilise [7,9-nido-C(2)B(10)](2-) dianions with respect to oxidation, and that the best practical substituent is 4-F(3)CC(6)F(4). Thus attention focussed on the reduction of 1,2-(4'-F(3)CC(6)F(4))(2)-1,2-closo-C(2)B(10)H(10), compound 6. The sequence 6/[6](-)/[6](2-) appears reversible on the cyclic voltammetric timescale but on the longer timescale of macroelectrolysis the radical anion is only partially stable. EPR study of the electrogenerated monoanions from the ortho
Wei, Lu; Zhou, Zhi-You; Chen, Sheng-Pei; Xu, Chang-Deng; Su, Dangsheng; Schuster, Manfred Erwin; Sun, Shi-Gang
2013-12-11
Pt triambic icosahedral nanocrystals (TIH NCs) enclosed by {771} high-index facets were successfully synthesized electrochemically, for the first time, in ChCl-urea based deep eutectic solvents, and exhibited higher electrocatalytic activity and stability towards ethanol electrooxidation than a commercial Pt black catalyst. PMID:24084858
Wei, Lu; Zhou, Zhi-You; Chen, Sheng-Pei; Xu, Chang-Deng; Su, Dangsheng; Schuster, Manfred Erwin; Sun, Shi-Gang
2013-12-11
Pt triambic icosahedral nanocrystals (TIH NCs) enclosed by {771} high-index facets were successfully synthesized electrochemically, for the first time, in ChCl-urea based deep eutectic solvents, and exhibited higher electrocatalytic activity and stability towards ethanol electrooxidation than a commercial Pt black catalyst.
ERIC Educational Resources Information Center
Hancock, Karen
2007-01-01
In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Crystal Symmetry Algorithms in a High-Throughput Framework for Materials
NASA Astrophysics Data System (ADS)
Taylor, Richard
The high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.
Symmetry-adapted digital modeling I. Axial symmetric proteins.
Janner, A
2016-05-01
Considered are axial symmetric proteins exemplified by the octameric mitochondrial creatine kinase, the Pyr RNA-binding attenuation protein, the D-aminopeptidase and the cyclophilin A-cyclosporin complex, with tetragonal (422), trigonal (32), pentagonal (52) and pentagonal (52) point-group symmetry, respectively. One starts from the protein enclosing form, which is characterized by vertices at points of a lattice (the form lattice) whose dimension depends on the point group. This allows the indexing of Cα's at extreme radial positions. The indexing is extended to additional residues on the basis of a finer lattice, the digital modeling lattice Λ, which includes the form lattice as a sublattice. This leads to a coarse-grained description of the protein. In the crystallographic point-group case, the planar indices are obtained from a projection of atomic positions along the rotation axis, taken as the z axis. The planar indices of a Cα are then those of the nearest projected lattice point. In the non-crystallographic case, low indices are an additional requirement. The coarse-grained bead follows from the condition imposed on the residues selected to have a z coordinate within a band of value δ above and below the height of lattice points. The choice of δ permits a variation of the coarse-grained bead model. For example, the value δ = 0.5 leads to a fine-grained indexing of the full set of residues, whereas with δ = 0.25 one gets a coarse-grained model which includes only about half of these residues. Within this procedure, the indexing of the Cα only depends on the choice of the digital modeling lattice and not on the value of δ. The characteristics which distinguish the present approach from other coarse-grained models of proteins on lattices are summarized at the end. PMID:27126107
Jach, T.; Zhang, Y.; Colella, R.; de Boissieu, M.; Boudard, M.; Goldman, A.I.; Lograsso, T.A.; Delaney, D.W.; Kycia, S.
1999-04-01
We have observed dynamical diffraction in the
Sharma, H. R. Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.
2014-05-07
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C{sub 60} on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C{sub 60} molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C{sub 60} molecules atop the Pb islands approaches zero, regardless of the overall C{sub 60} coverage.
Functional Symmetry of Endomembranes
2007-01-01
In higher eukaryotic cells pleiomorphic compartments composed of vacuoles, tubules and vesicles move from the endoplasmic reticulum (ER) and the plasma membrane to the cell center, operating in early biosynthetic trafficking and endocytosis, respectively. Besides transporting cargo to the Golgi apparatus and lysosomes, a major task of these compartments is to promote extensive membrane recycling. The endocytic membrane system is traditionally divided into early (sorting) endosomes, late endosomes and the endocytic recycling compartment (ERC). Recent studies on the intermediate compartment (IC) between the ER and the Golgi apparatus suggest that it also consists of peripheral (“early”) and centralized (“late”) structures, as well as a third component, designated here as the biosynthetic recycling compartment (BRC). We propose that the ERC and the BRC exist as long-lived “mirror compartments” at the cell center that also share the ability to expand and become mobilized during cell activation. These considerations emphasize the functional symmetry of endomembrane compartments, which provides a basis for the membrane rearrangements taking place during cell division, polarization, and differentiation. PMID:17267686
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Symmetries in the Schwarzschild Problem
NASA Astrophysics Data System (ADS)
Mioc, V.
The two-body problem associated to a force field described by a potential of the form U = A/r + B/r3 (r is a distance between particles, A and B are real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form isomorphic commutative groups endowed with an idempotent structure. Expressed in Levi-Civita's coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting an idempotent structure.
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
Broken Symmetries and Magnetic Dynamos
NASA Technical Reports Server (NTRS)
Shebalin, John V.
2007-01-01
Phase space symmetries inherent in the statistical theory of ideal magnetohydrodynamic (MHD) turbulence are known to be broken dynamically to produce large-scale coherent magnetic structure. Here, results of a numerical study of decaying MHD turbulence are presented that show large-scale coherent structure also arises and persists in the presence of dissipation. Dynamically broken symmetries in MHD turbulence may thus play a fundamental role in the dynamo process.
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
Anomalies and Discrete Chiral Symmetries
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Topologically induced semiconductivity in icosahedral Al-Pd-Re and its approximants
NASA Astrophysics Data System (ADS)
Krajčí, M.; Hafner, J.
2007-01-01
We demonstrate that the opening of a semiconducting band-gap in the electronic spectrum of the i-Al-Pd-Re quasicrystal and its approximants is due to the formation of a topological band-gap, in analogy to the band-gap found in the FeSi (B20) structure. In both systems we have identified a network of linear chains of alternating Si(Al) and transition-metal (TM) atoms extending along twofold symmetry directions. In i-Al-Pd-Re the chains of alternating Al and TM atoms extend from a center of the pseudo-Mackay (M) cluster over the surface of the Bergman cluster to the center of another neighboring M cluster. Substitutional Al/Pd defects and a fragmentation of the chains by phason defects lead to the formation of localized states in the band-gap. The band-gap of the real i-Al-Pd-Re quasicrystal is filled by localized states. The i-Al-Pd-Re quasicrystal thus behaves as a disordered semiconductor.
Na9K16TI~25: A New Phase Containing Naked Icosahedral Cluster Fragments Ti99-
Li, Bin; Corbett, John D.
2007-12-05
The phase Na{sub 9}K{sub 16}Tl{sub 25.25(2)} was synthesized by fusion of the elements in sealed Ta containers followed by quenching and annealing at 250 C. The structure established by single crystal X-ray diffraction means (P6{sub 3}/m, Z = 2, a = 19.376(3) {angstrom}, c = 11.480(2) {angstrom}) features Tl{sub 9}{sup 9-} clusters. These are well separated by cations that bridge between, faces, edges, and vertices of the clusters; sodium appears to be essential in this role. This is the third compound known to contain Tl{sub 9} clusters, but here two of nine sites are partially occupied, which can be interpreted as a 70:30 mixture of Tl{sub 9} and Tl{sub 7} units in the same cavity. This Tl{sub 9} example also displays lower symmetry (C{sub s}) but requires the same 2n skeletal electrons. EHTB electronic structure calculations indicate that the Fermi level intersects a finite densities-of-states (DOS), and only some bonds are optimized at E{sub F}, giving some insight regarding the site of Tl deficiency. Direct geometric relationships are found among Tl{sub 13}, Tl{sub 9}, Tl{sub 7} and Tl{sub 5} clusters through systematic removal of vertices.
Algorithms for computer detection of symmetry elements in molecular systems.
Beruski, Otávio; Vidal, Luciano N
2014-02-01
Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry. PMID:24403016
Symmetry in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.
1993-01-01
Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is
Notation Confusion of Symmetry Species for Molecules with Several Large-Amplitude Internal Motions
NASA Astrophysics Data System (ADS)
Groner, P.
2011-06-01
The Mulliken convention has become the standard notation for symmetry species (irreducible representations) of point groups for quasi-rigid molecules. No such convention exists for symmetry species of symmetry groups for semi-rigid or non-rigid molecules with large amplitude internal motions (LAMs). As a result, we have a situation where we create notations in a do-it-yourself fashion or adopt them from the literature, sometimes even without proper reference to its derivation or to the character table on which it is based. This may be just a nuisance for those who are comfortable enough with group theory and molecular symmetry groups to figure "it" out, but it represents a real problem for everybody else. The notation confusion is illustrated with examples from the literature (both old and new) on molecules with two or more LAMs. Most authors use the notation introduced by Myers and Wilson for molecules such as acetone or propane. No universal notation is in use for molecules with two methyl groups but lower overall symmetry. For example, the notation G_1_8 is used for one of these groups. As it turns out, different people use the same notation for different groups. This presentation is an attempt to bring some light into the dark and to combat confusion with a call for an anti-confusion convention. R. S. Mulliken, Phys. Rev. 43, 279 (1933). R. J. Myers, E. B. Wilson, J. Chem. Phys. 33, 186 (1960).
Novel symmetries in Christ-Lee model
NASA Astrophysics Data System (ADS)
Kumar, R.; Shukla, A.
2016-07-01
We demonstrate that the gauge-fixed Lagrangian of the Christ-Lee model respects four fermionic symmetries, namely; (anti-)BRST symmetries, (anti-)co-BRST symmetries within the framework of BRST formalism. The appropriate anticommutators amongst the fermionic symmetries lead to a unique bosonic symmetry. It turns out that the algebra obeyed by the symmetry transformations (and their corresponding conserved charges) is reminiscent of the algebra satisfied by the de Rham cohomological operators of differential geometry. We also provide the physical realizations of the cohomological operators in terms of the symmetry properties. Thus, the present model provides a simple model for the Hodge theory.
Larson, E.T.; Eilers, B.; Menon, S.; Reiter, D.; Ortmann, A.; Young, M.J.; Lawrence, C.M.
2009-06-03
Sulfolobus turreted icosahedral virus (STIV) was the first non-tailed icosahedral virus to be isolated from an archaeal host. Like other archaeal viruses, its 37 open reading frames generally lack sequence similarity to genes with known function. The roles of the gene products in this and other archaeal viruses are thus largely unknown. However, a protein's three-dimensional structure may provide functional and evolutionary insight in cases of minimal sequence similarity. In this vein, the structure of STIV F93 reveals a homodimer with strong similarity to the winged-helix family of DNA-binding proteins. Importantly, an interchain disulfide bond is found at the dimer interface, prompting analysis of the cysteine distribution in the putative intracellular proteins of the viral proteome. The analysis suggests that intracellular disulfide bonds are common in cellular STIV proteins, where they enhance the thermostability of the viral proteome.
Symmetry Guide to Ferroaxial Transitions.
Hlinka, J; Privratska, J; Ondrejkovic, P; Janovec, V
2016-04-29
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO_{2}, LuFe_{2}O_{4}, and URu_{2}Si_{2}.
Symmetry Guide to Ferroaxial Transitions
NASA Astrophysics Data System (ADS)
Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.
2016-04-01
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .
On the symmetries of integrability
Bellon, M.; Maillard, J.M.; Viallet, C. )
1992-06-01
In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil
2008-11-23
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Law-Hine, Didier; Sahoo, Anil K; Bailleux, Virginie; Zeghal, Mehdi; Prevost, Sylvain; Maiti, Prabal K; Bressanelli, Stéphane; Constantin, Doru; Tresset, Guillaume
2015-09-01
Viral capsids derived from an icosahedral plant virus widely used in physical and nanotechnological investigations were fully dissociated into dimers by a rapid change of pH. The process was probed in vitro at high spatiotemporal resolution by time-resolved small-angle X-ray scattering using a high brilliance synchrotron source. A powerful custom-made global fitting algorithm allowed us to reconstruct the most likely pathway parametrized by a set of stoichiometric coefficients and to determine the shape of two successive intermediates by ab initio calculations. None of these two unexpected intermediates was previously identified in self-assembly experiments, which suggests that the disassembly pathway is not a mirror image of the assembly pathway. These findings shed new light on the mechanisms and the reversibility of the assembly/disassembly of natural and synthetic virus-based systems. They also demonstrate that both the structure and dynamics of an increasing number of intermediate species become accessible to experiments. PMID:27120684
Step-terrace morphology and reactivity to C60 of the five-fold icosahedral Ag-In-Yb quasicrystal
NASA Astrophysics Data System (ADS)
Nugent, P. J.; Smerdon, J. A.; McGrath, R.; Shimoda, M.; Cui, C.; Tsai, A. P.; Sharma, H. R.
2011-07-01
The surface of the icosahedral i-Ag-In-Yb quasicrystal provides one of the first non-Al-based aperiodic surfaces that is suitable for study under ultra-high vacuum conditions. We present a scanning tunnelling microscopy (STM) study of the five-fold surface of this new quasicrystal demonstrating detailed structure of the terraces and steps. The analysis of the autocorrelation functions of STM images at opposite bias polarities and of the in-plane structure of the bulk model of i-Cd-Yb, which is isostructural to i-Ag-In-Yb, reveals that the surface terminations occur at the centres of the rhombic triacontrahedral (RTH) clusters, which are the basic building blocks of this material. The study further confirms that the unoccupied electronic states are located on Yb sites. Step edges display a Fibonacci sequence of truncated clusters, which can also be explained in terms of the model structure. Occasionally, a single terrace is found to display different structures at negative bias, whereas the same terrace shows a uniform structure at positive bias. Depositing C60 creates a disordered overlayer on the surface with no resulting FFT or LEED patterns.
Maniraj, M; Rai, Abhishek; Barman, S R; Krajci, M; Schlagel, Deborah L; Lograsso, Thomas A; Horn, K
2014-09-01
We study the unoccupied region of the electronic structure of the fivefold symmetric surface of an icosahedral (i) Al-Pd-Mn quasicrystal. A feature that exhibits parabolic dispersion with an effective mass of (1.15±0.1)m_{e} and tracks the change in the work function is assigned to an image potential resonance because our density functional calculation shows an absence of band gap in the respective energy region. We show that Sn grows pseudomorphically on i-Al-Pd-Mn as predicted by density functional theory calculations, and the energy of the image potential resonance tracks the change in the work function with Sn coverage. The image potential resonance appears much weaker in the spectrum from the related crystalline Al-Pd-Mn surface, demonstrating that its strength is related to the compatibility of the quasiperiodic wave functions in i-Al-Pd-Mn with the free-electron-like image potential states. Our investigation of the energy region immediately above E_{F} provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
NASA Astrophysics Data System (ADS)
Mukhopadhyay, N. K.; Ali, F.; Srivastava, V. C.; Yadav, T. P.; Sakaliyska, M.; Surreddi, K. B.; Scudino, S.; Uhlenwinkel, V.; Eckert, J.
