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
Onion-like inorganic fullerenes of icosahedral symmetry
Ch. Chang; A. B. C. Patzer; E. Sedlmayr; D. Sülzle; T. Steinke
2006-01-01
We report a theoretical density functional study (DFT\\/BP86\\/LANL2DZ) of a class of inorganic clusters of formal composition [X@Y12@Z20]?, which all possess high icosahedral point group symmetry (Ih) consisting of a central atom (X) surrounded by two polyhedral cages: an inner core icosahedron (Y) and an outer shell fullerene-like dodecahedron (Z).All species considered are energetically stable closed-shell systems having a metal\\/semi-metal
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.
Computation of relativistic symmetry orbitals for finite double point groups
J. Meyer; W.-D. Sepp; B. Fricke; A. Rosén
1989-01-01
A program is presented for the construction of relativistic symmetry-adapted molecular basis functions. It is applicable to 36 finite double point groups. The algorithm, based on the projection operator method, automatically generates linearly independent basis sets. Time reversal invariance is included in the program, leading to additional selection rules in the non-relativistic limit.
Do All Spherical Viruses Have Icosahedral Symmetry?
Eric Lewin Altschuler; Antonio Pérez--Garrido
2009-02-24
Recent high resolution structures for viral capsids with 12, 32 and 72 subunits ($T1$, $T3$ and $T7$ viruses) have confirmed theoretical predictions of an icosadeltahedral structure with 12 subunits having five nearest neighbors (pentamers) and $(10T+2)-12$ subunits having six nearest neighbor subunits (hexamers). Here we note that theoretical considerations of energy strain for $T4$, $T9$ $T16$ and $T25$ viruses by aligned pentamers and energy strain along with the sheer number of possible arrangement of pentamers as the number of subunits grows, and simulations for such numbers of subunits make an icosadeltahedral configuration either miraculously unlikely or indicate that there must be a principle of capsid assembly of unprecedented fidelity in Nature. We predict, for example, that high resolution data will show $T4$ capsids to have $D_{5h}$ not icosahedral symmetry.
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 C60 molecule. Specifically, we describe the existence of C70 in terms of breaking of the icosahedral symmetry of C60 by the insertion into its middle of an additional H2 decagon. The surface of C70 is formed by 12 regular pentagons and 25 regular hexagons. All 105 edges of C70 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
Symmetry, stability, and elastic properties of icosahedral incommensurate crystals
Bak, P.
1985-11-01
The symmetry and stability of icosahedral incommensurate structures and generalized two-dimensional Penrose pentagonal structures are studied. The crystallographic properties of Penrose lattices are described by five-dimensional (5D) super space groups, and the icosahedral structures are described by 6D space groups, with or without improper translations. The density in real space is given as the density along a three-dimensional plane in this 6D space. The fivefold symmetry of the diffraction spectrum of Mn-Al alloys, which is inconsistent with three-dimensional translational invariance, reflects a fivefold rotation axis of the 6D space group. The six continuous degrees of freedom associated with the 6D space represent the usual three orthogonal rigid displacements of the crystal, plus three phase shifts associated with internal rearrangements, leading to three acoustic-phonon modes and three phason modes. There are two independent elastic constants, which is fewer than in any regular crystal, representing one-dimensional and five-dimensional irreducible strains, respectively. If the phase degrees of freedom are included, there are five generalized elastic constants. The stability of icosahedral structures and ''lyotropic'' Penrose structures can be understood from a phenomenological Landau theory. The ideal icosahedral crystal has perfect positional order, which is stable with respect to thermal fluctuations at low temperatures. The melting transition is first order.
Virus templated plasmonic nanoclusters with icosahedral symmetry via directed assembly
NASA Astrophysics Data System (ADS)
Ratna, Banahalli; Fontana, Jake; Dressick, Walter; Phelps, Jamie; Johnson, John; Sampson, Travian; Rendell, Ronald; Soto, Carissa
2015-03-01
Controlling the spatial and orientational order of plasmonic nanoparticles may lead to structures with novel electromagnetic properties and applications such as sub-wavelength imaging and ultra-sensitive chemical sensors. Here we report the directed assembly of three-dimensional, icosahedral plasmonic nanoclusters with resonances at visible wavelengths. We show using transmission electron microcopy and in situ dynamic light scattering the nanoclusters consist of twelve gold nanospheres attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. We measured the bulk absorbance from aqueous suspensions of nanoclusters and reproduced the major features of the spectrum using finite-element simulations. Furthermore, because the viruses are easily produced in gram quantities the directed assembly approach is capable of high-throughput, providing a strategy to realize large quantities for applications. NRL summer intern under the HBCU/MI Summer Research Program.
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
ERIC Educational Resources Information Center
Casas, Lluís; Estop, Euge`nia
2015-01-01
Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…
The influence of symmetry on the probability of assembly pathways for icosahedral viral shells
Bona, Miklos
The influence of symmetry on the probability of assembly pathways for icosahedral viral shells on the probability space of assembly pathways that successfully lead to icosahedral viral shells. Several tractable (and hence probability) of an assembly pathway type (or symmetry class) for a T Â¼ 1 viral shell
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…
Simons, Jack
Chapter 10 Electronic Wavefunctions Must Also Possess Proper Symmetry. These Include Angular or trial wavefunction should be constrained to also be an eigenfunction of these symmetry operators wavefunctions should also conform to these spatial symmetries. This Chapter addresses those operators
J. Meyer; W.-D. Sepp; B. Fricke; A. Rosén
1996-01-01
A revised and extended version of the program TSYM is presented. Relativistic symmetry-adapted basis systems for molecular calculations are constructed from atomic orbitals according to the LCAO method. The molecular symmetry group can be one of 45 finite double point groups. The algorithm based on the projection operator formalism automatically ensures the linear independence of the symmetry orbitals. Time reversal
Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
Everett, Lisa L
2008-01-01
We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio. We present a basic toolbox for model-building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the Standard Model.
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
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.
Bodner, Mark; Bourret, Emmanuel; Patera, Jiri; Szajewska, Marzena
2015-05-01
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120. This subgroup is noted by A1 × A1, because it is isomorphic to the Weyl group of the semi-simple Lie algebra A1 × A1. Thirteen of the A1 × A1 orbits are rectangles and four are line segments. The orbits form a stack of parallel layers centered on the axis of C60 passing through the centers of two opposite edges between two hexagons on the surface of C60. These two edges are the only two line segment layers to appear on the surface shell. Among the 24 convex polytopes with shell formed by hexagons and 12 pentagons, having 84 vertices [Fowler & Manolopoulos (1992). Nature (London), 355, 428-430; Fowler & Manolopoulos (2007). An Atlas of Fullerenes. Dover Publications Inc.; Zhang et al. (1993). J. Chem. Phys. 98, 3095-3102], there are only two that can be identified with breaking of the H3 symmetry to A1 × A1. The remaining ones are just convex shells formed by regular hexagons and 12 pentagons without the involvement of the icosahedral symmetry. PMID:25921498
Kumar, Mohit
2013-01-01
Minor group human rhinoviruses bind low-density lipoprotein (LDL) receptors for endocytosis. Once they are inside endosomes, the acidic pH triggers their dissociation from the receptors and conversion into hydrophobic subviral A particles; these attach to the membrane and transfer their single-strand, positive-sense RNA genome into the cytosol. Here, we allowed human rhinovirus 2 (HRV2) A particles, produced in vitro by incubation at pH 5.4, to attach to liposomes; cryo-electron microscopy 3-dimensional single-particle image reconstruction revealed that they bind to the membrane around a 2-fold icosahedral symmetry axis. PMID:23946453
Distinct trivial phases protected by a point-group symmetry in quantum spin chains.
Fuji, Yohei; Pollmann, Frank; Oshikawa, Masaki
2015-05-01
The ground state of the S=1 antiferromagnetic Heisenberg chain belongs to the Haldane phase--a well-known example of the symmetry-protected topological phase. A staggered field applied to the S=1 antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a nonlocal order parameter are given in terms of a matrix-product state formulation. PMID:25978259
Distinct Trivial Phases Protected by a Point-Group Symmetry in Quantum Spin Chains
NASA Astrophysics Data System (ADS)
Fuji, Yohei; Pollmann, Frank; Oshikawa, Masaki
2015-05-01
The ground state of the S =1 antiferromagnetic Heisenberg chain belongs to the Haldane phase—a well-known example of the symmetry-protected topological phase. A staggered field applied to the S =1 antiferromagnetic chain breaks all the symmetries that protect the Haldane phase as a topological phase, reducing it to a trivial phase. That is, the Haldane phase is then connected adiabatically to an antiferromagnetic product state. Nevertheless, as long as the symmetry under site-centered inversion combined with a spin rotation is preserved, the phase is still distinct from another trivial phase. We demonstrate the existence of such distinct symmetry-protected trivial phases using a field-theoretical approach and numerical calculations. Furthermore, a general proof and a nonlocal order parameter are given in terms of a matrix-product state formulation.
NASA Astrophysics Data System (ADS)
Baena, J. D.; Jelinek, L.; Marqués, R.
2007-12-01
In this paper, a systematic approach to the design of bulk isotropic magnetic metamaterials is presented. The roles of the symmetries of both the constitutive element and the lattice are analyzed. For this purpose, it is assumed that the metamaterial is composed of cubic split ring resonators (SRRs) arranged in a cubic lattice. The minimum symmetries needed to ensure an isotropic behavior are analyzed, and some particular configurations are proposed. Besides, an equivalent circuit model is proposed for the considered cubic SRRs. Experiments are carried out in order to validate the proposed theory. We hope that this analysis will pave the way to the design of bulk metamaterials with strong isotropic magnetic response, including negative permeability and left-handed metamaterials.
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. PMID:25933753
Crystallography of decahedral and icosahedral particles. I - Geometry of twinning
NASA Technical Reports Server (NTRS)
Yang, C. Y.
1979-01-01
The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.
Dislocations in icosahedral quasicrystals.
Feuerbacher, Michael
2012-10-21
Dislocations in quasicrystals, as a direct result of the lack of translational symmetry in these materials, possess various salient features. The Burgers vector of a dislocation in an icosahedral quasicrystal is a 6-dimensional vector, which reflects the fact that the dislocation, besides the phonon-type strain field analogous to dislocations in ordinary crystals, is associated inseparably with a further type of defect, the phasons. Phasons are critically involved in the formation and motion of dislocations in quasicrystals and govern the macroscopic plastic behaviour of these materials. In this article the properties of dislocations in icosahedral quasicrystals are comprehensively reviewed, starting from a continuum-mechanical description, via core-structure simulation, to their full experimental characterization. The experimental results presented address the icosahedral phases in the well explored systems Al-Pd-Mn and Zn-Mg-Dy. PMID:22760204
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-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.
Icosahedral incommensurate crystals
Bak, P.
1985-01-01
The icosahedral structures can be described by 6d space group symmetries and their stability can be understood from a simple Landau theory. The task of the crystallographer is to determine the basis associated with the 6d Bravais lattice. The elastic properties and the elementary excitations can be discussed in terms of these symmetries. The ideal icosahedral structures have complete long range order, with sharp Bragg peaks; it is certainly incorrect to consider them to be intermediate between crystals and glasses; they are crystals. It is not difficult to show that the structures are stable with respect to thermal fluctuations, which simply give rise to a reduction of the Bragg peak intensity. The melting transition is first order since the free energy includes third order terms. In a sense the icosahedral structures are incommensurate structures with only one length scale 2..pi../tau/sub i/. The incommensurability comes about because of the relative rotations of the 6 fundamental vectors tau/sub i/: it is not possible to write any of the 6 vectors as sums of rational multiples of the remaining 5 vectors.
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.
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
NASA Astrophysics Data System (ADS)
Bourdillon, Antony
2012-11-01
The following facts about icosahedra need wider attention. 1) The golden section ? is as fundamental to the icosahedral structure (length /edge) as ? is to the sphere (circumference /diameter). 2) The diffraction series are in restricted Fibonacci order because the ratio of adjacent terms fn/fn-1 does not vary, but is the constant ?. The series is therefore geometric. 3) Because of the tetragonal subgroup in the icosahedral point group symmetry, many axes in the icosahedral structure have identical orientation to axes in the face centered cubic matrix of Al6Mn [1] (e.g. [100] and [111]). On these bases, a three dimensional stereographic projection will be presented. 4) A quasi-Bragg law is derived that correctly represents the diffraction series in powers of ? [2]. Furthermore, by employing the normal conventions of electron microscopy, all diffraction patterns are completely indexed in three dimensions. These are the topic of this presentation. Significant consequences will be presented elsewhere: 1) The diffraction pattern intensities near all main axes are correctly simulated, and all atoms are located on a specimen image. 2) The quasi-Bragg law has a special metric. Atomic locations are consistently calculated for the first time. 3) Whereas the Bragg law transforms a crystal lattice in real space into a reciprocal lattice in diffraction space, the quasi-Bragg law transforms a geometric diffraction pattern into a hierarchic structure. 4) Hyperspatial indexation [3] is superceded. [1] Shechtman, D.; Blech, I.; Gratias, D.; Cahn, J.W., Metallic phase with long-range orientational order and no translational symmetry, Phys. Rev. Lett., 1984, 53, 1951-3. [2] Bourdillon, A. J., Nearly free electron band structures in a logarithmically periodic solid, Sol. State Comm. 2009, 149, 1221-1225. [3] Duneau, M., and Katz, A., Phys Rev Lett 54, 2688-2691
Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis
L. Bendersky
1985-01-01
Studies of phase formation in rapidly solidified Al-Mn alloys (composition range 18-22 at. percent Mn) show that an icosahedral phase is replaced by another noncrystallographic phase, a decagonal phase. The decagonal phase is another example of quasicrystal: It has a noncrystallographic point group (10\\/m or 10\\/mmm) together with long-range orientational order and one-dimensional translational symmetry. The decagonal phase is an
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….
Hydrodynamics of icosahedral quasicrystals
T. C. Lubensky; Sriram Ramaswamy; John Toner
1985-01-01
The equations governing long-wavelength, low-frequency excitations in icosahedral quasicrystals are derived. It is found that while the speeds of the propagating modes are isotropic, the attenuations are not, implying that purely macroscopic experiments can in principle distinguish quasicrystals from crystals, glasses, or conventional incommensurate systems. The coefficient of the anisotropy is, regrettably, quite small. The complete spectrum consists of three
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.
So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal
Linus Pauling
1987-01-01
It is proposed that a molten alloy may contain a 104-atom cluster with icosahedral symmetry and largely icosahedral packing. The cluster may be described as involving twenty interpenetrating Friauf (1927) polyhedra. On rapid freezing these clusters form cubic crystals related to the beta-W structure. The structure is compatible with X-ray and neutron powder diffraction patterns, the single-crystal precession X-ray patterns
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.
Nanosize icosahedral quasicrystal in Mg90Ca10 glass: an ab initio molecular dynamics study.
Durandurdu, Murat
2012-07-21
Rapid solidification of Mg(90)Ca(10) from its liquid state is studied by means of an ab initio molecular dynamics technique, and its local structure is investigated by various analyzing methods. The liquid and amorphous states are found to have slightly different short range order even though the perfect and defective icosahedral bonding environments are major bonding elements of both liquid and amorphous states. Perfect icosahedrons with a small frequency exist in the liquid state, more develop during the cooling process and they become the leading building units in the glass state, indicating an icosahedral short range order in Mg(90)Ca(10) glass. Also the linked icosahedrons lead to an icosahedral medium range order. Furthermore, an ordered arrangement of some icosahedrons in the hexagonal symmetry is observed in the glass model, representing a nanoscale icosahedral quasicrystalline phase in Mg(90)Ca(10) glass. PMID:22830707
Prediction of stability changes upon mutation in an icosahedral capsid.
Hickman, Samuel J; Ross, James F; Paci, Emanuele
2015-09-01
Identifying the contributions to thermodynamic stability of capsids is of fundamental and practical importance. Here we use simulation to assess how mutations affect the stability of lumazine synthase from the hyperthermophile Aquifex aeolicus, a T?=?1 icosahedral capsid; in the simulations the icosahedral symmetry of the capsid is preserved by simulating a single pentamer and imposing crystal symmetry, in effect simulating an infinite cubic lattice of icosahedral capsids. The stability is assessed by estimating the free energy of association using an empirical method previously proposed to identify biological units in crystal structures. We investigate the effect on capsid formation of seven mutations, for which it has been experimentally assessed whether they disrupt capsid formation or not. With one exception, our approach predicts the effect of the mutations on the capsid stability. The method allows the identification of interaction networks, which drive capsid assembly, and highlights the plasticity of the interfaces between subunits in the capsid. Proteins 2015; 83:1733-1741. © 2015 The Authors. Proteins: Structure, Function, and Bioinformatics Published by Wiley Periodicals, Inc. PMID:26178267
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…
M. X. Dai; K. Urban
1993-01-01
Lamellar twins have been observed in the icosahedral phase in Al-Cu-Fe alloy. As indicated by both conventional and convergent-beam electron diffraction and high-resolution lattice fringe pictures, the twins are reflection twins with the twinning plane perpendicular to a fivefold axis of the icosahedral quasilattice.
3-jm, 6-j and isoscalar symbols for the icosahedral group
D. R. Pooler
1980-01-01
Using a complex base with a numerical system of labelling the author calculates symmetrised coupling symbols (the 3-jm symbols) for the icosahedral group. He makes full use of Racah's Lemma and explicitly states all the phase standardisations involved. The 3-jm symbols are chosen in a manner that leads to them possessing reordering symmetries that are almost as straightforward as in
Platonic solids back in the sky: Icosahedral inflation
Kang, Jonghee
2015-01-01
We generalize the model of solid inflation to an anisotropic cosmic solid. Barring fine tunings, the observed isotropy of the cosmological background and of the scalar two-point function isolate the icosahedral group as the only possible symmetry group of such a solid. In such a case, higher-point correlation functions---starting with the three-point one---are naturally maximally anisotropic, which makes the standard detection strategies highly inefficient and calls for a dedicated analysis of CMB data. The tensor two-point function can also be highly anisotropic, but only in the presence of sizable higher-derivative couplings.
Anze Losdorfer Bozic; Rudolf Podgornik
2013-01-11
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-H\\"uckel 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.
Matching of interest point groups with pairwise spatial constraints
Kingsbury, Nick
Matching of interest point groups with pairwise spatial constraints Ee Sin, Ng and Nick Kingsbury (University of Cambridge) Matching with pairwise spatial constraints ICIP 2010 1 / 33 #12;Scope Introduction Background Proposed algorithm Pairwise spatial constraints Matching algorithm Experimental results
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)
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.
Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials
Mihalkovic, M. [Department of Physics, Cornell University, Ithaca, New York 14853-2501 (United States)]|[Laboratoire de Thermodynamique et Physique-Chimie Metallurgiques, Ecole Nationale Superieure d`Electronique et d`Electromecanique de Grenoble, Boite Postale 75, 38402 St. Martin d`Heres Cedex (France); Zhu, W.; Henley, C.L. [Department of Physics, Cornell University, Ithaca, New York 14853-2501 (United States); Phillips, R. [Division of Engineering, Brown University, Providence, Rhode Island 02912 (United States)
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.}
Experimental Evidence of Icosahedral and Decahedral Packing in One-Dimensional Nanostructures
Velázquez-Salazar, J. Jesús; Esparza, Rodrigo; Mejía-Rosales, Sergio Javier; Estrada-Salas, Rubén; Ponce, Arturo; Deepak, Francis Leonard; Castro-Guerrero, Carlos; José-Yacamán, Miguel
2011-01-01
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
On the Characters and Representations of Continuous Point Groups.
ERIC Educational Resources Information Center
Flurry, R. L., Jr.
1979-01-01
Presents a method for carrying out the desired reduction which eliminates all ambiguities and trial-and-error. This method, which works with any properly constructed representation of any of the continuous points groups, is based upon the cosine form of the character for the arbitrary rotation operation. (HM)
Structure factor for an icosahedral quasicrystal within a statistical approach.
Strzalka, Radoslaw; Buganski, Ireneusz; Wolny, Janusz
2015-05-01
This paper describes a detailed derivation of a structural model for an icosahedral quasicrystal based on a primitive icosahedral tiling (three-dimensional Penrose tiling) within a statistical approach. The average unit cell concept, where all calculations are performed in three-dimensional physical space, is used as an alternative to higher-dimensional analysis. Comprehensive analytical derivation of the structure factor for a primitive icosahedral lattice with monoatomic decoration (atoms placed in the nodes of the lattice only) presents in detail the idea of the statistical approach to icosahedral quasicrystal structure modelling and confirms its full agreement with the higher-dimensional description. The arbitrary decoration scheme is also discussed. The complete structure-factor formula for arbitrarily decorated icosahedral tiling is derived and its correctness is proved. This paper shows in detail the concept of a statistical approach applied to the problem of icosahedral quasicrystal modelling. PMID:25921496
Quantum transport through single and multilayer icosahedral fullerenes
NASA Astrophysics Data System (ADS)
Lovey, Daniel A.; Romero, Rodolfo H.
2013-10-01
We use a tight-binding Hamiltonian and Green functions methods to calculate the quantum transmission through single-wall fullerenes and bilayered and trilayered onions of icosahedral symmetry attached to metallic leads. The electronic structure of the onion-like fullerenes takes into account the curvature and finite size of the fullerenes layers as well as the strength of the intershell interactions depending on to the number of interacting atom pairs belonging to adjacent shells. Misalignment of the symmetry axes of the concentric iscosahedral shells produces breaking of the level degeneracies of the individual shells, giving rise some narrow quasi-continuum bands instead of the localized discrete peaks of the individual fullerenes. As a result, the transmission function for non symmetrical onions is rapidly varying functions of the Fermi energy. Furthermore, we found that most of the features of the transmission through the onions are due to the electronic structure of the outer shell with additional Fano-like antiresonances arising from coupling with or between the inner shells.
X-ray diffuse scattering from icosahedral Al-Pd-Mn quasicrystals
NASA Astrophysics Data System (ADS)
Capitan, M. J.; Calvayrac, Y.; Quivy, A.; Joulaud, J. L.; Lefebvre, S.; Gratias, D.
1999-09-01
The diffuse scattering of the thermodynamically stable icosahedral phase i-AlPdMn has been studied by means of x-ray-diffraction technique. The overall diffuse intensity shows two main characteristics: (1) the global diffuse scattering intensity map is well taken into account by a Huang effect in the formalism developed by Jari? and Nelson [Phys. Rev. B 37, 4458 (1988)] for icosahedral symmetry which reproduces at once both the ``background'' diffuse intensity and the profile shape around the Bragg peaks; (2) the intensity level of the diffuse scattering is crucially dependent on the chemical composition of the sample; it varies drastically from almost free diffuse scattering samples close to an ``ideal'' composition, up to an overall increase by a factor of 20 of the diffuse scattering for samples with an off-stoichiometry less than 0.5% in manganese and palladium content. The relative shapes of the diffuse scattering contours around the Bragg peaks are qualitatively fairly well reproduced using the sole phason-phason term of hydrodynamical modes in the formalism of Jari? and Nelson [Phys. Rev. B 37, 4458 (1988)], suggesting that phasons in these F-type icosahedral quasicrystals induce minor relaxations in the atomic positions surrounding the flip locations.
Melting and Equilibrium Shape of Icosahedral Gold Nanoparticles
Teitel, Stephen L.
Melting and Equilibrium Shape of Icosahedral Gold Nanoparticles Yanting Wang a , S. Teitel a of gold nanoparticles of different size and morphology is particularly important. While bulk gold has dynamics simulations to study the melting of gold icosahedral clusters of a few thousand atoms. We pay
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.
Quantum hashing with the icosahedral group
Michele Burrello; Haitan Xu; Giuseppe Mussardo; Xin Wan
2010-03-23
We study an efficient algorithm to hash any single qubit gate (or unitary matrix) 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 pseudo-groups. 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(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
Castell, Martin
scales. One example of this is the formation of multiply twinned crystals with five-fold symmetryGrowth of Ag icosahedral nanocrystals on a SrTiO3,,001... support Fabien Silly and Martin R is the creation of nanocrystals with shapes and crystal structures that are not feasible on macroscopic length
Method of making an icosahedral boride structure
Hersee, Stephen D. (3712 Silver Ave. SE., Albuquerque, NM 87108); Wang, Ronghua (939 Buena Vista Dr., SE., Apt. F203, Albuquerque, NM 87106); Zubia, David (4409 Buckingham Dr., El Paso, TX 79902); Aselage, Terrance L. (62 Avenida Del Sol, Cedar Crest, NM 87008); Emin, David (1502 Harvard Ct. NE., Albuquerque, NM 87106)
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.
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
On the symmetry of simple 16-hedra.
Voytekhovsky, Yury L; Stepenshchikov, Dmitry G
2006-05-01
The symmetry point group statistics for all combinatorially non-isomorphic convex simple 16-hedra (17490241 in total) are contributed in the paper for the first time. The most symmetrical polyhedra with 6 to 56 automorphism group orders (165 in total) are drawn in Schlegel diagrams and characterized by facet symbols and symmetry point groups. PMID:16614497
Voytekhovsky, Yury L; Stepenshchikov, Dmitry G
2003-03-01
The symmetry point-group statistics for all combinatorially non-isomorphic 11-hedra (440564 in total) are contributed in the paper for the first time. The most symmetrical shapes with 3 to 36 automorphism group orders (305 in total) are drawn in Schlegel projection and characterized by facet symbols and symmetry point groups. PMID:12604860
Singh, A.; Ranganathan, S. [Indian Institute of Science, Bangalore (India). Centre for Advanced Study] [Indian Institute of Science, Bangalore (India). Centre for Advanced Study
1995-09-01
Twinning of the ordered icosahedral quasicrystals has been studied by transmission electron microscopy in a melt-spun Al{sub 75}Cu{sub 12.5}Fe{sub 12.5} alloy. Dendrites of about 10 {micro}m of the icosahedral phase, formed near the wheel side of the melt spun ribbons, have been observed to twin extensively so that a multiple twinning of the grains is observed. Regions of about 1 {micro}m size are twin related through a common five-fold axis to several neighboring regions. The possibility of different orientations of the twins formed by repeated twinning is infinite. Thus the multiple twinning gives rise to a random symmetry for the whole grain. Depending on the undercooling achieved across the melt-spun ribbons, several related phases like the decagonal quasicrystal and crystalline monoclinic Al{sub 3}Fe phase in ten-fold multiply twinned form were also observed.
