Pauling, Linus
1989-01-01
A doubly icosahedral complex involves roughly spherical clusters of atoms with icosahedral point-group symmetry, which are themselves, in parallel orientation, icosahedrally packed. These complexes may form cubic crystallites; three structures of this sort have been identified. Analysis of electron diffraction photographs of the decagonal quasicrystal Al6Pd has led to its description as involving pentagonal twinning of an orthorhombic crystal with a = 51.6 Å, b = 37.6 Å, and c = 33.24 Å, with about 4202 atoms in the unit, comprising two 1980-atom doubly icosahedral complexes, each involving icosahedral packing of 45 44-atom icosahedral complexes (at 0 0 0 and 1/2 1/2 1/2) and 242 interstitial atoms. The complexes and clusters are oriented with one of their fivefold axes in the c-axis direction. Images PMID:16594092
Pauling, Linus
1988-01-01
A 780-atom primitive tetragonal unit with edges 27.3, 27.3, and 12.6 Å is assigned to rapidly solidified Cu5Ni3Si2 and V15Ni10Si by analysis of electron diffraction photographs with the assumption that the crystals contain icosahedral clusters. There are thirty 26-atom clusters at the sigma-phase positions. Apparent 8-fold symmetry results from 45° twinning on the basal plane. PMID:16593915
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-foldâ€¦
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.
Anticoherence of spin states with point-group symmetries
NASA Astrophysics Data System (ADS)
Baguette, D.; Damanet, F.; Giraud, O.; Martin, J.
2015-11-01
We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then investigate in detail the case of small numbers of qubits and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.
Symmetry, Point Groups, and Character Tables, Part 3, Character Tables and Their Significance
ERIC Educational Resources Information Center
Orchin, Milton; Jaffe, H. H.
1970-01-01
Presents the third of a series of articles on symmetry. Describes the symmetry properties of molecules in translatiional and rotational motion. Presents these dynamic symmetry properties in character tables for five point groups. Supplements the article with more rigorous material involving spectroscopic states, degenerate point groups andâ€¦
Symmetry, Point Groups, and Character Tables, Part 3, Character Tables and Their Significance
ERIC Educational Resources Information Center
Orchin, Milton; Jaffe, H. H.
1970-01-01
Presents the third of a series of articles on symmetry. Describes the symmetry properties of molecules in translatiional and rotational motion. Presents these dynamic symmetry properties in character tables for five point groups. Supplements the article with more rigorous material involving spectroscopic states, degenerate point groups and…
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.
Breaking of Icosahedral Symmetry: C60 to C70
Bodner, Mark; Patera, Jiri; Szajewska, Marzena
2014-01-01
We describe the existence and structure of large fullerenes in terms of symmetry breaking of the molecule. Specifically, we describe the existence of in terms of breaking of the icosahedral symmetry of by the insertion into its middle of an additional decagon. The surface of is formed by 12 regular pentagons and 25 regular hexagons. All 105 edges of are of the same length. It should be noted that the structure of the molecules is described in exact coordinates relative to the non-orthogonal icosahedral bases. This symmetry breaking process can be readily applied, and could account for and describe other larger cage cluster fullerene molecules, as well as more complex higher structures such as nanotubes. PMID:24599292
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.
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
ERIC Educational Resources Information Center
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-01-01
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…
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
ERIC Educational Resources Information Center
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-01-01
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-fourâ€¦
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…
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
ERIC Educational Resources Information Center
Casas, LluÃs; 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 toâ€¦
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, aâ€¦
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…
Mechanical Deformation of Spherical Viruses with Icosahedral Symmetry
Vliegenthart, Gerard Adriaan; Gompper, Gerhard
2006-01-01
Virus capsids and crystalline surfactant vesicles are two examples of self-assembled shells in the nano- to micrometer size range. Virus capsids are particularly interesting since they have to sustain large internal pressures while encapsulating and protecting the viral DNA. We therefore study the mechanical properties of crystalline shells of icosahedral symmetry on a substrate under a uniaxial applied force by computer simulations. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number of elementary building blocks N (the capsomers in the case of viral shells), the Föppl-von Kármán number ? (which characterizes the relative importance of shear and bending elasticity), and the confining geometry. In particular, we show that whereas large shells are well described by continuum elasticity-theory, small shells of the size of typical viral capsids behave differently already for small deformations. Our results are essential to extract quantitative information about the elastic properties of viruses and vesicles from deformation experiments. PMID:16679375
Virus-templated plasmonic nanoclusters with icosahedral symmetry via directed self-assembly.
Fontana, Jake; Dressick, Walter J; Phelps, Jamie; Johnson, John E; Rendell, Ronald W; Sampson, Travian; Ratna, Banahalli R; Soto, Carissa M
2014-08-13
The assembly of plasmonic nanoparticles with precise spatial and orientational order may lead to structures with new electromagnetic properties at optical frequencies. The directed self-assembly method presented controls the interparticle-spacing and symmetry of the resulting nanometer-sized elements in solution. The self-assembly of three-dimensional (3D), icosahedral plasmonic nanosclusters (NCs) with resonances at visible wavelengths is demonstrated experimentally. The ideal NCs consist of twelve gold (Au) nanospheres (NSs) attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. In situ dynamic light scattering (DLS) measurements confirm the NSs assembly on the virus. Transmission electron micrographs (TEM) demonstrate the ability of the self-assembly method to control the nanoscopic symmetry of the bound NSs, which reflects the icosahedral symmetry of the virus. Both, TEM and DLS show that the NCs comprise of a distribution of capsids mostly covered (i.e., 6-12 NS/capsid) with NSs. 3D finite-element simulations of aqueous suspensions of NCs reproduce the experimental bulk absorbance measurements and major features of the spectra. Simulations results show that the fully assembled NCs give rise to a 10-fold surface-averaged enhancement of the local electromagnetic field. PMID:24733721
Virus-Templated Plasmonic Nanoclusters with Icosahedral Symmetry via Directed Self-Assembly
Fontana, Jake; Dressick, Walter J; Phelps, Jamie; Johnson, John E; Rendell, Ronald W; Sampson, Travian; Ratna, Banahalli R; Soto, Carissa M
2014-01-01
The assembly of plasmonic nanoparticles with precise spatial and orientational order may lead to structures with new electromagnetic properties at optical frequencies. The directed self-assembly method presented controls the interparticle-spacing and symmetry of the resulting nanometer-sized elements in solution. The self-assembly of three-dimensional (3D), icosahedral plasmonic nanosclusters (NCs) with resonances at visible wavelengths is demonstrated experimentally. The ideal NCs consist of twelve gold (Au) nanospheres (NSs) attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. In situ dynamic light scattering (DLS) measurements confirm the NSs assembly on the virus. Transmission electron micrographs (TEM) demonstrate the ability of the self-assembly method to control the nanoscopic symmetry of the bound NSs, which reflects the icosahedral symmetry of the virus. Both, TEM and DLS show that the NCs comprise of a distribution of capsids mostly covered (i.e., 6–12 NS/capsid) with NSs. 3D finite-element simulations of aqueous suspensions of NCs reproduce the experimental bulk absorbance measurements and major features of the spectra. Simulations results show that the fully assembled NCs give rise to a 10-fold surface-averaged enhancement of the local electromagnetic field. PMID:24733721
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 Ã— A1, because it is isomorphic to the Weyl group of the semi-simple Lie algebra A1 Ã— A1. Thirteen of the A1 Ã— 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 Ã— A1. The remaining ones are just convex shells formed by regular hexagons and 12 pentagons without the involvement of the icosahedral symmetry. PMID:25921498
Symmetry properties of tetraammine platinum(II) with C2v and C4v point groups
Moghani, Ghorban Ali; Ashrafi, Ali Reza; Hamadanian, Masood
2005-01-01
Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i?j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups. PMID:15682509
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.
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 C? 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
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
NASA Astrophysics Data System (ADS)
Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah
2014-07-01
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-Ã… structure of a cyanobacterial virus, Syn5, by electron cryo-microscopy and modelling. A CÎ± 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.
Icosahedral Packing of RNA Viral Genomes
NASA Astrophysics Data System (ADS)
Rudnick, Joseph; Bruinsma, Robijn
2005-01-01
Many spherelike RNA viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph-theoretical constraints forbid exact realization of icosahedral symmetry. This paper explores the consequences of graph-theoretical constraints on quasi-icosahedral genome structures. A key result is the prediction that the genome organization is a Hamiltonian path or cycle and that the associated assembly scenario of such single-stranded spherelike RNA viruses resembles that of cylindrical RNA viruses, such as tobacco mosaic viruses.
Icosahedral packing of RNA viral genomes.
Rudnick, Joseph; Bruinsma, Robijn
2005-01-28
Many spherelike RNA viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph-theoretical constraints forbid exact realization of icosahedral symmetry. This paper explores the consequences of graph-theoretical constraints on quasi-icosahedral genome structures. A key result is the prediction that the genome organization is a Hamiltonian path or cycle and that the associated assembly scenario of such single-stranded spherelike RNA viruses resembles that of cylindrical RNA viruses, such as tobacco mosaic viruses. PMID:15698326
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
Point Group Determination of Calcium Tartrate by Etch Figure
NASA Astrophysics Data System (ADS)
Nakatani, Noriyuki
1991-11-01
Etch figures of gel-grown orthorhombic calcium tartrate tetrahydrate crystals have been examined in order to determine the point group symmetry. Making a thorough investigation of etch-figure characters on natural surfaces of rhombic dodecahedron crystals, we reached the firm conclusion that the point group is nonpolar 222.
Growth of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Socolar, Joshua; Hann, Connor; Steinhardt, Paul
2015-03-01
The discovery of an icosahedral quasicrystal that formed naturally in a rock sample originating from a meteorite highlights fundamental questions about quasicrystal formation. ?The growth of a well-ordered quasicrystal through kinetics dominated by local energetics is known to be possible in principle for 2D systems: a Penrose tiling, for example, can be grown from a particular type of small seed by adding tiles only to surface sites where the tile type and orientation are unambiguously determined by already placed tiles that share a vertex. We consider the generalization of this result to icosahedral quasicrystal tilings comprised of Ammann rhombohedra. Numerical simulations strongly suggest that infinite, well-ordered, icosahedral quasicrystals can be generated. Unlike the 2D case, defects are generated outside the original seed, but the number of such defects appears to grow only linearly with the cluster radius. Analysis of the lift of the tiling to a 6D hypercubic lattice provides key insights into the growth mechanism.
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 ? 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….
NASA Astrophysics Data System (ADS)
Ilyushin, Vadim V.; Hougen, Jon T.
2013-06-01
We will present a new theoretical tool, a program called PAM-C2v-2tops, for analysis of the high-resolution torsion-rotation spectra of molecules with two equivalent methyl rotors and C_{2V} symmetry at equilibrium. The new tool belongs to the broad class of effective Hamiltonians, is based on Longuet-Higgins' group theoretical ideas and uses G_{36} permutation-inversion group-theoretical considerations, the principal axis method and a two-step diagonalization procedure. The program was used to carry out a weighted least-squares fit of 1720 microwave, millimeter-wave, and sub-millimeter-wave line frequencies of acetone [(CH_3)_2CO] that are available in the literature. The weighted root-mean-square deviation of 0.93 obtained for a joint fit of the microwave lines belonging to the ground, the lower torsional fundamental, and the higher torsional fundamental states of acetone represents significant progress in comparison with previous fitting attempts, especially for the excited torsional states.
Pauling, L
1990-01-01
An analysis of electron micrographs of Al5Mn quasicrystals obtained by rapidly cooling a molten alloy with composition Al17Mn and removing the Al matrix by electrosolution, revealing aggregates of 20 microcrystals at the corners of a pentagonal dodecahedron, supports the proposal that these microcrystals are cubic crystals twinned about an icosahedral seed, with each cubic microcrystal sharing a threefold axis and three symmetry planes with the seed. Images PMID:11607108
Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement
NASA Astrophysics Data System (ADS)
de Nijs, Bart; Dussi, Simone; Smallenburg, Frank; Meeldijk, Johannes D.; Groenendijk, Dirk J.; Filion, Laura; Imhof, Arnout; van Blaaderen, Alfons; Dijkstra, Marjolein
2015-01-01
Icosahedral symmetry, which is not compatible with truly long-range order, can be found in many systems, such as liquids, glasses, atomic clusters, quasicrystals and virus-capsids. To obtain arrangements with a high degree of icosahedral order from tens of particles or more, interparticle attractive interactions are considered to be essential. Here, we report that entropy and spherical confinement suffice for the formation of icosahedral clusters consisting of up to 100,000 particles. Specifically, by using real-space measurements on nanometre- and micrometre-sized colloids, as well as computer simulations, we show that tens of thousands of hard spheres compressed under spherical confinement spontaneously crystallize into icosahedral clusters that are entropically favoured over the bulk face-centred cubic crystal structure. Our findings provide insights into the interplay between confinement and crystallization and into how these are connected to the formation of icosahedral structures.
Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement.
de Nijs, Bart; Dussi, Simone; Smallenburg, Frank; Meeldijk, Johannes D; Groenendijk, Dirk J; Filion, Laura; Imhof, Arnout; van Blaaderen, Alfons; Dijkstra, Marjolein
2015-01-01
Icosahedral symmetry, which is not compatible with truly long-range order, can be found in many systems, such as liquids, glasses, atomic clusters, quasicrystals and virus-capsids. To obtain arrangements with a high degree of icosahedral order from tens of particles or more, interparticle attractive interactions are considered to be essential. Here, we report that entropy and spherical confinement suffice for the formation of icosahedral clusters consisting of up to 100,000 particles. Specifically, by using real-space measurements on nanometre- and micrometre-sized colloids, as well as computer simulations, we show that tens of thousands of hard spheres compressed under spherical confinement spontaneously crystallize into icosahedral clusters that are entropically favoured over the bulk face-centred cubic crystal structure. Our findings provide insights into the interplay between confinement and crystallization and into how these are connected to the formation of icosahedral structures. PMID:25173580
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…
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 andâ€¦
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 ? which characterizes the relative importance of shear and bending elasticity.
Structures of giant icosahedral eukaryotic dsDNA viruses
Xiao, Chuan; Rossmann, Michael G.
2011-01-01
In the last twenty years, numerous giant, dsDNA, icosahedral viruses have been discovered and assigned to the nucleocytoplasmic large dsDNA virus (NCLDV) clade. The major capsid proteins of these viruses consist of two consecutive jelly-roll domains, assembled into trimers, with pseudo 6-fold symmetry. The capsomers are assembled into arrays that have either p6 (as in Paramecium bursaria Chlorella virus-1) or p3 symmetry (as in Mimivirus). Most of the NCLDV viruses have a membrane that separates the nucleocapsid from the external capsid. PMID:21909343
NASA Astrophysics Data System (ADS)
LoÅ¡dorfer BoÅ¾iÄ, AnÅ¾e; Podgornik, Rudolf
2013-02-01
Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by patchy charge distributions exhibiting certain point group symmetries. We derive a general form of the electrostatic interaction energy of two permeable, arbitrarily charged spherical shells in the Debye-HÃ¼ckel approximation and apply it to the case of particles with icosahedral, octahedral, and tetrahedral inhomogeneous charge distributions. We analyze in detail how charge distribution symmetry modifies the interaction energy and find that local charge inhomogeneities reduce the repulsion of two overall equally charged particles, while sufficient orientational variation in the charge distribution can turn the minimum interaction energy into an attraction. Additionally, we show that larger patches and thus lower symmetries and wave numbers result in bigger attraction given the same variation.
LoÅ¡dorfer BoÅ¾iÄ, AnÅ¾e; Podgornik, Rudolf
2013-02-21
Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by patchy charge distributions exhibiting certain point group symmetries. We derive a general form of the electrostatic interaction energy of two permeable, arbitrarily charged spherical shells in the Debye-HuÌˆckel approximation and apply it to the case of particles with icosahedral, octahedral, and tetrahedral inhomogeneous charge distributions. We analyze in detail how charge distribution symmetry modifies the interaction energy and find that local charge inhomogeneities reduce the repulsion of two overall equally charged particles, while sufficient orientational variation in the charge distribution can turn the minimum interaction energy into an attraction. Additionally, we show that larger patches and thus lower symmetries and wave numbers result in bigger attraction given the same variation. PMID:23445030
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.
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)
Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials
Mihalkovic, M. |; Zhu, W.; Henley, C.L.; Phillips, R.
1996-04-01
We have constructed and relaxed over 200 different finite structure models for the quasicrystal {ital i}-AlMn based on decorations of the {open_quote}{open_quote}canonical-cell tiling.{close_quote}{close_quote} We adopted {ital ab} {ital initio}-based pair potentials with strong Friedel oscillations, which reproduce the phase diagram of real Al-Mn intermetallic crystal structures fairly well. Our various decoration rules encompass cases with face-centered icosahedral (FCI) symmetry and with simple icosahedral (SI) symmetry, and include additional variations in the occupancy and/or chemistry of certain site types. Each decoration was applied to 11 distinct periodic approximants of the tiling. We found that (i) the relaxed atomic positions of each site type can be closely approximated by fixed positions on each tile type, even though the environments (beyond the first neighbor) are inequivalent. (ii) Models with simple icosahedral (SI) space-group symmetry were better than those with face-centered icosahedral (FCI) space-group symmetry. (iii) {open_quote}{open_quote}Loose{close_quote}{close_quote} decorations, containing voids almost large enough for an atom, were better than the {open_quote}{open_quote}dense{close_quote}{close_quote} decorations which were suggested by packing considerations. (iv) Our results depended on using the realistic potentials; {ital short}-range potentials favor the {open_quote}{open_quote}dense{close_quote}{close_quote} structures, and many details depend on the second or further oscillations in the potentials. (v) For our best model, there is relatively little variation of the energy when tiles are rearranged, i.e., a {ital random}-{ital tiling} {ital model} is a good zero-order description of the system. {copyright} {ital 1996 The American Physical Society.}
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.
Beta cell device using icosahedral boride compounds
Aselage, Terrence L. (62 Avenida Del Sol, Cedar Crest, NM 87008); Emin, David (1502 Harvard Ct., NE., Albuquerque, NM 87106-3712)
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
VelÃ¡zquez-Salazar, J. JesÃºs; Esparza, Rodrigo; MejÃa-Rosales, Sergio Javier; Estrada-Salas, RubÃ©n; Ponce, Arturo; Deepak, Francis Leonard; Castro-Guerrero, Carlos; JosÃ©-YacamÃ¡n, Miguel
2011-01-01
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 affect the chemical and structural properties of the material, and hence, its potential applications. This report describes the experimental formation of five-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 five-fold symmetry. These icosahedral nanowire structures remind those of quasicrystals that 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. PMID:21790155
Stability of the X -Y phase of the two-dimensional C4 point group insulator
NASA Astrophysics Data System (ADS)
de Leeuw, Bart; Küppersbusch, Carolin; Juri?i?, Vladimir; Fritz, Lars
2015-06-01
Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this paper we consider an extension of the Bernevig-Hughes-Zhang model that describes a point group insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators but only if the Sz component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes, and the surface states localize, even if the crystalline symmetries are intact on average.
Systematic prediction of new inorganic ferroelectrics in point group 4.
Abrahams
1999-08-01
The latest release of the Inorganic Crystal Structure Database contains a total of 87 entries corresponding to 70 different materials in point group 4. The structures reported for 11 materials in space group P4 satisfy the criteria for ferroelectricity, as do four in P4(1), one each in P4(2) and P4(3), 12 in I4, including seven that form three families, and another three in I4(1). Three previously known ferroelectrics were also listed in I4 and one in I4(1). In addition, the listing for point group 4 contains 22 entries for nonferroelectric materials and three with misassigned space groups. Among the newly predicted ferroelectrics in point group 4, assuming the validity of the underlying structural reports, are Ce(5)B(2)C(6), modulated NbTe(4), Na(3)Nb(12)O(31)F, Ca(2)FeO(3)Cl, K(4)CuV(5)O(15)Cl, TlBO(2), CrOF(3), PbTeO(3), VO(HPO(3))(H(2)O).3H(2)O, MgB(2)O(OH)(6), beta-tetragonal boron, CuBi(2)O(4), WOBr(4), Na(8)PtO(6), SbF(2)Cl(3), Ba(1.2)Ti(8)O(16), Ni[SC(NH(2))(2)](4)Cl(2), Ca(2)SiO(3)Cl(2), the mineral caratiite, NbAs, beta-NbO(2) and Ag(3)BiO(3). PMID:10927391
Preparation and properties of icosahedral borides
Aselage, T.L.; Tallant, D.R.; Gieske, J.H.; Van Deusen, S.B.; Tissot, R.G.
1989-01-01
The electronic and thermal transport properties of refractory icosahedral boron-rich solids suggest the utilization of these unique solids as high-temperature semiconductors. Such applications will require high-quality, well-characterized materials. A variety of techniques have been used to prepare powders, ceramics, and single crystals of boron carbides and the icosahedral boron pnictides. X-ray diffraction, Raman spectroscopy, and ultrasound measurements have been used to probe boron carbide sample quality. Each of these measurements supports the structural model of boron carbides developed from analysis of transport data. Initial electrical conductivity (E{sub a} {approx} 0.17 eV) is consistent with a bipolaronic hopping mechanism. 43 refs., 6 figs., 1 tab.
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…
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 teachingâ€¦
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(?3-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 (?12-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. PMID:26790717
Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal.
Cui, C; Nugent, P J; Shimoda, M; Ledieu, J; Fournée, V; Tsai, A P; McGrath, R; Sharma, H R
2014-01-01
The structure of the twofold surface of the icosahedral (i-)Ag-In-Yb quasicrystal has been investigated using low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). The LEED confirms that the surface exhibits quasicrystalline long range order with the twofold rotational symmetry expected from the bulk. STM images reveal a step-terrace structure with terrace size comparable to that of the other high symmetry surfaces of the same quasicrystal. The distribution of step heights and high resolution STM images of terraces suggest that the surface terminates at bulk planes that intersect the center of rhombic triacontahedral clusters, the building blocks of the system, as in the case of the threefold and fivefold surfaces of the system. These planes are rich in Yb and In. No facets are observed on the surface, suggesting that the twofold surface is as stable as the other high symmetry surfaces. PMID:24263167
Topological Quantum Hashing with the Icosahedral Group
Burrello, Michele; Xu Haitan; Mussardo, Giuseppe; Wan Xin
2010-04-23
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(log{sup 2}(1/{epsilon})), we can approximate all SU(2) matrices to an average error {epsilon} with a cost of O(log(1/{epsilon})) in time. The algorithm is applicable to generic quantum compiling.
Confessions of an icosahedral virus crystallographer
Johnson, John E.
2013-01-01
This is a personal history of my structural studies of icosahedral viruses that evolved from crystallographic studies, to hybrid methods with electron cryo-microscopy and image reconstruction (cryoEM) and then developed further by incorporating a variety of physical methods to augment the high resolution crystallographic studies. It is not meant to be comprehensive, even for my own work, but hopefully provides some perspective on the growth of our understanding of these remarkable biologic assemblies. The goal is to provide a historical perspective for those new to the field and to emphasize the limitations of any one method, even those that provide atomic resolution information about viruses. PMID:23291268
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.
Symmetry arguments in?chemistry
Dunitz, Jack?D.
1996-01-01
The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity. PMID:8962036
Yang, Zheng; Bahar, Ivet; Widom, Michael
2009-06-01
Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses. PMID:19486668
NASA Astrophysics Data System (ADS)
Vail, Benjamin; Aris, Damian; Scarlete, Mihai
The present study proposes an algorithm for point-group analysis (PGA) of the vibrational activity of molecules, adapted for the efficient utilization of the linear packages incorporated into currently available symbolic computation engines (SCE), such as Maple, Mathcad, or Mathematica. By the creation of this algorithm, we have addressed the need for a numerically friendly environment, outside the "locked" procedures within molecular modeling packages, which will preserve its flexibility, transparency, and maneuverability, regardless of the complexity of the calculation. The format of the character tables of the point groups significant to chemical species has been adapted to ensure automatic numerization, and consistent input of the alphanumeric data from the existent character tables into the SCE templates designed to perform the PGA. The two proposed templates address two complementary objectives: (i) a totally transparent and interactive file has been designed to allow access to all intermediate results at all levels of the procedure for easy implementation of potential additional modules of special interest 1-5, and (ii) for fast output and routine calculations of the IR/Raman vibrational activity of molecules based on their point groups, a totally automatic file with a highly simplified input interface has been designed. The numerical interface conveniently replaces the usual graphic user interface that is common to most commercial molecular modeling software packages, requiring minimum input determination. The structure for both templates is based on the use of the digitized forms for the character tables, for the symmetry operations, and for symmetry elements, all saved in dedicated libraries uploaded to the numerical database of the SCE.
Analysis of phases in the structure determination of an icosahedral virus
Plevka, Pavel; Kaufmann, Bärbel; Rossmann, Michael G.
2012-03-15
The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to the correct solution, opposite enantiomorph, Babinet inversion and opposite enantiomorph with Babinet inversion. These incorrect solutions can be seeded from structure factors belonging to reciprocal-space volumes that lie close to icosahedral NCS axes where the structure amplitudes tend to be large and the phases tend to be 0 or {pi}. Furthermore, the false solutions can spread more easily if there are large errors in defining the envelope designating the region in which NCS averaging is performed.
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. PMID:26154440
F-type icosahedral phase and a related cubic phase in the Al-Rh-Cu system
Li, X.Z.; Park, K.T.; Sugiyama, K.; Hiraga, K.
1998-06-01
An F-type icosahedral phase and a related cubic phase (composition of Al{sub 66.1}Rh{sub 21.5}Cu{sub 12.3}, lattice constant a = l.5380(2) nm, and space group of Fm3) were observed in the Al{sub 63}Rh{sub 18.5}Cu{sub 18.5} alloy by transmission electron microscopy (TEM). The structure of the Al-Rh-Cu cubic phase was determined by single-crystal X-ray analysis. A high-resolution electron microscopic image of the Al-Rh-Cu cubic phase is presented together with a simulated image. The structure of the cubic phase can be described by two types of atom clusters, which have outer shells with icosahedral symmetry. It is suggested that the structure of the Al-Rh-Cu cubic phase is helpful for understanding the structure of the i-Al-Rh-Cu F-type icosahedral quasicrystal.
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.
Dynamical x-ray diffraction from an icosahedral quasicrystal
Kycia, S.W.; Goldman, A.I. ); Lograsso, T.A.; Delaney, D.W. ); Black, D. ); Sutton, M.; Dufresne, E.; Bruening, R. ); Rodricks, B. )
1993-08-01
We present direct evidence of dynamical diffraction of x rays from a quasicrystal. High-resolution x-ray-diffraction measurements of the Al-Pd-Mn face-centered icosahedral quasicrystal were performed, revealing a mosaic full width at half maximum of less than 0.001[degree]. In a second experiment, the anomalous transmission of x rays (the Borrmann effect) was observed. These measurements show that nearly perfect quasicrystals may be grown to centimeter-size dimensions allowing x-ray techniques based upon dynamical diffraction to be brought to bear on the analysis of icosahedral structures.
Analysis of grid imprinting on geodesic spherical icosahedral grids
NASA Astrophysics Data System (ADS)
Peixoto, Pedro S.; Barros, Saulo R. M.
2013-03-01
Numerical grid imprinting errors have often been observed in global atmospheric models on icosahedral grids. In this paper we analyse the sources of grid imprinting error related to the usual finite volume discretization of the divergence operator. We introduce the concept of alignment of computational cells, and establish that convergence of second order is attained on aligned cells. Moreover, we present strong evidence that grid imprinting errors are caused by the slow convergence on badly aligned cells. The analysis presented is not restricted to icosahedral grids, being valid for any geodesic spherical grid.
Microindentation of Al-Cu-Fe icosahedral quasicrystal
Giacometti, E.; Baluc, N.; Bonneville, J.; Rabier, J.
1999-10-08
Many different microindentation experiments have been performed at ambient temperature on icosahedral quasicrystals (QCs). They have shown that icosahedral QCs, such as Al-Cu-Fe, Al-Pd-Mn, Al-Li-Cu, Al-Ru-Cu and Mg-Zn-Y are rather hard and exhibit a low fracture toughness. In other respects, compression experiments have shown that these materials exhibit a brittle-to-ductile transition temperature (BDTT) at about 0.7 T{sub m} where T{sub m} is the melting temperature. Few results have been reported concerning microindentation experiments performed at high temperatures, either in the brittle or in the ductile regime. The hardness behavior of icosahedral QCs as a function of temperature has been presented in two cases, however: Al-Li-Cu and Al-Pd-Mn. This paper is aimed at providing information about microindentation measurements performed on an icosahedral Al-Cu-Fe alloy over an extended temperature range. The results are analyzed within the frame used for previous results obtained in the same alloy by means of compression experiments.
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.
