Topological phases protected by point group symmetry
NASA Astrophysics Data System (ADS)
Huang, Sheng-Jie; Song, Hao; Hermele, Michael
There has been remarkable progress in the theoretical understanding of symmetry protected topological (SPT) phases. However, most theories focus on internal, or on-site, symmetries, even though spatial symmetries are important in solids. In this talk, we classify bosonic SPT phases protected by crystalline point group symmetry, which we dub point group SPT (pgSPT) phases. Our approach is based on a procedure to reduce a d-dimensional pgSPT phase to lower-dimensional SPT phases protected by internal symmetry. For three-dimensional pgSPT phases, this approach allows us to gain insight into non-trivial properties at symmetry preserving surfaces. In particular, we obtain toy models for the surfaces of certain pgSPT phases at which there is a symmetry preserving Z2 topological order with anomalous symmetry fractionalization. We also discuss connections between bosonic pgSPT phases and electronic topological crystalline insulators. This research is supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES) under Award # DE-SC0014415.
Teaching Point-Group Symmetry with Three-Dimensional Models
ERIC Educational Resources Information Center
Flint, Edward B.
2011-01-01
Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold…
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
DNA Cages with Icosahedral Symmetry in Bionanotechnology
NASA Astrophysics Data System (ADS)
Jonoska, Nataša; Taormina, Anne; Twarock, Reidun
Blueprints for polyhedral cages with icosahedral symmetry made of circular DNA molecules are provided. The basic rule is that every edge of the cage is met twice in opposite directions by the DNA strand(s), and vertex junctions are realized by a set of admissible junction types. As nanocontainers for cargo storage and delivery, the icosidodecahedral cages are of special interest because they have the largest volume per surface ratio of all cages discussed here.
Anticoherence of spin states with point-group symmetries
NASA Astrophysics Data System (ADS)
Baguette, D.; Damanet, F.; Giraud, O.; Martin, J.
2015-11-01
We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then investigate in detail the case of small numbers of qubits and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.
Crystallography of decahedral and icosahedral particles. II - High symmetry orientations
NASA Technical Reports Server (NTRS)
Yang, C. Y.; Yacaman, M. J.; Heinemann, K.
1979-01-01
Based on the exact crystal structure of decahedral and icosahedral particles, high energy electron diffraction patterns and image profiles have been derived for various high symmetry orientations of the particles with respect to the incident beam. These results form a basis for the identification of small metal particle structures with advanced methods of transmission electron microscopy.
Virus templated plasmonic nanoclusters with icosahedral symmetry via directed assembly
NASA Astrophysics Data System (ADS)
Ratna, Banahalli; Fontana, Jake; Dressick, Walter; Phelps, Jamie; Johnson, John; Sampson, Travian; Rendell, Ronald; Soto, Carissa
2015-03-01
Controlling the spatial and orientational order of plasmonic nanoparticles may lead to structures with novel electromagnetic properties and applications such as sub-wavelength imaging and ultra-sensitive chemical sensors. Here we report the directed assembly of three-dimensional, icosahedral plasmonic nanoclusters with resonances at visible wavelengths. We show using transmission electron microcopy and in situ dynamic light scattering the nanoclusters consist of twelve gold nanospheres attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. We measured the bulk absorbance from aqueous suspensions of nanoclusters and reproduced the major features of the spectrum using finite-element simulations. Furthermore, because the viruses are easily produced in gram quantities the directed assembly approach is capable of high-throughput, providing a strategy to realize large quantities for applications. NRL summer intern under the HBCU/MI Summer Research Program.
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
ERIC Educational Resources Information Center
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-01-01
Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four…
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…
Comparison of Stretching Force Constants in Symmetry Coordinates between Td and C3v Point Groups
NASA Astrophysics Data System (ADS)
Julian, Maureen M.
1999-05-01
In this paper we consider what happens to the force constants of a silicate moiety (SiO4) when the length of one of its bonds is changed. This situation exists in the molecule O3SiObrSiO3, where Obr is the bridging oxygen atom connecting the two SiO3 moieties. The problem is to present a set of force constants such that when the structure of the more symmetric molecule is perturbed, the relevant force constants are also perturbed. Algebraic expressions are derived for the stretching force constants of SiO4 (tetrahedral point group Td) and ObrSiO3 (point group C3v) in symmetry coordinates. This paper is addressed to students and researchers in applied group theory who wish to compare force constants between similar molecules. We assume the reader has some familarity with the group theoretical methods presented by Wilson et al. (Wilson, E. B. Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover: New York, 1980). We cannot apply Wilson's method for obtaining symmetry coordinates from internal coordinates directly, as we demonstrate. Instead we must start with the irreducible representations of the symmetries of the moiety with the higher symmetry and then reduce them to the representations of the symmetries of the moiety with the lower symmetry. The symmetry coordinates are calculated for each species in order to factor the secular equation. The matrix representations of the generators of these point groups are a function of the specific symmetry coordinates. Finally, the symmetry coordinates are applied to the force constant matrix and the algebraic results are compared.
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
NASA Astrophysics Data System (ADS)
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-03-01
Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four students in a sophomore-level inorganic chemistry class at a small private university were divided by pre-selected lab groups into two groups, lecture and computer, for introductory information about point group symmetry. Both groups had low prior knowledge of symmetry elements although the lecture group had significantly higher knowledge than the computer group. After initial instruction, the lecture group scored significantly higher than the computer group on a point group assessment, even when prior knowledge was controlled. A second assessment, given after both groups had follow-up information from computer courseware, showed no significant difference between the groups. The computer group significantly improved between the two assessments, the lecture group did not. At the end-of-the semester post-test showed no significant difference between the two groups, although only 50% of the students in each group achieved mastery. Factors affecting the significant improvement of the low prior knowledge, computer group were examined and recommendations for future research provided.
Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections
ERIC Educational Resources Information Center
Chen, Lan; Sun, Hongwei; Lai, Chengming
2015-01-01
There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…
Three-dimensional photonic Dirac points stabilized by point group symmetry
NASA Astrophysics Data System (ADS)
Wang, HaiXiao; Xu, Lin; Chen, HuanYang; Jiang, Jian-Hua
2016-06-01
We discover a pair of stable three-dimensional (3D) Dirac points, a 3D photonic analog of graphene, in all-dielectric photonic crystals using structures commensurate with nanofabrication for visible-frequency photonic applications. The Dirac points carry nontrivial Z2 topology and emerge for a large range of material parameters in hollow cylinder hexagonal photonic crystals. From Kramers theorem and group theory, we find that only the C6 symmetry leads to point group symmetry stabilized Dirac points in 3D all-dielectric photonic crystals. The Dirac points are characterized using k ⃗.P ⃗ theory for photonic bands in combination with symmetry analysis. Breaking inversion symmetry splits the Dirac points into Weyl points. The physical properties and experimental consequences of Dirac points are also studied. The Dirac points are found to be robust against parameter tuning and weak disorders.
Virus-Templated Plasmonic Nanoclusters with Icosahedral Symmetry via Directed Self-Assembly
Fontana, Jake; Dressick, Walter J; Phelps, Jamie; Johnson, John E; Rendell, Ronald W; Sampson, Travian; Ratna, Banahalli R; Soto, Carissa M
2014-01-01
The assembly of plasmonic nanoparticles with precise spatial and orientational order may lead to structures with new electromagnetic properties at optical frequencies. The directed self-assembly method presented controls the interparticle-spacing and symmetry of the resulting nanometer-sized elements in solution. The self-assembly of three-dimensional (3D), icosahedral plasmonic nanosclusters (NCs) with resonances at visible wavelengths is demonstrated experimentally. The ideal NCs consist of twelve gold (Au) nanospheres (NSs) attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. In situ dynamic light scattering (DLS) measurements confirm the NSs assembly on the virus. Transmission electron micrographs (TEM) demonstrate the ability of the self-assembly method to control the nanoscopic symmetry of the bound NSs, which reflects the icosahedral symmetry of the virus. Both, TEM and DLS show that the NCs comprise of a distribution of capsids mostly covered (i.e., 6–12 NS/capsid) with NSs. 3D finite-element simulations of aqueous suspensions of NCs reproduce the experimental bulk absorbance measurements and major features of the spectra. Simulations results show that the fully assembled NCs give rise to a 10-fold surface-averaged enhancement of the local electromagnetic field. PMID:24733721
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.
Bodner, Mark; Bourret, Emmanuel; Patera, Jiri; Szajewska, Marzena
2015-05-01
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120. This subgroup is noted by A1 × 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
Binary icosahedral flavor symmetry for four generations of quarks and leptons
NASA Astrophysics Data System (ADS)
Chen, Chian-Shu; Kephart, Thomas W.; Yuan, Tzu-Chiang
2013-10-01
To include the quark sector, the A5≡ I (icosahedron) four generation lepton model is extended to a binary icosahedral symmetry I' flavor model. We find that the masses of fermions, including the heavy sectors, can be accommodated. At leading order the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the identity and the Pontecorvo-Maki-Nakagawa-Sakata (PMNS) matrix, resulting from the same set of vacua, corresponds to tribimaximal mixings.
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
Pentagonal and icosahedral order in rapidly cooled metals
NASA Astrophysics Data System (ADS)
Nelson, D. R.; Halperin, B. I.
1985-07-01
The discovery of an alloy of aluminum and manganese with sharp Bragg diffraction spots and an icosahedral point group symmetry was announced last year. The icosahedral symmetry appears to be an intrinsic property fo the material and not an artifact of twinning. There are remarkable similarities between the observed diffraction patterns and aperiodic tesselations of space called Penrose tiles. The relation between the experiments and Penrose tiles, as well as phenomenological descriptions of the icosahedral aluminum-manganese alloy as a superposition of incommensurate density waves, are reviewed. Other types of exotic crystallography are also discussed.
NASA Astrophysics Data System (ADS)
Robertson, Christopher; Worth, Graham A.
2015-10-01
The vibronic coupling Hamiltonian is a standard model used to describe the potential energy surfaces of systems in which non-adiabatic coupling is a key feature. This includes Jahn-Teller and Renner-Teller systems. The model approximates diabatic potential energy functions as polynomials expanded about a point of high symmetry. One must ensure the model Hamiltonian belongs to the totally symmetric irreducible representation of this point group. Here, a simple approach is presented to generate functions that form a basis for totally symmetric irreducible representations of non-Abelian groups and apply it to D∞h (2D) and O (3D). For the O group, the use of a well known basis-generating operator is also required. The functions generated for D∞h are then used to construct a ten state, four coordinate model of acetylene. The calculated absorption spectrum is compared to the experimental spectrum to serve as a validation of the approach.
Köppl, Christoph; Werner, Hans-Joachim
2015-04-28
Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally do not transform according to irreducible representations of the underlying point group symmetry. Instead, groups of LMOs become symmetry-equivalent and this can be exploited to accelerate local calculations. We describe an implementation of such a symmetry treatment for density-fitted local Møller-Plesset perturbation theory, using various types of virtual orbitals: Projected atomic orbitals, orbital specific virtuals, and pair natural orbitals. The savings by the symmetry treatment are demonstrated by calculations for several large molecules having different point group symmetries. Benchmarks for the parallel execution efficiency of our method are also presented.
Mathivathanan, Logesh; Cruz, Raquel; Raptis, Raphael G.
2016-01-01
The trinuclear triangular cuprate anion of the title compound, tris[bis(triphenylphosphoranylidene)ammonium] tris(μ2-4-chloropyrazolato-κ2 N:N′)-μ3-oxido-tris[(nitrato-κ2 O,O′)cuprate(II)] nitrate monohydrate, (C36H30P2N)[Cu3(C3H2ClN2)3(NO3)3O]NO3·H2O, has point group symmetry 3., with the μ3-O atom located on the threefold rotation axis. The distorted square-pyramidal coordination sphere of the CuII atom is completed by two N atoms of trans-bridging pyrazolate groups and a chelating nitrate anion. The complex anion is slightly bent, with the nitrate and pyrazolate groups occupying positions above and below the Cu3 plane, respectively. In the crystal, weak O—H⋯O and C—H⋯O hydrogen bonds, as well as π–π interactions, are present. PMID:27375872
Mathivathanan, Logesh; Cruz, Raquel; Raptis, Raphael G
2016-04-01
The trinuclear triangular cuprate anion of the title compound, tris-[bis-(tri-phenyl-phospho-ranyl-idene)ammonium] tris-(μ2-4-chloro-pyrazolato-κ(2) N:N')-μ3-oxido-tris-[(nitrato-κ(2) O,O')cuprate(II)] nitrate monohydrate, (C36H30P2N)[Cu3(C3H2ClN2)3(NO3)3O]NO3·H2O, has point group symmetry 3., with the μ3-O atom located on the threefold rotation axis. The distorted square-pyramidal coordination sphere of the Cu(II) atom is completed by two N atoms of trans-bridging pyrazolate groups and a chelating nitrate anion. The complex anion is slightly bent, with the nitrate and pyrazolate groups occupying positions above and below the Cu3 plane, respectively. In the crystal, weak O-H⋯O and C-H⋯O hydrogen bonds, as well as π-π inter-actions, are present. PMID:27375872
Symmetry-adapted digital modeling III. Coarse-grained icosahedral viruses.
Janner, A
2016-05-01
Considered is the coarse-grained modeling of icosahedral viruses in terms of a three-dimensional lattice (the digital modeling lattice) selected among the projected points in space of a six-dimensional icosahedral lattice. Backbone atomic positions (Cα's for the residues of the capsid and phosphorus atoms P for the genome nucleotides) are then indexed by their nearest lattice point. This leads to a fine-grained lattice point characterization of the full viral chains in the backbone approximation (denoted as digital modeling). Coarse-grained models then follow by a proper selection of the indexed backbone positions, where for each chain one can choose the desired coarseness. This approach is applied to three viruses, the Satellite tobacco mosaic virus, the bacteriophage MS2 and the Pariacoto virus, on the basis of structural data from the Brookhaven Protein Data Bank. In each case the various stages of the procedure are illustrated for a given coarse-grained model and the corresponding indexed positions are listed. Alternative coarse-grained models have been derived and compared. Comments on related results and approaches, found among the very large set of publications in this field, conclude this article. PMID:27126109
Crystallography of decahedral and icosahedral particles. I - Geometry of twinning
NASA Technical Reports Server (NTRS)
Yang, C. Y.
1979-01-01
The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah
2014-01-01
Marine viruses play crucial roles in shaping the dynamics of oceanic microbial communities and in the carbon cycle on Earth. Here we report a 4.7-Å structure of a cyanobacterial virus, Syn5, by electron cryo-microscopy and modelling. A Cα backbone trace of the major capsid protein (gp39) reveals a classic phage protein fold. In addition, two knob-like proteins protruding from the capsid surface are also observed. Using bioinformatics and structure analysis tools, these proteins are identified to correspond to gp55 and gp58 (each with two copies per asymmetric unit). The non 1:1 stoichiometric distribution of gp55/58 to gp39 breaks all expected local symmetries and leads to non-quasi-equivalence of the capsid subunits, suggesting a role in capsid stabilization. Such a structural arrangement has not yet been observed in any known virus structures. PMID:24985522
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 Cα backbone trace of the major capsid protein (gp39) reveals a classic phage protein fold. In addition, two knob-like proteins protruding from the capsid surface are also observed. Using bioinformatics and structure analysis tools, these proteins are identified to correspond to gp55 and gp58 (each with two copies per asymmetric unit). The non 1:1 stoichiometric distribution of gp55/58 to gp39 breaks all expected local symmetries and leads to non-quasi-equivalence of the capsid subunits, suggesting a role in capsid stabilization. Such a structural arrangement has not yet been observed in any known virus structures.
Crystallography of icosahedral crystals
NASA Astrophysics Data System (ADS)
Bak, P.
The crystallography of icosahedral crystals is constructed. The actual three-dimensional crystal is represented by a three-dimensional cut in a regular six-dimensional periodic crystal with symmetry described by a six-dimensional space group, and the positions of atoms correspond to an arrangement of hypersurface segments. The resulting crystal cannot in general be viewed as a space-filling arrangemment of a small number of different Penrose tiles. The intensities of Bragg spots are given directly as the intensities of Bragg spots of the six-dimensional crystal.
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
Janner, A
2011-11-01
The RNA viruses cowpea chlorotic mottle, satellite tobacco mosaic, pariacoto and MS2, already considered in part IV of this series of papers [Janner, A. (2011a), Acta Cryst. A67, 517-520], are investigated further, with the aim to arrive at a possible physical basis for their structural properties. The shell structure of the filled capsid is analyzed in terms of successive spherical boundaries of the sets of icosahedral equivalent chains. By inversion in the sphere enclosing the capsid, the internal boundaries are transformed into external ones, which are more easily visualized. This graphical procedure reveals the presence of regularly spaced shells with boundaries fitting with anti-nodal surfaces of the virus considered as an elastic resonator. The centers of gravity of the various chains occur in the nodal regions of eigenvibrations with wavelength λ = R(0)/K(0), where R(0) is the radius of the virus and K(0) takes one of the values 12, 6, 4, 3, depending on the mode. The resonator model is consistent with practically all spherical shell boundaries, whereas deviations are observed for the icosahedral axial modes, which apparently play a secondary role with respect to the spherical ones. Both the spherical and the axial anti-nodal surfaces fit very well with the packed structure of the viruses in the crystal which, accordingly, is expected to have eigenfrequencies related to those of the virus. These results open the way to a better understanding of the possibility of breaking the capsid using resonant forced oscillations excited, for example, by an applied elastic shock or by irradiation with femtosecond laser pulses, as already realised by K.-T. Tsen and co-workers. An alternative `plywood' model connected to the extreme elastic properties of the capsid is also considered. PMID:22011468
Computer Simulated Growth of Icosahedral Glass
NASA Astrophysics Data System (ADS)
Leino, Y. A. J.; Salomaa, M. M.
1990-01-01
One possible model for materials displaying classically forbidden symmetry properties (apart from perfect quasicrystals) is the icosahedral glass model. We simulate the random growth of two types of two-dimensional icosahedral glasses consisting of the Penrose tiles, First we restrict the growth with the arrow rules, then we let the structure develop totally freely. The diffraction patterns have a clear five-fold symmetry in both cases. The diffraction peak intensities do not differ, but shapes of the central peaks vary depending on whether the arrow rules are imposed or not. Finally, we show that the half-width of the central peak decreases when the size of the simulation increases until a finite disorder-limited value is achieved. This phenomenon is in agreement with the behaviour of physical quasicrystallites and in contradiction with perfect mathematical quasicrystals which have Bragg peaks of zero width.
NASA Astrophysics Data System (ADS)
Bourdillon, Antony
2012-11-01
The following facts about icosahedra need wider attention. 1) The golden section τ is as fundamental to the icosahedral structure (length /edge) as π 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 τ. 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 τ [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
About the atomic structures of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Quiquandon, Marianne; Gratias, Denis
2014-01-01
This paper is a survey of the crystallographic methods that have been developed these last twenty five years to decipher the atomic structures of the icosahedral stable quasicrystals since their discovery in 1982 by D. Shechtman. After a brief recall of the notion of quasiperiodicity and the natural description of Z-modules in 3-dim as projection of regular lattices in N>3-dim spaces, we give the basic geometrical ingredients useful to describe icosahedral quasicrystals as irrational 3-dim cuts of ordinary crystals in 6-dim space. Atoms are described by atomic surfaces (ASs) that are bounded volumes in the internal (or perpendicular) 3-dim space and the intersections of which with the physical space are the actual atomic positions. The main part of the paper is devoted to finding the major properties of quasicrystalline icosahedral structures. As experimentally demonstrated, they can be described with a surprisingly few high symmetry ASs located at high symmetry special points in 6-dim space. The atomic structures are best described by aggregations and intersections of high symmetry compact interpenetrating atomic clusters. We show here that the experimentally relevant clusters are derived from one generic cluster made of two concentric triacontahedra scaled by τ and an external icosidodecahedron. Depending on which ones of the orbits of this cluster are eventually occupied by atoms, the actual atomic clusters are of type Bergman, Mackay, Tsai and others….
Classification of point-group-symmetric orientational ordering tensors
NASA Astrophysics Data System (ADS)
Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan; Wu, Kai; Zaanen, Jan
2016-08-01
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational-symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e., O(3), to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge-theoretical framework, to address the three-dimensional point-group-symmetric orientational orders on a general footing. This unified approach allows us to enlist order parameter tensors for all three-dimensional point groups. By construction, these tensor order parameters are the minimal set of simplest tensors allowed by the symmetries that uniquely characterize the orientational order. We explicitly give these for the point groups {Cn,Dn,T ,O ,I } ⊂SO(3 ) and {Cn v,S2 n,Cn h,Dn h,Dn d,Th,Td,Oh,Ih} ⊂O(3 ) for n ,2 n ∈{1 ,2 ,3 ,4 ,6 ,∞ } . This central result may be perceived as a road map for identifying exotic orientational orders that may become more and more in reach in view of rapid experimental progress in, e.g., nanocolloidal systems and novel magnets.
Classification of point-group-symmetric orientational ordering tensors.
Nissinen, Jaakko; Liu, Ke; Slager, Robert-Jan; Wu, Kai; Zaanen, Jan
2016-08-01
The concept of symmetry breaking has been a propelling force in understanding phases of matter. While rotational-symmetry breaking is one of the most prevalent examples, the rich landscape of orientational orders breaking the rotational symmetries of isotropic space, i.e., O(3), to a three-dimensional point group remain largely unexplored, apart from simple examples such as ferromagnetic or uniaxial nematic ordering. Here we provide an explicit construction, utilizing a recently introduced gauge-theoretical framework, to address the three-dimensional point-group-symmetric orientational orders on a general footing. This unified approach allows us to enlist order parameter tensors for all three-dimensional point groups. By construction, these tensor order parameters are the minimal set of simplest tensors allowed by the symmetries that uniquely characterize the orientational order. We explicitly give these for the point groups {C_{n},D_{n},T,O,I}⊂SO(3) and {C_{nv},S_{2n},C_{nh},D_{nh},D_{nd},T_{h},T_{d},O_{h},I_{h}}⊂O(3) for n,2n∈{1,2,3,4,6,∞}. This central result may be perceived as a road map for identifying exotic orientational orders that may become more and more in reach in view of rapid experimental progress in, e.g., nanocolloidal systems and novel magnets. PMID:27627370
Bulk topological invariants in noninteracting point group symmetric insulators
NASA Astrophysics Data System (ADS)
Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
2012-09-01
We survey various quantized bulk physical observables in two- and three-dimensional topological band insulators invariant under translational symmetry and crystallographic point group symmetries (PGS). In two-dimensional insulators, we show that (i) the Chern number of a Cn-invariant insulator can be determined, up to a multiple of n, by evaluating the eigenvalues of symmetry operators at high-symmetry points in the Brillouin zone; (ii) the Chern number of a Cn-invariant insulator is also determined, up to a multiple of n, by the Cn eigenvalue of the Slater determinant of a noninteracting many-body system; and (iii) the Chern number vanishes in insulators with dihedral point groups Dn, and the quantized electric polarization is a topological invariant for these insulators. In three-dimensional insulators, we show that (i) only insulators with point groups Cn, Cnh, and Sn PGS can have nonzero 3D quantum Hall coefficient and (ii) only insulators with improper rotation symmetries can have quantized magnetoelectric polarization P3 in the term P3E·B, the axion term in the electrodynamics of the insulator (medium).
A crystallographic approach to structural transitions in icosahedral viruses.
Indelicato, Giuliana; Cermelli, Paolo; Salthouse, David G; Racca, Simone; Zanzotto, Giovanni; Twarock, Reidun
2012-04-01
Viruses with icosahedral capsids, which form the largest class of all viruses and contain a number of important human pathogens, can be modelled via suitable icosahedrally invariant finite subsets of icosahedral 3D quasicrystals. We combine concepts from the theory of 3D quasicrystals, and from the theory of structural phase transformations in crystalline solids, to give a framework for the study of the structural transitions occurring in icosahedral viral capsids during maturation or infection. As 3D quasicrystals are in a one-to-one correspondence with suitable subsets of 6D icosahedral Bravais lattices, we study systematically the 6D-analogs of the classical Bain deformations in 3D, characterized by minimal symmetry loss at intermediate configurations, and use this information to infer putative viral-capsid transition paths in 3D via the cut-and-project method used for the construction of quasicrystals. We apply our approach to the Cowpea Chlorotic Mottle virus (CCMV) and show that the putative transition path between the experimentally observed initial and final CCMV structures is most likely to preserve one threefold axis. Our procedure suggests a general method for the investigation and prediction of symmetry constraints on the capsids of icosahedral viruses during structural transitions, and thus provides insights into the mechanisms underlying structural transitions of these pathogens. PMID:21611828
NASA Astrophysics Data System (ADS)
Ilyushin, Vadim V.; Hougen, Jon. T.
2013-07-01
A program, called PAM_C2v_2tops, for fitting the high-resolution torsion-rotation spectra of molecules with two equivalent methyl rotors and C2v symmetry at equilibrium is described and applied to the spectrum of acetone [(CH3)2CO]. The G36 permutation-inversion group-theoretical considerations used in the design of the program are presented followed by a description of the structure of the program, which uses the principal axis method and a two-step diagonalization procedure. The program was used to carry out a weighted least-squares fit of 1720 microwave, millimeter-wave, and sub-millimeter-wave line frequencies of acetone that are available in the literature. The weighted standard deviation of 0.94 obtained here for a joint fit of rotational lines belonging to the ground, the lower torsional fundamental, and the higher torsional fundamental states of acetone represents significant progress in comparison with previous fitting attempts, especially for the excited torsional states.
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. PMID:26178267
Symmetry of Magnetically Ordered Quasicrystals
NASA Astrophysics Data System (ADS)
Lifshitz, Ron
1998-03-01
The notion of magnetic symmetry is reexamined in light of the recent observation of long-range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals, is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.
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.
Cubic Icosahedra? A Problem in Assigning Symmetry
ERIC Educational Resources Information Center
Lloyd, D. R.
2010-01-01
There is a standard convention that the icosahedral groups are classified separately from the cubic groups, but these two symmetry types have been conflated as "cubic" in some chemistry textbooks. In this note, the connection between cubic and icosahedral symmetries is examined, using a simple pictorial model. It is shown that octahedral and…
A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays
NASA Astrophysics Data System (ADS)
Zappa, Emilio; Dykeman, Eric C.; Geraets, James A.; Twarock, Reidun
2016-04-01
In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally proposed by Kramer, to the case of aperiodic structures with icosahedral symmetry; these rotations induce a rotation of the physical and orthogonal spaces invariant under the icosahedral group, and hence, via the cut-and-project method, a continuous transformation of the corresponding model sets. We prove that this approach allows for a characterisation of such transitions in a purely group theoretical framework, and provide explicit computations and specific examples. Moreover, we prove that this approach can be used in the case of finite point sets with icosahedral symmetry, which have a wide range of applications in carbon chemistry (fullerenes) and biology (viral capsids).