2011-07-01
A single-phase stable icosahedral quasicrystalline sample of high quality with the composition Al62.5Cu25Fe12.5 was produced by the spray forming technique. The material was further investigated by mechanical milling under an argon atmosphere to avoid oxidation during milling. At the initial stages of milling (within 5 h) a significant broadening of the diffraction peaks was observed, indicating a reduction of crystallite size and the introduction of lattice strain, which can be linked to phason strain of the quasilattice. Line broadening was noticed to increase with increasing milling time and in the material milled for longer time only a few broad diffraction peaks, which can be identified as a nanoscale bcc phase (i.e. disordered B2 phase, a ∼ 2.9 Å), were visible. At this stage the diffraction signals belonging to the quasicrystals were no longer observable, indicating a complete transformation of the quasicrystals into the bcc phase. Finally, the bcc phase formed during milling transformed back to the quasicrystalline phase during subsequent annealing treatment. The microhardness measured on the milled powders was found to decrease with increasing milling time, most likely as a consequence of the increased volume fraction of the ductile bcc phase. Attempts are made to rationalize the structural transformation.
Epitaxial Growth of Icosahedral Boride Semiconductors for Novel Energy Conversion Devices
Edgar, J.H.
2006-01-03
The chemical vapor deposition and properties of the boron-rich semiconductors B12As2 and B12P2 on 6H-SiC(0001) and silicon substrates were investigated. Crystalline, stoichiometric films were deposited between 1200 C and 1500 C using two types of reactants, hydrides (B2H6 and AsH3) for B12As2 and halides (BBr3 and PBr3) for B12P2. 6H-SiC proved to be the better substrate for B12As2 heteroepitaxy, in terms of the residual impurity concentrations. Films on Si substrates suffered from high concentrations of Si (up to 4at.%); in contrast, the Si and C concentrations in the B12As2 films deposited on 6H-SiC at 1300 C were at or below the detection limits of secondary ion mass spectrometry (SIMS). The deposition temperature was significant as films deposited at 1450 C contained high residual C and Si concentrations (>1020 cm-3), probably due to the decomposition of the substrate. The hydrogen concentration in all B12As2 films was relatively high, with a minimum concentration of 3x1019 cm-3 in undoped B12As2. SIMS measurements showed that the hydrogen concentration was directly proportional to and tracked the Si concentration, reaching values as high as 3 x 1020 cm-3. The structural properties of the B12As2 films were characterized by x-ray diffraction and transmission electron microscopy. The FWHM of typical high resolution x-ray rocking curves for the (333) peaks of the B12As2 films were 800 arcsec. The films are under tensile strain due the higher coefficient of thermal expansion for B12As2 than SiC. Rotational twins were present in B12As2 films deposited on (0001) oriented 6H-SiC substrates, as revealed by cross-sectional TEM and x-ray diffraction pole figures. While the c-plane 6H-SiC has six-fold rotational symmetry, rhombohedral B12As2 has only 3-fold symmetry (along its (111) axis), thus it randomly nucleates with two different in-plane orientations. The electrical properties of undoped and silicon-doped B12As2 deposited on semi-insulating 6H-SiC substrates were
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes. PMID:25008961
Strong coupling electroweak symmetry breaking
Barklow, T.L.; Burdman, G.; Chivukula, R.S.
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
Paper Models Illustrating Virus Symmetry.
ERIC Educational Resources Information Center
McCarthy, D. A.
1990-01-01
Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Monster symmetry and extremal CFTs
NASA Astrophysics Data System (ADS)
Gaiotto, Davide
2012-11-01
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-05-01
We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
Effect of temperature and substitution on Cope rearrangement: a symmetry perspective.
Tuvi-Arad, Inbal; Rozgonyi, Tamás; Stirling, András
2013-12-01
Many reactions feature symmetry variation along the reaction path on the potential energy surface. The interconversion of the point group symmetry of the stationary points can be characteristic of these processes. Increasing the temperature, however, leads to the loss of symmetry in its traditional yes-no language. We find that in such cases the instantaneous distance of the molecular structure from its symmetric counterpart is a suitable collective variable that can describe the reaction process. We show that this quantity, the continuous symmetry measure (CSM), has a positive linear relationship with temperature, implying that even highly symmetric molecules should be considered as asymmetric above 0 K. Using ab initio molecular dynamics, we simulate the temperature-induced Cope rearrangements of several fluxional molecules and employ different CSMs to follow the reaction progress. We use this methodology to demonstrate the validity of important concepts governing these reactions: Woodward-Hoffmann rules and TS aromaticity. Statistical analysis of the CSM distributions reveals that ligands connected to the carbon frame have profound effect on the reaction course. In particular, our results show that lower temperatures tend to enhance the differences between the TS-stabilizing effect of the substituents.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Yet another symmetry breaking to be discovered
NASA Astrophysics Data System (ADS)
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
Classification of Arnold-Beltrami flows and their hidden symmetries
NASA Astrophysics Data System (ADS)
Fré, P.; Sorin, A. S.
2015-07-01
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds ℳ3, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★ g d, which can be solved by using time-honored harmonic analysis. Taking for ℳ3, a torus T 3 constructed as ℝ3/Λ, where Λ is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B A of three-vectors in the momentum lattice *Λ. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group which contains all space groups as proper subgroups. We show that the ★ g d eigenfunctions are naturally arranged into irreducible representations of and by means of a systematic use of the branching rules with respect to various possible subgroups we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O24 and the Universal Classifying Group is a finite group G1536 of order |G1536| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G1536. In this way we obtain an
Lin, Qisheng; Corbett, John D
2010-11-15
The realm of Tsai-type (YCd(6)-type) quasicrystals (QCs) and their approximants (ACs) continues to expand to the east in the periodic table. The heavy tetrel Sn is now one of the major components in the new Ca(15.0(5))Au(60.0(4))Sn(25.0(2)) (atom %) icosahedral QC and in the corresponding 1/1 and 2/1 ACs. (The 2/1 AC with Yb is also established.) Single-crystal X-ray diffraction on a 1/1 AC gives the refined formula of Ca(3)Au(14.36(3))Sn(4.38(5)) in space group Im3, a = 15.131(1) Å, whereas a representative 2/1 AC gives Ca(13)Au(47.2(1))Sn(28.1(1)), Pa3 and a = 24.444(1) Å. Both ACs contain five-shell multiply endohedral triacontahedral clusters as the common building blocks, as in the parent structure of YCd(6). The 2/1 AC also contains four Ca(2)-dimer-centered prolate rhombohedra (PRs) in the unit cell. The long-range order between triacontahedra and PRs in the 2/1 AC is the same as those in Bergman-type 2/1 ACs. A TB-LMTO-ASA calculation on an ideal 1/1 AC model reveals a shallow pseudogap in the total densities-of-states data around the Fermi energy, as expected. The depth of the pseudogap is considerably enhanced through interactions between the Ca 3d states and s and p states of Au and Sn. PMID:20939550
Lin, Qisheng; Corbett, John D
2010-11-15
The realm of Tsai-type (YCd(6)-type) quasicrystals (QCs) and their approximants (ACs) continues to expand to the east in the periodic table. The heavy tetrel Sn is now one of the major components in the new Ca(15.0(5))Au(60.0(4))Sn(25.0(2)) (atom %) icosahedral QC and in the corresponding 1/1 and 2/1 ACs. (The 2/1 AC with Yb is also established.) Single-crystal X-ray diffraction on a 1/1 AC gives the refined formula of Ca(3)Au(14.36(3))Sn(4.38(5)) in space group Im3, a = 15.131(1) Å, whereas a representative 2/1 AC gives Ca(13)Au(47.2(1))Sn(28.1(1)), Pa3 and a = 24.444(1) Å. Both ACs contain five-shell multiply endohedral triacontahedral clusters as the common building blocks, as in the parent structure of YCd(6). The 2/1 AC also contains four Ca(2)-dimer-centered prolate rhombohedra (PRs) in the unit cell. The long-range order between triacontahedra and PRs in the 2/1 AC is the same as those in Bergman-type 2/1 ACs. A TB-LMTO-ASA calculation on an ideal 1/1 AC model reveals a shallow pseudogap in the total densities-of-states data around the Fermi energy, as expected. The depth of the pseudogap is considerably enhanced through interactions between the Ca 3d states and s and p states of Au and Sn.
Gracia-Espino, Eduardo; Hu, Guangzhi; Shchukarev, Andrey; Wågberg, Thomas
2014-05-01
Studies on noble-metal-decorated carbon nanostructures are reported almost on a daily basis, but detailed studies on the nanoscale interactions for well-defined systems are very rare. Here we report a study of reduced graphene oxide (rGOx) homogeneously decorated with palladium (Pd) nanoclusters with well-defined shape and size (2.3 ± 0.3 nm). The rGOx was modified with benzyl mercaptan (BnSH) to improve the interaction with Pd clusters, and N,N-dimethylformamide was used as solvent and capping agent during the decoration process. The resulting Pd nanoparticles anchored to the rGOx-surface exhibit high crystallinity and are fully consistent with six-shell cuboctahedral and icosahedral clusters containing ~600 Pd atoms, where 45% of these are located at the surface. According to X-ray photoelectron spectroscopy analysis, the Pd clusters exhibit an oxidized surface forming a PdO(x) shell. Given the well-defined experimental system, as verified by electron microscopy data and theoretical simulations, we performed ab initio simulations using 10 functionalized graphenes (with vacancies or pyridine, amine, hydroxyl, carboxyl, or epoxy groups) to understand the adsorption process of BnSH, their further role in the Pd cluster formation, and the electronic properties of the graphene-nanoparticle hybrid system. Both the experimental and theoretical results suggest that Pd clusters interact with functionalized graphene by a sulfur bridge while the remaining Pd surface is oxidized. Our study is of significant importance for all work related to anchoring of nanoparticles on nanocarbon-based supports, which are used in a variety of applications.
Structural stability of the icosahedral AlCuFe quasicrystal under high-pressure and high-temperature
NASA Astrophysics Data System (ADS)
Takagi, S.; Kyono, A.; Nakamoto, Y.; Hirao, N.
2015-12-01
We report high-pressure and high-temperature in-situ X-ray diffraction study of icosahedral (i)-AlCuFe quasicrystal "icosahedrite" which is the first known naturally occurring quasicrystal mineral discovered in the Khatyrka meteorite. The i-AlCuFe quasicrystal was synthesized in laboratory from a powder mixture with an atomic ratio of Al : Cu : Fe = 65 : 20 : 15. The high-temperature and high-pressure X-ray diffraction experiments were performed using the laser-heated diamond anvil cell system installed at BL10XU, SPring-8, Japan. The i-AlCuFe showed a characteristic X-ray diffraction pattern of quasicrystal. With only compression, the diffraction patterns of the i-AlCuFe were continued until 75 GPa. At a pressure of 87 GPa two small new peaks occurred and then kept up to the maximum pressure of 104 GPa in the study. The results indicate that the pressure-induced structural phase transition of the i-AlCuFe occurs above 87 GPa, and the structure of the i-AlCuFe remains unchanged at least up to 75 GPa. Under simultaneously high pressure and high temperature, on the other hand, the i-AlCuFe was readily transformed to crystalline phase. It can be characterized by an irreversible transformation process. The structure of the i-AlCuFe is therefore more affected by thermal metamorphism than by pressure metamorphism. The present high-pressure and high-temperature experiments clearly revealed the thermal and pressure stability of the i-AlCuFe quasicrystal which may help to explain the formation of the naturally occurring quasicrystal in the solar system.
Noether symmetries and duality transformations in cosmology
NASA Astrophysics Data System (ADS)
Paliathanasis, Andronikos; Capozziello, Salvatore
2016-09-01
We discuss the relation between Noether (point) symmetries and discrete symmetries for a class of minisuperspace cosmological models. We show that when a Noether symmetry exists for the gravitational Lagrangian, then there exists a coordinate system in which a reversal symmetry exists. Moreover, as far as concerns, the scale-factor duality symmetry of the dilaton field, we show that it is related to the existence of a Noether symmetry for the field equations, and the reversal symmetry in the normal coordinates of the symmetry vector becomes scale-factor duality symmetry in the original coordinates. In particular, the same point symmetry as also the same reversal symmetry exists for the Brans-Dicke scalar field with linear potential while now the discrete symmetry in the original coordinates of the system depends on the Brans-Dicke parameter and it is a scale-factor duality when ωBD = 1. Furthermore, in the context of the O’Hanlon theory for f(R)-gravity, it is possible to show how a duality transformation in the minisuperspace can be used to relate different gravitational models.
Superalgebra and fermion-boson symmetry
Miyazawa, Hironari
2010-01-01
Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617
NASA Astrophysics Data System (ADS)
Kesavan, Aruna; Ashtekar, Abhay
2016-03-01
Conservation laws of asymptotic symmetries are essential to quantify the amount of energy-momentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the Bondi-Metzner-Sachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding two-dimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984).
Facial symmetry in robust anthropometrics.
Kalina, Jan
2012-05-01
Image analysis methods commonly used in forensic anthropology do not have desirable robustness properties, which can be ensured by robust statistical methods. In this paper, the face localization in images is carried out by detecting symmetric areas in the images. Symmetry is measured between two neighboring rectangular areas in the images using a new robust correlation coefficient, which down-weights regions in the face violating the symmetry. Raw images of faces without usual preliminary transformations are considered. The robust correlation coefficient based on the least weighted squares regression yields very promising results also in the localization of such faces, which are not entirely symmetric. Standard methods of statistical machine learning are applied for comparison. The robust correlation analysis can be applicable to other problems of forensic anthropology.
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function.
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Tensionless strings from worldsheet symmetries
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Chakrabortty, Shankhadeep; Parekh, Pulastya
2016-01-01
We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.
Symmetry breaking around a wormhole
NASA Astrophysics Data System (ADS)
Choudhury, A. L.
1996-11-01
We have modified the extended version Coule and Maeda's version (D. H. Coule and Kei-ichi Maeda, Class.Quant.Grav.7,995(1990)) of the Gidding-Strominger model (S. B. Giddings and A. Strominger, Nucl.Phys. B307, 854(l988)) of the euclidean gravitational field interacting with axion. The new model has R-symmetry in contrast to the previous model. At the lowest perturbation case the model retains a wormhole solution. We assume that the scalar expands adiabatically and satisfies ideal gas law in a crude first approximation. Under the Higg's mechanism the symmetry can be broken at the tree approximation. This mechanism, we hope, can be used to introduce the degeneracy of quark masses.
Lepton mixing and discrete symmetries
NASA Astrophysics Data System (ADS)
Hernandez, D.; Smirnov, A. Yu.