Hu, Wen; Yi, Jianhong; Zheng, Biju; Wang, Limin
2013-06-01
Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti?.?V?.?Ni)????xScx (x=0.5–6) quaternary icosahedral quasicrystals have been successfully synthesized via arc-melting and subsequent melt-spinning techniques, and then their electrochemical performance toward hydrogen is explored. When the molar ratio of Sc addition is under 1%, a maximum discharge capacity of about 270 mA h g?¹ can be delivered. With further increasing Sc amount to 6%, good cycling stability as well as significantly retarded self-discharge rate (capacity retention 94% after 24 h relaxation) is observed. But meanwhile, the discharge capacities fall into 250-240 mA h g?¹, and the electrocatalytic activity improvement is highly demanded. - Graphical abstract: Quasicrystalline Ti–V–Ni–Sc hydrogen storage materials: Sc addition into Ti?.?V?.?Ni alloy forms the icosahedral phase (see picture). With optimal Sc dosage, the anodic cycling stability and self-discharge property are greatly enhanced. - Highlights: • Crystalline disallowed 5-fold symmetry is present in (Ti?.?V?.?Ni)????xScx alloys. • Ti-based metastable quasicrystalline alloys can store hydrogen electrochemically. • A maximum discharge capacity of 270 mA h g?¹ can be delivered. • Advantageous cycle stability and self-discharge property benefit from Sc addition. • Ti and V dissolution is suppressed by an oxide layer resulting from Sc corrosion.
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.
Dynamics and stability of icosahedral Fe-Pt nanoparticles.
Jochym, Pawe? T; ?a?ewski, Jan; Sternik, Ma?gorzata; Piekarz, Przemys?aw
2015-11-14
The structure, dynamics and stability of Fe-Pt nanoparticles have been investigated using DFT-based techniques: total energy calculations and molecular dynamics. The investigated systems included multi-shell and disordered nanoparticles of iron and platinum. The study concerns icosahedral particles with the magic number of atoms (55): iron-terminated Fe43Pt12, platinum-terminated Fe12Pt43, and disordered Fe27Pt28. Additionally, the Fe6Pt7 cluster has been investigated to probe the behaviour of extremely small Fe-Pt particles. Molecular dynamics simulations have been performed for a few temperatures between T = 150-1000 K. The calculations revealed high structural instability of the Fe-terminated nanoparticles and a strong stabilising effect of the Pt-termination in the shell-type icosahedral particles. The platinum termination prevented disordering of the particle even at T = 1000 K indicating very high melting temperatures of these Fe-Pt icosahedral structures. The analysis of evolution of the radial distribution function has shown a significant tendency of Pt atoms to move to the outside layer of the particles - even in the platinum deficient cases. PMID:25757479
Symmetry constraints on the elastoresistivity tensor
NASA Astrophysics Data System (ADS)
Shapiro, M. C.; Hlobil, Patrik; Hristov, A. T.; Maharaj, Akash V.; Fisher, I. R.
2015-12-01
The elastoresistivity tensor mi j ,k l characterizes changes in a material's resistivity due to strain. As a fourth-rank tensor, elastoresistivity can be a uniquely useful probe of the symmetries and character of the electronic state of a solid. We present a symmetry analysis of mi j ,k l (both in the presence and absence of a magnetic field) based on the crystalline point group, focusing for pedagogic purposes on the D4 h point group (of relevance to several materials of current interest). We also discuss the relation between mi j ,k l and various thermodynamic susceptibilities, particularly where they are sensitive to critical fluctuations proximate to a critical point at which a point-group symmetry is spontaneously broken.
NASA Astrophysics Data System (ADS)
Kurtuldu, Güven; Rappaz, Michel
2015-06-01
Recently, we have shown that minute Cr additions (typically 0.1 wt%) to Al-Zn alloys solidified in a uniform temperature field lead to the formation of fine equiaxed fcc Al grains [1]. Furthermore, these grains exhibit an unexpectedly large number of twin, or neartwin, relationships with their nearest neighbors and some of them even show a 5-fold symmetry multi-twin relationship with a common (110) direction. Similar observations have been made for yellow gold alloys (Au-12.5wt%Cu-12.5wt%Ag) inoculated with very small amounts of Ir (5-200 ppm) [2]. These results become fully consistent when one considers that the primary fcc phase forms on facets of icosahedral quasicrystals (iQC's), either by heteroepitaxy solidification or by peritectic transformation, with the following relationship: <111>fcc || 3-fold symmetry iQC axes, <110>fcc ? 2-fold symmetry iQC axes. The present study contributes to a better understanding of the frequency of twin boundary formation by the nucleation of fcc phase from an iQC template. A simple stereological model for the formation of equiaxed grains on such iQC templates has been derived. It is based on a 3D Voronoi tessellation of randomly distributed and oriented iQC template centers. Each iQC nucleation template site is the origin of 20 fcc grains with the heteroepitaxy relationships mentioned above on the 20 facets of the iQC. Therefore, the neighboring grains having a common iQC nucleation site contributes to the twin boundary frequency, while those coming from different iQC sites have random grain boundary orientations. The twin boundary frequency of the grains nucleated from iQC templates seen in 2D metallographic sections is compared with that measured in EBSD reconstructed grain structures.
Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Li, Tao; Chen, Jian-bing; Li, Jie
2016-03-01
The point group identification (PGI) algorithm is proposed to determine the representative point sets in response analysis of nonlinear stochastic dynamic systems. The PGI algorithm is employed to identify point groups and their feature points in an initial point set by combining subspace clustering analysis and the graph theory. Further, the representative point set of the random-variate space is determined according to the minimum generalized F-discrepancy. The dynamic responses obtained by incorporating the algorithm PGI into the probability density evolution method (PDEM) are compared with those by the Monte Carlo simulation method. The investigations indicate that the proposed method can reduce the number of the representative points, lower the generalized F-discrepancy of the representative point set, and also ensure the accuracy of stochastic structural dynamic analysis.
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 4Â°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.
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.
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.
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.
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.
NASA Astrophysics Data System (ADS)
Sargolzaei, Mahdi; Lotfizadeh, Neda
2011-04-01
We have demonstrated the electronic structures and magnetic properties of single 3d transition metal (TM) atoms encapsulated in noble metal clusters with icosahedral symmetry in the framework of relativistic density functional theory. Orbital polarization corrections have been used to obtain an upper-estimation for orbital magnetic moments of all individual 3d atoms. The relativistic corrections are marginally affected the spin magnetic moments, whereas they induce significant orbital magnetism in TM@X12 icosahedra. It is found that a superatomic picture has to be taken into account in order to explain the spin and orbital magnetism induced in TM@X12 icosahedron based on the Hund’s rules.
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 (?-B12) based chain [Bulletin of APS Annual Meeting, p265 (2013)] and ring structures has prompted us to study the two-dimensional (2D) ?-B12 based structures. Recently, we have carried out a systematic molecular dynamics study on the structural stabilities and electronic properties of the 2D ?-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 ?3, ?4, ?6 (flat triangular), and ?' types. We have found that the optimized structures are energetically in the order of ?6 < ?' < ?3 < ?4 which is different from the energy order of ?'< ?6 < ?4 < ?3 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.
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.
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 give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found. Images FIGURE 5 FIGURE 6 FIGURE 8 FIGURE 9 PMID:8312492
Neutron-diffraction study of icosahedral Al-Cu-Fe single quasicrystals
NASA Astrophysics Data System (ADS)
Cornier-Quiquandon, M.; Quivy, A.; Lefebvre, S.; Elkaim, E.; Heger, G.; Katz, A.; Gratias, D.
1991-08-01
This paper reports neutron-diffraction results on a single icosahedral quasicrystal of Al-Cu-Fe. The basic properties of the structure have been extracted using six-dimensional (6D) Patterson analysis from 219 independent orbits of reflections. Described in 6D space, the structure has hyperspace group F?m35 and is defined by the three atomic surfaces located at special points with full icosahedral symmetry of the F lattice. These points are the two inequivalent nodes of the underlying primitive lattice plus one of the two inequivalent body centers, the remaining one being empty. The atomic surfaces are embedded in perpendicular space and are well approximated by polyhedra bounded by two-fold planes. These are a large triacontahedron located at the origin, a triacontahedron of the same size truncated along the five-fold directions at the other node, and a small polyhedron bounded by twofold planes at the occupied body center. Although no speculation has been made for distributing the atomic species within these atomic surfaces, the raw reliability factor between experimental and calculated diffraction intensities is already 0.20 with no fitting parameters and the density is found only 2.9% lower than the experimental one. The model presented here can be considered as a zero-order structure to be used for subsequent modeling. The atomic surfaces generate no unacceptably short distances between atoms. Both interatomic distances and coordination numbers of the three first shells are in good agreement with the most recent extended x-ray-absorption fine-structure results. The atomic surfaces are connected together by 3D pieces embedded in the parallel space. They define a partition of the 6D space in hyperprisms, which can be decomposed in direct products of 3D facets located in perpendicular and parallel spaces similar to the oblique cell decomposition of the 3D Penrose tiling. Phasons can propagate along the five-fold and two-fold directions by atomic jumps of 0.1705 and 0.179 nm, respectively.
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.
VIRUS-LIKE PARTICLES WITH T=19 ICOSAHEDRAL SYMMETRY IN A HUMAN GASTROENTERITIS STOOL
Virus-like particles not previously described were observed in a human gastroenteritis stool using negative-stain TEM. The stool was among a number of acute-phase illness stools which had been collected in Egypt during 1980. The particles measured 65-70 nm in diameter, and it was...
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, an icosahedral hydrostatic dynamical core designed for consistency and versatility", in preparation.
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
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…
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 simpleâ€¦
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
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.
NASA Astrophysics Data System (ADS)
Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, D. S.
2004-03-01
Over a half-century ago, Charles Frank argued that liquid metals could be undercooled because of the development of icosahedral short-range order in the liquid, which is incompatible with the long-range translational periodicity of crystal phases. We present the results of in-situ synchrotron x-ray diffraction studies of electrostatically levitated droplets of a TiZrNi liquid alloy, which demonstrate that icosahedral short-range atomic order exists and becomes more developed with decreasing temperature below the melting temperature. The increased icosahedral order favors the transformation of the liquid to a metastable icosahedral quasicrystal phase, instead of the stable tetrahedrally coordinated crystal intermetallic phase, demonstrating a clear connection between the nucleation barrier and the local structure of the liquid and verifying Frank's hypothesis for the first time. *Supported by NASA under contract NAG 8-1682, and by the National Science Foundation under grants DMR 00-72787 and DMR 03-07410.
Structure and Decoration of the Icosahedral and Rhombohedral Phases in AlCuFe Alloys
NASA Astrophysics Data System (ADS)
Le Lann, A.; Devaud, J.
1995-01-01
Structural models for AlCuFe icosahedral and rhombohedral phases are obtained by decomposition, in perpendicular space, of the atomic surfaces into cells of identical local environment. The models are described in 3D real space and compared to the corresponding H.R.E.M. images obtained on structurally perfect icosahedral and rhombohedral phases. The specificity of their aperiodic structure and chemical decoration is outlined.
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.
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 ?-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)
Rappaz, Michel; Kurtuldu, GÃ¼ven
2015-08-01
We have recently shown that minute solute element additions to liquid metallic alloys can strongly influence the nucleation of the fcc phase and act as a grain refinement method. Electron back-scattered diffraction observations revealed a concomitant increase in the percentage of nearest neighbor (nn) grains that are in a twin relationship. Furthermore, multiple-twinned (MT) nn grain configurations with a fivefold symmetry around a common direction have been identified, an occurrence that can be explained when the symmetry of the icosahedron is accounted for. It was then conjectured that a new nucleation mechanism occurs in two steps: first, the formation of small icosahedral quasicrystals in the melt, followed by heteroepitaxy of the fcc phase on facets of these quasicrystals. In the present contribution, based on thermodynamics arguments, it is proposed that the first step occurs by spinodal decomposition of the liquid, in a manner similar to Guinier-Preston zones formation in solid state precipitation, while the second step is a transformation of these quasicrystal precursors into MT-fcc nanocrystals once the driving force for this transformation is sufficient to overcome the fcc-liquid interfacial energy and the elastic strains associated with MT-fcc nanoparticles. This explanation sets up guidelines for finding solute elements and composition ranges that favor this grain refinement mechanism.
NASA Astrophysics Data System (ADS)
Dewar, R. L.; Hudson, S. R.
1998-01-01
A simple and general definition of stellarator symmetry is presented and its relation to previous definitions discussed. It is shown that the field-line flow in systems possessing stellarator symmetry is time-reversal invariant if the the toroidal angle is regarded as “time”.
Finite size specimens with cracks of icosahedral Al—Pd—Mn quasicrystals
NASA Astrophysics Data System (ADS)
Yang, Lian-Zhi; Ricoeur, Andreas; He, Fan-Min; Gao, Yang
2014-05-01
Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral Al—Pd—Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon—phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral Al—Pd—Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon—phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of phonon—phason coupling effect on the icosahedral Al—Pd—Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.
Icosahedral quasicrystal structure determination: Al-Cu-Li
Qiu, S.Y.
1992-01-01
This dissertation reports the theoretical study of the determination of quasicrystal atomic structures. A new method is developed for phasing the quasicrystal diffraction data (neutron, X-ray diffraction). A mathematical model is built which explicitly relates quasicrystals to their related periodic crystals. A test of the method is made on a simple theoretical system, the icosahedral quasiperiodic Ammann tiling decorated with point scatterers (Dirac [sigma] scattering potential) on vertices. A success is achieved in reconstructing the phases of the quasicrystal. The method is applied to a real quasicrystal system, the icosahedral quasicrystal i(Al[sub .570]Cu[sub .108]Li[sub .322]), where single-grain X-ray as well as neutron diffraction data are available, and the structure of the related large-unit-cell crystal of R(Al[sub .564]Cu[sub .116]Li[sub .320]), is well known. The reconstructed phases give the density of scatterers, which can then be used in the analysis of the atomic structure, and provide a guide to the final structure modeling. The validity of the method is evaluated with respect to the non-negativity of the resulting electron densities. In order to identify the negativity due to the intensity cut-off, the negativity is evaluated as a function of the cut-off and compared with the exact and reconstructed quasiperiodic Ammann tilings as well as with the experimental and model crystal data of R(Al[sub .564]Cu[sub .116]Li[sub .320]). It is concluded that the negativity of the reconstructed quasiperiodic electron density of i(Al[sub .570]Cu[sub .108]Li[sub .322]) is consistent with a cut-off effect. Modeling of the i(Al[sub .570]Cu[sub .108]Li[sub .322]) atomic structure in six-dimensional hyperspace is discussed. It is assumed that atomic surfaces can be modeled by polyhedra which can be described by a finite number of parameters. The authors successfully generated a model which agrees with the experimental data.
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.; KoÅ¾elj, P.; Vrtnik, S.; JagodiÄ, M.; JagliÄiÄ‡, Z.; DolinÅ¡ek, 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 â†’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 â†’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.
Schein, Stan; Gayed, James Maurice
2014-01-01
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. PMID:24516137
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. PMID:24516137
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.
NASA Astrophysics Data System (ADS)
Hu, Wen; Yi, Jianhong; Zheng, Biju; Wang, Limin
2013-06-01
Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti1.6V0.4Ni)100-xScx (x=0.5-6) quaternary icosahedral quasicrystals have been successfully synthesized via arc-melting and subsequent melt-spinning techniques, and then their electrochemical performance toward hydrogen is explored. When the molar ratio of Sc addition is under 1%, a maximum discharge capacity of about 270 mA h g-1 can be delivered. With further increasing Sc amount to 6%, good cycling stability as well as significantly retarded self-discharge rate (capacity retention 94% after 24 h relaxation) is observed. But meanwhile, the discharge capacities fall into 250-240 mA h g-1, and the electrocatalytic activity improvement is highly demanded.
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 1.54â€…eV) and low formation energies (0.06 to 0.21â€…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]3âˆ’ and [Sn@Cu12@Sn20]12âˆ’, 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 ÂµB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices. PMID:25376938
Design of Three-shell Icosahedral Matryoshka Clusters A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd, Mn)
NASA Astrophysics Data System (ADS)
Huang, Xiaoming; Zhao, Jijun; Su, Yan; Chen, Zhongfang; King, R. Bruce
2014-11-01
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 ÂµB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices.
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
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
NASA Astrophysics Data System (ADS)
Mainzer, Klaus
Symmetry and complexity in early culture and philosophy -- Symmetry and complexity in mathematics -- Symmetry and complexity in physical sciences -- Symmetry and complexity in chemical sciences -- Symmetry and complexity in life sciences -- Symmetry and complexity in economic and social sciences -- Symmetry and complexity in computer science -- Symmetry and complexity in philosophy and arts.
Structural symmetry and protein function.
Goodsell, D S; Olson, A J
2000-01-01
The majority of soluble and membrane-bound proteins in modern cells are symmetrical oligomeric complexes with two or more subunits. The evolutionary selection of symmetrical oligomeric complexes is driven by functional, genetic, and physicochemical needs. Large proteins are selected for specific morphological functions, such as formation of rings, containers, and filaments, and for cooperative functions, such as allosteric regulation and multivalent binding. Large proteins are also more stable against denaturation and have a reduced surface area exposed to solvent when compared with many individual, smaller proteins. Large proteins are constructed as oligomers for reasons of error control in synthesis, coding efficiency, and regulation of assembly. Symmetrical oligomers are favored because of stability and finite control of assembly. Several functions limit symmetry, such as interaction with DNA or membranes, and directional motion. Symmetry is broken or modified in many forms: quasisymmetry, in which identical subunits adopt similar but different conformations; pleomorphism, in which identical subunits form different complexes; pseudosymmetry, in which different molecules form approximately symmetrical complexes; and symmetry mismatch, in which oligomers of different symmetries interact along their respective symmetry axes. Asymmetry is also observed at several levels. Nearly all complexes show local asymmetry at the level of side chain conformation. Several complexes have reciprocating mechanisms in which the complex is asymmetric, but, over time, all subunits cycle through the same set of conformations. Global asymmetry is only rarely observed. Evolution of oligomeric complexes may favor the formation of dimers over complexes with higher cyclic symmetry, through a mechanism of prepositioned pairs of interacting residues. However, examples have been found for all of the crystallographic point groups, demonstrating that functional need can drive the evolution of any symmetry. PMID:10940245
Pauling, Linus
1989-01-01
The twofold-axis electron-diffraction photographs of icosahedral quasicrystals are of three kinds, reflecting three different structures of the cubic crystals that by icosahedral twinning form the quasicrystals. The first kind, represented by Al13Cu4Fe3, contains two very large icosahedral complexes, each of about 4680 atoms, in the body-centered arrangement, with six smaller icosahedral complexes (104 atoms each) in the principal interstices. The second kind, represented by Al5Mn, contains four of the very large complexes in the face-centered arrangement (cubic close packing), with four of the smaller clusters in the interstices. The third kind, represented by Al6CuLi3, contains eight icosahedral complexes, each of about 1350 atoms, in the ?-W arrangement. The supporting evidence for these cubic structures is discussed as well as other evidence showing that the simple quasicrystal theory, which states that quasicrystals do not involve any translational identity operations, has to be modified. Images PMID:16594078
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.
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)
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.
Ultrathin Icosahedral Pt-Enriched Nanocage with Excellent Oxygen Reduction Reaction Activity.
He, Dong Sheng; He, Daping; Wang, Jing; Lin, Yue; Yin, Peiqun; Hong, Xun; Wu, Yuen; Li, Yadong
2016-02-10
Cost-efficient utilization of Pt in the oxygen reduction reaction (ORR) is of great importance for the potential industrial scale demand of proton-exchange membrane fuel cells. Designing a hollow structure of a Pt catalyst offers a great opportunity to enhance the electrocatalytic performance and maximize the use of precious Pt. Herein we report a routine to synthesize ultrathin icosahedral Pt-enriched nanocages. In detail, the Pt atoms were conformally deposited on the surface of Pd icosahedral seeds, followed by selective removal of the Pd core by a concentrated HNO3 solution. The icosahedral Pt-enriched nanocage that is a few atomic layers thick includes the merits of abundant twin defects, an ultrahigh surface/volume ratio, and an ORR-favored Pt{111} facet, all of which have been demonstrated to be promoting factors for ORR. With a 10 times higher specific activity and 7 times higher mass activity, this catalyst shows more extraordinary ORR activity than the commercial Pt/C. The ORR activity of icosahedral Pt-enriched nanocages outperforms the cubic and octahedral nanocages reported in the literature, demonstrating the superiority of the icosahedral nanocage structure. PMID:26808073
Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals
Parshin, P. P.; Zemlyanov, M. G. Brand, R. A.
2007-05-15
The atomic dynamics of an Al-Ni-Fe decagonal quasicrystal and an Al-Cu-Fe icosahedral quasicrystal are investigated experimentally using the isotopic contrast method in inelastic neutron scattering. The partial spectra of thermal vibrations of copper, nickel, iron, and aluminum atoms in the decagonal and icosahedral quasicrystals are reconstructed directly from the experimental data without recourse to model concepts. The limiting energies and positions of the main features in the partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals are determined. It is established that, in the quasicrystals under investigation, the copper and nickel atoms are bound more weakly than the iron atoms and that the partial vibrational spectrum of aluminum atoms in the quasicrystals is considerably harder than the spectrum of pure metallic aluminum.
Surface preparation and characterization of the icosahedral Al-Pd-Mn-Ga quasicrystal
Heinzig, Mark; Jenks, Cynthia J.; Van Hove, Michel; Fisher, Ian; Canfield, Paul; Thiel, Patricia A.
2002-01-08
Auger electron spectroscopy and low-energy electron diffraction (LEED) provide basic information about the structure and composition of the fivefold surface of the quaternary quasicrystal, icosahedral Al67Pd4Mn21Ga8. Surface preparation techniques established previously for two of the icosahedral ternary alloys, Al-Pd-Mn and Al-Cu-Fe, appear to be similarly effective for Al-Pd-Mn-Ga. After annealing in the range 600-950 K, the surface concentration of Ga is constant and low. After annealing in the range 900-950 K, a good LEED pattern is obtained. LEED indicates that Ga changes the surface structure significantly.
Does an icosahedral short-range order prevail in glass-forming Zr-Cu melts?
NASA Astrophysics Data System (ADS)
Holland-Moritz, Dirk; Yang, Fan; Kordel, Tobias; Klein, Stefan; Kargl, Florian; Gegner, Jan; Hansen, Thomas; Bednarcik, Jozef; Kaban, Ivan; Shuleshova, Olga; Mattern, Norbert; Meyer, Andreas
2012-12-01
We report on investigations of the static structure factors of glass-forming Zr-Cu alloy melts by combination of the containerless processing technique of electrostatic levitation with diffraction of neutron and synchrotron radiation. The partial Bhatia-Thornton structure factors SNN and SNC were determined from the two total structure factors. While it is widely assumed in literature that the good glass-forming ability of Zr-Cu is related to an icosahedral short-range order prevailing in the melt, our partial structure factors demonstrate that the liquid Zr-Cu is not characterized by a dominant icosahedral short-range order.
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…
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.
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…
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 ?m-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 ?m 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.
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...
Calculation of vibrational spectra of an icosahedral quasicrystal AlCuFe
Rudenko, A. N. Mazurenko, V. G.
2007-11-15
Vibrational spectra of an icosahedral quasicrystal AlCuFe have been calculated on the basis of a crystalline 1/1 approximant by the recurrence method. To describe the interaction of atoms in a quasicrystal, the semiempirical EAM model was used. It is shown that the calculated spectra are in satisfactory agreement with the experimental neutron inelastic scattering data.
Correlation of Atomic Cluster Symmetry and Glass-Forming Ability of Metallic Glass
Xi Xuekui; Li Lilong; Wu Yue; Zhang Bo; Wang Weihua
2007-08-31
Local structures play a crucial role in glass formation and properties. In addition to topological short-range order, the geometric property of site symmetry is another important but less known characteristic of local structures. It is shown that the observed sharp increase of glass forming ability of Ce{sub 70-x}Al{sub 10}Cu{sub 20}Co{sub x} upon Co addition is correlated with a dramatic increase of Al site symmetry, as reflected by decreasing quadrupole frequency measured by {sup 27}Al NMR. The result is consistent with the structure model of Al-centered icosahedral clusters as the predominant structural building blocks.
None
2011-10-06
- 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 ?massless? modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a ?massive? SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic ?vector? field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are ?scalar?? fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a ?renormalizable? theory. From our analysis of the preserved gauge symmetry, we suggested in 1966 that this is indeed the case, in contradistinction to the aforementioned earlier theories of charged massive vector fields. The full proof of ?renormalizability? is subtle and was achieved in the impressive work of ?t Hooft and Veltman. One gains some insight into the subtleties by making explicit the equivalence of Higgs? approach with ours. - To a large extend, the LHC was build to detect the massive SBS scalar boson, i.e. the fluctuations of the scalar field. More elaborate realizations of the mechanism without elementary scalars are possible, but their experimental confirmation may (or may not) be outside the scope of present available technology. - The mechanism of Brout, Englert and Higgs unified in the same theoretical framework short- and long-range forces. It became the cornerstone of the electroweak theory and opened the way to a modern view on unified laws of nature.
Spectral signatures of high-symmetry quantum dots and effects of symmetry breaking
NASA Astrophysics Data System (ADS)
Karlsson, K. F.; Oberli, D. Y.; Dupertuis, M. A.; Troncale, V.; Byszewski, M.; Pelucchi, E.; Rudra, A.; Holtz, P. O.; Kapon, E.
2015-10-01
High symmetry epitaxial quantum dots (QDs) with three or more symmetry planes provide a very promising route for the generation of entangled photons for quantum information applications. The great challenge to fabricate nanoscopic high symmetry QDs is further complicated by the lack of structural characterization techniques able to resolve small symmetry breaking. In this work, we present an approach for identifying and analyzing the signatures of symmetry breaking in the optical spectra of QDs. Exciton complexes in InGaAs/AlGaAs QDs grown along the [111]B crystalline axis in inverted tetrahedral pyramids are studied by polarization resolved photoluminescence spectroscopy combined with lattice temperature dependence, excitation power dependence and temporal photon correlation measurements. By combining such a systematic experimental approach with a simple theoretical approach based on a point-group symmetry analysis of the polarized emission patterns of each exciton complex, we demonstrate that it is possible to achieve a strict and coherent identification of all the observable spectral patterns of numerous exciton complexes and a quantitative determination of the fine structure splittings of their quantum states. This analysis is found to be particularly powerful for selecting QDs with the highest degree of symmetry (C3v and {D}3h) for potential applications of these QDs as polarization entangled photon sources. We exhibit the optical spectra when evolving towards asymmetrical QDs, and show the higher sensitivity of certain exciton complexes to symmetry breaking.
Nematic phases and the breaking of double symmetries
NASA Astrophysics Data System (ADS)
Mathy, C. J. M.; Bais, F. A.
2007-03-01
In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra Tr and the symmetry algebra U characterizing the effective "low energy" theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.
Nematic phases and the breaking of double symmetries
Mathy, C.J.M. . E-mail: cmathy@princeton.edu; Bais, F.A. . E-mail: bais@science.uva.nl
2007-03-15
In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra T{sub r} and the symmetry algebra U characterizing the effective 'low energy' theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.
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.).
Fuzzy symmetries of molecule and molecular orbital: characterization and simple application
NASA Astrophysics Data System (ADS)
Zhao, Xuezhuang; Xu, Xiufang; Wang, Guichang; Pan, Yinming; Cai, Zunsheng
A fuzzy point group has been constructed to describe imperfect molecular symmetry by using fuzzy set theory. Then the fuzzy symmetry of the molecular orbital has also been analyzed, and several concepts, such as fuzzy irreducible representation and fuzzy characters (fuzzy generalized parity) for molecular orbitals have been advanced. The results show that sometimes the symmetry of the molecule as a whole is not obvious, however, that of some molecular orbital may be obvious. Although oscillator strength in the electronic spectrum is not determined solely by fuzzy symmetry, it is obviously related to the fuzzy symmetry, which seems to be a fuzzy rule for the electronic spectrum.
NASA Astrophysics Data System (ADS)
Ting, Tan Yee; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Fauzi, Wan Nor Farhana Wan Mohd; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat
2014-12-01
A torsion free crystallographic group, which is known as a Bieberbach group, has many interesting properties. The properties of the groups can be explored by computing the homological functors of the groups. In the computation of the homological functors, the abelianization of groups plays an important role. The abelianization of a group can be constructed by computing its derived subgroup. In this paper, the construction of the abelianization of all Bieberbach groups of dimension four with symmetric point group of order six are shown. Groups, Algorithms and Programming (GAP) software is used to assist the construction.
NASA Astrophysics Data System (ADS)
Buchmuller, Wilfried; Dierigl, Markus; Ruehle, Fabian; Schweizer, Julian
2015-11-01
We consider six-dimensional supergravity with gauge group SO (10) × U(1)A, compactified on the orbifold T2 /Z2. Three quark-lepton generations arise as zero modes of a bulk 16-plet due to magnetic flux of the anomalous U(1)A. Boundary conditions at the four fixed points break SO (10) to subgroups whose intersection is the Standard Model gauge group. The gauge and Higgs sector consist of "split" SO (10) multiplets. As a consequence of the U(1)A flux, squarks and sleptons are much heavier than gauge bosons, Higgs bosons, gauginos and higgsinos. We thus obtain a picture similar to "split supersymmetry". The flavor structure of the quark and lepton mass matrices is determined by the symmetry breaking at the orbifold fixed points.