Icosahedral Gold Cage Clusters: M@Au??? (M = V, Nb, and Ta)
Zhai, Hua JIN.; Li, Jun; Wang, Lai S.
2004-11-01
We report the observation and characterization of a series of stable bimetallic 18-valence-electron clusters containing a highly symmetric 12-atom icosahedral Au cage with an encapsulated central heteroatom of group VB transition metals, M-Au??? (M = V, Nb, Ta). Electronic and structural properties of these clusters were probed by anion photoelectron spectroscopy and theoretical calculations. Characteristics of the M-Au??? species include their remarkably high binding energies and relatively simple spectral features, which reflect their high symmetry and stability. The adiabatic electronic binding energies of M-Au??? were measured to be 3.70 ? 0.03, 3.77 ? 0.03, and 3.76 ? 0.03 eV for M = V, Nb, and Ta, respectively. Comparison of density functional calculations with experimental data established the highly symmetric icosahedral structures for the 18-electron cluster anions, which may be promising building blocks for cluster-assembled nanomaterials in the form of stoichiometric [M-Au???]X? salts.
F-type icosahedral phase and a related cubic phase in the Al-Rh-Cu system
Li, X.Z. [Univ. of Oslo (Norway); Park, K.T.; Sugiyama, K.; Hiraga, K. [Tohoku Univ., Sendai (Japan). Inst. for Materials Research
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 algebraic theory of quasicrystals with five-fold symmetries
S. Berman; R. V. Moody
1994-01-01
An algebraic binary operation is introduced into quasicrystals admitting five-fold symmetry. In terms of this many quasicrystals displaying full pentagonal or icosahedral symmetry are seen to be finitely generated. Examples are given in dimensions 1, 2, 3 and 4. The operation of left quasicrystal addition is affine-linear. The monoid generated by these operators is discussed and a presentation for it
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.
Ladenstein, R; Meyer, B; Huber, R; Labischinski, H; Bartels, K; Bartunik, H D; Bachmann, L; Ludwig, H C; Bacher, A
1986-01-01
Heavy riboflavin synthase from Bacillus subtilis is an enzyme complex consisting of approximately three alpha-subunits (Mr 23.5 X 10(3)) and 60 beta-subunits (Mr 16 X 10(3)). The enzyme has been crystallized from phosphate buffer in a hexagonal crystal modification that belongs to space group P6(3)22. The asymmetric unit of the crystal cell contains ten beta-subunits. The structure of this unusual 10(6) Mr protein has been studied by small-angle X-ray scattering, electron microscopy of three-dimensional crystals, and crystallographic methods. The scattering curves can be interpreted in terms of a hollow sphere model with a ratio of inner and outer radius of 0.3:1. A diameter of 168 A was estimated from the scattering curves, in close agreement with electron microscopic studies. An aggregate with the stoichiometry beta 60, which was obtained by ligand-driven reaggregation of isolated beta-subunits, showed similar shape and dimensions, but a larger value for the ratio Ri/Ra. Electron micrographs of freeze-etched enzyme crystals showed approximately spherical molecules, which were arranged in hexagonal layers. The lattice constants found from the micrographs are in good agreement with the values derived from X-ray diffraction data. Rotation function calculations in Patterson space showed a set of peaks for 2-fold, 3-fold and 5-fold local rotation axes, accurately consistent with icosahedral symmetry and with the particle orientation A shown in the Appendix. The crystal packing can be described as follows: enzyme particles with icosahedral symmetry (point group 532) are located at points 32 of the hexagonal cell, corresponding to positions (0, 0, 0) and (0, 0, 1/2) on the 6-fold screw axes. From the data reported, it may be concluded that the enzyme structure can be described as an icosahedral capsid of 60 beta-subunits with the triangulation number T = 1. The alpha-subunits are located in the central core space of the capsid, but their spatial orientation is incompletely understood. PMID:3083109
Dynamical x-ray diffraction from an icosahedral quasicrystal
Kycia, S.W.; Goldman, A.I. (Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)); Lograsso, T.A.; Delaney, D.W. (Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)); Black, D. (National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)); Sutton, M.; Dufresne, E.; Bruening, R. (Department of Physics, Centre for the Physics of Materials, McGill University, Montreal, Quebec, H3A 2T8 (Canada)); Rodricks, B. (Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States))
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.
Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles
Shevchenko, Vladimir Ya., E-mail: shevchenko@isc.nw.ru; Madison, Alexey E. [Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, nab. Makarova 2, Saint Petersburg 199034 (Russian Federation); Mackay, Alan L. [School of Crystallography, Birkbeck College, University of London, Malet Street, London WC1E 7HX (United Kingdom); Grebenshchikov Institute of Silicate Chemistry, Russian Academy of Sciences, nab. Makarova 2, Saint Petersburg 199034 (Russian Federation)
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.
Icosahedral phase formation in rapidly quenched aluminum-ruthenium alloys
Anlage, Steven
Icosahedral phase formation in rapidly quenched aluminum- ruthenium alloys Steven M. Anlagea phases as a function of composition. We have chosen the aluminum-ruthenium alloy system because. %. The solidified alloys have been studied by electron microscopy and x-ray diffraction to determine
Melting of icosahedral gold nanoclusters from molecular dynamics simulations
Dellago, Christoph
already shown their promise for a wide range of applications, such as nanolithography,1 catalysts,2 is of great importance. While bulk gold has an fcc crystal structure, the compe- tition between bulk distorted fcc tetrahedra, with four 111 facets each, meeting at the center to form an icosahedral
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.
NASA Astrophysics Data System (ADS)
Chiu, Ying-Nan; Chow Chiu, Lue-Yung
1983-02-01
Electron spin-spin and second-order spin-orbit interaction operators are expanded as products of irreducible representations of symmetry point groups (Oh, Td, D5d, D6d, and C4v). From the transformation of the separated orbit and of the spin part, the selection rules for off-diagonal matrix elements may be deduced by taking direct products of the ``initial'' and ``final'' states. The special ?Ml selection rule for the orbital part of spin-spin interaction after expansion is also discussed. Emphasis is given to the ?S=2 change connected by these operators. Possible examples of ?S=2 change in d4, d5, and d6 configurations under the above mentioned point groups are given. As illustrations of the selection rules, the matrix elements for ?S=2 and ?Ms=2 for these configurations are evaluated in the decoupled representation and given in terms of common parameters. The relevance of these multiplicity change to catalysis and reaction of organo-transition metal complexes is briefly alluded to.
Hu, Wen [Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan (China); State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, CAS, Changchun 130022, Jilin (China); Yi, Jianhong; Zheng, Biju [Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan (China); Wang, Limin, E-mail: lmwang@ciac.jl.cn [State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, CAS, Changchun 130022, Jilin (China)
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.
On the symmetry of simple 12- and 13-hedra.
Voytekhovsky, Yury L; Stepenshchikov, Dmitry G
2002-09-01
The symmetry point groups for all combinatorially non-isomorphic simple 12- and 13-hedra (7595 and 49566, respectively) are contributed in the paper for the first time. The most symmetrical polyhedra with automorphism group orders not less than 3 are drawn as Schlegel diagrams and characterized by the facet symbols and symmetry point groups. PMID:12192124
On the symmetry of 9- and 10-hedra.
Voytekhovsky, Yury L; Stepenshchikov, Dmitry G
2002-07-01
The symmetry point groups for all combinatorially non-isomorphic 9- and 10-hedra (2606 and 32300, respectively) are contributed in the paper for the first time. The most symmetrical polyhedra of 3 to 32 automorphism group orders (50 and 187, respectively) are drawn in the Schlegel projections and characterized by the facet symbols and symmetry point groups. PMID:12089463
Energy-Momentum Stability of Icosahedral Configurations of Point Vortices on a Sphere
NASA Astrophysics Data System (ADS)
Newton, Paul K.; Ostrovskyi, Vitalii
2012-08-01
We investigate the nonlinear stability of the icosahedral relative equilibrium configuration of point vortices on a sphere. The relative equilibrium problem is formulated as a problem of finding the nullspace of the configuration matrix that encodes the geometry of the icosahedron, as in Jamaloodeen and Newton (Proc. Royal Soc. A, Math. Phys. Eng. Sci. 462(2075):3277, 2006). The seven-dimensional nullspace of the configuration matrix, A, associated with the icosahedral geometry gives rise to a basis set of vortex strengths for which the icosahedron stays in relative formation, and we use these values to form the augmented Hamiltonian governing the stability. We choose the basis set made up of (i) one element with equal strength vortices on every vertex of the icosahedron (the uniform icosahedron); (ii) six elements made up of equal and opposite antipodal pairs. We start by proving nonlinear stability of the antipodal vortex pair (by direct methods). Following the methods laid out in Simo et al. (Arch. Ration. Mech. Anal. 115(1):15-59, 1991) and Pekarsky and Marsden (J. Math. Phys. 39(11):5894-5907, 1998) and more generally in Marsden and Ratiu (Introduction to Mechanics and Symmetry, 1999), we then combine our knowledge of the nullspace structure of A with the structure of the underlying Hamiltonian, and analyze the stability of the icosahedron using the energy-momentum method. Because the parameter space is large, we focus on the physically motivated and important case obtained by combining the basis elements into (i) the uniform icosahedron; (ii) a von Kármán vortex street configuration of equal and opposite staggered, evenly spaced latitudinal rows equidistant from the equator (Chamoun et al. in Phys. Fluids 21:116603, 2009), and (iii) the North Pole-South Pole equal and opposite vortex pair. Stability boundaries in a three-parameter space are calculated for linear combinations of these grouped basis configurations.
Encapsulation of a polymer by an icosahedral virus
NASA Astrophysics Data System (ADS)
Elrad, Oren M.; Hagan, Michael F.
2010-12-01
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated with encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.
Reconstructing an icosahedral virus from single-particle diffraction experiments
NASA Astrophysics Data System (ADS)
Saldin, D. K.; Poon, H.-C.; Schwander, P.; Uddin, M.; Schmidt, M.
2011-08-01
The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce relatively low-resolution, low-noise diffraction patterns in so-called ``diffract-and-destroy'' experiments. We describe a very simple test on the angular correlations of measured diffraction data to determine if the scattering is from an icosahedral particle. If this is confirmed, the efficient algorithm proposed can then combine diffraction data from multiple shots of particles in random unknown orientations to generate a full 3D image of the icosahedral particle. We demonstrate this with a simulation for the satellite tobacco necrosis virus (STNV), the atomic coordinates of whose asymmetric unit is given in Protein Data Bank entry 2BUK.
Encapsulation of a polymer by an icosahedral virus
Elrad, Oren M.; Hagan, Michael F.
2011-01-01
The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration, and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated to encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids. PMID:21149971
Density functional theory for the stability of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Haymet, A. D. J.
1985-12-01
We present a density functional theory for icosahedral "quasicrystals", a structure postulated as that of the orientationally ordered Mn-Al alloy observed by Shechtman, Blech, Gratias and Cahn. The present theory has no adjustable or unknown parameters. Explicit formulae are presented for the stability of the ordered phase, its density, and the entropy change on formation. All these quantities are shown to be determined, to first order, by the structure factor of the corresponding liquid phase.
Transmission electron microscopy and the molecular structure of icosahedral viruses.
San Martín, Carmen
2015-09-01
The field of structural virology developed in parallel with methodological advances in X-ray crystallography and cryo-electron microscopy. At the end of the 1970s, crystallography yielded the first high resolution structure of an icosahedral virus, the T=3 tomato bushy stunt virus at 2.9Å. It took longer to reach near-atomic resolution in three-dimensional virus maps derived from electron microscopy data, but this was finally achieved, with the solution of complex icosahedral capsids such as the T=25 human adenovirus at ?3.5Å. Both techniques now work hand-in-hand to determine those aspects of virus assembly and biology that remain unclear. This review examines the trajectory followed by EM imaging techniques in showing the molecular structure of icosahedral viruses, from the first two-dimensional negative staining images of capsids to the latest sophisticated techniques that provide high resolution three-dimensional data, or snapshots of the conformational changes necessary to complete the infectious cycle. PMID:26072114
MATCHING OF INTEREST POINT GROUPS WITH PAIRWISE SPATIAL CONSTRAINTS E. S. Ng, N. G. Kingsbury
Kingsbury, Nick
MATCHING OF INTEREST POINT GROUPS WITH PAIRWISE SPATIAL CONSTRAINTS E. S. Ng, N. G. Kingsbury.K. {esn21,ngk10}@cam.ac.uk ABSTRACT We present an algorithm for finding robust matches be- tween images account for the layout and structure of features during matching, which produces more robust matches
On the definition of nonrigid motions of a molecule by improper elements of its point group
NASA Astrophysics Data System (ADS)
Burenin, A. V.
2015-05-01
The possibility of defining the nonrigid motions of a molecule by improper elements of its point group is considered. The proposed method is presented for the example of the inversional motion of the methane molecule CH4 in its ground electronic state.
Structure of the icosahedral Ti-Zr-Ni quasicrystal R. G. Hennig*
Henley, Christopher L.
Structure of the icosahedral Ti-Zr-Ni quasicrystal R. G. Hennig* Department of Physics, Ohio State; published 7 April 2003 The atomic structure of the icosahedral Ti-Zr-Ni quasicrystal is determined of the quasicrystal. The decoration model is optimized using a method of structural analysis combining a least
Soft materials design via self assembly of functionalized icosahedral particles
NASA Astrophysics Data System (ADS)
Muthukumar, Vidyalakshmi Chockalingam
In this work we simulate self assembly of icosahedral building blocks using a coarse grained model of the icosahedral capsid of virus 1m1c. With significant advancements in site-directed functionalization of these macromolecules [1], we propose possible application of such self-assembled materials for drug delivery. While there have been some reports on organization of viral particles in solution through functionalization, exploiting this behaviour for obtaining well-ordered stoichiometric structures has not yet been explored. Our work is in well agreement with the earlier simulation studies of icosahedral gold nanocrystals, giving chain like patterns [5] and also broadly in agreement with the wet lab works of Finn, M.G. et al., who have shown small predominantly chain-like aggregates with mannose-decorated Cowpea Mosaic Virus (CPMV) [22] and small two dimensional aggregates with oligonucleotide functionalization on the CPMV capsid [1]. To quantify the results of our Coarse Grained Molecular Dynamics Simulations I developed analysis routines in MATLAB using which we found the most preferable nearest neighbour distances (from the radial distribution function (RDF) calculations) for different lengths of the functional groups and under different implicit solvent conditions, and the most frequent coordination number for a virus particle (histogram plots further using the information from RDF). Visual inspection suggests that our results most likely span the low temperature limits explored in the works of Finn, M.G. et al., and show a good degree of agreement with the experimental results in [1] at an annealing temperature of 4°C. Our work also reveals the possibility of novel stoichiometric N-mer type aggregates which could be synthesized using these capsids with appropriate functionalization and solvent conditions.
Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals R. G. Hennig
Henley, Christopher L.
Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals R. G of the icosahedral TiZrNi quasicrystal. The complete ab initio zero-temperature ternary phase diagram is constructed, the icosahedral i-TiZrNi quasicrystal is approximated by periodic structures of up to 123 atoms/unit cell, based
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.
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
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.
Xiong, Dongxia; Lu, Lu; Wang, Jianbo; Zhao, Dongshan; Sun, Yufeng
2013-01-01
Non-centro-symmetric characteristics are observed in the experimental electron diffraction patterns (EDPs) from the icosahedral quasicrystalline precipitates in ZrAlNiCuNb alloys. Different from the well-known breaking of the Friedel's law, where a strong dynamical effect will reveal in EDPs the concealed non-centro-symmetry originated from the crystal structures themselves, the current results can be interpreted in terms of changes in deviation parameters due to a delicate combination of the linear phason strain characteristic of quasicrystals and the curvature of Ewald sphere. After taking this effect into consideration, the corresponding simulated EDPs fit quite well to the experimental data. PMID:24041584
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.
The atomic structure of the threefold 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
2012-11-01
We report a study of the atomic structure of the threefold icosahedral (i-)Ag-In-Yb quasicrystal surface using scanning tunneling microscopy (STM) and low energy electron diffraction (LEED). The LEED confirms that the surface exhibits quasicrystalline long-range order with the threefold symmetry expected from the bulk. The STM reveals large atomically flat terraces separated by steps of different heights. A comparison of atomically resolved STM images for the terraces and the step-height distribution with the bulk structure of isostructural i-Cd-Yb shows that the terraces are formed at bulk planes intersecting the centers of the rhombic triacontahedral clusters that make up the bulk structure of the system. However, the stability of particular terraces may be influenced by the density of atoms in the interstices (glue atoms that bind the clusters) in the terraces and also by the chemical environment in the underlying atomic plane. The surface exhibits screw dislocations, which is explained in terms of a continuous atomic density along the threefold axis. PMID:23044476
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
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.
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
Melting of icosahedral nickel clusters under hydrostatic pressure.
Fu, Bing; Chen, Li; Wang, Feifei; Xie, Yiqun; Ye, Xiang
2014-12-01
The thermal stabilities and melting behavior of icosahedral nickel clusters under hydrostatic pressure have been studied by constant-pressure molecular dynamics simulation. The potential energy and Lindemann index are calculated. The overall melting temperature exhibits a strong dependence on pressure. The Lindemann index of solid structure before melting varies slowly and is almost independent of pressure. However, after the clusters melt completely, the Lindemann index at the overall melting point strongly depends on pressure. The overall melting temperature is found to be increasing nonlinearly with increasing pressure, while the volume change during melting decreases linearly with increasing pressure. Under a high pressure and temperature environment, similar angular distributions were found between liquid and solid structures, indicating the existence of a converging local structure. PMID:25241855
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.
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.
On the symmetry of simple 14- and 15-hedra.
Voytekhovsky, Yury L; Stepenshchikov, Dmitry G
2003-07-01
The symmetry point-group statistics for all combinatorially non-isomorphic simple 14- (339722) and 15-hedra (2406841 in total) are contributed in the paper for the first time. The most symmetrical shapes with 6 to 48 and 6 to 52 automorphism group orders (61 and 36, respectively) are drawn in Schlegel projections and characterized by facet symbols and symmetry point groups. PMID:12832816
Design and manufacture of an icosahedral virus model for educational use
Stach, Laurie A. (Laurie Anna)
2005-01-01
A model of an icosahedral virus was designed and manufactured. Much consideration was given to the design of different aspects of the part. though there were many uncertainties about some parameters that disallowed precise ...
Metal-organic framework materials based on icosahedral boranes and carboranes
Mirkin, Chad A.; Hupp, Joseph T.; Farha, Omar K.; Spokoyny, Alexander M.; Mulfort, Karen L.
2010-11-02
Disclosed herein are metal-organic frameworks of metals and boron rich ligands, such as carboranes and icosahedral boranes. Methods of synthesizing and using these materials in gas uptake are disclosed.
Van Hove singularities of some icosahedral boron-rich solids by differential reflectivity spectra
NASA Astrophysics Data System (ADS)
Werheit, Helmut
2015-09-01
Differential reflectivity spectra of some icosahedral boron rich solids, ?-rhombohedral boron, boron carbide and YB66-type crystals, were measured. The derivatives yield the van Hove singularities, which are compared with results obtained by other experimental methods.
Highly ordered structure of icosahedral quasicrystals in Zn-Mg-RE (RE ? rare earth metals) systems
A. P. Tsai; A. Niikura; A. Inoue; T. Masumoto; Y. Nishida; K. Tsuda; M. Tanaka
1994-01-01
A new group of stable icosahedral phases (i-phases) in the Zn-Mg-RE system were found to have an ideal composition close to Zn50 Mg42RE8 (RE ? Y, Gd, Tb, Dy, Ho or Er). The new i-phases exhibit a highly ordered and nearly perfect face-centred icosahedral lattice as revealed by electron and X-ray diffraction and high-resolution electron microscopy. Powder X-ray diffraction indicates
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.
Generation of molecular symmetry orbitals for the point and double groups
NASA Astrophysics Data System (ADS)
Rykhlinskaya, K.; Fritzsche, S.
2005-09-01
Symmetry-adapted molecular basis functions are widely applied for the electronic structure computations of molecules and clusters. These functions are obtained by exploiting the symmetry of the system and often help to simplify the computations considerably. In order to facilitate their use in algebraic and numerical computations, here we provide a set of MAPLE procedures which generates these functions by means of projection operators, both within the nonrelativistic and relativistic theory. All commonly applied point and double groups are supported by the program including, in addition, the access to their group-theoretical data such as the symmetry operators, characters, or irreducible representations. Program summaryTitle of program:BETHE Catalogue identifier:ADVU Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVU Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed: All computers with a license of the computer algebra package MAPLE (Maple is a registered trademark of Waterloo Maple Inc.) Installations:University of Kassel (Germany) Operating systems or monitors under which the program has been tested:Linux 8.1+ and Windows2000 Programming language used:MAPLE 7 and 8 Memory required to execute with typical data:10-30 MB No. of lines in distributed program, including test data, etc.:14 190 No. of bytes in distributed program, including test data, etc.:370 795 Distribution format:tar.gz Nature of the physical problem:Molecular and solid-state quantum computations can be simplified considerably if the symmetry of the systems with respect to the rotation and inversion of the coordinates is taken into account. To exploit such symmetries, however, symmetry-adapted basis functions need to be constructed instead of using—as usual—the atomic orbitals as the (one-particle) basis. These so-called symmetry orbitals are invariant with respect to the symmetry operations of the group and are different for the point and double groups, i.e. for nonrelativistic and relativistic computations. Method of solution:Projection operator techniques are applied to generate the symmetry-adapted orbital functions as a linear combinations of atomic orbitals. Restrictions onto the complexity of the problem:The generation of the symmetry orbitals is supported for the cyclic and related groups C, C, C, C, C, the dihedral groups D, D, D, the improper cyclic groups S2n(n?10), the cubic groups O, T, O, T, T as well as the icosahedral groups I and I. In all these cases, the symmetry orbitals can be obtained for either the point or double groups by using a nonrelativistic or, respectively, relativistic framework for the computations. Unusual features of the program:All commands of the BETHE program are available for interactive work. Apart from the symmetry orbitals generation, the program also provides a simple access to the group theoretical data for the presently implemented groups from above. The notation of the symmetry operations and the irreducible representations follows the compilation by Altmann and Herzig [Point-Group Theory Tables, Clarendon Press, Oxford, 1994]. For a quick reference to the program, a description of all user-relevant commands is given in the (user) manual Bethe-commands.ps and is distributed together with the code. Typical running time:Although the program replies 'promptly' on most requests, the running time depends strongly on the particular task.
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.
Symmetries, Symmetry Breaking, Gauge Symmetries
Franco Strocchi
2015-07-02
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which account for the $\\theta$ vacua.
NASA Astrophysics Data System (ADS)
Abou-Ghantous, Michel; Polinger, Victor Z.; Dunn, Janette L.; Bates, Colin A.
2002-04-01
The Franck-Condon (FC) approximation is used to obtain analytical values for the second-order factors describing vibronic reduction for the case of the strongly coupled icosahedral T1u?hg Jahn-Teller (JT) system in which an electronic triplet ground state is coupled to vibrations of fivefold degeneracy. This is believed to be applicable to the ground state of the C60- ion and so the calculations should help in providing valuable physical information on this fullerene ion. The procedures for determining vibronic reduction effects depend critically on the particular JT system and upon the vibronic coupling strength. In the FC approximation, the major contributions to these reduction factors originate from virtual vertical transitions between the ground electronic adiabatic state and excited vibronic states associated with upper sheets in the adiabatic potential energy surface. At strong coupling, other transitions may be neglected. The FC results are compared with those obtained from an alternative approach involving a shift transformation. Details are given for perturbations containing orbital operators of threefold (T1) and fivefold (H) symmetry. The discussion emphasizes the inherent high symmetry of the system.
NASA Astrophysics Data System (ADS)
Rappaz, Michel; Kurtuldu, Güven
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.
Viruses and Fullerenes - Symmetry as a Common Thread?
Pierre-Philippe Dechant; Jess Wardman; Tom Keef; Reidun Twarock
2014-02-18
We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational principle in virus structure and assembly. We adapt this group theoretic framework here to the physical requirements dictated by carbon chemistry, and show that we can derive mathematical models for carbon onions within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in Nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.
Viruses and Fullerenes - Symmetry as a Common Thread?
Dechant, Pierre-Philippe; Keef, Tom; Twarock, Reidun
2014-01-01
We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational principle in virus structure and assembly. We adapt this group theoretic framework here to the physical requirements dictated by carbon chemistry, and show that we can derive mathematical models for carbon onions within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in Nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.
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.
Formation of F- and P-Type Icosahedral Quasicrystals in the Zn Mg Ho Alloy System*
NASA Astrophysics Data System (ADS)
Shimizu, Takayuki; Ishimasa, Tsutomu
1998-10-01
Two types of icosahedral quasicrystals, F- and P-types, formed at 563°C in the Zn60Mg40-xHox alloy depending on Ho content. In the composition range of 6?x?10, F-type icosahedral quasicrystal formed as a major phase in these alloys. The intensity of superlattice reflections which occurred due to F-type ordering became weaker in the alloys with lower Ho content. At x=5, P-type icosahedral quasicrystal formed, coexisting with MgZn2-type Laves phase at 563°C and 503°C. Some electron diffraction patterns of the P-type icosahedral quasicrystal exhibited diffuse scattering intensity at positions corresponding to F-type superlattice reflections. By annealing at 403°C, a mixture of the P-type icosahedral quasicrystal and the MgZn2-type phase changed to a mixture of the F-type quasicrystal and a decagonal quasicrystal. The former state was reversibly obtained by additional annealing at 503°C. These experimental results support the interpretation that the three types of quasicrystals form as a thermodynamically stable state in the Zn Mg Ho alloy system.