2012-09-01
The pattern of lepton mixing can emerge from breaking a flavor symmetry in different ways in the neutrino and charged lepton Yukawa sectors. In this framework, we derive the model-independent conditions imposed on the mixing matrix by the structure of discrete groups of the von Dyck type which include A4, S4, and A5. We show that, in general, these conditions lead to at least two equations for the mixing parameters (angles and CP phase δ). These constraints, which correspond to unbroken residual symmetries, are consistent with nonzero 13 mixing and deviations from maximal 2-3 mixing. For the simplest case, which leads to an S4 model and reproduces the allowed values of the mixing angles, we predict δ=(90°-120°).
Symmetry of cardiac function assessment
Bai, Xu-Fang; Ma, Amy X
2016-01-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Chiral symmetry and nucleon structure
Holstein, B.R. . Dept. of Physics and Astromony Washington Univ., Seattle, WA . Inst. for Nuclear Theory)
1992-01-01
Recently it has been realized that significant tests of the validity of QCD are available in low energy experiments (E < 500 MeV) by exploiting the property of (broken) chiral symmetry. This technique has been highly developed in The Goldstone boson sector by the work of Gasser and Leutwyler. Application to the nucleon system is much more difficult and is now being carefully developed.
Dark matter and global symmetries
NASA Astrophysics Data System (ADS)
Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.
2016-09-01
General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.
Symmetry-adapted excited states for the T1u⊗hg Jahn-Teller system
NASA Astrophysics Data System (ADS)
Qiu, Q. C.; Dunn, J. L.; Bates, C. A.
2001-08-01
Jahn-Teller (JT) systems typically contain a set of equivalent-energy wells in the lowest adiabatic potential-energy surface (APES). Quantum-mechanical tunneling between these wells (the dynamic JT effect) must be allowed for by taking appropriate symmetrized combinations of oscillator-type states associated with the wells. It is important to be able to describe the excited states of such systems for a number of reasons. One particular reason is that they are required for the calculation of second-order vibronic reduction factors, which in turn are useful for modeling experimental data using effective Hamiltonians. In this paper, projection-operator techniques are used to obtain general expressions for the symmetry-adapted excited states of the icosahedral T1u⊗hg JT system for the case of D5d minima in the APES. Analytical expressions for the states and their energies for one-phonon excitation are given explicitly. The energies of a selection of states with two-phonon excitations are also obtained and plotted. The results obtained in this paper are applicable to the C-60 molecule.
Yu, M; Chaudhuri, I; Leahy, C; Wu, S Y; Jayanthi, C S
2009-05-14
Structures and relative stabilities of carbon clusters belonging to different families have been investigated for diameters d < or = 5 nm based on an efficient semiempirical molecular dynamics (MD) scheme as well as a density functional theory based simulation. Carbon clusters studied include fullerenes and fullerene-derived structures (e.g., cages and onions), icosahedral structures, bucky-diamond structures, and clusters cut from the bulk diamond with spherical and facetted truncations. The reason for using a semiempirical MD is partly due to the large number of different cases (or carbon allotropes) investigated and partly due to the size of the clusters investigated in this work. The particular flavor of the semiempirical MD scheme is based on a self-consistent and environment-dependent Hamiltonian developed in the framework of linear combination of atomic orbitals. We find that (i) among the families of carbon clusters investigated, fullerene structures have the lowest energy with the relative energy ordering being E(fullerene) < E(onion) < E(icosahedral) < E(bucky-diamond) < E(bulk-truncated), (ii) a crossover between bucky-diamond and icosahedral structures is likely at d approximately 8 nm, (iii) the highest occupied molecular orbital-lowest unoccupied molecular orbital gap as a function of the diameter for the case of fullerenes shows an oscillatory behavior with the gap ranging from 2 eV to 6 meV, and the gap approaching that of gapless graphite for d > 3.5 nm, and (iv) there can be three types of phase transformations depending on the manner of heating and cooling in our simulated annealing studies: (a) a bucky-diamond structure --> an onionlike structure, (b) an onionlike --> a cage structure, and (c) a bucky-diamond --> a cage structure.
Maaty, Walid S. A.; Ortmann, Alice C.; Dlakić, Mensur; Schulstad, Katie; Hilmer, Jonathan K.; Liepold, Lars; Weidenheft, Blake; Khayat, Reza; Douglas, Trevor; Young, Mark J.; Bothner, Brian
2006-01-01
Icosahedral nontailed double-stranded DNA (dsDNA) viruses are present in all three domains of life, leading to speculation about a common viral ancestor that predates the divergence of Eukarya, Bacteria, and Archaea. This suggestion is supported by the shared general architecture of this group of viruses and the common fold of their major capsid protein. However, limited information on the diversity and replication of archaeal viruses, in general, has hampered further analysis. Sulfolobus turreted icosahedral virus (STIV), isolated from a hot spring in Yellowstone National Park, was the first icosahedral virus with an archaeal host to be described. Here we present a detailed characterization of the components forming this unusual virus. Using a proteomics-based approach, we identified nine viral and two host proteins from purified STIV particles. Interestingly, one of the viral proteins originates from a reading frame lacking a consensus start site. The major capsid protein (B345) was found to be glycosylated, implying a strong similarity to proteins from other dsDNA viruses. Sequence analysis and structural predication of virion-associated viral proteins suggest that they may have roles in DNA packaging, penton formation, and protein-protein interaction. The presence of an internal lipid layer containing acidic tetraether lipids has also been confirmed. The previously presented structural models in conjunction with the protein, lipid, and carbohydrate information reported here reveal that STIV is strikingly similar to viruses associated with the Bacteria and Eukarya domains of life, further strengthening the hypothesis for a common ancestor of this group of dsDNA viruses from all domains of life. PMID:16840341
NASA Astrophysics Data System (ADS)
Ektarawong, A.; Simak, S. I.; Alling, B.
2016-08-01
We investigate the thermodynamic stability of carbon-rich icosahedral boron carbide at different compositions, ranging from B4C to B2C , using first-principles calculations. Apart from B4C , generally addressed in the literature, B2.5C , represented by B10C2p (C-C), where Cp and (C-C) denote a carbon atom occupying the polar site of the icosahedral cluster and a diatomic carbon chain, respectively, is predicted to be thermodynamically stable under high pressures with respect to B4C as well as pure boron and carbon phases. The thermodynamic stability of B2.5C is determined by the Gibbs free energy G as a function of pressure p and temperature T , in which the contributions from the lattice vibrations and the configurational disorder are obtained within the quasiharmonic and the mean-field approximations, respectively. The stability range of B2.5C is then illustrated through the p -T phase diagrams. Depending on the temperatures, the stability range of B2.5C is predicted to be within the range between 40 and 67 GPa. At T ≳ 500 K, the icosahedral Cp atoms in B2.5C configurationally disorder at the polar sites. By investigating the properties of B2.5C , e.g., elastic constants and phonon and electronic density of states, we demonstrate that B2.5C is both mechanically and dynamically stable at zero pressure, and is an electrical semiconductor. Furthermore, based on the sketched phase diagrams, a possible route for experimental synthesis of B2.5C as well as a fingerprint for its characterization from the simulations of x-ray powder diffraction pattern are suggested.
Enhanced Facial Symmetry Assessment in Orthodontists.
Jackson, Tate H; Clark, Kait; Mitroff, Stephen R
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff-orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness.
Relativity symmetries and Lie algebra contractions
NASA Astrophysics Data System (ADS)
Cho, Dai-Ning; Kong, Otto C. W.
2014-12-01
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m , n) symmetry as an isometry on an m + n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m , n) preserving a symmetry of the same type at dimension m + n - 1, e.g. a G(m , n - 1) , together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2 , 4) , which is the particular case for our interest on the physics side as the proposed relativity symmetry for "quantum spacetime". The contractions from G(1 , 3) may be relevant to real physics.
Enhanced Facial Symmetry Assessment in Orthodontists
Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342
Symmetry breaking in neural nets.
Pessa, E
1988-01-01
In this paper two well-known homogeneous models of neural nets undergoing symmetry-breaking transitions are studied in order to see if, after the transition, there is the appearance of Goldstone modes. These have been found only in an approximate way; there are indications, however, that they can play a prominent role when the tissue is subjected to external inputs, constraining it to be slaved to the characteristics of those. This circumstance should be essential in explaining how a structured net can store complex inputs and give subsequently ordered outputs.
Hidden symmetries in jammed systems
NASA Astrophysics Data System (ADS)
Morse, Peter K.; Corwin, Eric I.
2016-07-01
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.
History of electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Kibble, T. W. B.
2015-07-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Kumar, A; Reddy, V S; Yusibov, V; Chipman, P R; Hata, Y; Fita, I; Fukuyama, K; Rossmann, M G; Loesch-Fries, L S; Baker, T S; Johnson, J E
1997-01-01
K. Fukuyama, S. S. Abdel-Meguid, J. E. Johnson, and M. G. Rossmann (J. Mol. Biol. 167:873-984, 1983) reported the structure of alfalfa mosaic virus assembled from the capsid protein as a T=1 icosahedral empty particle at 4.5-A resolution. The information contained in the structure included the particle size, protein shell thickness, presence of wide holes at the icosahedral fivefold axes, and a proposal that the capsid protein adopts a beta-barrel structure. In the present work, the X-ray diffraction data of Fukuyama et al. as well as the data subsequently collected by I. Fita, Y. Hata, and M. G. Rossmann (unpublished) were reprocessed to 4.0-A resolution, and the structure was solved by molecular replacement. The current structure allowed the tracing of the polypeptide chain of the capsid protein confirming the beta-sandwich fold and provides information on intersubunit interactions in the particle. However, it was not possible to definitively assign the amino acid sequence to the side chain density at 4-A resolution. The particle structure was also determined by cryoelectron microscopy and image reconstruction methods and found to be in excellent agreement with the X-ray model. PMID:9311881
Acidities of closo-1-COOH-1,7-C2B10H11 and amino acids based on icosahedral carbaboranes.
Dávalos, Juan Z; González, Javier; Ramos, Rocío; Hnyk, Drahomír; Holub, Josef; Santaballa, J Arturo; Canle-L, Moisés; Oliva, Josep M
2014-04-17
Carborane clusters are not found in Nature and are exclusively man-made. In this work we study, both experimentally and computationally, the gas-phase acidity (measured GA = 1325 kJ·mol(-1), computed GA = 1321 kJ·mol(-1)) and liquid-phase acidity (measured pKa = 2.00, computed pKa = 1.88) of the carborane acid closo-1-COOH-1,7-C2B10H11. The experimental gas-phase acidity was determined with electrospray tandem mass spectrometry (ESI/MS), by using the extended Cooks kinetic method (EKM). Given the similar spatial requirements of the title icosahedral cage and benzene and the known importance of aminoacids as a whole, such a study is extended, within an acid-base context, to corresponding ortho, meta, and para amino acids derived from icosahedral carborane cages, 1-COOH-n-NH2-1, n-R with {R = C2B10H10, n = 2, 7, 12}, and from benzene {R = C6H4, n = 2, 3, 4}. A remarkable difference is found between the proportion of neutral versus zwitterion structures in water for glycine and the carborane derived amino acids.
Peymann, T.; Knobler, C.B.; Hawthorne, M.F.
1999-06-16
The quest for globular structures possessing both hydrophobic surfaces and extraordinary kinetic stability stems from the search for novel modules with which to synthesize supramolecular structures, weakly coordinating anions, and space-controlling drug components. The fullerenes, characterized by unique chemistry and physical properties, represent one family of such precursors. Another family of globular hydrophobes, described by the authors as ``camouflaged`` carboranes, has been described. These species may approach the van der Waals diameter of C{sub 60} by attachment of methyl groups and functionalized methyl substituents to the icosahedral scaffolding of the aromatic [closo-C{sub n}B{sub 12{minus}n}H{sub 12}]{sup n{minus}2} (n = 0--2). Whereas hydrophobic and amphiphilic derivatives of this sort are known with n = 1 and 2, the fully methylated derivative of the parent species, dodecamethyl-closo-dodecaborate(2{minus}), (n = 0), is now reported for the first time. The authors describe a new permethylation technique for icosahedral closo-boranes employing trimethylaluminium and methyl iodide in the absence of a solvent.
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards
Contact symmetries and Hamiltonian thermodynamics
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-10-15
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Local discrete symmetries from superstring derived models
NASA Astrophysics Data System (ADS)
Faraggi, Alon E.
1997-02-01
Discrete and global symmetries play an essential role in many extensions of the Standard Model, for example, to preserve the proton lifetime, to prevent flavor changing neutral currents, etc. An important question is how can such symmetries survive in a theory of quantum gravity, like superstring theory. In a specific string model I illustrate how local discrete symmetries may arise in string models and play an important role in preventing fast proton decay and flavor changing neutral currents. The local discrete symmetry arises due to the breaking of the non-Abelian gauge symmetries by Wilson lines in the superstring models and forbids, for example dimension five operators which mediate rapid proton decay, to all orders of nonrenormalizable terms. In the context of models of unification of the gauge and gravitational interactions, it is precisely this type of local discrete symmetries that must be found in order to insure that a given model is not in conflict with experimental observations.
Symmetry properties in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.
Symmetry energy of dilute warm nuclear matter.
Natowitz, J B; Röpke, G; Typel, S; Blaschke, D; Bonasera, A; Hagel, K; Klähn, T; Kowalski, S; Qin, L; Shlomo, S; Wada, R; Wolter, H H
2010-05-21
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.
Quantum Deformations of Einstein's Relativistic Symmetries
Lukierski, Jerzy
2006-11-03
We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory -- the Poincare symmetries. The most complete way of introducing the modifications is via the noncocommutative Hopf-algebraic structure describing quantum symmetries. Two types of quantum relativistic symmetries are described, one with constant commutator of quantum Minkowski space coordinates ({theta}{mu}{nu}-deformation) and second with Lie-algebraic structure of quantum space-time, introducing so-called {kappa}-deformation. The third fundamental constant of Nature - fundamental mass {kappa} or length {lambda} - appears naturally in proposed quantum relativistic symmetry scheme. The deformed Minkowski space is described as the representation space (Hopf-module) of deformed Poincare algebra. Some possible perspectives of quantum-deformed relativistic symmetries will be outlined.
Symmetry-protected single-photon subradiance
NASA Astrophysics Data System (ADS)
Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.
2016-05-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook.
Issues in standard model symmetry breaking
Golden, M.
1988-04-01
This work discusses the symmetry breaking sector of the SU(2) x U(1) electroweak model. The first two chapters discuss Higgs masses in two simple Higgs models. The author proves low-enery theorems for the symmetry breaking sector: The threshold behavior of gauge-boson scattering is completely determined, whenever the symmetry breaking sector meets certain simple conditions. The author uses these theorems to derive event rates for the superconducting super collider (SSC). The author shows that the SSC may be able to determine whether the interactions of the symmetry breaking sector are strong or weak. 54 refs.