Mechanical properties of icosahedral virus capsids
NASA Astrophysics Data System (ADS)
Vliegenthart, G. A.; Gompper, G.
2007-12-01
Virus capsids are self-assembled protein shells in the size range of 10 to 100 nanometers. The shells of DNA-viruses have to sustain large internal pressures while encapsulating and protecting the viral DNA. We employ computer simulations to study the mechanical properties of crystalline shells with icosahedral symmetry that serve as a model for virus capsids. The shells are positioned on a substrate and deformed by a uni-axial force excerted by a small bead. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number N of elementary building blocks (capsomers), and the Föppl-von Kármán number γ which characterizes the relative importance of shear and bending elasticity.
Structures of giant icosahedral eukaryotic dsDNA viruses
Xiao, Chuan; Rossmann, Michael G.
2011-01-01
In the last twenty years, numerous giant, dsDNA, icosahedral viruses have been discovered and assigned to the nucleocytoplasmic large dsDNA virus (NCLDV) clade. The major capsid proteins of these viruses consist of two consecutive jelly-roll domains, assembled into trimers, with pseudo 6-fold symmetry. The capsomers are assembled into arrays that have either p6 (as in Paramecium bursaria Chlorella virus-1) or p3 symmetry (as in Mimivirus). Most of the NCLDV viruses have a membrane that separates the nucleocapsid from the external capsid. PMID:21909343
Prediction of stability changes upon mutation in an icosahedral capsid
Hickman, Samuel J.
2015-01-01
ABSTRACT 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
The Energetics and Symmetry of Quasicrystals.
NASA Astrophysics Data System (ADS)
Narasimhan, Subha
In a dramatic experiment in 1984, Shechtman and co-workers observed electron diffraction patterns in rapidly cooled Al-Mn alloys, exhibiting non-crystallographic symmetry, contrary to the conventional wisdom that solid structures could be broadly classified as glassy or amorphous, and crystalline. This and subsequent experiments have spurred an intense effort by the condensed matter physics community into understanding the nature and origin of solid structures, particularly in the light of earlier abstract mathematical structures ("tilings"), invented by Penrose and others, that are space filling but non-periodic and non-random in nature. This dissertation aims at understanding the energetics and symmetry of these "quasi-crystalline" structures. It consists of two parts. In the first part, the energetics of various observed quasi-crystalline phases have been studied by using a type of phenomenological Ginzburg-Landau theory that has been successful in predicting the qualitative features of a wide variety of phase transitions. It is found that qualitative agreement with experiment can indeed be had regarding the relative stability of these phases. The model also predicts the most likely equilibrium structure in various regimes of parameter space. The second part is focussed towards understanding the symmetries of the density function of these phases, the symmetry of the hydrodynamic degrees of freedom, the structure of the reciprocal lattice and so on. The harmonic elastic energy, invariant under the point group of the diffraction pattern is constructed for each of the observed phases. Finally, a formalism is developed for determining the various reciprocal lattices possible with a given arbitrary point group symmetry. It is then applied to the cases of 2D Pentagonal and 3D Icosahedral structures.
Platonic solids back in the sky: icosahedral inflation
NASA Astrophysics Data System (ADS)
Kang, Jonghee; Nicolis, Alberto
2016-03-01
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.
Group theory of icosahedral virus capsid vibrations: a top-down approach.
Peeters, Kasper; Taormina, Anne
2009-02-21
We explore the use of a top-down approach to analyse the dynamics of icosahedral virus capsids and complement the information obtained from bottom-up studies of viral vibrations available in the literature. A normal mode analysis based on protein association energies is used to study the frequency spectrum, in which we reveal a universal plateau of low-frequency modes shared by a large class of Caspar-Klug capsids. These modes break icosahedral symmetry and are potentially relevant to the genome release mechanism. We comment on the role of viral tiling theory in such dynamical considerations. PMID:19014954
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)
Radial vibrations of a sodium ion inside icosahedral C60
NASA Technical Reports Server (NTRS)
Ballester, J. L.; Dunlap, B. I.
1992-01-01
The very high symmetry of icosahedral C60 suggests that, as a first approximation, an atom trapped inside C60 would be subject to a potential that is radially symmetric about the center. All-electron local-density-functional calculations of the total energy of a sodium ion as a function of radial displacement from the center along the fivefold axis of C60 serve to refine such a radial potential. In particular, the calculations suggest studying potentials that have minima displaced from the center. An analytic functional form for a radial potential having a positive cusp at the origin is proposed, and the s-wave radial solutions of the corresponding Schroedinger equation are examined.
Exploring the symmetry and mechanism of virus capsid maturation via an ensemble of pathways.
May, Eric R; Feng, Jun; Brooks, Charles L
2012-02-01
Many icosahedral viruses undergo large-scale conformational transitions between icosahedrally symmetric conformations during their life cycles. However, whether icosahedral symmetry is maintained along the transition pathways for this process is unknown. By employing a simplified and directed structure-based potential we compute an ensemble of transition pathways for the maturation transition of bacteriophage HK97. We observe localized symmetry-breaking events, but find that the large-scale displacements are dominated by icosahedrally symmetric deformation modes. We find that all pathways obey a common mechanism characterized by formation of pentameric contacts early in the transition. PMID:22325284
On the generation of point groups in spaces of various dimensions.
Pokorny, A; Herzig, P; Altmann, S L
2001-09-01
In this paper the use of Clifford algebra in the parametrization of point groups in spaces of various dimensions is shown. Higher-dimensional spaces are of great interest especially when modulated crystals or quasicrystals are studied. While the quaternion units, which are useful to parametrize rotations in 3 dimensions, can be identified with rotations, the basic Clifford units may be regarded as mirrors from which all proper and improper symmetry operations can be generated. The practical implementation of this method of parametrization is demonstrated for the group of the hypercube in the 4-dimensional space, and generalisations to spaces of dimensions higher than 4 are suggested. PMID:11666073
Point group sensitive probes of the pseudogap electronic structure in Bi2212
NASA Astrophysics Data System (ADS)
Hinton, J. P.; Koralek, J. D.; Orenstein, J.; Firmo, I.; Hamidian, M.; Fujita, K.; Davis, J. C.
2011-03-01
We combine optical transient grating spectroscopy (TGS) and spectroscopic imaging scanning tunneling microscopy (SI-STM) to study the pseudogap electronic structure in the underdoped cuprate superconductor Bi 2 Sr 2 CaCu 2 O8 + δ . In TGS a pair of 50 fs pump pulses at 800 nm coincident on the sample surface generate a sinusoidal variation in the index of refraction. This index grating is phase sensitively probed, allowing us to clearly resolve two components in the optical response below Tc. We attribute one of the components to a coherent nonlinear optical process, whose properties are sensitive to the point group symmetry of the pseudogap electronic structure. We compare the results of these optical experiments with recent analysis of SI-STM data (M. J. Lawler et al Nature 466 , 347 (2010)) which measures the amplitude of peaks at various reciprocal lattice vectors in the Fourier transform of atomically resolved images of the pseudogap electronic structure. The symmetry properties of the SI-STM Bragg amplitudes provide additional evidence relevant to the point group of the pseudogap electronic structure.
Theoretical study on icosahedral water clusters
NASA Astrophysics Data System (ADS)
Loboda, Oleksandr; Goncharuk, Vladyslav
2010-01-01
Here we present a structural study of different gas hydrates using the B3LYP hybrid DFT exchange-correlation functional. A new concept for viewing the icosahedral cluster as an expansion of dodecahedral subclusters is introduced. The investigated structures consist of 280 water molecules. Structural and orientational features of various guest molecules occupying the central cavity of the clusters are established. It was found that water as the guest molecule has the highest stabilization energy in studied clusters. The conformational changes in dimer and trimer water molecules upon incorporation into hydrate cavity are discussed. The influence of second- and third-order solvent shells is illustrated on example of icosahedral water cluster derivatives.
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.
Icosahedral inclusions (carboxysomes) of Nitrobacter agilis.
Shively, J M; Bock, E; Westphal, K; Cannon, G C
1977-01-01
The icosahedral bodies of Nitrobacter agilis are about 120 nm in diameter and, as viewed by electron microscopy, consist of an outer shell enclosing 10-nm particles. The inner 10-nm particle is the enzyme D-ribulose 1,5-bisphosphate carboxylase. The bodies isolated from cells incubated 1 month without nitrite had a specific activity for the enzyme of 0.54 mu mol of CO2 fixed per min per mg of protein. Images PMID:199579
Three-Dimensional Icosahedral Phase Field Quasicrystal
NASA Astrophysics Data System (ADS)
Subramanian, P.; Archer, A. J.; Knobloch, E.; Rucklidge, A. M.
2016-08-01
We investigate the formation and stability of icosahedral quasicrystalline structures using a dynamic phase field crystal model. Nonlinear interactions between density waves at two length scales stabilize three-dimensional quasicrystals. We determine the phase diagram and parameter values required for the quasicrystal to be the global minimum free energy state. We demonstrate that traits that promote the formation of two-dimensional quasicrystals are extant in three dimensions, and highlight the characteristics required for three-dimensional soft matter quasicrystal formation.
Erickson, Jeremiah D; Mednikov, Evgueni G; Ivanov, Sergei A; Dahl, Lawrence F
2016-02-10
We present the first successful isolation and crystallographic characterization of a Mackay 55-metal-atom two-shell icosahedron, Pd55L12(μ3-CO)20 (L = PPr(i)3) (1). Its two-shell icosahedron of pseudo-Ih symmetry (without isopropyl substituents) enables a structural/bonding comparison with interior 55-metal-atom two-shell icosahedral geometries observed within the multi-shell capped 145-metal-atom three-shell Pd145(CO)72(PEt3)30 and 165-metal-atom four-shell Pt-centered (μ12-Pt)Pd164-xPtx(CO)72(PPh3)20 (x ≈ 7) nanoclusters, and within the recently reported four-shell Au133(SC6H4-p-Bu(t))52 nanocluster. DFT calculations carried out on a Pd55(CO)20(PH3)12 model analogue, with triisopropyl phosphine substituents replaced by H atoms, revealed a positive +0.84 e charge for the entire Pd55 core, with a highly positive second-shell Pd42 surface of +1.93 e. PMID:26790717
Molecular symmetry with quaternions.
Fritzer, H P
2001-09-01
A new and relatively simple version of the quaternion calculus is offered which is especially suitable for applications in molecular symmetry and structure. After introducing the real quaternion algebra and its classical matrix representation in the group SO(4) the relations with vectors in 3-space and the connection with the rotation group SO(3) through automorphism properties of the algebra are discussed. The correlation of the unit quaternions with both the Cayley-Klein and the Euler parameters through the group SU(2) is presented. Besides rotations the extension of quaternions to other important symmetry operations, reflections and the spatial inversion, is given. Finally, the power of the quaternion calculus for molecular symmetry problems is revealed by treating some examples applied to icosahedral symmetry. PMID:11666072
3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Vaid, Thomas P.
2014-01-01
Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching…
Confessions of an icosahedral virus crystallographer
Johnson, John E.
2013-01-01
This is a personal history of my structural studies of icosahedral viruses that evolved from crystallographic studies, to hybrid methods with electron cryo-microscopy and image reconstruction (cryoEM) and then developed further by incorporating a variety of physical methods to augment the high resolution crystallographic studies. It is not meant to be comprehensive, even for my own work, but hopefully provides some perspective on the growth of our understanding of these remarkable biologic assemblies. The goal is to provide a historical perspective for those new to the field and to emphasize the limitations of any one method, even those that provide atomic resolution information about viruses. PMID:23291268
3 nj-symbols and harmonic superposition coefficients: an icosahedral abacus
NASA Astrophysics Data System (ADS)
Aquilanti, Vincenzo; Coletti, Cecilia
2001-08-01
Angular momentum recoupling coefficients of angular momentum theory and matrix elements for basis set transformation of hyperspherical harmonics enjoy properties and sum rules crucial for applications but complicated without the guidance of graphical techniques. These coefficients being related to Racah's polynomials, the graphs also apply to polynomials of the hypergeometric family, their q-analogues and their `elliptic' extensions. A useful `abacus' exploiting the connections with presentations of icosahedral and related symmetries is introduced. Particular and limiting cases, such as those of the semiclassical type, allow a unified view of properties of angular and hyperangular momentum algebra, including relationships among vector coupling coefficients and rotation matrix elements.
Method of making an icosahedral boride structure
Hersee, Stephen D.; Wang, Ronghua; Zubia, David; Aselage, Terrance L.; Emin, David
2005-01-11
A method for fabricating thin films of an icosahedral boride on a silicon carbide (SiC) substrate is provided. Preferably the icosahedral boride layer is comprised of either boron phosphide (B.sub.12 P.sub.2) or boron arsenide (B.sub.12 As.sub.2). The provided method achieves improved film crystallinity and lowered impurity concentrations. In one aspect, an epitaxially grown layer of B.sub.12 P.sub.2 with a base layer or substrate of SiC is provided. In another aspect, an epitaxially grown layer of B.sub.12 As.sub.2 with a base layer or substrate of SiC is provided. In yet another aspect, thin films of B.sub.12 P.sub.2 or B.sub.12 As.sub.2 are formed on SiC using CVD or other vapor deposition means. If CVD techniques are employed, preferably the deposition temperature is above 1050.degree. C., more preferably in the range of 1100.degree. C. to 1400.degree. C., and still more preferably approximately 1150.degree. C.
Local growth of icosahedral quasicrystalline tilings
NASA Astrophysics Data System (ADS)
Hann, Connor T.; Socolar, Joshua E. S.; Steinhardt, Paul J.
2016-07-01
Icosahedral quasicrystals (IQCs) with extremely high degrees of translational order have been produced in the laboratory and found in naturally occurring minerals, yet questions remain about how IQCs form. In particular, the fundamental question of how locally determined additions to a growing cluster can lead to the intricate long-range correlations in IQCs remains open. In answer to this question, we have developed an algorithm that is capable of producing a perfectly ordered IQC yet relies exclusively on local rules for sequential, face-to-face addition of tiles to a cluster. When the algorithm is seeded with a special type of cluster containing a defect, we find that growth is forced to infinity with high probability and that the resultant IQC has a vanishing density of defects. The geometric features underlying this algorithm can inform analyses of experimental systems and numerical models that generate highly ordered quasicrystals.
A pseudo-icosahedral cage {Gd12} based on aminomethylphosphonate.
Zhang, Ze-Min; Zangana, Karzan H; Kostopoulos, Andreas K; Tong, Ming-Liang; Winpenny, Richard E P
2016-05-31
Reaction of (aminomethyl)phosphonic acid (ampH2) with a mixture of gadolinium and cobalt pivalates under solvothermal conditions, led to a pseudo-icosahedral cage {Gd12}, which shows a large magnetocaloric effect (MCE). PMID:27188600
NASA Astrophysics Data System (ADS)
Vail, Benjamin; Aris, Damian; Scarlete, Mihai
The present study proposes an algorithm for point-group analysis (PGA) of the vibrational activity of molecules, adapted for the efficient utilization of the linear packages incorporated into currently available symbolic computation engines (SCE), such as Maple, Mathcad, or Mathematica. By the creation of this algorithm, we have addressed the need for a numerically friendly environment, outside the "locked" procedures within molecular modeling packages, which will preserve its flexibility, transparency, and maneuverability, regardless of the complexity of the calculation. The format of the character tables of the point groups significant to chemical species has been adapted to ensure automatic numerization, and consistent input of the alphanumeric data from the existent character tables into the SCE templates designed to perform the PGA. The two proposed templates address two complementary objectives: (i) a totally transparent and interactive file has been designed to allow access to all intermediate results at all levels of the procedure for easy implementation of potential additional modules of special interest 1-5, and (ii) for fast output and routine calculations of the IR/Raman vibrational activity of molecules based on their point groups, a totally automatic file with a highly simplified input interface has been designed. The numerical interface conveniently replaces the usual graphic user interface that is common to most commercial molecular modeling software packages, requiring minimum input determination. The structure for both templates is based on the use of the digitized forms for the character tables, for the symmetry operations, and for symmetry elements, all saved in dedicated libraries uploaded to the numerical database of the SCE.
Polyhedra with noncrystallographic symmetry as the orbits of crystallographic point symmetry groups
NASA Astrophysics Data System (ADS)
Ovsetsina, T. I.; Chuprunov, E. V.
2015-11-01
Polyhedra with noncrystallographic symmetry are analyzed as the orbits of crystallographic point symmetry groups on a set of smooth or structured ("hatched") planes. Polyhedra with symmetrically equivalent faces, obtained using crystallographic point groups but having noncrystallographic symmetry, and polyhedra, the symmetry group T of which is crystallographic but can be implemented only on the assumption of a noncrystallographic character of the internal structure of polyhedron, are studied. The results of the analysis for all 32 point symmetry groups are listed in table.
Icosahedral Gold Cage Clusters: M@Au₁₂⁻ (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.
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.
Structure, Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions
Terrones, Mauricio; Terrones, Guillermo ); Terrones, Humberto
2001-12-01
We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, Ih, D2h, T). Our results demonstrate that it is also possible to create two new families of nested-chiral-icosahedral (I) fullerenes namely C260@ C560@ C980@ C1520@..and C140@ C380@ C740@ C1220@..., which exhibit interlayer separations of ca. 3.4. These chiral fullerenes are thought to possess non semiconducting properties. Finally, we study in detail the transformation of polyhedral graphitic particles into quasi-spherical nested giant fullerenes by reorganization of carbon atoms which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed if conditions during formation are extreme such as high energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.
Symmetry, Equivalence and Self-Assembly
NASA Astrophysics Data System (ADS)
Douglas, Jack
2006-03-01
Molecular self-assembly at equilibrium is central to the formation of many biological structures and the emulation of this process through the creation of synthetic counterparts offers great promise for nanofabrication. The central problems in this field are an understanding of how the symmetry of the interacting particles encodes the geometrical structure of the organized structure and the nature of the thermodynamic transitions involved. Our approach is inspired by the self-assembly of actin, tubulin and icosahedral structures of plant and animal viruses. We observe chain, membrane,`nanotube' and hollow icosahedron structures using `equivalent' particles exhibiting an interplay between directional (dipolar and multi-polar) interactions and short-range (van der Waals) interactions. Specifically, a dipolar potential (continuous rotational symmetry) gives rise to chain formation, while potentials having discrete rotational symmetries (e.g., square quadrupole or triangular ring of dipoles) led to the self-organization of nanotube and icosahedral structures with some resemblance to tubulin and icosahedral viruses. The simulations are compared to theoretical models of molecular self-assembly, especially in the case of dipolar fluids where the corresponding analytic theory of equilibrium polymerization is well developed. These computations give insights into the design elements required for the development of synthetic systems exhibiting this type of organization.
Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles
Shevchenko, Vladimir Ya. Madison, Alexey E.; Mackay, Alan L.
2007-03-01
In icosahedral carbon nanoparticles, the diamond-like core can undergo a reversible topological transition into and coexist coherently with the onion shells. The general approach for describing and designing complex hierarchical icosahedral structures is discussed. Structural models of icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually identical to that in diamond are derived. It is shown that icosahedral diamond-like particles can be transformed into onion-like shell structures (and vice versa) by the consecutive smoothing (puckering) of atomic networks without disturbance of their topological integrity. The possibility of coherent coexistence of icosahedral diamond-like core with onion shells is shown.
Protruding Features of Viral Capsids Are Clustered on Icosahedral Great Circles
Wilson, David P.
2016-01-01
Spherical viruses are remarkably well characterized by the Triangulation (T) number developed by Casper and Klug. The T-number specifies how many viral capsid proteins are required to cover the virus, as well as how they are further subdivided into pentamer and hexamer subunits. The T-number however does not constrain the orientations of these proteins within the subunits or dictate where the proteins should place their protruding features. These protrusions often take the form of loops, spires and helices, and are significant because they aid in stability of the capsid as well as recognition by the host organism. Until now there has be no overall understanding of the placement of protrusions for spherical viruses, other than they have icosahedral symmetry. We constructed a set of gauge points based upon the work affine extensions of Keef and Twarock, which have fixed relative angular locations with which to measure the locations of these features. This work adds a new element to our understanding of the geometric arrangement of spherical viral capsid proteins; chiefly that the locations of protruding features are not found stochastically distributed in an icosahedral manner across the viral surface, but instead these features are found only in specific locations along the 15 icosahedral great circles. We have found that this result holds true as the T number and viral capsids size increases, suggesting an underlying geometric constraint on their locations. This is in spite of the fact that the constraints on the pentamers and hexamer orientations change as a function of T-number, as you need to accommodate more hexamers in the same solid angle between pentamers. The existence of this angular constraint of viral capsids suggests that there is a fitness or energetic benefit to the virus placing its protrusions in this manner. This discovery may have profound impacts on identifying and eliminating viral pathogens, understanding evolutionary constraints as well as
Protruding Features of Viral Capsids Are Clustered on Icosahedral Great Circles.
Wilson, David P
2016-01-01
Spherical viruses are remarkably well characterized by the Triangulation (T) number developed by Casper and Klug. The T-number specifies how many viral capsid proteins are required to cover the virus, as well as how they are further subdivided into pentamer and hexamer subunits. The T-number however does not constrain the orientations of these proteins within the subunits or dictate where the proteins should place their protruding features. These protrusions often take the form of loops, spires and helices, and are significant because they aid in stability of the capsid as well as recognition by the host organism. Until now there has be no overall understanding of the placement of protrusions for spherical viruses, other than they have icosahedral symmetry. We constructed a set of gauge points based upon the work affine extensions of Keef and Twarock, which have fixed relative angular locations with which to measure the locations of these features. This work adds a new element to our understanding of the geometric arrangement of spherical viral capsid proteins; chiefly that the locations of protruding features are not found stochastically distributed in an icosahedral manner across the viral surface, but instead these features are found only in specific locations along the 15 icosahedral great circles. We have found that this result holds true as the T number and viral capsids size increases, suggesting an underlying geometric constraint on their locations. This is in spite of the fact that the constraints on the pentamers and hexamer orientations change as a function of T-number, as you need to accommodate more hexamers in the same solid angle between pentamers. The existence of this angular constraint of viral capsids suggests that there is a fitness or energetic benefit to the virus placing its protrusions in this manner. This discovery may have profound impacts on identifying and eliminating viral pathogens, understanding evolutionary constraints as well as
Symmetry breaking in molecular ferroelectrics.
Shi, Ping-Ping; Tang, Yuan-Yuan; Li, Peng-Fei; Liao, Wei-Qiang; Wang, Zhong-Xia; Ye, Qiong; Xiong, Ren-Gen
2016-07-11
Ferroelectrics are inseparable from symmetry breaking. Accompanying the paraelectric-to-ferroelectric phase transition, the paraelectric phase adopting one of the 32 crystallographic point groups is broken into subgroups belonging to one of the 10 ferroelectric point groups, i.e. C1, C2, C1h, C2v, C4, C4v, C3, C3v, C6 and C6v. The symmetry breaking is captured by the order parameter known as spontaneous polarization, whose switching under an external electric field results in a typical ferroelectric hysteresis loop. In addition, the responses of spontaneous polarization to other external excitations are related to a number of physical effects such as second-harmonic generation, piezoelectricity, pyroelectricity and dielectric properties. Based on these, this review summarizes recent developments in molecular ferroelectrics since 2011 and focuses on the relationship between symmetry breaking and ferroelectricity, offering ideas for exploring high-performance molecular ferroelectrics. PMID:27051889
Electronic transport in polycrystalline samples of icosahedral phases
NASA Astrophysics Data System (ADS)
Vekilov, Yu. Kh.; Chernikov, M. A.; Dolinichek, Ya.
2016-01-01
The low-temperature electronic transport in polycrystals of quasicrystalline phases with an icosahedral structure has been analyzed within the model of the granular electronic system. In this model, the grains (drops) of a metallic icosahedral phase are surrounded by extended defects and grain boundaries, which create an insulating environment. The electron transport in this model is determined by the size quantization of electronic states inside metallic grains, by intergranular tunneling, and by electrostatic barriers. Depending on the temperature and structural state of the system, the hopping conductivity with variable lengths of jumps in the Efros-Shklovskii or Mott regime is observed with predominantly elastic cotunneling. In the case of strong intergranular coupling, the system passes into the metallic regime with the exponential temperature dependence of the electrical conductivity.
Forging Unsupported Metal-Boryl Bonds with Icosahedral Carboranes.
Saleh, Liban M A; Dziedzic, Rafal M; Khan, Saeed I; Spokoyny, Alexander M
2016-06-13
In contrast to the plethora of metal-catalyzed cross-coupling methods available for the installation of functional groups on aromatic hydrocarbons, a comparable variety of methods are currently not available for icosahedral carboranes, which are boron-rich three-dimensional aromatic analogues of aryl groups. Part of this is due to the limited understanding of the elementary steps for cross-coupling involving carboranes. Here, we report our efforts in isolating metal-boryl complexes to further our understanding of one of these elementary steps, oxidative addition. Structurally characterized examples of group 10 M-B bonds featuring icosahedral carboranes are completely unknown. Use of mercurocarboranes as a reagent to deliver M-B bonds saw divergent reactivity for platinum and palladium, with a Pt-B bond being isolated for the former, and a rare Pd-Hg bond being formed for the latter. PMID:27017293
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
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.
Symmetry constraints on the elastoresistivity tensor
NASA Astrophysics Data System (ADS)
Shapiro, M. C.; Hlobil, Patrik; Hristov, A. T.; Maharaj, Akash V.; Fisher, I. R.
2015-12-01
The elastoresistivity tensor mi j ,k l characterizes changes in a material's resistivity due to strain. As a fourth-rank tensor, elastoresistivity can be a uniquely useful probe of the symmetries and character of the electronic state of a solid. We present a symmetry analysis of mi j ,k l (both in the presence and absence of a magnetic field) based on the crystalline point group, focusing for pedagogic purposes on the D4 h point group (of relevance to several materials of current interest). We also discuss the relation between mi j ,k l and various thermodynamic susceptibilities, particularly where they are sensitive to critical fluctuations proximate to a critical point at which a point-group symmetry is spontaneously broken.