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
Design of Three-shell Icosahedral Matryoshka Clusters A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd, Mn)
Huang, Xiaoming; Zhao, Jijun; Su, Yan; Chen, Zhongfang; King, R. Bruce
2014-01-01
We propose a series of icosahedral matryoshka clusters of A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd), which possess large HOMO-LUMO gaps (1.29 to 1.54?eV) and low formation energies (0.06 to 0.21?eV/atom). A global minimum search using a genetic algorithm and density functional theory calculations confirms that such onion-like three-shell structures are the ground states for these A21B12 binary clusters. All of these icosahedral matryoshka clusters, including two previously found ones, i.e., [As@Ni12@As20]3? and [Sn@Cu12@Sn20]12?, follow the 108-electron rule, which originates from the high Ih symmetry and consequently the splitting of superatom orbitals of high angular momentum. More interestingly, two magnetic matryoshka clusters, i.e., Sn@Mn12@Sn20 and Pb@Mn12@Pb20, are designed, which combine a large magnetic moment of 28 µB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices. PMID:25376938
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 µB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices.
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...
Magnetic properties of icosahedral Al-Cr-Mn-Ge alloys
McHenry, M.E. (Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (USA) Department of Metallurgical Engineering Materials Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (USA)); Dunlap, R.A.; Srinivas, V. (Department of Physics, Dalhousie University, Halifax, Nova Scotia, Canada B3H3J5 (CA)); Bahadur, D. (Advanced Centre for Materials Science, Indian Institute of Technology, Kanpur, India 208016 (IN)); O'Handley, R.C. (Department of Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA) Department of Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA))
1990-04-01
Alloys in the series Al{sub 65}Cr{sub 20{minus}{ital x}}Mn{sub {ital x}}Ge{sub 15} (0{le}{ital x}{le}20) have been produced by melt spinning. These rapidly solidified alloys have been found to be single phase and of the icosahedral structure. Magnetic-susceptibility measurements reveal a moment of 0.45{mu}{sub {ital B}} for Cr in the Al{sub 65}Cr{sub 20}Ge{sub 15} alloy. This is the first observation of a local moment on Cr in a quasicrystal. In the Al{sub 65}Mn{sub 20}Ge{sub 15} alloy a moment of 2.10{mu}{sub {ital B}} for Mn is observed, which is the largest moment observed in Al-Mn-metalloid quasicrystal alloys. The compositional dependence of the magnetic moment is consistent with at least two classes of magnetic sites. Spin-glass behavior is observed below 8 K in the Al{sub 65}Mn{sub 20}Ge{sub 15} alloy. Measurements of the time dependence of the magnetization, in a field of 1 T, and from the zero-field-cooled state have been made for the Al{sub 65}Mn{sub 20}Ge{sub 15} alloy, revealing logarithmic relaxation. Analysis of this data using a first-order rate equation and a distribution of energy barriers reveals an average energy barrier of 6.8 meV.
X-ray diffuse scattering in the icosahedral quasicrystal Al-Pd-Mn S. N. Ehrlich,2
Widom, Michael
X-ray diffuse scattering in the icosahedral quasicrystal Al-Pd-Mn Y. Zhang,1 S. N. Ehrlich,2 R source of diffuse scattering apart from Compton scattering . But in a quasicrystal the situation is quite to concentrate on icosahedral Al-Pd-Mn, be- cause it is a very ``perfect'' quasicrystal, in the sense
Anti-plane problem analysis for icosahedral quasicrystals under shear loadings
NASA Astrophysics Data System (ADS)
Li, Wu; Chai, Yu-Zhen
2014-11-01
The present paper is concerned with the longitudinal shear elasticity of three-dimensional icosahedral quasicrystals. By virtue of the Dugdale hypothesis along with the method of complex potential theory, it involves two defect problems of the icosahedral quasicrystals. The first one is the calculation of stress intensity factors and the size of the cohesive force zone in a half-infinite crack. Meanwhile, the crack tip tearing displacements can be exactly derived. The other is the demonstration of the generalized stress intensity factors induced by a sharp V-notch as an extension of a crack. The generalized E-integral around the notch tip gives the energy release rate when the V-notch degenerates into a crack. Apart from their own usefulness in carrying out some simplified crack analyses, the results obtained in this work can particularly serve as a basis for fracture mechanics of anti-plane defect problems of icosahedral quasicrystals.
Synthesis and characterization of monodispersed icosahedral Au using spherical aberration correction
NASA Astrophysics Data System (ADS)
Velazquez-Salazar, J. Jesus; Esparza, Rodrigo; Yacaman, Miguel Jose
2010-10-01
Monodisperse icosahedral Au nanoparticles were synthesized using one step protocol. The morphology and structural characteristics of the icosahedral Au nanoparticles with uniform size were studied in detail using ultra-high resolution scanning electron microscope (SEM) FEG Hitachi S-5500 (0.4 nm at 30 kV) with BF/DF Duo-STEM detector, high resolution transmission electron microscope (HRTEM) Jeol JEM-2010F with an accelerating voltage of 200 kV (resolution 0.19 nm point-to-point) and a scanning transmission electron microscope Jeol JEM-ARM200F (STEM) attachment with a spherical aberration corrector. The average size of the icosahedral Au nanoparticles was 10 nm. STEM Cs-corrected images showed the atomic structure of the nanoparticles, oriented mainly on the five and two fold exes. The nanoparticles were also characterized using UV/vis absorption spectrum.
Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals
Parshin, P. P.; Zemlyanov, M. G. [Russian Research Centre 'Kurchatov Institute' (Russian Federation)], E-mail: zeml@isssph.kiae.ru; Brand, R. A. [Gerhard-Mercator Universitaet Duisburg (Germany)
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.
An efficient code for calculation of the 6C, 9C and 12C symbols for C3v, T, and O point groups
NASA Astrophysics Data System (ADS)
Nikitin, A. V.
2012-03-01
A new code designed to calculate the 6 C, 9 C, and 12 C symbols for C3v, T, and O point groups is presented. The program is based on an algorithm that uses the symmetry property between pair and impair representations. This algorithm allows one to speed up the C-symbols calculation and increase the efficiency of spectroscopic programs based on the irreducible tensorial formalism. Program summaryProgram title: 6912C Catalogue identifier: AEKZ_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKZ_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 1214 No. of bytes in distributed program, including test data, etc.: 22 097 Distribution format: tar.gz Programming language: C++ Computer: Any computer with C, C++ compiler Operating system: Linux SUSE, Windows XP64 RAM: 400 Kb Classification: 4.2, 16.2, 16.3 Nature of problem: Spectroscopy of symmetric atmospheric molecules. Solution method: The program is based on an algorithm that uses the symmetry property between pair and impair representations. Running time: The test program provided takes a few seconds for C3v, a few minutes for T and a few days for O.
Anisotropic Spin Correlations in the Zn-Mg-Ho Icosahedral Quasicrystal
NASA Astrophysics Data System (ADS)
Sato, Taku J.; Takakura, Hiroyuki; Tsai, An Pang; Shibata, Kaoru
1998-09-01
Neutron scattering experiments have been performed on the Zn-Mg-Ho icosahedral quasicrystal using powder and single-crystalline samples. In contrast to a previous Letter [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)], the magnetic long-range order could not be detected in the icosahedral quasicrystal. It instead exhibits highly anisotropic diffuse scattering, which appears as satellite ridges of intense nuclear Bragg reflections, running parallel to the fivefold axis. The result suggests that quasi-five-dimensional spin correlations develop on a six-dimensional hypercubic lattice.
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.
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…
AUTO3DEM--an automated and high throughput program for image reconstruction of icosahedral particles
Baker, Timothy S.
AUTO3DEM--an automated and high throughput program for image reconstruction of icosahedral 2006 Abstract AUTO3DEM is an automation system designed to accelerate the computationally intensive. With minimal user input and intervention, AUTO3DEM manages the flow of data between the major image
Global ocean simulations by HYCOM on icosahedral and logically rectangular grids
NASA Astrophysics Data System (ADS)
Sun, Shan; Bleck, Rainer
2015-04-01
iHYCOM, short for "icosahedral HYbrid Coordinate Ocean Model", is being developed at the NOAA Earth System Research Laboratory. The purpose of formulating HYCOM on an icosahedral grid is to allow coupling to an existing icosahedral weather prediction model ("FIM", see http://fim.noaa.gov) unencumbered by interpolation problems at the air-sea-ice interface. We have tested the traditional HYCOM, formulated on a Mercator grid augmented by a bipolar pole patch, with iHYCOM for several decades at comparable horizontal mesh sizes in the 0.5-1.0 deg range, employing the same vertical resolution of 26 potential density (sigma_1) layers. These comparison runs were forced by CORE (Common Ocean-Ice Reference Experiment) fields. Several performance measures indicate that formulating HYCOM on an icosahedral mesh is feasible, although a numerically stable barotropic-baroclinic mode splitting scheme is not available yet. We compare the large scale circulations simulated by both model versions and investigate the model sensitivity to different horizontal grids.
Competition between face-centered cubic and icosahedral cluster structures R. S. Berry
Berry, R. Stephen
Competition between face-centered cubic and icosahedral cluster structures R. S. Berry University analysis of the competition between these structures. In this paper we carry out this analysis using the competition between structures by us- ing a ``phase diagram'' see Ref. 13 on which we plot the Morse
Synonymous Mutations Reduce Genome Compactness in Icosahedral ssRNA Viruses
Podgornik, Rudolf
Article Synonymous Mutations Reduce Genome Compactness in Icosahedral ssRNA Viruses Luca Tubiana,1 and subject to a number of known evolutionary constraints. In particular, we enforce mutation synonynimity of these restricted mutations still suffices to completely erase the characteristic compact- ness imprint of the viral
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., E-mail: ran@infoteck.ru; Mazurenko, V. G. [Ural State University (Russian Federation)
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.
Henley, Christopher L.
Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials M for the quasicrystal i-AlMn based on decorations of the ``canonical-cell tiling.'' We adopted ab initio-based pair zero-order description of the system. I. INTRODUCTION Quasicrystals raise at least two interesting
NASA Astrophysics Data System (ADS)
Arribas, Victor; Casas, Lluís; Estop, Eugènia; Labrador, Manuel
2014-01-01
Crystallography and X-ray diffraction techniques are essential topics in geosciences and other solid-state sciences. Their fundamentals, which include point symmetry groups, are taught in the corresponding university courses. In-depth meaningful learning of symmetry concepts is difficult and requires capacity for abstraction and spatial vision. Traditionally, wooden crystallographic models are used as support material. In this paper, we describe a new interactive tool, freely available, inspired in such models. Thirty-two PDF files containing embedded 3D models have been created. Each file illustrates a point symmetry group and can be used to teach/learn essential symmetry concepts and the International Hermann-Mauguin notation of point symmetry groups. Most interactive computer-aided tools devoted to symmetry deal with molecular symmetry and disregard crystal symmetry so we have developed a tool that fills the existing gap.
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.
J. B. ParisA; A. Vencovská
2011-01-01
We examine the idea that similar problems should have similar solutions (to paraphrase van Fraassen’s slogan ‘Problems which\\u000a are essentially the same must receive essentially the same solution’, see van Fraassen in Laws and symmetry, Oxford Univesity\\u000a Press, Oxford, 1989, p. 236) in the context of symmetries of sentence algebras within Inductive Logic and conclude that by itself this is
Analytical models of icosahedral shells for 3D optical imaging of viruses
Jafarpour, Aliakbar
2014-01-01
A modulated icosahedral shell with an inclusion is a concise description of many viruses, including recently-discovered large double-stranded DNA ones. Many X-ray scattering patterns of such viruses show major polygonal fringes, which can be reproduced in image reconstruction with a homogeneous icosahedral shell. A key question regarding a low-resolution reconstruction is how to introduce further changes to the 3D profile in an efficient way with only a few parameters. Here, we derive and compile different analytical models of such an object with consideration of practical optical setups and typical structures of such viruses. The benefits of such models include 1) inherent filtering and suppressing different numerical errors of a discrete grid, 2) providing a concise and meaningful set of descriptors for feature extraction in high-throughput classification/sorting and higher-resolution cumulative reconstructions, 3) disentangling (physical) resolution from (numerical) discretization step and having a vector ...
Ion beam induced destabilization of icosahedral structures in gas phase prepared FePt nanoparticles
NASA Astrophysics Data System (ADS)
Dmitrieva, Olga; Rellinghaus, Bernd; Kästner, Jochen; Liedke, Maciej Oskar; Fassbender, Jürgen
2005-05-01
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 L10 phase upon in-flight or post-deposition thermal annealing. Irradiation of these multiply twinned FePt particles with 5keV He ions, however, resulted in a transformation into predominantly single crystalline fcc particles at high ion fluences of f >1017ions/cm2. 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 L10 ordered FePt nanoparticles upon ion irradiation in these samples.
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.
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.
Formation of a well ordered ultrathin aluminum oxide film on icosahedral AlPdMn quasicrystal
Longchamp, J.-N.; Burkardt, S.; Weisskopf, Y. [Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich (Switzerland); Erbudak, M. [Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich (Switzerland); Department of Physics, Faculty of Arts and Sciences, Bogazici University, 34342 Bebek, Istanbul (Turkey)
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.
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.
Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy
Grigorieff, Nikolaus; Harrison, Stephen C.
2011-01-01
Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfill predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3 – 4 Å resolution. This review summarizes technical developments, both in instrumentation and in computation, that have led to the new structures, which advance our understanding of virus assembly and cell entry. PMID:21333526
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
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.
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
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.
Baker, Timothy S.
capsids and the phage decoration (Dec) protein. Three-dimensional image reconstructions of frozen symmetric capsids of icosahedral viruses make them attractive candidates for molecular display and hence
Translational symmetry Rotational symmetry
Lee, Carl
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Web-Supported Chemistry Education: Design of an Online Tutorial for Learning Molecular Symmetry
ERIC Educational Resources Information Center
Korkmaz, Ali; Harwood, William S.
2004-01-01
This paper describes our use of the ADDIE protocol to design and develop an interactive tutorial for students learning molecular symmetry operations and point groups. The tutorial provides a 3-D environment where students can examine molecules, structures, and symmetry elements. Most such tutorials are connected to courses or instructors in…
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…
On the symmetry of 4- to 11-hedra.
Voytekhovsky, Y L
2001-01-01
A table giving the statistics of the visible symmetry point groups for all non-isomorphic 4- to 8-hedra and simple 9- to 11-hedra is presented. Some disagreements between the previous data are eliminated. The main tendency for n-hedra to be asymmetric with increasing n is briefly discussed. PMID:11124510
C72 to C100 fullerenes: combinatorial types and symmetries.
Voytekhovsky, Yury L; Stepenshchikov, Dmitry G
2003-05-01
The symmetry point-group statistics for all combinatorially different C(72) to C(100) fullerenes with free 5-gonal facets only are suggested in the paper for the first time. The shapes with automorphism group orders not less than 3 are drawn in Schlegel diagrams. PMID:12714782
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.
Bodner, George M.
Icosahedral Carborane Derivatives Inorganic Chemistry, Vol. 13,No. IO,I 9 74 2321 Table 11 benzenesulfonate, 10531-13-2;malononitrile, 109-77-3. ' Contribution No. 2504 from the Department of Chemistry Phosphorus-31 Nuclear MagneticResonance Spectra of IcosahedralCarboraneDerivatives A. R. SIEDLE,Ia G. M
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.
Calculation of binary and ternary metallic immiscible clusters with icosahedral structures
NASA Astrophysics Data System (ADS)
Dzhurakhalov, Abdiravuf A.; Atanasov, Ivailo; Hou, Marc
2008-03-01
Recently, core-shell Ag-Co, Ag-Cu, and “onionlike” Cu-Co equilibrium configurations were predicted in the case of isolated face centered cubic (fcc) bimetallic clusters, and three shell onionlike configurations were predicted in the case of ternary metallic clusters with spherical and truncated octahedral morphologies. In the present paper, immiscible binary CuCo and ternary AgCuCo clusters with icosahedral structures are studied as functions of their size and composition. Clusters studied are formed by 13, 55, 147, 309, and 561 atoms corresponding to the five smallest possible closed shell icosahedral structures. An embedded atom model potential is used to describe their cohesion. Equilibrium configurations are investigated by means of Metropolis Monte Carlo free energy minimization in the (NPT) canonical ensemble. Most simulations are achieved at 10 and 300K . The effect of temperature on segregation ordering is systematically investigated. Selected cases are used to identify the effect of size and composition on melting. In contrast with fcc clusters, homogeneous onionlike configurations of binary clusters are not predicted. When it is allowed by the composition, a complete outer shell is formed by Cu in binary Cu-Co clusters and by Ag in ternary Ag-Cu-Co clusters. Depending on temperature, Co may precipitate into decahedral groups under the Cu vertices of the icosahedra in binary clusters, while the Co-Cu configuration in ternary clusters drastically depends on the Ag coating. Despite the multicomponent character of the clusters and the immiscibility of the species forming them, for most compositions and sizes, equilibrium structures remain close to perfectly icosahedral at 10K as well as at 300K .
NASA Astrophysics Data System (ADS)
Li, Wu; Fan, Tian You
By introducing a stress potential function, we transform the plane elasticity equations of two-dimensional quasicrystals of point group 10, /line {10} to a partial differential equation. And then we use the complex variable function method for classical elasticity theory to that of the quasicrystals. As an example, a decagonal quasicrystal in which there is an arc is subjected to a uniform pressure p in the elliptic notch of the decagonal quasicrystal is considered. With the help of conformal mapping, we obtain the exact solution for the elliptic notch problem of quasicrystals. The work indicates that the stress potential and complex variable function methods are very useful for solving the complicated boundary value problems of higher order partial differential equations which originate from quasicrystal elasticity.
Complex variable method for plane elasticity of icosahedral quasicrystals and elliptic notch problem
NASA Astrophysics Data System (ADS)
Li, Lianhe; Fan, Tianyou
2008-07-01
The complex variable method for the plane elasticity theory of icosahedral quasi-crystals is developed. Based on the general solution obtained previously, complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an analytic solution for the elliptic notch problem of the material is presented. The solution of the Griffith crack problem can be observed as a special case of the results. The stress intensity factor and energy release rate of the crack are also obtained.
Aquaplanet Tropical Variability in an Icosahedral Model with a Multiscale Modeling Framework
NASA Astrophysics Data System (ADS)
Dazlich, D. A.; Branson, M.; DeMott, C. A.; Heikes, R.; Randall, D. A.
2014-12-01
A multiscale modeling framework (MMF or superparameterization) has been installed in the Unified equations, horizontal Z-grid, Icosahedral Model (SUZI). The System for Atmospheric Modeling (SAM) has been installed as two-dimensional cloud-resolving model at each SUZI grid cell as a substitute for conventional physical parameterization. The tropical variability of SUZI is analyzed for both the height and sigma-pressure vertical coordinate versions for an aquaplanet with zonally uniform solstice sea surface temperature, and will be compared to simulations with Superparameterized CAM.
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.
Icosahedral packing of polymer-tethered nanospheres and stabilization of the Gyroid Phase
NSDL National Science Digital Library
Iacovella, Christopher R.
2006-05-17
We present results of molecular simulations that predict the phases formed by the selfassembly of model nanospheres functionalized with a single polymer “tether”. Microphase separation of the immiscible tethers and nanospheres induces the formation of the double gyroid, perforated lamella and crystalline bilayer phases. Confinement effects promote the formation of icosahedral arrangements of nanoparticles that help to stabilize the gyroid and perforated lamella phases. We also present a new metric for determining the local arrangement of particles in liquid and solid configurations.
Preprint, link to published version can be found below.
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. (Iowa State)
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.
Medium-range icosahedral order in quasicrystal-forming Zr{sub 2}Pd binary metallic glass
Huang Li [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Fang, X. W. [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Department of Physics and Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China); Wang, C. Z.; Ho, K. M. [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Department of Physics, Iowa State University, Ames, Iowa 50011 (United States); Kramer, M. J. [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States); Ding, Z. J. [Department of Physics and Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)
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.
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.
Theory of a reconstructive structural transformation in capsids of icosahedral viruses.
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. PMID:20365004
A mass conservative semi-implicit scheme for the shallow water equations on an icosahedral grid
NASA Astrophysics Data System (ADS)
Bonaventura, L.
2003-04-01
A mass conservative, semi-implicit discretization for the vector invariant formulation of the shallow water equations on the sphere is introduced. These equations are discretized on a quasi-uniform, geodesic, icosahedral Voronoi-Delaunay grid (see e.g. [Heikes and Randall, 1995]) with a C-grid variable arrangement, according to the approach introduced in [Casulli and Walters, 2000]. A finite volume discretization is employed for the continuity equation in conservation law form, using as control volumes either the hexagonal/pentagonal or the dual triangular cells. The momentum equation is discretized with an extension of the approach introduced in [Lin and Rood, 1997] to semi-implicit time discretization on the icosahedral grid. Various possible treatments of the Coriolis force terms will be compared. Results obtained in standard shallow water test cases will be presented, along with an analysis of the discretization properties regarding conservation of energy and potential vorticity. This work is being carried out within the preliminary phase of the ICON research project, which involves, along with Max Planck Institut für Meteorologie Hamburg and the Deutscher Wetterdienst, PIK Potsdam, Freie Universität Berlin, Universität Bonn, Technische Universität München and various other research institutions (see the web page at the project site icon.enes.org). The aim of this project is the development of a unified nonhydrostatic model for global and regional climate simulation and weather forecasting.
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.
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 80°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
Structural features in icosahedral Al sub 63 Cu sub 25 Fe sub 12
Howell, R.H.; Solal, F.; Turchi, P.E.A. (Lawrence Livermore National Lab., CA (United States)); Berger, C. (Centre National de la Recherche Scientifique (CNRS), 38 -Grenoble (France)); Calvayrac, Y. (Centre National de la Recherche Scientifique (CNRS), 94 - Vitry-sur-Seine (France). Centre d'Etudes de Chimie Metallurgique)
1991-08-20
Since the discovery of a quasicrystalline phase in Al-Mn alloys a substantial amount of work has been done to understand the structural and physical properties of this new class of materials. More recently the discovery of a thermodynamically stable icosahedral phase in AlCuFe presents the opportunity to study pure quasicrystalline phases of high structural quality by eliminating known defects, especially phason disorder by conventional heat treatment. In particular it was shown that annealing treatments of as quenched samples resulted in a dramatic reduction in the width of the diffraction peaks associated with the elimination of as quenched defects, present in other quasicrystals. Positron annihilation lifetime measurements have a high sensitivity to intrinsic defects and positron annihilation radiation angular correlation measurements are well suited to measurements of electronic structure in systems where the defect effects do not dominate. We have measured positron annihilation lifetime and angular correlations on quasicrystalline samples of Al{sub 63}Cu{sub 25}Fe{sub 12} in the pure icosahedral phase.
Structural features in icosahedral Al{sub 63}Cu{sub 25}Fe{sub 12}
Howell, R.H.; Solal, F.; Turchi, P.E.A. [Lawrence Livermore National Lab., CA (United States); Berger, C. [Centre National de la Recherche Scientifique (CNRS), 38 -Grenoble (France); Calvayrac, Y. [Centre National de la Recherche Scientifique (CNRS), 94 - Vitry-sur-Seine (France). Centre d`Etudes de Chimie Metallurgique
1991-08-20
Since the discovery of a quasicrystalline phase in Al-Mn alloys a substantial amount of work has been done to understand the structural and physical properties of this new class of materials. More recently the discovery of a thermodynamically stable icosahedral phase in AlCuFe presents the opportunity to study pure quasicrystalline phases of high structural quality by eliminating known defects, especially phason disorder by conventional heat treatment. In particular it was shown that annealing treatments of as quenched samples resulted in a dramatic reduction in the width of the diffraction peaks associated with the elimination of as quenched defects, present in other quasicrystals. Positron annihilation lifetime measurements have a high sensitivity to intrinsic defects and positron annihilation radiation angular correlation measurements are well suited to measurements of electronic structure in systems where the defect effects do not dominate. We have measured positron annihilation lifetime and angular correlations on quasicrystalline samples of Al{sub 63}Cu{sub 25}Fe{sub 12} in the pure icosahedral phase.
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.).
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.
The Jahn-Teller vibronic reduction factors in icosahedral G?(g?h) systems
NASA Astrophysics Data System (ADS)
Abou-Ghantous, M.; Oliete, P. B.; Bates, C. A.; Dunn, J. L.; Polinger, V. Z.; Huang, R.; Rough, S. P.
2002-05-01
Analytical expressions for the vibronic states and energy spectrum of the icosahedral G?(g?h) Jahn-Teller system are derived. From these states, expressions for first- and second-order vibronic reduction factors are determined as a function of the strengths of the coupling of the G orbital to the g and h modes of vibration. The possibility of the vibronic ground state being a singlet A state, rather than the G state that would be expected in the absence of vibronic coupling, is explored. The reduction factors obtained provide a convenient basis for the modelling of spectra involving some of the excited states of the fullerene molecule C60 and related ions.
Magnetic and electrical properties of a stable Zn-Mg-Ho icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Kashimoto, S.; Matsuo, S.; Nakano, H.; Shimizu, T.; Ishimasa, T.