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.
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. PMID:25747095
Electron momentum distribution of icosahedral Cd84Yb16 studied by Compton scattering
NASA Astrophysics Data System (ADS)
Okada, J. T.; Watanabe, Y.; Nanao, S.; Tamura, R.; Takeuchi, S.; Yokoyama, Y.; Hiraoka, N.; Itou, M.; Sakurai, Y.
2003-10-01
The electron momentum distribution in icosahedral Cd84Yb16 has been studied using the high-resolution Compton scattering technique with a momentum resolution of 0.16 a.u. The experimental valence-electron Compton profile is decomposed into two components: an inverted parabolalike one and a broad Gaussian-like one. We have found that the Fermi sphere, deduced from the number of electrons under the inverted parabolalike component, just coincides with the quasi-Brillouin zones constructed from the intense (211111) and (221001) reciprocal points. The Gaussian-like part is attributed to the electron occupation of the Yb 5d states. These facts are taken as signature that both the Hume-Rothery mechanism and the sp-d hybridization mechanism contribute to the formation of the pseudogap, stabilizing the icosahedral phase of Cd84Yb16.
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.
Formation of a well ordered ultrathin aluminum oxide film on icosahedral AlPdMn quasicrystal
Longchamp, J.-N.; Burkardt, S.; Weisskopf, Y.; Erbudak, M.
2007-09-01
We have exposed the pentagonal surface of icosahedral AlPdMn quasicrystal kept at 700 K to several hundred langmuirs of O{sub 2}, which results in the formation of a 5 A thick, well ordered aluminum oxide film. The local structure of the film resembles that of the oxide layers formed on ordered binary alloys of Al except that the quasicrystalline substrate makes the film consist of five pairs of nanometer-size aluminum oxide domains exposing their nominal (111) faces parallel to the substrate surface and rotated by 72 deg. with respect to each other. The orientational relationship between these domains and the substrate is a consequence of the affinity of the icosahedral structure of AlPdMn to the CsCl structure.
Icosahedral ordering in liquid iron studied via x-ray scattering and Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Inui, Masanori; Maruyama, Kenji; Kajihara, Yukio; Nakada, Masaru
2009-11-01
X-ray diffraction measurements were carried out for liquid iron near the melting temperature and atomic configurations were constructed from the structure factor S(Q) obtained, by reverse Monte Carlo modeling and Monte Carlo simulation with the effective pair potential deduced by the inverse method. The bond-orientational order parameter Å´6 calculated from the atomic configurations obtained from both simulations indicates a pronounced icosahedral ordering, and the fraction of nearly icosahedral configurations is estimated to be approximately 14% in liquid iron. These experimentally obtained results seem consistent with recent results of ab initio molecular-dynamics simulation for liquid iron [P. Ganesh and M. Widom, Phys. Rev. B 77, 014205 (2008)].
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.
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.
Dual-phase glassy/nanoscale icosahedral phase materials in Cuâ€“Zrâ€“Tiâ€“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 Cuâ€“Zrâ€“Tiâ€“Pd alloys. The data obtained indicate that the Cuâ€“Zrâ€“Tiâ€“Pd icosahedral phase is not a Cu-rich part of the compositional homogeneity area of the Zrâ€“Cuâ€“Pd one. Moreover, Ti, as well as Pd, is found to be an important element stabilizing quasicrystalline phase in the Cuâ€“Zrâ€“Tiâ€“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: â€¢ Formation kinetics, stability and homogeneity area of nanoscale icosahedral phase â€¢ Cuâ€“Zrâ€“Tiâ€“Pd icosahedral phase is not a Cu-rich part of Zrâ€“Cuâ€“Pd one. â€¢ Ti, as well as Pd, is an important element stabilizing quasicrystalline phase. â€¢ Difference in transformation kinetics above and below glass-transition region.
NASA Astrophysics Data System (ADS)
Tsai, An Pang
2008-04-01
We review the stability of various icosahedral quasicrystals (iQc) from a metallurgical viewpoint. The stability of stable iQcs is well interpreted in terms of Hume-Rothery rules, i.e. atomic size factor and valence electron concentration, e/a. For metastable iQcs, we discuss the role of phason disorder introduced by rapid solidification, in structural stability and its interplay with chemical order and composition. Invited paper.
B12Hn and B12Fn: planar vs icosahedral structures
2012-01-01
Using density functional theory and quantum Monte Carlo calculations, we show that B12Hn and B12Fn (n = 0 to 4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters. Moreover, we show that the fully planar B12F6 cluster is more stable than the three-dimensional counterpart. These results open up the possibility of designing larger boron-based nanostructures starting from quasi-planar or fully planar building blocks. PMID:22546348
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.
A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, Jin
2013-11-01
The Nonhydrostatic Icosahedral Model (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's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM uses innovations in model formulation similar to its hydrostatic version of the Flow-following Icosahedral Model (FIM) developed by Earth System Research Laboratory (ESRL) which has been tested and accepted for future use by the National Weather Service as part of their operational global prediction ensemble. Innovations from the FIM used in the NIM include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, et al., 2010), * All differentials evaluated as finite-volume integrals around the cells, *Icosahedral grid optimization (Wang and Lee, 2011) NIM extends the two-dimensional finite-volume operators used in FIM into the three-dimensional finite-volume solvers designed to improve pressure gradient calculation and orographic precipitation over complex terrain. The NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as warm bubble, density current, internal gravity wave, and mountain waves. Physical parameterizations have been incorporated into the NIM dynamic core and successfully tested with multimonth aqua-planet simulations. Recent results from NIM simulations will be presented at the Symposium.
Symmetry classification of bond order parameters in cuprates
NASA Astrophysics Data System (ADS)
Zeyher, Roland
2015-02-01
We study bond order parameters for generalized t -J models on a square lattice. Using the plane-wave limit the considered order parameters form basis functions for irreducible representations of the symmetry transformations of the point group and of time reversal. We show that, for instability wave vectors along the diagonals, all possible basis functions either are fine tuned (i.e., obey restrictions beyond the requirements of symmetry) or break time-reversal symmetry and thus describe flux states. For instability wave vectors along the crystalline axes, corresponding to the observed case in underdoped cuprates, there are only three representations with A1,B1, and E symmetry which do not break time-reversal symmetry in the general case. We suggest that one of them has recently been observed in resonant elastic x-ray scattering.
Computational self-assembly of a one-component icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Engel, Michael; Damasceno, Pablo F.; Phillips, Carolyn L.; Glotzer, Sharon C.
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.
Computational self-assembly of a one-component icosahedral quasicrystal.
Engel, Michael; Damasceno, Pablo F; Phillips, Carolyn L; Glotzer, Sharon C
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems. PMID:25485986
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
NASA Astrophysics Data System (ADS)
Iachello, Francesco
2012-10-01
After an historical introduction of the concept of symmetry, the many ways in which symmetry is used in physics are briefly reviewed. A generalization of the concept of symmetry to supersymmetry is also briefly reviewed. Examples of dynamic symmetries and supersymmetries are shown.
A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, Jin
2014-05-01
The Nonhydrostatic Icosahedral Model (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's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.
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.
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.
Solution growth of a binary icosahedral quasicrystal of Sc[subscript 12]Zn[subscript 88
Canfield, P.C.; Caudle, M.L.; Ho, C.-S.; Kreyssig, A.; Nandi, S.; Kim, M.G.; Lin, X.; Kracher, A.; Dennis, K.W.; McCallum, R.W.; Goldman, A.I.
2010-07-23
We report the discovery of a binary icosahedral phase in a Sc-Zn alloy obtained through solution-growth, producing millimeter-sized, facetted, single grain quasicrystals that exhibit different growth morphologies, pentagonal dodecahedra, and rhombic triacontahedra, under only marginally different growth conditions. These two morphologies manifest different degrees of quasicrystalline order. The discovery of i-Sc{sub 12}Zn{sub 88} suggests that a re-examination of binary phase diagrams at compositions close to crystalline approximant structures may reveal other binary quasicrystalline phases.
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.
Magnetic color symmetry of lattice rotations in a diamagnetic material.
Denev, S; Kumar, A; Biegalski, M D; Jang, H W; Folkman, C M; Vasudevarao, A; Han, Y; Reaney, I M; Trolier-McKinstry, S; Eom, C-B; Schlom, D G; Gopalan, V
2008-06-27
Oxygen octahedral rotations are the most common phase transitions in perovskite crystal structures. Here we show that the color symmetry of such pure elastic distortions is isomorphic to magnetic point groups, which allows their probing through distinguishing polar versus magnetic symmetry. We demonstrate this isomorphism using nonlinear optical probing of the octahedral rotational transition in a compressively strained SrTiO3 thin film that exhibits ferroelectric (4mm) and antiferrodistortive (4{'}mm{'}) phases evolving through independent phase transitions. The approach has broader applicability for probing materials with lattice rotations that can be mapped to color groups. PMID:18643702
Medium-range icosahedral order in quasicrystal-forming Zr{sub 2}Pd binary metallic glass
Huang Li; Fang, X. W.; Wang, C. Z.; Ho, K. M.; Kramer, M. J.; Ding, Z. J.
2011-06-06
Medium-range order in Zr{sub 2}Pd metallic glass was studied using a combination of x-ray diffraction experiment and atomistic simulations. We show that, in contrast to earlier experimental interpretations, the icosahedral-like polyhedron is centered around Pd, rather than Zr. Furthermore, we find that the ordered icosahedral packing around Pd extends to the third shell in the way similar to that in the Bergman-type clusters. The existence of Bergman-type clusters sheds interesting light into the formation of nanoquasicrystal phase during crystallization process of Zr{sub 2}Pd metallic glass.
Ion beam induced destabilization of icosahedral structures in gas phase prepared FePt nanoparticles
Dmitrieva, Olga; Rellinghaus, Bernd; Kaestner, Jochen; Liedke, Maciej Oskar; Fassbender, Juergen
2005-05-15
Multiply twinned FePt nanoparticles with icosahedral structures were prepared by dc magnetron sputtering in argon. The icosahedral structure of these particles is known to be very stable against structural transformations into both the face-centered cubic phase (fcc, A1) and the chemically ordered tetragonal L1{sub 0} phase upon in-flight or post-deposition thermal annealing. Irradiation of these multiply twinned FePt particles with 5 keV He ions, however, resulted in a transformation into predominantly single crystalline fcc particles at high ion fluences of f>10{sup 17} ions/cm{sup 2}. Adjacent particles were observed to coalesce under the effect of He irradiation, and the size of individual particles was found to be slightly reduced, which indicates a high atomic mobility owing to temporarily enhanced defect concentrations caused by the ion bombardment. Strikingly, there was no indication for the occurrence of L1{sub 0} ordered FePt nanoparticles upon ion irradiation in these samples.
The architecture and chemical stability of the archaeal Sulfolobus turreted icosahedral virus.
Khayat, Reza; Fu, Chi-yu; Ortmann, Alice C; Young, Mark J; Johnson, John E
2010-09-01
Viruses utilize a diverse array of mechanisms to deliver their genomes into hosts. While great strides have been made in understanding the genome delivery of eukaryotic and prokaryotic viruses, little is known about archaeal virus genome delivery and the associated particle changes. The Sulfolobus turreted icosahedral virus (STIV) is a double-stranded DNA (dsDNA) archaeal virus that contains a host-derived membrane sandwiched between the genome and the proteinaceous capsid shell. Using cryo-electron microscopy (cryo-EM) and different biochemical treatments, we identified three viral morphologies that may correspond to biochemical disassembly states of STIV. One of these morphologies was subtly different from the previously published 27-A-resolution electron density that was interpreted with the crystal structure of the major capsid protein (MCP). However, these particles could be analyzed at 12.5-A resolution by cryo-EM. Comparing these two structures, we identified the location of multiple proteins forming the large turret-like appendages at the icosahedral vertices, observed heterogeneous glycosylation of the capsid shell, and identified mobile MCP C-terminal arms responsible for tethering and releasing the underlying viral membrane to and from the capsid shell. Collectively, our studies allow us to propose a fusogenic mechanism of genome delivery by STIV, in which the dismantled capsid shell allows for the fusion of the viral and host membranes and the internalization of the viral genome. PMID:20592081
NASA Astrophysics Data System (ADS)
Kelton, Kenneth
2005-03-01
Over a half-century ago, Charles Frank argued that metallic liquids could be undercooled because of developing icosahedral short-range order (ISRO) in the liquid that is incompatible with the translational periodicity of crystal phases. Our recent high-energy x-ray diffraction and nucleation undercooling studies of electrostatically levitated droplets of a Ti-Zr-Ni liquid produced the first experimental proof of this hypothesis. In addition to coupling to the nucleation barrier for the ordered phase, the icosahedral order can significantly influence the thermophysical properties of the liquid. A sharp decrease in the specific heat that is correlated with the growing ISRO indicates a rapidly decreasing configurational entropy in the liquid, at temperatures far above the glass transition temperature. Surprisingly, our studies demonstrate that ISRO is evident even above the liquidus temperature in the Ti-Zr-Ni liquid as well as in liquid Ni. It is significantly distorted in liquid Ti, consistent with an increasing importance of the covalent character of the 3-d bonding, which frustrates the development of ISRO. Supported by NASA under contract NAG8-1682, and by the National Science Foundation under grant DMR 03-07410.
Theory of a reconstructive structural transformation in capsids of icosahedral viruses
NASA Astrophysics Data System (ADS)
Rochal, S. B.; Lorman, V. L.
2009-11-01
A theory of a reconstructive structural transformation in icosahedral capsid shells is developed for a whole family of virulent human viruses. It is shown that the reversible rearrangement of proteins during the virus maturation transformation is driven by the variation in the wave number l associated with the protein density distribution function. The collective displacement field of protein centers from their positions in the initial (procapsid) and the final (capsid) two-dimensional icosahderal structures is derived. The amplitude of the displacement field is shown to be small and it minimizes the calculated free energy of the transformation. The theory allows us to propose a continuous thermodynamical mechanism of the reconstructive procapsid-to-capsid transformation. In the frame of the density-wave approach, we also propose to take an equivalent plane-wave vector as a common structural feature for different icosahedral capsid shells formed by the same proteins. Using these characteristics, we explain the relation between the radii of the procapsid and capsid shells and generalize it to the case of the viral capsid polymorphism.
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 Auâ€“Au bonds have different stiffnesses depending on their lengths. The long Auâ€“Au bonds, which are more flexible than those in the bulk metal, are located at the icosahedral-based gold core surface. The short Auâ€“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 Auâ€“SR oligomers. PMID:26778685
The Structure of the NTPase That Powers DNA Packaging into Sulfolobus Turreted Icosahedral Virus 2
Happonen, Lotta J.; Oksanen, Esko; Liljeroos, Lassi; Goldman, Adrian; Kajander, Tommi
2013-01-01
Biochemical reactions powered by ATP hydrolysis are fundamental for the movement of molecules and cellular structures. One such reaction is the encapsidation of the double-stranded DNA (dsDNA) genome of an icosahedrally symmetric virus into a preformed procapsid with the help of a genome-translocating NTPase. Such NTPases have been characterized in detail from both RNA and tailed DNA viruses. We present four crystal structures and the biochemical activity of a thermophilic NTPase, B204, from the nontailed, membrane-containing, hyperthermoacidophilic archaeal dsDNA virus Sulfolobus turreted icosahedral virus 2. These are the first structures of a genome-packaging NTPase from a nontailed, dsDNA virus with an archaeal host. The four structures highlight the catalytic cycle of B204, pinpointing the molecular movement between substrate-bound (open) and empty (closed) active sites. The protein is shown to bind both single-stranded and double-stranded nucleic acids and to have an optimum activity at 80Â°C and pH 4.5. The overall fold of B204 places it in the FtsK-HerA superfamily of P-loop ATPases, whose cellular and viral members have been suggested to share a DNA-translocating mechanism. PMID:23698307
Hierarchy of bond stiffnesses within icosahedral-based gold clusters protected by thiolates
NASA Astrophysics Data System (ADS)
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.
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)
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.
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)
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 rectangular array just like cubed-sphere or lat-lon grids, the schemes computational performance is similar to that of the similar schemes on geodesic grids.
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. Physical parameterizations such as those used by GFS have been incorporated into NIM dynamic core and successfully tested with multi-months aqua-planet simulations as well as real data simulations. NIM has been implemented on GPUs and CPUs. Efficiency tests show GPU significantly speeds up model calculations.
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
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.
NASA Astrophysics Data System (ADS)
Tal, Alexey A.; Münger, E. Peter; Abrikosov, Igor A.
2015-07-01
The morphology transition from the thermodynamically favorable to the unfavorable phase during growth of freestanding copper nanoclusters is studied by molecular dynamics simulations. We give a detailed description of the kinetics and thermodynamics of the process. A universal mechanism of a solid-solid transition, from icosahedral to decahedral morphology in the nanoclusters, is proposed. We show that a formation of distorted NC during the growth process with islands of incoming atoms localized in certain parts of the grown particle may shift the energy balance between Ih and Dh phases in favor of the latter leading to the morphology transition deep within the thermodynamic stability field of the former. The role of diffusion in the morphology transition is revealed. In particular, it is shown that fast diffusion should suppress the morphology transition and favor homogeneous growth of the nanoclusters.
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; CoutÃ©, 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 Î¼m in diameter and adenineâ€“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 Î¼m in length and guanineâ€“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 Î¼m 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
DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility
NASA Astrophysics Data System (ADS)
Dubos, T.; Dubey, S.; Tort, M.; Mittal, R.; Meurdesoif, Y.; Hourdin, F.
2015-10-01
The design of the icosahedral 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 in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. 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. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.
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 ?m 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 ?m 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 ?m 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
Symmetries in BF and HAADF STEM image calculations.
Watanabe, K; Asano, E; Yamazaki, T; Kikuchi, Y; Hashimoto, I
2004-12-01
Reductions in bright-field (BF) scanning transmission electron microscopy (STEM) and high-angle annular dark-field (HAADF) STEM image calculations with the aid of Bloch wave symmetry are discussed under assumptions that an absorption potential is written by a local potential and a zero-order Laue zone lies parallel to the crystal surface. Translational symmetry allows us to take only partial incident beams in the first Brillouin zone instead of enormous number of partial incident beams in a large convergent disk. Two dimensional point group confines partial incident beams to an irreducible area in addition to factoring a dispersion matrix into noninteracting submatrices on a high symmetry line using the projection operator. The drastic reductions in computing time and memory enable us to readily calculate various BF STEM and HAADF STEM images. The validity and accuracy are demonstrated in comparisons with high resolution experimental BF STEM and HAADF STEM images. PMID:15556696
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.
Sekhar Chivukula
2010-01-08
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
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. PMID:24379431
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-01-01
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. PMID:24379431
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…
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 chargedâ€¦
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.
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.
Noether theorem for ?-symmetries
NASA Astrophysics Data System (ADS)
Cicogna, Giampaolo; Gaeta, Giuseppe
2007-09-01
We give a version of Noether theorem adapted to the framework of ?-symmetries this extends to such case recent work by Muriel, Romero and Olver in the framework of ?-symmetries, and connects ?-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this '?-conservation law' actually reduces to a standard one; we also note a relation between ?-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under ?-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting, ?-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
Crystallography of quasicrystals: The problem of restoration of broken symmetry
NASA Astrophysics Data System (ADS)
Koptsik, V. A.
In the paper, the concept of fuzzy packings of the structure units have been introduced which throw a new light on the crystallography of quasicrystals. With this concept one constructs the sructure of 2D-quasicrystal on a base of pentragrid from the rhombi on one kind which constitute a lacy cover of the plane. The space symmetry of such a structure is a positional colour groups isomorphous to wreath product of two generalized groups of the prototype phase begin{gathered}(T^1 × T^5 × T^{5^2 } × T^{5^3 } × T^{5^4 } ) ltimes bar 5m = (T_1 × T_2 )^{C_5 } ltimes C_{10v} = T^1 wr_q C_{10v} , \\T^1 = T_1 × T_2 ,T^5 = T_2 × T_3 ,T^{5^2 } = T_3 × T_4 ,T^{5^3 } = T_4 × T_5 ,T^{5^4 } = T_5 × T_1 describling the symmetry of a long and a short orders of the pentagrid correspondingly. The same is true for the symmetry group of the Penrose pattern which is dual to those pentagrid, its transformation being positional rigid translations and rotations accompanied by the appropriate local transformations of the inflation-deflation types rearranging the internal structures of the "physical points", the smallest domains of the pattern pocessing by the pentagonal colour point symmetry group. It is shown that colour and nD approaches constitute the isomorphic languages of description of the icosahedral quasicrystal phenomenon in the frame of common V (n) = V (3) E? V (d) 11
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
NASA Astrophysics Data System (ADS)
Stagno, Vincenzo; Bindi, Luca; Shibazaki, Yuki; Tange, Yoshinori; Higo, Yuji; Mao, H.-K.; Steinhardt, Paul J.; Fei, Yingwei
2014-07-01
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.
NASA Astrophysics Data System (ADS)
Hou, Zhao-Yang; Liu, Rang-Su; Tian, Ze-An; Wang, Jin-Guo
2011-06-01
A larger-scale Mg70Zn30 alloy system including 100000 atoms has been simulated by using the molecular dynamics method to investigate the icosahedral medium-range order (IMRO) formed in the Mg70Zn30 metallic glass. It is found that the simulated pair distribution function of Mg70Zn30 metallic glass is in good agreement with the experimental results. The glass transition temperature Tg is near 450 K under the cooling rate of 1×1012 K/s. The icosahedral local structures play a critical role in the formation of metallic glass, and they are the dominant local configurations in the Mg70Zn30 metallic glass. The IMRO in the Mg70Zn30 metallic glass is characterized by certain types of extended icosahedral clusters combined by intercross-sharing atoms in the form of chains or dendrites. The size distributions of these IMRO clusters present a magic number sequence of 19, 23, 25, 27, 29, 31, 33, 35, 37, 39, ..., and the magic clusters can be classified into three types according to their compactness. The IMRO clusters grow rapidly in a low-dimensional way with cooling, but this growth is limited near Tg.
NASA Astrophysics Data System (ADS)
Matveev, Alexei V.; Mayer, Markus; Rösch, Notker
2004-07-01
We describe a general strategy for exploiting spatial symmetry in density functional (DF) calculations of molecules and clusters, following the implementation in the parallel DF program PARAGAUSS. Point group elements are defined via a quaternion parametrization. Symmetrized irreducible bases of vector and projective representations as well as Clebsch-Gordan coefficients are constructed with the help of the eigenfunction method. We discuss the symmetrization of molecular orbitals for nonrelativistic and scalar relativistic DF calculations and molecular two- and four-component spinors for relativistic DF calculations that account for spin-orbit interaction. In addition, we present a strategy to symmetrize spinors simultaneously according to a double group and the corresponding point group. In relativistic DF calculations, this approach allows full exploitation of the symmetry of spin-free operators, e.g., in the numerical integration of the exchange-correlation potential.
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 (Ëœ10) low-frequency modes that are global and cooperative.
Icosahedral quasicrystals in Zn-T-Sc (T = Mn, Fe, Co or Ni) alloys
NASA Astrophysics Data System (ADS)
Maezawa, Ryo; Kashimoto, Shiro; Ishimasa, Tsutomu
2004-04-01
Starting from the Zn17Sc3 cubic approximant, new quasicrystal alloys were sought by replacement of Zn with transition elements T. In the cases when T = Mn, Fe, Co and Ni, new icosahedral quasicrystals are formed in as-cast alloys as major phases at alloy compositions of Zn75T10Sc15. All these quasicrystals belong to a primitive type and have six-dimensional lattice parameters a6D ranging from 7.044 to 7.107 Ã…. They have valence electron concentrations e/a ranging from 2.01 to 2.14, and almost the same ratios between the edge length aR of the Penrose tile and the averaged atomic diameter
Ortmann, Alice C.; Brumfield, Susan K.; Walther, Jasper; McInnerney, Kathleen; Brouns, Stan J. J.; van de Werken, Harmen J. G.; Bothner, Brian; Douglas, Trevor; van de Oost, John; Young, Mark J.
2008-01-01
Microarray analysis of infection by Sulfolobus turreted icosahedral virus (STIV) revealed insights into the timing and extent of virus transcription, as well as differential regulation of host genes. Using a microarray containing genes from both the host and the virus, the infection cycle of STIV was studied. Following infection of Sulfolobus solfataricus strain 2-2-12 with STIV, transcription of virus genes was first detected at 8 h postinfection (p.i.), with a peak at 24 h p.i. Lysis of cells was first detected at 32 h p.i. There was little temporal control of the transcription of virus genes, although the three open reading frames on the noncoding strand were transcribed later in the infection process. During the infection, 177 host genes were determined to be differentially expressed, with 124 genes up-regulated and 53 genes down-regulated. The up-regulated genes were dominated by genes associated with DNA replication and repair and those of unknown function, while the down-regulated genes, mostly detected at 32 h p.i., were associated with energy production and metabolism. Examination of infected cells by transmission electron microscopy revealed alterations in cell ultrastructure consistent with the microarray analysis. The observed patterns of transcription suggest that up-regulated genes are likely used by the virus to reprogram the cell for virus replication, while the down-regulated genes reflect the imminent lysis of the cells. PMID:18337566
Thermal conductivity and Seebeck coefficients of icosahedral boron arsenide films on silicon carbide
Gong, Y.; Kuball, M.; Zhang, Y.; Dudley, M.; Zhang, Y.; Edgar, J. H.; Heard, P. J.
2010-10-15
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 deg. 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 {mu}V/K and 136 {mu}V/K for samples grown at 1350 deg. C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Valence band structure of the icosahedral Ag-In-Yb quasicrystal
Sharma, H. R.; Simutis, G.; Dhanak, V. R.; Nugent, P. J.; McGrath, R.; Cui, C.; Shimoda, M.; Tsai, A. P.; Ishii, Y.
2010-03-01
The valence band structure of the icosahedral (i) Ag-In-Yb quasicrystal, which is isostructural to the binary i-Cd-Yb system, is investigated by ultraviolet photoemission spectroscopy (UPS). Experimental results are compared with electronic-structure calculations of a cubic approximant of the same phase. UPS spectra from the fivefold, threefold, and twofold i-Ag-In-Yb surfaces reveal that the valence band near to the Fermi level is dominated by Yb 4f-derived states, in agreement with calculations. The spectra also exhibit peaks which are surface core level shifted, caused by changes in the electronic structure in surface layers. Calculations yield a pseudogap in the density of states due to a hybridization of the Yb 5d band with the Ag 5p and In 5p bands. Both experimental and calculated band features are very similar to those of Cd-Yb. The modification of the band structure after surface treatment by sputtering and by oxidation is also studied. Additionally, the work function of i-Ag-In-Yb measured from the width of UPS spectrum is found to be almost unaffected by surface orientation, but increases after sputtering or oxidation.
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.
Lee, Kelly K; Tang, Jinghua; Taylor, Derek; Bothner, Brian; Johnson, John E
2004-07-01
Nudaurelia omega capensis virus (N omega V) capsids were previously characterized in two morphological forms, a T=4, 485-A-diameter round particle with large pores and a tightly sealed 395-A icosahedrally shaped particle with the same quasi-symmetric surface lattice. The large particle converts to the smaller particle when the pH is lowered from 7.6 to 5, and this activates an autocatalytic cleavage of the viral subunit at residue 570. Here we report that both 1-anilino-8 naphthalene sulfonate (ANS) and the covalent attachment of the thiol-reactive fluorophore, maleimide-ANS (MIANS), inhibit the structural transition and proteolysis at the lower pH. When ANS is exhaustively washed from the particles, the maturation proceeds normally; however, MIANS-modified particles are still inhibited after the same washing treatment, indicating that covalent attachment targets MIANS to a critical location for inhibition. Characterization of the low-pH MIANS product by electron cryo-microscopy (cryo-EM) and image reconstruction demonstrated a morphology intermediate between the two forms previously characterized. A pseudoatomic model of the intermediate configuration was generated by rigid body refinement of the X-ray structure of the subunits (previously determined in the assembled capsid) into the cryo-EM density, allowing a quantitative description of the inhibited intermediate and a hypothesis for the mechanism of the inhibition. PMID:15194797
Lee, Kelly K.; Tang, Jinghua; Taylor, Derek; Bothner, Brian; Johnson, John E.
2004-01-01
Nudaurelia ? capensis virus (N?V) capsids were previously characterized in two morphological forms, a T=4, 485-Å-diameter round particle with large pores and a tightly sealed 395-Å icosahedrally shaped particle with the same quasi-symmetric surface lattice. The large particle converts to the smaller particle when the pH is lowered from 7.6 to 5, and this activates an autocatalytic cleavage of the viral subunit at residue 570. Here we report that both 1-anilino-8 naphthalene sulfonate (ANS) and the covalent attachment of the thiol-reactive fluorophore, maleimide-ANS (MIANS), inhibit the structural transition and proteolysis at the lower pH. When ANS is exhaustively washed from the particles, the maturation proceeds normally; however, MIANS-modified particles are still inhibited after the same washing treatment, indicating that covalent attachment targets MIANS to a critical location for inhibition. Characterization of the low-pH MIANS product by electron cryo-microscopy (cryo-EM) and image reconstruction demonstrated a morphology intermediate between the two forms previously characterized. A pseudoatomic model of the intermediate configuration was generated by rigid body refinement of the X-ray structure of the subunits (previously determined in the assembled capsid) into the cryo-EM density, allowing a quantitative description of the inhibited intermediate and a hypothesis for the mechanism of the inhibition. PMID:15194797
Bulk electronic structure of Zn-Mg-Y and Zn-Mg-Dy icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Nayak, J.; Maniraj, M.; Gloskovskii, A.; Kraj?í, M.; Sebastian, S.; Fisher, I. R.; Horn, K.; Barman, S. R.