Soft materials design via self assembly of functionalized icosahedral particles
NASA Astrophysics Data System (ADS)
Muthukumar, Vidyalakshmi Chockalingam
In this work we simulate self assembly of icosahedral building blocks using a coarse grained model of the icosahedral capsid of virus 1m1c. With significant advancements in site-directed functionalization of these macromolecules [1], we propose possible application of such self-assembled materials for drug delivery. While there have been some reports on organization of viral particles in solution through functionalization, exploiting this behaviour for obtaining well-ordered stoichiometric structures has not yet been explored. Our work is in well agreement with the earlier simulation studies of icosahedral gold nanocrystals, giving chain like patterns [5] and also broadly in agreement with the wet lab works of Finn, M.G. et al., who have shown small predominantly chain-like aggregates with mannose-decorated Cowpea Mosaic Virus (CPMV) [22] and small two dimensional aggregates with oligonucleotide functionalization on the CPMV capsid [1]. To quantify the results of our Coarse Grained Molecular Dynamics Simulations I developed analysis routines in MATLAB using which we found the most preferable nearest neighbour distances (from the radial distribution function (RDF) calculations) for different lengths of the functional groups and under different implicit solvent conditions, and the most frequent coordination number for a virus particle (histogram plots further using the information from RDF). Visual inspection suggests that our results most likely span the low temperature limits explored in the works of Finn, M.G. et al., and show a good degree of agreement with the experimental results in [1] at an annealing temperature of 4°C. Our work also reveals the possibility of novel stoichiometric N-mer type aggregates which could be synthesized using these capsids with appropriate functionalization and solvent conditions.
Dynamic and Kinetic Assembly Studies of an Icosahedral Virus Capsid
NASA Astrophysics Data System (ADS)
Lee, Kelly
2011-03-01
Hepatitis B virus has an icosahedrally symmetrical core particle (capsid), composed of either 90 or 120 copies of a dimeric protein building block. We are using time-resolved, solution small-angle X-ray scattering and single-molecule fluorescence microscopy to probe the core particle assembly reaction at the ensemble and individual assembly levels. Our experiments to date reveal the assembly process to be highly cooperative with minimal population of stable intermediate species. Solution conditions, particularly salt concentration, appears to influence the partitioning of assembly products into the two sizes of shells. Funding from NIH R00-GM080352 and University of Washington.
Magnetism in icosahedral quasicrystals: current status and open questions
Goldman, Alan I.
2014-07-02
Progress in our understanding of the magnetic properties of R-containing icosahedral quasicrystals (R = rare earth element) from over 20 years of experimental effort is reviewed. This includes the much studied R-Mg-Zn and R-Mg-Cd ternary systems, as well as several magnetic quasicrystals that have been discovered and investigated more recently including Sc-Fe-Zn, R-Ag-In, Yb-Au-Al, the recently synthesized R-Cd binary quasicrystals, and their periodic approximants. In many ways, the magnetic properties among these quasicrystals are very similar. However, differences are observed that suggest new experiments and promising directions for future research.
Magnetism in icosahedral quasicrystals: current status and open questions
NASA Astrophysics Data System (ADS)
Goldman, Alan I.
2014-08-01
Progress in our understanding of the magnetic properties of R-containing icosahedral quasicrystals (R = rare earth element) from over 20 years of experimental effort is reviewed. This includes the much studied R-Mg-Zn and R-Mg-Cd ternary systems, as well as several magnetic quasicrystals that have been discovered and investigated more recently including Sc-Fe-Zn, R-Ag-In, Yb-Au-Al, the recently synthesized R-Cd binary quasicrystals, and their periodic approximants. In many ways, the magnetic properties among these quasicrystals are very similar. However, differences are observed that suggest new experiments and promising directions for future research.
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.
Unusual properties of icosahedral boron-rich solids
Emin, David . E-mail: emin@unm.edu
2006-09-15
Icosahedral boron-rich solids are materials containing boron-rich units in which atoms reside at an icosahedron's 12 vertices. These materials are known for their exceptional bonding and the unusual structures that result. This article describes how the unusual bonding generates other distinctive and useful effects. In particular, radiation-induced atomic vacancies and interstitials spontaneously recombine to produce the 'self-healing' that underlies these materials' extraordinary radiation tolerance. Furthermore, boron carbides, a group of icosahedral boron-rich solids, possess unusual electronic, magnetic and thermal properties. For example, the charge carriers, holes, localize as singlet pairs on icosahedra. The unusual origin of this localization is indicated by the absence of a concomitant photo-ionization. The thermally assisted hopping of singlet pairs between icosahedra produces Seebeck coefficients that are unexpectedly large and only weakly dependent on carrier concentration. These properties are exploited in devices: (1) long-lived high-power high-capacity beta-voltaic cells (2) very high temperature thermoelectrics and (3) solid-state neutron detectors. - Graphical abstract: Very high-resolution transmission electron microscopy shows no damage to B{sub 12}P{sub 2} after an intense bombardment (10{sup 18} electrons/cm{sup 2} s) by 400 keV electrons to a net dose of about 10{sup 23} electrons/cm{sup 2}.
Point group identification algorithm in dynamic response analysis of nonlinear stochastic systems
NASA Astrophysics Data System (ADS)
Li, Tao; Chen, Jian-bing; Li, Jie
2016-03-01
The point group identification (PGI) algorithm is proposed to determine the representative point sets in response analysis of nonlinear stochastic dynamic systems. The PGI algorithm is employed to identify point groups and their feature points in an initial point set by combining subspace clustering analysis and the graph theory. Further, the representative point set of the random-variate space is determined according to the minimum generalized F-discrepancy. The dynamic responses obtained by incorporating the algorithm PGI into the probability density evolution method (PDEM) are compared with those by the Monte Carlo simulation method. The investigations indicate that the proposed method can reduce the number of the representative points, lower the generalized F-discrepancy of the representative point set, and also ensure the accuracy of stochastic structural dynamic analysis.
Consistent polycyclic presentation of a Bieberbach group with a nonabelian point group
NASA Astrophysics Data System (ADS)
Mohammad, Siti Afiqah; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat
2016-02-01
Research on the nonabelian tensor square of a group is requisite on finding the other homological functors. One of the methods to explicate the nonabelian tensor square is to ensure the presentation of the group is polycyclic and to prove its consistency. In this research, the polycyclic presentation of a Bieberbach group with the quaternion point group of order eight is shown to be consistent.
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.
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
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...
Aselage, T.L.; Tallant, D.R.
1998-02-01
The structure of silicon boride, SiB{sub 3}, is based on 12-atom, boron-rich icosahedra in which silicon atoms substitute for some boron atoms. Raman bands associated with vibrations of icosahedral atoms in SiB{sub 3} are quite broad, reflecting this substitutional disorder. Comparing the Raman spectra of other icosahedral borides with SiB{sub 3}, only boron carbides have similarly broad icosahedral Raman bands. The direct correlation of broad icosahedral Raman bands with substitutional disorder supports the proposition that carbon atoms replace icosahedral boron atoms in boron carbides of all compositions. {copyright} {ital 1998} {ital The American Physical Society}
The symmetry of single-molecule conduction.
Solomon, Gemma C; Gagliardi, Alessio; Pecchia, Alessandro; Frauenheim, Thomas; Di Carlo, Aldo; Reimers, Jeffrey R; Hush, Noel S
2006-11-14
We introduce the conductance point group which defines the symmetry of single-molecule conduction within the nonequilibrium Green's function formalism. It is shown, either rigorously or to within a very good approximation, to correspond to a molecular-conductance point group defined purely in terms of the properties of the conducting molecule. This enables single-molecule conductivity to be described in terms of key qualitative chemical descriptors that are independent of the nature of the molecule-conductor interfaces. We apply this to demonstrate how symmetry controls the conduction through 1,4-benzenedithiol chemisorbed to gold electrodes as an example system, listing also the molecular-conductance point groups for a range of molecules commonly used in molecular electronics research. PMID:17115774
A Convenient Route to Diversely Substituted Icosahedral Closomer Nanoscaffolds
Jalisatgi, Satish S.; Kulkarni, Vikas S.; Tang, Betty; Houston, Zachary H.; Lee, Mark W.; Hawthorne, M. Frederick
2011-01-01
The design and synthesis of icosahedral polyhedral borane closomer motifs based upon carbonate and carbamate anchoring groups for biomedical applications are described. Dodecacarbamate closomers containing easily accessible groups of interest at their linker termini were synthesized via activation of the B-OH vertices as aryl carbonates and their subsequent reaction with primary amines. Novel dodecacarbonate closomers were successfully synthesized for the first time by reacting [closo-B12(OH)12]2− with an excess of respective aryl chloroformates, utilizing relatively short reaction times, mild conditions and simple purification strategies, all of which had previously presented difficulties in closomer chemistry. This methodology for the 12-fold degenerate synthesis of carbonate and carbamate closomers will greatly facilitate further exploration of closomers as monodisperse nanomolecular delivery platforms. PMID:21766843
Icosahedral capsid formation by capsomers and short polyions
NASA Astrophysics Data System (ADS)
Zhang, Ran; Linse, Per
2013-04-01
Kinetical and structural aspects of the capsomer-polyion co-assembly into icosahedral viruses have been simulated by molecular dynamics using a coarse-grained model comprising cationic capsomers and short anionic polyions. Conditions were found at which the presence of polyions of a minimum length was necessary for capsomer formation. The largest yield of correctly formed capsids was obtained at which the driving force for capsid formation was relatively weak. Relatively stronger driving forces, i.e., stronger capsomer-capsomer short-range attraction and/or stronger electrostatic interaction, lead to larger fraction of kinetically trapped structures and aberrant capsids. The intermediate formation was investigated and different evolving scenarios were found by just varying the polyion length.
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
Point-group sensitive orientation mapping of non-centrosymmetric crystals
Winkelmann, Aimo; Nolze, Gert
2015-02-16
We demonstrate polarity-sensitive orientation mapping of non-centrosymmetric phases by Electron Backscatter Diffraction (EBSD). The method overcomes the restrictions of kinematic orientation determination by EBSD, which is limited to the centro-symmetric Laue-groups according to Friedel's rule. Using polycrystalline GaP as an example, we apply a quantitative pattern matching approach based on simulations using the dynamical theory of electron diffraction. This procedure results in a distinct assignment of the local orientation according to the non-centrosymmetric point group of the crystal structure under investigation.
Demina, Tatiana A.; Pietilä, Maija K.; Svirskaitė, Julija; Ravantti, Janne J.; Atanasova, Nina S.; Bamford, Dennis H.
2016-01-01
ABSTRACT Despite their high genomic diversity, all known viruses are structurally constrained to a limited number of virion morphotypes. One morphotype of viruses infecting bacteria, archaea, and eukaryotes is the tailless icosahedral morphotype with an internal membrane. Although it is considered an abundant morphotype in extreme environments, only seven such archaeal viruses are known. Here, we introduce Haloarcula californiae icosahedral virus 1 (HCIV-1), a halophilic euryarchaeal virus originating from salt crystals. HCIV-1 also retains its infectivity under low-salinity conditions, showing that it is able to adapt to environmental changes. The release of progeny virions resulting from cell lysis was evidenced by reduced cellular oxygen consumption, leakage of intracellular ATP, and binding of an indicator ion to ruptured cell membranes. The virion contains at least 12 different protein species, lipids selectively acquired from the host cell membrane, and a 31,314-bp-long linear double-stranded DNA (dsDNA). The overall genome organization and sequence show high similarity to the genomes of archaeal viruses in the Sphaerolipoviridae family. Phylogenetic analysis based on the major conserved components needed for virion assembly—the major capsid proteins and the packaging ATPase—placed HCIV-1 along with the alphasphaerolipoviruses in a distinct, well-supported clade. On the basis of its virion morphology and sequence similarities, most notably, those of its core virion components, we propose that HCIV-1 is a member of the PRD1-adenovirus structure-based lineage together with other sphaerolipoviruses. This addition to the lineage reinforces the notion of the ancient evolutionary links observed between the viruses and further highlights the limits of the choices found in nature for formation of a virion. PMID:27435460
Metal-organic framework materials based on icosahedral boranes and carboranes
Mirkin, Chad A.; Hupp, Joseph T.; Farha, Omar K.; Spokoyny, Alexander M.; Mulfort, Karen L.
2010-11-02
Disclosed herein are metal-organic frameworks of metals and boron rich ligands, such as carboranes and icosahedral boranes. Methods of synthesizing and using these materials in gas uptake are disclosed.
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…
Speckle in the diffraction patterns of Hendricks-Teller and icosahedral glass models
NASA Technical Reports Server (NTRS)
Garg, Anupam; Levine, Dov
1988-01-01
It is shown that the X-ray diffraction patterns from the Hendricks-Teller model for layered systems and the icosahedral glass models for the icosahedral phases show large fluctuations between nearby scattering wave vectors and from sample to sample, that are quite analogous to laser speckle. The statistics of these fluctuations are studied analytically for the first model and via computer simulations for the second. The observability of these effects is discussed briefly.
Stable Icosahedral Hollow Cage Clusters: Stannapherene (Sn12 2-) and Plumbaspherene (Pb12 2-)
Cui, Lifeng; Wang, Lai S.
2008-01-01
One of the major objectives of cluster science is to discover stable atomic clusters, which may be used as building blocks for cluster-assembled nanomaterials. The discovery and bulk synthesis of the fullerenes have sprouted new research disciplines in chemistry and nanoscience and precipitated intense interests to search for other similar stable clusters. However, despite major research efforts, no other analogous gas-phase clusters have been found and yielded to bulk syntheses. In this article, we review our recent discoveries in cluster beam experiments of stannaspherene (Sn12 2–) and plumbaspherene (Pb12 2–), which are highly stable and symmetric cage clusters. The names for these two clusters derive from their icosahedral (Ih) symmetry and delocalized spherical π-bonding that are characteristics of buckminsterfullerene C60. Stannaspherene and plumbaspherene have diameters comparable to that of C60 and can be considered as inorganic analogs of the buckyball. The large internal space in Sn12 2– has been shown to be able to trap any transition metal atom to form new endohedral cage clusters, M@Sn12 –, analogous to endohedral fullerenes. The doped atom in M@Sn12 – keeps its quasi-atomic nature with large magnetic moments. These endohedral cages form a rich class of new building blocks for cluster-assembled materials with tunable magnetic, electronic, and chemical properties. During our attempt to synthesize endohedral stannaspherenes, we crystallized a new Pd2@Sn18 4– cluster, which can be viewed as the fusion of two Pd@Sn12 2– clusters. This result suggests that stannaspherene, plumbaspherene, and a large number of their endohedrally doped species can be synthesized in the bulk.
Is space-time symmetry a suitable generalization of parity-time symmetry?
NASA Astrophysics Data System (ADS)
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-01
We discuss space-time symmetric Hamiltonian operators of the form H =H0 + igH‧, where H0 is Hermitian and g real. H0 is invariant under the unitary operations of a point group G while H‧ is invariant under transformation by elements of a subgroup G‧ of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0 < g
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
Multiple diffraction in an icosahedral Al-Cu-Fe quasicrystal
NASA Astrophysics Data System (ADS)
Fan, C. Z.; Weber, Th.; Deloudi, S.; Steurer, W.
2011-07-01
In order to reveal its influence on quasicrystal structure analysis, multiple diffraction (MD) effects in an icosahedral Al-Cu-Fe quasicrystal have been investigated in-house on an Oxford Diffraction four-circle diffractometer equipped with an Onyx™ CCD area detector and MoKα radiation. For that purpose, an automated approach for Renninger scans (ψ-scans) has been developed. Two weak reflections were chosen as the main reflections (called P) in the present measurements. As is well known for periodic crystals, it is also observed for this quasicrystal that the intensity of the main reflection may significantly increase if the simultaneous (H) and the coupling (P-H) reflections are both strong, while there is no obvious MD effect if one of them is weak. The occurrence of MD events during ψ-scans has been studied based on an ideal structure model and the kinematical MD theory. The reliability of the approach is revealed by the good agreement between simulation and experiment. It shows that the multiple diffraction effect is quite significant.
Many-molecule encapsulation by an icosahedral shell
Perlmutter, Jason D; Mohajerani, Farzaneh; Hagan, Michael F
2016-01-01
We computationally study how an icosahedral shell assembles around hundreds of molecules. Such a process occurs during the formation of the carboxysome, a bacterial microcompartment that assembles around many copies of the enzymes ribulose 1,5-bisphosphate carboxylase/ oxygenase and carbonic anhydrase to facilitate carbon fixation in cyanobacteria. Our simulations identify two classes of assembly pathways leading to encapsulation of many-molecule cargoes. In one, shell assembly proceeds concomitantly with cargo condensation. In the other, the cargo first forms a dense globule; then, shell proteins assemble around and bud from the condensed cargo complex. Although the model is simplified, the simulations predict intermediates and closure mechanisms not accessible in experiments, and show how assembly can be tuned between these two pathways by modulating protein interactions. In addition to elucidating assembly pathways and critical control parameters for microcompartment assembly, our results may guide the reengineering of viruses as nanoreactors that self-assemble around their reactants. DOI: http://dx.doi.org/10.7554/eLife.14078.001 PMID:27166515
Schottky effect in the i -Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant
NASA Astrophysics Data System (ADS)
Jazbec, S.; Kashimoto, S.; Koželj, P.; Vrtnik, S.; Jagodič, M.; Jagličić, Z.; Dolinšek, J.
2016-02-01
The analysis of low-temperature specific heat of rare-earth (RE)-containing quasicrystals and periodic approximants and consequent interpretation of their electronic properties in the T →0 limit is frequently hampered by the Schottky effect, where crystalline electric fields lift the degeneracy of the RE-ion Hund's rule ground state and introduce additional contribution to the specific heat. In this paper we study the low-temperature specific heat of a thulium-containing i -Zn-Ag-Sc-Tm icosahedral quasicrystal and its 1/1 Zn-Sc-Tm approximant, both being classified as "Schottky" systems. We have derived the crystal-field Hamiltonian for pentagonal symmetry of the crystalline electric field, pertinent to the class of Tsai-type icosahedral quasicrystals and their approximants, where the RE ions are located on fivefold axes of the icosahedral atomic cluster. Using the leading term of this Hamiltonian, we have calculated analytically the Schottky specific heat in the presence of an external magnetic field and made comparison to the experimental specific heat of the investigated quasicrystal and approximant. When the low-temperature specific heat C is analyzed in a C /T versus T2 scale (as it is customarily done for metallic specimens), the Schottky specific heat yields an upturn in the T →0 limit that cannot be easily distinguished from a similar upturn produced by the electron-electron interactions in exchange-enhanced systems and strongly correlated systems. Our results show that extraction of the electronic properties of RE-containing quasicrystals from their low-temperature specific heat may be uncertain in the presence of the Schottky effect.
Comparative Study of Non-Enveloped Icosahedral Viruses Size
Nikitin, Nikolai; Trifonova, Ekaterina; Evtushenko, Evgeniy; Kirpichnikov, Mikhail; Atabekov, Joseph; Karpova, Olga
2015-01-01
Now, as before, transmission electron microscopy (TEM) is a widely used technique for the determination of virions size. In some studies, dynamic light scattering (DLS) has also been applied for this purpose. Data obtained by different authors and using different methods could vary significantly. The process of TEM sample preparation involves drying on the substrate, which can cause virions to undergo morphology changes. Therefore, other techniques should be used for measurements of virions size in liquid, (i.e. under conditions closer to native). DLS and nanoparticle tracking analysis (NTA) provide supplementary data about the virions hydrodynamic diameter and aggregation state in liquid. In contrast to DLS, NTA data have a higher resolution and also are less sensitive to minor admixtures. In the present work, the size of non-enveloped icosahedral viruses of different nature was analyzed by TEM, DLS and NTA: the viruses used were the encephalomyocarditis virus (animal virus), and cauliflower mosaic virus, brome mosaic virus and bean mild mosaic virus (plant viruses). The same, freshly purified, samples of each virus were used for analysis using the different techniques. The results were compared with earlier published data and description databases. DLS data about the hydrodynamic diameter of bean mild mosaic virus, and NTA data for all examined viruses, were obtained for the first time. For all virus samples, the values of size obtained by TEM were less than virions sizes determined by DLS and NTA. The contribution of the electrical double layer (EDL) in virions hydrodynamic diameter was evaluated. DLS and NTA data adjusted for EDL thickness were in better agreement with TEM results. PMID:26545232
NASA Astrophysics Data System (ADS)
Venderbos, J. W. F.
2016-03-01
In this work we introduce a symmetry classification for electronic density waves which break translational symmetry due to commensurate wave-vector modulations. The symmetry classification builds on the concept of extended point groups: symmetry groups which contain, in addition to the lattice point group, translations that do not map the enlarged unit cell of the density wave to itself, and become "nonsymmorphic"-like elements. Multidimensional representations of the extended point group are associated with degenerate wave vectors. Electronic properties such as (nodal) band degeneracies and topological character can be straightforwardly addressed, and often follow directly. To further flesh out the idea of symmetry, the classification is constructed so as to manifestly distinguish time-reversal invariant charge (i.e., site and bond) order, and time-reversal breaking flux order. For the purpose of this work, we particularize to spin-rotation invariant density waves. As a first example of the application of the classification we consider the density waves of a simple single- and two-orbital square lattice model. The main objective, however, is to apply the classification to two-dimensional (2D) hexagonal lattices, specifically the triangular and the honeycomb lattices. The multicomponent density waves corresponding to the commensurate M -point ordering vectors are worked out in detail. To show that our results generally apply to 2 D hexagonal lattices, we develop a general low-energy SU(3 ) theory of (spinless) saddle-point electrons.
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.
NASA Technical Reports Server (NTRS)
Curreri, Peter A. (Technical Monitor); Kelton, K. F.; Gangopadhyay, A.; Lee, G. W.; Hyers, R. W.; Rathz, R. J.; Rogers, J.; Schenk, T.; Simonet, V.; Holland-Moritz, D.
2003-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si, for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.
NASA Technical Reports Server (NTRS)
Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.; Holland-Moritz, D.; Curreri, Peter A. (Technical Monitor)
2002-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si(3), for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron X-ray and high flux neutron facilities.
NASA Technical Reports Server (NTRS)
Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.
2003-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si[3], for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.
Accurate design of megadalton-scale two-component icosahedral protein complexes.
Bale, Jacob B; Gonen, Shane; Liu, Yuxi; Sheffler, William; Ellis, Daniel; Thomas, Chantz; Cascio, Duilio; Yeates, Todd O; Gonen, Tamir; King, Neil P; Baker, David
2016-07-22
Nature provides many examples of self- and co-assembling protein-based molecular machines, including icosahedral protein cages that serve as scaffolds, enzymes, and compartments for essential biochemical reactions and icosahedral virus capsids, which encapsidate and protect viral genomes and mediate entry into host cells. Inspired by these natural materials, we report the computational design and experimental characterization of co-assembling, two-component, 120-subunit icosahedral protein nanostructures with molecular weights (1.8 to 2.8 megadaltons) and dimensions (24 to 40 nanometers in diameter) comparable to those of small viral capsids. Electron microscopy, small-angle x-ray scattering, and x-ray crystallography show that 10 designs spanning three distinct icosahedral architectures form materials closely matching the design models. In vitro assembly of icosahedral complexes from independently purified components occurs rapidly, at rates comparable to those of viral capsids, and enables controlled packaging of molecular cargo through charge complementarity. The ability to design megadalton-scale materials with atomic-level accuracy and controllable assembly opens the door to a new generation of genetically programmable protein-based molecular machines. PMID:27463675
Ultrathin Icosahedral Pt-Enriched Nanocage with Excellent Oxygen Reduction Reaction Activity.
He, Dong Sheng; He, Daping; Wang, Jing; Lin, Yue; Yin, Peiqun; Hong, Xun; Wu, Yuen; Li, Yadong
2016-02-10
Cost-efficient utilization of Pt in the oxygen reduction reaction (ORR) is of great importance for the potential industrial scale demand of proton-exchange membrane fuel cells. Designing a hollow structure of a Pt catalyst offers a great opportunity to enhance the electrocatalytic performance and maximize the use of precious Pt. Herein we report a routine to synthesize ultrathin icosahedral Pt-enriched nanocages. In detail, the Pt atoms were conformally deposited on the surface of Pd icosahedral seeds, followed by selective removal of the Pd core by a concentrated HNO3 solution. The icosahedral Pt-enriched nanocage that is a few atomic layers thick includes the merits of abundant twin defects, an ultrahigh surface/volume ratio, and an ORR-favored Pt{111} facet, all of which have been demonstrated to be promoting factors for ORR. With a 10 times higher specific activity and 7 times higher mass activity, this catalyst shows more extraordinary ORR activity than the commercial Pt/C. The ORR activity of icosahedral Pt-enriched nanocages outperforms the cubic and octahedral nanocages reported in the literature, demonstrating the superiority of the icosahedral nanocage structure. PMID:26808073
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.
Aroyo, Mois I; Kirov, Asen; Capillas, Cesar; Perez-Mato, J M; Wondratschek, Hans
2006-03-01
The Bilbao Crystallographic Server is a web site with crystallographic programs and databases freely available on-line (http://www.cryst.ehu.es). The server gives access to general information related to crystallographic symmetry groups (generators, general and special positions, maximal subgroups, Brillouin zones etc.). Apart from the simple tools for retrieving the stored data, there are programs for the analysis of group-subgroup relations between space groups (subgroups and supergroups, Wyckoff-position splitting schemes etc.). There are also software packages studying specific problems of solid-state physics, structural chemistry and crystallography. This article reports on the programs treating representations of point and space groups. There are tools for the construction of irreducible representations, for the study of the correlations between representations of group-subgroup pairs of space groups and for the decompositions of Kronecker products of representations. PMID:16489249
Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals
Parshin, P. P.; Zemlyanov, M. G. Brand, R. A.
2007-05-15
The atomic dynamics of an Al-Ni-Fe decagonal quasicrystal and an Al-Cu-Fe icosahedral quasicrystal are investigated experimentally using the isotopic contrast method in inelastic neutron scattering. The partial spectra of thermal vibrations of copper, nickel, iron, and aluminum atoms in the decagonal and icosahedral quasicrystals are reconstructed directly from the experimental data without recourse to model concepts. The limiting energies and positions of the main features in the partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals are determined. It is established that, in the quasicrystals under investigation, the copper and nickel atoms are bound more weakly than the iron atoms and that the partial vibrational spectrum of aluminum atoms in the quasicrystals is considerably harder than the spectrum of pure metallic aluminum.