1998-12-01
We investigated the electrical resistivity and the magnetism of heavy-rare-earth-based Zn 60Mg 30Ho 10 F-type icosahedral quasicrystals in the temperature region between 2 K and room temperature below 80 kOe in magnetic field. The maximum value of the electrical resistivity is 159 ?? cm which is comparatively lower than other quasicrystal systems. Below 15 K, the magnetic-field dependence exhibits a magnetoresistance maximum which has not been observed in quasicrystals studied to date, and the temperature dependence shows a resistance minimum. The temperature dependence of the magnetic susceptibility follows, a Curie-Weiss law between 10 K and room temperature corresponding to the effective number of Bohr magneton 10.6 for every Ho atom in the sample. The earlier mentioned anomalies are considered to be related to the dense and large magnetic moments located at the quasiperiodic lattice.
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.
Statistical analysis of the formation of icosahedral metallic nanowires under stretching
NASA Astrophysics Data System (ADS)
Peláez, S.; Serena, P. A.; García-Mochales, P.; Paredes, R.; Guerrero, C.
2009-01-01
Icosahedral or pentagonal nanowires are formed by subsequent staggered parallel pentagonal rings (with a relative rotation of ?/5) connected with single atoms, showing a characteristic -5-1-5-1- ordering. These structures have been found on simulated nanowires of different species [1-3]. However, the statistical study of their formation from stretching of metallic samples has been only addressed for Ni up to date [3,4]. In this work we present an algorithm that allows the automatic identification of pentagonal ring structures. With this methodology we are able to differentiate pentagonal and non-pentagonal regions along the nanowire axis, as well as their lengths. We have obtained for many different nanowires (Al, Ni and Cu, hundreds of ruptures with different crystalline orientations, sizes and temperatures), the distribution of lengths of the pentagonal region Lp as well as the distribution of the number of pentagonal rings np before the nanowire breaks.
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.
Martin R. Zirnbauer
2010-01-05
Physical systems exhibiting stochastic or chaotic behavior are often amenable to treatment by random matrix models. In deciding on a good choice of model, random matrix physics is constrained and guided by symmetry considerations. The notion of 'symmetry class' (not to be confused with 'universality class') expresses the relevance of symmetries as an organizational principle. Dyson, in his 1962 paper referred to as the Threefold Way, gave the prime classification of random matrix ensembles based on a quantum mechanical setting with symmetries. In this article we review Dyson's Threefold Way from a modern perspective. We then describe a minimal extension of Dyson's setting to incorporate the physics of chiral Dirac fermions and disordered superconductors. In this minimally extended setting, where Hilbert space is replaced by Fock space equipped with the anti-unitary operation of particle-hole conjugation, symmetry classes are in one-to-one correspondence with the large families of Riemannian symmetric spaces.
Moubayidin, Laila; Østergaard, Lars
2015-09-01
985 I. 985 II. 986 III. 987 IV. 988 V. 989 989 References 989 SUMMARY: The development of multicellular organisms depends on correct establishment of symmetry both at the whole-body scale and within individual tissues and organs. Setting up planes of symmetry must rely on communication between cells that are located at a distance from each other within the organism, presumably via mobile morphogenic signals. Although symmetry in nature has fascinated scientists for centuries, it is only now that molecular data to unravel mechanisms of symmetry establishment are beginning to emerge. As an example we describe the genetic and hormonal interactions leading to an unusual bilateral-to-radial symmetry transition of an organ in order to promote reproduction. PMID:26086581
Prediction of the behavior for fullerene C20 inside the icosahedral outer shell of C240
NASA Astrophysics Data System (ADS)
Glukhova, O. E.; Kolesnikova, A. S.; Slepchenkov, M. M.; Shunaev, V. V.
2014-05-01
In this work, we study the behavioral regularity of fullerene C20 inside the icosahedral outer shell of fullerene C240. The feature of such two-shell fullerenes is that the internal fullerene will move at low temperatures in a certain way: between the potential wells. The aim of this work is to reveal the regularities for motion of small fullerenes in nanospace of large external icosahedral fullerene, including the identification of the spatial configuration for a multi-well potential of interaction between two objects and prediction of possible movement for the internal object between potential wells. For the fullerene C20 it was found twenty potential wells in the direction of the fifth order axes for icosahedron of fullerene C240 cage, thirty towards in the direction of the middle of the ribs and twenty potential wells towards centers of the faces of the icosahedron. The prediction of possible moving for the internal object between potential wells and the regularities of this movement were made based on the relief analysis of the interaction energy surface of fullerenes. The numerical simulation of C20 motion in the field of C240 was carried out to test the prediction of movement. As results of the experiment, it was found that the fullerene C20 is easy to jump between the potential wells even at low temperatures up to 300K. Molecular dynamics simulations confirmed our conclusions about regularities of C20 movement between potential wells. Thus, one can conclude that the analysis of the topology of the energy surface of van der Waals interaction between the components of nanoparticles gives a true predictive picture of the regularities of the internal molecule behavior. Probably, the phenomenon of fullerene C20 movement in a cell of another fullerene can be used in modern technologies, such as determining a local temperature by increase of jumping velocity.
DYNAMICO, 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.
2015-02-01
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.
Pauling, Linus
1988-01-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, “noise”) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals. PMID:16593948
P. Danielewicz
2006-07-15
Examination of symmetry energy is carried out on the basis of an elementary binding-energy formula. Constraints are obtained on the energy value at the normal nuclear density and on the density dependence of the energy at subnormal densities.
Jaakkola, Salla T.; Penttinen, Reetta K.; Vilén, Silja T.; Jalasvuori, Matti; Rönnholm, Gunilla; Bamford, Jaana K. H.; Bamford, Dennis H.
2012-01-01
Studies on viral capsid architectures and coat protein folds have revealed the evolutionary lineages of viruses branching to all three domains of life. A widespread group of icosahedral tailless viruses, the PRD1-adenovirus lineage, was the first to be established. A double ?-barrel fold for a single major capsid protein is characteristic of these viruses. Similar viruses carrying genes coding for two major capsid proteins with a more complex structure, such as Thermus phage P23-77 and haloarchaeal virus SH1, have been isolated. Here, we studied the host range, life cycle, biochemical composition, and genomic sequence of a new isolate, Haloarcula hispanica icosahedral virus 2 (HHIV-2), which resembles SH1 despite being isolated from a different location. Comparative analysis of these viruses revealed that their overall architectures are very similar except that the genes for the receptor recognition vertex complexes are unrelated even though these viruses infect the same hosts. PMID:22357274
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.
New Icosahedral Grid-Point Discretizations of the Shallow Water Equations on the Sphere
NASA Astrophysics Data System (ADS)
Stuhne, G. R.; Peltier, W. R.
1999-01-01
We describe the implementation of numerical models of shallow water flow on the surface of the sphere, models which include the nondivergent barotropic limit as a special case. All of these models are specified in terms of a new grid-point-based methodology which employs an heirarchy of tesselations derivative of successive dyadic refinements of the spherical icosahedron. Among the potential advantages of such methods is the O( n) complexity in operation count that can be achieved for an ndegree of freedom model if multigrid techniques are employed to solve the associated elliptic problems. Currently prevalent spectral transform models are, in contrast, O( n2) complex due to the Legendre transform that must be performed to transform between spectral and grid-point representations of model fields at each time step. Using the new methodology, we have implemented two different formulations of each of the barotropic and shallow water dynamical systems. In one formulation, the vector velocity field is directly advanced in time; in the other, time integration is carried out entirely in terms of scalar quantities (i.e., absolute vorticity in the barotropic model and, in the more general shallow water model, height and velocity potential). We describe discretizations of the governing equations in which all calculations are performed in Cartesian coordinates in local neighbourhoods of the almost uniform icosahedral grid, a methodology that avoids potential mathematical and numerical problems associated with the poles in spherical coordinates. A number of standard numerical tests are performed with the resulting models and the results employed to compare them with each other and with previously published results obtained using other methodologies. Initial tests are performed for a standard suite that now constitutes the generally accepted benchmark for shallow water models on the sphere. The advantages and the disadvantages of the two shallow water formulations (vector and scalar) are contrasted and employed to demonstrate that the new icosahedral methodology is highly competitive with previously suggested grid-point models. The remaining results which we discuss relate to the process of erosion of a stratospheric polar vortex by a forced stationary Rossby wave disturbance, a physical problem which has previously been analyzed in detail in several well-known spectral transform simulations. It is shown that all of our models properly simulate this intensely nonlinear and computationally challenging physical process.
The icosahedral RNA virus as a grotto: organizing the genome into stalagmites and stalactites.
Harvey, Stephen C; Zeng, Yingying; Heitsch, Christine E
2013-03-01
There are two important problems in the assembly of small, icosahedral RNA viruses. First, how does the capsid protein select the viral RNA for packaging, when there are so many other candidate RNA molecules available? Second, what is the mechanism of assembly? With regard to the first question, there are a number of cases where a particular RNA sequence or structure--often one or more stem-loops--either promotes assembly or is required for assembly, but there are others where specific packaging signals are apparently not required. With regard to the assembly pathway, in those cases where stem-loops are involved, the first step is generally believed to be binding of the capsid proteins to these "fingers" of the RNA secondary structure. In the mature virus, the core of the RNA would then occupy the center of the viral particle, and the stem-loops would reach outward, towards the capsid, like stalagmites reaching up from the floor of a grotto towards the ceiling. Those viruses whose assembly does not depend on protein binding to stem-loops could have a different structure, with the core of the RNA lying just under the capsid, and the fingers reaching down into the interior of the virus, like stalactites. We review the literature on these alternative structures, focusing on RNA selectivity and the assembly mechanism, and we propose experiments aimed at determining, in a given virus, which of the two structures actually occurs. PMID:23860866
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.
Scanning tunneling microscopy of cleaved AlPdMn icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Urban, K.
1997-03-01
Quasicrystal surfaces produced by in-situ cleavage in ultra-high vacuum have been investigated by scanning tunneling microscopy. Twofold and fivefold surfaces of icosahedral AlPdMn single-quasicrystals have been studied. The surfaces were found to be rough. Their structure is determined by cluster aggregates of various sizes formed on the basis of an elementary cluster whose contrast behavior and diameter of about 1 nm point to the Mackay-type cluster [1]. The surface of these elementary clusters exhibits a smooth density of electronic states. These observations agree with the predictions of recent models on the quasicrystal structure and electronic properties in which the Mackay-type clusters play a dominant role [2]. In particular, these clusters are believed to act as deep potential wells leading to electron states primarily bound to these. Crack propagation during cleavage occurs along zones of lower strength between the clusters indicating that these act as rigid entities. This corroborates the assumption made in modern treatments of quasicrystal plasticity that the Mackay-type clusters control the mechanical properties [3,4]. [1] Ph. Ebert, M. Feuerbacher, N. Tamura, M. Wollgarten, and K. Urban, Phys. Rev. Lett. 77, 3827 (1996). [2] C. Janot, Phys. Rev. B 53, 181 (1996). [3] M. Feuerbacher, B. Baufeld, R. Rosenfeld, M. Bartsch, G. Hanke, M. Beyss, M. Wollgarten, and K. Urban, Philos. Mag. Lett. 71, 91 (1995). [4] F. Krul, R. Mikulla, P. Gumbsch, and H.-R. Trebin (to be published).
NASA Astrophysics Data System (ADS)
Dykeman, Eric C.; Sankey, Otto F.
2010-02-01
We describe a technique for calculating the low-frequency mechanical modes and frequencies of a large symmetric biological molecule where the eigenvectors of the Hessian matrix are determined with full atomic detail. The method, which follows order N methods used in electronic structure theory, determines the subset of lowest-frequency modes while using group theory to reduce the complexity of the problem. We apply the method to three icosahedral viruses of various T numbers and sizes; the human viruses polio and hepatitis B, and the cowpea chlorotic mottle virus, a plant virus. From the normal-mode eigenvectors, we use a bond polarizability model to predict a low-frequency Raman scattering profile for the viruses. The full atomic detail in the displacement patterns combined with an empirical potential-energy model allows a comparison of the fully atomic normal modes with elastic network models and normal-mode analysis with only dihedral degrees of freedom. We find that coarse-graining normal-mode analysis (particularly the elastic network model) can predict the displacement patterns for the first few (˜10) low-frequency modes that are global and cooperative.
Valence band structure of the icosahedral Ag-In-Yb quasicrystal
Sharma, H. R.; Simutis, G.; Dhanak, V. R.; Nugent, P. J.; McGrath, R. [Surface Science Research Centre and Department of Physics, University of Liverpool, Liverpool L69 3BX (United Kingdom); Cui, C. [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577 (Japan); Shimoda, M. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Tsai, A. P. [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577 (Japan); National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Ishii, Y. [Department of Physics, Chuo University, Kasuga, Tokyo 112-8551 (Japan)
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.
Finite Symmetry Transformation Groups and Exact Solutions of Konopelchenko-Dubrovsky Equation
NASA Astrophysics Data System (ADS)
Zhang, Huan-Ping; Li, Biao; Chen, Yong
2009-09-01
Based on the general direct method developed by Lou et al. [J. Phys. A: Math. Gen. 38 (2005) L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenko-Dubrovsky (KD) equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.
The origin of order in random matrices with symmetries
Calvin W. Johnson
2012-06-25
From Noether's theorem we know symmetries lead to conservation laws. What is left to nature is the ordering of conserved quantities; for example, the quantum numbers of the ground state. In physical systems the ground state is generally associated with `low' quantum numbers and symmetric, low-dimensional irreps, but there is no \\textit{a priori} reason to expect this. By constructing random matrices with nontrivial point-group symmetries, I find the ground state is always dominated by extremal low-dimensional irreps. Going further, I suggest this explains the dominance of J=0 g.s. even for random two-body interactions.
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…
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
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
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 analysi
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.
Chen, N. [Department of Materials Science, Graduate School, Tohoku University, Sendai 980-8577 (Japan) and Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai 980-8577 (Japan)]. E-mail: asyzxy@imr.edu; Louzguine, D.V. [Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai 980-8577 (Japan); Ranganathan, S. [Department of Metallurgy, Indian Institute of Science, Bangalore 560 012 (India); Inoue, A. [Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai 980-8577 (Japan)
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.
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.
Shackelford, Scott A; Belletire, John L; Boatz, Jerry A; Schneider, Stefan; Wheaton, Amanda K; Wight, Brett A; Ammon, Herman L; Peryshkov, Dmitry V; Strauss, Steven H
2010-06-18
Thirteen bridged triazolium and imidazolium dicationic salts, which uniquely pair closo-icosahedral perfluoroborane [B(12)F(12)](2-), borane [B(12)H(12)](2-), or carborane [CB(11)H(12)](-) anionic species with unsaturated bridged heterocyclium dications, were synthesized using an aqueous benchtop method. This considerably extends the scope of a reported aqueous synthesis of binary [heterocyclium](2)[B(12)H(12)] and [heterocyclium][CB(11)H(12)] salts. Also, the one-step preparation of five new precursor bridged heterocyclium dicationic dihalide salts using conventional procedures and in one case a microwave-assisted method is described. PMID:20499850
Simulation of ion-beam channeling in icosahedral Al[sub 63]Cu[sub 25]Fe[sub 12
du Marchie van Voorthuysen, E.H.; Smulders, P.J.M.; van Smaalen, S. (Materials Science Centre, University of Groningen, Nijenborgh 4, NL 9747 AG Groningen (Netherlands))
1993-10-01
Monte Carlo simulations of channeling on the icosahedral quasicrystal Al[sub 63]Cu[sub 25]Fe[sub 12] were made, using an experimentally determined structure model for this phase. The channeling effect was found to be nearly as good as for a normal, periodic crystal. Dip widths are in agreement with experimental values, but minimum yields are not. The minimum yield is inversely proportional to the beam energy at low energy. Future experiments to be done are proton-induced-x-ray-channeling experiments and Rutherford-backscattering-channeling experiments at low energy.
Lograsso, T.A.; Delaney, D.W. [Metallurgy and Ceramics Program, Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, Iowa 50011 (United States)
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.}
Symmetry detection through local skewed symmetries
Cham, Tat Jen
Symmetry detection through local skewed symmetries Tat-Jen Cham and Roberto Cipolla We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by consider- ing the tangents and curvatures of local
Kelton, K F; Lee, G W; Gangopadhyay, A K; Hyers, R W; Rathz, T J; Rogers, J R; Robinson, M B; Robinson, D S
2003-05-16
To explain the unusual stability of undercooled liquids against crystallization, Frank hypothesized that the local structures of undercooled liquids contain a significant degree of icosahedral short-range order, which is incompatible with long-range periodicity. We present here the first direct experimental demonstration of Frank's complete hypothesis, showing a correlation between the nucleation barrier and a growing icosahedral short-range order with decreasing temperature in a Ti39.5Zr39.5Ni21 liquid. A new experimental facility, BESL (Beamline Electrostatic Levitation), was developed to enable the synchrotron x-ray structural studies on deeply undercooled, reactive liquids. PMID:12785956
O. Babelon; D. Bernard
1991-11-20
We study Lie-Poisson actions on symplectic manifolds. We show that they are generated by non-Abelian Hamiltonians. We apply this result to the group of dressing transformations in soliton theories; we find that the non-Abelian Hamiltonian is just the monodromy matrix. This provides a new proof of their Lie-Poisson property. We show that the dressing transformations are the classical precursors of the non-local and quantum group symmetries of these theories. We treat in detail the examples of the Toda field theories and the Heisenberg model.
A highly symmetric four-dimensional quasicrystal
Veit Elser; N. J. A. Sloane
1987-01-01
A quasiperiodic pattern (or quasicrystal) is constructed in real four-dimensional Euclidean space, having the noncrystallographic reflection group (3,3,5) of order 14400 as its point group. It is obtained as a projection of the eight-dimensional lattice E 8, and has as a cross-section a three-dimensional quasicrystal with icosahedral symmetry.
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-?) 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
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.
NASA Astrophysics Data System (ADS)
Takeuchi, Tsunehiro
2015-03-01
The bulk thermal rectifiers usable at high temperature were developed using the unusual increase of electron thermal conductivity of icosahedral quasicrystals (ICQ's) at high temperature. Our previously performed analyses in terms of linear response theory suggested that the unusual increase of electron thermal conductivity of ICQ was brought about by the synergy effect of quasiperiodicity and narrow pseudogap at the Fermi level. Since the linear response theory suggests that the unusual increase of electron thermal conductivity is coupled with the small magnitude of Seebeck coefficient, the composition of Al-Cu-Fe ICQ, where the thermal conductivity shows the most significant increase with increasing temperature, was determined with a great help of Seebeck coefficient measurements. Consequently obtained Al61.5Cu26.5Fe12.0 ICQ, which was characterized by the small magnitude of Seebeck coefficient, possessed 9 times larger value of thermal conductivity at 1000 K than that observed at 300 K. The increasing tendency of electron thermal conductivity with increasing temperature was further enhanced by means of small amount of Re substitution for Fe. This substitution definitely reduced the lattice thermal conductivity while the electron thermal conductivity was kept unchanged. The lattice thermal conductivity was reduced by 35 % under the presence of 0.5 at.% Re, and the thermal conductivity at 1000 K consequently became about 11 times larger than that at 300 K. The thermal rectifiers were constructed using our newly developed ICQ (Al61.5Cu26.5Fe12.0 or Al61.0Si0.5Cu26.5Fe11.5Re0.5) together with one of the selected materials (Si, Al2O3, CuGeTe2 or Ag2Te) that possess thermal conductivity decreasing with increasing temperature. The heat current flowing in the rectifiers was confirmed to show significant direction dependence. The consequently obtained TRR =|
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.
Buchmuller, Wilfried; Ruehle, Fabian; Schweizer, Julian
2015-01-01
We consider six-dimensional supergravity with gauge group $SO(10)\\times U(1)_A$, compactified on the orbifold $T^2 / \\mathbb{Z}_2$. Three quark-lepton generations arise as zero modes of a bulk $\\bf16$-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 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.
Wei, Lu; Zhou, Zhi-You; Chen, Sheng-Pei; Xu, Chang-Deng; Su, Dangsheng; Schuster, Manfred Erwin; Sun, Shi-Gang
2013-12-11
Pt triambic icosahedral nanocrystals (TIH NCs) enclosed by {771} high-index facets were successfully synthesized electrochemically, for the first time, in ChCl-urea based deep eutectic solvents, and exhibited higher electrocatalytic activity and stability towards ethanol electrooxidation than a commercial Pt black catalyst. PMID:24084858
Andrej Karshikov; Rudolf Ladenstein
1989-01-01
The role of the electrostatic interactions in the stability of the icosahedral pso capsid of heavy riboflavin synthase from Bacillus subtilis has been investigated using an approach based on the theory of Kirkwood and Tanford. The pH dependence of the electro- static subunit interactions agrees well with ex- perimental data. The electrostatic subunit in- teraction energy has a pronounced minimum
NASA Astrophysics Data System (ADS)
Li, Lian He; You Fan, Tian
2006-11-01
The plane elasticity equations of two-dimensional quasicrystals of point group 10 are reduced to a single partial differential equation with eighth order by introducing a stress potential function. Further, we develop the complex variable function method for classical elasticity theory to that of the quasicrystals. The complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is presented. The solution of the Griffith crack problem as a special case of the results is also observed. This work shows that the stress potential and complex variable function methods are powerful for solving the complicated boundary value problems of higher order partial differential equations originating from quasicrystal elasticity.
de Boissieu, M; Francoual, S; Kaneko, Y; Ishimasa, T
2005-09-01
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(2)(per) 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(per) reciprocal space component. PMID:16196940
Sharma, H. R., E-mail: H.R.Sharma@liv.ac.uk; Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R. [Surface Science Research Centre and Department of Physics, The University of Liverpool, Liverpool L69 3BX (United Kingdom)] [Surface Science Research Centre and Department of Physics, The University of Liverpool, Liverpool L69 3BX (United Kingdom); McLeod, I.; Dhanak, V. R. [Department of Physics and the Stephenson Institute for Renewable Energy, The University of Liverpool, Liverpool L69 3BX (United Kingdom)] [Department of Physics and the Stephenson Institute for Renewable Energy, The University of Liverpool, Liverpool L69 3BX (United Kingdom); Shimoda, M. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan)] [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Tsai, A. P. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan) [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577 (Japan)
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.
Boissieu, M. de [Laboratoire de Thermodynamique et de Physico-Chimie Metallurgique, UMR CNRS 5614, ENSEEG-INPG, BP 75, 38402 Saint Martin d'Heres (France); Francoual, S. [Laboratoire de Thermodynamique et de Physico-Chimie Metallurgique, UMR CNRS 5614, ENSEEG-INPG, BP 75, 38402 Saint Martin d'Heres (France); Institut Laue Langevin, BP 156, 38042 Grenoble Cedex 9 (France); Kaneko, Y.; Ishimasa, T. [Research Group of Material Physics, Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo, 060-8628 (Japan)
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.
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
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.
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.
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
Van Isacker, P. [Grand Accelerateur National d'Ions Lourds, CEA/DSM-CNRS/IN2P3 BP 55027, F-14076 Caen Cedex 5 (France)
2011-03-21
The use of dynamical symmetries or spectrum generating algebras for the solution of the nuclear many-body problem is reviewed. General notions of symmetry and dynamical symmetry in quantum mechanics are introduced and illustrated with simple examples such as the SO(4) symmetry of the hydrogen atom and the isospin symmetry in nuclei. Two nuclear models, the shell model and the interacting boson model, are reviewed with particular emphasis on their use of group-theoretical techniques.
Larson, E.T.; Eilers, B.; Menon, S.; Reiter, D.; Ortmann, A.; Young, M.J.; Lawrence, C.M.
2009-06-03
Sulfolobus turreted icosahedral virus (STIV) was the first non-tailed icosahedral virus to be isolated from an archaeal host. Like other archaeal viruses, its 37 open reading frames generally lack sequence similarity to genes with known function. The roles of the gene products in this and other archaeal viruses are thus largely unknown. However, a protein's three-dimensional structure may provide functional and evolutionary insight in cases of minimal sequence similarity. In this vein, the structure of STIV F93 reveals a homodimer with strong similarity to the winged-helix family of DNA-binding proteins. Importantly, an interchain disulfide bond is found at the dimer interface, prompting analysis of the cysteine distribution in the putative intracellular proteins of the viral proteome. The analysis suggests that intracellular disulfide bonds are common in cellular STIV proteins, where they enhance the thermostability of the viral proteome.
Symmetry Breaking NICTA and UNSW
Walsh, Toby
Symmetry Breaking Toby Walsh NICTA and UNSW #12;Outline · What · What is symmetry? · Why · Why is symmetry a problem? · How · How do we deal with symmetry? #12;Apology · Symmetry in constraint programming workshop, Nantes 2006 · 1st International Symmetry Conference, Edinburgh 2007 #12;Symmetry · Within objects
Alavi, Ali
, comprises each element of the group exactly once. 2. Find the equivalence classes of the point group D4h symmetry. [You may find it helpful to note that Oh is the direct product of the groups O and Ci, that the set of h products RS obtained for a fixed element S, when R ranges over the h elements of the group
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.
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
NASA Astrophysics Data System (ADS)
Duguet, T.
2015-02-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.
NSDL National Science Digital Library
Exploratorium
2010-01-01
In this activity, learners use pattern blocks and mirrors to explore symmetry. Learners work in pairs and build mirror images of each other's designs. In doing so, learners will examine principles of symmetry and reflection.
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.
Symmetry-adapted bases for the parametrization of anisotropic properties
van de Walle, Axel; Demers, Steve; Hong, Qijun; Kowalski, Adam; Miljacic, Ljubomir; Pomrehn, Gregory; Tiwary, Pratyush
2013-01-01
We present a simple and general method to generate a set of basis functions suitable for parametrizing the anisotropy of a given physical property in the presence of symmetry constraints. This mathematical tool has direct applications in various fields, for instance, to parametrize the orientation-dependence of interface energies or to represent the so-called constituent strain elastic energy of superlattice structures in the long wavelength limit. The proposed method can be easily implemented using generic linear algebra operations without having consider many different subcases that depend on the point group symmetry considered. The method exploits a direct correspondence between spherical harmonics and polynomial functions of a unit vectors expressed in tensor notation. The method has been implemented in the "gencs" code of the Alloy Theoretic Automated Toolkit (ATAT).