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
Functional ferroic heterostructures with tunable integral symmetry.
Becher, C; Trassin, M; Lilienblum, M; Nelson, C T; Suresha, S J; Yi, D; Yu, P; Ramesh, R; Fiebig, M; Meier, D
2014-07-02
The relation between symmetry and functionality was pinpointed by Pierre Curie who stated that it is the symmetry breaking that creates physical properties. This fundamental principle is nowadays used for engineering heterostructures whose integral symmetry leads to exotic phenomena such as one-way transparency. For switching devices, however, such symmetry-related functionalities cannot be used because the symmetry in conventional heterostructures is immutable once the material has been synthesized. Here we demonstrate a concept for post-growth symmetry control in PbZr0.2Ti0.8O3 and BiFeO3-based heterostructures. A conducting oxide is sandwiched between two ferroelectric layers, and inversion symmetry is reversibly switched on or off by layer-selective electric-field poling. The generalization of our approach to other materials and symmetries is discussed. We thus establish ferroic trilayer structures as device components with reversibly tunable symmetry and demonstrate their use as light emitters that can be activated and deactivated by applying moderate electric voltages.
Search for primordial symmetry breakings in CMB
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke
2016-06-01
There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
Fake conformal symmetry in unimodular gravity
NASA Astrophysics Data System (ADS)
Oda, Ichiro
2016-08-01
We study Weyl symmetry (local conformal symmetry) in unimodular gravity. It is shown that the Noether currents for both Weyl symmetry and global scale symmetry vanish exactly as in conformally invariant scalar-tensor gravity. We clearly explain why in the class of conformally invariant gravitational theories, the Noether currents vanish by starting with conformally invariant scalar-tensor gravity. Moreover, we comment on both classical and quantum-mechanical equivalences in Einstein's general relativity, conformally invariant scalar-tensor gravity, and the Weyl-transverse gravity. Finally, we discuss the Weyl current in the conformally invariant scalar action and see that it is also vanishing.
A K3 sigma model with : symmetry
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.; Taormina, Anne; Volpato, Roberto; Wendland, Katrin
2014-02-01
The K3 sigma model based on the -orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra . By combining these different viewpoints we show that the = (4 , 4) preserving symmetries of this theory are described by the discrete symmetry group : . This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.
PREFACE: Symmetries in Science XV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2012-08-01
Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Rare Isotopes and Fundamental Symmetries
NASA Astrophysics Data System (ADS)
Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy
2009-01-01
Experiments searching for new interactions in nuclear beta decay / Klaus P. Jungmann -- The beta-neutrino correlation in sodium-21 and other nuclei / P. A. Vetter ... [et al.] -- Nuclear structure and fundamental symmetries/ B. Alex Brown -- Schiff moments and nuclear structure / J. Engel -- Superallowed nuclear beta decay: recent results and their impact on V[symbol] / J. C. Hardy and I. S. Towner -- New calculation of the isospin-symmetry breaking correlation to superallowed Fermi beta decay / I. S. Towner and J. C. Hardy -- Precise measurement of the [symbol]H to [symbol]He mass difference / D. E. Pinegar ... [et al.] -- Limits on scalar currents from the 0+ to 0+ decay of [symbol]Ar and isospin breaking in [symbol]Cl and [symbol]Cl / A. Garcia -- Nuclear constraints on the weak nucleon-nucleon interaction / W. C. Haxton -- Atomic PNC theory: current status and future prospects / M. S. Safronova -- Parity-violating nucleon-nucleon interactions: what can we learn from nuclear anapole moments? / B. Desplanques -- Proposed experiment for the measurement of the anapole moment in francium / A. Perez Galvan ... [et al.] -- The Radon-EDM experiment / Tim Chupp for the Radon-EDM collaboration -- The lead radius Eexperiment (PREX) and parity violating measurements of neutron densities / C. J. Horowitz -- Nuclear structure aspects of Schiff moment and search for collective enhancements / Naftali Auerbach and Vladimir Zelevinsky -- The interpretation of atomic electric dipole moments: Schiff theorem and its corrections / C. -P. Liu -- T-violation and the search for a permanent electric dipole moment of the mercury atom / M. D. Swallows ... [et al.] -- The new concept for FRIB and its potential for fundamental interactions studies / Guy Savard -- Collinear laser spectroscopy and polarized exotic nuclei at NSCL / K. Minamisono -- Environmental dependence of masses and coupling constants / M. Pospelov.
Neutrino properties and fundamental symmetries
Bowles, T.J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). There are two components to this work. The first is a development of a new detection scheme for neutrinos. The observed deficit of neutrinos from the Sun may be due to either a lack of understanding of physical processes in the Sun or may be due to neutrinos oscillating from one type to another during their transit from the Sun to the Earth. The Sudbury Neutrino Observatory (SNO) is designed to use a water Cerenkov detector employing one thousand tonnes of heavy water to resolve this question. The ability to distinguish muon and tau neutrinos from electron neutrinos is crucial in order to carry out a model-independent test of neutrino oscillations. We describe a developmental exploration of a novel technique to do this using {sup 3}He proportional counters. Such a method offers considerable advantages over the initially proposed method of using Cerenkov light from capture on NaCl in the SNO. The second component of this work is an exploration of optimal detector geometry for a time-reversal invariance experiment. The question of why time moves only in the forward direction is one of the most puzzling problems in modern physics. We know from particle physics measurements of the decay of kaons that there is a charge-parity symmetry that is violated in nature, implying time-reversal invariance violation. Yet, we do not understand the origin of the violation of this symmetry. To promote such an understanding, we are developing concepts and prototype apparatus for a new, highly sensitive technique to search for time-reversal-invariance violation in the beta decay of the free neutron. The optimized detector geometry is seven times more sensitive than that in previous experiments. 15 refs.
Flavor symmetries and fermion masses
Rasin, A.
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V{sub ub}/V{sub cb} = {radical}m{sub u}/m{sub c} and V{sub td}/V{sub ts} = {radical}m{sub d}/m{sub s}, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay {beta} {yields} s{gamma} constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tan{Beta}, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
NASA Astrophysics Data System (ADS)
Jin, Yan; Jia, Man; Lou, Sen-Yue
2012-12-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
Symmetry is less than meets the eye.
Apthorp, Deborah; Bell, Jason
2015-03-30
Symmetry is a ubiquitous feature in the visual environment and can be detected by a variety of species, ranging from insects through to humans [1,2]. Here we show it can also bias estimates of basic scene properties. Mirror (reflective) symmetry can be detected in as little as 50 ms, in both natural and artificial visual scenes, and even when embedded within cluttered backgrounds [1]. In terms of its biological relevance, symmetry is a key determinant in mate selection; the degree of symmetry in a face is positively associated with perceived healthiness and attractiveness ratings [3]. In short, symmetry processing mechanisms are an important part of the neural machinery of vision. We reveal that the importance of symmetry extends beyond the processing of shape and objects. Mirror symmetry biases our perception of scene content, with symmetrical patterns appearing to have fewer components than their asymmetric counterparts. This demonstrates an interaction between two fundamental dimensions of visual analysis: symmetry [1] and number [4]. We propose that this numerical underestimation results from a processing bias away from the redundant information within mirror symmetrical displays, extending existing theories regarding redundancy in visual analysis [5,6]. PMID:25829006
Symmetry in critical random Boolean network dynamics.
Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
Symmetry is less than meets the eye.
Apthorp, Deborah; Bell, Jason
2015-03-30
Symmetry is a ubiquitous feature in the visual environment and can be detected by a variety of species, ranging from insects through to humans [1,2]. Here we show it can also bias estimates of basic scene properties. Mirror (reflective) symmetry can be detected in as little as 50 ms, in both natural and artificial visual scenes, and even when embedded within cluttered backgrounds [1]. In terms of its biological relevance, symmetry is a key determinant in mate selection; the degree of symmetry in a face is positively associated with perceived healthiness and attractiveness ratings [3]. In short, symmetry processing mechanisms are an important part of the neural machinery of vision. We reveal that the importance of symmetry extends beyond the processing of shape and objects. Mirror symmetry biases our perception of scene content, with symmetrical patterns appearing to have fewer components than their asymmetric counterparts. This demonstrates an interaction between two fundamental dimensions of visual analysis: symmetry [1] and number [4]. We propose that this numerical underestimation results from a processing bias away from the redundant information within mirror symmetrical displays, extending existing theories regarding redundancy in visual analysis [5,6].
Order in the Universe: The Symmetry Principle.
ERIC Educational Resources Information Center
Foundation for Integrative Education, Inc., New York, NY.
The first two papers in this booklet provide a review of the pervasiveness of symmetry in nature and art, discussing how symmetry can be traced through every domain open to our understanding, from all aspects of nature to the special provinces of man; the checks and balances of government, the concept of equal justice, and the aesthetic ordering…
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
Hidden flavor symmetries of SO(10) GUT
NASA Astrophysics Data System (ADS)
Bajc, Borut; Smirnov, Alexei Yu.
2016-08-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2 ×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have U(1) 3 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.
Teaching symmetry in the introductory physics curriculum
Hill, C. T.; Lederman, L. M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
Complementarity and Symmetry in Family Therapy Communication.
ERIC Educational Resources Information Center
Heatherington, Laurie; Friedlander, Myrna L.
1990-01-01
Examined relational control communication patterns in systemic family therapy sessions. Results from 29 families showed significantly more complementarity than symmetry. Neither complementarity nor symmetry was predictive of family members' perceptions of the therapeutic alliance as measured by Couple and Family Therapy Alliance Scales. (Author/NB)
Symmetry in critical random Boolean network dynamics
NASA Astrophysics Data System (ADS)
Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
S4 flavored CP symmetry for neutrinos
NASA Astrophysics Data System (ADS)
Mohapatra, R. N.; Nishi, C. C.
2012-10-01
A generalized CP symmetry for leptons is presented where CP transformations are part of an S4 symmetry that connects different families. We study its implications for lepton mixings in a gauge model realization of the idea using a type II seesaw for neutrino masses. The model predicts maximal atmospheric mixing, nonzero θ13 and maximal Dirac phase δD=±(π)/(2).
Tests of gravitational symmetries with radio pulsars
NASA Astrophysics Data System (ADS)
Shao, LiJing; Wex, Norbert
2016-09-01
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
NASA Astrophysics Data System (ADS)
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation
Cicogna, G.; Pegoraro, F.; Ceccherini, F.
2010-10-15
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-10-01
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain "anomalous" SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H4(G ,U (1 )) , which also precisely labels the set of 3D SPT phases, with symmetry group G . An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U (1 )2 ] topological order with a reduced symmetry Z2×Z2⊂SO (3 ) , which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
Veesler, David; Ng, Thiam-Seng; Sendamarai, Anoop K; Eilers, Brian J; Lawrence, C Martin; Lok, Shee-Mei; Young, Mark J; Johnson, John E; Fu, Chi-yu
2013-04-01
Sulfolobus turreted icosahedral virus (STIV) was isolated in acidic hot springs where it infects the archeon Sulfolobus solfataricus. We determined the STIV structure using near-atomic resolution electron microscopy and X-ray crystallography allowing tracing of structural polypeptide chains and visualization of transmembrane proteins embedded in the viral membrane. We propose that the vertex complexes orchestrate virion assembly by coordinating interactions of the membrane and various protein components involved. STIV shares the same coat subunit and penton base protein folds as some eukaryotic and bacterial viruses, suggesting that they derive from a common ancestor predating the divergence of the three kingdoms of life. One architectural motif (β-jelly roll fold) forms virtually the entire capsid (distributed in three different gene products), indicating that a single ancestral protein module may have been at the origin of its evolution.
NASA Astrophysics Data System (ADS)
Bruhwiler, P. A.; Shen, Y.; Schnatterly, S. E.; Poon, S. J.
1987-11-01
We have measured the soft-x-ray emission spectra of icosahedral-phase (I) Al74Mn20Si6 and α-phase Al100Mn24Si14. In addition, we present measurements of elemental Al and Si and of the solid solution Al97Si3. All spectra represent emission from single-phase samples. α- and I-phase spectra are quite similar in overall structure. Mn is seen to play a central role in determining the local electronic structure associated with Al and Si in the ternary alloys. Analysis of the differences in the lower Al emission band of these alloys supports the idea that there is more than one Mn site in both phases. The electronic structure of Si in the two systems is anomalous. Comparisons of L-emission spectra of Al and Si in various alloys are made, and the validity of the equivalent core approximation is discussed.
Bakalova, S.; Gong, Y; Cobet, C; Esser, N; Zhang, Y; Edgar, J; Zhang, Y; Dudley, M; Kuball, M
2010-01-01
An experimental and theoretical study on the dielectric-response function of icosahedral B{sub 12}As{sub 2} in the spectral region between 1.24 and 9.8 eV is presented. Comprehensive experimental information on the energy band structure from the analysis of features in the optical dispersion was complemented by spin-orbit first-principles calculations. The lowest indirect band gap width is 3.2 eV; the two lowest direct interband transitions are at 3.46 and 3.9 eV. High-energy critical points are assigned to specific electron transitions in the Brillouin zone and their dimensionality was determined. The static dielectric constant of B{sub 12}As{sub 2} is uniaxially anisotropic with values of 7.84 and 9.02 for polarization perpendicular and parallel to the trigonal axis. Hole and electron effective masses are derived from the band dispersions.
NASA Astrophysics Data System (ADS)
Karbowiak, M.; Rudowicz, C.; Gnutek, P.
2011-06-01
Triclinic site symmetry presents considerable challenges in the studies of energy levels and crystal-field parameters (CFPs) for rare earth (RE) ions in crystals. Assignment of the spectral features to the irreducible representations of low symmetry point groups is difficult and may be unreliable. Fittings of large number of CFPs, even if the number of the available experimental energy levels is sufficient, often yield multiple solutions with relatively low and close rms deviations. These challenges call for better methods of fitting and analysis of CFPs. In this paper, we employ the ascent/descent in symmetry (ADS) method and three computational approaches: (i) a crystallographic data analysis program to identify approximated higher symmetry, (ii) the superposition model (SPM) analysis, and (iii) the pseudosymmetry axes method (PAM) for the combined coordination factors obtained using SPM. As a case study, the experimental CF splittings of Pr 3+ and Nd 3+ ions at triclinic C 1 sites in tellurium oxides RE 2Te 4O 11 are re-analyzed. Two alternative ADS chains C 1 ↔ C 2 ↔ D 2 and C 1 ↔ C s ↔ C 2v were independently obtained. For each approximation of the actual C 1 symmetry of the REO 8 polyhedron in RE 2Te 4O 11, the ligands' positions are determined and used in SPM to calculate CFP sets, which are used as starting for additional fittings. Comparative analysis of the fitted and calculated CFP sets enables assignment of appropriate axis system to the fitted CFP sets, thus avoiding the ambiguities occurring in previous ADS applications. The very good compatibility and consistency of the newly determined CFP sets indicate high reliability of both approaches. These CFP sets were used to simulate magnetic susceptibility data for polycrystalline samples of Pr 2Te 4O 11 and Nd 2Te 4O 11. Wider applications of the proposed procedures in optical spectroscopy studies of low symmetry systems may improve reliability of the CFP sets reported in literature.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
Natural quasicrystal with decagonal symmetry.