Geometrical symmetries of nuclear systems: {{ D }}_{3h} and {{ T }}_{d} symmetries in light nuclei
NASA Astrophysics Data System (ADS)
Bijker, Roelof
2016-07-01
The role of discrete (or point-group) symmetries in α-cluster nuclei is discussed in the framework of the algebraic cluster model which describes the relative motion of the α-particles. Particular attention is paid to the discrete symmetry of the geometric arrangement of the α-particles, and the consequences for the structure of the corresponding rotational bands. The method is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in a simple way as a consequence of the underlying discrete symmetry that characterizes the geometrical configuration of the α-particles, i.e. an equilateral triangle with {{ D }}3h symmetry for 12C, and a tetrahedron with {{ T }}d symmetry for 16O. The structure of rotational bands provides a fingerprint of the underlying geometrical configuration of α-particles.
NASA Astrophysics Data System (ADS)
Kah, Cherno Baba; Yu, M.; Jayanthi, C. S.; Wu, S. Y.
2014-03-01
Our previous study on one-dimensional icosahedral B12 cluster (α-B12) based chain [Bulletin of APS Annual Meeting, p265 (2013)] and ring structures has prompted us to study the two-dimensional (2D) α-B12 based structures. Recently, we have carried out a systematic molecular dynamics study on the structural stabilities and electronic properties of the 2D α-B12 based structures using the SCED-LCAO method [PRB 74, 15540 (2006)]. We have considered several types of symmetry for these 2D structures such as δ3, δ4, δ6 (flat triangular), and α' types. We have found that the optimized structures are energetically in the order of δ6 < α' < δ3 < δ4 which is different from the energy order of α'< δ6 < δ4 < δ3 found in the 2D boron monolayer sheets [ACS Nano 6, 7443 (2012)]. A detailed discussion of this study will be presented. The first author acknowledges the McSweeny Fellowship for supporting his research in this work.
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.
ERIC Educational Resources Information Center
Attanucci, Frank J.; Losse, John
2008-01-01
In a first calculus course, it is not unusual for students to encounter the theorems which state: If f is an even (odd) differentiable function, then its derivative is odd (even). In our paper, we prove some theorems which show how the symmetry of a continuous function f with respect to (i) the vertical line: x = a or (ii) with respect to the…
Symmetry and equivalence restrictions in electronic structure calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Taylor, Peter R.
1988-01-01
A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.
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.
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...
Capping-agent-free synthesis of substrate-supported porous icosahedral gold nanoparticles
NASA Astrophysics Data System (ADS)
Wu, Ji Hong; Guan, Zhenping; Yang, Su Ke; Yuan, Peiyan; Xu, Qing-Hua; Xu, Guo Qin
2013-03-01
We report a new capping-agent-free strategy for the synthesis of substrate-supported porous icosahedral Au nanoparticles (NPs) with rough naked surfaces, based on the crystallization from substrate-supported thin solution layers followed by solid-phase thermolysis. The plasmonic properties of icosahedral Au NPs have been studied using single particle dark-field scattering microscopy and spectroscopy. The two distinct localized surface plasmon resonance (LSPR) bands observed in the single particle dark-field spectra can be ascribed to the quadrupole resonance at ca. 425 nm and the size-dependent dipole resonance in the red region (645-708 nm). The unique rough naked surface, the facile synthesis, together with the ability to control the nanoparticle size and to vary the LSPR frequency in the red region, would make the substrate-supported porous icosahedral Au NPs promising on multiple levels in the applications of catalysis, ultrasensitive biosensors, and in surface-enhanced Raman scattering (SERS).We report a new capping-agent-free strategy for the synthesis of substrate-supported porous icosahedral Au nanoparticles (NPs) with rough naked surfaces, based on the crystallization from substrate-supported thin solution layers followed by solid-phase thermolysis. The plasmonic properties of icosahedral Au NPs have been studied using single particle dark-field scattering microscopy and spectroscopy. The two distinct localized surface plasmon resonance (LSPR) bands observed in the single particle dark-field spectra can be ascribed to the quadrupole resonance at ca. 425 nm and the size-dependent dipole resonance in the red region (645-708 nm). The unique rough naked surface, the facile synthesis, together with the ability to control the nanoparticle size and to vary the LSPR frequency in the red region, would make the substrate-supported porous icosahedral Au NPs promising on multiple levels in the applications of catalysis, ultrasensitive biosensors, and in surface
Dynamic Paper Constructions for Easier Visualization of Molecular Symmetry
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.
2010-01-01
A system for construction of simple poster-board models is described. The models dynamically demonstrate the symmetry operations of proper rotation, improper rotation, reflection, and inversion for the chemically important point groups D[subscript 3h], D[subscript 4h], D[subscript 5h], D[subscript 6h], T[subscript d], and O[subscript h]. The…
Web-Supported Chemistry Education: Design of an Online Tutorial for Learning Molecular Symmetry
ERIC Educational Resources Information Center
Korkmaz, Ali; Harwood, William S.
2004-01-01
This paper describes our use of the ADDIE protocol to design and develop an interactive tutorial for students learning molecular symmetry operations and point groups. The tutorial provides a 3-D environment where students can examine molecules, structures, and symmetry elements. Most such tutorials are connected to courses or instructors in…
NASA Astrophysics Data System (ADS)
Cummings, F. R.; Muller, T. F. G.; Malgas, G. F.; Arendse, C. J.
2015-10-01
Potentiostatic anodization of commercially pure, 50 μm-thick titanium (Ti) foil was performed in aqueous, phosphate electrolytes at increasing experimental timeframes at a fixed applied potential for the synthesis of titania nanotube arrays (TNAs). High resolution scanning electron microscopy images, combined with energy dispersive spectroscopy and x-ray diffraction spectra reveal that anodization of the Ti foil in a 1 M NaF+0.5 M H3PO4 electrolyte for 4 h yields a titanate surface with pore diameters ranging between 100 and 500 nm. The presence of rods on the Ti foil surface with lengths exceeding 20 μm and containing high concentrations of phosphor on the exterior was also detected at these conditions, along with micro-sized coral reef-like titanate balls. We propose that the formation of these structures play a major role during the anodization process and impedes nanotube growth during the anodization process. High spatially resolved scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) performed along the length of a single anodized TiO2 nanotube reveals a gradual evolution of the nanotube crystallinity, from a rutile-rich bottom to a predominantly anatase TiO2 structure along its length.
Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
NASA Astrophysics Data System (ADS)
Jiang, Shan; Shen, Yonggang; Zheng, Yonggang; Chen, Zhen
2013-07-01
We show by molecular dynamics simulations that symmetrical quasi-icosahedral structures can be formed in fivefold twinned metallic nanowires (Cu, Au, and Ag) under dynamic tensile loading. The quasi-icosahedral structure, different from the icosahedral nanoclusters found in the past, consists of a twisted original fivefold twinned axis and ten secondary fivefold deformation twins, with five preexisting prismatic and fifteen tetrahedral subunits joined adjacently. Formation of these structures is observed in the necking region during the plastic deformation with successive twinning processes and is found to be independent on the cross-sectional shape as well as the tensile strain rate of the nanowires.
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
Nematic phases and the breaking of double symmetries
Mathy, C.J.M. . E-mail: cmathy@princeton.edu; Bais, F.A. . E-mail: bais@science.uva.nl
2007-03-15
In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra T{sub r} and the symmetry algebra U characterizing the effective 'low energy' theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.
Nematic phases and the breaking of double symmetries
NASA Astrophysics Data System (ADS)
Mathy, C. J. M.; Bais, F. A.
2007-03-01
In this paper, we present a phase classification of (effectively) two-dimensional non-Abelian nematics, obtained using the Hopf symmetry breaking formalism. In this formalism, one exploits the underlying double symmetry which treats both ordinary and topological modes on equal footing, i.e., as representations of a single (non-Abelian) Hopf symmetry. The method introduced in the literature [F.A. Bais, B.J. Schroers, J.K. Slingerland, Broken quantum symmetry and confinement phases in planar physics, Phys. Rev. Lett. 89 (2002) 181601; F.A. Bais, B.J. Schroers, J.K. Slingerland, Hopf symmetry breaking and confinement in (2+1)-dimensional gauge theory, JHEP 05 (2003) 068.] and further developed in a paper published in parallel [F.A. Bais, C.J.M. Mathy, The breaking of quantum double symmetries by defect condensation, 2006, arXiv:cond-mat/0602115.] allows for a full classification of defect mediated as well as ordinary symmetry breaking patterns and a description of the resulting confinement and/or liberation phenomena. After a summary of the formalism, we determine the double symmetries for tetrahedral, octahedral, and icosahedral nematics and their representations. Subsequently the breaking patterns which follow from the formation of admissible defect condensates are analyzed systematically. This leads to a host of new (quantum and classical) nematic phases. Our result consists of a listing of condensates, with the corresponding intermediate residual symmetry algebra Tr and the symmetry algebra U characterizing the effective "low energy" theory of surviving unconfined and liberated degrees of freedom in the broken phase. The results suggest that the formalism is applicable to a wide variety of two-dimensional quantum fluids, crystals and liquid crystals.
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.).
NASA Astrophysics Data System (ADS)
Lowe, M.; Yadav, T. P.; Fournée, V.; Ledieu, J.; McGrath, R.; Sharma, H. R.
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
Lowe, M.; McGrath, R.; Sharma, H. R.; Yadav, T. P.; Fournée, V.; Ledieu, J.
2015-03-07
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe{sub 3}O{sub 4} rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
Opening of an icosahedral boron framework: A combined infrared spectroscopic and computational study
NASA Astrophysics Data System (ADS)
Fagiani, Matias R.; Liu Zeonjuk, L.; Esser, Tim K.; Gabel, Detlef; Heine, Thomas; Asmis, Knut R.; Warneke, Jonas
2015-04-01
The opening of an icosahderal boron cage in the periodinated closo-dodecaborate B12I122- upon deiodination is studied using cryogenic ion trap vibrational spectroscopy combined with electronic structure calculations. Comparison of simulated vibrational spectra to the infrared photodissociation spectra of messenger-tagged B12I122- and B12In- (n = 7-9) formed by skimmer collision induced dissociation shows that the larger clusters absorb exclusively below 975 cm-1 and hence exhibit quasi-icosahedral B12-cage structures, while the higher energy absorptions in-between 1000 and 1300 cm-1 observed for n = 7 can only be recovered by considering a breakup of the icosahedral cage upon deiodination from n = 8 to n = 7.
Scanning Tunneling Microscopy Studies of Surface Structures of Icosahedral Al-Cu-Fe Quasicrystals
Tanhong Cai
2002-12-31
Three papers are included in this dissertation. The first paper: ''Structural aspects of the fivefold quasicrystalline Al-Cu-Fe surface from STM and dynamical LEED studies'', is in press with ''Surface Science''. The second paper: ''An STM study of the atomic structure of the icosahedral Al-Cu-Fe fivefold surface'' is submitted to ''Physical Review B, Rapid Communication''. The third paper: ''Pseudomorphic starfish: arrangement of extrinsic metal atoms on a quasicrystalline substrate'' is submitted to ''Nature''. Following the third paper are general conclusions and appendices that document the published paper ''Structural aspects of the three-fold surface of icosahedral Al-Pd-Mn'' (appearing in volume 461, issue 1-3 of ''Surface Science'' on page L521-L527, 2000), the design as well as the specifications of the aluminum evaporator used in the aluminum deposition study in this dissertation, an extended discussion of the aluminum deposition on the quasicrystalline surface, and the STM database.
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.
Dual-phase glassy/nanoscale icosahedral phase materials in Cu–Zr–Ti–Pd system alloys
Louzguine-Luzgin, Dmitri V.; Churyumov, A.Yu.
2014-10-15
The present work is devoted to an investigation of the formation kinetics, stability and homogeneity area of the nanoscale icosahedral phase formed on heating in the dual-phase glassy/quasicrystalline phase Cu–Zr–Ti–Pd alloys. The data obtained indicate that the Cu–Zr–Ti–Pd icosahedral phase is not a Cu-rich part of the compositional homogeneity area of the Zr–Cu–Pd one. Moreover, Ti, as well as Pd, is found to be an important element stabilizing quasicrystalline phase in the Cu–Zr–Ti–Pd alloys. The formation criteria for Cu- and Zr/Hf-based icosahedral phases are discussed based on the quasilattice constant to average atomic diameter ratio. Deviation from a certain ratio leads to destabilization of the icosahedral phase. By using the isothermal calorimetry traces transformation kinetics above and below the glass-transition region was analyzed. Some difference in the transformation kinetics above and below the glass-transition region allows us to suggest that possible structure changes occur upon glass-transition. - Highlights: • Formation kinetics, stability and homogeneity area of nanoscale icosahedral phase • Cu–Zr–Ti–Pd icosahedral phase is not a Cu-rich part of Zr–Cu–Pd one. • Ti, as well as Pd, is an important element stabilizing quasicrystalline phase. • Difference in transformation kinetics above and below glass-transition region.
Vibration isolation support system for a truncated icosahedral gravitational wave antenna
NASA Astrophysics Data System (ADS)
Velloso, W. F.; Melo, J. L.; Aguiar, O. D.
2000-06-01
We designed a mechanical isolation system for an icosahedral resonant gravitational wave detector we plan to construct in Brazil. We have used the NASTRAN finite element software to perform the numerical analysis. Our results show that the designed system could allow a damping factor better than -200 dB in the spectral range of interest, which is adequate to the sensibility level we want for the antenna.
NASA Astrophysics Data System (ADS)
Fauzi, Wan Nor Farhana Wan Mohd; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah; Sarmin, Nor Haniza
2014-07-01
The nonabelian tensor product was originated in homotopy theory as well as in algebraic K-theory. The nonabelian tensor square is a special case of the nonabelian tensor product where the product is defined if the two groups act on each other in a compatible way and their action are taken to be conjugation. In this paper, the computation of nonabelian tensor square of a Bieberbach group, which is a torsion free crystallographic group, of dimension five with dihedral point group of order eight is determined. Groups, Algorithms and Programming (GAP) software has been used to assist and verify the results.
The structure of cucurbitin: subunit symmetry and organization in situ.
Colman, P M; Suzuki, E; Van Donkelaar, A
1980-02-01
The low-resolution (2 nm) subunit symmetry of cucurbitin, the crystalline seed storage globulin of cucurbits, has been determined by X-ray diffraction. The wet crystals belong to the cubic space group F23 and there are 4 molecules per unit cell. The molecules therefore possess point-group symmetry 23 and contain 12 structural units which at this resolution are indistinguishable. On drying, the crystal lattice dimension shrinks from 13.6 nm to 12.4 nm with no apparent change in symmetry. Diffraction patterns of small crystals spun into a pellet, and sections of dry and wet native seed indicate that in situ the protein is organised in microcrystals of the same unit cell and symmetry. Edestin, the crystalline storage globulin from cannabis, and a crystalline globulin from tobacco seed both have the same crystal lattice as cucurbitin and, very likely, the same subunit symmetry. PMID:7358051
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
Symmetry-protected entangling boundary zero modes in crystalline topological insulators
NASA Astrophysics Data System (ADS)
Chang, Po-Yao; Mudry, Christopher; Ryu, Shinsei
2014-09-01
Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.
NASA Astrophysics Data System (ADS)
Matsuda, H.; Nakayama, T.; Kimura, K.; Murakami, Y.; Suematsu, H.; Kobayashi, M.; Higashi, I.
1995-08-01
This study performs dc conductivity and static magnetic-susceptibility measurements on Li- and Cu-doped β-rhombohedral boron (β-rhombohedral B), which is a unique polymorphic semiconducting (group III) material composed of B12 icosahedral clusters. dc conductivity results show a variable-range-hopping (VRH)-type temperature dependence with a typical localization length of about ~1 Å. In addition, the density of states (DOS) at the Fermi energy, which is calculated from fitted parameters of VRH conduction, was found to have a peak with respect to metal concentration, such that at the highest concentration (Li7.9B105 and Cu4.2B105), metal-doped β-rhombohedral B appears to revert back to an insulator, instead of showing insulator-to-metal transition. Corresponding static magnetic-susceptibility results, however, show a contribution from Pauli paramagnetism in the temperature-independent component χ0, where a similar concentration dependence is shows to that in the DOS of VRH conduction. Based on these properties, we discuss the possibility of filling the intrinsic acceptor band, which originates from the uppermost molecular bonding orbital of the B12 icosahedral cluster that is split by the Jahn-Teller effect. β-rhombohedral B's crystalline structure can also be viewed as a slightly distorted face-centered cubic (fcc) packing of B84 soccer-ball-shaped clusters covalently bound to each other and containing a relatively large number of large-size interstitial doping sites. This structure is considered to be topologically similar to that of fcc C60, although the bonding mechanisms of their clusters are different, and therefore we also describe the similarities and differences between them.
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.
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.
2014-01-01
Background Low-power ultrashort pulsed (USP) lasers operating at wavelengths of 425 nm and near infrared region have been shown to effectively inactivate viruses such as human immunodeficiency virus (HIV), M13 bacteriophage, and murine cytomegalovirus (MCMV). It was shown previously that non-enveloped, helical viruses such as M13 bacteriophage, were inactivated by a USP laser through an impulsive stimulated Raman scattering (ISRS) process. Recently, enveloped virus like MCMV has been shown to be inactivated by a USP laser via protein aggregation induced by an ISRS process. However, the inactivation mechanism for a clinically important class of viruses – non-enveloped, icosahedral viruses remains unknown. Results and discussions We have ruled out the following four possible inactivation mechanisms for non-enveloped, icosahedral viruses, namely, (1) inactivation due to ultraviolet C (UVC) photons produced by non-linear optical process of the intense, fundamental laser beam at 425 nm; (2) inactivation caused by thermal heating generated by the direct laser absorption/heating of the virion; (3) inactivation resulting from a one-photon absorption process via chromophores such as porphyrin molecules, or indicator dyes, potentially producing reactive oxygen or other species; (4) inactivation by the USP lasers in which the extremely intense laser pulse produces shock wave-like vibrations upon impact with the viral particle. We present data which support that the inactivation mechanism for non-enveloped, icosahedral viruses is the impulsive stimulated Raman scattering process. Real-time PCR experiments show that, within the amplicon size of 273 bp tested, there is no damage on the genome of MNV-1 caused by the USP laser irradiation. Conclusion We conclude that our model non-enveloped virus, MNV-1, is inactivated by the ISRS process. These studies provide fundamental knowledge on photon-virus interactions on femtosecond time scales. From the analysis of the transmission
Experimentally Founded Charge Transport Model for Icosahedral Boron-Rich Solids
NASA Astrophysics Data System (ADS)
Werheit, Helmut
Charge transport in icosahedral boron-rich solids, in particular in boron carbide, has been controversially discussed. Theoretical band structure calculations, based on idealized instead of real structures, yield qualitatively wrong results; metallic instead of semiconducting behavior in consequence of neglecting intrinsic structural defects. The theoretical bipolaron hypothesis is not compatible with numerous experimental results. In contrast, the actual energy band schemes of β-rhombohedral boron and boron carbide mainly derived from optical investigations allows the consistent description of most of the experimental results. Electronic transport is a superposition of hopping-type and band-type transport, whose share depends on the actual conditions and the antecedent.
NASA Technical Reports Server (NTRS)
Bleck, Rainer; Bao, Jian-Wen; Benjamin, Stanley G.; Brown, John M.; Fiorino, Michael; Henderson, Thomas B.; Lee, Jin-Luen; MacDonald, Alexander E.; Madden, Paul; Middlecoff, Jacques; Rosinski, James; Smirnova, Tanya G.; Sun, Shan; Wang, Ning
2015-01-01
A hydrostatic global weather prediction model based on an icosahedral horizontal grid and a hybrid terrain following/ isentropic vertical coordinate is described. The model is an extension to three spatial dimensions of a previously developed, icosahedral, shallow-water model featuring user-selectable horizontal resolution and employing indirect addressing techniques. The vertical grid is adaptive to maximize the portion of the atmosphere mapped into the isentropic coordinate subdomain. The model, best described as a stacked shallow-water model, is being tested extensively on real-time medium-range forecasts to ready it for possible inclusion in operational multimodel ensembles for medium-range to seasonal prediction.
Medium-range icosahedral order in quasicrystal-forming Zr{sub 2}Pd binary metallic glass
Huang Li; Fang, X. W.; Wang, C. Z.; Ho, K. M.; Kramer, M. J.; Ding, Z. J.
2011-06-06
Medium-range order in Zr{sub 2}Pd metallic glass was studied using a combination of x-ray diffraction experiment and atomistic simulations. We show that, in contrast to earlier experimental interpretations, the icosahedral-like polyhedron is centered around Pd, rather than Zr. Furthermore, we find that the ordered icosahedral packing around Pd extends to the third shell in the way similar to that in the Bergman-type clusters. The existence of Bergman-type clusters sheds interesting light into the formation of nanoquasicrystal phase during crystallization process of Zr{sub 2}Pd metallic glass.
Hierarchy of bond stiffnesses within icosahedral-based gold clusters protected by thiolates
Yamazoe, Seiji; Takano, Shinjiro; Kurashige, Wataru; Yokoyama, Toshihiko; Nitta, Kiyofumi; Negishi, Yuichi; Tsukuda, Tatsuya
2016-01-01
Unique thermal properties of metal clusters are believed to originate from the hierarchy of the bonding. However, an atomic-level understanding of how the bond stiffnesses are affected by the atomic packing of a metal cluster and the interfacial structure with the surrounding environment has not been attained to date. Here we elucidate the hierarchy in the bond stiffness in thiolate-protected, icosahedral-based gold clusters Au25(SC2H4Ph)18, Au38(SC2H4Ph)24 and Au144(SC2H4Ph)60 by analysing Au L3-edge extended X-ray absorption fine structure data. The Au–Au bonds have different stiffnesses depending on their lengths. The long Au–Au bonds, which are more flexible than those in the bulk metal, are located at the icosahedral-based gold core surface. The short Au–Au bonds, which are stiffer than those in the bulk metal, are mainly distributed along the radial direction and form a cyclic structural backbone with the rigid Au–SR oligomers. PMID:26778685
NASA Astrophysics Data System (ADS)
Bleck, Rainer; Sun, Shan; Li, Haiqin; Benjamin, Stan
2016-04-01
Current efforts to close the gap between weather prediction and climate models have led to the construction of a coupled ocean-atmosphere system consisting of two high-resolution component models, operating on matching icosahedral grids and utilizing adaptive, near-isentropic/isopycnic vertical coordinates. The two components models, FIM and HYCOM (the latter converted to an icosahedral mesh for this purpose), have been tested extensively in twice-daily global medium-range weather prediction (http://fim.noaa.gov) and in real-time ocean data assimilation (http://hycom.org), respectively. The use of matching horizontal grids, currently at resolutions of 15km, 30km and 60km, avoids coastline ambiguities and interpolation errors at the air-sea interface. The intended purpose of the coupled model being subseasonal-to-seasonal prediction, our focus is on mid-term precipitation biases and the statistical steadiness of the atmospheric circulation (blocking frequency, Rossby wave breaking, meridional heat transport, etc.), as well as on possible causes of ocean model drift. An attempt is made to isolate the weather model's role in modifying water mass properties and ocean circulations (including meridional overturning) by comparing coupled model results to ocean-only experiments forced by observed atmospheric boundary conditions. A multi-decadal run at 60km resolution is used to illustrate ENSO variability in the coupled system.
Hierarchy of bond stiffnesses within icosahedral-based gold clusters protected by thiolates.
Yamazoe, Seiji; Takano, Shinjiro; Kurashige, Wataru; Yokoyama, Toshihiko; Nitta, Kiyofumi; Negishi, Yuichi; Tsukuda, Tatsuya
2016-01-01
Unique thermal properties of metal clusters are believed to originate from the hierarchy of the bonding. However, an atomic-level understanding of how the bond stiffnesses are affected by the atomic packing of a metal cluster and the interfacial structure with the surrounding environment has not been attained to date. Here we elucidate the hierarchy in the bond stiffness in thiolate-protected, icosahedral-based gold clusters Au25(SC2H4Ph)18, Au38(SC2H4Ph)24 and Au144(SC2H4Ph)60 by analysing Au L3-edge extended X-ray absorption fine structure data. The Au-Au bonds have different stiffnesses depending on their lengths. The long Au-Au bonds, which are more flexible than those in the bulk metal, are located at the icosahedral-based gold core surface. The short Au-Au bonds, which are stiffer than those in the bulk metal, are mainly distributed along the radial direction and form a cyclic structural backbone with the rigid Au-SR oligomers. PMID:26778685
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2003-12-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
NASA Astrophysics Data System (ADS)
Brading, Katherine; Castellani, Elena
2010-01-01
Preface; Copyright acknowledgements; List of contributors; 1. Introduction; Part I. Continuous Symmetries: 2. Classic texts: extracts from Weyl and Wigner; 3. Review paper: On the significance of continuous symmetry to the foundations of physics C. Martin; 4. The philosophical roots of the gauge principle: Weyl and transcendental phenomenological idealism T. Ryckman; 5. Symmetries and Noether's theorems K. A. Brading and H. R. Brown; 6. General covariance, gauge theories, and the Kretschmann objection J. Norton; 7. The interpretation of gauge symmetry M. Redhead; 8. Tracking down gauge: an ode to the constrained Hamiltonian formalism J. Earman; 9. Time-dependent symmetries: the link between gauge symmetries and indeterminism D. Wallace; 10. A fourth way to the Aharanov-Bohm effect A. Nounou; Part II. Discrete Symmetries: 11. Classic texts: extracts from Lebniz, Kant and Black; 12. Review paper: Understanding permutation symmetry S. French and D. Rickles; 13. Quarticles and the identity of discernibles N. Hugget; 14. Review paper: Handedness, parity violation, and the reality of space O. Pooley; 15. Mirror symmetry: what is it for a relational space to be orientable? N. Huggett; 16. Physics and Leibniz's principles S. Saunders; Part III. Symmetry Breaking: 17: Classic texts: extracts from Curie and Weyl; 18. Extract from G. Jona-Lasinio: Cross-fertilization in theoretical physics: the case of condensed matter and particle physics G. Jona-Lasinio; 19. Review paper: On the meaning of symmetry breaking E. Castellani; 20. Rough guide to spontaneous symmetry breaking J. Earman; 21. Spontaneous symmetry breaking: theoretical arguments and philosophical problems M. Morrison; Part IV. General Interpretative Issues: 22. Classic texts: extracts from Wigner; 23. Symmetry as a guide to superfluous theoretical structure J. Ismael and B. van Fraassen; 24. Notes on symmetries G. Belot; 25. Symmetry, objectivity, and design P. Kosso; 26. Symmetry and equivalence E. Castellani.