Neutrinos and flavor symmetries
NASA Astrophysics Data System (ADS)
Tanimoto, Morimitsu
2015-07-01
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the ?13 and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing ?13 is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Roelof Bijker
2005-09-02
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and Lie algebras, and Noether's theorem. In the second part, some applications of symmetries in physics are discussed, ranging from isospin and flavor symmetry to more recent developments involving the interacting boson model and its extension to supersymmetries in nuclear physics.
Igoshin, Oleg
Magazine R459 Primer Breaking symmetry in myxobacteria Oleg A. Igoshin1, Dale Kaiser2 and George in the uniform skin ectoderm of vertebrates. This breaking of symmetry within groups of equivalent cells depends on cellcell interactions that stabilize themselves. Common regulatory systems that break symmetry
Symmetry Breaking Toby Walsh #
Walsh, Toby
Symmetry Breaking Toby Walsh # National ICT Australia and School of CSE, University of New South Wales, Sydney, Australia, tw@cse.unsw.edu.au Symmetry occurs in many problems in aritifical intelligence be able to swap them around without changing the performance of the computer. Symmetries come in many di
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)
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.
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.
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
Maniraj, M [UGC-DAE Confortium for Scientific Research; Rai, Abhishek [UGC-DAE Confortium for Scientific Research; Barman, S R [UGC-DAE Confortium for Scientific Research; Krajci, M [Slovak Academy of Sciences; Schlagel, Deborah L [Ames Laboratory; Lograsso, Thomas A [Ames Laboratory; Horn, K [Fritz-Haber-Institut der Max-Planck-Gesellschaft
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.
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.
Baryogenesis from Symmetry Principle
Fong, Chee Sheng
2015-01-01
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 identity 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.
Baryogenesis from Symmetry Principle
Chee Sheng Fong
2015-08-14
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 identity 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.
Lin, Qisheng; Corbett, John D
2010-11-15
The realm of Tsai-type (YCd(6)-type) quasicrystals (QCs) and their approximants (ACs) continues to expand to the east in the periodic table. The heavy tetrel Sn is now one of the major components in the new Ca(15.0(5))Au(60.0(4))Sn(25.0(2)) (atom %) icosahedral QC and in the corresponding 1/1 and 2/1 ACs. (The 2/1 AC with Yb is also established.) Single-crystal X-ray diffraction on a 1/1 AC gives the refined formula of Ca(3)Au(14.36(3))Sn(4.38(5)) in space group Im3, a = 15.131(1) Å, whereas a representative 2/1 AC gives Ca(13)Au(47.2(1))Sn(28.1(1)), Pa3 and a = 24.444(1) Å. Both ACs contain five-shell multiply endohedral triacontahedral clusters as the common building blocks, as in the parent structure of YCd(6). The 2/1 AC also contains four Ca(2)-dimer-centered prolate rhombohedra (PRs) in the unit cell. The long-range order between triacontahedra and PRs in the 2/1 AC is the same as those in Bergman-type 2/1 ACs. A TB-LMTO-ASA calculation on an ideal 1/1 AC model reveals a shallow pseudogap in the total densities-of-states data around the Fermi energy, as expected. The depth of the pseudogap is considerably enhanced through interactions between the Ca 3d states and s and p states of Au and Sn. PMID:20939550
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 present at the classical level. Quantum Chromodynamics (QCD), the modern theory of the strong interactions, exemplify each of these possibilities. The interplay of these effects determine the spectrum of particles that we observe and, ultimately, account for 99% of the mass of ordinary matter.
Symmetries in atmospheric sciences
Alexander Bihlo
2009-02-24
Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models. This is illustrated with the barotropic vorticity equation. Moreover, the possibility for construction of partially-invariant solutions is discussed for this model. A further point is a discussion of using symmetries for relating different classes of differential equations. This is illustrated with the spherical and the potential vorticity equation. Finally, discrete symmetries are used to derive the minimal finite-mode version of the vorticity equation first discussed by E. Lorenz (1960) in a sound mathematical fashion.
Twisted symmetries and integrable systems
G. Cicogna; G. Gaeta
2010-02-07
Symmetry properties are at the basis of integrability. In recent years, it appeared that so called "twisted symmetries" are as effective as standard symmetries in many respects (integrating ODEs, finding special solutions to PDEs). Here we discuss how twisted symmetries can be used to detect integrability of Lagrangian systems which are not integrable via standard symmetries.
David Wallace
2009-07-03
A systematic analysis is made of the relations between the symmetries of a classical field and the symmetries of the one-particle quantum system that results from quantizing that field in regimes where interactions are weak. The results are applied to gain a greater insight into the phenomenon of antimatter.
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…
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.
Symmetry in Mathematics Learning.
ERIC Educational Resources Information Center
Dreyfus, Tommy; Eisenberg, Theodore
1989-01-01
Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)
NASA Astrophysics Data System (ADS)
Meshkov, Sydney
2009-11-01
The study of the symmetries of nature has fascinated scientists for eons. The application of the formal mathematical description of symmetries during the last century has produced many breakthroughs in our understanding of the substructure of matter. In this talk, a number of these advances are discussed, and the important role that George Sudarshan played in their development is emphasized
ERIC Educational Resources Information Center
Schuler, Joan
2001-01-01
Investigated whether 3- to 6-year-olds in a Montessori school created more symmetrical than asymmetrical designs when working with building materials. Found that symmetry occurred in designs of children as young as age 3, with the tendency increasing with age. Examined the need for increased use of building materials for teaching symmetry in the…
NSDL National Science Digital Library
2012-07-09
In this hands-on activity, learners make New Year's Eve party hats out of wrapping paper. Learners use symmetry and measurement to cut out shapes they need to assemble the hats. In a related video, Mr. O and his assistants explain how to make the party hats using rotational symmetry. Learners can watch this video before creating their hats.
A. A. Kirillov; A. A. Korotkevich; S. G. Rubin
2012-10-16
The mechanism of symmetry formation is discussed in the framework of multidimensional gravity. It is shown that this process is strictly connected to the entropy decrease of compact space. The existence of low energy symmetries is not postulated from the beginning. They could be absent during the inflationary stage under certain conditions discussed in the paper.
Jach, T. [National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)] [National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States); Zhang, Y.; Colella, R. [Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States)] [Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States); de Boissieu, M.; Boudard, M. [LTPCM-ENSEEG, BP 75, 38402 St. Martin d`Heres Cedex (France)] [LTPCM-ENSEEG, BP 75, 38402 St. Martin d`Heres Cedex (France); Goldman, A.I.; Lograsso, T.A.; Delaney, D.W. [Department of Physics and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)] [Department of Physics and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States); Kycia, S. [CHESS, Cornell University, Ithaca, New York 14853 (United States)] [CHESS, Cornell University, Ithaca, New York 14853 (United States)
1999-04-01
We have observed dynamical diffraction in the
Temperature-reflection symmetry
NASA Astrophysics Data System (ADS)
Ba?ar, Gökçe; Cherman, Aleksey; McGady, David A.; Yamazaki, Masahito
2015-05-01
We point out the presence of a T ?-T temperature-reflection (T -reflection) symmetry for the partition functions of many physical systems. Without knowledge of the origin of the symmetry, we have only been able to test the existence of T -reflection symmetry in systems with exactly calculable partition functions. We show that T -reflection symmetry is present in a variety of conformal and nonconformal field theories and statistical mechanics models with known partition functions. For example, all minimal model partition functions in two-dimensional conformal field theories are invariant under T -reflections. An interesting property of the T -reflection symmetry is that it can be broken by shifts of the vacuum energy.
Goswami, Lalit N; Ma, Lixin; Kueffer, Peter J; Jalisatgi, Satish S; Hawthorne, M Frederick
2013-01-01
An icosahedral closo-B??²? scaffold based nano-sized assembly capable of carrying a high payload of Gd³?-chelates in a sterically crowded configuration is developed by employing the azide-alkyne click reaction. The twelve copies of DO3A-t-Bu-ester ligands were covalently attached to an icosahedral closo-B??²? core via suitable linkers through click reaction. This nanomolecular structure supporting a high payload of Gd³?-chelate is a new member of the closomer MRI contrast agents that we are currently developing in our laboratory. The per Gd ion relaxivity (r?) of the newly synthesized MRI contrast agent was obtained in PBS, 2% tween/PBS and bovine calf serum using a 7 Tesla micro MRI instrument and was found to be slightly higher (r? = 4.7 in PBS at 25 °C) compared to the clinically used MRI contrast agents Omniscan (r? = 4.2 in PBS at 25 °C) and ProHance (r? = 3.1 in PBS at 25 °C). PMID:23899836
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.
Lang, C. B.; Schroeck, Mario
2011-10-15
In quantum chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of {rho} and a{sub 1} approach each other) while confining properties persist.
Castanos, Octavio [Instituto de Ciencias Nucleares, Universidad Nacional Autonoma de Mexico, Apartado Postal 70-543, Mexico D. F., C.P. 04510 (Mexico)
2010-09-10
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.
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.
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.
Polymer quantization and Symmetries
Ghanashyam Date; Nirmalya Kajuri
2013-02-24
Polymer quantization was discovered during the construction of Loop Quantum Cosmology. For the simplest quantum theory of one degree of freedom, the implications for dynamics were studied for the harmonic oscillator as well as some other potentials. For more degrees of freedom, the possibility of continuous, kinematic symmetries arises. While these are realised on the Hilbert space of polymer quantum mechanics, their infinitesimal versions are not supported. For an invariant Hamiltonian, these symmetry realizations imply infinite degeneracy suggesting that the symmetry should be spontaneously or explicitly broken. The estimation of symmetry violations in some cases have been analysed before. Here we explore the alternative of shifting the arena to the distributional states. We discuss both the polymer quantum mechanics case as well as polymer quantized scalar field.
Trapped surfaces and symmetries
Marc Mars; José M. M. Senovilla
2003-10-16
We prove that strictly stationary spacetimes cannot contain closed trapped nor marginally trapped surfaces. The result is purely geometric and holds in arbitrary dimension. Other results concerning the interplay between (generalized) symmetries and trapped submanifolds are also presented.
Matthias Neubert
1994-01-01
We review the current status of heavy-quark symmetry and its applications to weak decays of hadrons containing a single heavy quark. After an introduction to the underlying physical ideas, we discuss in detail the formalism of the heavy-quark effective theory, including a comprehensive treatment of symmetry breaking corrections. We then illustrate some nonperturbative approaches, which aim at a dynamical, QCD-based
On symmetries of substructures.
Grosse-Kunstleve, R W; Adams, P D
2003-11-01
This paper accompanies a lecture given at the 2003 CCP4 Study Weekend on experimental phasing. With the audience of the CCP4 Study Weekend in mind, an overview is given of symmetries of substructures and the implications for single isomorphous replacement and single anomalous diffraction phasing procedures, as well as difference Fourier analyses. Pointers are also provided to practical tools for working with substructure symmetries. PMID:14573952
Christian Fleischhack
2015-03-21
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries: Firstly, paths that are parts of an integral curve of a fundamental vector field on $M$ (continuous symmetry). Secondly, paths that can be decomposed into finitely many pieces, each of which is the translate of some free segment, where possibly the translate is cut at the two ends of the paths (discrete symmetry). Here, a free segment is a path $e$ whose $G$-translates either equal $e$ or intersect it in at most finitely many points. Note that all the statements above are understood up to the parametrization of the paths. We will show, for the category of analytic manifolds, that each path is of exactly one of either types. For the proof, we use that the overlap of a path $\\gamma$ with one of its translates is encoded uniquely in a mapping between subsets of $\\dom\\gamma$. Running over all translates, these mappings form the so-called reparametrization set to $\\gamma$. It will turn out that, up to conjugation with a diffeomorphism, any such set is given by the action of a Lie subgroup of $O(2)$ on $S^1$, restricted in domain and range to some compact interval on $S^1$. Now, the infinite subgroups correspond to the continuous symmetry above, finite ones to the discrete symmetry.
Finite group symmetry breaking
G. Gaeta
2005-10-02
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and field theory. The breaking of finite groups symmetry has thus been thoroughly studied, and general approaches exist to investigate it. In Landau theory, the state of a system is described by a finite dimensional variable (the {\\it order parameter}), and physical states correspond to minima of a potential, invariant under a group. In this article we describe the basics of symmetry breaking analysis for systems described by a symmetric polynomial; in particular we discuss generic symmetry breakings, i.e. those determined by the symmetry properties themselves and independent on the details of the polynomial describing a concrete system. We also discuss how the plethora of invariant polynomials can be to some extent reduced by means of changes of coordinates, i.e. how one can reduce to consider certain types of polynomials with no loss of generality. Finally, we will give some indications on extension of this theory, i.e. on how one deals with symmetry breakings for more general groups and/or more general physical systems.
Classification of Arnold-Beltrami Flows and their Hidden Symmetries
Pietro Fre; Alexander S. Sorin
2015-01-19
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the ABC-flow introduced by Beltrami, Arnold and Childress. Beltrami equation is the eigenstate equation for the first order Laplace-Beltrami operator *d, which we solve by using harmonic analysis. Taking torus T^3 constructed as R^3/L, where L is a crystallographic lattice, we present a general algorithm to construct solutions of Beltrami equation which utilizes as main ingredient the orbits under the action of the point group P_L of three-vectors in the momentum lattice L*. We introduce the new notion of a Universal Classifying Group GU_L which contains all crystallographic space groups as proper subgroups. We show that the *d-eigenfunctions are naturally arranged into irreducible representations of GU_L and by means of a systematic use of the branching rules with respect to various possible subgroups H of GU_L we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group P_L is the proper octahedral group O_24 and the Universal Classifying Group is finite group G_1536 of order 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O_24 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 G_1536. 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 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 possibly make contact with M-theory and the geometry of flux-compactifications.
Symmetry in Numbers David Marshall
Marshall, David
Symmetry in Numbers David Marshall Monmouth University April 13, 2005 808 -2 3 + 3 -169 54 + 1007 18 + 3 -169 54 - 1007 18 Typeset by FoilTEX #12;Symmetry One of the guiding principles group of symmetries. -Paul Yale, in Geometry and Symmetry 2. Due or just proportion; harmony of parts
Symmetry: between indecision equality Barakova Spaanenburg,
Zimmer, Uwe
Symmetry: between indecision equality of choice. Barakova Spaanenburg, Rijksuniversiteit Groningen balance between knowl randomness symmetry. Symmetry beneficial anddetrimental to the learning process--hill a better match. Symmetry randomness influence itinerary. symmetries in landscape, signified by crests
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.
On the symmetry of three identical interacting particles in a one-dimensional box
Paolo Amore; Francisco M. Fernández
2015-04-07
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group $D_{3d}$. Group theory greatly facilitates the application of perturbation theory and the Rayleigh-Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.
Crystal Symmetry Algorithms in a High-Throughput Framework for Materials
NASA Astrophysics Data System (ADS)
Taylor, Richard
The high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.
Symmetry of priapulids (Priapulida). 2. Symmetry of larvae.
Adrianov, A V; Malakhov, V V
2001-02-01
Larvae of priapulids are characterized by radial symmetry evident from both external and internal characters of the introvert and lorica. The bilaterality appears as a result of a combination of several radial symmetries: pentaradial symmetry of the teeth, octaradial symmetry of the primary scalids, 25-radial symmetry of scalids, biradial symmetry of the neck, and biradial and decaradial symmetry of the trunk. Internal radiality is exhibited by musculature and the circumpharyngeal nerve ring. Internal bilaterality is evident from the position of the ventral nerve cord and excretory elements. Externally, the bilaterality is determined by the position of the anal tubulus and two shortened midventral rows of scalids bordering the ventral nerve cord. The lorical elements define the biradial symmetry that is missing in adult priapulids. The radial symmetry of larvae is a secondary appearance considered an evolutionary adaptation to a lifestyle within the three-dimensional environment of the benthic sediment. PMID:11223922
Symmetry in context: Salience of mirror symmetry in natural patterns
Cohen, Elias H.; Zaidi, Qasim
2013-01-01
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual phenomenon. Mirror symmetry detection is considered particularly rapid and efficient, based on experiments with random noise. Symmetry detection in natural settings, however, is often accomplished against structured backgrounds. To measure salience of symmetry in diverse contexts, we assembled mirror symmetric patterns from 101 natural textures. Temporal thresholds for detecting the symmetry axis ranged from 28 to 568 ms indicating a wide range of salience (1/Threshold). We built a model for estimating symmetry-energy by connecting pairs of mirror-symmetric filters that simulated cortical receptive fields. The model easily identified the axis of symmetry for all patterns. However, symmetry-energy quantified at this axis correlated weakly with salience. To examine context effects on symmetry detection, we used the same model to estimate approximate symmetry resulting from the underlying texture throughout the image. Magnitudes of approximate symmetry at flanking and orthogonal axes showed strong negative correlations with salience, revealing context interference with symmetry detection. A regression model that included the context-based measures explained the salience results, and revealed why perceptual symmetry can differ from mathematical characterizations. Using natural patterns thus produces new insights into symmetry perception and its possible neural circuits. PMID:23729773
Tests of fundamental symmetries
NASA Astrophysics Data System (ADS)
Budker, Dmitry
2015-04-01
``Fundamental symmetry'' refers to invariance of the laws of Nature, including the values of fundamental constants, with respect to a continuous or discrete transformation such as translation in space or time, rotation, spatial (P), time (T), or charge (C) reversal, combinations of these, or permutation of identical quantum particles. All discrete symmetries except for the combined CPT and the permutation symmetry are experimentally known to be violated by the weak interactions; intense searches are conducted for possible small violations of the still-standing discrete as well as the continuous symmetries, which may result from exotic beyond-the-standard-model interactions. In this talk, I will describe some of the recent fundamental-symmetry tests involving our research group (for up-to-date bibliography see http://budker.berkeley.edu/PubList.html), including measuring the effect of the gravitation-field gradient on the value of the fine-structure ``constant,'' and searching for transient and time-dependent effects on atomic magnetometers and clocks.
Jana, Partha P; Lidin, Sven
2015-02-01
The ? phase in the Au-Cd binary system has been synthesized, and the structure has been analyzed by single-crystal X-ray diffraction. The compound ?-AuCd(4) crystallizes in the hexagonal space group P6(3)/m (No. 176). The unit cell contains ?273 atoms. The compound AuCd(4) represents a ?3a × ?3a × c superstructure of the AgMg(4) type. The structure can be well described by icosahedral and trigonal-prismatic clusters. A phase transition to the high-temperature ? phase occurs exothermically at around 578 K. The compound is formed at a sharp valence electron concentration of 1.8 e/a. The compound can be understood within the framework of the Hume-Rothery stabilization mechanism. PMID:24934260
Shackelford, Scott A; Belletire, John L; Boatz, Jerry A; Schneider, Stefan; Wheaton, Amanda K; Wight, Brett A; Hudgens, Leslie M; Ammon, Herman L; Strauss, Steven H
2009-06-18
Ten new salts that pair triazolium and imidazolium cations with closo-icosahedral anions [B(12)H(12)](2-) and [CB(11)H(12)](-) were synthesized in water solvent using an open-air, benchtop method. These unreported [Heterocyclium](2)[B(12)H(12)] and [Heterocyclium][CB(11)H(12)] salts extend reports of [Imidazolium][CB(11)H(12)] and [Pyridinium][CB(11)H(12)] salts that were synthesized in anhydrous organic solvents under an inert atmosphere with glovebox or Schlenk techniques. Spectroscopic data, melting points, and densities are reported for each salt. Single-crystal X-ray structures are provided for the five new [B(12)H(12)](2-) salts. PMID:19441856
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
Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M
2014-02-01
A comparison of periodic approximants and their quasicrystalline counterparts offers the opportunity to better understand the structure, physical properties and stabilizing mechanisms of these complex phases. We present a combined experimental and computational study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare these to the lattice dynamics of the cubic 1/1-approximant Zn6Sc. The two phases, quasicrystal and approximant, are built up from the same atomic clusters, which are packed either quasiperiodically or on a body centered cubic lattice, respectively. Using inelastic neutron scattering and atomic scale simulations, we show that the vibrational spectra of these three systems are very similar, however, they contain a clear signature of the increasing structural complexity from approximant to quasicrystal. PMID:24445750
Gavilano, J.L.; Ambrosini, B.; Vonlanthen, P.; Chernikov, M.A.; Ott, H.R. [Laboratorium fuer Festkoerperphysik, Eidgenoessische Technische Hochschule-Hoenggerberg, CH-8093 Zuerich (Switzerland)] [Laboratorium fuer Festkoerperphysik, Eidgenoessische Technische Hochschule-Hoenggerberg, CH-8093 Zuerich (Switzerland)
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}
Persson, K.; Schneider, G.; Jordan, D. B.; Viitanen, P. V.; Sandalova, T.
1999-01-01
Lumazine synthase catalyzes the penultimate step in the synthesis of riboflavin in plants, fungi, and microorganisms. The enzyme displays two quaternary structures, the pentameric forms in yeast and fungi and the 60-meric icosahedral capsids in plants and bacteria. To elucidate the structural features that might be responsible for differences in assembly, we have determined the crystal structures of lumazine synthase, complexed with the inhibitor 5-nitroso-6-ribitylamino-2,4-pyrimidinedione, from spinach and the fungus Magnaporthe grisea to 3.3 and 3.1 A resolution, respectively. The overall structure of the subunit and the mode of inhibitor binding are very similar in these enzyme species. The core of the subunit consists of a four-stranded parallel beta-sheet sandwiched between two helices on one side and three helices on the other. The packing of the five subunits in the pentameric M. grisea lumazine synthase is very similar to the packing in the pentameric substructures in the icosahedral capsid of the plant enzyme. Two structural features can be correlated to the differences in assembly. In the plant enzyme, the N-terminal beta-strand interacts with the beta-sheet of the adjacent subunit, thus extending the sheet from four to five strands. In fungal lumazine synthase, an insertion of two residues after strand beta1 results in a completely different orientation of this part of the polypeptide chain and this conformational difference prevents proper packing of the subunits at the trimer interface in the icosahedron. In the spinach enzyme, the beta-hairpin connecting helices alpha4 and alpha5 participates in the packing at the trimer interface of the icosahedron. Another insertion of two residues at this position of the polypeptide chain in the fungal enzyme disrupts the hydrogen bonding in the hairpin, and the resulting change in conformation of this loop also interferes with proper intrasubunit contacts at the trimer interface. PMID:10595538
Binary Tetrahedral Flavor Symmetry
Eby, David A
2013-01-01
A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibb...
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.
Seeing Science through Symmetry
NASA Astrophysics Data System (ADS)
Gould, L. I.
Seeing Through Symmetry is a course that introduces non-science majors to the pervasive influence of symmetry in science. The concept of symmetry is usedboth as a link between subjects (such as physics, biology, mathematics, music, poetry, and art) and as a method within a subject. This is done through the development and use of interactive multimedia learning environments to stimulate learning. Computer-based labs enable the student to further explore the concept by being gently led from the arts to science. This talk is an update that includes some of the latest changes to the course. Explanations are given on methodology and how a variety of interactive multimedia tools contribute to both the lecture and lab portion of the course (created in 1991 and taught almost every semester since then, including one in Sweden).
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.
NASA Astrophysics Data System (ADS)
Brown, J. David
2008-10-01
The BSSN (Baumgarte Shapiro Shibata Nakamura) formulation of the Einstein evolution equations is written in spherical symmetry. These equations can be used to address a number of technical and conceptual issues in numerical relativity in the context of a single Schwarzschild black hole. One of the benefits of spherical symmetry is that the numerical grid points can be tracked on a Kruskal Szekeres diagram. Boundary conditions suitable for puncture evolution of a Schwarzschild black hole are presented. Several results are shown for puncture evolution using a fourth-order finite difference implementation of the equations.
Varzielas, I de Medeiros
2015-01-01
CP-odd invariants, independent of basis and valid for any choice of CP transformation are a powerful tool in the study of CP. They are particularly convenient to study the CP properties of models with family symmetries. After interpreting the consequences of adding specific CP symmetries to a Lagrangian invariant under $\\Delta(27)$, I use the invariant approach to systematically study Yukawa-like Lagrangians with an increasing field content in terms of $\\Delta(27)$ representations. Included in the Lagrangians studied are models featuring explicit CP violation with calculable phases (referred to as explicit geometrical CP violation) and models that automatically conserve CP, despite having all the $\\Delta(27)$ representations.
I. de Medeiros Varzielas
2015-10-08
CP-odd invariants, independent of basis and valid for any choice of CP transformation are a powerful tool in the study of CP. They are particularly convenient to study the CP properties of models with family symmetries. After interpreting the consequences of adding specific CP symmetries to a Lagrangian invariant under $\\Delta(27)$, I use the invariant approach to systematically study Yukawa-like Lagrangians with an increasing field content in terms of $\\Delta(27)$ representations. Included in the Lagrangians studied are models featuring explicit CP violation with calculable phases (referred to as explicit geometrical CP violation) and models that automatically conserve CP, despite having all the $\\Delta(27)$ representations.
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.
Francois Gieres
1997-12-16
The goal of this introduction to symmetries is to present some general ideas, to outline the fundamental concepts and results of the subject and to situate a bit the following lectures of this school. [These notes represent the write-up of a lecture presented at the fifth ``Seminaire Rhodanien de Physique: Sur les Symetries en Physique" held at Dolomieu (France), 17-21 March 1997. Up to the appendix and the graphics, it is to be published in "Symmetries in Physics", F.Gieres, M.Kibler,C.Lucchesi and O.Piguet, eds. (Editions Frontieres, 1998).