2015-06-01
We use bulk sensitive hard x-ray photoelectron spectroscopy to provide unambiguous evidence for a pseudogap in the density of states around the Fermi level in icosahedral Zn-Mg-Y and Zn-Mg-Dy quasicrystals, in agreement with our density functional theory calculations. The pseudogap in these Zn-based quasicrystals is less pronounced compared to the Al-based ones such as Al-Pd-Mn and Al-Cu-Fe [J. Nayak et al., Phys. Rev. Lett. 109, 216403 (2012), 10.1103/PhysRevLett.109.216403]. This observation is in agreement with transport studies that indicate a larger charge carrier concentration in the Zn-based quasicrystals. Compared to Zn-Mg-Dy, the pseudogap is somewhat deeper in Zn-Mg-Y. The larger width of the Mg 1 s and Zn 2 p core-level spectra in Zn-Mg-Y is explained by different configurations of the local atomic surrounding compared to Zn-Mg-Dy.
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.
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.
Metropolis, N; Rota, G C; Stein, J A
1991-01-01
Although a great deal of work has gone into construction of the irreducible representations of the symmetric group n (and of the general linear group) a simple, intuitive characterization of the symmetry classes is missing. Relying on a systematic distinction between permutations of variables and permutations of places, we provide two such characterizations, showing that elements belonging to any such symmetry class can be described in one of two ways: (i) as the solutions of explicitly given (though not independent) sets of linear equations or (ii) as linear combinations of "simple" elements of a given symmetry class, a simple element being a generalization to an arbitrary symmetry class of the notion of a decomposable skew-symmetric tensor. PMID:11607215
NASA Astrophysics Data System (ADS)
Lam, C. S.
2007-11-01
Neutrino mixing is studied from a symmetry perspective, both bottom-up and top-down. In the bottom-up approach, we start from the tri-bimaximal mixing, or one of its three partial patterns, and construct a list of horizontal symmetry groups capable of reproducing the mixing without adjustment of parameters. This list, labeled by an integer n â©¾ 3, is explicitly calculated for n = 3. In the top-down approach, we start from any finite group possessing a three-dimensional irreducible representation and an order-2 element, give a recipe to determine what mixing pattern it contains, and how to construct a dynamical model to reveal a particular mixing. Finally, we point out that if quark mixing is controlled by symmetry in this way, then there is an exciting possibility to determine most of the CKM mixing parameters by symmetry alone.
Second order symmetry operators
NASA Astrophysics Data System (ADS)
Andersson, Lars; Bäckdahl, Thomas; Blue, Pieter
2014-07-01
Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four-dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed and used to systematically reduce the equations to a form which allows geometrical interpretation.
Superconductivity and symmetry breaking
NASA Astrophysics Data System (ADS)
Sarasua, L. G.
2012-02-01
In the present work we consider the relation between superconductivity and spontaneous gauge symmetry breaking (SGBS). We show that ODLRO does not require in principle SBGS, even in the presence of particle number fluctuations, by examining exact solutions of a fermionic pairing model. The criteria become equivalent if a symmetry breaking field is allowed, which can be attributed to the interaction with the environment. However, superconducting states without SBGS are not forbidden.
Pauling, Linus
1988-01-01
Single-grain precession x-ray diffraction photographs of Al6CuLi3 have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 Å, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the ?-W arrangement. In this compound two of the clusters consist of 104 atoms and six consist of 136 atoms, with 24 atoms shared. The same structure is assigned to the C-phase, Al37Cu3Li21Mg3, and to GaMg2Zn3. A theory of icosahedral quasicrystals and amorphous metals is described. PMID:16593929
NASA Astrophysics Data System (ADS)
Ciobîrc?, Costin C?t?lin
Tensor fields with mixed symmetry transform in irreducible representations of GL (D, R) corresponding to Young diagrams with at least two columns ('exotic' representations of the Lorentz group). This class of fields appears in the context of many physically interesting theories, like superstrings, supergravities or supersymmetric high spin theories. One of the most important matters related to mixed symmetry-type tensor fields is the study of their consistent interactions, among themselves, as well as with higher-spin gauge theories. Beyond any doubt, the best approach to this problem is the cohomological one, based on the deformation of the solution to the classical master equation. This method is based on the reformulation of the problem of consistent deformations in gauge theories as a deformation problem of the solution to the classical master equation and further on solving the deformation equations withe the help of the local Becchi-Rouet-Stora-Tyutin (BRST) cohomology of the free theory. In this work we approach the problem of constructing certain classes of interacting gauge theories with mixed symmetry tensors by using the deformation of the solution to the classical master equation combined with specific cohomological techniques. The main hypotheses used at the construction of the previously mentioned interactions are on space-time locality, Poincare invariance, smoothness of the deformations in the coupling constant, and the conservation of the number of derivatives on each field. The main subjects developed in this work can be synthesized into: 1) analysis of self-interactions for precise classes of gauge theories with mixed symmetry tensors; 2) study of the couplings between several models with mixed symmetry tensors and arbitrary matter fields; 3) investigation of the existence of interactions between various classes of gauge theories with mixed symmetry tensors and the Pauli-Fierz field; 4) construction of the couplings between two types of tensor fields with mixed symmetries and p-forms, for specific values of p.
Regulation of icosahedral virion capsid size by the in vivo activity of a cloned gene product.
Agarwal, M; Arthur, M; Arbeit, R D; Goldstein, R
1990-01-01
Determination of icosahedral virion capsid size can be directly studied during helper-dependent lytic development of satellite P4 because the assembly pathway specified by the P2 helper virus is altered to yield smaller-sized capsids. Size determination (sid) mutations identify a P4-encoded function regulating this process. To determine whether the sid gene product is necessary and sufficient to redirect the assembly pathway, we (i) cloned the sid structural gene in a plasmid vector (pMA30) under the control of an inducible promoter and (ii) constructed a packaging substrate (pMA1), a P4 genome-sized plasmid containing only that region of P4, the cos site, necessary for encapsidation. Superinfection by P2 of a host carrying pMA30 under induced conditions resulted in a shift from large to small capsid production. P2 superinfection of a host carrying the cos plasmid pMA1 plus pMA30 under induced conditions yielded pMA1-transducing particles of P4 capsid size. These cloning-based analyses directly demonstrate that sid protein is the only P4 gene product required for small-capsid size determination. In the absence of the P2 O gene product no capsids of any size are assembled during solo infection by P2. Nevertheless, P2 Oam mutant superinfection of a host carrying pMA1 and pMA30 under induced conditions yielded small P4-sized transducing particles. We therefore propose that (i) the sid gene product competes with the O gene product to determine the assembly of small vs. large capsid sizes and (ii) both gene products probably function as temporary scaffolding proteins. Images PMID:2181437
THOR-ICO: a General Circulation Model for Exoplanets on an Icosahedral Grid
NASA Astrophysics Data System (ADS)
Mendonca, J.; Heng, K.; Grimm, S.
2014-04-01
The study of extrasolar planets has become important since the discovery of a large number of these astronomical objects. The diversity of planetary characteristics observed raises questions about the variety of climates. The influence of the astronomical and planetary bulk parameters in driving the atmospheric circulations continues to be poorly understood. In the solar system the results from planetary spacecraft missions have demonstrated how different the planetary climate and atmospheric circulations can be. The study of exoplanets is going to require a study of a far greater range of physical and orbital parameters than the ones that characterise our neighbour planets (in the solar system). For this reason the study of exoplanets will involve an even greater diversity of circulation and climate regimes. We are developing a dedicated General Circulation Model (GCM) for extrasolar planets called "Exoclimes Simulation Platform". This model will solve the complex physical and dynamical equations that include fundamental principles of atmospheric fluid dynamics and various idealisations of, for example, radiative transfer [1] and dry or moist convection. The interpretation and analysis of the results from this complex model will help us to have a better understanding on the diversity of climates and atmospheric circulations. Here we present the first results of our recent scheme which represents the fluid dynamical phenomena in the atmosphere. This new code solves the atmospheric fluid equations in a rotating sphere (fully compressible - elastic - nonhydrostatic system) using an icosahedral grid. The grid is also modified to improve the uniformity of the grid point distribution applying a method called spring dynamics [2]. The results shown include 3D experiments of gravity and acustic waves, Held-Suarez test case [3] and an idealized hot-Jupiter case.
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.
Pauling, Linus
1988-01-01
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. PMID:16593990
Chen, N. . E-mail: asyzxy@imr.edu; Louzguine, D.V.; Ranganathan, S.; Inoue, A.
2005-02-01
From the quaternary Ti-Zr-Hf-Ni phase diagram, the cross-section at 20 at.% Ni was selected for investigation. The icosahedral quasicrystalline, crystalline and amorphous phases were observed to form in nine kinds of rapidly solidified (Ti{sub x}Zr{sub y}Hf{sub z}){sub 80}Ni{sub 20} (x + y + z = 1) alloys at different compositions. The quasilattice constants of 0.519 and 0.531 nm were obtained for the icosahedral phase formed in the melt-spun Ti{sub 40}Zr{sub 20}Hf{sub 20}Ni{sub 20} and Ti{sub 20}Zr{sub 40}Hf{sub 20}Ni{sub 20} alloys, respectively. The icosahedral phase formed in the melt-spun Ti{sub 40}Zr{sub 20}Hf{sub 20}Ni{sub 20} alloy especially is thermodynamically stable. The supercooled liquid region of the Ti{sub 20}Zr{sub 20}Hf{sub 40}Ni{sub 20} glassy alloy reached 64 K. From these results a comparison of quasicrystal-forming and glass-forming abilities was carried out. The quasicrystal-forming ability was reduced and glass-forming ability was improved with an increase in Hf and Zr contents in the (Ti{sub x}Zr{sub y}Hf{sub z}){sub 80}Ni{sub 20} alloys. On the other hand, an increase in Ti content caused an improvement in quasicrystal-forming ability.
Symmetry recognition in images
NASA Astrophysics Data System (ADS)
Eswaran, Kumar
1999-07-01
This paper is concerned with the problem of separation of data, by a neural based computer recognition system. To this end certain types of data which are `tricky' are studied in order to see if they can be separated (i.e. classified) by a neural network or by a Kohonen based classifier. It is shown that there exist data which cannot simply be separated by a nearest distance classifier and yet can be treated well by a neural network, these correspond to the symmetry problem in images. In this paper the question that is posed and answered is: `If we are given a set of binary images, is it possible to devise an algorithm which will enable the computer to automatically recognize those images which have an inherent symmetry or near-symmetry?' It is demonstrated that a neural based algorithm can be trained to do the job efficaciously.
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.
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.
Lograsso, T.A.; Delaney, D.W.
1996-09-01
A cyclic heat-treatment process was used to prepare single grains of the quasicrystalline icosahedral phase, {psi}{endash}Al{sub 65}Cu{sub 23}Fe{sub 12}. Alloys of appropriate composition are melted and chill cast into copper molds. Multiple cyclic heat treatments at successively higher temperatures below 860{degree}C, the peritectic decomposition temperature of the quasicrystal phase, are used to enhance the growth of the {psi} phase. Single grains up to 10 mm{times}5 mm{times}5 mm have been prepared. {copyright} {ital 1996 Materials Research Society.}
NASA Astrophysics Data System (ADS)
Ismael, Jenann Tareq
1997-04-01
Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.
Weakly broken galileon symmetry
NASA Astrophysics Data System (ADS)
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar phi invariant under the internal galileon symmetry phi?phi+b? x? 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, ?, ? and ? 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 have to be rather clever to recognize that the particle interactions were rotationally invariant. Nambu and Goldstone showed that the spontaneous breakdown of a (continuous) symmetry implied the existence of massless scalar particles, referred to as Nambu Goldstone bosons, or simply Goldstone bosons. Meanwhile Anderson, in his study of (non-relativistic) superconductivity, showed that the exclusion of magnetic flux (Meissner effect) corresponds to a finite range for the electromagnetic field and hence to a `massive photon'. In a relativistic context Englert, Brout, Guralnik and more particularly Higgs showed that a spontaneous breaking of a gauge symmetry resulted in a massive, instead of a massless, gauge particle and no Goldstone particle; in the jargon of the day, the massless gauge particle had `eaten' the massless Goldstone boson and become massive; exactly Anderson's observation. It is this phenomenon which has been invoked so successfully to explain the masses of the W and Z bosons of weak interactions. Spontaneous symmetry breaking, therefore, has played a major role in the development of the Standard Model of particle physics, and it has also proved an important tool in condensed matter physics, for example in the understanding of phase transitions. At the same time, however, in the understanding of most (or all) particle physicists, and perhaps also condensed matter physicists, the notion of spontaneous symmetry breaking has been inexorably linked to that of a degenerate vacuum. This is the background and the starting point for Strocchi's book. Recognizing the power and importance of the concept of spontaneous symmetry breaking in theoretical physics, he defines it in a more refined and general way than usual. `Despite the many popular accounts', he writes, `the phenomenon of spontaneous symmetry breaking is deep and subtle and it is not without [reason] that it has been fully understood only in recent times.' Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the existence of non-symmetric ground states and the infinite extension of the system. The book is divided into two parts, treating respectively the classical and quantum regimes. In classical field theory the symmetry breaking is explained in terms of the occurrence of disjoint sectors, or different phases, of a physical system. In the quantum regime the mechanism is characterized by a symmetry breaking order parameter, for which non-perturbative criteria are discussed, following the work of Wightman, in contrast to the usual Goldstone perturbative strategy. Strocchi's main interest is in condensed matter, rather than particle, physics, and the topics he covers include spin systems, Fermi and Bose gases and finite temperature field theory. The book is based on lectures given over a number of years. It is written in a pleasing style at a level suitable for graduate students in theoretical physics. While mathematically proper, it is not forbidding for a physics readership; the author is always aware this subject is a branch of physics. It should make profitable reading for many theoretical physicists.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar Ï• invariant under the internal galileon symmetryÏ•â†’Ï•+b{sub Î¼}x{sup Î¼} 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 galileonâ€™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.
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. PMID:23797312
Dynamical (super) symmetry breaking
Murayama, Hitoshi
2000-10-03
Dynamical Symmetry Breaking (DSB) is a concept theoristsrely on very often in the discussions of strong dynamics, model building,and hierarchy problems. In this talk, I will discuss why this is such apermeating concept among theorists and how they are used in understandingphysics. I also briefly review recent progress in using dynamicalsymmetry breaking to construct models of supersymmetry breaking andfermion masses.
ERIC Educational Resources Information Center
Renshaw, Barbara S.
1986-01-01
Trademark designs provide a familiar yet innovative way for students to look at a number of mathematical concepts. How line and rotational symmetry can be presented using trademarks is the focus of this article. The emphasis is on the design of bulletin boards. (MNS)
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.
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)
Bosonic symmetry-protected topological phases with reflection symmetry
NASA Astrophysics Data System (ADS)
Yoshida, Tsuneya; Morimoto, Takahiro; Furusaki, Akira
2015-12-01
We study two-dimensional bosonic symmetry-protected topological (SPT) phases that are protected by reflection symmetry and local symmetry [ZN?R , ZN×R , U(1)?R , or U(1)×R ], in the search for two-dimensional bosonic analogs of topological crystalline insulators in integer-S spin systems with reflection and spin-rotation symmetries. To classify them, we employ a Chern-Simons approach and examine the stability of edge states against perturbations that preserve the assumed symmetries. We find that SPT phases protected by ZN?R symmetry are classified as Z2×Z2 for even N and 0 (no SPT phase) for odd N , while those protected by U(1)?R symmetry are Z2. We point out that the two-dimensional Affleck-Kennedy-Lieb-Tasaki state of S =2 spins on the square lattice is a Z2 SPT phase protected by reflection and ? -rotation symmetries.
Gauging without initial symmetry
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Î£, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(Î£ , G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / âˆ¼. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
Kalko, S G; Cachau, R E; Silva, A M
1992-01-01
An analysis of the crystallographically determined structures of the icosahedral protein coats of Tomato Bushy Stunt Virus, Southern Bean Mosaic Virus, Satellite Tobacco Necrosis Virus, Human Rhinovirus 14 and Mengovirus around their fivefold axes is presented. Accessibilities surfaces, electrostatic energy profile calculations, ion-protein interaction energy calculations, free energy perturbation methods and comparisons with structures of chelating agents are used in this study. It is concluded that the structures built around the viral fivefold axes would be adequate for ion binding and transport. Relative ion preferences are derived for the binding sites, using free energy perturbation methods, which are consistent with the experimental data when available. In the cases where crystallographic studies determined the existence of ions on the fivefold axes, our results indicate that they would correspond to ions in crystallization or purification buffers. The environment of the fivefold axes are rich in polar residues in all icosahedral viral structures whose atomic coordinates are available, including some that are not being analyzed in detail in this work. The fivefold channel-like structures have most of the basic properties expected for real ion channels including a funnel at the entrance, a polar internal environment with frequent alternation of acidic and basic residues, ion binding sites, the capability to induce ion dehydration and ion transit from the external viral surface to the binding sites. Images FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7 PMID:1384743
NASA Astrophysics Data System (ADS)
Nakayama, Ryu-suke; Takeuchi, Tsunehiro
2015-01-01
In this study, a new thermal rectifier working at high temperatures above 300 K was developed using Al61.5Cu26.5Fe12 icosahedral quasicrystal and Ag2Te. The thermal conductivity of Al61.5Cu26.5Fe12 increased drastically with temperature and, at 1000 K, reached a value nine times larger than that at 300 K. The thermal conductivity of Ag2Te showed a sudden decrease at around 400 K, and the thermal conductivity at 423 K became 60% smaller than that at 300 K. By making a composite consisting of Al61.5Cu26.5Fe12 icosahedral quasicrystal and Ag2Te, we succeeded in obtaining a large thermal rectification ratio (TRR) of | J large|/| J small| = 1.63 using two heat reservoirs maintained at T H = 543 K and T L = 300 K. The obtained TRR value is the largest among those ever reported for bulk thermal rectifiers.
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-â„«) 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
Nanoscale icosahedral packing in amorphous Mg50Ni50: An ab initio study
NASA Astrophysics Data System (ADS)
Tetik, Erkan; Durandurdu, Murat; KaradaÄŸ, Faruk
2012-10-01
We present the atomic structure of amorphous Mg50Ni50 alloy based on an ab initio molecular-dynamics method. Our simulation reveals that Ni atoms form predominantly perfect or defective icosahedrons and a non-negligible amount of low coordinated prism-like structures. An ordered icosahedrons packing with a hexagonal symmetry is also observed in the model. The physical origin of a low activation energy for the crystallization and better hydrogenation in amorphous Mg50Ni50 is discussed.
On group Fourier analysis and symmetry preserving discretizations of PDEs
NASA Astrophysics Data System (ADS)
Munthe-Kaas, H. Z.
2006-05-01
In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie group- and exponential-time integrators for differential equations, we will in the first part of the paper present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetric PDEs, where the discretization preserves the 120 symmetries of the icosahedral group. This motivates the study of spectral element discretizations based on triangular subdivisions. In the second part of the paper, we introduce novel applications of multivariate non-separable Chebyshev polynomials in the construction of spectral element bases on triangular and simplicial sub-domains. These generalized Chebyshev polynomials are intimately connected to the theory of root systems and Weyl groups (used in the classification of semi-simple Lie algebras), and these polynomials share most of the remarkable properties of the classical Chebyshev polynomials, such as near-optimal Lebesgue constants for the interpolation error, the existence of FFT-based algorithms for computing interpolants and pseudo-spectral differentiation and existence of Gaussian integration rules. The two parts of the paper can be read independently.
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…
Helical symmetry in linear systems
Bicak, Jiri; Schmidt, Bernd G.
2007-11-15
We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman-Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.
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…
Broken symmetries and signatures
NASA Astrophysics Data System (ADS)
Fitzpatrick, Andrew Liam
We consider three possible extensions of the Standard Model. In the first model, we explore the possibility to solve the strong CP problem and flavor puzzle in a model with fermions in the bulk of a warped extra dimensions, making use of the enhanced spacetime symmetries present in extra dimensions. In the second, we systematically explore the possible low-energy spectrum arising from gauge-mediated supersymmetry breaking when the messenger sector obeys a U(1) R-symmetry and all allowed renormalizable operators in the messenger sector are included. In the third, we study single-field models of inflation using an effective theory for the pions of spontaneously broken time translation invariance and explicitly prove a consistency relation for the three-point function of density perturbations.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
P. PAGE; T. GOLDMAN; J. GINOCCHIO
2000-08-01
Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.
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.
General interaction-induced density wave states from a symmetry perspective
NASA Astrophysics Data System (ADS)
Venderbos, J. W. F.
2014-03-01
We present a symmetry classification of particle-hole condensates, i.e. general density wave states, to show how an organization in terms of translational and point group symmetries provides immediate insight into the electronic properties of such states. We discuss site, bond and flux ordered density wave states in systems with square and hexagonal symmetry. We establish a robust connection between the transformation behavior under lattice symmetries of such density waves and the low-energy description of the electronic properties, which is independent of specific lattices and fully determined by symmetry. In addition, we show how an organization in terms of lattice symmetry is helpful in identifying and predicting electronic states matter with topological quantum numbers. For systems with hexagonal symmetry we propose a new class of time-reversal invariant spin-bond ordered density waves. We address how interactions may induce the formation of these density waves in real materials and make contact with recent works which indicate that symmetric density waves are good variational ground state candidates for interacting lattice fermion models.
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.
Boissieu, M. de; Francoual, S.; Kaneko, Y.; Ishimasa, T.
2005-09-02
We report on the absolute scale measurement of the x-ray diffuse scattering in the ZnMgSc icosahedral quasicrystal and its periodic approximant. Whereas the diffuse scattering in the approximant is purely accounted for by thermal diffuse scattering, an additional signal is observed in the quasicrystal. It is related to phason fluctuations as indicated by its Q{sub per}{sup 2} dependence. Moreover, when compared to previous measurements carried out on the i-AlPdMn phase, we find that the amount of diffuse scattering is smaller in the i-ZnMgSc phase, in agreement with larger phason elastic constants in this phase. This is confirmed by the observation of a large number of weak Bragg peaks having a high Q{sub per} reciprocal space component.
NASA Astrophysics Data System (ADS)
Sharma, H. R.; Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.; McGrath, R.
2014-05-01
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 C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 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 C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage.
Sharma, H R; Smerdon, J A; Nugent, P J; Ribeiro, A; McLeod, I; Dhanak, V R; Shimoda, M; Tsai, A P; McGrath, R
2014-05-01
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 C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 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 C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage. PMID:24811658
Sharma, H. R. Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.; Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577
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.
NASA Astrophysics Data System (ADS)
Yamamoto, Akiji; Takakura, Hiroyuki
2003-10-01
A six-dimensional (6D) structure of i-Al-Pd-Mn quasicrystal determined recently [Yamamoto et al., J. Alloys Compd. 342, 159 (2002)] leads to two 1/1 approximant structures of i-Al-Pd-Mn and i-Al-Cu-Ru with the space group Pm3¯ (? Al-Pd-Mn-Si and ? Al-Ru-Cu) by the introduction of appropriate uniform (linear) phason strains. The different clusters in the 1/1 approximants are obtained from the different 3D hyperplane passing through (1,1,1,1,1,1)/4 and (1,0,0,0,0,0)/2 in the 6D icosahedral lattice. It is shown that for all cubic approximant represented by consecutive Fibonacci numbers Fn+1/Fn, two different structures can be obtained in the same manner.
Symmetries in noncommutative physics
NASA Astrophysics Data System (ADS)
Qureshi, Babar Ahmed
Quantum field theories on noncommutative spaces are an important area of research in high energy physics because of their importance as a tool to capture aspects of Planck scale physics, where one expects the spacetime to show noncommutative behavior, their emergence in string theory and also as a tool to regularize quantum field theories. An important issue in the study of noncommutative quantum field theories (NCQFT's) is that of symmetries. Introduction of noncommutativity explicitly breaks Lorentz invariance. However, the classical actions of noncommutative field theories are invariant under a twisted action of the Poincare group. In this thesis we study the consequences of such twisted symmetries at the quantum level. We give complete construction of quantum field theories covariant under the twisted Poincare action including the explicit form of the twisted Poincare generators. We find some striking results such as twisting of Bose and Fermi statistics and removal of UV-IR mixing in the non-gauge theories. We also apply the idea of twisting to gauge symmetries and construct gauge theories covariant under twisted action of gauge and Poincare groups. Any gauge group can be treated using our formulation, unlike the ordinary noncommutative gauge theories where only U(N) groups admit direct treatment. We derive the Feynman rules for this theory and find interesting results such as violation of Pauli principle and violation of Lorentz invariance due to failure of a generalized form of locality. We also treat the twisted form of supersymmetry. Finally we study the formulation of supersymmetry on fuzzy sphere and construct fuzzy supersymmetric instanton. We find the zero modes in the instanton sector and study their index theory.
Applications of chiral symmetry
NASA Astrophysics Data System (ADS)
Davoudiasl, Hooman
We study some applications of the chiral symmetry of quantum chromodynamics in treating phenomena involving hadrons at low energies, where perturbative methods are not valid. We begin by introducing the concepts of global symmetry breaking and the consequent generation of Goldstone bosons. It is shown how these concepts are realized through chiral symmetry breaking and provide an understanding of some of the features of strong interactions at low energies. This leads us to the chiral perturbation theory effective Lagrangian for the low energy interactions of the light pseudo-scalars. We use this effective Lagrangian, and the considerations that led to it, as the basis of our approach in studying three different problems. First, we find the rates for the Ï„ lepton decays /tau /to V/pi/nu/sb/tau, where V stands for /rho,/ K*, or Ï‰, and extract the magnitude of the Ïomega/pi coupling, /vert g2(/rho)/vert = 0.6. Next, we use this coupling to find the decay rate for D0/to /bar K*0/pi/sp- e+/nu/sb/varepsilon, in a certain kinematic regime. This rate depends on the DD*/pi coupling and our results can provide an extraction of this coupling, given data on this decay. The third problem we address is that of finding solutions that represent the qualitative behavior of the disoriented chiral condensate in the non- linear sigma model at [/cal O](p4). We show that these solutions do not become singular at short distances where the [/cal O](p2) solutions begin to diverge.
NASA Astrophysics Data System (ADS)
Messio, Laura; Lhuillier, Claire; Misguich, Grégoire
2013-03-01
Projective symmetry groups are the mathematical tools which make it possible to list and classify mean-field spin liquids (SLs) based on a parton construction. The seminal work of Wen [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.65.165113 65, 165113 (2002)] and its subsequent extension to bosons by Wang and Vishwanath [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.74.174423 74, 174423 (2006)] concerned the so-called symmetric SLs; i.e., states that break neither lattice symmetries nor time reversal invariance. Here we generalize this tool to chiral (time reversal symmetry breaking) SLs described in a Schwinger boson mean-field approach and illustrate it on the triangular lattice, which can harbor nine different weakly symmetric SLs (two symmetric SLs and seven chiral SLs) with nearest neighbor bond operators only. Results for other lattices (square and kagome) are given in the Appendixes. Application of this new approach has recently led to the discovery of two chiral ground states on the kagome lattice [Messio , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.207204 108, 207204 (2012); Fåk , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.037208 109, 037208 (2012)]. The signature of a time reversal symmetry breaking SL is the presence in the ground state of nontrivial fluxes of loop operators that break some lattice point group symmetries. The physical significance of these gauge invariant quantities is discussed both in the classical limit and in the quantum SL and their expressions in terms of spin observables are given.
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.
Thermal symmetry in isoscaling
Escudero, C. R.; Lopez, J. A.; Dorso, C. O.
2007-02-12
It is determined that isoscaling data, if produced by two isotopic reactions under similar thermodynamic conditions, should satisfy a simple numerical relationship. This, which helps to explore the symmetry of thermodynamic conditions of isotopic reactions, is studied using molecular dynamics simulations of 40Ca+40Ca, 48Ca+48Ca, and 52Ca+52Ca, at beam energies from 35 MeV / A to 85 MeV / A, and as a function of time. Strong deviations from the rule are detected in the beginning of the collision, with an excellent convergence at long times for some energies. A comparison with experimental data and other calculations is also included.