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.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
Performance Analysis of high-order remap-type advection scheme on icosahedral-hexagonal grid
NASA Astrophysics Data System (ADS)
Mittal, Rashmi; Dubey, Sarvesh; Saxena, Vaibhav; Meurdesoif, Yann
2014-05-01
A comparative performance analysis on computational cost of second order advection schemes FF-CSLAM (Flux form conservative semi-Lagrangian multi-tracer transport scheme) and it's two simplifications on Icosahedral grid has been presented. Tracer transport is one of the main building blocks in atmospheric models and hence their performance greatly determines the overall performance of the model. FF-CSLAM falls in the category of arbitrary Lagrangian Eulerian (ALE) scheme. It exploits the finite volume formulation and therefore it is inherently conservative. Flux-area through edges are approximated with great circle arcs in an upwind fashion. Bi-quadratic sub-grid scale reconstructions using weighted least-squares method is employed to approximate trace field. Area integrals on the overlapped region of flux-area and static Eulerian meshes are evaluated via line-integrals. A brief description of implementation of FF-CSLAM on icosahedral -hexagonal meshes along with and its numerical accuracy in terms of standard test cases will be presented. A comparative analysis of the computational overhead is necessary to assess the suitability of FF-CSLAM for massively parallel and multi-threading computer architectures in comparison to other advection schemes implemented on icosahedral grids. The main focus of this work is to present the implementation of the shared memory parallelization and to describe the memory access pattern of the numerical scheme. FF-CSLAM is a remap-type advection scheme, thus extra calculation are done in comparison to the other advection schemes. The additional computations are associated with the search required to find the overlap area between the area swept through the edge and the underlining grid. But the experiments shows that the associated computational overhead is minimal for multi-tracer transport. It will be shown that for the Courant Number less than one, FF-CSLAM, the computations are not expensive. Since the grid cells are arranged in
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
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 π/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.
Thermal Conductivity and Seebeck Coefficients of Icosahedral Boron Arsenide Films on Silicon Carbide
Y Gong; Y Zhang; M Dudley; Y Zhang; J Edgar; P Heard; M Kuball
2011-12-31
The thermal conductivity of icosahedral boron arsenide (B{sub 12}As{sub 2}) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3{omega} technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 {micro}V/K and 136 {micro}V/K for samples grown at 1350 C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Defining criteria for oligomannose immunogens for HIV using icosahedral virus capsid scaffolds.
Astronomo, Rena D; Kaltgrad, Eiton; Udit, Andrew K; Wang, Sheng-Kai; Doores, Katie J; Huang, Cheng-Yuan; Pantophlet, Ralph; Paulson, James C; Wong, Chi-Huey; Finn, M G; Burton, Dennis R
2010-04-23
The broadly neutralizing antibody 2G12 recognizes a conserved cluster of high-mannose glycans on the surface envelope spike of HIV, suggesting that the "glycan shield" defense of the virus can be breached and may, under the right circumstances, serve as a vaccine target. In an attempt to recreate features of the glycan shield semisynthetically, oligomannosides were coupled to surface lysines on the icosahedral capsids of bacteriophage Q beta and cowpea mosaic virus (CPMV). The Q beta glycoconjugates, but not CPMV, presented oligomannose clusters that bind the antibody 2G12 with high affinity. However, antibodies against these 2G12 epitopes were not detected in immunized rabbits. Rather, alternative oligomannose epitopes on the conjugates were immunodominant and elicited high titers of anti-mannose antibodies that do not crossreact with the HIV envelope. The results presented reveal important design considerations for a carbohydrate-based vaccine component for HIV. PMID:20416507
Reinvestigation of long-range magnetic ordering in icosahedral Tb-Mg-Zn
NASA Astrophysics Data System (ADS)
Islam, Z.; Fisher, I. R.; Zarestky, J.; Canfield, P. C.; Stassis, C.; Goldman, A. I.
1998-05-01
We present results of a study of possible magnetic ordering in the icosahedral phase of Tb-Mg-Zn probed by bulk magnetization measurements and neutron diffraction. Measurements on both crushed single grains and cast polycrystalline samples of Tb-Mg-Zn were performed. Magnetization measurements on both samples reveal only a spin-glass-like transition at approximately 5.8 K. Neutron diffraction from the crushed single grains reveals only short-range magnetic ordering at low temperatures, with no evidence of the long-range magnetic ordering reported previously [Charrier, Ouladdiaf, and Schmitt, Phys. Rev. Lett. 78, 4637 (1997)]. Likewise, the cast polycrystalline samples exhibit primarily diffuse magnetic scattering at low temperature, but at least one relatively sharp diffraction peak was observed. Our results indicate that for single grain samples there is no long-range magnetic ordering and that, at best, the magnetic ordering in these quasicrystalline alloys is not very robust.
Observation of Quasimagnetic Structures in Rare-Earth-Based Icosahedral Quasicrystals
Charrier, B.; Schmitt, D.; Ouladdiaf, B.
1997-06-01
The first observation of long-range quasiperiodic antiferromagnetic structures in quasicrystals, namely the heavy rare-earth-based icosahedral R{sub 8}Mg{sub 42}Zn{sub 50} compounds (R=Tb , Dy, Ho, Er), is reported. This {ital quasimagnetic} ordering is characterized by the propagation vector {bold Q}=((1)/(4),0,0,0,0,0) in the six-dimensional notation. Simultaneously, broad magnetic peaks appear in the neutron diffraction patterns, characteristic of a short-range ordering. The coexistence of two different magnetic correlation lengths suggests the presence of two types of crystallographic sites for the rare-earth atoms. {copyright} {ital 1997} {ital The American Physical Society}
Terrace-dependent nucleation of small Ag clusters on a five-fold icosahedral quasicrystal surface
Unal, B.; Evans, J.W.; Lograsso, T.A.; Ross, A.R.; Jenks, C.J.; Thiel, P.A.
2007-07-21
Nucleation of Ag islands on the five-fold surface of icosahedral Al-Pd-Mn is influenced strongly by trap sites. Submonolayers of Ag prepared by deposition at 365 K and with a flux of 1 x 10{sup -3} monolayers/s exhibit a variation in Ag island densities across different terraces. Comparisons with previous work and with rate equation analysis indicate that trap sites are not saturated under these experimental conditions and that the difference in island densities is not necessarily due to variation in trap densities. While it could have a number of different origins, our results point to a terrace-dependent value of the effective diffusion barrier for Ag adatoms.
Reinterpretation of the zero-temperature conductivity in icosahedral AlPdRe
NASA Astrophysics Data System (ADS)
Rapp, Ö.
2016-07-01
The zero-temperature conductivity σ (0 ) of icosahedral (i )-AlPdRe has been found to be simply related to the resistance ratio R =ρ4.2 K/ρ295 K by a power law, σ (0 ) ˜R-1.74 , over four orders of magnitude in σ (0 ) . This relation includes metallic single grain samples, and polygrain samples of different morphologies which are metallic for small R values, and insulatinglike at large R . Electronic transport properties of single grain i -AlPdRe samples are thus found to be on common ground with polygrain i -AlPdRe. The relation between R and σ (0 ) can be qualitatively understood from published band-structure calculations on quasicrystalline approximants.
Development of a genetic system for the archaeal virus Sulfolobus turreted icosahedral virus (STIV).
Wirth, Jennifer Fulton; Snyder, Jamie C; Hochstein, Rebecca A; Ortmann, Alice C; Willits, Deborah A; Douglas, Trevor; Young, Mark J
2011-06-20
Our understanding of archaeal viruses has been limited by the lack of genetic systems for examining viral function. We describe the construction of an infectious clone for the archaeal virus Sulfolobus turreted icosahedral virus (STIV). STIV was isolated from a high temperature (82°C) acidic (pH 2.2) hot spring in Yellowstone National Park and replicates in the archaeal model organism Sulfolobus solfataricus (Rice et al., 2004). While STIV is one of most studied archaeal viruses, little is known about its replication cycle. The development of an STIV infectious clone allows for directed gene disruptions and detailed genetic analysis of the virus. The utility of the STIV infectious clone was demonstrated by gene disruption of STIV open reading frame (ORF) B116 which resulted in crippled virus replication, while disruption of ORFs A197, C381 and B345 was lethal for virus replication. PMID:21496857
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-03-18
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine-thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine-cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590
DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility
NASA Astrophysics Data System (ADS)
Dubos, T.; Dubey, S.; Tort, M.; Mittal, R.; Meurdesoif, Y.; Hourdin, F.
2015-10-01
The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-01-01
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine–thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine–cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590
Classification of stable Dirac and Weyl semimetals with reflection and rotational symmetry
NASA Astrophysics Data System (ADS)
Gao, Zihao; Hua, Meng; Zhang, Haijun; Zhang, Xiao
2016-05-01
Three-dimensional (3D) Dirac and Weyl semimetals are novel states of quantum matter. We classify stable 3D Dirac and Weyl semimetals with reflection and rotational symmetry in the presence of time reversal symmetry and spin-orbit coupling, which belong to seventeen different point groups. They have two classes of reflection symmetry, with the mirror plane parallel and perpendicular to rotation axis. In both cases two types of Dirac points, existing through accidental band crossing (ABC) or at a time reversal invariant momentum (TBC), are determined by four different reflection symmetries. We classify those two types of Dirac points with a combination of different reflection and rotational symmetries. We further classify Dirac and Weyl line nodes to show in which types of mirror plane they can exist. Finally we discuss that Weyl line nodes and Dirac points can exist at the same time taking C4 v symmetry as an example.
Multiporous carbon allotropes transformed from symmetry-matched carbon nanotubes
NASA Astrophysics Data System (ADS)
Cai, Yingxiang; Wang, Hao; Xu, Shengliang; Hu, Yujie; Liu, Ning; Xu, Xuechun
2016-06-01
Carbon nanotubes (CNTs) with homogeneous diameters have been proven to transform into new carbon allotropes under pressure but no studies on the compression of inhomogeneous CNTs have been reported. In this study, we propose to build new carbon allotropes from the bottom-up by applying pressure on symmetry-matched inhomogeneous CNTs. We find that the (3,0) CNT with point group C3v and the (6,0) CNT with point group C6v form an all sp3 hybridized hexagonal 3060-Carbon crystal, but the (4,0) CNT with point group D4h and the (8,0) CNT with point group D8h polymerize into a sp2+sp3 hybridized tetragonal 4080-Carbon structure. Their thermodynamic, mechanical and dynamic stabilities show that they are potential carbon allotropes to be experimentally synthesized. The multiporous structures, excellently mechanical properties and special electronic structures (semiconductive 3060-Carbon and semimetallic 4080-Carbon) imply their many potential applications, such as gases purification, hydrogen storage and lightweight semiconductor devices. In addition, we simulate their feature XRD patterns which are helpful for identifying the two carbon crystals in future experimental studies.
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.
Gray, J E; Vogt, A
1997-01-01
Is symmetry informative? The answer is both yes and no. We examine what information and symmetry are and how they are related. Our approach is primarily mathematical, not because mathematics provides the final word, but because it provides an insightful and relatively precise starting point. Information theory treats transformations that messages undergo from source to destination. Symmetries are information that leave some property of interest unchanged. In this respect the studies of information and symmetry can both be regarded as a Quest for the identity transformation. PMID:9224554
NASA Astrophysics Data System (ADS)
Li, Dong
1997-11-01
A systematic study of the electronic structures, total energies and optical properties of B12-based boron and boron-rich compounds and boron oxide compounds has been conducted by the first-principles orthogonalized linear combination of atomic orbitals method. The materials involved are: α-r-B12, B12As2,/ B12P2,/ B11C(CBC)/ (or/ B4C),/ B13C2,/ B12O2,/ (B10Si2)Si2,/ (B10Si2)Si2-I, B2O3-I and B2O3-II. The band structures show that α-r-B12,/ B12As2,/ B12P2,/ B11C(CBC),/ B12O2,/ (B10Si2)Si2, and (B10Si2)Si2-I are semiconductors with band gaps ranging from 1.29 eV to 3.04 eV while B13C2 is a metal with an intrinsic hole at the top of the valence band below a semiconductor-like gap. The study also shows that B2O3-I and B2O3-II are wide gap insulators with calculated LDA gaps of 6.20 eV and 8.85 eV separately. The calculated density of states are resolved into atomic and orbital partial components and the valence-charge distributions are also studied. The natural bonding characteristics in these crystals are illuminated by evaluating the Mulliken effective charges on each atom and overlap populations between pairs of atoms. It is shown that inter-icosahedral bonding is much stronger than the intra-icosahedral bonding in the B12- based crystals. The chain elements in B12As2,/ B12P2,/ (B10Si2)Si2 and (B10Si2)Si2-I donate electrons to the icosahedra, while B11C(CBC),/ B13C2 and B12O2 gain a slight amount of charge in forming strong covalent bonds. For boron oxide compounds, B2O3-II is found to be more ionic than B2O3-I. It is also concluded that the sp2 planar bonding in B2O3-I is stronger than the sp3 tetrahedral bonding in B2O3-II. The bulk moduli of α-r-B12,/ B12As2,/ B12P2,/ B11C(CBC),/ B13C2 and B12O2 are estimated by means of total energy calculation as a function of crystal volume, and are to be considered as upper limits. We have also calculated the interband optical conductivities and the complex dielectric functions. Static dielectric constants for icosahedral
Pauling, L. )
1988-07-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, noise) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals.
Geometrical symmetries in atomic nuclei: From theory predictions to experimental verifications
NASA Astrophysics Data System (ADS)
Dudek, J.; Góźdź, A.; Molique, H.; Curien, D.
2013-02-01
In the lectures delivered at the 2012 Predeal School an overview has been presented of the contemporary theory of the nuclear geometrical (shape) symmetries. The formalism combines two most powerful theory tools applicable in the context: The group- and group-representation theory together with the modern realistic mean-field theory. We suggest that all point-groups of symmetry of the mean-field Hamiltonian, sufficiently rich in symmetry elements (as discussed in the text) may lead to the magic numbers that characterise such a group in analogy with the spherical magic gaps characterising nuclear sphericity. We discuss in simple terms the mathematical and physical arguments for the presence of such symmetries in nuclei. In our opinion: It is not so much the question of Whether? - but rather: Where in the Nuclear Chart several of the point group-symmetries will be seen? We focus our presentation on the tetrahedral symmetry with the magic numbers calculated to be 32, 40, 56, 64, 70, 90 and 136, and discuss qualitatively the problem of the formulation of the experimental criteria which would allow for the final discovery of the tetrahedral symmetry in subatomic physics.
Ab initio Ti-Zr-Ni phase diagram predicts stability of icosahedral TiZrNi quasicrystals
NASA Astrophysics Data System (ADS)
Hennig, R. G.; Carlsson, A. E.; Kelton, K. F.; Henley, C. L.
2005-04-01
The ab initio phase diagram determines the energetic stability of the icosahedral TiZrNi quasicrystal. The complete ab initio zero-temperature ternary phase diagram is constructed from the calculated energies of the elemental, binary and ternary Ti-Zr-Ni phases. For this, the icosahedral i -TiZrNi quasicrystal is approximated by periodic structures of up to 123 atoms/unit cell, based on a decorated-tiling model [R. G. Hennig, K. F. Kelton, A. E. Carlsson, and C. L. Henley, Phys. Rev. B 67, 134202 (2003)]. The approximant structures containing the 45-atom Bergman cluster are nearly degenerate in energy, and are all energetically stable against the competing phases. It is concluded that i -TiZrNi is a ground-state quasicrystal, as it is experimentally the low-temperature phase for its composition.
"Quasi-Antiferromagnetic" Ordering in the R-Mg-Zn Icosahedral Alloys? The Case of Tb-Mg-Zn
NASA Astrophysics Data System (ADS)
Goldman, A. I.; Islam, Z.; Fisher, I. R.; Panchula, A. F.; Cheon, K. O.; Canfield, P. C.; Stassis, C.; Zarestky, J.
1998-03-01
Recently, it was reported that long-range magnetic ordering was observed in several of the new rare earth containing icosahedral alloys, R-Mg-Zn (R=Tb, Dy, Ho, Er) (B. Charrier et al., Phys. Rev. Lett. 78, 4637, 1997.). At low temperatures, the antiferromagnetic Bragg peaks, while weak, could be indexed to the icosahedral parent phase with good accuracy. In addition, significant magnetic diffuse scattering, indicating only short-range magnetic order, was also observed. However, bulk magnetization measurements have evidenced only a spin-glass transition at low temperatures, and no antiferromagnetic transition. We will report on new neutron scattering measurements of the magnetic order in Tb-Mg-Zn powder samples produced from crushed single-crystals, used to improve sample purity. Our results for these samples show only the diffuse component of the magnetic scattering at low temperature, and no antiferromagnetic Bragg peaks. We will discuss several possibilities for the discrepencies between the two experiments.
Chern, I-Liang
1994-08-01
Two versions of a control volume method on a symmetrized icosahedral grid are proposed for solving the shallow-water equations on a sphere. One version expresses of the equations in the 3-D Cartersian coordinate system, while the other expresses the equations in the northern/southern polar sterographic coordinate systems. The pole problem is avoided because of these expressions in both versions and the quasi-homogenity of the icosahedral grid. Truncation errors and convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence test for a steady zonal flow is demonstrated. Several simulations of Rossby-Haurwitz waves with various numbers are also performed.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Symmetries of Spectral Problems
NASA Astrophysics Data System (ADS)
Shabat, A.
Deriving abelian KdV and NLS hierarchies, we describe non-abelian symmetries and "pre-Lax" elementary approach to Lax pairs. Discrete symmetries of spectral problems are considered in Sect. 4.2. Here we prove Darboux classical theorem and discuss a modern theory of dressing chains.
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 Effects in Computation
NASA Astrophysics Data System (ADS)
Yao, Andrew Chi-Chih
2008-12-01
The concept of symmetry has played a key role in the development of modern physics. For example, using symmetry, C.N. Yang and other physicists have greatly advanced our understanding of the fundamental laws of physics. Meanwhile, computer scientists have been pondering why some computational problems seem intractable, while others are easy. Just as in physics, the laws of computation sometimes can only be inferred indirectly by considerations of general principles such as symmetry. The symmetry properties of a function can indeed have a profound effect on how fast the function can be computed. In this talk, we present several elegant and surprising discoveries along this line, made by computer scientists using symmetry as their primary tool. Note from Publisher: This article contains the abstract only.
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 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.
Speculation of equilibrium pressure of Ti36Zr40Ni20Pd4 icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Huang, Huogen; Chen, Liang
2015-08-01
Ti-Zr-Ni quasicrystals have been demonstrated to store a large number of hydrogen atoms, which implies strong potential application in hydrogen energy field for them. However, the desorption of hydrogen atoms in the quasicrystals is quite difficult, with the indication of high desorption temperature and slow desorption rate. The shortage limits their use in the field to a large extent. But this kind of quasicrystals might be used in nuclear fusion energy field, because tritium as a coral fuel for nuclear fusion needs tight storage. However, equilibrium pressure at room temperature of Ti-Zr-Ni quasicrystals, important for their application in fusion energy field, has not been clear yet. In this work, we designed a gas-solid reaction system with the pressure resolution of 10-8Pa and carried out hydrogen desorption investigation at different temperatures on Ti36Zr40Ni20Pd4 icosahedral quasicrystal. Based on three Pressure-Composition-Temperature desorption curves, we speculate according to Van't Hoff theory about hydrogen storage that its equilibrium pressure at room temperature could be at the magnitude of 10-6Pa, displaying good stability of hydrogen in the quasicrystal and also implying application prospects in fusion energy field for quasicrystals of this type.
Atomic structure and phason modes of the Sc–Zn icosahedral quasicrystal
Yamada, Tsunetomo; Takakura, Hiroyuki; Euchner, Holger; Pay Gómez, Cesar; Bosak, Alexei; Fertey, Pierre; de Boissieu, Marc
2016-01-01
The detailed atomic structure of the binary icosahedral (i) ScZn7.33 quasicrystal has been investigated by means of high-resolution synchrotron single-crystal X-ray diffraction and absolute scale measurements of diffuse scattering. The average atomic structure has been solved using the measured Bragg intensity data based on a six-dimensional model that is isostructural to the i-YbCd5.7 one. The structure is described with a quasiperiodic packing of large Tsai-type rhombic triacontahedron clusters and double Friauf polyhedra (DFP), both resulting from a close-packing of a large (Sc) and a small (Zn) atom. The difference in chemical composition between i-ScZn7.33 and i-YbCd5.7 was found to lie in the icosahedron shell and the DFP where in i-ScZn7.33 chemical disorder occurs on the large atom sites, which induces a significant distortion to the structure units. The intensity in reciprocal space displays a substantial amount of diffuse scattering with anisotropic distribution, located around the strong Bragg peaks, that can be fully interpreted as resulting from phason fluctuations, with a ratio of the phason elastic constants K 2/K 1 = −0.53, i.e. close to a threefold instability limit. This induces a relatively large perpendicular (or phason) Debye–Waller factor, which explains the vanishing of ‘high-Q perp’ reflections. PMID:27437112
Valence band structure of the icosahedral Ag-In-Yb quasicrystal
Sharma, H. R.; Simutis, G.; Dhanak, V. R.; Nugent, P. J.; McGrath, R.; Cui, C.; Shimoda, M.; Tsai, A. P.; Ishii, Y.
2010-03-01
The valence band structure of the icosahedral (i) Ag-In-Yb quasicrystal, which is isostructural to the binary i-Cd-Yb system, is investigated by ultraviolet photoemission spectroscopy (UPS). Experimental results are compared with electronic-structure calculations of a cubic approximant of the same phase. UPS spectra from the fivefold, threefold, and twofold i-Ag-In-Yb surfaces reveal that the valence band near to the Fermi level is dominated by Yb 4f-derived states, in agreement with calculations. The spectra also exhibit peaks which are surface core level shifted, caused by changes in the electronic structure in surface layers. Calculations yield a pseudogap in the density of states due to a hybridization of the Yb 5d band with the Ag 5p and In 5p bands. Both experimental and calculated band features are very similar to those of Cd-Yb. The modification of the band structure after surface treatment by sputtering and by oxidation is also studied. Additionally, the work function of i-Ag-In-Yb measured from the width of UPS spectrum is found to be almost unaffected by surface orientation, but increases after sputtering or oxidation.
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.
Reinvestigation of long-range magnetic ordering in icosahedral Tb-Mg-Zn
Islam, Z.; Fisher, I.R.; Zarestky, J.; Canfield, P.C.; Stassis, C.; Goldman, A.I.
1998-05-01
We present results of a study of possible magnetic ordering in the icosahedral phase of Tb-Mg-Zn probed by bulk magnetization measurements and neutron diffraction. Measurements on both crushed single grains and cast polycrystalline samples of Tb-Mg-Zn were performed. Magnetization measurements on both samples reveal only a spin-glass-like transition at approximately 5.8K. Neutron diffraction from the crushed single grains reveals only short-range magnetic ordering at low temperatures, with no evidence of the long-range magnetic ordering reported previously [Charrier, Ouladdiaf, and Schmitt, Phys. Rev. Lett. {bold 78}, 4637 (1997)]. Likewise, the cast polycrystalline samples exhibit primarily diffuse magnetic scattering at low temperature, but at least one relatively sharp diffraction peak was observed. Our results indicate that for single grain samples there is no long-range magnetic ordering and that, at best, the magnetic ordering in these quasicrystalline alloys is not very robust. {copyright} {ital 1998} {ital The American Physical Society}
Thermal conductivity and Seebeck coefficients of icosahedral boron arsenide films on silicon carbide
Gong, Y.; Kuball, M.; Zhang, Y.; Dudley, M.; Zhang, Y.; Edgar, J. H.; Heard, P. J.
2010-10-15
The thermal conductivity of icosahedral boron arsenide (B{sub 12}As{sub 2}) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3{omega} technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 deg. C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 {mu}V/K and 136 {mu}V/K for samples grown at 1350 deg. C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Aspects of emergent symmetries
NASA Astrophysics Data System (ADS)
Gomes, Pedro R. S.
2016-03-01
These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.
Sequential flavor symmetry breaking
Feldmann, Thorsten; Jung, Martin; Mannel, Thomas
2009-08-01
The gauge sector of the standard model exhibits a flavor symmetry that allows for independent unitary transformations of the fermion multiplets. In the standard model the flavor symmetry is broken by the Yukawa couplings to the Higgs boson, and the resulting fermion masses and mixing angles show a pronounced hierarchy. In this work we connect the observed hierarchy to a sequence of intermediate effective theories, where the flavor symmetries are broken in a stepwise fashion by vacuum expectation values of suitably constructed spurion fields. We identify the possible scenarios in the quark sector and discuss some implications of this approach.
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.
NASA Astrophysics Data System (ADS)
Golubitsky, Martin
2012-04-01
Many gaits of four-legged animals are described by symmetry. For example, when a horse paces it moves both left legs in unison and then both right legs and so on. The motion is described by two symmetries: Interchange front and back legs, and swap left and right legs with a half-period phase shift. Biologists postulate the existence of a central pattern generator (CPG) in the neuronal system that sends periodic signals to the legs. CPGs can be thought of as electrical circuits that produce periodic signals and can be modeled by systems with symmetry. In this lecture we discuss animal gaits; use gait symmetries to construct a simplest CPG architecture that naturally produces quadrupedal gait rhythms; and make several testable predictions about gaits.
NASA Astrophysics Data System (ADS)
Lovelady, Benjamin C.; Wheeler, James T.
2016-04-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dimensional Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected S O (n ) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an S O (n -1 ,1 ) connection on the spacetime. The principal fiber bundle character of the original S O (n ) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
NASA Astrophysics Data System (ADS)
Castaños, Octavio
2010-09-01
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
Schein, Stan; Gayed, James Maurice
2014-01-01
The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry––tetrahedral, octahedral, and icosahedral––are the 5 Platonic polyhedra, the 13 Archimedean polyhedra––including the truncated icosahedron or soccer ball––and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, “Goldberg polyhedra,” which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a “Goldberg triangle.” We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler’s rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry. PMID:24516137
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.
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
Pauling, L. )
1988-11-01
A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals.
Point symmetry in x-ray shadow imaging systems
Aristov, V.V.; Shabel'nikov, L.G.