Grand unification of ?- ? symmetry
NASA Astrophysics Data System (ADS)
Mohapatra, R. N.; Nasri, S.; Yu, Hai-Bo
2006-05-01
Near maximal neutrino mixing needed to understand atmospheric neutrino data can be interpreted to be a consequence of an interchange symmetry between the muon and tau neutrinos in the neutrino mass matrix in the flavor basis. This idea can be tested by a measurement of the neutrino mixing parameter ?13 and looking for its correlation with ?23 - ? / 4. We present a supersymmetric SU(5) grand unified model for quarks and leptons which obeys this exchange symmetry and is a realistic model that can fit all observations. GUT embedding shifts ?13 from its zero ?- ? symmetric value to a nonzero value keeping it under an upper limit.
Skewed Rotation Symmetry Group Detection
Seungkyu Lee; Yanxi Liu
2010-01-01
Abstract—We present a novel and effective algorithm for affinely skewed,rotation symmetry,group detection from real-world images. We define a complete,skewed,rotation symmetry,detection problem,as discovering,five independent,properties of a skewed,rotation symmetry,group: (1) the center of rotation; (2) the affine deformation; (3) the type of the symmetry,group; (4) the cardinality of the symmetry,group; and (5) the supporting,region of the symmetry,group in the image. We propose,a
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
Binary tetrahedral flavor symmetry
NASA Astrophysics Data System (ADS)
Eby, David A.
A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibbo angle, and a dark matter candidate that remains outside the limits of current tests. Additionally, we include mention of a number of unanswered questions and remaining areas of interest for future study. Taken together, we believe these results speak to the promising potential of finite groups and flavor symmetries to act as an approximation of nature.
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)
Binary Tetrahedral Flavor Symmetry
David A. Eby
2013-04-15
A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibbo angle, and a dark matter candidate that remains outside the limits of current tests. Additionally, we include mention of a number of unanswered questions and remaining areas of interest for future study. Taken together, we believe these results speak to the promising potential of finite groups and flavor symmetries to act as an approximation of nature.
NSDL National Science Digital Library
Children's Museum of Houston
2014-09-19
In this math activity, learners experiment with the concept of symmetry. Learners use mirrors to identify which pictures, letters, and shapes are symmetrical and then complete the missing halves for images. This activity guide contains a material list, sample questions to ask, literary connections, extensions, and alignment to local and national standards.
Killing Tensors and Symmetries
David Garfinkle; E. N. Glass
2010-03-10
A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvin's magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The method requires less computation than solving the full Killing tensor equations directly, and it can be used even when the spacetime is not algebraically special.
Symmetries of Conservation Laws
Sanja Konjik
2007-01-01
The aim of this paper is to apply techniques of symmetry group analysis in solving two systems of conservation laws: a model of two strictly hyperbolic conservation laws and a zero pressure gas dynamics model, which both have no global solution, but whose solution consists of singular shock waves. We show that these shock waves are solutions in the sense
Associate symmetries: A novel procedure for finding contact symmetries
NASA Astrophysics Data System (ADS)
Jefferson, G. F.; Carminati, J.
2014-03-01
A new method for finding contact symmetries is proposed for both ordinary and partial differential equations. Symmetries more general than Lie point are often difficult to find owing to an increased dependency of the infinitesimal functions on differential quantities. As a consequence, the invariant surface condition is often unable to be “split” into a reasonably sized set of determining equations, if at all. The problem of solving such a system of determining equations is here reduced to the problem of finding its own point symmetries and thus subsequent similarity solutions to these equations. These solutions will (in general) correspond to some subset of symmetries of the original differential equations. For this reason, we have termed such symmetries associate symmetries. We use this novel method of associate symmetries to determine new contact symmetries for a non-linear PDE and a second order ODE which could not previously be found using computer algebra packages; such symmetries for the latter are particularly difficult to find. We also consider a differential equation with known contact symmetries in order to illustrate that the associate symmetry procedure may, in some cases, be able to retrieve all such symmetries.
Hari Krovi
2007-11-12
A discrete-time quantum walk on a graph is the repeated application of a unitary evolution operator to a Hilbert space corresponding to the graph. Hitting times for discrete quantum walks on graphs give an average time before the walk reaches an ending condition. We derive an expression for hitting time using superoperators, and numerically evaluate it for the walk on the hypercube for various coins and decoherence models. We show that, by contrast to classical walks, quantum walks can have infinite hitting times for some initial states. We seek criteria to determine if a given walk on a graph will have infinite hitting times, and find a sufficient condition for their existence. The phenomenon of infinite hitting times is in general a consequence of the symmetry of the graph and its automorphism group. Symmetries of a graph, given by its automorphism group, can be inherited by the evolution operator. Using the irreducible representations of the automorphism group, we derive conditions such that quantum walks defined on this graph must have infinite hitting times for some initial states. Symmetry can also cause the walk to be confined to a subspace of the original Hilbert space for certain initial states. We show that a quantum walk confined to the subspace corresponding to this symmetry group can be seen as a different quantum walk on a smaller quotient graph and we give an explicit construction of the quotient graph. We conjecture that the existence of a small quotient graph with finite hitting times is necessary for a walk to exhibit a quantum speed-up. Finally, we use symmetry and the theory of decoherence-free subspaces to determine when the subspace of the quotient graph is a decoherence-free subspace of the dynamics.
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…
Breaking Generator Symmetry George Katsirelos
Walsh, Toby
Breaking Generator Symmetry George Katsirelos NICTA Sydney, Australia george problematic. One solution is to focus on just sym- metries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete, there are also cases
Symmetry Energy in Nuclear Surface
Pawel Danielewicz; Jenny Lee
2008-12-25
Interplay between the dependence of symmetry energy on density and the variation of nucleonic densities across nuclear surface is discussed. That interplay gives rise to the mass dependence of the symmetry coefficient in an energy formula. Charge symmetry of the nuclear interactions allows to introduce isoscalar and isovector densities that are approximately independent of the magnitude of neutron-proton asymmetry.
Algorithms for computer detection of symmetry elements in molecular systems.
Beruski, Otávio; Vidal, Luciano N
2014-02-01
Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry. PMID:24403016
A Reflective Symmetry Descriptor Michael Kazhdan,
A Reflective Symmetry Descriptor Michael Kazhdan, Bernard Chazelle, David Dobkin, Adam Finkelstein, and Thomas Funkhouser Princeton University, Princeton NJ 08544, USA Abstract. Computing reflective symmetries, we introduce a new reflective symmetry descriptor that repre- sents a measure of reflective symmetry
Sullivan, John M.
Math 303 Planar Wallpaper Symmetry Groups A finite figure with mirror symmetry has dihedral Dn symmetry for some n, meaning that there are n mirror lines meeting at equal angles of /n. In a wallpaper symmetry. To classify its further symmetries (if any), you should first look for mirror symmetry. Any
Hexagonal projected symmetries.
Oliveira, Juliane F; Castro, Sofia B S D; Labouriau, Isabel S
2015-09-01
In the study of pattern formation in symmetric physical systems, a three-dimensional structure in thin domains is often modelled as a two-dimensional one. This paper is concerned with functions in {\\bb R}^{3} that are invariant under the action of a crystallographic group and the symmetries of their projections into a function defined on a plane. A list is obtained of the crystallographic groups for which the projected functions have a hexagonal lattice of periods. The proof is constructive and the result may be used in the study of observed patterns in thin domains, whose symmetries are not expected in two-dimensional models, like the black-eye pattern. PMID:26317198
P. M. Lo; E. S. Swanson
2010-10-06
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 that the pattern of symmetry breaking maintains parity but breaks chiral symmetry. We also find that chiral symmetry is restored at a critical number of fermion flavours in our truncation scheme. The Coleman-Hill theorem is used to demonstrate that the results are reasonably accurate.
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.
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
Davood Momeni; Ratbay Myrzakulov
2014-10-04
The symmetry issue for Galileons has been studied. In particular we address scaling (conformal) and Noether symmetrized Galileons. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have been made on Galileons. We have been proven that for Galileons always is possible to find a way to "symmetrized" Galileo's field .
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
Guo, Fei; Liu, Zheng; Vago, Frank; Ren, Yue; Wu, Weimin; Wright, Elena T.; Serwer, Philip; Jiang, Wen
2013-01-01
Motor-driven packaging of a dsDNA genome into a preformed protein capsid through a unique portal vertex is essential in the life cycle of a large number of dsDNA viruses. We have used single-particle electron cryomicroscopy to study the multilayer structure of the portal vertex of the bacteriophage T7 procapsid, the recipient of T7 DNA in packaging. A focused asymmetric reconstruction method was developed and applied to selectively resolve neighboring pairs of symmetry-mismatched layers of the portal vertex. However, structural features in all layers of the multilayer portal vertex could not be resolved simultaneously. Our results imply that layers with mismatched symmetries can join together in several different relative orientations, and that orientations at different interfaces assort independently to produce structural isomers, a process that we call combinatorial assembly isomerism. This isomerism explains rotational smearing in previously reported asymmetric reconstructions of the portal vertex of T7 and other bacteriophages. Combinatorial assembly isomerism may represent a new regime of structural biology in which globally varying structures assemble from a common set of components. Our reconstructions collectively validate previously proposed symmetries, compositions, and sequential order of T7 portal vertex layers, resolving in tandem the 5-fold gene product 10 (gp10) shell, 12-fold gp8 portal ring, and an internal core stack consisting of 12-fold gp14 adaptor ring, 8-fold bowl-shaped gp15, and 4-fold gp16 tip. We also found a small tilt of the core stack relative to the icosahedral fivefold axis and propose that this tilt assists DNA spooling without tangling during packaging. PMID:23580619
Guo, Fei; Liu, Zheng; Vago, Frank; Ren, Yue; Wu, Weimin; Wright, Elena T; Serwer, Philip; Jiang, Wen
2013-04-23
Motor-driven packaging of a dsDNA genome into a preformed protein capsid through a unique portal vertex is essential in the life cycle of a large number of dsDNA viruses. We have used single-particle electron cryomicroscopy to study the multilayer structure of the portal vertex of the bacteriophage T7 procapsid, the recipient of T7 DNA in packaging. A focused asymmetric reconstruction method was developed and applied to selectively resolve neighboring pairs of symmetry-mismatched layers of the portal vertex. However, structural features in all layers of the multilayer portal vertex could not be resolved simultaneously. Our results imply that layers with mismatched symmetries can join together in several different relative orientations, and that orientations at different interfaces assort independently to produce structural isomers, a process that we call combinatorial assembly isomerism. This isomerism explains rotational smearing in previously reported asymmetric reconstructions of the portal vertex of T7 and other bacteriophages. Combinatorial assembly isomerism may represent a new regime of structural biology in which globally varying structures assemble from a common set of components. Our reconstructions collectively validate previously proposed symmetries, compositions, and sequential order of T7 portal vertex layers, resolving in tandem the 5-fold gene product 10 (gp10) shell, 12-fold gp8 portal ring, and an internal core stack consisting of 12-fold gp14 adaptor ring, 8-fold bowl-shaped gp15, and 4-fold gp16 tip. We also found a small tilt of the core stack relative to the icosahedral fivefold axis and propose that this tilt assists DNA spooling without tangling during packaging. PMID:23580619
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.
Simple and collective twisted symmetries
Giuseppe Gaeta
2014-10-29
After the introduction of $\\lambda$-symmetries by Muriel and Romero, several other types of so called "twisted symmetries" have been considered in the literature (their name refers to the fact they are defined through a deformation of the familiar prolongation operation); they are as useful as standard symmetries for what concerns symmetry reduction of ODEs or determination of special (invariant) solutions for PDEs and have thus attracted attention. The geometrical relation of twisted symmetries to standard ones has already been noted: for some type of twisted symmetries (in particular, $\\lambda$ and $\\mu$-symmetries), this amounts to a certain kind of gauge transformation. In a previous review paper [G. Gaeta, "Twisted symmetries of differential equations", {\\it J. Nonlin. Math. Phys.}, {\\bf 16-S} (2009), 107-136] we have surveyed the first part of the developments of this theory; in the present paper we review recent developments. In particular, we provide a unifying geometrical description of the different types of twisted symmetries; this is based on the classical Frobenius reduction applied to distribution generated by Lie-point (local) symmetries.
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.
Hajime Moriya
2006-08-27
We consider the univalence superselection rule. One would say perhaps ``There is no indication in nature to invalidate this rule. Fermions do not condensate!'' To explain our motivation, let us recall the correspondence of fermion systems and Pauli systems by the Jordan-Wigner transformation. For a finite lattice, fermion grading symmetry corresponds to the Pauli grading. For an infinite lattice, the Pauli-grading can be spontaneously broken e.g. for the XY-model. What is the status of the fermion grading? Nature tells that fermion grading symmmetry cannot be broken for any physical model. But it seems that its rigorous support is needed.
Chiral symmetry and confinement
Goldman, T.
1989-01-01
Two principle features underlie the appearance of (approximate) chiral symmetry in hadronic systems. The first is that the conventional Dirac bispinor description of massless quarks hides the fact that this object is a direct sum of inequivalent representations of the Lorentz group. The second essential feature is that the dynamics must be chiral invariant as well. QCD satisfies this requirement by coupling equally to left and right chiral projections of the (nominally vector) color current (V /plus minus/ A) and so, to the separated components of the Dirac bispinor. The remainder of this paper describes these features.
Surface defects and symmetries
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph
2015-04-01
In quantum field theory, defects of various codimensions are natural ingredients and carry a lot of interesting information. In this contribution we concentrate on topological quantum field theories in three dimensions, with a particular focus on Dijkgraaf-Witten theories with abelian gauge group. Surface defects in Dijkgraaf-Witten theories have applications in solid state physics, topological quantum computing and conformal field theory. We explain that symmetries in these topological field theories are naturally defined in terms of invertible topological surface defects and are thus Brauer-Picard groups.
Holographic heavy quark symmetry
NASA Astrophysics Data System (ADS)
Hashimoto, Koji; Ogawa, Noriaki; Yamaguchi, Yasuhiro
2015-06-01
We investigate the heavy quark spin symmetry, i.e. the mass degeneracy of pseudo-scalar and vector quarkonia at heavy quark limit, by using the gauge/gravity correspondence. We allow generic D3-like geometry with a flavor D7-brane, to avoid supersymmetric mass degeneracy. For geometries admitting physical QCD-like properties, we find that the mass degeneracy is generically achieved in a good accuracy, up to a few percent mass splitting. We also compute spectra of excited quarkonia states, and discuss comparisons with experiments and quark-model calculations.
Holographic Heavy Quark Symmetry
Koji Hashimoto; Noriaki Ogawa; Yasuhiro Yamaguchi
2015-05-13
We investigate the heavy quark spin symmetry, i.e. the mass degeneracy of pseudo-scalar and vector quarkonia at heavy quark limit, by using the gauge/gravity correspondence. We allow generic D3-like geometry with a flavor D7-brane, to avoid supersymmetric mass degeneracy. For geometries admitting physical QCD-like properties, we find that the mass degeneracy is generically achieved in a good accuracy, up to a few percent mass splitting. We also compute spectra of excited quarkonia states, and discuss comparisons with experiments and quark-model calculations.
NASA Astrophysics Data System (ADS)
Mohapatra, R. N.; Nasri, S.
2005-02-01
If an exact ??? symmetry is the explanation of the maximal atmospheric neutrino mixing angle, it has interesting implications for the origin of matter via leptogenesis in models where small neutrino masses arise via the seesaw mechanism. For seesaw models with two right-handed neutrinos (N?,N?), lepton asymmetry vanishes in the exact ??? symmetric limit, even though there are nonvanishing Majorana phases in the neutrino mixing matrix. On the other hand, for three right-handed neutrino models, lepton asymmetry is nonzero and is given directly by the solar mass difference square. We also find an upper bound on the lightest neutrino mass.
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.
Shukla, A. K.; Dhaka, R. S.; Biswas, C.; Banik, S.; Barman, S. R.; Horn, K.; Ebert, Ph.; Urban, K. [UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore, 452017, Madhya Pradesh (India); Fritz-Haber-Institut der Max-Planck-Gesellschaft, 14195 Berlin (Germany); Institut fuer Festkoerperforschung, Forschungszentrum Juelich GmbH, 52425 Juelich (Germany)
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.
Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Kaneko, Y; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M
2013-03-20
A comparison of periodic approximants and their quasicrystalline counterparts offers the opportunity to better understand the structure, physical properties and stabilizing mechanisms of these complex phases. We present a combined experimental and molecular dynamics study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare it to recently published results obtained for the cubic 1/1-approximant Zn(6)Sc. Both phases, quasicrystal and approximant, are built up from large atomic clusters which contain a tetrahedral shell at the cluster centre and are packed either quasiperiodically or on a bcc lattice. Using quasielastic neutron scattering and atomic scale simulations, we show that in the quasicrystal the tetrahedra display a dynamics similar to that observed in the 1/1-approximant: the tetrahedra behave as a 'single molecule' and reorient dynamically on a timescale of the order of a few ps. The tetrahedra reorientation is accompanied by a large distortion of the surrounding cluster shells which provide a unique dynamical flexibility to the quasicrystal. However, whereas in the 1/1-approximant the tetrahedron reorientation is observed down to T(c) = 160 K, where a phase transition takes place, in the quasicrystal the tetrahedron dynamics is gradually freezing from 550 to 300 K, similarly to a glassy system. PMID:23411496
Quantum Mechanics in symmetry language
Houri Ziaeepour
2014-09-17
We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better understood in this view. In particular, the abstract concept of symmetry provides a basis-independent definition for observables. Moreover, we show that the apparent projection/collapse of the state as the final step of measurement or decoherence is the result of breaking of symmetries. This phenomenon is comparable with a phase transition by spontaneous symmetry breaking, and makes the process of decoherence and classicality a natural fate of complex systems consisting of many interacting subsystems. Additionally, we demonstrate that the property of state space as a vector space representing symmetries is more fundamental than being an abstract Hilbert space, and its $L2$ integrability can be obtained from the imposed condition of being a representation of a symmetry group and general properties of probability distributions.
NASA Technical Reports Server (NTRS)
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
NASA Astrophysics Data System (ADS)
Tsurumaru, Toyohiro
2010-01-01
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of “rank two” can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
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.
Nuclear Symmetries and Anomalies
NASA Astrophysics Data System (ADS)
Zamick, Larry; Escuderos, Alberto
2007-04-01
First in a single-j-shell calculation (j = f7/2) we discuss various symmetries, e.g., two to one in 44Ti vs. 43Ti. We note that the wave function amplitudes for T(higher) states are coefficients of fractional parentage, and that orthogonality of T(higher) and T(lower) states leads to useful results. Then we consider what happens if T = 0 two-body matrix elements are set equal to zero. We find a partial dynamical symmetry with several interesting degeneracies. It is noted that some formulae developed for identical particles also apply to different (companion) problems involving mixed systems of protons and neutrons. In the g9/2 shell, where one can have for the first time seniority violation for identical particles, we find some interesting yet unproven results. Finally, we discuss shell-model calculations for the magnetic moments of different nuclei, such as 52Ti, even-even Ca isotopes, and N = Z nuclei.
Givental graphs and inversion symmetry
P. Dunin-Barkowski; S. Shadrin; L. Spitz
2012-12-17
Inversion symmetry is a very non-trivial discrete symmetry of Frobenius manifolds. It was obtained by Dubrovin from one of the elementary Schlesinger transformations of a special ODE associated to a Frobenius manifold. In this paper, we review the Givental group action on Frobenius manifolds in terms of Feynman graphs and obtain an interpretation of the inversion symmetry in terms of the action of the Givental group. We also consider the implication of this interpretation of the inversion symmetry for the Schlesinger transformations and for the Hamiltonians of the associated principle hierarchy.
Physical Theories with Average Symmetry
Roberto C. Alamino
2013-05-03
This Letter probes the existence of physical laws invariant only in average when subjected to some transformation. The concept of a symmetry transformation is broadened to include corruption by random noise and average symmetry is introduced by considering functions which are invariant only in average under these transformations. It is then shown that actions with average symmetry obey a modified version of Noether's Theorem with dissipative currents. The relation of this with possible violations of physical symmetries, as for instance Lorentz invariance in some quantum gravity theories, is briefly commented.
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.
Robert B. Howlett Chapter 1: Symmetry
Howlett, Robert Brian
Aspects of Symmetry Robert B. Howlett #12;Contents Chapter 1: Symmetry §1a An example of abstract symmetry 2 §1b Structure preserving transformations 3 §1c The symmetries of some structured sets 7 §1d Some and inadmissibility proofs 105 Index of notation 110 Index 111 iv #12;1Symmetry Of the following geometrical objects
Generalized SYZ and Homological Mirror Symmetry
Lau, Siu-Cheong
Generalized SYZ and Homological Mirror Symmetry Siu-Cheong Lau Harvard University joint work to construct and understand mirror symmetry - Homological mirror symmetry (category) - Genus-zero closed-string mirror symmetry (Frobenius structure) - Higher-genus mirror symmetry (quantization) - Global mirror
Leptogenesis, ?-? symmetry and ?13
NASA Astrophysics Data System (ADS)
Mohapatra, R. N.; Nasri, S.; Yu, Hai-bo
2005-06-01
We show that in theories where neutrino masses arise from type I see-saw formula with three right-handed neutrinos and where large atmospheric mixing angle owes its origin to an approximate leptonic ?-? interchange symmetry, the primordial lepton asymmetry of the Universe, ?l can be expressed in a simple form in terms of low energy neutrino oscillation parameters as ?l = (a?m?2 + b?mA2?132), where a and b are parameters characterizing high scale physics and are each of order ?10-2 eV-2. We also find that for the case of two right-handed neutrinos, ?l ??132 as a result of which, the observed value of baryon to photon ratio implies a lower limit on ?13. For specific choices of the CP phase ? we find ?13 is predicted to be between 0.10-0.15.
NASA Astrophysics Data System (ADS)
Weber, S. V.; Casey, D. T.; Pino, J. E.; Rowley, D. P.; Smalyuk, V. A.; Spears, B. K.; Tipton, R. E.
2013-10-01
NIF CH ablator symmetry capsules are filled with hydrogen or helium gas. SymCaps have more moderate convergence ratios ~ 15 as opposed to ~ 35 for ignition capsules with DT ice layers, and better agreement has been achieved between simulations and experimental data. We will present modeling of capsules with CD layers and tritium fill, for which we are able to match the dependence of DT yield on recession distance of the CD layer from the gas. We can also match the performance of CH capsules with D3 He fill. The simulations include surface roughness, drive asymmetry, a mock-up of modulation introduced by the tent holding the capsule, and an empirical prescription for ablator-gas atomic mix. NIF CH ablator symmetry capsules are filled with hydrogen or helium gas. SymCaps have more moderate convergence ratios ~ 15 as opposed to ~ 35 for ignition capsules with DT ice layers, and better agreement has been achieved between simulations and experimental data. We will present modeling of capsules with CD layers and tritium fill, for which we are able to match the dependence of DT yield on recession distance of the CD layer from the gas. We can also match the performance of CH capsules with D3 He fill. The simulations include surface roughness, drive asymmetry, a mock-up of modulation introduced by the tent holding the capsule, and an empirical prescription for ablator-gas atomic mix. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
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.)
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…
Algebraic aspects of chiral symmetry
Hosaka, Atsushi
2010-12-28
Algebraic realization of chiral symmetry and its implications are studied. Hadrons are classified by linear representations with mixing when chiral symmetry is spontaneously broken. The axial vector coupling constant is then determined by representation mixing. Phenomenological test for measuring g{sub A} of a nucleon resonance is discussed.
Asymptotic Symmetries and Electromagnetic Memory
Sabrina Pasterski
2015-05-04
Recent investigations into asymptotic symmetries of gauge theory and gravity have illuminated connections between gauge field zero-mode sectors, the corresponding soft factors, and their classically observable counterparts -- so called "memories." Here we complete this triad for the case of large U(1) gauge symmetries at null infinity.
Duality Symmetries in String Theory
Massimo Bianchi
1995-12-21
We review the status of duality symmetries in superstring theories. These discrete symmetries mark the striking differences between theories of pointlike objects and theories of extended objects. They prove to be very helpful in understanding non-perturbative effects in string theories. We will also briefly discuss the strange role played by open strings and their solitons in the emerging scenario.
BRST symmetry of Unimodular Gravity
Upadhyay, S; Bufalo, R
2015-01-01
We derive the BRST symmetry for two versions of unimodular gravity, namely, fully diffeomorphism-invariant unimodular gravity and unimodular gravity with fixed metric determinant. The BRST symmetry is generalized further to the finite field-dependent BRST, in order to establish the connection between different gauges in each of the two versions of unimodular gravity.
NSDL National Science Digital Library
2011-01-01
This website provides text, images, animations, and interactive Java applets to teach bilateral and rotational symmetry. Learners are given drawing and painting challenges as well as recreational activities such as making a virtual kaleidoscope. Clicking on the first button 'Best Symmetry Animation' takes students through the entire sequence.
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
Tomas Andrade; Donald Marolf
2015-08-11
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 Poincar\\'e 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 AdS$_3$ 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.
Asymptotic Symmetries from finite boxes
Andrade, Tomas
2015-01-01
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 Poincar\\'e 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 AdS$_3$ 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.
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 Ångström 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.
PT symmetry and spontaneous symmetry breaking in a microwave billiard.
Bittner, S; Dietz, B; Günther, U; Harney, H L; Miski-Oglu, M; Richter, A; Schäfer, F
2012-01-13
We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP. PMID:22324686
PT symmetry and spontaneous symmetry breaking in a microwave billiard
S. Bittner; B. Dietz; U. Guenther; H. L. Harney; M. Miski-Oglu; A. Richter; F. Schaefer
2011-12-02
We demonstrate the presence of parity-time (PT) symmetry for the non-Hermitian two-state Hamiltonian of a dissipative microwave billiard in the vicinity of an exceptional point (EP). The shape of the billiard depends on two parameters. The Hamiltonian is determined from the measured resonance spectrum on a fine grid in the parameter plane. After applying a purely imaginary diagonal shift to the Hamiltonian, its eigenvalues are either real or complex conjugate on a curve, which passes through the EP. An appropriate basis choice reveals its PT symmetry. Spontaneous symmetry breaking occurs at the EP.