Symmetry and perturbation theory
NASA Astrophysics Data System (ADS)
Gaeta, Giuseppe
A co-chain map for the G invariant De Rham complex -- New examples of trihamiltonian structures linking different Lenard chains -- Wave propagation in an elastic medium: GDS equations -- Parametric excitation in nonlinear dynamics -- Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 -- The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems -- Shadowing chains of collision orbits for the elliptic 3-body problem -- Similarity reductions of an optical model -- Fold, transcritical and pitchfork singularities for time-reversible systems -- Homographic three-body motions with positive and negative masses -- Remarks on conformal Killing tensors and separation of variables -- A regularity theory for optimal partition problems -- Lambda and mu-symmetries -- Potential symmetries and linearization of some evolution equations -- Periodic solutions for zero mass nonlinear wave equations -- Fundamental covariants in the invariant theory of Killing tensors -- Global geometry of 3-body trajectories with vanishing angular momentum -- The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension -- On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure -- An explicit solution of the (quantum) elliptic Calogero-Sutherland model -- An application of the Melnikov integral to a restricted three body problem -- Reductions of integrable equations and automorphic Lie algebras -- Geometric reduction of Poisson operators -- Closed manifolds admitting metrics with the same geodesics -- A transcritical-flip bifurcation in a model for a robot-arm -- Alignment and the classification of Lorentz-signature tensors -- Renormalization group symmetry and gas dynamics -- Refined computation of hypernormal forms -- New order reductions for Euler-Lagrange equations -- Regularity of pseudogroup orbits -- Relaxation times to equilibrium in Fermi-Pasta-Ulam system -- Energy cascade in Fermi-Pasta-Ulam models -- On Birkhoff method for integrable lagrangian systems -- Symmetry of singularities and orbit spaces of compact linear groups -- Symmetric solutions in molecular potentials -- Variational approach to soliton generation and stability analysis of multidimensional nonlinear Schrodinger equation -- Differential invariants for infinite-dimensional algebras.
Applications of chiral symmetry
Pisarski, R.D.
1995-03-01
The author discusses several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T{sub {chi}} implies that the {rho} and a{sub 1} vector mesons are degenerate in mass. In a gauged linear sigma model the {rho} mass increases with temperature, m{sub {rho}}(T{sub {chi}}) > m{sub {rho}}(0). The author conjectures that at T{sub {chi}} the thermal {rho} - a{sub 1}, peak is relatively high, at about {approximately}1 GeV, with a width approximately that at zero temperature (up to standard kinematic factors). The {omega} meson also increases in mass, nearly degenerate with the {rho}, but its width grows dramatically with temperature, increasing to at least {approximately}100 MeV by T{sub {chi}}. The author also stresses how utterly remarkable the principle of vector meson dominance is, when viewed from the modern perspective of the renormalization group. Secondly, he discusses the possible appearance of disoriented chiral condensates from {open_quotes}quenched{close_quotes} heavy ion collisions. It appears difficult to obtain large domains of disoriented chiral condensates in the standard two flavor model. This leads to the last topic, which is the phase diagram for QCD with three flavors, and its proximity to the chiral critical point. QCD may be very near this chiral critical point, and one might thereby generated large domains of disoriented chiral condensates.
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.
Perturbative Symmetries on Noncommutative Spaces
NASA Astrophysics Data System (ADS)
Blohmann, Christian
Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.
Symmetry fractionalization and twist defects
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Lindner, Netanel H.; Fidkowski, Lukasz
2016-03-01
Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitationsâ€”anyonsâ€”and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalizationâ€”termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectorsâ€”i.e. does not change one type of anyon into a different type of anyonâ€”one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic â€˜twistâ€™ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.
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.
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
Symmetry and surface symmetry energies in finite nuclei
Lee, S. J.; Mekjian, A. Z.
2010-12-15
A study of the properties of the symmetry energy of nuclei is presented based on density-functional theory. Calculations for finite nuclei are given so that the study includes isospin-dependent surface symmetry considerations as well as isospin-independent surface effects. Calculations are done at both zero and nonzero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature-dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of {beta} stability. Differences of several MeV are shown over a good fraction of the total mass range in A. Also given are calculations for the bulk, surface and Coulomb terms.
The force of symmetry revisited: symmetry-to-noise ratios regulate (a)symmetry effects.
Csathó, Arpád; van der Vloed, Gert; van der Helm, Peter A
2004-11-01
Freyd and Tversky's [Am. J. Psychol. 97 (1984) 109] data suggested that human observers tend to overestimate relatively high levels of symmetry (symmetry effect), and tend to underestimate relatively low levels of symmetry (asymmetry effect). However, on the basis of their holographic approach to visual regularity, van der Helm and Leeuwenberg [Psychol. Rev. 103(3) (1996) 429] predicted that, at any level of symmetry, both symmetry and asymmetry effects may occur as a consequence of correct estimates of symmetry-to-noise ratios. This prediction was tested in two experiments, with tasks and stimuli similar to those in Freyd and Tversky's study. First, subjects had to judge whether a noisy symmetry is more similar to a slightly more symmetrical variant or to a slightly less symmetrical variant. Second, for every pair of stimuli in such a triadic comparison, subjects had to judge which stimulus is the more symmetrical one. The results from both experiments show that the occurrence of (a)symmetry effects indeed depends on symmetry-to-noise ratios. PMID:15500805
Asymptotic symmetries on Killing horizons
NASA Astrophysics Data System (ADS)
Koga, Jun-Ichirou
2001-12-01
We investigate asymptotic symmetries regularly defined on spherically symmetric Killing horizons in Einstein theory with or without the cosmological constant. These asymptotic symmetries are described by asymptotic Killing vectors, along which the Lie derivatives of perturbed metrics vanish on a Killing horizon. We derive the general form of the asymptotic Killing vectors and find that the group of asymptotic symmetries consists of rigid O(3) rotations of a horizon two-sphere and supertranslations along the null direction on the horizon, which depend arbitrarily on the null coordinate as well as the angular coordinates. By introducing the notion of asymptotic Killing horizons, we also show that local properties of Killing horizons are preserved not only under diffeomorphisms but also under nontrivial transformations generated by the asymptotic symmetry group. Although the asymptotic symmetry group contains the Diff(S1) subgroup, which results from supertranslations dependent only on the null coordinate, it is shown that the Poisson brackets algebra of the conserved charges conjugate to asymptotic Killing vectors does not acquire nontrivial central charges. Finally, by considering extended symmetries, we discuss the fact that unnatural reduction of the symmetry group is necessary in order to obtain the Virasoro algebra with nontrivial central charges, which is not justified when we respect the spherical symmetry of Killing horizons.
Sterile neutrinos and global symmetries
Sayre, J.; Wiesenfeldt, S.; Willenbrock, S.
2005-07-01
We use an effective-field-theory approach to construct models with naturally light sterile neutrinos, due to either exact or accidental global symmetries. The most attractive models we find are based on gauge symmetries, either discrete or continuous. We give examples of simple models based on Z{sub N}, U(1){sup '}, and SU(2){sup '}.
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.)
Symmetry chains and adaptation coefficients
Fritzer, H.P.; Gruber, B.
1985-06-01
Given a symmetry chain of physical significance it becomes necessary to obtain states which transform properly with respect to the symmetries of the chain. In this article we describe a method which permits us to calculate symmetry-adapted quantum states with relative ease. The coefficients for the symmetry-adapted linear combinations are obtained, in numerical form, in terms of the original states of the system and can thus be represented in the form of numerical tables. In addition, one also obtains automatically the matrix elements for the operators of the symmetry groups which are involved, and thus for any physical operator which can be expressed either as an element of the algebra or of the enveloping algebra. The method is well suited for computers once the physically relevant symmetry chain, or chains, have been defined. While the method to be described is generally applicable to any physical system for which semisimple Lie algebras play a role we choose here a familiar example in order to illustrate the method and to illuminate its simplicity. We choose the nuclear shell model for the case of two nucleons with orbital angular momentum l = 1. While the states of the entire shell transform like the smallest spin representation of SO(25) we restrict our attention to its subgroup SU(6) x SU(2)/sub T/. We determine the symmetry chains which lead to total angular momentum SU(2)/sub J/ and obtain the symmetry-adapted states for these chains.
Activities: Line and Rotational Symmetry.
ERIC Educational Resources Information Center
Whitman, Nancy
1991-01-01
Provided are student activities to introduce the geometric concepts of line symmetry and rotational symmetry as related to Hawaiian quilting patterns. Paper squares, scissors, and folding techniques afford the teacher the chance to stimulate class discussion about pattern recognition and to integrate mathematics with the cultural world outside the…
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 ofâ€¦
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.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smoli?, 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.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, TomÃ¡s; 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 PoincarÃ© 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.
Wang, Xue; Figueroa-Cosme, Legna; Yang, Xuan; Luo, Ming; Liu, Jingyue; Xie, Zhaoxiong; Xia, Younan
2016-02-10
Engineering the surface structure of noble-metal nanocrystals offers an effective route to the development of catalysts or electrocatalysts with greatly enhanced activity. Here, we report the synthesis of Pt-based icosahedral nanocages whose surface is enclosed by both {111} facets and twin boundaries while the wall thickness can be made as thin as six atomic layers. The nanocages are derived from Pd@Pt4.5L icosahedra by selectively etching away the Pd in the core. During etching, the multiply twinned structure can be fully retained whereas the Pt atoms in the wall reconstruct to eliminate the corrugated structure built in the original Pt shell. The Pt-based icosahedral nanocages show a specific activity of 3.50 mA cm(-2) toward the oxygen reduction reaction, much greater than those of the Pt-based octahedral nanocages (1.98 mA cm(-2)) and a state-of-the-art commercial Pt/C catalyst (0.35 mA cm(-2)). After 5000 cycles of accelerated durability test, the mass activity of the Pt-based icosahedral nanocages drops from 1.28 to 0.76 A mg(-1)Pt, which is still about four times greater than that of the original Pt/C catalyst (0.19 A mg(-1)Pt). PMID:26760681
NASA Astrophysics Data System (ADS)
Tuan, S. F.
2002-06-01
The suggestion by Jaffe that if sigma is a light q2q2 state 0++ then even the fundamental chiral transformation properties of the sigma becomes unclear, has stimulated much interest. Adler pointed out that in fact the seminal work on chiral symmetry via PCAC consistency, is really quite consistent with the sigma being predominantly q2q2. This interpretation was actually backed by subsequent work on effective Lagrangian methods for linear and non linear realizations. More recent work of Achasov suggests that intermediate four-quark states determine amplitudes involving other scalars a0(980) and f0(980) below 1 GeV, and the report by Ning Wu that study on sigma meson in J/psi [right arrow] omega][pi]+[pi- continue to support a non qq sigma with mass as low as 390 MeV. It is also noted that more recent re-analysis of piK scattering by S. Ishida et al. together with the work of the E791 Collaboration, support the existence of the scalar kappa particle with comparatively light mass as well.
Symmetries of Dynamically Equivalent Theories
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Tyutin, I. V.
2006-03-01
A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially the relation between the constraint structure with the symmetries of the Lagrangian action. An important preliminary step in this direction is a strict demonstration, and this is the aim of the present article, that the symmetry structures of the Hamiltonian action and of the Lagrangian action are the same. This proved, it is sufficient to consider the symmetry structure of the Hamiltonian action. The latter problem is, in some sense, simpler because the Hamiltonian action is a first-order action. At the same time, the study of the symmetry of the Hamiltonian action naturally involves Hamiltonian constraints as basic objects. One can see that the Lagrangian and Hamiltonian actions are dynamically equivalent. This is why, in the present article, we consider from the very beginning a more general problem: how the symmetry structures of dynamically equivalent actions are related. First, we present some necessary notions and relations concerning infinitesimal symmetries in general, as well as a strict definition of dynamically equivalent actions. Finally, we demonstrate that there exists an isomorphism between classes of equivalent symmetries of dynamically equivalent actions.
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.
Spontaneous symmetry breaking of arbitrage
NASA Astrophysics Data System (ADS)
Choi, Jaehyung
2012-06-01
We introduce the concept of spontaneous symmetry breaking to arbitrage modeling. In the model, the arbitrage strategy is considered as being in the symmetry breaking phase and the phase transition between arbitrage mode and no-arbitrage mode is triggered by a control parameter. We estimate the control parameter for a momentum strategy with real historical data. The momentum strategy aided by symmetry breaking shows stronger performance and has a better risk measure than the naive momentum strategy in U.S. and South Korean markets.
Entropy from scaling symmetry breaking
NASA Astrophysics Data System (ADS)
Cavalcante, Neymar; Diles, Saulo; Gupta, Kumar S.; de Queiroz, Amilcar R.
2015-05-01
The scaling symmetry in conformal quantum mechanics (CQM) can be broken due to the boundary conditions that follow from the requirement of a unitary time evolution of the Hamiltonian. We show that the scaling symmetry of CQM can be restored by introducing a suitable mixed state, which is associated with a nonvanishing von Neumann entropy. We give an explicit formula for the entropy arising from the mixed state in CQM. Our work provides a direct link between the restoration of a broken symmetry and the von Neumann entropy.
Unification of gauge symmetries in theories with dynamical symmetry breaking
NASA Astrophysics Data System (ADS)
Christensen, Neil D.; Shrock, Robert
2005-08-01
We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize electric charge, (ii) attempt to unify the three standard-model gauge interactions in a simple Lie group that forms a direct product with an extended technicolor group, and, most ambitiously, (iii) attempt to unify the standard-model gauge interactions with (extended) technicolor in a simple Lie group.
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 (1.15Â±0.1)me 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 iâˆ’Alâˆ’Pdâˆ’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 iâˆ’Alâˆ’Pdâˆ’Mn with the free-electron-like image potential states. Our investigation of the energy region immediately above EF provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
Brumfield, Susan K.; Ortmann, Alice C.; Ruigrok, Vincent; Suci, Peter; Douglas, Trevor; Young, Mark J.
2009-01-01
Little is known about the replication cycle of archaeal viruses. We have investigated the ultrastructural changes of Sulfolobus solfataricus P2 associated with infection by Sulfolobus turreted icosahedral virus (STIV). A time course of a near synchronous STIV infection was analyzed using both scanning and transmission electron microscopy. Assembly of STIV particles, including particles lacking DNA, was observed within cells, and fully assembled STIV particles were visible by 30 h postinfection (hpi). STIV was determined to be a lytic virus, causing cell disruption beginning at 30 hpi. Prior to cell lysis, virus infection resulted in the formation of pyramid-like projections from the cell surface. These projections, which have not been documented in any other host-virus system, appeared to be caused by the protrusion of the cell membrane beyond the bordering S-layer. These structures are thought to be sites at which progeny virus particles are released from infected cells. Based on these observations of lysis, a plaque assay was developed for STIV. From these studies we propose an overall assembly model for STIV. PMID:19357174
NASA Astrophysics Data System (ADS)
Jakse, N.; Pasturel, A.
2015-08-01
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al80Ni20 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 TX = 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 TX 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.
New building blocks in the 2/1 crystalline approximant of a Bergman-type icosahedral quasicrystal
Lin, Qisheng; Corbett, John D.
2006-01-01
The refined x-ray crystal structure of the phase Mg27Al10.7(2)Zn47.3(2) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsulates an Al2 dimer. This phase exhibits the same long-range order as recently established for the Tsai-type Sc–Mg–Zn 2/1 approximant crystal, with substantial geometric and atomic distribution differences between the two only in the short range orders. This common feature suggests that Bergman- and Tsai-type quasicrystals may be more similar than earlier conceived. Factors germane to the formation of, and the differences between, Bergman- vs. Tsai-type 1/1 and 2/1 approximate structures are considered, including notably different distributions of the more electropositive elements. PMID:16950873
NASA Astrophysics Data System (ADS)
Maniraj, M.; Rai, Abhishek; Barman, S. R.; Kraj?í, M.; Schlagel, D. L.; Lograsso, T. 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)me 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 EF provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
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 Al80Ni20 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 TX = 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 TX 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. PMID:26328857
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).
Mamone, Salvatore; Johnson, Mark R; Ollivier, Jacques; Rols, Stéphane; Levitt, Malcolm H; Horsewill, Anthony J
2016-01-21
The fine structure of the rotational ground state of molecular ortho-hydrogen confined inside the fullerene cage C60 is investigated by inelastic neutron scattering (INS). The INS line corresponding to transitions between the three sub-levels comprising the ortho ground state to the non-degenerate para ground state was studied as a function of temperature down to 60 mK in neutron energy gain. The experiments show that at ambient pressure the three ortho sub-levels are split into a low energy non-degenerate level and a high energy doubly degenerate level separated by 0.135 ± 0.010 meV. This observation is consistent with hydrogen molecules being located at sites with axial symmetry superseding the icosahedral symmetry of isolated rigid C60 cages in the solid phase. To gain insight into the role of inter-cage interactions in determining the symmetry breaking potential, the effects of hydrostatic pressure on the fine structure of the line was also investigated. The analysis of the INS spectra shows that the potential and the energy levels of H2 are sensitive to the orientation of neighbouring cages, consistent with the low-temperature crystalline phase of C60. PMID:26687060
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, VÃctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; CossÃo, 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 PoincarÃ©-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.
Combining Flavour and CP Symmetries
NASA Astrophysics Data System (ADS)
Feruglio, Ferruccio
2013-07-01
I shortly review the impact of the most recent neutrino oscillation data on our attempts to construct a realistic model for neutrino masses and mixing angles. Models based on anarchy and its variants remain an open possibility, reinforced by the latest experimental findings. Many models based on discrete symmetries no longer work in their simplest realizations. I illustrate several proposals that can rescue discrete symmetries. In particular I discuss the possibility of combining discrete flavour symmetries and CP, and I describe a recently proposed symmetry breaking pattern that allows to predict all mixing parameters, angles and phases, in terms of a single real unknown. I analyze several explicit examples of this construction, providing new realistic mixing patterns.
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.
Symmetry and quaternionic integrable systems
NASA Astrophysics Data System (ADS)
Gaeta, G.; RodrÃguez, M. A.
2015-01-01
Given a hyperkahler manifold M, the hyperkahler structure defines a triple of symplectic structures on M; with these, a triple of Hamiltonians defines a so-called hyperHamiltonian dynamical system on M. These systems are integrable when can be mapped to a system of quaternionic oscillators. We discuss the symmetry of integrable hyperHamiltonian systems, i.e. quaternionic oscillators, and conversely how these symmetries characterize, at least in the Euclidean case, integrable hyperHamiltonian systems.
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.
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 observed that e and e(sub 0) are increasing with incident angle and e is greater than e(sub 0) at L-band because of the directional feature of sea surface waves. Symmetry properties of geophysical media can also be used to calibrate polarimetric radars.
NASA Astrophysics Data System (ADS)
Doh, Hyeonjin; Kee, Hae-Young
2007-06-01
An electronic nematic state spontaneously breaks a point-group symmetry of an underlying lattice. As a result, the nematic-isotropic transition accompanies a Fermi surface distortion. However, the anisotropic nature of the nematic state at a macroscopic scale can be easily wiped out when domains of different orientations of nematic order exist. We suggest that a spatial pattern of local density of states (LDOS) in the presence of a nonmagnetic impurity can be a direct probe of the nematic order. We study various patterns of LDOS across the quantum phase transition between the isotropic and nematic phases. Specifically, the Fourier transformed local density of states, which can be deduced from scanning tunneling microscope images, represents a transparent symmetry of an electronic structure. The application of our results to the bilayer ruthenate, Sr3Ru2O7 , is also discussed.
Janner, A
2011-03-01
The relation between serotype differentiation and crystallographic symmetry, revealed by the contact fingerprint diagrams investigated in Part II [Janner (2010). Acta Cryst. A66, 312-326] for the human rhinovirus, is extended to the Picornaviridae family. The approach, outlined in Part I [Janner (2010). Acta Cryst. A66, 301-311] and Part II for biomacromolecules packed in a crystal and based on concepts such as packing lattice, kissing points and crystal-packing parameters, can directly be applied to the picornaviruses. In particular, the contact fingerprint diagrams of 20 different virus strains have been derived. In these cases, as for the rhinovirus, these diagrams are serotype/strain specific, justifying the name fingerprint. The molecular basis for the serotype variability, and the associated conservation requirements, is usually analysed by considering antigenic sites, where capsid residues bind with antibodies, and receptor sites, where other residues bind with molecular receptors of the host cell membrane. Both the antigenic variation and the receptor conservation allow repeated infection of the host cells of the given animals. The graphical description of these sites is usually done by footprints and roadmap diagrams, mapping properties of the capsid surface and using the icosahedral symmetry of the capsid. The alternative fingerprint diagrammatic description, based on the crystal symmetry, adopted in Part II for the contact sites, where a capsid is bound to the next one in the crystal packing, is extended to the antigenic and receptor binding sites. Again, the antigenic/receptor fingerprints are specific, at least for the nine picornaviruses investigated so far, despite the more than a factor of ten larger coarse graining with respect to the corresponding footprint and roadmap diagrams. The latter are based on a grid spacing of about 2 Ã…, whereas the spacing implied by the packing-lattice approximation adopted in fingerprints varies typically from 20 to 50 Ã…. The fingerprint diagrams are accordingly simpler (because approximated), but nevertheless still serotype specific, despite the complex character of the interactions involved. PMID:21325720
Symmetry-protected entanglement renormalization
NASA Astrophysics Data System (ADS)
Singh, Sukhwinder; Vidal, Guifre
2013-09-01
Entanglement renormalization is a real-space renormalization group (RG) transformation for quantum many-body systems. It generates the multiscale entanglement renormalization ansatz (MERA), a tensor network capable of efficiently describing a large class of many-body ground states, including those of systems at a quantum critical point or with topological order. The MERA has also been proposed to be a discrete realization of the holographic principle of string theory. Here we propose the use of symmetric tensors as a mechanism to build a symmetry-protected RG flow, and discuss two important applications of this construction. First, we argue that symmetry-protected entanglement renormalization produces the proper structure of RG fixed points, namely, a fixed-point for each symmetry-protected phase. Second, in the context of holography, we show that by using symmetric tensors, a global symmetry at the boundary becomes a local symmetry in the bulk, thus explicitly realizing in the MERA a characteristic feature of the AdS/CFT correspondence.
Annular symmetry nonlinear frequency converters.
Kasimov, Dror; Arie, Ady; Winebrand, Emil; Rosenman, Gil; Bruner, Ariel; Shaier, Pnina; Eger, David
2006-10-01
We present a new type of two-dimensional nonlinear structure for quasi-phase matching. This structure has continuous rotational symmetry, and in contrary to the commonly used periodic structures, is not lattice shaped and has no translation symmetry. It is shown that this annular symmetry structure possesses interesting phase matching attributes that are significantly different than those of periodic structures. In particular, it enables simultaneous phase-matched frequency doubling of the same pump into several different directions. Moreover, it has extremely wide phase-mismatch tolerance, since a change in the phase matching conditions does not change the second harmonic power, but only changes its propagation direction. Several structures were fabricated using either the indirect e-beam method in LiNbO(3) or the electric field poling method in stoichiometric LiTaO(3), and their conversion efficiencies, as well as angular and thermal dependencies, were characterized by second harmonic generation. PMID:19529321
Aspects of Dynamical Symmetry Breaking
NASA Astrophysics Data System (ADS)
Cohler, Lucien Eugene
In order to develop some insight into dynamical symmetry breaking in four dimensional nonabelian theories, a toy model is examined that exhibits some of the features of the more realistic model but remains tractable. The model that is studied is that of QED in three dimensions with N fermion flavors. It will be shown that there are configurations that dynamically break the chiral symmetry of the model. By taking a large number of flavors, a 1/N expansion may be used to simplify the problem which is approached by numerically solving the Schwinger-Dyson equations for the fermion self energy. By comparing the effective potentials of the broken and unbroken solutions it will be shown that the dynamics favors symmetry breaking. In addition, the low energy impact of having a composite Higgs sector will be examined by estimating its contribution to the (rho) parameter.
Symmetries, Lie Algebras and Representations
NASA Astrophysics Data System (ADS)
Fuchs, JÃ¼rgen; Schweigert, Christoph
2003-10-01
Preface; 1. Symmetries and conservation laws; 2. Basic examples; 3. The Lie algebra su(3) and hadron symmetries; 4. Formalization: algebras and Lie algebras; 5. Representations; 6. The Cartan-Weyl basis; 7. Simple and affine Lie algebras; 8. Real Lie algebras and real forms; 9. Lie groups; 10. Symmetries of the root system. The Weyl group; 11. Automorphisms of Lie algebras; 12. Loop algebras and central extensions; 13. Highest weight representations; 14. Verma modules, Casimirs, and the character formula; 15. Tensor products of representations; 16. Clebsch-Gordan coefficients and tensor operators; 17. Invariant tensors; 18. Subalgebras and branching rules; 19. Young tableaux and the symmetric group; 20. Spinors, Clifford algebras, and supersymmetry; 21. Representations on function spaces; 22. Hopf algebras and representation rings; Epilogue; References; Index.
Maaty, Walid S. A.; Ortmann, Alice C.; Dlaki?, 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
Nonholonomic Mechanical Systems with Symmetry
NASA Astrophysics Data System (ADS)
Bloch, Anthony M.; Krishnaprasad, P. S.; Marsden, Jerrold E.; Murray, Richard M.
1996-12-01
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control-theoretical applications. The basic methodology is that of geometric mechanics applied to the Lagrange-d'Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case. We begin by formulating the mechanics of nonholonomic systems using an Ehresmann connection to model the constraints, and show how the curvature of this connection enters into Lagrange's equations. Unlike the situation with standard configuration-space constraints, the presence of symmetries in the nonholonomic case may or may not lead to conservation laws. However, the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables. This momentum equation, which plays an important role in control problems, involves parallel transport operators and is computed explicitly in coordinates. An alternative description using a “body reference frame” relates part of the momentum equation to the components of the Euler-Poincaré equations along those symmetry directions consistent with the constraints. One of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not. An example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard, a modified version of the skateboard which uses momentum coupling for locomotion generation. We construct a synthesis of the mechanical connection and the Ehresmann connection defining the constraints, obtaining an important new object we call the nonholonomic connection. When the nonholonomic connection is a principal connection for the given symmetry group, we show how to perform Lagrangian reduction in the presence of nonholonomic constraints, generalizing previous results which only held in special cases. Several detailed examples are given to illustrate the theory.
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.
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.
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).
Skyrmion crystals and their symmetries
Kugler, M. ); Shtrikman, S. )
1989-11-15
We discuss the phase diagram of Skyrmion crystals as a function of both density and pressure. The use of symmetry properties of the various phases and of Fourier expansions tailored to fit these symmetries facilitates our discussion. A simple cubic arrangement of half-Skyrmions is, almost everywhere, the lowest-energy phase. At very high densities the simple cubic phase undergoes a transition to a body-centered-cubic crystal of half-Skyrmions. The transition to a crystal of Skyrmions at low densities, that was previously suggested, is not accessible thermodynamically. A first-order phase transition leading to a phase separation occurs before the previous transition can be reached.
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.
Chiral symmetry in quarkyonic matter
Kojo, T.
2012-05-15
The 1/N{sub c} expansion classifies nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, <{psi}-bar exp (2i{mu}{sub q} z{gamma}{sup 0} {gamma}{sup z}){psi}> . An extension to multiple chiral spirals is also briefly discussed.
Effective field theory for spacetime symmetry breaking
NASA Astrophysics Data System (ADS)
Hidaka, Yoshimasa; Noumi, Toshifumi; Shiu, Gary
2015-08-01
We discuss the effective field theory for spacetime symmetry breaking from the local symmetry point of view. By gauging spacetime symmetries, the identification of Nambu-Goldstone (NG) fields and the construction of the effective action are performed based on the breaking pattern of diffeomorphism, local Lorentz, and (an)isotropic Weyl symmetries as well as the internal symmetries including possible central extensions in nonrelativistic systems. Such a local picture distinguishes, e.g., whether the symmetry breaking condensations have spins and provides a correct identification of the physical NG fields, while the standard coset construction based on global symmetry breaking does not. We illustrate that the local picture becomes important in particular when we take into account massive modes associated with symmetry breaking, the masses of which are not necessarily high. We also revisit the coset construction for spacetime symmetry breaking. Based on the relation between the Maurer-Cartan one form and connections for spacetime symmetries, we classify the physical meanings of the inverse-Higgs constraints by the coordinate dimension of broken symmetries. Inverse Higgs constraints for spacetime symmetries with a higher dimension remove the redundant NG fields, whereas those for dimensionless symmetries can be further classified by the local symmetry breaking pattern.
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 ?3, 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 ?3, a torus T 3 constructed as ?3/?, where ? 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 *?. 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 exhaustive classification of all generalized ABC- flows and of their hidden symmetries. We make several conceptual comments about the need of a field-theory yielding Beltrami equation as a field equation and/or an instanton equation and on the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that are different from the non-linear one proposed by Arnold and possibly make contact with M-theory and the geometry of flux-compactifications.
Nonlocal aspects of ?-symmetries and ODEs reduction
NASA Astrophysics Data System (ADS)
Catalano Ferraioli, D.