1988-04-01
General geometrical features have been examined to identify point-group symmetries in x-ray imaging systems. In a stereospecific system, the group is the b/w antisymmetry group 2/m'. In a computerized tomography system, the symmetry is described by the limiting Curie group /infinity//m/center dot/m, while for a tomosynthesis system (transaxial tomography), it is /infinity//m. The operations in these groups have been examined in the production of shadow images involving distributed attenuation coefficients, particularly for stereospecific images recorded with an MIR-3 x-ray microscope. Curie's principle is used to show that reconstructed paired images for two intersecting objects can be considered as the equivalent of stereoscopic pairs for computer-aided tomography, which is not so for transaxial tomography.
Bubeck, Doryen; Filman, David J.; Kuzmin, Mikhail; Fuller, Stephen D.; Hogle, James M.
2008-01-01
During the entry process many icosahedral viruses must adopt a lower-order symmetry or incur a symmetry mismatch to release their genome through a single site. A membrane model system in which poliovirus was bound to receptor-decorated liposomes was used to pioneer techniques that studied the break in the symmetry of the initial attachment complex by cryo-electron microscopy. Novel methods involving a fiducial marker for the membrane contact point were developed to objectively determine the symmetry of this complex and provide a starting model to initiate a bootstrap orientation refinement. Here we analyze how errors in the subjective assignment of this position affect the determination of symmetry, and the accuracy of calculating Euler angles for each raw image. In this study we have optimized the method and applied it to study the membrane-attachment complex of Semliki Forest virus (SFV), a model system for enveloped virus fusion. The resulting reconstruction of the SFV-membrane complex with a fiducial provides the first experimental evidence that this pre-fusion cell entry intermediate approaches the membrane along the viral 5fold axis. The analysis reported here, and its subsequent application to enveloped virus fusion, indicate that this is a robust tool for solving the structures of mixed-symmetry complexes. PMID:18442921
Chen, N. . E-mail: asyzxy@imr.edu; Louzguine, D.V.; Ranganathan, S.; Inoue, A.
2005-02-01
From the quaternary Ti-Zr-Hf-Ni phase diagram, the cross-section at 20 at.% Ni was selected for investigation. The icosahedral quasicrystalline, crystalline and amorphous phases were observed to form in nine kinds of rapidly solidified (Ti{sub x}Zr{sub y}Hf{sub z}){sub 80}Ni{sub 20} (x + y + z = 1) alloys at different compositions. The quasilattice constants of 0.519 and 0.531 nm were obtained for the icosahedral phase formed in the melt-spun Ti{sub 40}Zr{sub 20}Hf{sub 20}Ni{sub 20} and Ti{sub 20}Zr{sub 40}Hf{sub 20}Ni{sub 20} alloys, respectively. The icosahedral phase formed in the melt-spun Ti{sub 40}Zr{sub 20}Hf{sub 20}Ni{sub 20} alloy especially is thermodynamically stable. The supercooled liquid region of the Ti{sub 20}Zr{sub 20}Hf{sub 40}Ni{sub 20} glassy alloy reached 64 K. From these results a comparison of quasicrystal-forming and glass-forming abilities was carried out. The quasicrystal-forming ability was reduced and glass-forming ability was improved with an increase in Hf and Zr contents in the (Ti{sub x}Zr{sub y}Hf{sub z}){sub 80}Ni{sub 20} alloys. On the other hand, an increase in Ti content caused an improvement in quasicrystal-forming ability.
NASA Astrophysics Data System (ADS)
Loebbert, Florian
2016-08-01
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfel’d's original motivation to construct solutions to the quantum Yang–Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in quantum, two-dimensional field theories and how its generators are renormalized. Implications of Yangian symmetry on the two-dimensional scattering matrix are investigated. We furthermore consider the important case of discrete Yangian symmetry realized on integrable spin chains. Finally we give a brief introduction to Yangian symmetry in planar, four-dimensional super Yang–Mills theory and indicate its impact on the dilatation operator and tree-level scattering amplitudes. These lectures are illustrated by several examples, in particular the two-dimensional chiral Gross–Neveu model, the Heisenberg spin chain and { N }=4 superconformal Yang–Mills theory in four dimensions.
Obaid, R.; Leibscher, M.
2015-02-14
We present a molecular symmetry analysis of electronic states and transition dipole moments for molecules which undergo large amplitude intramolecular torsions. The method is based on the correlation between the point group of the molecule at highly symmetric configurations and the molecular symmetry group. As an example, we determine the global irreducible representations of the electronic states and transition dipole moments for the quinodimethane derivative 2-[4-(cyclopenta-2,4-dien-1-ylidene)cyclohexa-2,5-dien-1-ylidene]-2H-1, 3-dioxole for which two torsional degrees of freedom can be activated upon photo-excitation and construct the resulting symmetry adapted transition dipole functions.
Icosahedral short-range order in amorphous Cu80Si20 by ab initio molecular dynamics simulation study
Wu, S.; Kramer, Matthew J.; Fang, Xiaowei; Wang, Shy-Guey; Wang, Cai-Zhuang; Ho, Kai-Ming; Ding, Z.J.; Chen, L.Y.
2012-04-26
Short-range order in liquid and amorphous structures of Cu80Si20 is studied by ab initio molecular dynamics simulations. We performed the simulations at 1140 and 300 K respectively to investigate the local structure change from liquid to amorphous. The result of structure factor in comparison with experimental data indicates that our simulation of amorphous Cu80Si20 is reliable. By using the bond-angle distribution function, Honeycutt–Andersen index, Voronoi tessellation method, and the atomistic cluster alignment method, the icosahedral short-range order in the system is revealed. Strong Cu–Si interaction was also observed.
Tai, K. P.; Gao, N.; Dai, X. D.; Li, J. H.; Lai, W. S.; Liu, B. X.
2006-08-28
Metallic glasses are obtained in an immiscible Nb-Ag system by ion beam mixing and an atomic configuration in the amorphous structure is discovered, i.e., an icositetrahedral ordering, which, together with an icosahedral ordering also observed in the Nb-Ag metallic glasses and in some previously reported systems, helps in formulating a structural spectrum of the amorphous solids. The experimental characterization and atomistic modeling with an ab initio derived Nb-Ag potential demonstrate the significance of structural heredity, i.e., the crystalline structures of the constituent metals play a decisive role in determining the atomic structure of the metallic glasses in the system.
NASA Astrophysics Data System (ADS)
Fang, Yi-Nan; Dong, Guo-Hui; Zhou, Duan-Lu; Sun, Chang-Pu
2016-04-01
Symmetry is conventionally described in a polarized manner that the system is either completely symmetric or completely asymmetric. Using group theoretical approach to overcome this dichotomous problem, we introduce the degree of symmetry (DoS) as a non-negative continuous number ranging from zero to unity. DoS is defined through an average of the fidelity deviations of Hamiltonian or quantum state over its transformation group G, and thus is computable by making use of the completeness relations of the irreducible representations of G. The monotonicity of DoS can effectively probe the extended group for accidental degeneracy while its multi-valued natures characterize some (spontaneous) symmetry breaking. Supported by the National Natural Science Foundation of China under Grant Nos. 11421063, 11534002, 11475254 and the National 973 Program under Grant Nos. 2014CB921403, 2012CB922104, and 2014CB921202
Chanowitz, M.S.
1990-09-01
The Higgs mechanism is reviewed in its most general form, requiring the existence of a new symmetry-breaking force and associated particles, which need not however be Higgs bosons. The first lecture reviews the essential elements of the Higgs mechanism, which suffice to establish low energy theorems for the scattering of longitudinally polarized W and Z gauge bosons. An upper bound on the scale of the symmetry-breaking physics then follows from the low energy theorems and partial wave unitarity. The second lecture reviews particular models, with and without Higgs bosons, paying special attention to how the general features discussed in lecture 1 are realized in each model. The third lecture focuses on the experimental signals of strong WW scattering that can be observed at the SSC above 1 TeV in the WW subenergy, which will allow direct measurement of the strength of the symmetry-breaking force. 52 refs., 10 figs.
NASA Astrophysics Data System (ADS)
Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi
2013-08-01
Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified.
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)
Gradišek, A.; Kocjan, A.; McGuiness, P. J.; Apih, T.; Kim, Hae Jin; Dolinšek, J.
2008-11-01
The Ti40Zr40Ni20 hydrogen-absorbing alloy was prepared in the icosahedral and amorphous phases by controlling the rotation speed of the melt-spinning method of sample preparation, and the deuterium dynamics was investigated by 2H NMR dynamic lineshape and spin-lattice relaxation. The results were analysed by the lineshape and relaxation models that assume deuterium thermally activated hopping within a manifold of different chemical environments. The observed 8% larger activation energy for the deuterium hopping over the interstitial sites and the 10% larger static spectrum width of the amorphous phase, as compared to the icosahedral phase, can be accounted for by the larger deuterium content of the investigated amorphous sample. From the deuterium dynamics point of view, the icosahedral phase is not special with respect to the amorphous modification of the same material.
NASA Astrophysics Data System (ADS)
West, Carl T.; Kottos, Tsampikos; Prosen, Tomaz
2010-03-01
We study a new class of chaotic systems with dynamical localization, where gain/loss processes break the hermiticity, while allowing for parity-time PT symmetry. For a value γPT of the gain/loss parameter the spectrum undergoes a spontaneous phase transition from real (exact phase) to complex values (broken phase). We develop a one parameter scaling theory for γPT, and show that chaos assists the exact PT-phase. Our results will have applications to the design of optical elements with PT-symmetry.
NASA Astrophysics Data System (ADS)
Arzano, Michele; Kowalski-Glikman, Jerzy
2016-09-01
We construct discrete symmetry transformations for deformed relativistic kinematics based on group valued momenta. We focus on the specific example of κ-deformations of the Poincaré algebra with associated momenta living on (a sub-manifold of) de Sitter space. Our approach relies on the description of quantum states constructed from deformed kinematics and the observable charges associated with them. The results we present provide the first step towards the analysis of experimental bounds on the deformation parameter κ to be derived via precision measurements of discrete symmetries and CPT.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar ϕ invariant under the internal galileon symmetryϕ→ϕ+b{sub μ}x{sup μ} have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon’s quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
NASA Astrophysics Data System (ADS)
Moore, Gregory
The vanishing of the one-loop string cosmological constant in nontrivial non supersymmetric backgrounds can be understood by viewing the path integral as an inner product of orthogonal wave functions. For special backgrounds the string theory has an extra symmetry, expressed as a transformation on moduli space. When left- and right-moving wave functions transform in different representations of this symmetry the cosmological constant must vanish. Specific examples of the mechanism are given at one loop for theories in two and four dimensions. Various suggestions are made for the higher loop extension of this idea.
BOOK REVIEW: Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ryder, L. H.
2005-11-01
One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, Σ, Λ and Ξ particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would
Simple Treatment of the Symmetry Labels for the d-d States of Octahedral Complexes
NASA Astrophysics Data System (ADS)
Smith, Derek W.
1996-06-01
The derivation of the symmetry labels for d-d states of cubic (octahedral and tetrahedral) complexes of d block elements is not readily accessible to students having an elementary knowledge of group theory. This paper shows how the d-d states of octahedral d^n complexes (in the point group O) can be worked out by descent in symmetry to D2, using the relevant character tables and multiplication tables for their irreducible representations. A letter from Derek W. Smith in our April 2000 issue addresses the above.
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 =|
Baker, T. S.; Olson, N. H.; Fuller, S. D.
1999-01-01
Viruses are cellular parasites. The linkage between viral and host functions makes the study of a viral life cycle an important key to cellular functions. A deeper understanding of many aspects of viral life cycles has emerged from coordinated molecular and structural studies carried out with a wide range of viral pathogens. Structural studies of viruses by means of cryo-electron microscopy and three-dimensional image reconstruction methods have grown explosively in the last decade. Here we review the use of cryo-electron microscopy for the determination of the structures of a number of icosahedral viruses. These studies span more than 20 virus families. Representative examples illustrate the use of moderate- to low-resolution (7- to 35-Å) structural analyses to illuminate functional aspects of viral life cycles including host recognition, viral attachment, entry, genome release, viral transcription, translation, proassembly, maturation, release, and transmission, as well as mechanisms of host defense. The success of cryo-electron microscopy in combination with three-dimensional image reconstruction for icosahedral viruses provides a firm foundation for future explorations of more-complex viral pathogens, including the vast number that are nonspherical or nonsymmetrical. PMID:10585969
NASA Astrophysics Data System (ADS)
Tandy, Paul; Yu, Ming; Jayanthi, C. S.; Wu, Shi-Yu; Condensed Matter Theory Group Team
2013-03-01
A successful development of a parameterized semi-empirical Hamiltonian (SCED-LCAO) for boron based on a LCAO framework using a sp3 basis set will be discussed. The semi-empirical Hamiltonian contains environment-dependency and electron screening effects of a many-body Hamiltonian and allows for charge self-consistency. We have optimized the parameters of the SCED-LCAO Hamiltonian for boron by fitting the properties (e.g., the binding energy, bond length, etc.) of boron sheets, small clusters and boron alpha to first-principles calculations based on DFT calculations. Although extended phases of boron alpha and beta have been studied, large clusters of boron with icosahedral structures such as those cut from boron alpha are difficult if not impossible to simulate with ab initio methods. We will demonstrate the effectiveness of the SCED-LCAO Hamiltonian in studying icosahedral boron clusters containing up to 800 atoms and will report on some novel boron clusters and computational speed. Support has been provided by the Dillion Fellowship.
ERIC Educational Resources Information Center
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
NASA Astrophysics Data System (ADS)
Maes, Christian; Salazar, Alberto
2014-01-01
In contrast with the understanding of fluctuation symmetries for entropy production, similar ideas applied to the time-symmetric fluctuation sector have been less explored. Here we give detailed derivations of time-symmetric fluctuation symmetries in boundary-driven particle systems such as the open Kawasaki lattice gas and the zero-range model. As a measure of time-symmetric dynamical activity over time T we count the difference (Nℓ - Nr)/T between the number of particle jumps in or out at the left edge and those at the right edge of the system. We show that this quantity satisfies a fluctuation symmetry from which we derive a new Green-Kubo-type relation. It will follow then that the system is more active at the edge connected to the particle reservoir with the largest chemical potential. We also apply these exact relations derived for stochastic particle models to a deterministic case, the spinning Lorentz gas, where the symmetry relation for the activity is checked numerically.
ERIC Educational Resources Information Center
McGehe, Carol
1991-01-01
Presents math activities, problems, and games for teaching elementary students to recognize the world's natural symmetry and understand the mathematical qualities it represents; suggests activities with construction paper, blocks, and calculators. Instructions for using the calculator to create palindromes are included. (SM)
Gauging without initial symmetry
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time Σ, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(Σ , G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / ∼. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
Gravity from Lorentz Symmetry Violation
Potting, Robertus
2006-06-19
In general relativity, the masslessness of gravitons can be traced to symmetry under diffeomorphisms. In this talk, we consider another possibility, whereby the masslessness arises from spontaneous violation of Lorentz symmetry.
Chivukula, R. Sekhar; Simmons, Elizabeth H.; Di Chiara, Stefano; Foadi, Roshan
2009-11-01
We introduce a toy model implementing the proposal of using a custodial symmetry to protect the Zb{sub L}b{sub L} coupling from large corrections. This 'doublet-extended standard model' adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4)xU(1){sub X}{approx}SU(2){sub L}xSU(2){sub R}xP{sub LR}xU(1){sub X} symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2){sub L}xU(1){sub Y} electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M{yields}0) and standard-model-like (M{yields}{infinity}) limits. In this simple model, we find that the experimental limits on the Zb{sub L}b{sub L} coupling favor smaller M while the presence of a potentially sizable negative contribution to {alpha}T strongly favors large M. Comparison with precision electroweak data shows that the heavy partner of the top quark must be heavier than about 3.4 TeV, making it difficult to search for at LHC. This result demonstrates that electroweak data strongly limit the amount by which the custodial symmetry of the top-quark mass generating sector can be enhanced relative to the standard model. Using an effective field theory calculation, we illustrate how the leading contributions to {alpha}T, {alpha}S, and the Zb{sub L}b{sub L} coupling in this model arise from an effective operator coupling right-handed top quarks to the Z boson, and how the effects on these observables are correlated. We contrast this toy model with extradimensional models in which the extended custodial symmetry is invoked to control the size of additional contributions to {alpha}T and the Zb{sub L}b{sub L} coupling, while leaving the standard model contributions essentially unchanged.
Dynamical Symmetries in Classical Mechanics
ERIC Educational Resources Information Center
Boozer, A. D.
2012-01-01
We show how symmetries of a classical dynamical system can be described in terms of operators that act on the state space for the system. We illustrate our results by considering a number of possible symmetries that a classical dynamical system might have, and for each symmetry we give examples of dynamical systems that do and do not possess that…
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…
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
P. PAGE; T. GOLDMAN; J. GINOCCHIO
2000-08-01
Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.
A broken symmetry ontology: Quantum mechanics as a broken symmetry
Buschmann, J.E.
1988-01-01
The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.
Chiral symmetry and pentaquarks
Dmitri Diakonov
2004-07-01
Spontaneous chiral symmetry breaking, mesons and baryons are illustrated in the language of the Dirac theory. Various forces acting between quarks inside baryons are discussed. I explain why the naive quark models typically overestimate pentaquark masses by some 500 MeV and why in the fully relativistic approach to baryons pentaquarks turn out to be light. I discuss briefly why it can be easier to produce pentaquarks at low than at high energies.
NASA 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.
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
NASA Astrophysics Data System (ADS)
Christodoulides, Demetrios
2015-03-01
Interest in complex Hamiltonians has been rekindled after the realization that a wide class of non-Hermitian Hamiltonians can have entirely real spectra as long as they simultaneously respect parity and time reversal operators. In non-relativistic quantum mechanics, governed by the Schrödinger equation, a necessary but not sufficient condition for PT symmetry to hold is that the complex potential should involve real and imaginary parts which are even and odd functions of position respectively. As recently indicated, optics provides a fertile ground to observe and utilize notions of PT symmetry. In optics, the refractive index and gain/loss profiles play the role of the real and imaginary parts of the aforementioned complex potentials. As it has been demonstrated in several studies, PT-symmetric optical structures can exhibit peculiar properties that are otherwise unattainable in traditional Hermitian (conservative) optical settings. Among them, is the possibility for breaking this symmetry through an abrupt phase transition, band merging effects and unidirectional invisibility. Here we review recent developments in the field of -symmetric optics.
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.
Sharma, H. R. Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.
2014-05-07
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C{sub 60} on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C{sub 60} molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C{sub 60} molecules atop the Pb islands approaches zero, regardless of the overall C{sub 60} coverage.
NASA Astrophysics Data System (ADS)
Dubey, Sarvesh; Mittal, Rashmi; Lauritzen, Peter H.
2014-06-01
A high-order incremental "remap-type" transport scheme is presented (FF-CSLAM). The scheme utilizes bi-quadratic polynomial subgrid-cell reconstruction functions based on the weighted least squares method. The integration of the reconstruction functions over flux areas, which is inherent in remap schemes, makes use of CSLAM approach of line integration. Though the formal order of the scheme is second order, yet quadratic subgrid scale polynomial reconstruction does lead to improvement in the overall accuracy of the scheme. Since the rigorous search for overlap areas between flux areas and grid cells is cumbersome, two simplifications have been suggested in the literature. The main objectives of this paper are (a) to formulate flux-form CSLAM for the icosahedral-hexagonal grid and (b) to assess the accuracy of two flux-integral simplifications.
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
Pressure-Driven Quantum Criticality and T/H Scaling in the Icosahedral Au-Al-Yb Approximant
NASA Astrophysics Data System (ADS)
Matsukawa, Shuya; Deguchi, Kazuhiko; Imura, Keiichiro; Ishimasa, Tsutomu; Sato, Noriaki K.
2016-06-01
We report on ac magnetic susceptibility measurements under pressure of the Au-Al-Yb alloy, a crystalline approximant to the icosahedral quasicrystal that shows unconventional quantum criticality. In describing the susceptibility as χ(T)-1 - χ(0)-1 ∝ Tγ, we find that χ(0)-1 decreases with increasing pressure and vanishes to zero at the critical pressure P{c} ≃ 2 GPa, with γ ( ≃ 0.5) unchanged. We suggest that this quantum criticality emerges owing to critical valence fluctuations. Above Pc, the approximant undergoes a magnetic transition at T ≃ 100 mK. These results are contrasted with the fact that, in the quasicrystal, the quantum criticality is robust against the application of pressure. The applicability of the so-called T/H scaling to the approximant is also discussed.
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.
Thermal symmetry in isoscaling
Escudero, C. R.; Lopez, J. A.; Dorso, C. O.
2007-02-12
It is determined that isoscaling data, if produced by two isotopic reactions under similar thermodynamic conditions, should satisfy a simple numerical relationship. This, which helps to explore the symmetry of thermodynamic conditions of isotopic reactions, is studied using molecular dynamics simulations of 40Ca+40Ca, 48Ca+48Ca, and 52Ca+52Ca, at beam energies from 35 MeV / A to 85 MeV / A, and as a function of time. Strong deviations from the rule are detected in the beginning of the collision, with an excellent convergence at long times for some energies. A comparison with experimental data and other calculations is also included.
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.
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.
Leptogenesis and residual CP symmetry
NASA Astrophysics Data System (ADS)
Chen, Peng; Ding, Gui-Jun; King, Stephen F.
2016-03-01
We discuss flavour dependent leptogenesis in the framework of lepton flavour models based on discrete flavour and CP symmetries applied to the type-I seesaw model. Working in the flavour basis, we analyse the case of two general residual CP symmetries in the neutrino sector, which corresponds to all possible semi-direct models based on a preserved Z 2 in the neutrino sector, together with a CP symmetry, which constrains the PMNS matrix up to a single free parameter which may be fixed by the reactor angle. We systematically study and classify this case for all possible residual CP symmetries, and show that the R-matrix is tightly constrained up to a single free parameter, with only certain forms being consistent with successful leptogenesis, leading to possible connections between leptogenesis and PMNS parameters. The formalism is completely general in the sense that the two residual CP symmetries could result from any high energy discrete flavour theory which respects any CP symmetry. As a simple example, we apply the formalism to a high energy S 4 flavour symmetry with a generalized CP symmetry, broken to two residual CP symmetries in the neutrino sector, recovering familiar results for PMNS predictions, together with new results for flavour dependent leptogenesis.
Symmetry fractionalization and twist defects
NASA Astrophysics Data System (ADS)
Tarantino, Nicolas; Lindner, Netanel H.; Fidkowski, Lukasz
2016-03-01
Topological order in two-dimensions can be described in terms of deconfined quasiparticle excitations—anyons—and their braiding statistics. However, it has recently been realized that this data does not completely describe the situation in the presence of an unbroken global symmetry. In this case, there can be multiple distinct quantum phases with the same anyons and statistics, but with different patterns of symmetry fractionalization—termed symmetry enriched topological order. When the global symmetry group G, which we take to be discrete, does not change topological superselection sectors—i.e. does not change one type of anyon into a different type of anyon—one can imagine a local version of the action of G around each anyon. This leads to projective representations and a group cohomology description of symmetry fractionalization, with the second cohomology group {H}2(G,{{ A }}{{abelian}}) being the relevant group. In this paper, we treat the general case of a symmetry group G possibly permuting anyon types. We show that despite the lack of a local action of G, one can still make sense of a so-called twisted group cohomology description of symmetry fractionalization, and show how this data is encoded in the associativity of fusion rules of the extrinsic ‘twist’ defects of the symmetry. Furthermore, building on work of Hermele (2014 Phys. Rev. B 90 184418), we construct a wide class of exactly-solvable models which exhibit this twisted symmetry fractionalization, and connect them to our formal framework.
Jach, T.; Zhang, Y.; Colella, R.; de Boissieu, M.; Boudard, M.; Goldman, A.I.; Lograsso, T.A.; Delaney, D.W.; Kycia, S.
1999-04-01
We have observed dynamical diffraction in the
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)
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. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
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.
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.
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…
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.)
Generalized Atkin-Lehner symmetry
NASA Astrophysics Data System (ADS)
Dienes, Keith R.
1990-09-01
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner ``selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Generalized Atkin-Lehner symmetry
Dienes, K.R. )
1990-09-15
Atkin-Lehner symmetry was proposed several years ago as a mechanism for obtaining a vanishing one-loop cosmological constant in nonsupersymmetric superstring models, but for models formulated in four-dimensional spacetime this symmetry cannot be realized. We therefore investigate various means of retaining the general Atkin-Lehner idea without having strict Atkin-Lehner symmetry. We first explicitly construct non-Atkin-Lehner-symmetric partition functions which not only lead to vanishing cosmological constants but which also avoid a recent proof that Atkin-Lehner-symmetric partition functions cannot arise from physically viable string models in greater than two dimensions. We then develop a systematic generalization of Atkin-Lehner symmetry, basing our considerations on the use of non-Hermitian operators as well as on a general class of possible congruence subgroups of the full modular group. We find that whereas in many instances our resulting symmetries reduce to either strict Atkin-Lehner symmetry or symmetries closely related to it, in other cases we obtain symmetries of a fundamentally new character. Our results therefore suggest possible new avenues for retaining the general Atkin-Lehner selection rule'' approach for obtaining a vanishing one-loop cosmological constant.
Spin-Orbit-Free Topological Insulators without Time-Reversal Symmetry
NASA Astrophysics Data System (ADS)
Alexandradinata, A.; Fang, Chen; Gilbert, Matthew J.; Bernevig, B. Andrei
2014-09-01
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 Cnv 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 Cnv 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.
Ultraviolet completion without symmetry restoration
NASA Astrophysics Data System (ADS)
Endlich, Solomon; Nicolis, Alberto; Penco, Riccardo
2014-03-01
We show that it is not possible to UV complete certain low-energy effective theories with spontaneously broken spacetime symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform nonlinearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of spacetime and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smolić, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Tarumi, Ryuichi
2013-01-01
We investigated free-vibration acoustic resonance (FVAR) of two-dimensional St Venant–Kirchhoff-type hyperelastic materials and revealed the existence and structure of colour symmetry embedded therein. The hyperelastic material is isotropic and frame indifferent and includes geometrical nonlinearity in its constitutive equation. The FVAR state is formulated using the principle of stationary action with a subsidiary condition. Numerical analysis based on the Ritz method revealed the existence of four types of nonlinear FVAR modes associated with the irreducible representations of a linearized system. Projection operation revealed that the FVAR modes can be classified on the basis of a single colour (black or white) and three types of bicolour (black and white) magnetic point groups: , , and . These results demonstrate that colour symmetry naturally arises in the finite amplitude nonlinear FVAR modes, and its vibrational symmetries are explained in terms of magnetic point groups rather than the irreducible representations that have been used for linearized systems. We also predicted a grey colour nonlinear FVAR mode which cannot be derived from a linearized system. PMID:24204182
Huang, Z. )
1992-12-01
We examine an interesting scenario to solve the domain-wall problem recently suggested by Preskill, Trivedi, Wilczek, and Wise. The effective potential is calculated in the presence of the QCD axial anomaly. It is shown that some discrete symmetries such as {ital CP} and {ital Z}{sub 2} can be anomalous due to a so-called {ital K} term induced by instantons. We point out that the {ital Z}{sub 2} domain-wall problem in the two-doublet standard model can be resolved by two types of solutions: the {ital CP}-conserving one and the {ital CP}-breaking one. In the first case, there exist two {ital Z}{sub 2}-related local minima whose energy splitting is provided by the instanton effect. In the second case, there is only one unique vacuum so that the domain walls do not form at all. The consequences of this new source of {ital CP} violation are discussed and shown to be well within the experimental limits in weak interactions.