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S; Andronicos, Christopher L; Distler, Vadim V; Eddy, Michael P; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J; Steinhardt, William M; Yudovskaya, Marina; Steinhardt, Paul J
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Structural symmetry in evolutionary games
McAvoy, Alex; Hauert, Christoph
2015-01-01
In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time, for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be ‘evolutionarily equivalent’ in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term ‘homogeneous’ should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry. PMID:26423436
Symmetry and range limits in importance indices.
Seifan, Tal; Seifan, Merav
2015-10-01
Recently, Mingo has analyzed the properties of I imp, an importance index, and demonstrated that its range is not symmetrical. While agreeing with this comment, we believe that more light needs to be shed on the issue of symmetry in relation to such indices. Importance indices are calculated using three values: performance of the organism in the absence and in the presence of neighbors and maximum performance of the organism in ideal conditions. Because of this structure, importance indices can hardly ever achieve symmetry along the whole range of potential performances. We discuss the limitation of the symmetry range for different symmetry types and for both additive and multiplicative indices. We conclude that importance indices, as other interactions indices, are practical tools for interpreting ecological outcomes, especially while comparing between studies. Nevertheless, the current structure of importance indices prevents symmetry along their whole range. While the lack of "perfect" symmetry may call for the development of more sophisticated importance metrics, the current indices are still helpful for the understanding of biological systems and should not be discarded before better alternatives are well established. To prevent potential confusion, we suggest that ecologists present the relevant index symmetry range in addition to their results, thus minimizing the probability of misinterpretation. PMID:26668718
Symmetry and range limits in importance indices.
Seifan, Tal; Seifan, Merav
2015-10-01
Recently, Mingo has analyzed the properties of I imp, an importance index, and demonstrated that its range is not symmetrical. While agreeing with this comment, we believe that more light needs to be shed on the issue of symmetry in relation to such indices. Importance indices are calculated using three values: performance of the organism in the absence and in the presence of neighbors and maximum performance of the organism in ideal conditions. Because of this structure, importance indices can hardly ever achieve symmetry along the whole range of potential performances. We discuss the limitation of the symmetry range for different symmetry types and for both additive and multiplicative indices. We conclude that importance indices, as other interactions indices, are practical tools for interpreting ecological outcomes, especially while comparing between studies. Nevertheless, the current structure of importance indices prevents symmetry along their whole range. While the lack of "perfect" symmetry may call for the development of more sophisticated importance metrics, the current indices are still helpful for the understanding of biological systems and should not be discarded before better alternatives are well established. To prevent potential confusion, we suggest that ecologists present the relevant index symmetry range in addition to their results, thus minimizing the probability of misinterpretation.
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W.
2014-12-15
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n−1, e.g. a G(m,n−1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
Exploring Symmetry to Assist Alzheimer's Disease Diagnosis
NASA Astrophysics Data System (ADS)
Illán, I. A.; Górriz, J. M.; Ramírez, J.; Salas-Gonzalez, D.; López, M.; Padilla, P.; Chaves, R.; Segovia, F.; Puntonet, C. G.
Alzheimer's disease (AD) is a progressive neurodegenerative disorder first affecting memory functions and then gradually affecting all cognitive functions with behavioral impairments and eventually causing death. Functional brain imaging as Single-Photon Emission Computed Tomography (SPECT) is commonly used to guide the clinician's diagnosis. The essential left-right symmetry of human brains is shown to play a key role in coding and recognition. In the present work we explore the implications of this symmetry in AD diagnosis, showing that recognition may be enhanced when considering this latent symmetry.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Electromagnetic radiation under explicit symmetry breaking.
Sinha, Dhiraj; Amaratunga, Gehan A J
2015-04-10
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna.
Lie symmetry theorem of fractional nonholonomic systems
NASA Astrophysics Data System (ADS)
Sun, Yi; Chen, Ben-Yong; Fu, Jing-Li
2014-11-01
The Lie symmetry theorem of fractional nonholonomic systems in terms of combined fractional derivatives is established, and the fractional Lagrange equations are obtained by virtue of the d'Alembert—Lagrange principle with fractional derivatives. As the Lie symmetry theorem is based on the invariance of differential equations under infinitesimal transformations, by introducing the differential operator of infinitesimal generators, the determining equations are obtained. Furthermore, the limit equations, the additional restriction equations, the structural equations, and the conserved quantity of Lie symmetry are acquired. An example is presented to illustrate the application of results.
\\cal{PT} -symmetry in Rydberg atoms
NASA Astrophysics Data System (ADS)
Ziauddin; Chuang, You-Lin; Lee, Ray-Kuang
2016-07-01
We propose a scheme to realize parity-time ( {PT} )-symmetry in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. We show that Rydberg-dressed 87Rb atoms in a four-level inverted Y-type configuration is highly efficient to generate the refractive index for a probe field, with a symmetric (antisymmetric) profile spatially in the corresponding real (imaginary) part. Comparing with earlier investigations, the present scheme provides a versatile platform to control the system from {PT} -symmetry to non-PT -symmetry via different external parameters, i.e., coupling field detuning, probe field intensity and control field intensity.
Electromagnetic radiation under explicit symmetry breaking.
Sinha, Dhiraj; Amaratunga, Gehan A J
2015-04-10
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna. PMID:25910163
Electromagnetic Radiation under Explicit Symmetry Breaking
NASA Astrophysics Data System (ADS)
Sinha, Dhiraj; Amaratunga, Gehan A. J.
2015-04-01
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna.
The zonal satellite problem. III. Symmetries
NASA Astrophysics Data System (ADS)
Mioc, V.
The two-body problem associated with a force field described by a potential of the form U=sum_{k=1}nak/rk (r = distance between particles, ak = real parameters) is resumed from the only standpoint of symmetries. Such symmetries, expressed in Hamiltonian coordinates, or in standard polar coordinates, are recovered for McGehee-type coordinates of both collision-blow-up and infinity-blow-up kind. They form diffeomorphic commutative groups endowed with a Boolean structure. Expressed in Levi-Civita's coordinates, the problem exhibits a larger group of symmetries, also commutative and presenting a Boolean structure.
Symmetries in the Anisotropic Kepler Problem
NASA Astrophysics Data System (ADS)
Mioc, Vasile
The two-body problem associated to an anisotropic Newtonian-type potential function is being considered. We point out the complex symmetries that feature this problem. Such symmetries, expressed in standard polar coordinates, are recovered for McGee-type coordinates of both collision-blow-up kind and infinity-blow-up kind. They form isomorphic commutative groups endowed with an idempotent structure. Expressed in Levi-Civita's coordinates, the problem exhibits a larger group of symmetries, also commutative and endowed with an idempotent structure.
Personal recollections on chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Kobayashi, Makoto
2016-07-01
The author's work on the mass of pseudoscalar mesons is briefly reviewed. The emergence of the study of CP violation in the renormalizable gauge theory from consideration of chiral symmetry in the quark model is discussed.
Shift symmetry and inflation in supergravity
Brax, Philippe; Martin, Jerome
2005-07-15
We consider models of inflation in supergravity with a shift symmetry. We focus on models with one modulus and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the modulus, but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the {eta} problem is alleviated. Combining the KKLT mechanism for modulus stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we find models reminiscent of 'mutated hybrid inflation' where the inflationary trajectory is curved in the modulus-inflaton plane. We analyze the phenomenology of these models and stress their differences with both chaotic and hybrid inflation.
Symmetry and the Cosmic Microwave Background
NASA Technical Reports Server (NTRS)
Wollock, Edward J.
2012-01-01
A brief historical introduction to the development of observational astronomy and cosmology will be presented. The close relationship between the properties of light, symmetry, and our understanding the contents of our universe will be explored.
Dynamical symmetries in contemporary nuclear structure applications
NASA Astrophysics Data System (ADS)
Georgieva, A. I.; Ivanov, M. I.; Drenska, S. L.; Sviratcheva, K. D.; Draayer, J. P.
2010-12-01
In terms of group theory—the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of group-subgroup structures that define the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems. We review two types of applications of dynamical symmetries in contemporary theoretical nuclear structure physics: first for a classification of the many-body systems under consideration, with respect to an important characteristic of their behavior; and second for the creation of exactly solvable algebraic models that describe specific aspects of this behavior. This is illustrated with the boson and fermion realizations of symplectic structures. In the first case with an application of the sp(4, R) classification scheme of even-even nuclei within the major nuclear shells and next with of the sp(4) microscopic model for the description of isovector pairing correlations.
Modelling Symmetry Classes 233 and 432.
ERIC Educational Resources Information Center
Dutch, Steven I.
1986-01-01
Offers instructions and geometrical data for constructing solids of the enantiomorphous symmetry classes 233 and 432. Provides background information for each class and highlights symmetrical relationships and construction patterns. (ML)
Matrix Models, Emergent Spacetime and Symmetry Breaking
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2009-12-15
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
Spatial Symmetries of the Local Densities
Rohozinski, S.; Dobaczewski, J.; Nazarewicz, Witold
2010-01-01
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Breaking of Gauge Symmetry: A Geometrical View.
ERIC Educational Resources Information Center
Moriyasu, K.
1980-01-01
Presents a simple introduction to the fundamental physical ideas involved in the breaking of local gauge symmetry. The purpose of this article is to show how these ideas can be understood independently of any particular application. (Author/HM)
Soliton surfaces in the generalized symmetry approach
NASA Astrophysics Data System (ADS)
Grundland, A. M.
2016-09-01
We investigate some features of generalized symmetries of integrable systems aiming to obtain the Fokas-Gel'fand formula for the immersion of two-dimensional soliton surfaces in Lie algebras. We show that if there exists a common symmetry of the zero-curvature representation of an integrable partial differential equation and its linear spectral problem, then the Fokas-Gel'fand immersion formula is applicable in its original form. In the general case, we show that when the symmetry of the zero-curvature representation is not a symmetry of its linear spectral problem, then the immersion function of the two-dimensional surface is determined by an extended formula involving additional terms in the expression for the tangent vectors. We illustrate these results with examples including the elliptic ordinary differential equation and the C P N-1 sigma-model equation.
Symmetry breaking of quasihelical stellarator equilibria
Weening, R.H. )
1993-04-01
A mean-field Ohm's law is used to determine the effects of the bootstrap current on quasihelically symmetric stellarator equilibria. The Ohm's law leads to the conclusion that the effects of the bootstrap current break the quasihelical stellarator symmetry at second order in an inverse aspect ratio expansion of the magnetic field strength. The level of symmetry breaking suggests that good approximations to quasihelical stellarator fusion reactors may not be attainable.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
Density dependence of nuclear symmetry energy
NASA Astrophysics Data System (ADS)
Behera, B.; Routray, T. R.; Tripathy, S. K.
2016-10-01
High density behavior of nuclear symmetry energy is studied on the basis of the stiffest density dependence of asymmetric contribution to energy per nucleon in charge neutral n + p + e + μ matter under beta equilibrium. The density dependence of nuclear symmetry energy obtained in this way is neither very stiff nor soft at high densities and is found to be in conformity with recent observations of neutron stars.
Squeezing lepton pairs out of broken symmetries
NASA Astrophysics Data System (ADS)
Dutt-Mazumder, A. K.; Gale, C.; Majumder, A.; Teodorescu, O.
2002-04-01
We discuss two possible signatures of symmetry breaking that can appear in dilepton spectra, as measured in relativistic heavy ion collisions. The first involves scalar-vector meson mixing and is related to the breaking of Lorentz symmetry by a hot medium. The second is related to the breaking of Furry's theorem by a charged quark-gluon plasma. Those signals will be accessible to upcoming measurements to be performed at the GSI, RHIC, and the LHC. .
Symmetry calculation for molecules and transition states.
Vandewiele, Nick M; Van de Vijver, Ruben; Van Geem, Kevin M; Reyniers, Marie-Françoise; Marin, Guy B
2015-01-30
The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three-dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label-stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules.
Fluency Expresses Implicit Knowledge of Tonal Symmetry.
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences.
A new paradigm for animal symmetry.
Holló, Gábor
2015-12-01
My aim in this article is to soften certain rigid concepts concerning the radial and bilateral symmetry of the animal body plan, and to offer a more flexible framework of thinking for them, based on recent understandings of how morphogenesis is regulated by the mosaically acting gene regulatory networks. Based on general principles of the genetic regulation of morphogenesis, it can be seen that the difference between the symmetry of the whole body and that of minor anatomical structures is only a question of a diverse timing during development. I propose that the animal genome, as such, is capable of expressing both radial and bilateral symmetries, and deploys them according to the functional requirements which must be satisfied by both the anatomical structure and body as a whole. Although it may seem paradoxical, this flexible view of symmetry, together with the idea that symmetry is strongly determined by function, bolsters the concept that the presence of the two main symmetries in the animal world is not due to chance: they are necessary biological patterns emerging in evolution.
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
Symmetries and elasticity of nematic gels
NASA Astrophysics Data System (ADS)
Lubensky, T. C.; Mukhopadhyay, Ranjan; Radzihovsky, Leo; Xing, Xiangjun
2002-07-01
A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials.
Symmetries and elasticity of nematic gels.
Lubensky, T C; Mukhopadhyay, Ranjan; Radzihovsky, Leo; Xing, Xiangjun
2002-07-01
A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these materials. PMID:12241370
Fluency Expresses Implicit Knowledge of Tonal Symmetry
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences. PMID:26869960
Exploring symmetry in near-vacuum hohlraums
NASA Astrophysics Data System (ADS)
Berzak Hopkins, L.; Le Pape, S.; Divol, L.; Meezan, N.; MacKinnon, A.; Ho, D. D.; Jones, O.; Khan, S.; Ma, T.; Milovich, J.; Pak, A.; Ross, J. S.; Thomas, C.; Turnbull, D.; Amendt, P.; Wilks, S.; Zylstra, A.; Rinderknecht, H.; Sio, H.; Petrasso, R.
2015-11-01
Recent experiments with near-vacuum hohlraums, which utilize a minimal but non-zero helium fill, have demonstrated performance improvements relative to conventional gas-filled (0.96 - 1.6 mg/cc helium) hohlraums: minimal backscatter, reduced capsule drive degradation, and minimal suprathermal electron generation. Because this is a low laser-plasma interaction platform, implosion symmetry is controlled via pulse-shaping adjustments to laser power balance. Extending this platform to high-yield designs with high-density carbon capsules requires achieving adequate symmetry control throughout the pulse. In simulations, laser propagation is degraded suddenly by hohlraum wall expansion interacting with ablated capsule material. Nominal radiation-hydrodynamics simulations have not yet proven predictive on symmetry of the final hotspot, and experiments show more prolate symmetry than preshot calculations. Recent efforts have focused on understanding the discrepancy between simulated and measured symmetry and on alternate designs for symmetry control through varying cone fraction, trade-offs between laser power and energy, and modifications to case-to-capsule ratio. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.