2007-05-01
A reduction method of ODEs not possessing Lie point symmetries makes use of the so-called ?-symmetries (Muriel and Romero 2001 IMA J. Appl. Math. 66 111). The notion of covering for an ODE {\\cal Y} is used here to recover ?-symmetries of {\\cal Y} as nonlocal symmetries. In this framework, by embedding {\\cal Y} into a suitable system {\\cal Y}^{\\prime} determined by the function ?, any ?-symmetry of {\\cal Y} can be recovered by a local symmetry of {\\cal Y}^{\\prime} . As a consequence, the reduction method of Muriel and Romero follows from the standard method of reduction by differential invariants applied to {\\cal Y}^{\\prime} .
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
On extended symmetries for the Galileon
NASA Astrophysics Data System (ADS)
Noller, Johannes; Sivanesan, Vishagan; von Strauss, Mikael
2015-09-01
We investigate a large class of infinitesimal, but fully nonlinear in the field, transformations of the Galileon and search for extended symmetries. The transformations involve powers of the coordinates x and the field Ï€ up to any finite order N . Up to quadratic order the structure of these symmetry transformations is the unique generalization of both the infinitesimal version of the standard Galileon shift symmetry as well as a recently discovered infinitesimal extension of this symmetry. The only higher-order extensions of this symmetry we recover are ("Galileon dual" versions of) symmetries of the standard kinetic term.
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 Ioffeâ€™s formula for the baryon mass.
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)
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 mathematicalâ€¦
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…
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…
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…
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.
Entanglement renormalization and gauge symmetry
Tagliacozzo, L.; Vidal, G.
2011-03-15
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z{sub 2} lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16x16 sites (16{sup 2}x2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.
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 toâ€¦
A Futures Curriculum for Symmetry.
ERIC Educational Resources Information Center
Dickmann, Leonore W.
The paper describes a model to aid curriculum developers as they design futures curricula. The objective is to demonstrate how curricula can be holistic in perspective and balanced in provision for student future-focused role image as well as subject matter. The model, based on symmetry (within the individual and the curriculum), has seven facets:…
Simple current symmetries in RCFT
NASA Astrophysics Data System (ADS)
Bantay, P.
2005-01-01
The question ``Which abelian permutation groups arise as group of simple currents in Rational Conformal Field Theory?'' is investigated using the formalism of weighted permutation actions. After a review of the relevant properties of simple current symmetries, the general theory of WPA-s and admissibility conditions are described, and classification results are illustrated by a couple of examples.
NASA Astrophysics Data System (ADS)
Yu, Fengmei; Zou, Huamin; Wang, Jianbo; Wang, Renhui
2004-10-01
The atomic positions are obtained from a modified non-spherical model of icosahedral AlPdMn quasicrystal (Fang et al 2003 J. Phys.: Condens. Matter 15 4947) by the cut method. The four-shell pseudo-Mackay clusters (PMCs) were searched for in a box of 400 Å × 400 Å × 400 Å. The results show that the number of atoms in the fourth shell, an icosidodecahedron, of the pseudo-Mackay cluster can vary from 15 to 30 because of the cluster overlap, and about 99.96% of the total atoms are included in such incomplete pseudo-Mackay clusters. The characteristics of the atom distribution in the planes perpendicular to a fivefold axis indicate that the planes, which are 1.56 Å apart from their neighbouring planes, are expected to be the terminal surfaces. If one such a plane and its closest neighbouring plane, between which the spacing is 0.48 Å, are considered as a thin layer or a corrugated surface, these layers are also the layers with the maximum density. The pair of corrugated surfaces that are 1.56 Å apart have almost identical chemical composition. These planes form terraces that follow the rule of the Fibonacci sequence with two step heights, 6.60 and 4.08 Å. On the corrugated surfaces perpendicular to a fivefold axis the pentagonal holes arise from the interspaces of adjacent incomplete PMCs. For the atomic planes normal to a twofold axis, the planes with spacing of 1.48 Å from their adjacent planes might be expected to be the terminal surfaces, which form terraces with step heights of 6.28 and 3.88 Å following the rule of the Fibonacci sequence. For the atomic planes normal to a threefold axis, the planes with spacing of 0.86 Å from their adjacent planes might be expected to be the terminal surfaces. No similar results were found for the atomic layers perpendicular to a pseudo-twofold axis.
Huang, D.P.; Dong, Z.D.; Corbett, J.D.
1998-11-02
The title compound is synthesized by direct reaction of the elements at 500 C followed by slow cooling. Na{sub 12}K{sub 38}Tl{sub 48}Au{sub 2} crystallizes hexagonal and is constituted (in terms of oxidation states) as (Na{sup +}){sub 12}(K{sup +}){sub 38}(Tl{sub 7}{sup 7{minus}}){sub 3}(Tl{sub 9}{sup 9{minus}}){sub 3}(Au{sup {minus}}){sub 2}. Both clusters have C{sub 2{nu}} symmetry and can be viewed as fragments of a centered icosahedral Tl{sub 13}. The Tl{sub 7}{sup 7{minus}} cluster is an oblate pentagonal bipyramid with an apex-apex bond distance of 3.39 {angstrom}, and Tl{sub 9}{sup 9{minus}} can be best derived from the centered icosahedron by removal of four adjoining vertexes (or as two fused pentagonal bipyramids). The isolated Au{sup {minus}} is bound in a trigonal antiprism of potassium. The compound is structurally electron-precise (Zintl phase), but it shows characteristics of a very poor metal ({rho}{sub 298} {approximately} 760 {mu}{Omega}(cm)) with a Pauli-like susceptibility of {approximately}1.4 {times} 10{sup {minus}3} emu/mol over 50--300 K after correction for Larmor precession of cluster orbitals. EHMO results for the bonding in Tl{sub 7}{sup 7{minus}} and factors that stabilize this compound are presented and discussed.
Quantum group and quantum symmetry
NASA Astrophysics Data System (ADS)
Chang, Zhe
1995-11-01
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the SchrÃ¶dinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion.
NASA Astrophysics Data System (ADS)
Tsuji, Masaharu; Nakamura, Nozomi; Tang, Xinling; Uto, Keiko; Matsunaga, Mika
2014-11-01
We previously reported that trapezoid, plate-like and mono- or bi-tetrahedral Ag-flag structures are evolved from side facets of Ag-nanorod (NR) seeds when AgNO3 was reduced in N,N-dimethylformamide (DMF) in the presence of polyvinylpyrrolidone (PVP). In this study, we examined what shapes are grown by further growth of bitetrahedral flags based on TEM and SEM observations. For this purpose, we initially studied effects of the reaction temperature, concentrations of PVP, and molecular weights of PVP for the shape evolution of flag types of Ag nanostructures from Ag-NR seeds. Results show that shape and size of flags can be controlled by changing these parameters and reaction times. Under an appropriate experimental condition, we found that decahedral and icosahedral flags and their intermediates having {1 1 1} facets were finally grown by stepwise growth of tetrahedral units, although yield of perfect decahedral and icosahedral flags were low because of occurrence of homogenous nucleation at high AgNO3 concentration.
Symmetry-adapted excited states for the T1uâŠ—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 T1uâŠ—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.
Steven, A C; Roberts, C R; Hay, J; Bisher, M E; Pun, T; Trus, B L
1986-01-01
The structures of the hexavalent capsomers of herpes simplex virus type 2 were analyzed by negative staining electron microscopy of capsomer patches derived from partially disrupted nucleocapsids. Optimally computer-averaged images were formed for each of the three classes of capsomer distinguished by their respective positions on the surface of the icosahedral capsid with a triangulation number of 16; in projection, each capsomer exhibited unequivocal sixfold symmetry. According to correspondence analysis of our set of capsomer images, no significant structural differences were detected among the three classes of capsomers, as visualized under these conditions. Taking into account information from images of freeze-dried, platinum-shadowed nucleocapsid fragments, it was established that each hexavalent capsomer is a hexamer of the 155-kilodalton major capsid protein. The capsomer has the form of a sixfold hollow cone approximately 12 nm in diameter and approximately 15 nm in depth, whose axial channel tapers in width from the outside towards the inner capsid surface. Images PMID:3003389
From additional symmetries to linearization of Virasoro symmetries
NASA Astrophysics Data System (ADS)
Wu, Chao-Zhong
2013-04-01
We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. Considered as certain reductions of the two-component BKP hierarchy, the Drinfeld-Sokolov hierarchies of type D are proved to possess symmetries written as the linear action of a series of Virasoro operators on the tau function. It results in that the Drinfeld-Sokolov hierarchies of type D coincide with Dubrovin and Zhang’s hierarchies associated to the Frobenius manifolds for Coxeter groups of type D, and that every solution of such a hierarchy together with the string equation is annihilated by certain combinations of the Virasoro operators and the time derivations of the hierarchy.
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.
What symmetries can do for you
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2015-04-01
Several applications of Lie symmetries and its generalisation are presented: from turning butterflies into tornados, to its applications in epidemics, population dynamics, and ultimately converting classical problems into the quantum realm. Applications of nonclassical symmetries are also illustrated.
Notes on generalized global symmetries in QFT
NASA Astrophysics Data System (ADS)
Sharpe, Eric
2015-11-01
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.
Irregular matrix model with { W } symmetry
NASA Astrophysics Data System (ADS)
Choi, Sang Kwan; Rim, Chaiho
2016-02-01
We present an irregular matrix model which has {{ W }}3 and Virasoro symmetry. The irregular matrix model is obtained using the colliding limit of the Toda field theories and produces the inner product between irregular modules of {{ W }}3 symmetry. We evaluate the partition function using the flow equation which is the realization of Virasoro and { W } symmetry.
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
Symmetries in bacterial?motility
Berg, Howard?C.
1996-01-01
Descriptions are given of three kinds of symmetries encountered in studies of bacterial locomotion, and of the ways in which they are circumvented or broken. A bacterium swims at very low Reynolds number: it cannot propel itself using reciprocal motion (by moving through a sequence of shapes, first forward and then in reverse); cyclic motion is required. A common solution is rotation of a helical filament, either right- or left-handed. The flagellar rotary motor that drives each filament generates the same torque whether spinning clockwise or counterclockwise. This symmetry is broken by coupling to the filament. Finally, bacterial populations, grown in a nutrient medium from an inoculum placed at a single point, usually move outward in symmetric circular rings. Under certain conditions, the cells excrete a chemoattractant, and the rings break up into discrete aggregates that can display remarkable geometric order. PMID:8962029
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. PMID:22150845
Adding CP to flavour symmetries
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, I.
2015-07-01
I propose the use of CP-odd invariants, which are independent of basis and valid for any choice of CP transformation, as a powerful approach to study CP in the presence of flavour symmetries. As examples of the approach I focus on Lagrangians invariant under ?(27). I comment on the consequences of adding a specific CP symmetry to a Lagrangian and distinguish cases where several ?(27) singlets are present depending on how they couple to the triplets. One of the examples included is a very simple toy model with explicit CP violation with calculable phases, which is referred to as explicit geometrical CP violation by comparison with previously known cases of (spontaneous) geometrical CP violation.
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.
Dirac neutrinos from flavor symmetry
NASA Astrophysics Data System (ADS)
Aranda, Alfredo; Bonilla, Cesar; Morisi, S.; Peinado, E.; Valle, J. W. F.
2014-02-01
We present a model where Majorana neutrino mass terms are forbidden by the flavor symmetry group ?(27). Neutrinos are Dirac fermions and their masses arise in the same way as those of the charged fermions, due to very small Yukawa couplings. The model fits current neutrino oscillation data and correlates the octant of the atmospheric angle ?23 with the magnitude of the lightest neutrino mass, with maximal mixing excluded for any neutrino mass hierarchy.
Fermion mass without symmetry breaking
NASA Astrophysics Data System (ADS)
Catterall, Simon
2016-01-01
We examine a model of reduced staggered fermions in three dimensions interacting through an SO (4) invariant four fermion interaction. The model is similar to that considered in a recent paper by Ayyer and Chandrasekharan [1]. We present theoretical arguments and numerical evidence which support the idea that the system develops a mass gap for sufficiently strong four fermi coupling without producing a symmetry breaking fermion bilinear condensate. Massless and massive phases appear to be separated by a continuous phase transition.
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
BÃºa, Lucia; Bucataru, Ioan; LeÃ³n, Manuel de; Salgado, Modesto; VilariÃ±o, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1Ï€ of a fiber bundle Ï€ : E â†’ â„k where â„k is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
The New Charge Symmetry Breaking
Stephenson, E. J.
2007-06-13
For few body systems, the treatment of charge symmetry breaking (CSB) that is based on meson-exchange models is being replaced by effective field theories whose CSB originates in the down-up quark mass difference and quark electromagnetic effects. In parallel, two new observations of CSB in {pi}0 production (the fore-aft asymmetry in n+p{yields}d+{pi}0 and the total cross section for d+d{yields}4He+{pi}0) provide applicable data.
Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ?Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator ? ˆ =Rˆy (?) T ˆ, which involves the product of two distinct symmetries, namely, continuous and discrete. Therefore, new guidelines are required for testing its commutation with the system Hamiltonian. One of the primary objectives of this study is to lay down these guidelines. Further, the possible impact of chiral symmetry on the geometrical arrangement of angular momentum vectors and investigation of observables unique to nuclear chiral-twins is carried out. In our model, the angular momentum components (J1, J2, J3) occupy three mutually perpendicular axes of triaxial shape and represent a non-planar configuration. At certain threshold energy, the equation of motion in angular momentum develops a second order phase transition and as a result two distinct frames (i.e., the left- and right-handed) are formed. These left- and right-handed states correspond to a double well system and are related to each other through chiral operator. At this critical angular momentum, the centrifugal and Coriolis interactions lower the barrier in the double well system. The tunneling through the double well starts, which subsequently lifts the degeneracy among the rotational states. A detailed analysis of the behavior of rotational energies, spin-staggering, and the electromagnetic transition probabilities of the resulting twin-rotational bands is presented. The ensuing model results exhibit similarities with many observed features of the chiral-twins. An advantage of our formalism is that it is quite simple and it allows us to pinpoint the understanding of physical phenomenon which lead to chiral-twins in rotating systems.
Symmetry analysis of talus bone
Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.
2014-01-01
Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391
Interfacial Fermi Loops from Interfacial Symmetries
NASA Astrophysics Data System (ADS)
Takahashi, Ryuji; Murakami, Shuichi
2014-12-01
We propose a concept of interfacial symmetries such as interfacial particle-hole symmetry and interfacial time-reversal symmetry, which appear in interfaces between two regions related to each other by particle-hole or time-reversal transformations. These symmetries result in novel dispersion of interface states. In particular, for the interfacial particle-hole symmetry, the gap closes along a loop ("Fermi loop") at the interface. We numerically demonstrate this for the Fu-Kane-Mele tight-binding model. We show that the Fermi loop originates from a sign change of a Pfaffian of a product between the Hamiltonian and a constant matrix.
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.
Symmetry-directed control of electronic coupling for singlet fission in covalent bis-acene dimers.
Damrauer, Niels H; Snyder, Jamie L
2015-11-19
While singlet fission (SF) has developed in recent years within material settings, much less is known about its control in covalent dimers. Such platforms are of fundamental importance and may also find practical use in next-generation dye-sensitized solar cell applications or for seeding SF at interfaces following exciton transport. Here, facile theoretical tools based on Boys localization methods are used to predict diabatic coupling for SF via determination of one-electron orbital coupling matrix elements. The results expose important design rules that are rooted in point group symmetry. For Cs-symmetric dimers, pathways for SF that are mediated by virtual charge transfer excited states destructively interfere with negative impact on the magnitude of diabatic coupling for SF. When dimers have C2 symmetry, constructive interference is enabled for certain readily achievable interchromophore orientations. Three sets of dimers exploiting these ideas are explored: a bis-tetracene pair and two sets of aza-substituted tetracene dimers. Remarkable control is shown. In one aza-substituted set, symmetry has no impact on SF reaction thermodynamics but leads to a 16-fold manipulation in SF diabatic coupling. This translates to a difference of nearly 300 in kSF with the faster of the two dimers (C2) being predicted to undergo the process on a nearly ultrafast 1.5 ps time scale. PMID:26505732
Gavilano, J.L.; Ambrosini, B.; Vonlanthen, P.; Chernikov, M.A.; Ott, H.R.
1997-10-01
We report the results of a {sup 27}Al nuclear magnetic resonance study of icosahedral quasicrystalline Al{sub 70}Re {sub 8.6}Pd{sub 21.4} at temperatures between 0.04 and 300K and in magnetic fields between 1.5 and 7T. At very low temperatures we have found that the temperature dependence of the spin-lattice relaxation rate T{sup {minus}1}{sub 1}(T) shows new and unexpected features which we associate with a gradual real-space localization of the itinerant charge carriers. Above 20K, T{sup {minus}1}{sub 1}(T) contains both a linear- and a cubic-in-{ital T} term, previously observed for other quasicrystals. {copyright} {ital 1997} {ital The American Physical Society}
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
2013-01-01
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 (?-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. PMID:23520050
Dai, Tie; Schutgens, Nick A J; Goto, Daisuke; Shi, Guangyu; Nakajima, Teruyuki
2014-12-01
A new global aerosol assimilation system adopting a more complex icosahedral grid configuration is developed. Sensitivity tests for the assimilation system are performed utilizing satellite retrieved aerosol optical depth (AOD) from the Moderate Resolution Imaging Spectroradiometer (MODIS), and the results over Eastern Asia are analyzed. The assimilated results are validated through independent Aerosol Robotic Network (AERONET) observations. Our results reveal that the ensemble and local patch sizes have little effect on the assimilation performance, whereas the ensemble perturbation method has the largest effect. Assimilation leads to significantly positive effect on the simulated AOD field, improving agreement with all of the 12 AERONET sites over the Eastern Asia based on both the correlation coefficient and the root mean square difference (assimilation efficiency). Meanwhile, better agreement of the Ångström Exponent (AE) field is achieved for 8 of the 12 sites due to the assimilation of AOD only. PMID:25017412
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.
Spontaneous violation of mirror symmetry
NASA Astrophysics Data System (ADS)
Dyatlov, I. T.
2015-11-01
A model of the violation of symmetry is considered for a system that can spontaneously choose between nearly identical states that differ only in the weak-interaction properties ( R â†” L). This mirror symmetrymakes it possible to reproduce the observed qualitative properties of the quark and lepton mixing matrices. In this case, the lepton mixing matrix is indicative of an inverse character of the spectrum of Standard Model neutrinos and their Dirac nature. Despite the Dirac properties of the neutrinos, leptonnumber- changing processes of the e - + Î¼ + â†’ e + + Î¼ - type are possible here, but they may involve exclusively leptons.
Skyrmion and chiral symmetry breaking
Braghin, F.L.
2004-12-02
A chiral coupling is considered for the Skyrme model to a light scalar meson which develops a classical component, eventually representing the scalar quark-anti-quark condensate of the spontaneous breakdown of chiral symmetry. This scalar field leads to a modification in the chiral radius which becomes a dynamical variable and tends to acquire values close to zero inside the topological soliton. A chiral rotation of the scalar and pseudoscalar fields can lead to the linear sigma model favoring the identification of the scalar field to the scalar sigma. The role of the scalar field mass is discussed.
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.
Reflection symmetry-integrated image segmentation.
Sun, Yu; Bhanu, Bir
2012-09-01
This paper presents a new symmetry-integrated region-based image segmentation method. The method is developed to obtain improved image segmentation by exploiting image symmetry. It is realized by constructing a symmetry token that can be flexibly embedded into segmentation cues. Interesting points are initially extracted from an image by the SIFT operator and they are further refined for detecting the global bilateral symmetry. A symmetry affinity matrix is then computed using the symmetry axis and it is used explicitly as a constraint in a region growing algorithm in order to refine the symmetry of the segmented regions. A multi-objective genetic search finds the segmentation result with the highest performance for both segmentation and symmetry, which is close to the global optimum. The method has been investigated experimentally in challenging natural images and images containing man-made objects. It is shown that the proposed method outperforms current segmentation methods both with and without exploiting symmetry. A thorough experimental analysis indicates that symmetry plays an important role as a segmentation cue, in conjunction with other attributes like color and texture. PMID:22201051
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the Ising×Ising¯ phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci × Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
Hadler, Amelia B; Harris, Nicholas A; Fredrickson, Daniel C
2013-11-20
Despite significant progress in the structural characterization of the quasicrystalline state, the chemical origins of long- and short-range icosahedral order remain mysterious and a subject of debate. In this Article, we present the crystal structure of a new complex intermetallic phase, Ca10Cd27Cu2 (mC234.24), whose geometrical features offer clues to the driving forces underlying the icosahedral clusters that occur in Bergman-type quasicrystals. Ca10Cd27Cu2 adopts a C-centered monoclinic superstructure of the 1/1 Bergman approximant structure, in which [110] layers of Bergman clusters in the 1/1 structure are separated through the insertion of additional atoms (accompanied by substantial positional disorder). An examination of the coordination environments of Ca and Cu (in the ordered regions) reveals that the structure can be viewed as a combination of coordination polyhedra present in the nearest binary phases in the Ca-Cd-Cu compositional space. A notable feature is the separation of Ca-Cd and Cu-Cd interactions, with Bergman clusters emerging as Ca-Cd Friauf polyhedra (derived from the MgZn2-type CaCd2 phase) encapsulate a Cu-Cd icosahedron similar to those appearing in Cu2Cd5. DFT chemical pressure calculations on nearby binary phases point to the importance of this segregation of Ca-Cd and Cu-Cd interactions. The mismatch in atomic size between Cu and Cd leads to an inability to satisfy Ca-Cu and Ca-Cd interactions simultaneously in the Friauf polyhedra of the nearby Laves phase CaCd2. The relegation of the Cu atoms to icosahedra prevents this frustration while nucleating the formation of Bergman clusters. PMID:24147875
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 this end, we will show the possible link between the features in Saturn's magnetic field and dynamics in the semi-conducting region of Saturn.
Introduction to Electroweak Symmetry Breaking
Dawson,S.
2008-10-02
The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.
Radiation Symmetry of NIF Hohlraums
NASA Astrophysics Data System (ADS)
Jones, O. S.; Suter, L. J.; Pollaine, S. M.; Haan, S. W.
1997-11-01
We have used the three-dimensional, view-factor radiation transport code, Gertie (G. Zimmerman, D. Munroe, R. Kirkpatrick, and D. Bailey.), to analyze the symmetry of indirect drive ignition experiments on the National Ignition Facility (NIF). These calculations directly consider vacuum radiation only. Plasma effects enter indirectly through specification of the time-dependent albedos and effective dimensions of the hohlraum and capsule. These specifications come from seperate simulations with the radiation hydrodynamics code Lasnex. First, we examine the intrinsic azimuthal asymmetry of NIF's full 192 beam configuration using highly refined grids. Next, we quantify the sensitivity of the overall symmetry to systematic effects such as laser power imbalance and beam pointing errors. The power balance analysis includes the effects of correlations due to shared amplifiers among pairs of beam quads. Finally, we estimate the degree of radiation asymmetries that may exist during the NIF activation phase. The NIF activation plan (M. Lane, B. Van Wontergrun, LLNL, private communication, 1997.) will allow target physics experiments as banks of beams come online. This set of calculations provides an idea of the degree of asymmetry that will exist during various phases of NIF activation, and thus allows us to assess how we might best use these early experiments.
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 Fisherâ€™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.
Classification of topological phases with reflection symmetry
NASA Astrophysics Data System (ADS)
Yoshida, Tsuneya; Morimoto, Takahiro; Furusaki, Akira
2015-03-01
In Z2 topological band insulators, the time-reversal symmetry protects their topological structure. In these years such a notion is extended to correlated systems including bosonic systems, and these nontrivial phases are referred to as symmetry protected topological (SPT) phases. Parallel to this progress, a topological crystalline insulator, protected by spatial symmetry, is found for SnTe. Thus, SPT phases protected by this type of symmetry are naturally expected, and classifications of such phases are desired. In this article, we address this issue by focusing on a reflection symmetry. Our analysis based on the Chern-Simons approach proposes periodic tables for bosonic and fermionic SPT phases in two dimensions. Besides that, we show an SPT phase with the reflection symmetry is stabilized in a spin model of honeycomb lattice.
Interface gapless states from interfacial symmetries
NASA Astrophysics Data System (ADS)
Takahashi, Ryuji; Murakami, Shuichi
2015-03-01
Previously we have shown that at an interface between two topological insulators with opposite Dirac velocities, gapless interface states protected by mirror symmetry appear. We can calculate the interface dispersion using the Fu-Kane-Mele (FKM) tight-binding model, and it typically consists of Dirac cones. In this presentation, we report another kind of interface metallic states; the Fermi surface forms loops (``Fermi loop''), rather than isolated Dirac points, sometimes seen in the interface of the FKM models. Such a degeneracy along a loop is unexpected. This Fermi loop appears when the whole junction system preserves particle-hole symmetry, while each system breaks particle-hole symmetry. We call this symmetry ``interfacial particle-hole symmetry'' (IPHS). We discuss the IPHS in general systems and show that the Fermi loop results from a sign change of a Pfaffian of some matrix, defined only in junctions with IPHS symmetry.
Symmetry and symmetry breaking in Rydberg-atom intrashell dynamics
Pilskog, I.; Fregenal, D.; Frette, O.; Foerre, M.; Horsdal, E.; Waheed, A.
2011-04-15
We have investigated experimentally and theoretically the dynamics of Stark-Zeeman split states in Li(n=25) Rydberg atoms when they are exposed to a superposition of a slowly varying field and a harmonic RF field. Regular oscillatory structures are observed in the intrashell transitions. By solving the time-dependent Schroedinger equation for the problem it is shown that the dynamics is strongly influenced by the nonhydrogenic core which breaks the dynamical symmetry of the Coulomb problem. It is also shown that the dynamics effectively reduces to that of a two-level atom. The oscillations are remnants of interferences that arise partly due to a phase difference which develops between the two levels when they go through two consecutive one-photon resonances, and partly due to an effective change of the carrier-envelope phase of the coupling field.
Symmetry and symmetry breaking in Rydberg-atom intrashell dynamics
NASA Astrophysics Data System (ADS)
Pilskog, I.; Fregenal, D.; Frette, Ø.; Førre, M.; Horsdal, E.; Waheed, A.
2011-04-01
We have investigated experimentally and theoretically the dynamics of Stark-Zeeman split states in Li(n=25) Rydberg atoms when they are exposed to a superposition of a slowly varying field and a harmonic RF field. Regular oscillatory structures are observed in the intrashell transitions. By solving the time-dependent Schrödinger equation for the problem it is shown that the dynamics is strongly influenced by the nonhydrogenic core which breaks the dynamical symmetry of the Coulomb problem. It is also shown that the dynamics effectively reduces to that of a two-level atom. The oscillations are remnants of interferences that arise partly due to a phase difference which develops between the two levels when they go through two consecutive one-photon resonances, and partly due to an effective change of the carrier-envelope phase of the coupling field.
Patterns of dynamical gauge symmetry breaking
NASA Astrophysics Data System (ADS)
Chen, Ning; Ryttov, Thomas A.; Shrock, Robert
2010-12-01
We construct and analyze theories with a gauge symmetry in the ultraviolet of the form G?Gb, in which the vectorial, asymptotically free Gb gauge interaction becomes strongly coupled at a scale where the G interaction is weakly coupled and produces bilinear fermion condensates that dynamically break the G symmetry. Comparisons are given between Higgs and dynamical symmetry-breaking mechanisms for various models.
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. PMID:25354765
Nonlocal dynamics and infinite nonrelativistic conformal symmetries
NASA Astrophysics Data System (ADS)
Andrzejewski, K.; Bolonek-LasoÅ„, K.
2016-03-01
We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite-dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the nonrelativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model, and on the quantum level, it leads to the centrally extended Virasoro algebra.
Interpretation of symmetry experiments on Omega
NASA Astrophysics Data System (ADS)
Lours, Laurence; Bastian, Josiane; Monteil, Marie-Christine; Philippe, Franck; Jadaud, Jean-Paul
2006-10-01
The interpretation of the symmetry experiments performed on Omega in 2005 with 3 cone LMJ-like irradiation is presented here. The goal of this campaign was the characterization of the irradiation symmetry by X-ray imaging of the D2Ar capsule. Images of backlit implosion (as done in earlier campaigns with foam balls) and core emission were obtained on the same shot, and can be compared to FCI2 simulations. This set of shots comfirms former results with foam balls of a good symmetry control with 3 cones in empty hohlraums. The influence of the hohlraum shape on symmetry is also studied by comparison of cylindrical hohlraums vs rugby ones.
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
2014-01-01
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. PMID:24985711
Functional ferroic heterostructures with tunable integral symmetry
NASA Astrophysics Data System (ADS)
Becher, C.; Trassin, M.; Lilienblum, M.; Nelson, C. T.; Suresha, S. J.; Yi, D.; Yu, P.; Ramesh, R.; Fiebig, M.; Meier, D.
2014-07-01
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.
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.
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.
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 FÃ¶rderern der J W Goethe-UniversitÃ¤t 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 FÃ¶rderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There were also two colleagues who would have liked to participate but were unable to do so (M Horn and A Solomon); we agreed to incorporate their manuscripts into the Proceedings. We would like to thank the staff of Collegium Mehrerau for their hospitality. Once more special thanks to the Schenk Family for their continuing friendship and generous support. The informal evening meetings in these stimulating surroundings probably contributed as much to the scientific success as the lectures during the day and many personal contacts were made. Last, but not least, we would like to thank Yvette again for her unremitting support. Dieter Schuch and Michael Ramek Frankfurt am Main and Graz, July 2012 Conference photograph
Permutation symmetry for theta functions
Carlson, B.C.