Jalasvuori, Matti; Jaatinen, Silja T; Laurinavicius, Simonas; Ahola-Iivarinen, Elina; Kalkkinen, Nisse; Bamford, Dennis H; Bamford, Jaana K H
2009-09-01
We have sequenced the genome and identified the structural proteins and lipids of the novel membrane-containing, icosahedral virus P23-77 of Thermus thermophilus. P23-77 has an approximately 17-kb circular double-stranded DNA genome, which was annotated to contain 37 putative genes. Virions were subjected to dissociation analysis, and five protein species were shown to associate with the internal viral membrane, while three were constituents of the protein capsid. Analysis of the bacteriophage genome revealed it to be evolutionarily related to another Thermus phage (IN93), archaeal Halobacterium plasmid (pHH205), a genetic element integrated into Haloarcula genome (designated here as IHP for integrated Haloarcula provirus), and the Haloarcula virus SH1. These genetic elements share two major capsid proteins and a putative packaging ATPase. The ATPase is similar with the ATPases found in the PRD1-type viruses, thus providing an evolutionary link to these viruses and furthering our knowledge on the origin of viruses. PMID:19587059
Maniraj, M; Rai, Abhishek; Barman, S R; Krajci, M; Schlagel, Deborah L; Lograsso, Thomas A; Horn, K
2014-09-01
We study the unoccupied region of the electronic structure of the fivefold symmetric surface of an icosahedral (i) Al-Pd-Mn quasicrystal. A feature that exhibits parabolic dispersion with an effective mass of (1.15±0.1)m_{e} and tracks the change in the work function is assigned to an image potential resonance because our density functional calculation shows an absence of band gap in the respective energy region. We show that Sn grows pseudomorphically on i-Al-Pd-Mn as predicted by density functional theory calculations, and the energy of the image potential resonance tracks the change in the work function with Sn coverage. The image potential resonance appears much weaker in the spectrum from the related crystalline Al-Pd-Mn surface, demonstrating that its strength is related to the compatibility of the quasiperiodic wave functions in i-Al-Pd-Mn with the free-electron-like image potential states. Our investigation of the energy region immediately above E_{F} provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
Law-Hine, Didier; Sahoo, Anil K; Bailleux, Virginie; Zeghal, Mehdi; Prevost, Sylvain; Maiti, Prabal K; Bressanelli, Stéphane; Constantin, Doru; Tresset, Guillaume
2015-09-01
Viral capsids derived from an icosahedral plant virus widely used in physical and nanotechnological investigations were fully dissociated into dimers by a rapid change of pH. The process was probed in vitro at high spatiotemporal resolution by time-resolved small-angle X-ray scattering using a high brilliance synchrotron source. A powerful custom-made global fitting algorithm allowed us to reconstruct the most likely pathway parametrized by a set of stoichiometric coefficients and to determine the shape of two successive intermediates by ab initio calculations. None of these two unexpected intermediates was previously identified in self-assembly experiments, which suggests that the disassembly pathway is not a mirror image of the assembly pathway. These findings shed new light on the mechanisms and the reversibility of the assembly/disassembly of natural and synthetic virus-based systems. They also demonstrate that both the structure and dynamics of an increasing number of intermediate species become accessible to experiments. PMID:27120684
Step-terrace morphology and reactivity to C60 of the five-fold icosahedral Ag-In-Yb quasicrystal
NASA Astrophysics Data System (ADS)
Nugent, P. J.; Smerdon, J. A.; McGrath, R.; Shimoda, M.; Cui, C.; Tsai, A. P.; Sharma, H. R.
2011-07-01
The surface of the icosahedral i-Ag-In-Yb quasicrystal provides one of the first non-Al-based aperiodic surfaces that is suitable for study under ultra-high vacuum conditions. We present a scanning tunnelling microscopy (STM) study of the five-fold surface of this new quasicrystal demonstrating detailed structure of the terraces and steps. The analysis of the autocorrelation functions of STM images at opposite bias polarities and of the in-plane structure of the bulk model of i-Cd-Yb, which is isostructural to i-Ag-In-Yb, reveals that the surface terminations occur at the centres of the rhombic triacontrahedral (RTH) clusters, which are the basic building blocks of this material. The study further confirms that the unoccupied electronic states are located on Yb sites. Step edges display a Fibonacci sequence of truncated clusters, which can also be explained in terms of the model structure. Occasionally, a single terrace is found to display different structures at negative bias, whereas the same terrace shows a uniform structure at positive bias. Depositing C60 creates a disordered overlayer on the surface with no resulting FFT or LEED patterns.
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.
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Hidden symmetries and black holes
NASA Astrophysics Data System (ADS)
Frolov, Valeri P.
2009-10-01
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.
Crystallographic characterization and molecular symmetry of edestin, a legumin from hemp.
Patel, S; Cudney, R; McPherson, A
1994-01-01
Edestin, a legumin class reserve protein from hemp seeds having six identical subunits was crystallized from ammonium phosphate at pH 5 and subsequently characterized by X-ray diffraction. The crystals are of space group R32 with a = 127 A and gamma = 116 degrees having an equivalent triply centered hexagonal cell of a = b = 215 A, c = 80 A. There is one hexameric protein in the rhombohedral unit cell, hence the subunits of the Edestin molecule must be arranged with 32 point group symmetry. PMID:8289257
Coupling effects in low-symmetry planar split-ring resonator arrays.
Decker, Manuel; Linden, Stefan; Wegener, Martin
2009-05-15
We introduce a particular low-symmetry (point group of unit cell C(1)) planar periodic arrangement of magnetic split-ring resonators that acts as an effective optical wave plate. We show that this behavior specifically results from the in-plane interactions among the individual split-ring resonators. Measured normal-incidence transmittance and conversion spectra of gold-based samples fabricated via electron-beam lithography show fundamental resonances at around 235 THz frequency (1,275 nm wavelength) that are in good agreement with theory. PMID:19448827
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
Combining Flavour and CP Symmetries
NASA Astrophysics Data System (ADS)
Feruglio, Ferruccio
2013-07-01
I shortly review the impact of the most recent neutrino oscillation data on our attempts to construct a realistic model for neutrino masses and mixing angles. Models based on anarchy and its variants remain an open possibility, reinforced by the latest experimental findings. Many models based on discrete symmetries no longer work in their simplest realizations. I illustrate several proposals that can rescue discrete symmetries. In particular I discuss the possibility of combining discrete flavour symmetries and CP, and I describe a recently proposed symmetry breaking pattern that allows to predict all mixing parameters, angles and phases, in terms of a single real unknown. I analyze several explicit examples of this construction, providing new realistic mixing patterns.
Liu, Y.; Keller, J.
1996-09-01
It is proved that there exists an additional intrinsic symmetry in the left-handed and right-handed fermions (and other fields). The corresponding group of transformations is induced by the Poincar{acute e} translations in the space{endash}time manifold. This symmetry predicts an additional intrinsic energy-momentum for fermions. Considering this symmetry as local leads to introduction of a gauge field and of a nonintegrable phase angle, the corresponding Berry-type phase depends on the topology of the Riemannian space{endash}time manifold as determined by the vierbein. This additional symmetry provides us with the possibility of considering the fermions as gauge fields on the nonvector bundle. {copyright} {ital 1996 American Institute of Physics.}
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
Trace formula for broken symmetry
Creagh, S.C.
1996-05-01
We derive a trace formula for systems that exhibit an approximate continuous symmetry. It interpolates between the sum over continuous families of periodic orbits that holds in the case of exact continuous symmetry, and the discrete sum over isolated orbits that holds when the symmetry is completely broken. It is based on a simple perturbation expansion of the classical dynamics, centered around the case of exact symmetry, and gives an approximation to the usual Gutzwiller formula when the perturbation is large. We illustrate the computation with some 2-dimensional examples: the deformation of the circular billiard into an ellipse, and anisotropic and anharmonic perturbations of a harmonic oscillator. Copyright {copyright} 1996 Academic Press, Inc.
Notation Confusion of Symmetry Species for Molecules with Several Large-Amplitude Internal Motions
NASA Astrophysics Data System (ADS)
Groner, P.
2011-06-01
The Mulliken convention has become the standard notation for symmetry species (irreducible representations) of point groups for quasi-rigid molecules. No such convention exists for symmetry species of symmetry groups for semi-rigid or non-rigid molecules with large amplitude internal motions (LAMs). As a result, we have a situation where we create notations in a do-it-yourself fashion or adopt them from the literature, sometimes even without proper reference to its derivation or to the character table on which it is based. This may be just a nuisance for those who are comfortable enough with group theory and molecular symmetry groups to figure "it" out, but it represents a real problem for everybody else. The notation confusion is illustrated with examples from the literature (both old and new) on molecules with two or more LAMs. Most authors use the notation introduced by Myers and Wilson for molecules such as acetone or propane. No universal notation is in use for molecules with two methyl groups but lower overall symmetry. For example, the notation G_1_8 is used for one of these groups. As it turns out, different people use the same notation for different groups. This presentation is an attempt to bring some light into the dark and to combat confusion with a call for an anti-confusion convention. R. S. Mulliken, Phys. Rev. 43, 279 (1933). R. J. Myers, E. B. Wilson, J. Chem. Phys. 33, 186 (1960).
Momentum dependence of symmetry energy
NASA Astrophysics Data System (ADS)
Coupland, Daniel D.; Youngs, Michael; Chajecki, Zbigniew; Lynch, William; Tsang, Betty; Zhang, Yingxun; Famiano, Michael; Ghosh, Tilak; Giacherio, B.; Kilburn, Micha; Lee, Jenny; Lu, Fei; Russotto, Paulo; Sanetullaev, Alisher; Showalter, Rachel; Verde, Giuseppe; Winkelbauer, Jack
2014-09-01
One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn +124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. One of the main uncertainties in the Equation of State of neutron-rich nuclear matter concerns the density and momentum dependence of the nuclear symmetry energy. Some constraints on the density dependence of the symmetry energy at sub-saturation densities have been recently obtained. However questions remain, especially concerning the momentum dependence of the symmetry mean-field potential that can make the neutron and proton effective masses different. We probe the momentum dependence of this isovector mean-field potential by comparing the energy spectra of neutrons and protons emitted in 112Sn+112Sn and 124Sn+124Sn collisions at incident energies of E/A = 50 and 120 MeV. We achieve an experimental precision that can discriminate between transport model predictions for the n/p double ratio for different momentum dependencies of the symmetry mean-field potential. PHY-1102511.
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.
Dynamical symmetries in nuclear structure
Casten, R.F.
1986-01-01
In recent years the concept of dynamical symmetries in nuclei has witnessed a renaissance of interest and activity. Much of this work has been developed in the context of the Interacting Boson Approximation (or IBA) model. The appearance and properties of dynamical symmetries in nuclei will be reviewed, with emphasis on their characteristic signatures and on the role of the proton-neutron interaction in their formation, systematics and evolution. 36 refs., 20 figs.
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
Creutz, M.
2009-09-07
The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.
Symmetry in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.
1993-01-01
Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is
Structural stability of the icosahedral AlCuFe quasicrystal under high-pressure and high-temperature
NASA Astrophysics Data System (ADS)
Takagi, S.; Kyono, A.; Nakamoto, Y.; Hirao, N.
2015-12-01
We report high-pressure and high-temperature in-situ X-ray diffraction study of icosahedral (i)-AlCuFe quasicrystal "icosahedrite" which is the first known naturally occurring quasicrystal mineral discovered in the Khatyrka meteorite. The i-AlCuFe quasicrystal was synthesized in laboratory from a powder mixture with an atomic ratio of Al : Cu : Fe = 65 : 20 : 15. The high-temperature and high-pressure X-ray diffraction experiments were performed using the laser-heated diamond anvil cell system installed at BL10XU, SPring-8, Japan. The i-AlCuFe showed a characteristic X-ray diffraction pattern of quasicrystal. With only compression, the diffraction patterns of the i-AlCuFe were continued until 75 GPa. At a pressure of 87 GPa two small new peaks occurred and then kept up to the maximum pressure of 104 GPa in the study. The results indicate that the pressure-induced structural phase transition of the i-AlCuFe occurs above 87 GPa, and the structure of the i-AlCuFe remains unchanged at least up to 75 GPa. Under simultaneously high pressure and high temperature, on the other hand, the i-AlCuFe was readily transformed to crystalline phase. It can be characterized by an irreversible transformation process. The structure of the i-AlCuFe is therefore more affected by thermal metamorphism than by pressure metamorphism. The present high-pressure and high-temperature experiments clearly revealed the thermal and pressure stability of the i-AlCuFe quasicrystal which may help to explain the formation of the naturally occurring quasicrystal in the solar system.
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
Physical symmetry and lattice symmetry in the lattice Boltzmann method
Cao, N.; Chen, S.; Jin, S.; Martinez, D.
1997-01-01
The lattice Boltzmann method (LBM) is regarded as a specific finite difference discretization for the kinetic equation of the discrete velocity distribution function. We argue that for finite sets of discrete velocity models, such as LBM, the physical symmetry is necessary for obtaining the correct macroscopic Navier-Stokes equations. In contrast, the lattice symmetry and the Lagrangian nature of the scheme, which is often used in the lattice gas automaton method and the existing lattice Boltzmann methods and directly associated with the property of particle dynamics, is not necessary for recovering the correct macroscopic dynamics. By relaxing the lattice symmetry constraint and introducing other numerical discretization, one can also obtain correct hydrodynamics. In addition, numerical simulations for applications, such as nonuniform meshes and thermohydrodynamics can be easily carried out and numerical stability can be ensured by the Courant-Friedricks-Lewey condition and using the semi-implicit collision scheme. {copyright} {ital 1997} {ital The American Physical Society}
Symmetry in finite phase plane
NASA Astrophysics Data System (ADS)
Zak, J.
2010-03-01
The known symmetries in one-dimensional systems are inversion and translations. These symmetries persist in finite phase plane, but a novel symmetry arises in view of the discrete nature of the coordinate xi and the momentum pi : xi and pi can undergo permutations. Thus, if xi assumes M discrete values, i = 0, 1,2,..., M - 1, a permutation will change the order of the set x0,x1,..., xM-1 into a new ordered set. Such a symmetry element does not exist for a continuous x-coordinate in an infinite phase plane. Thus, in a finite phase plane, translations can be replaced by permutations. This is also true for the inversion operator. The new permutation symmetry has been used for the construction of conjugate representations and for the splitting of the M-dimensional vector space into independent subspaces. This splitting is exhaustive in the sense that if M = iMi with Mi being prime numbers, the M-dimensional space splits into M1,M2,...Mn-dimensional independent subspaces. It is shown that following this splitting one can design new potentials with appropriate constants of motion. A related problem is the Weyl-Heisenberg group in the M-dimensional space which turns into a direct product of its subgroups in the Mi-dimensional subspaces. As an example we consider the case of M = 8.
On the symmetries of integrability
Bellon, M.; Maillard, J.M.; Viallet, C. )
1992-06-01
In this paper the authors show that the Yang-Baxter equations for two-dimensional models admit as a group of symmetry the infinite discrete group A{sub 2}{sup (1)}. The existence of this symmetry explains the presence of a spectral parameter in the solutions of the equations. The authors show that similarly, for three-dimensional vertex models and the associated tetrahedron equations, there also exists an infinite discrete group of symmetry. Although generalizing naturally the previous one, it is a much bigger hyperbolic Coxeter group. The authors indicate how this symmetry can help to resolve the Yang-Baxter equations and their higher-dimensional generalizations and initiate the study of three-dimensional vertex models. These symmetries are naturally represented as birational projective transformations. They may preserve non-trivial algebraic varieties, and lead to proper parametrizations of the models, be they integrable or not. The authors mention the relation existing between spin models and the Bose-Messner algebras of algebraic combinatorics. The authors' results also yield the generalization of the condition q{sup n} = 1 so often mentioned in the theory of quantum groups, when no q parameter is available.
Symmetry Guide to Ferroaxial Transitions
NASA Astrophysics Data System (ADS)
Hlinka, J.; Privratska, J.; Ondrejkovic, P.; Janovec, V.
2016-04-01
The 212 species of the structural phase transitions with a macroscopic symmetry breaking are inspected with respect to the occurrence of the ferroaxial order parameter, the electric toroidal moment. In total, 124 ferroaxial species are found, some of them being also fully ferroelectric (62) or fully ferroelastic ones (61). This ensures a possibility of electrical or mechanical switching of ferroaxial domains. Moreover, there are 12 ferroaxial species that are neither ferroelectric nor ferroelastic. For each species, we have also explicitly worked out a canonical form for a set of representative equilibrium property tensors of polar and axial nature in both high-symmetry and low-symmetry phases. This information was gathered into the set of 212 mutually different symbolic matrices, expressing graphically the presence of nonzero independent tensorial components and the symmetry-imposed links between them, for both phases simultaneously. Symmetry analysis reveals the ferroaxiality in several currently debated materials, such as VO2 , LuFe2 O4 , and URu2 Si2 .
Yu, M; Chaudhuri, I; Leahy, C; Wu, S Y; Jayanthi, C S
2009-05-14
Structures and relative stabilities of carbon clusters belonging to different families have been investigated for diameters d < or = 5 nm based on an efficient semiempirical molecular dynamics (MD) scheme as well as a density functional theory based simulation. Carbon clusters studied include fullerenes and fullerene-derived structures (e.g., cages and onions), icosahedral structures, bucky-diamond structures, and clusters cut from the bulk diamond with spherical and facetted truncations. The reason for using a semiempirical MD is partly due to the large number of different cases (or carbon allotropes) investigated and partly due to the size of the clusters investigated in this work. The particular flavor of the semiempirical MD scheme is based on a self-consistent and environment-dependent Hamiltonian developed in the framework of linear combination of atomic orbitals. We find that (i) among the families of carbon clusters investigated, fullerene structures have the lowest energy with the relative energy ordering being E(fullerene) < E(onion) < E(icosahedral) < E(bucky-diamond) < E(bulk-truncated), (ii) a crossover between bucky-diamond and icosahedral structures is likely at d approximately 8 nm, (iii) the highest occupied molecular orbital-lowest unoccupied molecular orbital gap as a function of the diameter for the case of fullerenes shows an oscillatory behavior with the gap ranging from 2 eV to 6 meV, and the gap approaching that of gapless graphite for d > 3.5 nm, and (iv) there can be three types of phase transformations depending on the manner of heating and cooling in our simulated annealing studies: (a) a bucky-diamond structure --> an onionlike structure, (b) an onionlike --> a cage structure, and (c) a bucky-diamond --> a cage structure. PMID:19449944
NASA Astrophysics Data System (ADS)
Ektarawong, A.; Simak, S. I.; Alling, B.
2016-08-01
We investigate the thermodynamic stability of carbon-rich icosahedral boron carbide at different compositions, ranging from B4C to B2C , using first-principles calculations. Apart from B4C , generally addressed in the literature, B2.5C , represented by B10C2p (C-C), where Cp and (C-C) denote a carbon atom occupying the polar site of the icosahedral cluster and a diatomic carbon chain, respectively, is predicted to be thermodynamically stable under high pressures with respect to B4C as well as pure boron and carbon phases. The thermodynamic stability of B2.5C is determined by the Gibbs free energy G as a function of pressure p and temperature T , in which the contributions from the lattice vibrations and the configurational disorder are obtained within the quasiharmonic and the mean-field approximations, respectively. The stability range of B2.5C is then illustrated through the p -T phase diagrams. Depending on the temperatures, the stability range of B2.5C is predicted to be within the range between 40 and 67 GPa. At T ≳ 500 K, the icosahedral Cp atoms in B2.5C configurationally disorder at the polar sites. By investigating the properties of B2.5C , e.g., elastic constants and phonon and electronic density of states, we demonstrate that B2.5C is both mechanically and dynamically stable at zero pressure, and is an electrical semiconductor. Furthermore, based on the sketched phase diagrams, a possible route for experimental synthesis of B2.5C as well as a fingerprint for its characterization from the simulations of x-ray powder diffraction pattern are suggested.
CKM matrix and flavor symmetries
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Ishida, Hiroyuki; Ishimori, Hajime; Kobayashi, Tatsuo; Ogasahara, Atsushi
2013-11-01
Following the way proposed recently by Hernandez and Smirnov, we seek possible residual symmetries in the quark sector with a focus on the von Dyck groups. We begin with two extreme cases in which both θ13 and θ23 or only θ13 are set to zero. Then, cases where all the Cabibbo-Kobayashi-Maskawa parameters are allowed to take nonzero values are explored. The Z7 symmetry is favorable to realize only the Cabibbo angle. On the other hand, larger groups are necessary in order to be consistent with all the mixing parameters. Possibilities of embedding the obtained residual symmetries into the Δ(6N2) series are also briefly discussed.
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
Heisenberg symmetry and hypermultiplet manifolds
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Derendinger, Jean-Pierre; Marios Petropoulos, P.; Siampos, Konstantinos
2016-04-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N = 2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U (1) × U (1) at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry - as opposed to Heisenberg ⋉ U (1). We finally discuss the realization of the latter by gauging appropriate Sp (2 , 4) generators in N = 2 conformal supergravity.
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.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
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).
NASA Astrophysics Data System (ADS)
Yu, Fengmei; Zou, Huamin; Wang, Jianbo; Wang, Renhui
2004-10-01
The atomic positions are obtained from a modified non-spherical model of icosahedral AlPdMn quasicrystal (Fang et al 2003 J. Phys.: Condens. Matter 15 4947) by the cut method. The four-shell pseudo-Mackay clusters (PMCs) were searched for in a box of 400 Å × 400 Å × 400 Å. The results show that the number of atoms in the fourth shell, an icosidodecahedron, of the pseudo-Mackay cluster can vary from 15 to 30 because of the cluster overlap, and about 99.96% of the total atoms are included in such incomplete pseudo-Mackay clusters. The characteristics of the atom distribution in the planes perpendicular to a fivefold axis indicate that the planes, which are 1.56 Å apart from their neighbouring planes, are expected to be the terminal surfaces. If one such a plane and its closest neighbouring plane, between which the spacing is 0.48 Å, are considered as a thin layer or a corrugated surface, these layers are also the layers with the maximum density. The pair of corrugated surfaces that are 1.56 Å apart have almost identical chemical composition. These planes form terraces that follow the rule of the Fibonacci sequence with two step heights, 6.60 and 4.08 Å. On the corrugated surfaces perpendicular to a fivefold axis the pentagonal holes arise from the interspaces of adjacent incomplete PMCs. For the atomic planes normal to a twofold axis, the planes with spacing of 1.48 Å from their adjacent planes might be expected to be the terminal surfaces, which form terraces with step heights of 6.28 and 3.88 Å following the rule of the Fibonacci sequence. For the atomic planes normal to a threefold axis, the planes with spacing of 0.86 Å from their adjacent planes might be expected to be the terminal surfaces. No similar results were found for the atomic layers perpendicular to a pseudo-twofold axis.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Charge symmetry at the partonic level
Londergan, J. T.; Peng, J. C.; Thomas, A. W.
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
ERIC Educational Resources Information Center
Brown, Laurie M.
This document is a monograph intended for advanced undergraduate students, or beginning graduate students, who have some knowledge of modern physics as well as classical physics, including the elementary quantum mechanical treatment of the hydrogen atom and angular momentum. The first chapter introduces symmetry and relates it to the mathematical…
Paper Models Illustrating Virus Symmetry.
ERIC Educational Resources Information Center
McCarthy, D. A.
1990-01-01
Instructions are given for constructing two models, one to illustrate the general principles of symmetry in T=1, T=3, and T=4 viruses, and the other to illustrate the disposition of protein subunits in the T=3 plant viruses and the picornaviruses. (Author/CW)
Entanglement renormalization and gauge symmetry
Tagliacozzo, L.; Vidal, G.
2011-03-15
A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z{sub 2} lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16x16 sites (16{sup 2}x2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
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…
From symmetries to number theory
Tempesta, P.
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.
Circular codes, symmetries and transformations.
Fimmel, Elena; Giannerini, Simone; Gonzalez, Diego Luis; Strüngmann, Lutz
2015-06-01
Circular codes, putative remnants of primeval comma-free codes, have gained considerable attention in the last years. In fact they represent a second kind of genetic code potentially involved in detecting and maintaining the normal reading frame in protein coding sequences. The discovering of an universal code across species suggested many theoretical and experimental questions. However, there is a key aspect that relates circular codes to symmetries and transformations that remains to a large extent unexplored. In this article we aim at addressing the issue by studying the symmetries and transformations that connect different circular codes. The main result is that the class of 216 C3 maximal self-complementary codes can be partitioned into 27 equivalence classes defined by a particular set of transformations. We show that such transformations can be put in a group theoretic framework with an intuitive geometric interpretation. More general mathematical results about symmetry transformations which are valid for any kind of circular codes are also presented. Our results pave the way to the study of the biological consequences of the mathematical structure behind circular codes and contribute to shed light on the evolutionary steps that led to the observed symmetries of present codes. PMID:25008961
Strong coupling electroweak symmetry breaking
Barklow, T.L.; Burdman, G.; Chivukula, R.S.
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
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…
Quantitative Analysis of Face Symmetry.