Neutrino mass, mixing and discrete symmetries
NASA Astrophysics Data System (ADS)
Smirnov, Alexei Y.
2013-07-01
Status of the discrete symmetry approach to explanation of the lepton masses and mixing is summarized in view of recent experimental results, in particular, establishing relatively large 1-3 mixing. The lepton mixing can originate from breaking of discrete flavor symmetry Gf to different residual symmetries Gl and Gv in the charged lepton and neutrino sectors. In this framework the symmetry group condition has been derived which allows to get relations between the lepton mixing elements immediately without explicit model building. The condition has been applied to different residual neutrino symmetries Gv. For generic (mass independent) Gv = Z2 the condition leads to two relations between the mixing parameters and fixes one column of the mixing matrix. In the case of Gv = Z2 × Z2 the condition fixes the mixing matrix completely. The non-generic (mass spectrum dependent) Gv lead to relations which include mixing angles, neutrino masses and Majorana phases. The symmetries Gl, Gv, Gf are identified which lead to the experimentally observed values of the mixing angles and allow to predict the CP phase.
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals
Mei, Jun; Chen, Zeguo; Wu, Ying
2016-01-01
We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound. PMID:27587311
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals.
Mei, Jun; Chen, Zeguo; Wu, Ying
2016-01-01
We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound. PMID:27587311
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals
NASA Astrophysics Data System (ADS)
Mei, Jun; Chen, Zeguo; Wu, Ying
2016-09-01
We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound.
Perception of Mirror Symmetry in Autism Spectrum Disorders
ERIC Educational Resources Information Center
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…
Residual symmetries of the gravitational field
NASA Astrophysics Data System (ADS)
Ayón-Beato, Eloy; Velázquez-Rodríguez, Gerardo
2016-02-01
We develop a geometric criterion that unambiguously characterizes the residual symmetries of a gravitational Ansatz. It also provides a systematic and effective computational procedure for finding all the residual symmetries of any gravitational Ansatz. We apply the criterion to several examples starting with the Collinson Ansatz for circular stationary axisymmetric spacetimes. We reproduce the residual symmetries already known for this Ansatz including their conformal symmetry, for which we identify the corresponding infinite generators spanning the two related copies of the Witt algebra. We also consider the noncircular generalization of this Ansatz and show how the noncircular contributions on the one hand break the conformal invariance and on the other hand enhance the standard translation symmetries of the circular Killing vectors to supertranslations depending on the direction along which the circularity is lost. As another application of the method, the well-known relation defining conjugate gravitational potentials introduced by Chandrasekhar, which makes possible the derivation of the Kerr black hole from a trivial solution of the Ernst equations, is deduced as a special point of the general residual symmetry of the Papapetrou Ansatz. In this derivation we emphasize how the election of Weyl coordinates, which determines the Papapetrou Ansatz, breaks also the conformal freedom of the stationary axisymmetric spacetimes. Additionally, we study AdS waves for any dimension generalizing the residual symmetries already known for lower dimensions and exhibiting a very complex infinite-dimensional Lie algebra containing three families: two of them span the semidirect sum of the Witt algebra and scalar supertranslations and the third generates vector supertranslations. Independently of this complexity we manage to comprehend the true meaning of the infinite connected group as the precise diffeomorphisms subgroup allowing to locally deform the AdS background into Ad
Relativistic symmetries in nuclear single-particle spectra
NASA Astrophysics Data System (ADS)
Guo, Jian-You; Liang, Hao Zhao; Meng, Jie; Zhou, Shan-Gui
Symmetry is a fundamental concept in quantum physics. The quasi-degeneracy between single-particle orbitals (n, l, j = l + 1/2) and (n -1, l + 2, j = l + 3/2) indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry. Since the pseudospin symmetry was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry for anti-nucleons, and many new concepts have been introduced. In this Chapter, we will illustrate the schematic picture of spin and pseudospin symmetries, derive the basic formalism, highlight the recent progress from several different aspects, and discuss selected open issues in this topic.
Guo, Yiming; Stacey, Timothy E; Fredrickson, Daniel C
2014-05-19
The crystal structures of intermetallic phases offer a wealth of geometrical features (helices, multishelled clusters, and host-guest motifs) whose formation has yet to be explained or predicted by chemical theory. A recently developed extension of the acid-base concept to metallic systems, the μ3-acidity model, provides an avenue for developing this understanding for intermetallics formed from transition metals. In this Article, we illustrate how this approach can be used to understand one of the most striking geometrical entities to emerge in intermetallic chemistry, the Mackay cluster of icosahedral quasicrystals. We present μ3-acidity analyses, based on DFT-calibrated Hückel calculations, for a series of Sc-Ir intermetallics: ScIr (CsCl-type), Sc2Ir (Ti2Ni-type), Sc11Ir4, and the Mackay cluster containing phases Sc57Ir13 and Sc44Ir7. We begin by illustrating that a μ3-acidity model correctly predicts that each of these phases is stable relative to disproportionation into their neighboring compounds when a common set of Hückel parameters and d-orbital occupancies is used. Next, we explain these results by developing a relationship between the distance distribution of homoatomic contacts within an atom's coordination sphere and the μ3-neutralization it experiences. For a given average homoatomic distance, the role of heteroatomic contacts is higher when the distribution of homoatomic contacts is narrower. This effect is key to the strength of the acid-base neutralization of the Sc-rich phases, where the Sc atoms find a scarcity of Ir atoms from which to obtain neutralization. Under these circumstances, Sc-Ir contacts should be maximized, whereas the number and distance variations of the Sc-Sc contacts should be minimized. These expectations are borne out by the observed crystal structures. In particular, the Mackay clusters of Sc57Ir13 and Sc44Ir7, in which a central Ir atom is icosahedrally coordinated by a pentagonal dodecahedral array of face-sharing Sc
Symmetry in social exchange and health
NASA Astrophysics Data System (ADS)
Siegrist, Johannes
2005-10-01
Symmetry is a relevant concept in sociological theories of exchange. It is rooted in the evolutionary old norm of social reciprocity and is particularly important in social contracts. Symmetry breaking through violation of the norm of reciprocity generates strain in micro-social systems and, above all, in victims of non-symmetric exchange. In this contribution, adverse healthconsequences of symmetry breaking in contractual social exchange are analysed, with a main focus on the employment contract. Scientific evidence is derived from prospective epidemiological studies testing the model of effort-reward imbalance at work. Overall, a twofold elevated risk of incident disease is observed in employed men and women who are exposed to non-symmetric exchange. Health risks include coronary heart disease, depression and alcohol dependence, among others. Preliminary results suggest similar effects on health produced by symmetry breaking in other types of social relationships (e.g. partnership, parental roles). These findings underline the importance of symmetry in contractual social exchange for health and well-being.
Graph fibrations and symmetries of network dynamics
NASA Astrophysics Data System (ADS)
Nijholt, Eddie; Rink, Bob; Sanders, Jan
2016-11-01
Dynamical systems with a network structure can display remarkable phenomena such as synchronisation and anomalous synchrony breaking. A methodology for classifying patterns of synchrony in networks was developed by Golubitsky and Stewart. They showed that the robustly synchronous dynamics of a network is determined by its quotient networks. This result was recently reformulated by DeVille and Lerman, who pointed out that the reduction from a network to a quotient is an example of a graph fibration. The current paper exploits this observation and demonstrates the importance of self-fibrations of network graphs. Self-fibrations give rise to symmetries in the dynamics of a network. We show that every network admits a lift with a semigroup or semigroupoid of self-fibrations. The resulting symmetries impact the global dynamics of the network and can therefore be used to explain and predict generic scenarios for synchrony breaking. Also, when the network has a trivial symmetry groupoid, then every robust synchrony in the lift is determined by symmetry. We finish this paper with a discussion of networks with interior symmetries and nonhomogeneous networks.
Symmetries in proteins: A knot theory approach
NASA Astrophysics Data System (ADS)
Chen, Shi-Jie; Dill, Ken A.
1996-04-01
Whereas the symmetries of small molecules are described by the methods of group theory, there is no corresponding way to describe the complex symmetries in proteins. We develop a quantitative method to define and classify symmetries in compact polymers, based on the mathematical theory of graphs and knots. We represent different chain folds by their ``polymer graphs,'' equivalent to contact maps. We transform those graphs into mathematical knots to give a parsing of different possible chain folds into conformational taxonomies. We use Alexander-Conway knot polynomials to characterize the knots. We find that different protein structures with the same tertiary fold, e.g., a βαβ motif with different lengths of α helix and β sheet, can be described in terms of the different powers of the propagation matrices of the knot polynomial. This identifies a fundamental type of topological length invariance in proteins, ``elongatable'' symmetries. For example, ``helix,'' ``sheet,'' ``helix-turn-helix,'' and other secondary, supersecondary, and tertiary structures define structures of any chain length. Possibly the nine superfolds identified by Thornton et al. have elongatable symmetries.
Reflections on the concept of symmetry
NASA Astrophysics Data System (ADS)
Lorenz, Kuno
2005-10-01
The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, "being symmetric" in general usage is synonymous with "being harmonious", and in technical usage, as in Euclid's Elements, it is synonymous with "commensurable". Due to the second meaning, which is close to the etymology of συ´μμɛτρoς, "with measure" has likewise to be read as "being [in] rational [ratios]" and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.
Weyl-gauge symmetry of graphene
Iorio, Alfredo
2011-05-15
Research Highlights: > Graphene action's Weyl symmetry identifies shapes for which the DOS is invariant. > Electrons on graphene might experience a general-relativistic-like spacetime. > Rich mathematical structures, such as the Liouville's equation, naturally arise. - Abstract: The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.
The symmetries of the Carroll superparticle
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric; Gomis, Joaquim; Parra, Lorena
2016-05-01
Motivated by recent applications of Carroll symmetries we investigate, using the method of nonlinear realizations, the geometry of flat and curved (AdS) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case. In the bosonic case we find that the Carroll particle possesses an infinite-dimensional symmetry which only in the flat case includes dilatations. The duality between the Bargmann and Carroll algebra, relevant for the flat case, does not extend to the curved case. In the supersymmetric case we study the dynamics of the { N }=1 AdS Carroll superparticle. Only in the flat limit we find that the action is invariant under an infinite-dimensional symmetry that includes a supersymmetric extension of the Lifshitz Carroll algebra with dynamical exponent z = 0. We also discuss in the flat case the extension to { N }=2 supersymmetry and show that the flat { N }=2 superparticle is equivalent to the (non-moving) { N }=1 superparticle and that therefore it is not BPS unlike its Galilei counterpart. This is due to the fact that in this case kappa-symmetry eliminates the linearized supersymmetry. In an appendix we discuss the { N }=2 curved case in three-dimensions only and show that there are two { N }=2 theories that are physically different.
Breaking the Symmetry in Molecular Nanorings
2016-01-01
Because of their unique electronic properties, cyclic molecular structures ranging from benzene to natural light-harvesting complexes have received much attention. Rigid π-conjugated templated porphyrin nanorings serve as excellent model systems here because they possess well-defined structures that can readily be controlled and because they support highly delocalized excitations. In this study, we have deliberately modified a series of six-porphyrin nanorings to examine the impact of lowering the rotational symmetry on their photophysical properties. We reveal that as symmetry distortions increase in severity along the series of structures, spectral changes and an enhancement of radiative emission strength occur, which derive from a transfer of oscillator strength into the lowest (k = 0) state. We find that concomitantly, the degeneracy of the dipole-allowed first excited (k = ±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906
Facial aesthetics: babies prefer attractiveness to symmetry.
Samuels, C A; Butterworth, G; Roberts, T; Graupner, L; Hole, G
1994-01-01
The visual preferences of human infants for faces that varied in their attractiveness and in their symmetry about the midline were explored. The aim was to establish whether infants' visual preference for attractive faces may be mediated by the vertical symmetry of the face. Chimeric faces, made from photographs of attractive and unattractive female faces, were produced by computer graphics. Babies looked longer at normal and at chimeric attractive faces than at normal and at chimeric unattractive faces. There were no developmental differences between the younger and older infants: all preferred to look at the attractive faces. Infants as young as 4 months showed similarity with adults in the 'aesthetic perception' of attractiveness and this preference was not based on the vertical symmetry of the face. PMID:7845772
Facial aesthetics: babies prefer attractiveness to symmetry.
Samuels, Curtis A; Butterworth, George; Roberts, Tony; Graupner, Lida; Hole, Graham
2013-01-01
The visual preferences of human infants for faces that varied in their attractiveness and in their symmetry about the midline were explored. The aim was to establish whether infants' visual preference for attractive faces may be mediated by the vertical symmetry of the face. Chimeric faces, made from photographs of attractive and unattractive female faces, were produced by computer graphics. Babies looked longer at normal and at chimeric attractive faces than at normal and at chimeric unattractive faces. There were no developmental differences between the younger and older infants: all preferred to look at the attractive faces. Infants as young as 4 months showed similarity with adults in the 'aesthetic perception' of attractiveness and this preference was not based on the vertical symmetry of the face. PMID:24601036
Approximate flavor symmetries in the lepton sector
Rasin, A. ); Silva, J.P. )
1994-01-01
Approximate flavor symmetries in the quark sector have been used as a handle on physics beyond the standard model. Because of the great interest in neutrino masses and mixings and the wealth of existing and proposed neutrino experiments it is important to extend this analysis to the leptonic sector. We show that in the seesaw mechanism the neutrino masses and mixing angles do not depend on the details of the right-handed neutrino flavor symmetry breaking, and are related by a simple formula. We propose several [ital Ansa]$[ital uml]---[ital tze] which relate different flavor symmetry-breaking parameters and find that the MSW solution to the solar neutrino problem is always easily fit. Further, the [nu][sub [mu]-][nu][sub [tau
Workshop on electroweak symmetry breaking: proceedings
Hinchliffe, I.
1984-10-01
A theoretical workshop on electroweak symmetry breaking at the Superconducting Supercollider was held at Lawrence Berkeley Laboratory, June 4-22, 1984. The purpose of the workshop was to focus theoretical attention on the ways in which experimentation at the SSC could reveal manifestations of the phenomenon responsible for electroweak symmetry breaking. This issue represents, at present, the most compelling scientific argument for the need to explore the energy region to be made accessible by the SSC, and a major aim of the workshop was to involve a broad cross section of particle theorists in the ongoing process of sharpening the requirements for both accelerator and detector design that will ensure detection and identification of meaningful signals, whatever form the electroweak symmetry breaking phenomenon should actually take. Separate entries were prepared for the data base for the papers presented.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Facial aesthetics: babies prefer attractiveness to symmetry.