2011-01-21
This paper does for combinations of theta functions most of what Carlson (2004) [1] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral R{sub F} of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas.
NASA Astrophysics Data System (ADS)
Gu, Pei-Hong
2012-07-01
We propose a novel SU (3)c Ã— SU (2)L Ã— SU (2)R Ã— U(1) B - L left-right symmetric model where the standard model fermion and Higgs fields are SU (2)L doublets or SU (2) singlets while their mirror partners are SU (2)R doublets or SU (2) singlets. The scalar fields also include a real singlet for dark matter and two SU (2) triplets for seesaw. The mixing between the standard model and mirror fermions is forbidden by a Z2 Ã— Z2â€§ discrete symmetry. The mirror charged fermions can decay into their standard model partners with the dark-matter scalar while the mirror neutrinos can decay into the mirror charged fermions through the right-handed gauge interactions. Our model can have new implications on the strong CP problem, leptogenesis, collider phenomenology and dark matter detection.
Symmetry breaking in tensor models
NASA Astrophysics Data System (ADS)
Benedetti, Dario; Gurau, Razvan
2015-11-01
In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.
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.
Polyhedra, complexes, nets and symmetry.
Schulte, Egon
2014-05-01
Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial and algebraic properties. They can be viewed as finite or infinite 3-periodic graphs (nets) equipped with additional structure imposed by the faces, allowed to be skew, zigzag or helical. A polyhedron or complex is regular if its geometric symmetry group is transitive on the flags (incident vertex-edge-face triples). There are 48 regular polyhedra (18 finite polyhedra and 30 infinite apeirohedra), as well as 25 regular polygonal complexes, all infinite, which are not polyhedra. Their edge graphs are nets well known to crystallographers and they are identified explicitly. There are also six infinite families of chiral apeirohedra, which have two orbits on the flags such that adjacent flags lie in different orbits. PMID:24815970
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350â€‰â€‰GeVâ‰²mSâ‰²3â€‰â€‰TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
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.
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.
NASA Astrophysics Data System (ADS)
Fan, Jiji
The Standard Model provides a successful description of presently known particle phenomena up to scale of hundreds of GeV. Still, the Standard Model is a work in progress and could be extended to describe physics at higher energies, for instance, the TeV scale which will be explored soon at the Large Hadron Collider. In this thesis, we present several projects exploring possible new physics beyond Standard Model and their collider signatures. The first part is dedicated to a particular supersymmetric scenario characterized by cascade decays with copious lepton production. The scenario has striking signatures that can be probed by the Large Hadron Collider even in the 10 TeV run with as little as 200 pb-1 of data, provided the squark masses are about 1 TeV. Its spectrum arises in several well-motivated models and its signatures are long-lived sleptons, numerous isolated leptons, abundant Higgs production, rather energetic jets, and no missing energy. The Higgs can be discovered in the h ? bb¯ mode via the 4 leptons+4 jets channel because the leptons accompanying Higgs production suppress the background. We present a low-scale gaugino mediation model that realizes the scenario and reconstruct the spectrum via several clean channels. The second part explores scenarios where the electroweak symmetry breaking sector is nearly scale invariant and consequently gives rise to a light CP even scalar particle. We study the couplings of the light scalar to the Standard Model particles that can arise from the explicit breaking of scale invariance focusing on the possible differences with the minimal Standard Model. The couplings of the light scalar to light fermions, as well as to the massless gauge bosons, can be significantly enhanced. We find possible new discovery channels due to the decays of the conformal scalar into e +e- and mu+mu - pairs as well as new production channels via, light quark annihilation. In the third part, we present a calculable 'node! of electroweak symmetry breaking in which the Higgs doublet emerges from the meta-stable supersymmetry breaking sector as a pseudo Nambu-Goldstone boson. The Higgs boson mass is further protected by the little Higgs mechanism, and naturally suppressed by a two-loop factor from the supersymmetry breaking scale of 10 TeV. The last part discusses one Lorentz violation scheme where the spacetime symmetry is a subgroup of the full Lorentz group and atomic experiment constraints on this scheme.
Polarization and Symmetry of Electronic Transitions in Long Fluorescence Lifetime Triangulenium Dyes
Thyrhaug, Erling; Sørensen, Thomas Just; Gryczynski, Ignacy; Gryczynski, Zygmunt; Laursen, Bo W.
2013-01-01
To fully exploit the capabilities of fluorescence probes in modern experiments, where advanced instrumentation is used to probe complex environments, other photophysical properties than emission color and emission intensity are monitored. Each dye property can be addressed individually as well as collectively to provide in-depth information unavailable from the standard intensity measurements. Dyes with long emission lifetimes and strongly polarized transitions enable the monitoring of lifetime changes as well as emission polarization (or anisotropy). Thus experiments can be designed to follow slow dynamics. In this article the UV and visible electronic transitions of a series of red emitting dyes based on the triangulenium motif are investigated. We resolve overlapping features in the spectra and assign transition moment of the molecular axes. The result is the complete Jablonski diagram for the UV and visible spectral region. The symmetries of the studied dyes are shown to have a large influence on the optical response and they are clearly separated into two groups of symmetry by their photophysical properties. The C2v symmetric dyes: azadioxatriangulenium (ADOTA+) and diazaoxatriangulenium (DAOTA+) have high emission anisotropies, fluorescence lifetimes around 20 ns, and fluorescence quantum yields of ~50%. The trioxatriangulenium (TOTA+) and triazatriangulenium (TATA+) dyes—nominally of D3h symmetry—have fluorescence lifetimes around 10 ns lifetimes and fluorescence quantum yields of 10-15%. However, the D3h-symmetry is shown to be lowered to a point group, where the axes transform uniquely such that the degeneracy of the E’-states is lifted. PMID:23391292
Seitz symbols for crystallographic symmetry operations.
Glazer, A Michael; Aroyo, Mois I; Authier, André
2014-05-01
The aim of this report is to describe the Seitz notation for symmetry operations adopted by the Commission on Crystallographic Nomenclature as the standard convention for Seitz symbolism of the International Union of Crystallography. The established notation follows the existing crystallographic conventions in the descriptions of symmetry operations. PMID:24815978
The Absolute Normal Scores Test for Symmetry.
ERIC Educational Resources Information Center
Penfield, Douglas A.; Sachdeva, Darshan
Behavioral scientists often wish to determine if a sample has been taken from a symmetric population. Similarly, classroom teachers are interested in symmetry if they wish to grade on a "curve." Previously, the sign test, the Wilcoxon test and the t-test have been used to test a hypothesis concerning the symmetry of a distribution of scores about…
On systems having Poincaré and Galileo symmetry
NASA Astrophysics Data System (ADS)
Holland, Peter
2014-12-01
Using the wave equation in d ? 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d = 1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d > 1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell's equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, Fiona; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-03-01
In addition to fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in unusual ways such as carrying fractional quantum numbers, 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 consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain SETs are anomalous in that they can only occur on the surface of a 3D symmetry protected topological (SPT) phase. In this paper we describe a procedure for identifying an anomalous SET which has a discrete unitary symmetry group G. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to defining a consistent topological theory involving both the original anyons and the gauge fluxes. We point out that a class of obstructions are captured by the fourth cohomology group H4 (G , U (1)) , which also labels the set of 3D SPT phases, providing an explicit link to surface topological orders. We illustrate this using the simplest possible example - the projective semion model - where a Z2 ×Z2 symmetry acts on a chiral semion in a way which is only possible on the surface of a 3D SPT phase.
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
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 PoincarÃ© generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstoneâ€™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-Mannâ€“Oakesâ€“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: â€¢A proof (the first) of Goldstoneâ€™s theorem on a null-plane is given. â€¢The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. â€¢The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
Copper Keplerates: High-Symmetry Magnetic Molecules.
Palacios, Maria A; Moreno Pineda, Eufemio; Sanz, Sergio; Inglis, Ross; Pitak, Mateusz B; Coles, Simon J; Evangelisti, Marco; Nojiri, Hiroyuki; Heesing, Christian; Brechin, Euan K; Schnack, Jürgen; Winpenny, Richard E P
2016-01-01
Keplerates are molecules that contain metal polyhedra that describe both Platonic and Archimedean solids; new copper keplerates are reported, with physical studies indicating that even where very high molecular symmetry is found, the low-temperature physics does not necessarily reflect this symmetry. PMID:26530901
Topological symmetry breaking by quantum wormholes
Mignemi, S.; Moss, I. )
1993-10-15
In multiply connected spacetimes which contain quantum wormholes it may be possible to break gauge symmetries without the usual Higgs fields. In a simple model, symmetry breaking is favored by the quantum effects of Dirac Fermions and leads to vector boson masses related to the wormhole separation.
PT-symmetry in honeycomb photonic lattices
Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We apply gain and loss to honeycomb photonic lattices and show that the dispersion relation is identical to tachyons--particles with imaginary mass that travel faster than the speed of light. This is accompanied by -symmetry breaking in this structure. We further show that the -symmetry can be restored by deforming the lattice.
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.
Hojman symmetry in f(T) theory
NASA Astrophysics Data System (ADS)
Wei, Hao; Zhou, Ya-Nan; Li, Hong-Yu; Zou, Xiao-Bo
2015-11-01
Today, f(T) theory has been one of the popular modified gravity theories to explain the accelerated expansion of the universe without invoking dark energy. In this work, we consider the so-called Hojman symmetry in f(T) theory. Unlike Noether conservation theorem, the symmetry vectors and the corresponding conserved quantities in Hojman conservation theorem can be obtained by using directly the equations of motion, rather than Lagrangian or Hamiltonian. We find that Hojman symmetry can exist in f(T) theory, and the corresponding exact cosmological solutions are obtained. We find that the functional form of f(T) is restricted to be the power-law or hypergeometric type, while the universe experiences a power-law or hyperbolic expansion. These results are different from the ones obtained by using Noether symmetry in f(T) theory. Therefore, it is reasonable to find exact cosmological solutions via Hojman symmetry.
Natural Electroweak Breaking from a Mirror Symmetry
Chacko, Z.; Goh, Hock-Seng; Harnik, Roni
2006-06-16
We present ''twin Higgs models,'' simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.
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.
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.
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 ?3-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 ?3-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 ?3-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 ?3-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 octahedra, represent a natural way of merging the competing needs for enhancing Sc-Ir interactions while diminishing those between the Sc atoms. PMID:24801239
Unal, Baris
2008-12-01
The present work in this dissertation mainly focuses on the clean fivefold surfaces of i-Al-Pd-Mn quasicrystals as well as the nucleation and growth of Ag films on these surfaces. In addition, Ag film growth on NiAl(110) has been explored in the frame of this dissertation. First, we have investigated the equilibration of a fivefold surface of icosahedral Al-Pd-Mn quasicrystal at 900-915 K and 925-950 K, using Omicron variable temperature scanning tunneling microscope (STM). Annealing at low temperatures resulted in many voids on some terraces while the others were almost void-free. After annealing at 925-950K, void-rich terraces became much rarer. Our STM images suggest that through growth and coalescence of the voids, a different termination becomes exposed on host terraces. All of these observations in our study indicate that even after the quasicrystalline terrace-step structure appears, it evolves with time and temperature. More specifically, based on the STM observations, we conclude that during the annealing a wide range of energetically similar layers nucleate as surface terminations, however, with increasing temperature (and time) this distribution gets narrower via elimination of the metastable void-rich terraces. Next, we have examined the bulk structural models of icosahedral Al-Pd-Mn quasicrystal in terms of the densities, compositions and interplanar spacings for the fivefold planes that might represent physical surface terminations. In our analyses, we mainly have focused on four deterministic models which have no partial or mixed occupancy but we have made some comparisons with an undeterministic model. We have compared the models with each other and also with the available experimental data including STM, LEED-IV, XPD and LEIS. In all deterministic models, there are two different families of layers (a pair of planes), and the nondeterministic model contains similar group of planes. These two families differ in terms of the chemical decoration of their top planes. Hence, we name them as Pd+(with Pd) and Pd-(without Pd). Based on their planer structure and the step height, it can be said that these two families can be viable surface terminations. However, besides the Pd content, these two sets differ in terms of relative densities of their top planes as well as the gap separating the layer from the nearest atomic plane. The experimental data and other arguments lead to the conclusion that the Pd- family is favored over the Pd+. This has an important implication on the interpretation of local motifs seen in the high resolution STM images. In other words, the dark stars are not formed by cut-Bergmans rather they are formed by cut-Mackays.
Pauling, L
1991-01-01
The low-Q peaks on three pulsed-neutron powder patterns (total, U differential, and Pd differential) of the icosahedral quasicrystal Pd3SiU have been indexed on the basis of an assumed cubic structure of the crystals that by icosahedral twinning form the quasicrystal. The primitive unit cube is found to have edge length 56.20 A and to contain approximately 12,100 atoms. Similar analyses of pulsed-neutron patterns of Al55Cu10Li35, Al55Cu10Li30Mg5, and Al510Cu125Li235Mg130 give values of the cube edge length 58.3, 58.5, and 58.4 A, respectively, with approximately 11,650 atoms in the unit cube. It is suggested that the unit contains eight complexes in the beta-W positions, plus some small interstitial groups of atoms, with each complex consisting of a centered icosahedron of 13 clusters, each of 116 atoms with the icosahedral structure found in the body-centered cubic crystal Mg32(Al,Zn)49. PMID:11607201
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-session, topics ranging from theoretical chemistry and molecular physics via fundamental problems in quantum theory to thermodynamics, nonlinear dynamics, soliton theory and finally cosmology, were examined and lively discussed. Nearly all the talks can also be viewed on the conference website. The majority of participants contributed to these Proceedings but some were unable to do so as their results were either previously submitted or published elsewhere. We refer to: Â· Quesne C 2013, J. Math. Phys. 54, 102102. Â· Spera M 2013, (Nankai Series in Pure, Applied Mathematics and Theoretical Physics): 11 Symmetries and Groups in Contemporary Physics: pp. 593-598 Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics Tianjin, China, 20 - 26 August 2012 (World Scientific, Singapore) Â· Snobl L and Winternitz P 2014, Classification and Identification of Lie Algebras, CRM Monograph Series 33 (Montreal) ISBN-10: 0-8218-4355-9, ISBN-13: 978-0-8218-4355-0 (http://www.ams.org/bookstore?fn=20&arg1=crmmseries&ikey=CRMM-33). Our personal thanks to Daniel and family! Endless support from the Schenk Family who, among other things, sponsored (yet again) the entire conference dinner (including wines and banquet hall) meant that some costs could be alleviated. We could therefore assist various colleagues from economically-weak countries, despite the lack of external funding. A financial deficit meant we would have had to forego the Conference Proceedings, published in previous years by IOP. After long deliberations, and with donations from Gerhard BerssenbrÃ¼gge, Dr. Dr. Stephan Hauk and Dr. Volker Weisswange, this could be facilitated. We are very grateful to these private donors for their generous and wholehearted support. The staff of Collegium Mehrerau is also to be thanked for their hospitality. Finally, our sincere thanks to Yvette not only for her preparatory work and support during the conference, but also for her persistent interest and help in producing the Proceedings within a reasonable time. Dieter Schuch, Frankfurt am Main, Germany Michael Ramek, Graz, Austria August 2014
Supertwistors, massive superparticles and ?-symmetry
NASA Astrophysics Data System (ADS)
de Azcárraga, J. A.; Izquierdo, J. M.; Lukierski, J.
2009-01-01
We consider a D = 4 two-twistor lagrangian for a massive particle that incorporates the mass-shell condition in an algebraic way, and extend it to a two-supertwistor model with N = 2 supersymmetry and central charge identified with the mass. In the purely supertwistorial picture the two D = 4 super twistors are coupled through a Wess-Zumino term in their fermionic sector. We demonstrate how the ?-gauge symmetry appears in the purely supertwistorial formulation and reduces by half the fermionic degrees of freedom of the two supertwistors; a formulation of the model in terms of ?-invariant degrees of freedom is also obtained. We show that the ?-invariant supertwistor coordinates can be obtained by dimensional (D = 6 ? D = 4) reduction from a D = 6 supertwistor. We derive as well by 6 ? 4 reduction the N = 2 D = 4 massive superparticle model with Wess-Zumino term introduced in 1982. Finally, we comment on general superparticle models constructed with more than two supertwistors.
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
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
Natural quasicrystal with decagonal symmetry
NASA Astrophysics Data System (ADS)
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.
2015-03-01
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.
Discrete Symmetries CP, T, CPT
NASA Astrophysics Data System (ADS)
Bernabeu, J.
2015-07-01
CP-Violation (CPV) was discovered in 1964 in the weak decays of neutral Kaons. This Symmetry Breaking is understood in the Standard Model as a consequence of its Particle Content, codified in the 3×3 Cabibbo-Kobayashi-Maskawa Unitary Mixing Matrix. The measured CPV asymmetries for Kaons and B's are well described by this Mechanism, but the current level of experimental accuracy and theoretical uncertainties leaves room for additional sources of CPV, as demanded by Baryogenesis. A direct Time-Reversal-Violation (TRV) Effect was clearly observed in 2012 in the time evolution of neutral B-mesons. The conceptual basis to bypass the irreversibility of decays, and prepare in the B-Factories both the Reference and the T-reverse transitions, is provided by the quantum properties of Entanglement and the Decay as a Filtering Measurement. Flavour and CP eigenstate decay channels allow a separate independent measurement of CP, T and CPT asymmetries. Prospects for extending such a programmeto any pair of B-decays and for Kaonsin DAPHNE are discussed. The interest in measuring CPTV asymmetries in transitions is emphasized. This includes the search for CPT-breaking as well as the case of not having a well-defined CPT operator.
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 Yuri? 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 Proceedings though some were unable to do so as their results were either previously submitted or published elsewhere. In order to make these contributions also available to readers of the Proceedings, we now list the respective references as follow: Albertsson C, Hlavatý L and Šnobl L 2008 On the Poisson-Lie T-plurality of boundary conditions J. Math. Phys. 49 032301-23, arXiv:0706.0820; Bender C M, Brody D C and Hook D W 2008 Quantum effects in classical systems having complex energy J. Phys. A: Math. Theor. 41 352003 (15 pp); Kanellopoulos V, Kleber M and Kramer T 2009 Use of Lambert's theorem for the n-dimensional Coulomb problem Phys. Rev. A 80 012101; Kramer P 2010 Platonic topology and CMB fluctuations: homotopy anisotropy and multipole selection rules Class. Quantum Grav. 27 095013 (27 pp), arXiv:0909.2758v1; Quesne C 2009 Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics SIGMA 5 084 (24 pp). On the other hand, some colleagues planning on attending the meeting had to forfeit their participation due to unforeseeable circumstances. As they had prepared their contributions particularly for our symposium, we have also allowed their input. The articles of Kibler, Leach, Reinisch and Wolf have therefore been included though the authors were absent. Marcos Moshinsky and Yuri? Smirnov, two long-standing colleagues and friends who attended the symposium on multiple occasions passed away in the year before the conference. A memorial service was held at the chapel of the Mehrerau during the meeting. The commemorative words from Father Vinzenz were based on information from our own experience, from an article by Alejandro Frank in Letras Libres Junio 2009, p.54 (a monthly literary magazine published by Editorial Vuelta, in Spanish) and articles from "TESTIMONIOS, Marcos Moshinsky: 80 años de vida y 60 años de trabajo científico" 2001 Frank A and Wolf K B eds. Two contributions dedicated especially in their memory are also included in these Proceedings. It was especially rewarding and greatly appreciated that symposium-founder Bruno Gruber attended all the sessions and that Dr. Hubert Regner, a distinguished official of the provincial administration and ardent supporter of the symposia for over twenty years, honoured us with a visit and an encouraging address to the participants. We wish to express our sincere gratitude to the local community, particularly the Schenk Family and the staff of Collegium Mehrerau for the selfless friendship, generosity and kind hospitality they offered our gathering. It made a lasting impression on participants and guests alike and provided an excellent basis for fruitful scientific discussions and personal interactions. This and the positive resonance from participants have encouraged us to take the experiment a step further to "Symmetries in Science 2011"! Thanks also to Yvette for continuous and reliable support. The conference and proceedings would probably not have materialized without her. Frankfurt am Main and Graz, June 2010 Dieter Schuch Michael Ramek Conference photograph
Anisotropic Weyl symmetry and cosmology
Moon, Taeyoon; Oh, Phillial; Sohn, Jongsu E-mail: ploh@skku.edu
2010-11-01
We construct an anisotropic Weyl invariant theory in the ADM formalism and discuss its cosmological consequences. It extends the original anisotropic Weyl invariance of Ho?ava-Lifshitz gravity using an extra scalar field. The action is invariant under the anisotropic transformations of the space and time metric components with an arbitrary value of the critical exponent z. One of the interesting features is that the cosmological constant term maintains the anisotropic symmetry for z = ?3. We also include the cosmological fluid and show that it can preserve the anisotropic Weyl invariance if the equation of state satisfies P = z?/3. Then, we study cosmology of the Einstein-Hilbert-anisotropic Weyl (EHaW) action including the cosmological fluid, both with or without anisotropic Weyl invariance. The correlation of the critical exponent z and the equation of state parameter ?-bar provides a new perspective of the cosmology. It is also shown that the EHaW action admits a late time accelerating universe for an arbitrary value of z when the anisotropic conformal invariance is broken, and the anisotropic conformal scalar field is interpreted as a possible source of dark energy.
Symmetries of Ginsparg-Wilson chiral fermions
Mandula, Jeffrey E.
2009-10-15
The group structure of the variant chiral symmetry discovered by Luescher in the Ginsparg-Wilson description of lattice chiral fermions is analyzed. It is shown that the group contains an infinite number of linearly independent symmetry generators, and the Lie algebra is given explicitly. CP is an automorphism of this extended chiral group, and the CP transformation properties of the symmetry generators are found. The group has an infinite-parameter invariant subgroup, and the factor group, whose elements are its cosets, is isomorphic to the continuum chiral symmetry group. Features of the currents associated with these symmetries are discussed, including the fact that some different, noncommuting symmetry generators lead to the same Noether current. These are universal features of lattice chiral fermions based on the Ginsparg-Wilson relation; they occur in the overlap, domain-wall, and perfect-action formulations. In a solvable example, free overlap fermions, these noncanonical elements of lattice chiral symmetry are related to complex energy singularities that violate reflection positivity and impede continuation to Minkowski space.
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; PÃ©rez-Espigares, Carlos; del Pozo, JesÃºs 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 Gallavottiâ€“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 Onsagerâ€™s reciprocity relations and Greenâ€“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
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.
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+nâˆ’1, e.g. a G(m,nâˆ’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 â€œquantum spacetimeâ€. The contractions from G(1,3) may be relevant to real physics.
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.
Nonanomalous discrete R symmetry decrees three generations.
Evans, Jason L; Ibe, Masahiro; Kehayias, John; Yanagida, Tsutomu T
2012-11-01
We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R symmetry larger than R parity, provided that the supersymmetric standard model can be minimally embedded into a grand unified theory. This connects an explanation for the number of generations with seemingly unrelated problems such as supersymmetry breaking, proton decay, the Î¼ problem, and the cosmological constant through a discrete R symmetry. We also show that three generations is uniquely required by a nonanomalous discrete R symmetry in classes of grand unified theories such as the ones based on (semi)simple gauge groups. PMID:23215270
Neutrino mixing and leptogenesis in ? -? symmetry
NASA Astrophysics Data System (ADS)
Lashin, E. I.; Chamoun, N.; Hamzaoui, C.; Nasri, S.
2015-06-01
We study the consequences of the Z2 symmetry behind the ? -? universality in the neutrino mass matrix. We then implement this symmetry in the type-I seesaw mechanism and show how it can accommodate all sorts of lepton mass hierarchies and generate enough lepton asymmetry to interpret the observed baryon asymmetry in the universe. We also show how a specific form of a high-scale perturbation is kept when translated via the seesaw into the low scale domain, where it can accommodate the neutrino mixing data. We finally present a realization of the high scale perturbed texture through the addition of matter and extra exact symmetries.
Shearconductivity as evidence for broken mirror symmetries
NASA Astrophysics Data System (ADS)
Hlobil, Patrik; Raghu, Srinivas; Maharaj, Akash; Hosur, Pavan
2015-03-01
We propose the possible detection of broken mirror symmetries in highly correlated two-dimensional materials by elastotransport measurements. Using linear response theory we calculate the shearconductance ?xx , xy = ??xx / ??xy , the linear change of the longitudinal conductivity ?xx due to a shear strain ?xy. This quantity can only be non-vanishing if the in-plane mirror symmetries are broken and we show that a square lattice with checkerboard charge and bond density wave shows a finite shearconductivity. This implies that a measurement of ?xx , xy opens the possibility to verify broken mirror symmetry in the pseudogap regime of high-Tc superconductors. Experimental setups to detect shearconductance are presented.
Yang-Mills Origin of Gravitational Symmetries
NASA Astrophysics Data System (ADS)
Anastasiou, A.; Borsten, L.; Duff, M. J.; Hughes, L. J.; Nagy, S.
2014-12-01
By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized approximation, the gravitational symmetries of general covariance, p -form gauge invariance, local Lorentz invariance, and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincaré symmetry. As a concrete example, we focus on the new minimal (12 +12 ) off shell version of simple four-dimensional supergravity obtained by tensoring the off shell Yang-Mills multiplets (4 +4 , NL=1 ) and (3 +0 , NR=0 ).
Shift-symmetries at higher order
NASA Astrophysics Data System (ADS)
Abel, Steven; Stewart, Richard J.
2016-02-01
The fate of shift-symmetries in effective string models is considered beyond tree-level. Such symmetries have been proposed in the past as a way to maintain a hierarchically small Higgs mass and also play a role in schemes of cosmological relaxation. It is argued that on general grounds one expects shift-symmetries to be restored in the limit of certain asymmetric compactifications, to all orders in perturbation theory. This behaviour is verified by explicit computation of the KÃ¤hler potential to one-loop order.
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.
Fermionic symmetry protected topological phases and cobordisms
NASA Astrophysics Data System (ADS)
Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex; Wang, Zitao
2015-12-01
It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with {Z}_2 symmetry, where {Z}_2 is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ? 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases.
Discrete symmetries and de Sitter spacetime
Cot?escu, 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 ?-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. PMID:25910163
Constraints on leptogenesis from a symmetry viewpoint
Gonzalez Felipe, R.; Serodio, H.
2010-03-01
It is shown that type I seesaw models based on the standard model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis CP asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are diagonal in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.
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.
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.
Ambrose, Rebecca L.; Lander, Gabriel C.; Maaty, Walid S.; Bothner, Brian; Johnson, John E.; Johnson, Karyn N.
2009-01-01
The vinegar fly, Drosophila melanogaster, is a popular model for the study of invertebrate antiviral immune responses. Several picorna-like viruses are commonly found in both wild and laboratory populations of D. melanogaster. The best-studied and most pathogenic of these is the dicistrovirus Drosophila C virus. Among the uncharacterized small RNA viruses of D. melanogaster, Drosophila A virus (DAV) is the least pathogenic. Historically, DAV has been labelled as a picorna-like virus based on its particle size and the content of its RNA genome. Here, we describe the characterization of both the genome and the virion structure of DAV. Unexpectedly, the DAV genome was shown to encode a circular permutation in the palm-domain motifs of the RNA-dependent RNA polymerase. This arrangement has only been described previously for a subset of viruses from the double-stranded RNA virus family Birnaviridae and the T=4 single-stranded RNA virus family Tetraviridae. The 8?Å (0.8?nm) DAV virion structure computed from cryo-electron microscopy and image reconstruction indicates that the virus structural protein forms two discrete domains within the capsid. The inner domain is formed from a clear T=3 lattice with similarity to the ?-sandwich domain of tomato bushy stunt virus, whilst the outer domain is not ordered icosahedrally, but forms a cage-like structure that surrounds the core domain. Taken together, this indicates that DAV is highly divergent from previously described viruses. PMID:19474243
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
Electrochemical hydrogen storage in Ti(1.6)V(0.4)Ni(1-x)Co(x) icosahedral quasicrystalline alloys.