Huang, Chih-Chia; Lai, Wei-Cheng; Tsai, Chia-Yi; Yang, Chih-Hui; Yeh, Chen-Sheng
2012-03-26
A solution approach based on Au(CN)(2)(-) chemistry is reported for the formation of nanoparticles. The covalent character of the Au(CN)(2)(-) precursor was exploited in the formation of sub-10?nm nanospheres (?2.4?nm) and highly monodisperse icosahedral Au nanoparticles (?8?nm) at room temperature in a one-pot aqueous synthesis. The respective spherical and icosahedral Au morphologies can be controlled by either the absence or presence of the polymer polyvinylpyrrolidone (PVP). Using Au(CN)(2)(-) as a metal ion source, our findings suggest that the addition of citrate ions is necessary to enhance the particle formation rate as well as to generate a more homogeneous colloidal dispersion. Because of the presence of oxygen and the operation of a CN(-) etching process associated with Au(CN)(2)(-) complex formation, an interesting reversible formation-dissolution process was observed, which allowed us to repeatedly prepare spherical and icosahedral Au nanoparticles. Time-dependent TEM images and UV/Vis spectra were carefully acquired to study the reversibility of this formation-dissolution process. In view of the accompanying generation of toxic cyanide anions, we have developed a protocol to recycle cyanide in the presence of citrate ions through ferric ferrocyanide formation. After completion of particle formation, the residual solutions containing citrate ions and cyanide ions were processed to stain iron oxide nanoparticles endocytosized in cells. Additionally, the as-prepared 8?nm Au icosahedra could be isolated and grown to larger 57?nm-sized icosahedra using the seed-mediated growth approach. PMID:22344979
Hennig, R. G. [Department of Physics, Ohio State University, Columbus, Ohio 43210, U.S.A. (United States); Department of Physics, Washington University, St. Louis, Missouri 63130, U.S.A. (United States); Majzoub, E. H. [Sandia National Laboratories, Livermore, California 94550, U.S.A. (United States); Department of Physics, Washington University, St. Louis, Missouri 63130, U.S.A. (United States); Kelton, K. F. [Department of Physics, Washington University, St. Louis, Missouri 63130, U.S.A. (United States)
2006-05-01
We present a determination of hydrogen sites in the 1/1 approximant structure of the icosahedral TiZrNi quasicrystal. A Rietveld refinement of neutron and x-ray diffraction data determines the locations of interstitial hydrogen atoms. Density-functional methods calculate the energy of hydrogen on all possible interstitial sites. The Rietveld refinement shows that the hydrogen atoms are preferentially located in the two lowest-energy sites. The filling of the remaining hydrogen sites is dominated by the repulsive hydrogen-hydrogen interaction at short distances.
Spin-orbit-free topological insulators without time-reversal symmetry.
Alexandradinata, A; Fang, Chen; Gilbert, Matthew J; Bernevig, B Andrei
2014-09-12
We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n=3,4, and 6 of the C_{nv} groups, we find the first-known 3D topological insulators without spin-orbit coupling, and with surface modes that are protected only by point groups; i.e., the relevant symmetries are purely crystalline and do not include time reversal. To describe these C_{nv} systems, we introduce the notions of (a) a halved mirror chirality, an integer invariant which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent Chern number, the traditional Thouless-Kohmoto-Nightingale-den Nijs invariant generalized to bent 2D manifolds. We find that a Weyl semimetallic phase intermediates two gapped phases with distinct halved chiralities. In addition to electronic systems without spin-orbit coupling, our findings also apply to intrinsically spinless systems such as photonic crystals and ultracold atoms. PMID:25259991
Hidden Symmetries and Black Holes
Valeri P. Frolov
2009-01-11
The paper contains a brief review of recent results on hidden symmetries in higher dimensional black hole spacetimes. We show how the existence of a principal CKY tensor (that is a closed conformal Killing-Yano 2-form) allows one to generate a `tower' of Killing-Yano and Killing tensors responsible for hidden symmetries. These symmetries imply complete integrability of geodesic equations and the complete separation of variables in the Hamilton-Jacobi, Klein-Gordon, Dirac and gravitational perturbation equations in the general Kerr-NUT-(A)dS metrics. Equations of the parallel transport of frames along geodesics in these spacetimes are also integrable.
Spectral theorem and partial symmetries
Gozdz, A. [University of Maria Curie-Sklodowska, Department of Mathematical Physics, Institute of Physics (Poland); Gozdz, M. [University of Maria Curie-Sklodowska, Department of Complex Systems and Neurodynamics, Institute of Informatics (Poland)
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
Discrete symmetries from hidden sectors
Pascal Anastasopoulos; Robert Richter; A. N. Schellekens
2015-02-09
We study the presence of abelian discrete symmetries in globally consistent orientifold compactifications based on rational conformal field theory. We extend previous work [1] by allowing the discrete symmetries to be a linear combination of U(1) gauge factors of the visible as well as the hidden sector. This more general ansatz significantly increases the probability of finding a discrete symmetry in the low energy effective action. Applied to globally consistent MSSM-like Gepner constructions we find multiple models that allow for matter parity or Baryon triality.
Strangeness and Chiral Symmetry Breaking
Dahiya, Harleen
2010-01-01
The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model ($\\chi$CQM). The role of hidden strangeness component has been investigated for the scalar matrix elements of the nucleon with an emphasis on the meson-nucleon sigma terms. The $\\chi$CQM is able to give a qualitative and quantitative description of the "quark sea" generation through chiral symmetry breaking. The significant contribution of the strangeness is consistent with the recent available experimental observations.
Unification of gauge symmetries in theories with dynamical symmetry breaking
Christensen, Neil D.; Shrock, Robert [C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794 (United States)
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.
Electroweak Symmetry Breaking: With Dynamics
Chivukula, R. Sekhar
2005-03-22
In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
Natural quasicrystal with decagonal symmetry
Bindi, Luca
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al[subscript 71]Ni[subscript 24]Fe[subscript 5], was discovered in the Khatyrka meteorite, a recently ...
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.
Anomalies and discrete chiral symmetries
Michael Creutz
2009-10-06
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.
Linear aggregation beyond isodesmic symmetry
J. R. Henderson
2008-06-20
Exactly solvable models of linear aggregation have been known since Ising's seminal one-dimensional model. This model is defined by a unique nearest-neighbour bond strength that is independent of the length of the cluster; known as isodesmic symmetry. Linear aggregation in real systems has often been associated with broken isodesmic symmetry. Here we show that important examples can be mapped to a class of one-dimensional models that are also exactly solvable.
Symmetry and quaternionic integrable systems
NASA Astrophysics Data System (ADS)
Gaeta, G.; Rodríguez, 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.
Canonoid transformations and master symmetries
José F. Cariñena; Fernando Falceto; Manuel F. Rañada
2013-03-25
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and then the properties of master symmetries are also analyzed. The relations between the existence of constants of motion and the properties of canonoid symmetries is discussed making use of a family of boundary and coboundary operators.
Canonoid transformations and master symmetries
Cariñena, José F; Rañada, Manuel F
2013-01-01
Different types of transformations of a dynamical system, that are compatible with the Hamiltonian structure, are discussed making use of a geometric formalism. Firstly, the case of canonoid transformations is studied with great detail and then the properties of master symmetries are also analyzed. The relations between the existence of constants of motion and the properties of canonoid symmetries is discussed making use of a family of boundary and coboundary operators.
Finiteness, duality and fermionic symmetry
NASA Astrophysics Data System (ADS)
Kawamura, Yoshiharu
2015-06-01
We propose a framework for a new type of finite field theories based on a hidden duality between an ultraviolet and an infrared region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of the duality transformation, and this feature is compatible with models possessing a specific fermionic symmetry. Theories can be tested indirectly by relations among parameters, reflecting underlying symmetries.
Flavored Peccei-Quinn symmetry
Ahn, Y H
2014-01-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a $\\mu$--$\\tau$ power law in the lepton sector, such that relatively large 13 mixing angle with bi-large ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong CP problem, in a way that no domain wall problem occurs, based on $A_{4}\\times U(1)_{X}$ symmetry in a supersymmetric framework. Here we refer to the global $U(1)_X$ symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry". In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under $U(1)_X$, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected each other. So, the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around $10^{12}$ GeV se...
Symmetry in Matrix Models Pierre Flener
Walsh, Toby
Symmetry in Matrix Models Pierre Flener , Alan Frisch ¡ , Brahim Hnich ¢ , Zeynep Kiziltan models, sym- metry is an important feature. We study and generalise symmetry-breaking techniques with symmetry in such models in a uniform way. We thereby reduce the burden on the user of eliminating symmetry
General Symmetry Breaking Constraints Toby Walsh1
Walsh, Toby
General Symmetry Breaking Constraints Toby Walsh1 National ICT Australia and School of CSE constraints for breaking symmetries in constraint satisfaction problems. These constraints can be used to break symmetries acting on variables, values, or both. We also consider symmetry breaking constraints
Combining Symmetry Breaking and Global Constraints
Walsh, Toby
Combining Symmetry Breaking and Global Constraints George Katsirelos, Nina Narodytska, and Toby together lexi- cographical ordering constraints for symmetry breaking with other common global constraints of modeling are symmetry and global constraints. A common and effective method of dealing with symmetry
General Symmetry Breaking Constraints Toby Walsh 1
Walsh, Toby
General Symmetry Breaking Constraints Toby Walsh 1 National ICT Australia and School of CSE constraints for breaking symmetries in constraint satisfaction problems. These constraints can be used to break symmetries acting on variables, values, or both. We also consider symmetry breaking constraints
CHAOTIC ATTRACTORS AND EVOLVING PLANAR SYMMETRY
Reiter, Clifford A.
CHAOTIC ATTRACTORS AND EVOLVING PLANAR SYMMETRY JEFFREY P. DUMONT Lafayette College, Box 7756 of chaotic functions with planar symmetries, we explore evolving attractors from one symmetry type to another. We observe different ways the symmetries evolve and pay attention to those which exhibit degenerate
Discrete R Symmetries: Macrophysics and Microphysics
California at Santa Cruz, University of
Discrete R Symmetries: Macrophysics and Microphysics String Phenomenology 2010, Paris Michael Dine March, 2010 Michael Dine Discrete R Symmetries: Macrophysics and Microphysics #12;Discrete R Symmetries Give rise to accidental, continuous, R symmetries, as required by theorem of Nelson and Seiberg
Exploiting Symmetry In Temporal Logic Model Checking
Edmund M. Clarke; Thomas Filkorn; Somesh Jha
1993-01-01
In practice, finite state concurrent systems often exhibit considerable symmetry. We investigate techniques for reducing the complexity of temporal logic model checking in the presence of symmetry. In particular, we show that symmetry can frequently be used to reduce the size of the state space that must be explored during model checking. In the past, symmetry has been exploited in
O'Hanlon actions by Noether symmetry
F. Darabi
2015-04-14
By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials respecting Noether symmetry in O'Hanlon action in Einstein frame.
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.
Symmetry protected topological orders and the group cohomology of their symmetry group
Wen, Xiao-Gang
Symmetry protected topological orders and the group cohomology of their symmetry group Xie Chen,1 Canada Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G, which can all be smoothly connected to the same trivial product state if we break the symmetry
Structural Symmetry in Membrane Proteins.
Forrest, Lucy R
2015-01-01
Symmetry is a common feature among natural systems, including protein structures. A strong propensity toward symmetric architectures has long been recognized for water-soluble proteins, and this propensity has been rationalized from an evolutionary standpoint. Proteins residing in cellular membranes, however, have traditionally been less amenable to structural studies, and thus the prevalence and significance of symmetry in this important class of molecules is not as well understood. In the past two decades, researchers have made great strides in this area, and these advances have provided exciting insights into the range of architectures adopted by membrane proteins. These structural studies have revealed a similarly strong bias toward symmetric arrangements, which were often unexpected and which occurred despite the restrictions imposed by the membrane environment on the possible symmetry groups. Moreover, membrane proteins disproportionately contain internal structural repeats resulting from duplication and fusion of smaller segments. This article discusses the types and origins of symmetry in membrane proteins and the implications of symmetry for protein function. PMID:26098517
Fearful symmetry in aposematic plants.
Lev-Yadun, Simcha
2011-11-01
Symmetry has been proposed to increase the efficiency of visual aposematic displays in animals, and I suggest that it may also be true for many aposematic spiny or poisonous plants. For instance, in the very spiny plant taxa cacti, Aloe sp., Agave sp. and Euphorbia sp., which have been proposed to be aposematic because of their colorful spine system, the shoots, and in cacti, the spiny fruits as well, are usually radially symmetric. Moreover, in the radial symmetric shoots of Agave and Aloe their individual spiny leaves are also bilaterally symmetric. Spiny or poisonous fruits of various other taxa, the symmetric spiny leaf rosettes and flowering spiny heads of many Near Eastern species of the Asteraceae and other taxa, and poisonous colorful flowers in taxa that were proposed to be aposematic are also symmetric. Thus, in plants, like in animals, symmetry seems to be commonly associated with visual aposematism and probably contributes to its effectiveness. Symmetry may stem from developmental constraints, or like in flowers, have other signaling functions. However, because of the better perception of symmetry by animals it may exploit inherited modes of animal sensing that probably result in paying more attention to symmetric shapes. All these possible alternatives do not negate the probable deterring role of symmetry in plant aposematism. PMID:22067106
C20 to C60 fullerenes: combinatorial types and symmetries.
Voytekhovsky, Y L; Stepenshchikov, D G
2001-11-01
A figure giving the point groups for all combinatorially non-isomorphic C20 to C60 fullerenes (5770 in common) is contributed. The fullerenes of 6 to 120 automorphism group orders (80 in common) are drawn in the Shlegel projections and characterized by the point groups. PMID:11679707
Symmetry protected topological orders and the group cohomology of their symmetry group
Chen, Xie
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase ...
Symmetries in geometrical optics: theory
NASA Astrophysics Data System (ADS)
Szilagyi, M.; Mui, P. H.
1995-12-01
A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [J. Opt. Soc. Am. 12, XXXX (1995)]. Copyright (c) 1995 Optical Society of America
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.
Flavored Peccei-Quinn symmetry
NASA Astrophysics Data System (ADS)
Ahn, Y. H.
2015-03-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a ? - ? power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4×U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the ? - ? power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma?2.53 ×1 0-5 eV and the axion coupling to photon ga ? ??1.33 ×1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.
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).
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.
Order Symmetry of Weak Measurements
Lars M. Johansen; Pier A. Mello
2009-07-30
Weak values are usually associated with weak measurements of an observable on a pre- and post-selected ensemble. We show that more generally, weak values are proportional to the correlation between two pointers in a successive measurement. We show that this generalized concept of weak measurements displays a symmetry under reversal of measurement order. We show that the conditions for order symmetry are the same as in classical mechanics. We also find that the imaginary part of the weak value has a counterpart in classical mechanics. This scheme suggests new experimental possibilities.
Spontaneous violation of mirror symmetry
Dyatlov, Igor T
2015-01-01
A symmetry violation model is considered for a system that can spontaneously choose between identical states which differ from each other only in weak properties (R-L). Such mirror symmetry allows reproduction of observed qualitative properties of quark and lepton mixing matrices. The lepton mixing matrix evidences in this case in favor of the inverse mass spectrum and the Dirac nature of SM neutrino. Notwithstanding the Dirac properties of neutrino, an exchange of lepton numbers such as $e^{-}+\\mu^{+}\\rightarrow e^{+}+\\mu^{-}$ is possible but with only leptons participating in the process.
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil
2008-11-23
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
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.
General-Purpose Icosahedral Structure
NASA Technical Reports Server (NTRS)
Evans, J.
1984-01-01
Scheme based on geodesic sphere approximated by regular icosahedron. Structure rigid and lightweight. Allows access to all subsystems and equipment from outside. Regular icosahedron constructed from triangular panels. Five panels meeting at each corner all rigidly attached to fivesided adapter. Strengthened version useful on Earth for rapidly-erectable temporary shelters, industrial structures, or playground equipment.
Charge Symmetry at the Partonic Level
J.T. Londergan, J.-C. Peng, A.W. Thomas
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Charge Symmetry at the Partonic Level
J. T. Londergan; J. C. Peng; A. W. Thomas
2009-07-14
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
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 ? 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
NASA Astrophysics Data System (ADS)
Gorsky, A.; Krikun, A.
2014-07-01
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe's formula for the baryon mass.
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…
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…
Exploiting Symmetry on Parallel Architectures.
NASA Astrophysics Data System (ADS)
Stiller, Lewis Benjamin
1995-01-01
This thesis describes techniques for the design of parallel programs that solve well-structured problems with inherent symmetry. Part I demonstrates the reduction of such problems to generalized matrix multiplication by a group-equivariant matrix. Fast techniques for this multiplication are described, including factorization, orbit decomposition, and Fourier transforms over finite groups. Our algorithms entail interaction between two symmetry groups: one arising at the software level from the problem's symmetry and the other arising at the hardware level from the processors' communication network. Part II illustrates the applicability of our symmetry -exploitation techniques by presenting a series of case studies of the design and implementation of parallel programs. First, a parallel program that solves chess endgames by factorization of an associated dihedral group-equivariant matrix is described. This code runs faster than previous serial programs, and discovered it a number of results. Second, parallel algorithms for Fourier transforms for finite groups are developed, and preliminary parallel implementations for group transforms of dihedral and of symmetric groups are described. Applications in learning, vision, pattern recognition, and statistics are proposed. Third, parallel implementations solving several computational science problems are described, including the direct n-body problem, convolutions arising from molecular biology, and some communication primitives such as broadcast and reduce. Some of our implementations ran orders of magnitude faster than previous techniques, and were used in the investigation of various physical phenomena.
Tetraquark Spectroscopy: A Symmetry Analysis
J. Vijande; A. Valcarce
2009-12-18
We present a detailed analysis of the symmetry properties of a four-quark wave function and its solution by means of a variational approach for simple Hamiltonians. We discuss several examples in the light and heavy-light meson sector.
Symmetry in American Folk Art.
ERIC Educational Resources Information Center
Zaslavsky, Claudia
1990-01-01
Described is how folk art can be used to teach spatial thinking and symmetry. Activities are open-ended and can be used for all age groups and levels of development. Mathematics is integrated with the study of culture, art, and history in these activities. (KR)
The Geometry of Reflectance Symmetries.
Tan, Ping; Quan, Long; Zickler, Todd
2011-02-17
Different materials reflect light in different ways, and this reflectance interacts with shape, lighting, and viewpoint to determine an object's image. Common materials exhibit diverse reflectance effects, and this is a significant source of difficulty for image analysis. One strategy for dealing with this diversity is to build computational tools that exploit reflectance symmetries, such as reciprocity and isotropy, that are exhibited by broad classes of materials. By building tools that exploit these symmetries, one can create vision systems that are more likely to succeed in real-world, non-Lambertian environments. In this paper, we develop a framework for representing and exploiting reflectance symmetries. We analyze the conditions for distinct surface points to have local view and lighting conditions that are equivalent under these symmetries, and we represent these conditions in terms of the geometric structure they induce on the Gaussian sphere and its abstraction, the projective plane. We also study the behavior of these structures under perturbations of surface shape and explore applications to both calibrated and un-calibrated photometric stereo. PMID:21339528
Monster symmetry and extremal CFTs
NASA Astrophysics Data System (ADS)
Gaiotto, Davide
2012-11-01
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
Monster symmetry and Extremal CFTs
Davide Gaiotto
2008-01-07
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in $AdS_3$. We prove that no $c=48$ extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
From symmetries to number theory
Tempesta, P., E-mail: p.tempesta@fis.ucm.e [Universidad Complutense, Departamento de Fisica Teorica II, Facultad de Fisicas (Spain)
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
Strong coupling electroweak symmetry breaking
Barklow, T.L. [Stanford Linear Accelerator Center, Menlo Park, CA (United States); Burdman, G. [Univ. of Wisconsin, Madison, WI (United States). Dept. of Physics; Chivukula, R.S. [Boston Univ., MA (United States). Dept. of Physics
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. [School of Mathematics and Physics, University of Queensland, QLD 4072 (Australia)
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.
Neutrino Mixing from CP Symmetry
Peng Chen; Chang-Yuan Yao; Gui-Jun Ding
2015-07-13
The neutrino mass matrix has remnant CP symmetry expressed in terms of the lepton mixing matrix, and vice versa the remnant CP transformations allow us to reconstruct the mixing matrix. We study the scenario that all the four remnant CP transformations are preserved by the neutrino mass matrix. The most general parameterization of remnant CP transformations is presented. The lepton mixing matrix is completely fixed by the remnant CP, and its explicit form is derived. The necessary and sufficient condition for conserved Dirac CP violating phase is found. If the Klein four flavor symmetry generated by the postulated remnant CP transformations arises from a finite flavor symmetry group, the phenomenologically viable lepton flavor mixing would be the trimaximal pattern, both Dirac CP phase $\\delta_{CP}$ and Majorana phase $\\alpha_{31}$ are either $0$ or $\\pi$ while another Majorana phase $\\alpha_{21}$ is a rational multiple of $\\pi$. These general results are confirmed to be true in the case that the finite flavor symmetry group is $\\Delta(6n^2)$.
Planar Homological Mirror Symmetry II
Konishi, Eiji
2008-01-01
In the planar limit of B-model open string field theory in the Dijkgraaf-Vafa context, an enlarged cyclic symmetry is formulated by introducing the idea of homotopy Lie categories ($L_{\\infty}$ categories) on a set of sequences of holomorphic functions (prepotentials with Whitham deformations) following the work of Itoyama and Kanno.
Book Reviews A Fearful Symmetry
Denardo, Dale
, and before the report by the Save The Tiger Fund and its partners, Worldwide Fund for Nature, WildlifeBook Reviews A Fearful Symmetry Tiger Bone & Rhino Horn: the Destruction of Wildlife for Tradi for understand- ing a new and rapidly unfolding effort to stem illegal wildlife trade. Accord- ing to the U
Kohn's theorem and Galilean symmetry
NASA Astrophysics Data System (ADS)
Zhang, P.-M.; Horvathy, P. A.
2011-08-01
The relation between the separability of a system of charged particles in a uniform magnetic field and Galilean symmetry is revisited using Duval's “Bargmann framework”. If the charge-to-mass ratios of the particles are identical, ea/ma=? for all particles, then the Bargmann space of the magnetic system is isometric to that of an anisotropic harmonic oscillator. Assuming that the particles interact through a potential which only depends on their relative distances, the system splits into one representing the center of mass plus a decoupled internal part, and can be mapped further into an isolated system using Niederer's transformation. Conversely, the manifest Galilean boost symmetry of the isolated system can be “imported” to the oscillator and to the magnetic systems, respectively, to yield the symmetry used by Gibbons and Pope to prove the separability. For vanishing interaction potential the isolated system is free and our procedure endows all our systems with a hidden Schrödinger symmetry, augmented with independent internal rotations. All these properties follow from the cohomological structure of the Galilei group, as explained by Souriau's “décomposition barycentrique”.
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…
Honours Project Symmetry Classifications of
Aslaksen, Helmer
's periodic tilings in Table 1 (see appendix). Firstly, it aims to provide the readers an overview in Table 1 (appendix). Therefore, finally, given an Escher's periodic tiling the reader would be ableHonours Project Symmetry Classifications of Periodic Tilings Escher's drawings Name: Kavitha d
Symmetry Classes of Disordered Fermions
P. Heinzner; A. Huckleberry; M. R. Zirnbauer
2005-01-01
Building upon Dyson’s fundamental 1962 article known in random-matrix theory as the threefold way, we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important physical examples are afforded by noninteracting quasiparticles in disordered metals and superconductors, and by relativistic fermions in random gauge field backgrounds.
SYMMETRY AND HETEROGENEITY IN HIGH
physics is needed for the design of room temperature superconductors, for controlling the decoherenceSYMMETRY AND HETEROGENEITY IN HIGH TEMPERATURE SUPERCONDUCTORS #12;#12;Kluwer Academic Publishers AND HETEROGENEITY IN HIGH TEMPERATURE SUPERCONDUCTORS edited by Antonio Bianconi University of Rome "La Sapienza
SYMMETRIES OF QUASICRYSTALS Charles Radin *
SYMMETRIES OF QUASICRYSTALS by Charles Radin * Department of Mathematics, University of Texas, Austin, TX 78712 Abstract We consider tiling models of ``round quasicrystals'' which would have supported in part by NSF Grant No. DMSÂ9531584 and Texas ARP Grant 003658Â152 #12; Quasicrystals were
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.
Inflation, symmetry, and B-modes
Hertzberg, Mark Peter
We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing ...
Testing Lorentz symmetry with atoms and Light
Neil Russell
2011-09-04
This article reports on the Fifth Meeting on CPT and Lorentz Symmetry, CPT'10, held at the end of June 2010 in Bloomington, Indiana, USA. The focus is on recent tests of Lorentz symmetry using atomic and optical physics.
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.
Embedded Representations and Quasi-Dynamical Symmetry
Rowe, D J
2011-01-01
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical" symmetry. The existence of quasi-dynamical symmetry in physical systems and its significance for understanding collective dynamics in complex nuclei is explained in terms of the precise mathematical concept of an "embedded representation". Examples are given which exhibit quasi-dynamical symmetry to a remarkably high degree. Understanding this unusual symmetry and why it occurs, is important for recognizing why dynamical symmetries appear to be much moreprevalent than they would otherwise have any right to be and for interpreting the implications of a model's successes. We indicate when quasi-dynamical symmetry is expected to apply and present a challenge as to how best to make use of this potentially powerful algebraic structure.
Notes on generalized global symmetries in QFT
Sharpe, E
2015-01-01
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.