Samuels, Curtis A; Butterworth, George; Roberts, Tony; Graupner, Lida; Hole, Graham
2013-01-01
The visual preferences of human infants for faces that varied in their attractiveness and in their symmetry about the midline were explored. The aim was to establish whether infants' visual preference for attractive faces may be mediated by the vertical symmetry of the face. Chimeric faces, made from photographs of attractive and unattractive female faces, were produced by computer graphics. Babies looked longer at normal and at chimeric attractive faces than at normal and at chimeric unattractive faces. There were no developmental differences between the younger and older infants: all preferred to look at the attractive faces. Infants as young as 4 months showed similarity with adults in the 'aesthetic perception' of attractiveness and this preference was not based on the vertical symmetry of the face.
Facial symmetry assessment based on geometric features
NASA Astrophysics Data System (ADS)
Xu, Guoping; Cao, Hanqiang
2015-12-01
Face image symmetry is an important factor affecting the accuracy of automatic face recognition. Selecting high symmetrical face image could improve the performance of the recognition. In this paper, we proposed a novel facial symmetry evaluation scheme based on geometric features, including centroid, singular value, in-plane rotation angle of face and the structural similarity index (SSIM). First, we calculate the value of the four features according to the corresponding formula. Then, we use fuzzy logic algorithm to integrate the value of the four features into a single number which represents the facial symmetry. The proposed method is efficient and can adapt to different recognition methods. Experimental results demonstrate its effectiveness in improving the robustness of face detection and recognition.
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Topological phases with generalized global symmetries
NASA Astrophysics Data System (ADS)
Yoshida, Beni
2016-04-01
We present simple lattice realizations of symmetry-protected topological phases with q -form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d +1 ) -colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Elasticity and Broken Symmetry in Nematic Elastomers
NASA Astrophysics Data System (ADS)
Mukhopadhyay, Ranjan; Lubensky, T. C.; Xing, Xiangjun; Radzihovsky, Leo
2002-03-01
In nematic elastomers, the coupling between the internal liquid crystalline degrees of freedom and elastic strains lead to novel thermodynamic and mechanical behavior. Their remarkable properties make them candidates for a number of applications including artificial muscles and actuators. Other than their technological importance, their behavior highlights a major theme of physics: the interplay between broken symmetries and long-wavelength elasticity and hydrodynamics. In this talk my primary focus will be to show how the elastic "softness" and the pronounced nonlinear stress-strain relations in these materials arise as a consequence of broken rotational symmetry. We will reproduce these properties using simple models in a way that highlights this interplay between broken rotational symmetry and elasticity.
Preserving Symmetry in Preconditioned Krylov Subspace Methods
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Chow, E.; Saad, Y.; Yeung, M. C.
1996-01-01
We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M. In the symmetric case, one can recover symmetry by using M-inner products in the conjugate gradient (CG) algorithm. This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the new algorithms are mathematically equivalent to split preconditioning, but do not require M to be factored. Better robustness in a specific sense can also be observed. When combined with truncated versions of iterative methods, tests show that this is more effective than the common practice of forfeiting near-symmetry altogether.
Collective neutrino oscillations and spontaneous symmetry breaking
NASA Astrophysics Data System (ADS)
Duan, Huaiyu
2015-08-01
Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem to have "reset" this progress by showing that these models may not be compatible with collective neutrino oscillations because the latter can break the symmetries spontaneously if they are not imposed. We review some of the key concepts of collective neutrino oscillations by using a few simple toy models. We also elucidate the breaking of spatial and directional symmetries in these models because of collective oscillations.
SU(3) breaking and hidden local symmetry
Benayoun, M.; OConnell, H.B.
1998-10-01
We study the various existing implementations of SU(3) breaking in the hidden local symmetry model for the low energy hadronic sector following a mechanism originally proposed by Bando, Kugo and Yamawaki (BKY). We pay particular attention to Hermiticity and current conservation. Following this, we present a new method for including symmetry breaking effects which preserves the BKY mass relation among vector mesons. Symmetry breaking (SB) necessarily requires a transformation of the pseudoscalar fields, which, following BKY, we refer to as field renormalization. We examine the consequences of propagating this through all Lagrangian terms including the anomalous ones. We thus explore the consequences of these various SB schemes for both charged and neutral pseudoscalar decay constants as measured in weak and anomalous decays respectively. {copyright} {ital 1998} {ital The American Physical Society}
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which - apart from their rather specific expressions in terms of w(z) - are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Viable axion from gauged flavor symmetries
Berenstein, David; Perkins, Erik
2010-11-15
We consider a string-inspired nonsupersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz (GS) mechanism to cancel mixed anomalies. The additional required scalars provide Stueckelberg masses for the Z{sup '} particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field {phi} to generate Froggatt-Nielsen mass terms for light particles, giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energies. The associated pseudo-Goldstone mode is the phase of the {phi} scalar field, and it becomes the dominant contribution to the physical axion. An effective field theory analysis that includes neutrino masses gives a prediction for the axion decay constant. We find a simple model where the axion decay constant is in the center of the allowed window.
Hidden conformal symmetry and quasinormal modes
NASA Astrophysics Data System (ADS)
Chen, Bin; Long, Jiang
2010-12-01
We provide an algebraic way to calculate the quasinormal modes of a black hole, which possesses a hidden conformal symmetry. We construct an infinite tower of quasinormal modes from the highest-weight mode, in a simple and elegant way. For the scalar, the hidden conformal symmetry manifests itself in the fact that the scalar Laplacian could be rewritten in terms of the SL(2,R) quadratic Casimir. For the vector and the tensor, the hidden conformal symmetry acts on them through Lie derivatives. We show that for three-dimensional black holes, with an appropriate combination of the components, the radial equations of the vector and the tensor could be written in terms of the Lie-induced quadratic Casimir. This makes the algebraic construction of the quasinormal modes feasible. Our results are in good agreement with the previous study.
New Algorithms For Automated Symmetry Recognition
NASA Astrophysics Data System (ADS)
Paul, Jody; Kilgore, Tammy Elaine; Klinger, Allen
1988-02-01
In this paper we present new methods for computer-based symmetry identification that combine elements of group theory and pattern recognition. Detection of symmetry has diverse applications including: the reduction of image data to a manageable subset with minimal information loss, the interpretation of sensor data,1 such as the x-ray diffraction patterns which sparked the recent discovery of a new "quasicrystal" phase of solid matter,2 and music analysis and composition.3,4,5 Our algorithms are expressed as parallel operations on the data using the matrix representation and manipulation features of the APL programming language. We demonstrate the operation of programs that characterize symmetric and nearly-symmetric patterns by determining the degree of invariance with respect to candidate symmetry transformations. The results are completely general; they may be applied to pattern data of arbitrary dimension and from any source.
Law-Hine, Didier; Zeghal, Mehdi; Bressanelli, Stéphane; Constantin, Doru; Tresset, Guillaume
2016-08-10
Viruses are astonishing edifices in which hundreds of molecular building blocks fit into the final structure with pinpoint accuracy. We established a robust kinetic model accounting for the in vitro self-assembly of a capsid shell derived from an icosahedral plant virus by using time-resolved small-angle X-ray scattering (TR-SAXS) data at high spatiotemporal resolution. By implementing an analytical model of a spherical patch into a global fitting algorithm, we managed to identify a major intermediate species along the self-assembly pathway. With a series of data collected at different protein concentrations, we showed that free dimers self-assembled into a capsid through an intermediate resembling a half-capsid. The typical lifetime of the intermediate was a few seconds and yet the presence of so large an oligomer was not reported before. The progress in instrumental detection along with the development of powerful algorithms for data processing contribute to shedding light on nonequilibrium processes in highly complex systems such as viruses. PMID:27444997
Liu, Xiangan; Jiang, Wen; Jakana, Joanita; Chiu, Wah
2007-01-01
Accurately determining a cryoEM particle’s alignment parameters is crucial to high resolution single particle 3-D reconstruction. We developed Multi-Path Simulated Annealing, a Monte Carlo type of optimization algorithm, for globally aligning the center and orientation of a particle simultaneously. A consistency criterion was developed to ensure the alignment parameters are correct and to remove some bad particles from a large pool of images of icosahedral particles. Without using any a priori model, this procedure is able to reconstruct a structure from a random initial model. Combining the procedure above with a new empirical double threshold particle selection method, we are able to pick tens of best quality particles to reconstruct a subnanometer resolution map from scratch. Using the best 62 particles of rice dwarf virus, the reconstruction reached 9.6Å resolution at which 4 helices of the P3A subunit of RDV are resolved. Furthermore, with the 284 best particles, the reconstruction is improved to 7.9Å resolution, and 21 of 22 helices and 6 of 7 beta sheets are resolved. PMID:17698370
Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Kaneko, Y; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M
2013-03-20
A comparison of periodic approximants and their quasicrystalline counterparts offers the opportunity to better understand the structure, physical properties and stabilizing mechanisms of these complex phases. We present a combined experimental and molecular dynamics study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare it to recently published results obtained for the cubic 1/1-approximant Zn(6)Sc. Both phases, quasicrystal and approximant, are built up from large atomic clusters which contain a tetrahedral shell at the cluster centre and are packed either quasiperiodically or on a bcc lattice. Using quasielastic neutron scattering and atomic scale simulations, we show that in the quasicrystal the tetrahedra display a dynamics similar to that observed in the 1/1-approximant: the tetrahedra behave as a 'single molecule' and reorient dynamically on a timescale of the order of a few ps. The tetrahedra reorientation is accompanied by a large distortion of the surrounding cluster shells which provide a unique dynamical flexibility to the quasicrystal. However, whereas in the 1/1-approximant the tetrahedron reorientation is observed down to T(c) = 160 K, where a phase transition takes place, in the quasicrystal the tetrahedron dynamics is gradually freezing from 550 to 300 K, similarly to a glassy system.
NASA Astrophysics Data System (ADS)
Thuburn, J.; Cotter, C. J.; Dubos, T.
2014-05-01
A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
NASA Astrophysics Data System (ADS)
Thuburn, J.; Cotter, C. J.; Dubos, T.
2013-12-01
A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank-Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal-icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.
Jakse, N.; Pasturel, A.
2015-08-28
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al{sub 80}Ni{sub 20} alloy upon cooling. Our results evidence a huge increase of local icosahedral ordering (ISRO) in the undercooled regime which is more developed around Ni than Al atoms. We show that ISRO has a strong impact on self-diffusion coefficients of both species and is at the origin of their crossover from Arrhenius to non-Arrhenius behavior around a crossover temperature T{sub X} = 1000 K, located in the undercooled region. We also clearly identify that this temperature corresponds to the development of dynamic heterogeneities and to the breakdown of the Stokes-Einstein relation. At temperatures below this crossover, we find that the behavior of the diffusion and relaxation dynamics is mostly incompatible with predictions of the mode-coupling theory. Finally, an analysis of the van Hove function indicates that the crossover temperature T{sub X} marks the onset of a change in the diffusion mechanism from a normal flow to an activated process with hopping. From these results, the glass-forming ability of the alloy is discussed.
Shukla, A. K.; Dhaka, R. S.; Biswas, C.; Banik, S.; Barman, S. R.; Horn, K.; Ebert, Ph.; Urban, K.
2006-02-01
We report x-ray photoelectron spectroscopy (XPS) study of Na and K adlayers on icosahedral Al{sub 70.5}Pd{sub 21}Mn{sub 8.5} (i-Al-Pd-Mn) quasicrystal. The Na 1s core-level exhibits a continuous linear shift of 0.8 eV towards lower binding energies (BE) with increasing coverage up to one monolayer (ML) saturation coverage. In the case of K/i-Al-Pd-Mn, a similar linear shift in the K 2p spectra towards lower BE is observed. In both cases, the plasmon related loss features are observed only above 1 ML. The substrate core-level peaks, such as Al 2p, do not exhibit any shift with the adlayer deposition up to the highest coverage. Based on these experimental observations and previous studies of alkali metal growth on metals, we conclude that below 1 ML, both Na and K form a dispersed phase on i-Al-Pd-Mn and there is hardly any charge transfer to the substrate. The variation of the adlayer and substrate core-level intensities with coverage indicates layer by layer growth.
Huang, Huogen; Chen, Liang
2015-08-17
Ti-Zr-Ni quasicrystals have been demonstrated to store a large number of hydrogen atoms, which implies strong potential application in hydrogen energy field for them. However, the desorption of hydrogen atoms in the quasicrystals is quite difficult, with the indication of high desorption temperature and slow desorption rate. The shortage limits their use in the field to a large extent. But this kind of quasicrystals might be used in nuclear fusion energy field, because tritium as a coral fuel for nuclear fusion needs tight storage. However, equilibrium pressure at room temperature of Ti-Zr-Ni quasicrystals, important for their application in fusion energy field, has not been clear yet. In this work, we designed a gas-solid reaction system with the pressure resolution of 10{sup −8}Pa and carried out hydrogen desorption investigation at different temperatures on Ti{sub 36}Zr{sub 40}Ni{sub 20}Pd{sub 4} icosahedral quasicrystal. Based on three Pressure-Composition-Temperature desorption curves, we speculate according to Van’t Hoff theory about hydrogen storage that its equilibrium pressure at room temperature could be at the magnitude of 10{sup −6}Pa, displaying good stability of hydrogen in the quasicrystal and also implying application prospects in fusion energy field for quasicrystals of this type.
Law-Hine, Didier; Zeghal, Mehdi; Bressanelli, Stéphane; Constantin, Doru; Tresset, Guillaume
2016-08-10
Viruses are astonishing edifices in which hundreds of molecular building blocks fit into the final structure with pinpoint accuracy. We established a robust kinetic model accounting for the in vitro self-assembly of a capsid shell derived from an icosahedral plant virus by using time-resolved small-angle X-ray scattering (TR-SAXS) data at high spatiotemporal resolution. By implementing an analytical model of a spherical patch into a global fitting algorithm, we managed to identify a major intermediate species along the self-assembly pathway. With a series of data collected at different protein concentrations, we showed that free dimers self-assembled into a capsid through an intermediate resembling a half-capsid. The typical lifetime of the intermediate was a few seconds and yet the presence of so large an oligomer was not reported before. The progress in instrumental detection along with the development of powerful algorithms for data processing contribute to shedding light on nonequilibrium processes in highly complex systems such as viruses.
Miyazaki, Naoyuki; Higashiura, Akifumi; Higashiura, Tomoko; Akita, Fusamichi; Hibino, Hiroyuki; Omura, Toshihiro; Nakagawa, Atsushi; Iwasaki, Kenji
2016-02-01
The minor outer capsid protein P2 of Rice dwarf virus (RDV), a member of the genus Phytoreovirus in the family Reoviridae, is essential for viral cell entry. Here, we clarified the structure of P2 and the interactions to host insect cells. Negative stain electron microscopy (EM) showed that P2 proteins are monomeric and flexible L-shaped filamentous structures of ∼20 nm in length. Cryo-EM structure revealed the spatial arrangement of P2 in the capsid, which was prescribed by the characteristic virion structure. The P2 proteins were visualized as partial rod-shaped structures of ∼10 nm in length in the cryo-EM map and accommodated in crevasses on the viral surface around icosahedral 5-fold axes with hydrophobic interactions. The remaining disordered region of P2 assumed to be extended to the radial direction towards exterior. Electron tomography clearly showed that RDV particles were away from the cellular membrane at a uniform distance and several spike-like densities, probably corresponding to P2, connecting a viral particle to the host cellular membrane during cell entry. By combining the in vitro and in vivo structural information, we could gain new insights into the detailed mechanism of the cell entry of RDV.