Hu, Wen; Niu, Xiao D; Watada, Masaharu; Kawabe, Yoshiteru; Wu, Yao M; Wang, Li D; Wang, Li M
2010-01-18
The discovery of the icosahedral phase (i-phase) in rapidly quenched Ti(1.6)V(0.4)Ni(1-x)Co(x) (x=0.02-0.1) alloys is described herein. The i-phase occurs in a similar amount relative to the coexisting beta-Ti phase. The electron diffraction patterns show the distinct spot anisotropy, indicating that the i-phase is metastable. The electrochemical hydrogen storage performances of these five alloy electrodes are also reported herein. The hydrogen desorption of nonelectrochemical recombination in the cyclic voltammetric (CV) response exhibits the demand for electrocatalytic activity improvement. A discharge capacity of 261.5 mA h g(-1) was measured in a Ti(1.6)V(0.4)Ni(0.96)Co(0.04) alloy electrode at 30 mA g(-1) and 303 K and it is shown that an appropriate amount of Co element addition would enhance the cycling stability at the expense of high-rate discharging ability. PMID:19911407
Zheng, Qiang; Wagner, Frank R; Ormeci, Alim; Prots, Yurii; Burkhardt, Ulrich; Schmidt, Marcus; Schnelle, Walter; Grin, Yuri; Leithe-Jasper, Andreas
2015-11-01
Two ternary borides MNi9 B8 (M=Al, Ga) were synthesized by thermal treatment of mixtures of the elements. Single-crystal X-ray diffraction data reveal AlNi9 B8 and GaNi9 B8 crystallizing in a new type of structure within the space group Cmcm and the lattice parameters a=7.0896(3)?Å, b=8.1181(3)?Å, c=10.6497(4)?Å and a=7.0897(5)?Å, b=8.1579(4)?Å, c=10.6648(7)?Å, respectively. The boron atoms build up two-dimensional layers, which consist of puckered [B16 ] rings with two tailing B atoms, whereas the M atoms reside in distorted vertices-condensed [Ni12 ] icosahedra, which form a three-dimensional framework interpenetrated by boron porphyrin-reminiscent layers. An unusual local arrangement resembling a giant metallo-porphyrin entity is formed by the [B16 ] rings, which, due to their large annular size of approximately 8?Å, chelate four of the twelve icosahedral Ni atoms. An analysis of the chemical bonding by means of the electron localizability approach reveals strong covalent B?B interactions and weak Ni?Ni interactions. Multi-center dative B?Ni interaction occurs between the Al-Ni framework and the boron layers. In agreement with the chemical bonding analysis and band structure calculations, AlNi9 B8 is a Pauli-paramagnetic metal. PMID:26418894
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 âˆ¼20 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 âˆ¼10 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. PMID:26374901
NASA Astrophysics Data System (ADS)
Goto, D.; Nakajima, T.; Masaki, S.
2014-12-01
Air pollution has a great impact on both climate change and human health. One effective way to tackle with these issues is a use of atmospheric aerosol-chemistry models with high-resolution in a global scale. For this purpose, we have developed an aerosol-chemistry model based on a global cloud-resolving model (GCRM), Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Tomita and Satoh, Fluid. Dyn. Res. 2004; Satoh et al., J. Comput. Phys. 2008, PEPS, 2014) under MEXT/RECCA/SALSA project. In the present study, we have simulated aerosols and tropospheric ozone over Japan by our aerosol-chemistry model "NICAM-Chem" with a stretched-grid system of approximately 10 km resolution, for saving the computer resources. The aerosol and chemistry modules are based on Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS; Takemura et al., J. Geophys. Res., 2005) and Chemical AGCM for Study of Atmospheric Environment and Radiative Forcing (CHASER; Sudo et al., J. Geophys. Res., 2002). We found that our model can generally reproduce both aerosols and ozone, in terms of temporal variations (daily variations of aerosols and diurnal variations of ozone). Under MEXT/RECCA/SALSA project, we also have used these results obtained by NICAM-Chem for the assessment of their impact on human health.
NASA Astrophysics Data System (ADS)
Nakamoto, Kazuo; McKinney, Michael A.
2000-06-01
The C60 molecule (Buckyball/soccer ball) exhibits only 4 IR and 10 Raman bands although it possesses 174 (3 x 60 - 6) normal vibrations. This striking reduction in the number of observed bands is evidently due to the molecule's extremely high symmetry (Ih point group). First, the 120 symmetry elements of its truncated icosahedral structure are identified and the local (site) symmetry of the carbon atoms (Cc) is determined. Use of molecular models greatly facilitates the process in determining the local and molecular symmetries. Then the correlation method is used to derive a table that classifies the 174 normal vibrations into the respective symmetry species of the Ih point group. In this method, symmetry properties of atomic displacements in terms of the local point group (Cc) are correlated with those in terms of the molecular point group (Ih). After the normal vibrations are classified into respective symmetry species, the numbers of IR- and Raman-active vibrations can be determined by the symmetry selection rules for IR and Raman spectra. The vibrational spectra of C60 and C70 (rugby ball) are analyzed by the above procedure, and the results obtained for C28, C32, C50, and dodecahedrane are provided.
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.
Anderson transition in systems with chiral symmetry
NASA Astrophysics Data System (ADS)
García-García, Antonio M.; Cuevas, Emilio
2006-09-01
Anderson localization is a universal quantum feature caused by destructive interference. On the other hand chiral symmetry is a key ingredient in different problems of theoretical physics: from nonperturbative QCD to highly doped semiconductors. We investigate the interplay of these two phenomena in the context of a three-dimensional disordered system. We show that chiral symmetry induces an Anderson transition (AT) in the region close to the band center. Typical properties at the AT such as multifractality and critical statistics are quantitatively affected by this additional symmetry. The origin of the AT has been traced back to the power-law decay of the eigenstates; this feature may also be relevant in systems without chiral symmetry.
Space and time from translation symmetry
Schwarz, A.
2010-01-15
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Permutation Symmetry Determines the Discrete Wigner Function.
Zhu, Huangjun
2016-01-29
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry transformation. We prove that, in the discrete scenario, this permutation symmetry is equivalent to the symmetry group being a unitary 2 design. Such a highly symmetric representation can only appear in odd prime power dimensions besides dimensions 2 and 8. It suffices to single out a unique discrete Wigner function among all possible quasiprobability representations. In the course of our study, we show that this discrete Wigner function is uniquely determined by Clifford covariance, while no Wigner function is Clifford covariant in any even prime power dimension. PMID:26871314
Permutation Symmetry Determines the Discrete Wigner Function
NASA Astrophysics Data System (ADS)
Zhu, Huangjun
2016-01-01
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry transformation. We prove that, in the discrete scenario, this permutation symmetry is equivalent to the symmetry group being a unitary 2 design. Such a highly symmetric representation can only appear in odd prime power dimensions besides dimensions 2 and 8. It suffices to single out a unique discrete Wigner function among all possible quasiprobability representations. In the course of our study, we show that this discrete Wigner function is uniquely determined by Clifford covariance, while no Wigner function is Clifford covariant in any even prime power dimension.
Neutrino mass textures and partial ? -? symmetry
NASA Astrophysics Data System (ADS)
Lashin, E. I.; Chamoun, N.; Hamzaoui, C.; Nasri, S.
2014-05-01
We discuss the viability of the ? -? interchange symmetry imposed on the neutrino mass matrix in the flavor space. Whereas the exact symmetry is shown to lead to textures of a completely degenerate spectrum, which is incompatible with the neutrino oscillation data, introducing small perturbations into the preceding textures, inserted in a minimal way, leads, however, to four deformed textures representing an approximate ?-? symmetry. We motivate the form of these "minimal" textures, which disentangle the effects of the perturbations, and present some concrete realizations assuming exact ? -? at the Lagrangian level but at the expense of adding new symmetries and matter fields. We find that all of these deformed textures are capable of accommodating the experimental data, and in all types of neutrino mass hierarchies, particularly the nonvanishing value for the smallest mixing angle.
From Symmetries to Quarks and Beyond
NASA Astrophysics Data System (ADS)
Meshkov, Sydney
2015-03-01
Attempts to understand the plethora of meson baryon and meson resonances by the introduction of symmetries, which led to the invention of quarks and the quark model, and finally to the formulation of QCD, are described.
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.
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.
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.
Projective representations from quantum enhanced graph symmetries
NASA Astrophysics Data System (ADS)
Kaufmann, R. M.; Khlebnikov, S.; Wehefritz—Kaufmann, B.
2015-04-01
We define re-gaugings and enhanced symmetries for graphs with group labels on their edges. These give rise to interesting projective representations of subgroups of the automorphism groups of the graphs. We furthermore embed this construction into several higher levels of generalization using category theory and show that they are natural in that language. These include projective representations of the re-gauging groupoid and a novel generalization to all symmetries of the graph.
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. .
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.
Nanostructure symmetry: Relevance for physics and computing
Dupertuis, Marc-AndrÃ©; Oberli, D. Y.; Karlsson, K. F.; Dalessi, S.; Gallinet, B.; Svendsen, G.
2014-03-31
We review the research done in recent years in our group on the effects of nanostructure symmetry, and outline its relevance both for nanostructure physics and for computations of their electronic and optical properties. The exemples of C3v and C2v quantum dots are used. A number of surprises and non-trivial aspects are outlined, and a few symmetry-based tools for computing and analysis are shortly presented.
Relabeling symmetries in hydrodynamics and magnetohydrodynamics
Padhye, N.; Morrison, P.J.
1996-04-01
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics relabeling results in Ertel`s theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism.
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. PMID:25421576
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.
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
Symmetry in Flowers: Diversity and Evolution.
Endress
1999-11-01
This article traces research on floral symmetry back to its beginnings. It brings together recent advances from different fields that converge in floral symmetry and new unpublished material on diversity and development of floral symmetry. During floral development, symmetry may change: monosymmetric flowers may have a polysymmetric early phase; polysymmetric flowers may have a monosymmetric or even asymmetric early phase; more than one symmetry change is also possible. In Lamiales s.l. (comprising the model plant Antirrhinum, where the cycloidea gene produces monosymmetric flowers with the adaxial side of the androecium reduced), taxa also occur in which the androecium is reduced on both sides, adaxial and abaxial. As a trend in asymmetric flowers, enantiomorphy (with two mirror-image morphs) at the level of individuals seems to occur only in groups in which the flowers are predominantly of a relatively simple construction. In contrast, one morph is fixed at the level of species or higher taxa in groups with more complicated flowers. This is indicated by the apparent lack of enantiomorphy in corolla contortion in asterids but its predominance in rosids with contort flowers, or by the apparent lack of enantiomorphy in the pollination organs of asymmetric flowers in Faboideae but its presence in asymmetric flowers in Caesalpinioideae. To study the evolution of the diverse symmetry patterns, a concerted approach from different fields including molecular developmental genetics, pollination biology, and comparative diversity research is necessary. PMID:10572019
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. PMID:26640644
Symmetry energy in cold dense matter
NASA Astrophysics Data System (ADS)
Jeong, Kie Sang; Lee, Su Houng
2016-01-01
We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.
Local conformal symmetry: The missing symmetry component for space and time
NASA Astrophysics Data System (ADS)
’T Hooft, Gerard
2015-07-01
Local conformal symmetry is usually considered to be an approximate symmetry of nature, which is explicitly and badly broken. Arguments are brought forward here why it has to be turned into an exact symmetry that is spontaneously broken. As in the BEH mechanism in Yang-Mills theories, we then will have a formalism for disclosing the small-distance structure of the gravitational force. The symmetry could be as fundamental as Lorentz invariance, and guide us towards a complete understanding of physics at the Planck scale.
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…
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. Individualsâ€¦
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; HoÅ™ava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Residual symmetries of the gravitational field
NASA Astrophysics Data System (ADS)
AyÃ³n-Beato, Eloy; VelÃ¡zquez-RodrÃguez, 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 AdS waves.
King, R Bruce
2004-11-01
Nickel and palladium atoms with their closed-shell d(10) electronic configurations are encapsulated in the icosahedral clusters [Ni@Ni(10)E(2)(CO)(18)](4-)(E = Sb, Bi, Sb[rightward arrow]Ni(CO)(3), CH(3)Sn and n-C(4)H(9)Sn) and the geometrically related pentagonal antiprismatic cluster Pd@Bi(10)(4+) found in Bi(14)PdBr(16). Such endohedral d(10) atoms in pentagonal antiprismatic clusters are donors of zero skeletal electrons and interact only weakly with the atoms in the surrounding polyhedron so that they may be regarded as analogous to endohedral noble gases in fullerenes such as He@C(60). On the other hand, endohedral nickel and palladium atoms in 10- and 11-vertex flattened deltahedral bare metal clusters of group 13 metals without five-fold symmetry, such as Ni@E(10)(10-) found in Na(10)NiE(10)(E = Ga, In) and Pd@Tl(11)(7-) found in A(8)Tl(11)Pd (A = Cs, Rb, K), interact significantly with the cluster atoms, particularly those at the flattened vertices of the deltahedron. The role of endohedral d(10) atoms Ni and Pd in polyhedra with five-fold symmetry as "pseudo-noble-gases" can be related to their positions at the "composite divide" of the "Metallurgists' Periodic Table" proposed by H. E. N. Stone on the basis of alloy systematics as well as the equivalence of the five d orbitals in polyhedra with five-fold symmetry. PMID:15510254
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.
NASA Astrophysics Data System (ADS)
Dai, Tie; Shi, Guangyu; Nakajima, Teruyuki
2015-06-01
Aerosol optical properties are simulated using the Spectral Radiation Transport Model for Aerosol Species (SPRINTARS) coupled with the Non-hydrostatic ICosahedral Atmospheric Model (NICAM). The 3-year global mean all-sky aerosol optical thickness (AOT) at 550 nm, the Ã…ngstrÃ¶m Exponent (AE) based on AOTs at 440 and 870 nm, and the single scattering albedo (SSA) at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Aerosol Robotic Network (AERONET). The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the opposite is found over regions dominated by hydrophobic aerosol.
NASA Astrophysics Data System (ADS)
Lv, Bin-Jiang; Peng, Jian; Chu, Zhong
2015-09-01
The effect of Icosahedral phase (I-phase) on hot deformation behavior, dynamic recrystallization (DRX) evolution, and hot workability of Mg-2.0Zn-0.3Zr-0.2Y alloy has been investigated in the temperature range of 300-500 Â°C and strain rate range of 0.001-1 s-1 using Gleeble 3500D thermo-mechanical simulator. Based on regression analysis for Arrhenius-type equation of flow behavior, the average activation energy of deformation was determined as Q = 277.8 kJ/mol. The model of DRX evolution is . The DRX model agreed well with the microstructure evolution of the alloy at all deformation conditions. At lower strain rates (0.001-0.01 s-1), continuous DRX (CDRX) is the main DRX mechanism that occurred near the original grain boundaries. Twin-dynamic recrystallization (TDRX) began to occur at lower deformation temperatures and higher strain rates (0.1-1 s-1). At a deformation temperature range of 250 to 350 Â°C and a strain rate of 1 s-1, the main DRX mechanism is TDRX, and the density of twins decreased, and CDRX began to occur near the original grain boundaries. When the deformation temperature increased to 400 Â°C, TDRX disappeared and CDRX occurred near original grain boundaries and I-phase particles. According to the flow stress behavior and DRX model, the processing maps have exhibited the optimum deformation conditions to be 450 Â°C and the strain rate range of 0.01-0.001 s-1.
Statistical palaeomagnetic field modelling and symmetry considerations
NASA Astrophysics Data System (ADS)
Hulot, G.; Bouligand, C.
2005-06-01
In the present paper, we address symmetry issues in the context of the so-called giant gaussian process (GGP) modelling approach, currently used to statistically analyse the present and past magnetic field of the Earth at times of stable polarity. We first recall the principle of GGP modelling, and for the first time derive the complete and exact constraints a GGP model should satisfy if it is to satisfy statistical spherical, axisymmetrical or equatorially symmetric properties. We note that as often correctly claimed by the authors, many simplifying assumptions used so far to ease the GGP modelling amount to make symmetry assumptions, but not always exactly so, because previous studies did not recognize that symmetry assumptions do not systematically require a lack of cross-correlations between Gauss coefficients. We further note that GGP models obtained so far for the field over the past 5Myr clearly reveal some spherical symmetry breaking properties in both the mean and the fluctuating field (as defined by the covariance matrix of the model) and some equatorial symmetry breaking properties in the mean field. Non-zonal terms found in the mean field of some models and mismatches between variances defining the fluctuating field (in models however not defined in a consistent way) would further suggest that axial symmetry also is broken. The meaning of this is discussed. Spherical symmetry breaking trivially testifies for the influence of the rotation of the Earth on the geodynamo (a long-recognized fact). Axial symmetry breaking, if confirmed, could hardly be attributed to anything else but some influence of the core-mantle boundary (CMB) conditions on the geodynamo (also a well-known fact). By contrast, equatorial symmetry breaking (in particular the persistence of an axial mean quadrupole) may not trivially be considered as evidence of some influence of CMB conditions. To establish this, one would need to better investigate whether or not this axial quadrupole has systematically reversed its polarity with the axial dipole in the past and whether dynamo simulations run under equatorial symmetric CMB conditions display additional transitions (mirror transitions, which we describe) only allowed in such instances. This remains to be fully investigated.
Group Parametrized Tunneling and Local Symmetry Conditions
NASA Astrophysics Data System (ADS)
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar ? ^i {bar g}_i of operators in dual symmetry group bar G. The coefficients bar ? ^i are parameters that define a complete set of allowed paths for any H with G-symmetry and are related thru spectral decomposition of G to eigensolutions of H. Quantum G vs.bar G duality generalizes lab -vs. -body and state -vs. -particle. The number of relevant bar ? ^i-parameters is reduced if a system tends to stick in states of a local symmetry subgroup LsubsetG so the H spectrum forms level clusters labeled by induced representations d(?)(L)\\uparrowG. A cluster-(?) has one E(epsilon)-level labeled by G species (epsilon) for each L species (?) in Depsilon(G)downarrowL by Frobenius reciprocity. Then we apply local symmetry conditions to each irrep Depsilon(bar ? ^i {bar g}_i) that has already been reduced with respect to local symmetry L. This amounts to setting each off-diagonal component Dj,kepsilon(H) to zero. Local symmetry conditions may tell which bar ? ^i-parameters are redundant or zero and directly determine d(?)\\uparrowG tunneling matrix eigenvalues that give E(epsilon)-levels as well as eigenvectors. Otherwise one may need to choose a particular localizing subgroup chain LsubsetL_1subsetL_2...G and further reduce the number of path parameters to facilitate spectral fitting. J.T. Hougen, 2009 MSS RJ01, {J Mol Spect 123, 197 (1987) W.G. Harter and J. C. Mitchell, 2009 MSS RJ05 (See also following talk.) R.P. Feynman, R. B. Leighton, M. Sands, Lectures on Physics Vol.3 (Addison Wesley 1964) p.9-1 W.G. Harter, Principles of Symmetry, Dynamics, and Spectroscopy, (Wiley Interscience, 1993) p.265
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.
Discrete R symmetries and low energy supersymmetry
Dine, Michael; Kehayias, John
2010-09-01
If nature exhibits low energy supersymmetry, discrete (non-Z{sub 2}) R symmetries may well play an important role. In this paper, we explore such symmetries. We generalize gaugino condensation, constructing large classes of models which are classically scale invariant, and which spontaneously break discrete R symmetries (but not supersymmetry). The order parameters for the breaking include chiral singlets. These simplify the construction of models with metastable dynamical supersymmetry breaking. We explain that in gauge mediation, the problem of the cosmological constant makes ''retrofitting'' particularly natural--almost imperative. We describe new classes of models, with interesting scales for supersymmetry breaking, and which allow simple solutions of the {mu} problem. We argue that models exhibiting such R symmetries can readily solve not only the problem of dimension four operators and proton decay, but also dimension five operators. On the other hand, in theories of ''gravity mediation,'' the breaking of an R symmetry is typically of order M{sub p}; R parity is required to suppress dimension four B and L violating operators, and dimension five operators remain problematic.
Broken symmetry as a stabilizing remnant
NASA Astrophysics Data System (ADS)
Law, Sandy S. C.; McDonald, Kristian L.
2010-11-01
The Goldberger-Wise mechanism enables one to stabilize the length of the warped extra dimension employed in Randall-Sundrum models. In this work we generalize this mechanism to models with multiple warped throats sharing a common ultraviolet brane. For independent throats this generalization is straightforward. If the throats possess a discrete interchange symmetry like Zn, the stabilizing dynamics may respect the symmetry, resulting in equal throat lengths, or they may break it. In the latter case the ground state of an initially symmetric configuration is a stabilized asymmetric configuration in which the throat lengths differ. We focus on two- (three-) throat setups with a Z2 (Z3) interchange symmetry and present stabilization dynamics suitable for either breaking or maintaining the symmetry. Though admitting more general application, our results are relevant for existing models in the literature, including the two-throat model with Kaluza-Klein parity, and the three-throat model of flavor with a broken Z3 symmetry.
Broken symmetry as a stabilizing remnant
Law, Sandy S. C.; McDonald, Kristian L.
2010-11-15
The Goldberger-Wise mechanism enables one to stabilize the length of the warped extra dimension employed in Randall-Sundrum models. In this work we generalize this mechanism to models with multiple warped throats sharing a common ultraviolet brane. For independent throats this generalization is straightforward. If the throats possess a discrete interchange symmetry like Z{sub n}, the stabilizing dynamics may respect the symmetry, resulting in equal throat lengths, or they may break it. In the latter case the ground state of an initially symmetric configuration is a stabilized asymmetric configuration in which the throat lengths differ. We focus on two- (three-) throat setups with a Z{sub 2} (Z{sub 3}) interchange symmetry and present stabilization dynamics suitable for either breaking or maintaining the symmetry. Though admitting more general application, our results are relevant for existing models in the literature, including the two-throat model with Kaluza-Klein parity, and the three-throat model of flavor with a broken Z{sub 3} symmetry.
Mednikov, Evgueni G; Jewell, Matthew C; Dahl, Lawrence F
2007-09-19
Presented herein are the preparation and crystallographic/microanalytical/magnetic/spectroscopic characterization of the Pt-centered four-shell 165-atom Pd-Pt cluster, (mu(12)-Pt)Pd(164-x)Pt(x)(CO)(72)(PPh(3))(20) (x approximately 7), 1, that replaces the geometrically related capped three-shell icosahedral Pd(145) cluster, Pd(145)(CO)(x)(PEt(3))(30) (x approximately 60), 2, as the largest crystallographically determined discrete transition metal cluster with direct metal-metal bonding. A detailed comparison of their shell-growth patterns gives rise to important stereochemical implications concerning completely unexpected structural dissimilarities as well as similarities and provides new insight concerning possible synthetic approaches for generation of multi-shell metal clusters. 1 was reproducibly prepared in small yields (<10%) from the reaction of Pd(10)(CO)(12)(PPh(3))(6) with Pt(CO)(2)(PPh(3))(2). Its 165-atom metal-core geometry and 20 PPh(3) and 72 CO ligands were established from a low-temperature (100 K) CCD X-ray diffraction study. The well-determined crystal structure is attributed largely to 1 possessing cubic T(h) (2/m3) site symmetry, which is the highest crystallographic subgroup of the noncrystallographic pseudo-icosahedral I(h) (2/m35) symmetry. The "full" four-shell Pd-Pt anatomy of 1 consists of: (a) shell 1 with the centered (mu(12)-Pt) atom encapsulated by the 12-atom icosahedral Pt(x)Pd(12-x) cage, x = 1.2(3); (b) shell 2 with the 42-atom nu(2) icosahedral Pt(x)Pd(42-x) cage, x = 3.5(5); (c) shell 3 with the anti-Mackay 60-atom semi-regular rhombicosidodecahedral Pt(x)Pd(60-x) cage, x = 2.2(6); (d) shell 4 with the 50-atom nu(2) pentagonal dodecahedral Pd(50) cage. The total number of crystallographically estimated Pt atoms, 8 +/- 3, which was obtained from least-squares (Pt(x)/Pd(1-x))-occupancy analysis of the X-ray data that conclusively revealed the central atom to be pure Pt (occupancy factor, x = 1.00(3)), is fortuitously in agreement with that of 7.6(7) found from an X-ray Pt/Pd microanalysis (WDS spectrometer) on three crystals of 1. Our utilization of this site-occupancy (Pt(x)Pd(1-x))-analysis for shells 1-3 originated from the microanalytical results; otherwise, the presumed metal-core composition would have been (mu(12)-Pt)Pd(164). [Alternatively, the (mu(12)-Pt)M(164) core-geometry of 1 may be viewed as a pseudo-Ih Pt-centered six-shell successive nu(1) polyhedral system, each with radially equivalent vertex atoms: Pt@M(12)(icosahedron)@M(30)(icosidodecahedron)@M(12)(icosahedron)@M(60)(rhombicosidodecahedron)@M(30)(icosidodecahedron)@M(20)(pentagonal dodecahedron)]. Completely surprising structural dissimilarities between 1 and 2 are: (1) to date 1 is only reproducibly isolated as a heterometallic Pd-Pt cluster with a central Pt instead of Pd atom; (2) the 50 atoms comprising the outer fourth nu(2) pentagonal dodecahedral shell in 1 are less than the 60 atoms of the inner third shell in 1, in contradistinction to shell-by-shell growth processes in all other known shell-based structures; (3) the 10 fewer PR3 ligands in 1 necessitate larger bulky PPh(3) ligands to protect the Pd-Pt core-geometry; (4) the 72 CO ligands consist of six bridging COs within each of the 12 pentagons in shell 4 that are coordinated to intershell metal atoms. SQUID magnetometry measurements showed a single-crystal sample of 1 to be diamagnetic over the entire temperature range of 10-300 K. PMID:17722929
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 Ï€-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 = Â±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906
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.
Symmetry-related decompositions of uncertainty
NASA Astrophysics Data System (ADS)
Viana, Marlos
2012-10-01
In statistics, the sample mean and variance are intimately related to the symmetries of the full symmetric group describing all possible permutations of assignments of observations to sampling units. While those symmetries yield exactly two invariant subspaces (in a sense to be defined in the text) in correspondence to those summary statistics, the invariant subspaces associated with specific subgroups of the full symmetric group may then lead to much detailed decompositions of the experimental uncertainty. In the present chapter we discuss the symmetry-related summaries of data arising from dihedral experiments, specifically in the context of multinomial models for frequency counts in symbolic sequences. Special examples are given to dihedral summaries that can be potentially interpreted as measures of (molecular) chirality or handedness.
Arbitrary lattice symmetries via block copolymer nanomeshes
NASA Astrophysics Data System (ADS)
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-06-01
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.
Gravitino dark matter and flavor symmetries
NASA Astrophysics Data System (ADS)
Monteux, Angelo; Carlson, Eric; Cornell, Jonathan M.
2014-08-01
In supersymmetric theories without R-parity, the gravitino can play the role of a decaying Dark Matter candidate without the problem of late NLSP decays affecting Big Bang Nucleosynthesis. In this work, we elaborate on recently discussed limits on R- parity violating couplings from decays to antideuterons and discuss the implications for two classes of flavor symmetries: horizontal symmetries, and Minimal Flavor Violation. In most of the parameter space the antideuteron constraints on R-parity violating couplings are stronger than low-energy baryon-number-violating processes. Even in the absence of flavor symmetries, we find strong new limits on couplings involving third-generation fields, and discuss the implications for LHC phenomenology. For TeV scale superpartners, we find that the allowed MFV parameter space is a corner with gravitino masses smaller than (10) GeV and small tan Î².
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)
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.
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.
Detection of symmetry-enriched topological phases
NASA Astrophysics Data System (ADS)
Huang, Ching-Yu; Chen, Xie; Pollmann, Frank
2014-07-01
Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry-enriched topological (SET) phases. We introduce simple methods to detect certain SET orders directly from a complete set of topologically degenerate ground-state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a nonlocal order parameter can be measured to detect SET phases. The usefulness of the proposed approach is demonstrated by examining two concrete model states which exhibit SET phases: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond (RVB) state on a kagome lattice. We conclude that the spin-1 model and the RVB state are in the same SET phases.
Spontaneous symmetry breaking in interdependent networked game.
Jin, Qing; Wang, Lin; Xia, Cheng-Yi; Wang, Zhen
2014-01-01
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor ? is smaller than a threshold value ?(C), the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds ?(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method. PMID:24526076
Approximate gauge symmetry of composite vector bosons
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2010-08-01
It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
Dark matter stability without new symmetries
NASA Astrophysics Data System (ADS)
CatÃ , Oscar; Ibarra, Alejandro
2014-09-01
The stability of dark matter is normally achieved by imposing extra symmetries beyond those of the Standard Model of particle physics. In this paper we present a framework where the dark matter stability emerges as a consequence of the Standard Model symmetries. The dark matter particle is an antisymmetric tensor field (analogous to the one used for spin-1 mesons in QCD), singlet under the Standard Model gauge group. The Lagrangian possesses an accidental Z2 symmetry which makes the dark matter stable on cosmological time scales. Interactions with the Standard Model fields proceed through the Higgs portal, which allows the observed dark matter abundance to be generated via thermal freeze-out. We also discuss the prospects for observing this dark matter particle in direct detection experiments.
Yang-Mills origin of gravitational symmetries.
Anastasiou, A; Borsten, L; Duff, M J; Hughes, L J; Nagy, S
2014-12-01
By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized approximation, the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance, and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-PoincarÃ© symmetry. As a concrete example, we focus on the new minimal (12+12) off shell version of simple four-dimensional supergravity obtained by tensoring the off shell Yang-Mills multiplets (4+4, N_{L}=1) and (3+0, N_{R}=0). PMID:25526117
How center vortices break chiral symmetry
NASA Astrophysics Data System (ADS)
Faber, Manfried; Höllwieser, Roman
2016-01-01
We investigate the chiral properties of near-zero modes for thick classical center vortices in SU(2) lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.