Sato, K.; Kobayashi, Y.; Arinuma, K.; Kanazawa, I.; Tamura, R.; Shibuya, T.; Takeuchi, S. [National Institute of Advanced Industrial Science and Technology (AIST), 1-1-1 Higashi, Tsukuba, Ibaraki 305-8565 (Japan); Department of Physics, Tokyo Gakugei University, 4-1-1 Koganei, Tokyo 184-8501 (Japan); Department of Materials Science and Technology, Tokyo University of Science, Noda, Chiba 278-8501 (Japan)
2004-09-01
Previously, we showed that the icosahedral quasicrystal Cd{sub 5.7}Yb possesses similar structural vacancies to those in its cubic 1/1-approximant Cd{sub 6}Yb by positron lifetime measurements [K. Sato, H. Uchiyama, K. Arinuma, I. Kanazawa, R. Tamura, T. Shibuya, and S. Takeuchi, Phys. Rev. B 66, 052201 (2002)]. In the present paper, the local chemical environment around the structural vacancies is specifically investigated by two-detector coincident Doppler broadening spectroscopy. Essentially the same annihilation sites with Cd-rich chemical environments are identified for the two phases. This strongly suggests that the quasicrystal is composed of the same cluster as the approximant. The difference in the structural vacancy density between the two phases is examined by positron diffusion experiments using a slow positron beam. The structural vacancy density in the quasicrystal is found to be 20% lower than that in the approximant.
T-duality versus Gauge Symmetry
Olaf Hohm
2011-01-18
We review the recently constructed `double field theory' which introduces in addition to the conventional coordinates associated to momentum modes coordinates associated to winding modes. Thereby, T-duality becomes a global symmetry of the theory, which can be viewed as an `O(D,D) covariantization' of the low-energy effective space-time action of closed string theory. We discuss its symmetries with a special emphasis on the relation between global duality symmetries and local gauge symmetries.
R-symmetry breaking versus supersymmetry breaking
Ann E. Nelson; Nathan Seiberg
1994-01-01
We point out a connection between R-symmetry and supersymmetry breaking. We show that the existence of an R-symmetry is a necessary condition for supersymmetry breaking and a spontaneously broken R-symmetry is a sufficient condition provided two conditions are satisfied. These conditions are: genericity, i.e. the effective lagrangian is a generic lagrangian consistent with the symmetries of the theory (no fine
Tunneling Through Quantum Dots with Discrete Symmetries
Yshai Avishai; Konstantin Kikoin
2009-01-01
We describe in this short review the influence of discrete symmetries in\\u000acomplex quantum dots on the Kondo co-tunneling through these nano-objects.\\u000aThese discrete symmetries stem from the geometrical structure of the tunneling\\u000adevices (e.g spatial symmetry of multivalley quantum dot in a tunneling contact\\u000awith leads). They affect the dynamical symmetry of spin multiplets\\u000acharacterizing the ground state and
Tunneling through Quantum Dots with Discrete Symmetries
Yshai Avishai; Konstantin Kikoin
2008-01-01
We describe in this short review the influence of discrete symmetries in complex quantum dots on the Kondo co-tunneling through these nano-objects. These discrete symmetries stem from the geometrical structure of the tunneling devices (e.g spatial symmetry of multivalley quantum dot in a tunneling contact with leads). They affect the dynamical symmetry of spin multiplets characterizing the ground state and
Quasicrystalline decagonal and related crystalline approximant structures
Daulton, T.L.
1992-01-01
The icosahedral phase is a condensed phase of matter that has a noncrystallographic point group with long range orientational and translational order but lacks strict periodicity. Periodicity is replaced in all dimensions by a mathematically well defined quasiperiodicity. Two and one dimensional quasicrystals also form in the same metallic-alloy systems as does the icosahedral quasicrystal. The decagonal phase is an example of a two-dimensional quasicrystal that occurs with dicrete one dimensional periodicites of approximately 4 [angstrom] x (1, 2, 3, and 4). The different periodicity decagonal phases are studied with an analytical transmission electron microscope (TEM), using high resolution electron microscopy (HREM), convergent beam electron diffraction (CBED), selected area diffraction (SAD), energy-dispersive x-ray spectroscopy (EDXS), and electron energy-loss spectroscopy (EELS). X-ray powder diffraction studies are also presented. Closely related crystalline structures that approximate well the noncrystallographic symmetries of quasicrystals, were also studied. These crystals also exhibit the same discrete periodicities present in the decagonal phases. The striking similarities between the different periodicity decagonal phases, the icosahedral phase, and the crystalline approximant structures suggest that they all contain similar fundamental atomic clusters. Further, the discrete decagonal periodicities observed suggest that the decagonal structures are formed by different stacking sequences of similar atomic clusters. An atomic model that is based on distorted icosahedrally symmetric clusters that are stacked with different interpenentration depths to form the different periodicity decagonal phases is presented.
From Additional Symmetries to Linearization of Virasoro Symmetries
Chao-Zhong Wu
2011-12-01
We construct the additional symmetries and derive the Adler-Shiota-van Moerbeke formula for the two-component BKP hierarchy. We also show that the Drinfeld-Sokolov hierarchies of type D, which are reduced from the two-component BKP hierarchy, possess symmetries written as the action of a series of linear 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.
General Formalism For the BRST Symmetry
Suhail Ahmad
2013-09-20
In this paper we will discuss Faddeev-Popov method for field theories with a gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory.
Symmetry in Chinese Arts Yip Lixia, Sabrina
Aslaksen, Helmer
Symmetry in Chinese Arts Done by: Group 3 Lim Li Yan Yip Lixia, Sabrina Lee Weitian, Ivan Zhong Shengmin Goh Yoon Keong 1 #12;2 CONTENTS · Introduction · Symmetry in Chinese Literature · Chinese Paper Cuttings · Symmetry in Chinese buildings · Chinese Music · Conclusion · Bibliography #12;3 Introduction
Symmetry violation in nuclei Vladimir Gudkov1
Symmetry violation in nuclei Vladimir Gudkov1 1 Department of Physics and Astronomy, University of South Carolina, Columbia, SC, 29208 The study of symmetry violation in nuclei, including parity (PV of the fundamental symmetries tests and a search for new physics is underlined in the third recommendation
Horizontal Symmetry from the Bottom Up
C. S. Lam
2010-03-02
A general method to derive horizontal symmetry from a mixing matrix is reviewed. The technique has been applied to deduce leptonic symmetry from the tri-bimaximal neutrino mixing matrix and three of its variations. The question of how the quark mixing can be accommodated within the leptonic symmetry group is discussed, including in this connection an example based on the group $D_4$.
Symmetry Breaking with SetVariables
Walsh, Toby
Symmetry Breaking with SetVariables Toby Walsh NICTA and UNSW #12;Variables · Finite domain · Equivalent to BC (GAC) on characteristic function representation #12;Why use set vars? · Eliminate symmetry playing in group i on week j #12;Why use set vars? · Eliminates (some) symmetry in a problem · Still may
Symmetry in Nature Unit code: MATH45082
Sidorov, Nikita
MATH45082 Symmetry in Nature Unit code: MATH45082 Credit Rating: 15 Unit level: Level 4 Teaching Prerequisite MATH20201 - Algebraic Structures 1 (Compulsory) Aims To develop an understanding of symmetry. Overview Symmetry arises frequently, both in Nature and in Mathematical models of Nature
Symmetry in Nature Unit code: MATH35082
Sidorov, Nikita
MATH35082 Symmetry in Nature Unit code: MATH35082 Credit Rating: 10 Unit level: Level 3 Teaching-requisites Aims To develop an understanding of symmetry as it arises in nature, and to develop the mathematical will be able to: · understand and analyze symmetry from a mathematical perspective · apply the orbit
Deep Symmetry Networks Robert Gens Pedro Domingos
Domingos, Pedro
Deep Symmetry Networks Robert Gens Pedro Domingos Department of Computer Science and Engineering by symmetry groups, sets of composable transformations that preserve object identity. Convolutional neural. In this paper, we introduce deep symmetry networks (symnets), a generalization of convnets that forms feature
GEOMETRIC PHASES IN DISSIPATIVE SYSTEMS WITH SYMMETRY
Andersson, Sean B.
GEOMETRIC PHASES IN DISSIPATIVE SYSTEMS WITH SYMMETRY Sean B. Andersson 1 Division of Engineering with symmetry can exhibit a geometric phase effect wherein an adiabatic variation of a parameter drives a shift in the symmetry direction. Viewing the parameter as a control variable, the effect may be useful in the parametric
Evidential Symmetry and Mushy Credence Roger White
Fitelson, Branden
1 Evidential Symmetry and Mushy Credence Roger White MIT rog@mit.edu draft 4/07 The Principle should not always be sharp. 1. Evidential Symmetry Let's say that Propositions p and q are evidentially), Gillies (2000), North (ms.), and Sober (2003). #12;2 There are different ways that evidential symmetry can
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
? - ? Symmetry, Nonzero ?13, and CP Violation
NASA Astrophysics Data System (ADS)
Damanik, Asan
2015-03-01
If we impose the ? - ? symmetry, as a constraint into neutrino mass matrix, one find that the Jarlskog rephasing invariant: JCP = 0 which implies that CP violation cannot be accommodated in the ? - ? symmetry scheme. By introducing a small parameter x that perturb the neutrino mass matrix with ? - ? symmetry with trace of neutrino mass matrix remain constant, we can obtain JCP ? 0 and consequently ?13 ? 0.
Dressing Symmetries of Holomorphic BF Theories
T. A. Ivanova; A. D. Popov
2000-02-15
We consider holomorphic BF theories, their solutions and symmetries. The equivalence of Cech and Dolbeault descriptions of holomorphic bundles is used to develop a method for calculating hidden (nonlocal) symmetries of holomorphic BF theories. A special cohomological symmetry group and its action on the solution space are described.
Man Sik Park Symmetry and Separability In
Man Sik Park Symmetry and Separability In Spatial-Temporal Processes Man Sik Park, Montserrat Fuentes Symmetry and Separability In Spatial-Temporal Processes 1 #12;Man Sik Park Motivation · In general-pollution data. Symmetry and Separability In Spatial-Temporal Processes 2 #12;Man Sik Park Research Objectives 1
Frieze and Wallpaper Symmetry Groups Classification under
- cussed. #12;1 Motivation Any subset S of the Euclidean space Rn is associated with a symmetry groupFrieze and Wallpaper Symmetry Groups Classification under Affine and Perspective Distortion Yanxi repeated patterns in terms of their respective symmetry groups -- the well-known seven Frieze groups and 17
Man Sik Park Symmetry and Separability In
Man Sik Park Symmetry and Separability In Spatial-Temporal Processes Man Sik Park, Montserrat Fuentes Symmetry and Separability In Spatial-Temporal Processes 1 #12;Man Sik Park Motivation Â· In general-pollution data. Symmetry and Separability In Spatial-Temporal Processes 2 #12;Man Sik Park Research Objectives 1
Instantaneous Symmetry and Symmetry on Average in the CouetteTaylor and Faraday
Instantaneous Symmetry and Symmetry on Average in the CouetteTaylor and Faraday Experiments November 16, 1993 Abstract We describe some recent results on symmetry of attractors for dy namical systems with symmetry and consider the implications for the CouetteTaylor experiment and the Faraday
Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry
NASA Astrophysics Data System (ADS)
Kochetov, Bogdan A.
2014-06-01
In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein-Gordon-Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein-Gordon-Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.
Spinor structure and internal symmetries
Varlamov, V V
2014-01-01
Space-time and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries $P$, $T$ and their combination $PT$ are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation $C$ is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation $C$ allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Quotient representations of the Lorentz group and their possible relations with $P$- and $CP$-violations are considered. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A ce...
Mirror Symmetry And Loop Operators
Benjamin Assel; Jaume Gomis
2015-06-04
Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.
Adding CP to flavour symmetries
Varzielas, I de Medeiros
2015-01-01
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 $\\Delta(27)$. I comment on the consequences of adding a specific CP symmetry to a Lagrangian and distinguish cases where several $\\Delta(27)$ 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.
Mirror Symmetry And Loop Operators
Assel, Benjamin
2015-01-01
Wilson loops in gauge theories pose a fundamental challenge for dualities. Wilson loops are labeled by a representation of the gauge group and should map under duality to loop operators labeled by the same data, yet generically, dual theories have completely different gauge groups. In this paper we resolve this conundrum for three dimensional mirror symmetry. We show that Wilson loops are exchanged under mirror symmetry with Vortex loop operators, whose microscopic definition in terms of a supersymmetric quantum mechanics coupled to the theory encode in a non-trivial way a representation of the original gauge group, despite that the gauge groups of mirror theories can be radically different. Our predictions for the mirror map, which we derive guided by branes in string theory, are confirmed by the computation of the exact expectation value of Wilson and Vortex loop operators on the three-sphere.
Measuring complexity through average symmetry
NASA Astrophysics Data System (ADS)
Alamino, Roberto C.
2015-07-01
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle—measuring the average amount of symmetry broken by an object. It attributes low (although different) complexity to either deterministic or random homogeneous densities and higher complexity to the intermediate cases. This new measure is easily computable, breaks the coarse graining paradigm and can be straightforwardly generalized, including to continuous cases and general networks. By applying this measure to a series of objects, it is shown that it can be consistently used for both small scale structures with exact symmetry breaking and large scale patterns, for which, differently from similar measures, it consistently discriminates between repetitive patterns, random configurations and self-similar structures
Tensionless Strings from Worldsheet Symmetries
Bagchi, Arjun; Parekh, Pulastya
2015-01-01
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.
No Classicalization Beyond Spherical Symmetry
Ratindranath Akhoury; Shinji Mukohyama; Ryo Saotome
2011-09-17
We point out that a field theory that exhibits the classicalization phenomenon for perfect spherical symmetry ceases to do so when the spherical symmetry is significantly relaxed. We first investigate a small non-spherical deformation and show that the classicalization radius tends to decrease in a region where a shell made of the field is slightly flattened. Next, in order to describe a sufficiently large flattened region, we consider a high-energy collision of planar shells and show that the system never classicalizes before reaching sub-cutoff lengths. This no-go result is further strengthened by an analysis of a small non-planar deformation. Finally, we show that the shape of a scattered planar wave is UV sensitive.
Symmetry restoration and quantumness reestablishment
Guo-Mo Zeng; Lian-Ao Wu; Hai-Jun Xing
2014-09-18
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.
Symmetry restoration and quantumness reestablishment
NASA Astrophysics Data System (ADS)
Zeng, Guo-Mo; Wu, Lian-Ao; Xing, Hai-Jun
2014-09-01
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.
Dark Matter and Global Symmetries
Yann Mambrini; Stefano Profumo; Farinaldo S. Queiroz
2015-08-26
General considerations in general relativity and quantum mechanics rule out global symmetries in the context of any consistent theory of quantum gravity. Motivated by this, we derive stringent and robust bounds from gamma-ray, X-ray, cosmic ray, neutrino and CMB data on models that invoke global symmetries to stabilize the dark matter particle. Under realistic assumptions we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime. We then specialize our analysis and apply our bounds to specific models such as the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. In the supplemental material we derive robust, updated model-independent limits on the dark matter lifetime.
Dark Matter and Global Symmetries
Mambrini, Yann; Queiroz, Farinaldo S
2015-01-01
General considerations in general relativity and quantum mechanics rule out global symmetries in the context of any consistent theory of quantum gravity. Motivated by this, we derive stringent and robust bounds from gamma-ray, X-ray, cosmic ray, neutrino and CMB data on models that invoke global symmetries to stabilize the dark matter particle. Under realistic assumptions we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime. We then specialize our analysis and apply our bounds to specific models such as the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. In the supplemental material we derive robust, updated model-independent limits on the dark matter lifetime.
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.
Dark energy from conformal symmetry breaking
F. Darabi
2013-06-18
The breakdown of conformal symmetry in a conformally invariant scalar-tensor gravitational model is revisited in the cosmological context. Although the old scenario of conformal symmetry breaking in cosmology containing scalar field has already been used in many earlier works, it seems that no special attention has been paid for the investigation on the possible connection between the breakdown of conformal symmetry and the existence of dark energy. In this paper, it is shown that the old scenario of conformal symmetry breaking in cosmology, if properly interpreted, not only has a potential ability to describe the origin of dark energy as a symmetry breaking effect, but also may resolve the coincidence problem.
Entanglement and symmetry in permutation symmetric states
Damian J. H. Markham
2011-07-01
We investigate the relationship between multipartite entanglement and symmetry, focusing on permutation symmetric states. We use the Majorana representation, where these states correspond to points on a sphere. Symmetry of the representation under rotation is equivalent to symmetry of the states under products of local unitaries. The geometric measure of entanglement is thus phrased entirely as a geometric optimisation, and a condition for the equivalence of entanglement measures written in terms of point symmetries. Finally we see that different symmetries of the states correspond to different types of entanglement with respect to SLOCC interconvertibility.
Symmetry in Integer Linear Programming
François Margot
\\u000a An integer linear program (ILP) is symmetric if its variables can be permuted without changing the structure of the problem.\\u000a Areas where symmetric ILPs arise range from applied settings (scheduling on identical machines), to combinatorics (code construction),\\u000a and to statistics (statistical designs construction). Relatively small symmetric ILPs are extremely difficult to solve using\\u000a branch-and-cut codes oblivious to the symmetry in
?-symmetry, supersymmetry and intersecting branes
E A Bergshoeff; Renata E Kallosh; Tomas Ortín; G J Papadopoulos
1997-01-01
We present a new form of ?-symmetry transformations for D-branes in which the dependence on the Born-Infeld field strength is expressed as a relative rotation on the left- and right-moving fields with opposite parameters. Then, we apply this result to investigate the supersymmetry preserved by certain intersecting brane configurations at arbitrary angles and with non-vanishing constant Born-Infeld fields. We also
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.
Symmetries in Lagrangian Field Theory
Lucía Búa; Ioan Bucataru; Manuel de León; Modesto Salgado; Silvia Vilariño
2015-02-03
By generalizing 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 $J^1\\pi$ of a fiber bundle $\\pi:E\\to {\\mathbb R}^k$ where ${\\mathbb R}^k$ is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether Theorem is proved.
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
Clifford modules and symmetries of topological insulators
Abramovici, Gilles
2011-01-01
We complete the classification of symmetry constraints on gapped quadratic fermion hamiltonians proposed by Kitaev. The symmetry group is supposed compact and can include arbitrary unitary or antiunitary operators in the Fock space that conserve the algebra of quadratic observables. We analyze the multiplicity spaces of {\\em real} irreducible representations of unitary symmetries in the Nambu space. The joint action of intertwining operators and antiunitary symmetries provides these spaces with the structure of Clifford module: we prove a one-to-one correspondence between the ten Altland-Zirnbauer symmetry classes of fermion systems and the ten Morita equivalence classes of real and complex Clifford algebras. The antiunitary operators, which occur in seven classes, are projectively represented in the Nambu space by unitary "chiral symmetries". The space of gapped symmetric hamiltonians is homotopically equivalent to the product of classifying spaces indexed by the dual object of the group of unitary symmetrie...
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.
Faddeev-Jackiw approach to hidden symmetries
Wotzasek, C
1994-01-01
The study of hidden symmetries within Dirac's formalism does not possess a systematic procedure due to the lack of first-class constraints to act as symmetry generators. On the other hand, in the Faddeev-Jackiw approach, gauge and reparametrization symmetries are generated by the null eigenvectors of the sympletic matrix and not by constraints, suggesting the possibility of dealing systematically with hidden symmetries through this formalism. It is shown in this paper that indeed hidden symmetries of noninvariant or gauge fixed systems are equally well described by null eigenvectors of the sympletic matrix, just as the explicit invariances. The Faddeev-Jackiw approach therefore provide a systematic algorithm for treating all sorts of symmetries in an unified way. This technique is illustrated here by the SL(2,R) Kac-Moody current algebra of the 2-D induced gravity proposed by Polyakov, which is a hidden symmetry in the canonical approach of constrained systems via Dirac's method, after conformal and reparamet...
Symmetries in nuclei: New methods and applications
NASA Astrophysics Data System (ADS)
Caprio, Mark A.
2011-04-01
When a symmetry is a ``good'' symmetry of the nuclear system, as in the dynamical symmetries of the shell model and interacting boson model, this symmetry can directly give the spectroscopic properties of the nucleus, without the need for involved calculations. However, even if a symmetry is strongly broken, it nonetheless provides a calculational tool, classifying the basis states used in a full computational treatment of the many-body problem and greatly simplifying the underlying computational machinery. The symmetry then serves as the foundation for a physically meaningful truncation scheme for the calculation. This talk will provide an introduction to new applications of symmetry approaches to the nuclear problem, including the required mathematical developments. Supported by the US DOE under grant DE-FG02-95ER-40934 and by the Research Corporation for Science Advancement under a Cottrell Scholar Award.
Type II hidden symmetries through weak symmetries for some wave equations
NASA Astrophysics Data System (ADS)
Gandarias, M. L.; Bruzón, M. S.
2010-02-01
The Type II hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a Lie-point symmetry. In [Gandarias RML. Type-II hidden symmetries through weak symmetries for nonlinear partial differential equations. J Math Anal Appl 2008;348:752-9] it was shown that the provenance of the Type II Lie point hidden symmetries found for differential equations can be explained by considering weak symmetries or conditional symmetries of the original PDE. In this paper we analyze the connection between one of the methods analyzed in [Abraham-Shrauner B, Govinder KS. Provenance of Type II hidden symmetries from nonlinear partial differential equations. J Nonlin Math Phys 2006;13:612-22] and the weak symmetries of some partial differential equations in order to determine the source of these hidden symmetries. We have considered some of the models presented in [Abraham-Shrauner B, Govinder KS. Provenance of Type II hidden symmetries from nonlinear partial differential equations. J Nonlin Math Phys 2006;13:612-22], as well as the linear two-dimensional and three-dimensional wave equations [Abraham-Shrauner B, Govinder KS, Arrigo JA. Type II hidden symmetries of the linear 2D and 3D wave equations. J h Phys A Math Theor 2006;39:5739-47].
Symmetry, Defects, and Gauging of Topological Phases
Maissam Barkeshli; Parsa Bonderson; Meng Cheng; Zhenghan Wang
2014-11-12
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the topological symmetry group, which characterizes the symmetry of the emergent topological quantum numbers of a topological phase $\\mathcal{C}$, and we describe its relation with the microscopic symmetry of the underlying physical system. We derive a general framework to classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter $\\mathcal{C}$ with symmetry group $G$. The algebraic theory of the defects, known as a $G$-crossed braided tensor category $\\mathcal{C}_{G}^{\\times}$, allows one to compute many properties, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes, braiding exchange transformations, a generalized Verlinde formula for the defects, and modular transformations of the $G$-crossed extensions of topological phases. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic $G$-defects are turned into deconfined quasiparticle excitations, which results in a different topological phase $\\mathcal{C}/G$. A number of instructive and/or physically relevant examples are studied in detail.
Symmetry, Defects, and Gauging of Topological Phases
NASA Astrophysics Data System (ADS)
Bonderson, Parsa; Barkeshli, Maissam; Cheng, Meng; Wang, Zhenghan
2015-03-01
We examine the interplay of symmetry and topological order in 2+1D topological phases of matter. We define the topological symmetry group, characterizing symmetry of the emergent topological quantum numbers, and describe its relation with the microscopic symmetry of the physical system. We derive a general framework to classify symmetry fractionalization in topological phases, including phases that are non-Abelian and symmetries that permute the quasiparticle types and/or are anti-unitary. We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group G, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter with symmetry. The algebraic theory of the defects (G-crossed braided tensor category), allows one to compute many properties, such as the topologically distinct types of defects, their fusion rules, quantum dimensions, zero modes, braiding transformations, a generalized Verlinde formula, and modular transformations of the G-crossed extensions of topological phases. We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic defects are turned into deconfined quasiparticle excitations, which results in a different topological phase.
History of electroweak symmetry breaking
Kibble, T W B
2015-01-01
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.
Screw symmetry in columnar crystals
A. Mughal
2013-06-12
We show that the optimal packing of hard spheres in an infinitely long cylinder yields structures characterised by a screw symmetry. Each packing can be assembled by stacking a basic unit cell ad infinitum along the length of the cylinder with each subsequent unit cell rotated by the same twist angle with respect to the previous one. In this paper we quantitatively describe the nature of this screw operation for all such packings in the range 1 <= D/d <= 2.715 and also briefly discuss their helicity.
History of electroweak symmetry breaking
T. W. B. Kibble
2015-02-22
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.
Dynamical symmetries in noncommutative theories
Amorim, Ricardo [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro (Brazil)
2008-11-15
In the present work we study dynamical space-time symmetries in noncommutative relativistic theories by using the minimal canonical extension of the Doplicher, Fredenhagen, and Roberts algebra. Our formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity {theta}{sup {mu}}{sup {nu}}. In this framework we consider theories that are invariant under the Poincare group P or under its extension P{sup '}, when translations in the extra dimensions are permitted. The Noether's formalism adapted to such extended x+{theta} space-time is employed.
Bimetric theory with exchange symmetry
Hossenfelder, S. [Perimeter Institute for Theoretical Physics, 31 Caroline Street N, Waterloo, Ontario, N2L 2Y5 (Canada)
2008-08-15
We propose an extension of general relativity with two different metrics. To each metric we define a Levi-Cevita connection and a curvature tensor. We then consider two types of fields, each of which moves according to one of the metrics and its connection. To obtain the field equations for the second metric we impose an exchange symmetry on the action. As a consequence of this ansatz, additional source terms for Einstein's field equations are generated. We discuss the properties of these additional fields, and consider the examples of the Schwarzschild solution, and the Friedmann-Robertson-Walker metric.
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.
Symmetry energy of dilute warm nuclear matter
J. B. Natowitz; G. Ropke; S. Typel; D. Blaschke; A. Bonasera; K. Hagel; T. Klahn; S. Kowalski; L. Qin; S. Shlomo; R. Wada; H. H. Wolter
2010-02-25
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular by the appearance of bound states. A recently developed quantum statistical (QS) approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.