Black Hole Thermodynamics and Lorentz Symmetry
NASA Astrophysics Data System (ADS)
Jacobson, Ted; Wall, Aron C.
2010-08-01
Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.
Non-standard symmetries and quantum anomalies
Visinescu, Anca; Visinescu, Mihai
2008-08-31
Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.
Symmetry breaking in individual plasmonic nanoparticles
Wang, Hui; Wu, Yanpeng; Lassiter, Britt; Nehl, Colleen L.; Hafner, Jason H.; Nordlander, Peter; Halas, Naomi J.
2006-01-01
The plasmon resonances of a concentric metallic nanoshell arise from the hybridization of primitive plasmon modes of the same angular momentum on its inner and outer surfaces. For a nanoshell with an offset core, the reduction in symmetry relaxes these selection rules, allowing for an admixture of dipolar components in all plasmon modes of the particle. This metallodielectric nanostructure with reduced symmetry exhibits a core offset-dependent multipeaked spectrum, seen in single-particle spectroscopic measurements, and exhibits significantly larger local-field enhancements on its external surface than the equivalent concentric spherical nanostructure. PMID:16829573
Broken symmetry in ideal magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1993-01-01
A numerical study of the long-time evolution of a number of cases of inviscid, isotropic, incompressible, three-dimensional fluid, and magneto-fluid turbulence has been completed. The results confirm that ideal magnetohydrodynamic turbulence is non-ergodic if there is no external magnetic field present. This is due essentially to a canonical symmetry being broken in an arbitrary dynamical representation. The broken symmetry manifests itself as a coherent structure, i.e., a non-zero time-averaged part of the turbulent magnetic field. The coherent structure is observed, in one case, to contain about eighteen percent of the total energy.
Cosmoparticle physics of family symmetry breaking
NASA Astrophysics Data System (ADS)
Khlopov, Maxim Yu.
1993-07-01
The foundations of both particle theory and cosmology are hidden at super energy scale and can not be tested by direct laboratory means. Cosmoparticle physics is developed to probe these foundations by the proper combination of their indirect effects, thus providing definite conclusions on their reliability. Cosmological and astrophysical tests turn to be complementary to laboratory searches of rare processes, induced by new physics, as it can be seen in the case of gauge theory of broken symmetry of quark and lepton families, ascribing to the hierarchy of the horizontal symmetry breaking the observed hierarchy of masses and the mixing between quark and lepton families.
Wormholes and Peccei-Quinn symmetries
Choi, K.; Holman, R. )
1990-01-08
We show how wormholes and Peccei-Quinn symmetries are in fact complementary in solving the strong {ital CP} problem. On the one hand, Peccei-Quinn symmetries are shown to provide us with a wormhole parameter that couples only to the QCD anomaly. This then allows us to implement the wormhole solution to the strong {ital CP} problem constructed previously by the present authors as well as by Preskill, Trivedi, and Wise. On the other hand, wormholes are shown to drive the axion mass to zero or to the wormhole scale, thus avoiding the axion-energy-density crisis in either case.
Routh symmetry in the Chaplygin's rolling ball
NASA Astrophysics Data System (ADS)
Kim, Byungsoo
2011-12-01
The Routh integral in the symmetric Chaplygin's rolling ball has been regarded as a mysterious conservation law due to its interesting form of sqrt {I_1 I_3 + m< {I_s ,s} rangle } Ω _3 . In this paper, a new form of the Routh integral is proposed as a Noether's pairing form of a conservation law. An explicit symmetry vector for the Routh integral is proved to associate the conserved quantity with the invariance of the Lagrangian function under the rollingly constrained nonholonomic variation. Then, the form of the Routh symmetry vector is discussed for its origin as the linear combination of the configurational vectors.
Spontaneous symmetry breaking in gauge theories.
Kibble, T W B
2015-01-13
The aim of this historical article is to describe the development of the idea of spontaneous symmetry breaking in gauge theories as seen from my perspective as a member of Abdus Salam's group at Imperial College London, UK. Beginning with an account of particle physics in the years after the Second World War, I describe early attempts at constructing a unified theory of weak and electromagnetic interactions, the obstacles encountered and how they were eventually overcome with the mass-generating mechanism incorporating the idea of spontaneous symmetry breaking, one of whose features is the now-famous Higgs boson.
Parity-time symmetry under magnetic flux
NASA Astrophysics Data System (ADS)
Jin, L.; Song, Z.
2016-06-01
We study a parity-time-(PT -) symmetric ring lattice, with one pair of balanced gain and loss located at opposite positions. The system remains PT -symmetric when threaded by a magnetic flux; however, the PT symmetry is sensitive to the magnetic flux in the presence of a large balanced gain and loss, or in a large system. We find a threshold gain or loss above which any nontrivial magnetic flux breaks the PT symmetry. We obtain the maximally tolerable magnetic flux for the exact PT -symmetric phase, which is approximately linearly dependent on a weak gain or loss.
Hopf bifurcation in the presence of symmetry
NASA Technical Reports Server (NTRS)
Golubitsky, M.; Stewart, I.
1985-01-01
Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.
On the dynamic viscous permeability tensor symmetry.
Perrot, Camille; Chevillotte, Fabien; Panneton, Raymond; Allard, Jean-François; Lafarge, Denis
2008-10-01
Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment.
Mirror symmetry breaking at the molecular level.
Avetisov, V; Goldanskii, V
1996-01-01
Reasoning from two basic principles of molecular physics, P invariance of electromagnetic interaction and the second law of thermodynamics, one would conclude that mirror symmetry retained in the world of chiral molecules. This inference is fully consistent with what is observed in inorganic nature. However, in the bioorganic world, the reverse is true. Mirror symmetry there is definitely broken. Is it possible to account for this phenomenon without going beyond conventional concepts of the kinetics of enantioselective processes? This study is an attempt to survey all existing hypotheses containing this phenomenon. Images Fig. 1 Fig. 2 Fig. 3 Fig. 4 Fig. 5 PMID:8876153
Neutron matter, symmetry energy and neutron stars
Stefano, Gandolfi; Steiner, Andrew W
2016-01-01
Recent progress in quantum Monte Carlo with modern nucleon-nucleon interactions have enabled the successful description of properties of light nuclei and neutron-rich matter. Of particular interest is the nuclear symmetry energy, the energy cost of creating an isospin asymmetry, and its connection to the structure of neutron stars. Combining these advances with recent observations of neutron star masses and radii gives insight into the equation of state of neutron-rich matter near and above the saturation density. In particular, neutron star radius measurements constrain the derivative of the symmetry energy.
Quregisters, Symmetry Groups and Clifford Algebras
NASA Astrophysics Data System (ADS)
Cervantes, D.; Morales-Luna, G.
2016-03-01
Natural one-to-one and two-to-one homomorphisms from SO(3) into SU(2) are built conventionally, and the collection of qubits, is identified with a subgroup of SU(2). This construction is suitable to be extended to corresponding tensor powers. The notions of qubits, quregisters and qugates are translated into the language of symmetry groups. The corresponding elements to entangled states in the tensor product of Hilbert spaces reflect entanglement properties as well, and in this way a notion of entanglement is realised in the tensor product of symmetry groups.
Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion ω ˜kn (n =2 ,3 ,… ), whose naturalness is protected by polynomial shift symmetries. Here, we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of n changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.
Symmetry considerations in structural phase transitions
NASA Astrophysics Data System (ADS)
Perez-Mato, J. M.; Aroyo, M. I.; Orobengoa, D.
2012-03-01
The most important symmetry arguments to be considered in the analysis of structural phase transitions are reviewed. A practical approach is used, with the discussion of many examples. In particular, we stress the straightforward application of computer tools freely available in internet to solve these symmetry-related problems. We focus on programs available on the Bilbao Crystallographic Server (www.cryst.ehu.es), but also the use of some programs from the ISOTROPY site (http://stokes.byu.edu/isotropy.html) is discussed.
Weak Lie symmetry and extended Lie algebra
Goenner, Hubert
2013-04-15
The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).
Dual technicolor with hidden local symmetry
Belitsky, A. V.
2010-08-15
We consider a dual description of the technicolor-like gauge theory within the D4/D8-brane configuration with varying confinement and electroweak symmetry breaking scales. Constructing an effective truncated model valid below a certain cutoff, we identify the particle spectrum with Kaluza-Klein modes of the model in a manner consistent with the hidden local symmetry. Integrating out heavy states, we find that the low-energy action receives nontrivial corrections stemming from the mixing between standard model and heavy gauge bosons, which results in reduction of oblique parameters.
Mirror symmetry, chiral symmetry breaking, and antihydrogen states in natural atomic H
NASA Astrophysics Data System (ADS)
van Hooydonk, G.
2002-10-01
Molecular band spectra reveal a left-right symmetry for atoms [Van Hooydonk, Spectrochim. Acta A 56, 2273 (2000)]. Intra-atomic left-right symmetry points to antiatom states and, to make sense, this must also show in line spectra. H Lyman ns singlets show a mirror plane at quantum number n0=1/2π. A symmetry-breaking oscillator (1-1/2π/n)2 means that some of these n states are antihydrogenic. This view runs ahead of CERN's antiproton decelerator project on antihydrogen.
Dynamics symmetries of Hamiltonian system on time scales
Peng, Keke Luo, Yiping
2014-04-15
In this paper, the dynamics symmetries of Hamiltonian system on time scales are studied. We study the symmetries and quantities based on the calculation of variation and Lie transformation group. Particular focus lies in: the Noether symmetry leads to the Noether conserved quantity and the Lie symmetry leads to the Noether conserved quantity if the infinitesimal transformations satisfy the structure equation. As the new application of result, at end of the article, we give a simple example of Noether symmetry and Lie symmetry on time scales.
Symmetry groups associated with tilings on a flat torus.
Loyola, Mark L; De Las Peñas, Ma Louise Antonette N; Estrada, Grace M; Santoso, Eko Budi
2015-01-01
This work investigates symmetry and color symmetry properties of Kepler, Heesch and Laves tilings embedded on a flat torus and their geometric realizations as tilings on a round torus in Euclidean 3-space. The symmetry group of the tiling on the round torus is determined by analyzing relevant symmetries of the planar tiling that are transformed to axial symmetries of the three-dimensional tiling. The focus on studying tilings on a round torus is motivated by applications in the geometric modeling of nanotori and the determination of their symmetry groups.
Disordered cold atoms in different symmetry classes
NASA Astrophysics Data System (ADS)
Pinheiro, Fernanda; Larson, Jonas
2015-08-01
We consider an experimentally realizable model of noninteracting but randomly coupled atoms in a two-dimensional optical lattice. By choosing appropriate real or complex-valued random fields and species-dependent energy offsets, this system can be used to analyze effects of disorder in four different symmetry classes: the chiral BDI and AIII and the nonchiral A and AI. These chiral classes are known to support a metallic phase at zero energy, which here, due to the inevitable finite size of the system, should also persist in a neighborhood of nonzero energies. As we discuss, this is of particular interest for experiments involving quenches. Away from the center of the spectrum, we find that excitations appear as domain walls in the cases with time-reversal symmetry or as vortices in the cases where time-reversal symmetry is absent. Therefore, a quench in a system with uniform density would lead to the formation of either vortices or domain walls depending on the symmetry class. For the nonchiral models in classes A and AI, a population imbalance between the two atomic species naturally occurs. In these cases, one of the two species is seen to favor a more uniform density. We also study the onset of localization as the disorder strength is increased for the different classes, and by deriving an effective model for the nonchiral cases we show how their eigenstates remain extended for larger values of the coupling with the disorder when compared to the nonchiral ones.
Inversion Symmetry Breaking in Endohedral C_60
NASA Astrophysics Data System (ADS)
Clougherty, Dennis; Anderson, Frederick
1998-03-01
A pseudo--Jahn--Teller model describing central atom distortions is proposed for endohedral fullerenes of the form A@C_60 where A is either a rare gas or a metal atom. A critical (dimensionless) coupling gc is found, at or below which the symmetric configuration is stable and above which inversion symmetry is broken. Vibronic parameters are given for selected endohedral fullerenes.
Translational Symmetry-Breaking for Spiral Waves
NASA Astrophysics Data System (ADS)
LeBlanc, V. G.; Wulff, C.
2000-10-01
Spiral waves are observed in numerous physical situations, ranging from Belousov-Zhabotinsky (BZ) chemical reactions, to cardiac tissue, to slime-mold aggregates. Mathematical models with Euclidean symmetry have recently been developed to describe the dynamic behavior (for example, meandering) of spiral waves in excitable media. However, no physical experiment is ever infinite in spatial extent, so the Euclidean symmetry is only approximate. Experiments on spiral waves show that inhomogeneities can anchor spirals and that boundary effects (for example, boundary drifting) become very important when the size of the spiral core is comparable to the size of the reacting medium. Spiral anchoring and boundary drifting cannot be explained by the Euclidean model alone. In this paper, we investigate the effects on spiral wave dynamics of breaking the translation symmetry while keeping the rotation symmetry. This is accomplished by introducing a small perturbation in the five-dimensional center bundle equations (describing Hopf bifurcation from one-armed spiral waves) which is SO(2)-equivariant but not equivariant under translations. We then study the effects of this perturbation on rigid spiral rotation, on quasi-periodic meandering and on drifting.
Symmetries in confined classical Coulomb systems
Schiffer, J.P.
1991-01-01
The properties of charged particles confined in a harmonic oscillator potential have become of increased interest lately in view of the development of techniques in ion traps and storage rings. The symmetries in such systems intrigued the imagination of Ted Hecht in connection with the storage ring at Heidelberg, and so perhaps it is an appropriate subject for this symposium.
SFT Symmetry, Mathematics (Experimental): 5212.48.
ERIC Educational Resources Information Center
Dade County Public Schools, Miami, FL.
This is the third in a series of four guidebooks on minimum course content designed to develop geometric concepts intuitively, using the "slides, flips, and turns" approach developed by the University of Illinois, Committee on School Mathematics. Topics include the development of the concept of symmetry, triangles and quadrilateral…
Equilibria with incompressible flows from symmetry analysis
Kuiroukidis, Ap E-mail: gthroum@cc.uoi.gr; Throumoulopoulos, G. N. E-mail: gthroum@cc.uoi.gr
2015-08-15
We identify and study new nonlinear axisymmetric equilibria with incompressible flow of arbitrary direction satisfying a generalized Grad Shafranov equation by extending the symmetry analysis presented by Cicogna and Pegoraro [Phys. Plasmas 22, 022520 (2015)]. In particular, we construct a typical tokamak D-shaped equilibrium with peaked toroidal current density, monotonically varying safety factor, and sheared electric field.