Tamir, Abraham
2015-06-01
The major objective of this article was to report quantitatively the degree of human face symmetry for reported images taken from the Internet. From the original image of a certain person that appears in the center of each triplet, 2 symmetric combinations were constructed that are based on the left part of the image and its mirror image (left-left) and on the right part of the image and its mirror image (right-right). By applying a computer software that enables to determine length, surface area, and perimeter of any geometric shape, the following measurements were obtained for each triplet: face perimeter and area; distance between the pupils; mouth length; its perimeter and area; nose length and face length, usually below the ears; as well as the area and perimeter of the pupils. Then, for each of the above measurements, the value C, which characterizes the degree of symmetry of the real image with respect to the combinations right-right and left-left, was calculated. C appears on the right-hand side below each image. A high value of C indicates a low symmetry, and as the value is decreasing, the symmetry is increasing. The magnitude on the left relates to the pupils and compares the difference between the area and perimeter of the 2 pupils. The major conclusion arrived at here is that the human face is asymmetric to some degree; the degree of asymmetry is reported quantitatively under each portrait. PMID:26080172
Classification of Arnold-Beltrami flows and their hidden symmetries
NASA Astrophysics Data System (ADS)
Fré, P.; Sorin, A. S.
2015-07-01
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds ℳ3, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ★ g d, which can be solved by using time-honored harmonic analysis. Taking for ℳ3, a torus T 3 constructed as ℝ3/Λ, where Λ is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B A of three-vectors in the momentum lattice *Λ. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group which contains all space groups as proper subgroups. We show that the ★ g d eigenfunctions are naturally arranged into irreducible representations of and by means of a systematic use of the branching rules with respect to various possible subgroups we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O24 and the Universal Classifying Group is a finite group G1536 of order |G1536| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G1536. In this way we obtain an
PT Symmetry, Conformal Symmetry, and the Metrication of Electromagnetism
NASA Astrophysics Data System (ADS)
Mannheim, Philip D.
2016-05-01
We present some interesting connections between PT symmetry and conformal symmetry. We use them to develop a metricated theory of electromagnetism in which the electromagnetic field is present in the geometric connection. However, unlike Weyl who first advanced this possibility, we do not take the connection to be real but to instead be PT symmetric, with it being iA_{μ } rather than A_{μ } itself that then appears in the connection. With this modification the standard minimal coupling of electromagnetism to fermions is obtained. Through the use of torsion we obtain a metricated theory of electromagnetism that treats its electric and magnetic sectors symmetrically, with a conformal invariant theory of gravity being found to emerge. An extension to the non-Abelian case is provided.
Symmetry-adapted excited states for the T1u⊗hg Jahn-Teller system
NASA Astrophysics Data System (ADS)
Qiu, Q. C.; Dunn, J. L.; Bates, C. A.
2001-08-01
Jahn-Teller (JT) systems typically contain a set of equivalent-energy wells in the lowest adiabatic potential-energy surface (APES). Quantum-mechanical tunneling between these wells (the dynamic JT effect) must be allowed for by taking appropriate symmetrized combinations of oscillator-type states associated with the wells. It is important to be able to describe the excited states of such systems for a number of reasons. One particular reason is that they are required for the calculation of second-order vibronic reduction factors, which in turn are useful for modeling experimental data using effective Hamiltonians. In this paper, projection-operator techniques are used to obtain general expressions for the symmetry-adapted excited states of the icosahedral T1u⊗hg JT system for the case of D5d minima in the APES. Analytical expressions for the states and their energies for one-phonon excitation are given explicitly. The energies of a selection of states with two-phonon excitations are also obtained and plotted. The results obtained in this paper are applicable to the C-60 molecule.
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.
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Yet another symmetry breaking to be discovered
NASA Astrophysics Data System (ADS)
Yoshimura, M.
2016-07-01
The discovery of spontaneous symmetry breaking in particle physics was the greatest contribution in Nambu's achievements. There is another class of symmetries that exist in low-energy nature, yet is doomed to be broken at high energy, due to a lack of protection of the gauge symmetry. I shall review our approach to searching for this class of symmetry breaking, the lepton number violation linked to the generation of the matter-antimatter asymmetry in our universe.
Partial Dynamical Symmetry in Nuclear Systems
Escher, J E
2003-06-02
Partial dynamical symmetry (PDS) extends and complements the concepts of exact and dynamical symmetry. It allows one to remove undesired constraints from an algebraic theory, while preserving some of the useful aspects of a dynamical symmetry, and to study the effects of symmetry breaking in a controlled manner. An example of a PDS in an interacting fermion system is presented. The associated PDS Hamiltonians are closely related with a realistic quadrupole-quadrupole interaction and provide new insights into this important interaction.
Symmetry Breaking for Black-Scholes Equations
NASA Astrophysics Data System (ADS)
Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng
2007-06-01
Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.
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
Applications of Symmetry to Problem Solving.
ERIC Educational Resources Information Center
Leikin, Roza; Berman, Abraham; Zaslavsky, Orit
2000-01-01
Symmetry is an important mathematical concept that plays an extremely important role as a problem solving technique. Presents examples of problems from several branches of mathematics that can be solved using different types of symmetry. Discusses teachers' attitudes and beliefs regarding the use of symmetry in the solutions of these problems.…
CP symmetry in optical systems
NASA Astrophysics Data System (ADS)
Dana, Brenda; Bahabad, Alon; Malomed, Boris A.
2015-04-01
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity dispersion in the two cores, and a phase-velocity mismatch between them. The coupler is embedded into an active host medium, which provides for the linear coupling of a gain-loss type between the two cores. The same system can be derived, without phenomenological assumptions, by considering the three-wave propagation in a medium with the quadratic nonlinearity, provided that the depletion of the second-harmonic pump is negligible. This linear system offers an optical realization of the charge-parity symmetry, while the addition of the intracore cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.
Symmetry of cardiac function assessment
Bai, Xu-Fang; Ma, Amy X
2016-01-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Symmetry of cardiac function assessment.
Bai, Xu-Fang; Ma, Amy X
2016-09-01
Both right and left ventricles are developed from two adjacent segments of the primary heart tube. Though they are different with regard to shape and power, they mirror each other in terms of behavior. This is the first level of symmetry in cardiac function assessment. Both cardiac muscle contraction and relaxation are active. This constructs the second level of symmetry in cardiac function assessment. Combination of the two levels will help to find some hidden indexes or approaches to evaluate cardiac function. In this article, four major indexes from echocardiography were analyzed under this principal, another seventeen indexes or measurement approaches came out of the shadow, which is very helpful in the assessment of cardiac function, especially for the right cardiac function and diastolic cardiac function. PMID:27582768
Tensionless strings from worldsheet symmetries
NASA Astrophysics Data System (ADS)
Bagchi, Arjun; Chakrabortty, Shankhadeep; Parekh, Pulastya
2016-01-01
We revisit the construction of the tensionless limit of closed bosonic string theory in the covariant formulation in the light of Galilean conformal symmetry that rises as the residual gauge symmetry on the tensionless worldsheet. We relate the analysis of the fundamentally tensionless theory to the tensionless limit that is viewed as a contraction of worldsheet coordinates. Analysis of the quantum regime uncovers interesting physics. The degrees of freedom that appear in the tensionless string are fundamentally different from the usual string states. Through a Bogoliubov transformation on the worldsheet, we link the tensionless vacuum to the usual tensile vacuum. As an application, we show that our analysis can be used to understand physics of strings at very high temperatures and propose that these new degrees of freedom are naturally connected with the long-string picture of the Hagedorn phase of free string theory. We also show that tensionless closed strings behave like open strings.
NASA Astrophysics Data System (ADS)
Kesavan, Aruna; Ashtekar, Abhay
2016-03-01
Conservation laws of asymptotic symmetries are essential to quantify the amount of energy-momentum and angular momentum carried away by gravitational radiation from isolated systems. The asymptotic symmetry group of asymptotically flat spacetimes at null infinity is the Bondi-Metzner-Sachs (BMS) group. While the flux associated to an arbitrary BMS vector field was provided by Ashtekar and Streubel (1981) using symplectic methods, the tensorial expression of a corresponding two-dimensional charge integral linear in an arbitrary BMS vector field has not been available in the literature. We fill this gap by providing such a charge. I will discuss its properties and relation to Geroch's supermomentum and the charge of Dray and Streubel (1984).
Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ≥Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator χ ˆ =Rˆy (π) T ˆ, which involves the product of two distinct symmetries, namely, continuous and discrete. Therefore, new guidelines are required for testing its commutation with the system Hamiltonian. One of the primary objectives of this study is to lay down these guidelines. Further, the possible impact of chiral symmetry on the geometrical arrangement of angular momentum vectors and investigation of observables unique to nuclear chiral-twins is carried out. In our model, the angular momentum components (J1, J2, J3) occupy three mutually perpendicular axes of triaxial shape and represent a non-planar configuration. At certain threshold energy, the equation of motion in angular momentum develops a second order phase transition and as a result two distinct frames (i.e., the left- and right-handed) are formed. These left- and right-handed states correspond to a double well system and are related to each other through chiral operator. At this critical angular momentum, the centrifugal and Coriolis interactions lower the barrier in the double well system. The tunneling through the double well starts, which subsequently lifts the degeneracy among the rotational states. A detailed analysis of the behavior of rotational energies, spin-staggering, and the electromagnetic transition probabilities of the resulting twin-rotational bands is presented. The ensuing model results exhibit similarities with many observed features of the chiral-twins. An advantage of our formalism is that it is quite simple and it allows us to pinpoint the understanding of physical phenomenon which lead to chiral-twins in rotating systems.
Symmetry and Stochastic Gene Regulation
NASA Astrophysics Data System (ADS)
Ramos, Alexandre F.; Hornos, José E. M.
2007-09-01
Lorentz-like noncompact Lie symmetry SO(2,1) is found in a spin-boson stochastic model for gene expression. The invariant of the algebra characterizes the switch decay to equilibrium. The azimuthal eigenvalue describes the affinity between the regulatory protein and the gene operator site. Raising and lowering operators are constructed and their actions increase or decrease the affinity parameter. The classification of the noise regime of the gene arises from the group theoretical numbers.
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
Dark matter and global symmetries
NASA Astrophysics Data System (ADS)
Mambrini, Yann; Profumo, Stefano; Queiroz, Farinaldo S.
2016-09-01
General considerations in general relativity and quantum mechanics are known to potentially rule out continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino, and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds to specific models including the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that (ii) the non-renormalizable operators mediating dark matter decay have O (1) couplings, that (iii) the dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime.
Painlevé property, symmetries and symmetry reductions of the coupled Burgers system
NASA Astrophysics Data System (ADS)
Lian, Zeng-Ju; Chen, Li-Li; Lou, Sen-Yue
2005-08-01
The Painlevé property, inverse recursion operator, infinite number of symmetries and Lie symmetry reductions of the coupled Burgers equation are given explicitly. Three sets of infinitely many symmetries of the considered model are obtained by acting the recursion operator and the inverse recursion operator on the trivial symmetries such as the identity transformation, the space translation and the scaling transformation respectively. These symmetries constitute an infinite dimensional Lie algebra while its finite dimensional Lie point symmetry subalgebra is used to find possible symmetry reductions and then the group invariant solutions.
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.
Enhanced Facial Symmetry Assessment in Orthodontists
Jackson, Tate H.; Clark, Kait; Mitroff, Stephen R.
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff—orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342
Symmetry measures of the electron density.
Casanova, David; Alemany, Pere; Alvarez, Santiago
2010-10-01
In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C(6) symmetry along the B(2u) distortion mode of benzene and an analysis of rotational symmetry for different six-member ring heterocycles. PMID:20652983
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.
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
Hadler, Amelia B; Harris, Nicholas A; Fredrickson, Daniel C
2013-11-20
Despite significant progress in the structural characterization of the quasicrystalline state, the chemical origins of long- and short-range icosahedral order remain mysterious and a subject of debate. In this Article, we present the crystal structure of a new complex intermetallic phase, Ca10Cd27Cu2 (mC234.24), whose geometrical features offer clues to the driving forces underlying the icosahedral clusters that occur in Bergman-type quasicrystals. Ca10Cd27Cu2 adopts a C-centered monoclinic superstructure of the 1/1 Bergman approximant structure, in which [110] layers of Bergman clusters in the 1/1 structure are separated through the insertion of additional atoms (accompanied by substantial positional disorder). An examination of the coordination environments of Ca and Cu (in the ordered regions) reveals that the structure can be viewed as a combination of coordination polyhedra present in the nearest binary phases in the Ca-Cd-Cu compositional space. A notable feature is the separation of Ca-Cd and Cu-Cd interactions, with Bergman clusters emerging as Ca-Cd Friauf polyhedra (derived from the MgZn2-type CaCd2 phase) encapsulate a Cu-Cd icosahedron similar to those appearing in Cu2Cd5. DFT chemical pressure calculations on nearby binary phases point to the importance of this segregation of Ca-Cd and Cu-Cd interactions. The mismatch in atomic size between Cu and Cd leads to an inability to satisfy Ca-Cu and Ca-Cd interactions simultaneously in the Friauf polyhedra of the nearby Laves phase CaCd2. The relegation of the Cu atoms to icosahedra prevents this frustration while nucleating the formation of Bergman clusters. PMID:24147875
Killing symmetries as Hamiltonian constraints
NASA Astrophysics Data System (ADS)
Lusanna, Luca
2016-02-01
The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time, while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.
Hidden symmetries in jammed systems
NASA Astrophysics Data System (ADS)
Morse, Peter K.; Corwin, Eric I.
2016-07-01
There are deep, but hidden, geometric structures within jammed systems, associated with hidden symmetries. These can be revealed by repeated transformations under which these structures lead to fixed points. These geometric structures can be found in the Voronoi tesselation of space defined by the packing. In this paper we examine two iterative processes: maximum inscribed sphere (MIS) inversion and a real-space coarsening scheme. Under repeated iterations of the MIS inversion process we find invariant systems in which every particle is equal to the maximum inscribed sphere within its Voronoi cell. Using a real-space coarsening scheme we reveal behavior in geometric order parameters which is length-scale invariant.
History of electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Kibble, T. W. B.
2015-07-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the Ising×Ising¯ phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci × Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
Symmetry-directed control of electronic coupling for singlet fission in covalent bis-acene dimers.
Damrauer, Niels H; Snyder, Jamie L
2015-11-19
While singlet fission (SF) has developed in recent years within material settings, much less is known about its control in covalent dimers. Such platforms are of fundamental importance and may also find practical use in next-generation dye-sensitized solar cell applications or for seeding SF at interfaces following exciton transport. Here, facile theoretical tools based on Boys localization methods are used to predict diabatic coupling for SF via determination of one-electron orbital coupling matrix elements. The results expose important design rules that are rooted in point group symmetry. For Cs-symmetric dimers, pathways for SF that are mediated by virtual charge transfer excited states destructively interfere with negative impact on the magnitude of diabatic coupling for SF. When dimers have C2 symmetry, constructive interference is enabled for certain readily achievable interchromophore orientations. Three sets of dimers exploiting these ideas are explored: a bis-tetracene pair and two sets of aza-substituted tetracene dimers. Remarkable control is shown. In one aza-substituted set, symmetry has no impact on SF reaction thermodynamics but leads to a 16-fold manipulation in SF diabatic coupling. This translates to a difference of nearly 300 in kSF with the faster of the two dimers (C2) being predicted to undergo the process on a nearly ultrafast 1.5 ps time scale. PMID:26505732
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards
Spinor Structure and Internal Symmetries
NASA Astrophysics Data System (ADS)
Varlamov, V. V.
2015-10-01
Spinor structure 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. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.
Contact symmetries and Hamiltonian thermodynamics
Bravetti, A.; Lopez-Monsalvo, C.S.; Nettel, F.
2015-10-15
It has been shown that contact geometry is the proper framework underlying classical thermodynamics and that thermodynamic fluctuations are captured by an additional metric structure related to Fisher’s Information Matrix. In this work we analyse several unaddressed aspects about the application of contact and metric geometry to thermodynamics. We consider here the Thermodynamic Phase Space and start by investigating the role of gauge transformations and Legendre symmetries for metric contact manifolds and their significance in thermodynamics. Then we present a novel mathematical characterization of first order phase transitions as equilibrium processes on the Thermodynamic Phase Space for which the Legendre symmetry is broken. Moreover, we use contact Hamiltonian dynamics to represent thermodynamic processes in a way that resembles the classical Hamiltonian formulation of conservative mechanics and we show that the relevant Hamiltonian coincides with the irreversible entropy production along thermodynamic processes. Therefore, we use such property to give a geometric definition of thermodynamically admissible fluctuations according to the Second Law of thermodynamics. Finally, we show that the length of a curve describing a thermodynamic process measures its entropy production.
Duality symmetries in string theory
Nunez, Carmen A.
1999-10-25
The search for a unified theory of quantum gravity and gauge interactions leads naturally to string theory. This field of research has received a revival of interest after the discovery of duality symmetries in recent years. We present a self contained account of some non-perturbative aspects of string theory which have been recently understood. The spectrum and interactions of the five consistent superstring theories in ten dimensions are recollected and the fundamental principles underlying this initial stage in the construction of the theory are briefly reviewed. We next discuss some evidences that these apparently different superstrings are just different aspects of one unique theory. The key to this development is given by the non-perturbative duality symmetries which have modified and improved our understanding of string dynamics in many ways. In particular, by relating the fundamental objects of one theory to solitons of another theory, they have unraveled the presence of extended objects in the theory which stand on an equal footing with strings. We introduce these higher dimensional objects, named D-branes, and discuss applications of D-brane physics.
Introduction to Electroweak Symmetry Breaking
Dawson,S.
2008-10-02
The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.
Discrete symmetries and mixing of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Esmaili, Arman; Smirnov, Alexei Yu.
2015-11-01
We study the mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: Gν=Zn with n ≥3 . The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them, we have found all new relations between mixing parameters and corresponding symmetry assignments, which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry Gℓ=Z2. The relations involve elements of the rows of the Pontecorvo-Maki-Nakagawa-Sakata matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the C P violation phase. For larger symmetries Gℓ, an agreement with the data can be achieved if ˜10 % corrections related to breaking of Gℓ and Gν are included.
Symmetry properties in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.
Emergence of symmetry breaking in fucoid zygotes.
Homblé, Fabrice; Léonetti, Marc
2007-06-01
Fucoid zygotes are model cells for the study of symmetry breaking in plants. After fertilization, their initial spherical symmetry reduces to an axial symmetry, even in the absence of any external cue. This indicates that zygotes have an intrinsic ability to break symmetry in a way that is solely dependent on their internal biochemical and/or biophysical state. In our opinion, symmetry breaking is a self-organized process. It arises around the fucoid zygotes from the ion dynamics through channels (voltage-dependent calcium channels and a potassium leak) and outside the membrane (electrodiffusion owing to slower calcium diffusion compared with potassium). The robustness of this self-organized process and its lability ensure its relevance in plants where symmetry breaking is correlated with transcellular ion currents. PMID:17499009
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook. PMID:25354765
Scars of symmetries in quantum chaos
Delande, D.; Gay, J.C.
1987-10-19
The hydrogen atom in a magnetic field is a classically chaotic Hamiltonian system. The energy-level fluctuations have been shown recently to obey a random-matrix model. Here we go beyond the statistical analysis by studying the destruction of the low-field dynamical symmetries. We especially establish the existence of scars of symmetries in the chaotic regime. The symmetry properties are no longer associated with one given level, but fractalized onto clusters of levels, generating a long-range order.
Symmetry-protected single-photon subradiance
NASA Astrophysics Data System (ADS)
Cai, Han; Wang, Da-Wei; Svidzinsky, Anatoly A.; Zhu, Shi-Yao; Scully, Marlan O.
2016-05-01
We study the protection of subradiant states by the symmetry of the atomic distributions in the Dicke limit, in which collective Lamb shifts cannot be neglected. We find that antisymmetric states are subradiant states for distributions with reflection symmetry. Continuous symmetry can also be used to achieve subradiance. This study is relevant to the problem of robust quantum memory with long storage time and fast readout.
Search for primordial symmetry breakings in CMB
NASA Astrophysics Data System (ADS)
Shiraishi, Maresuke
2016-06-01
There are possibilities to violate symmetries (e.g. parity and rotational invariance) in the primordial cosmological fluctuations. Such symmetry breakings can imprint very rich signatures in late-time phenomena, which may be possible to observe. Especially, Cosmic Microwave Background (CMB) will change its face drastically, corresponding to the symmetry-breaking types, since the harmonic-space representation is very sensitive to the statistical, spin and angular dependences of cosmological perturbations. Here, we discuss (1) general responses of CMB to the symmetry breakings, (2) some theoretical models creating interesting CMB signatures, and (3) aspects of the estimation from observational data.
Asymptotic symmetries of Yang-Mills theory
NASA Astrophysics Data System (ADS)
Strominger, Andrew
2014-07-01
Asymptotic symmetries at future null infinity ( +) of Minkowski space for electrodynamics with massless charged fields, as well as nonabelian gauge theories with gauge group G, are considered at the semiclassical level. The possibility of charge/color flux through + suggests the symmetry group is infinite-dimensional. It is conjectured that the symmetries include a G Kac-Moody symmetry whose generators are "large" gauge transformations which approach locally holomorphic functions on the conformal two-sphere at + and are invariant under null translations. The Kac-Moody currents are constructed from the gauge field at the future boundary of +. The current Ward identities include Weinberg's soft photon theorem and its colored extension.
Evidence for tetrahedral symmetry in (16)O.
Bijker, R; Iachello, F
2014-04-18
We derive the rotation-vibration spectrum of a 4α configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of (16)O. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band. PMID:24785032
A K3 sigma model with : symmetry
NASA Astrophysics Data System (ADS)
Gaberdiel, Matthias R.; Taormina, Anne; Volpato, Roberto; Wendland, Katrin
2014-02-01
The K3 sigma model based on the -orbifold of the D 4-torus theory is studied. It is shown that it has an equivalent description in terms of twelve free Majorana fermions, or as a rational conformal field theory based on the affine algebra . By combining these different viewpoints we show that the = (4 , 4) preserving symmetries of this theory are described by the discrete symmetry group : . This model therefore accounts for one of the largest maximal symmetry groups of K3 sigma models. The symmetry group involves also generators that, from the orbifold point of view, map untwisted and twisted sector states into one another.
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
Issues in standard model symmetry breaking
Golden, M.
1988-04-01
This work discusses the symmetry breaking sector of the SU(2) x U(1) electroweak model. The first two chapters discuss Higgs masses in two simple Higgs models. The author proves low-enery theorems for the symmetry breaking sector: The threshold behavior of gauge-boson scattering is completely determined, whenever the symmetry breaking sector meets certain simple conditions. The author uses these theorems to derive event rates for the superconducting super collider (SSC). The author shows that the SSC may be able to determine whether the interactions of the symmetry breaking sector are strong or weak. 54 refs.
PREFACE: Symmetries in Science XV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2012-08-01
Logo Bregenz, the peaceful monastery of Mehrerau and the Opera on the Floating Stage again provided the setting for the international symposium 'Symmetries in Science'. The series which has been running for more than 30 years brings together leading theoreticians whose area of research is, in one way or another, related to symmetry. Since 1992 the meeting took place biannually in Brengez until 2003. In 2009, with the endorsement of the founder, Professor Bruno Gruber, we succeeded in re-establishing the series without external funding. The resounding success of that meeting encouraged us to continue in 2011 and, following on the enthusiasm and positive feedback of the participants, we expect to continue in 2013. Yet again, our meeting in 2011 was very international in flavour and brought together some 30 participants representing 12 nationalities, half of them from countries outside the European Union (from New Zealand to Mexico, Russia to Israel). The broad spectrum, a mixture of experienced experts and highly-motivated newcomers, the intensive exchange of ideas in a harmonious and relaxed atmosphere and the resulting joint projects are probably the secrets of why this meeting is considered to be so special to its participants. At the resumption in 2009 some leading experts and younger scientists from economically weak countries were unable to attend due to the lack of financial resources. This time, with the very worthy and unbureaucratic support of the 'Vereinigung von Freunden und Förderern der J W Goethe-Universität Frankfurt am Main' (in short: 'Friends and Supporters of the Frankfurt University'), it was possible for all candidates to participate. In particular some young, inspired scientists had the chance of presenting their work to a very competent, but also friendly, audience. We wish to thank the 'Freunde und Förderer' for supporting Symmetries in Science XV. Almost all participants contributed to the publication of this Conference Proceedings. There
Voit, E O
1992-04-01
An S-system is a set of first-order nonlinear differential equations that all have the same structure: The derivative of a variable is equal to the difference of two products of power-law functions. S-systems have been used as models for a variety of problems, primarily in biology. In addition, S-systems possess the interesting property that large classes of differential equations can be recast exactly as S-systems, a feature that has been proven useful in statistics and numerical analysis. Here, simple criteria are introduced that determine whether an S-system possesses certain types of symmetries and how the underlying transformation groups can be constructed. If a transformation group exists, families of solutions can be characterized, the number of S-system equations necessary for solution can be reduced, and some boundary value problems can be reduced to initial value problems. PMID:1591448
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350 GeV≲mS≲3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.
Neutrino properties and fundamental symmetries
Bowles, T.J.
1996-07-01
This is the final report of a three-year, Laboratory-Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). There are two components to this work. The first is a development of a new detection scheme for neutrinos. The observed deficit of neutrinos from the Sun may be due to either a lack of understanding of physical processes in the Sun or may be due to neutrinos oscillating from one type to another during their transit from the Sun to the Earth. The Sudbury Neutrino Observatory (SNO) is designed to use a water Cerenkov detector employing one thousand tonnes of heavy water to resolve this question. The ability to distinguish muon and tau neutrinos from electron neutrinos is crucial in order to carry out a model-independent test of neutrino oscillations. We describe a developmental exploration of a novel technique to do this using {sup 3}He proportional counters. Such a method offers considerable advantages over the initially proposed method of using Cerenkov light from capture on NaCl in the SNO. The second component of this work is an exploration of optimal detector geometry for a time-reversal invariance experiment. The question of why time moves only in the forward direction is one of the most puzzling problems in modern physics. We know from particle physics measurements of the decay of kaons that there is a charge-parity symmetry that is violated in nature, implying time-reversal invariance violation. Yet, we do not understand the origin of the violation of this symmetry. To promote such an understanding, we are developing concepts and prototype apparatus for a new, highly sensitive technique to search for time-reversal-invariance violation in the beta decay of the free neutron. The optimized detector geometry is seven times more sensitive than that in previous experiments. 15 refs.
Flavor symmetries and fermion masses
Rasin, A.
1994-04-01
We introduce several ways in which approximate flavor symmetries act on fermions and which are consistent with observed fermion masses and mixings. Flavor changing interactions mediated by new scalars appear as a consequence of approximate flavor symmetries. We discuss the experimental limits on masses of the new scalars, and show that the masses can easily be of the order of weak scale. Some implications for neutrino physics are also discussed. Such flavor changing interactions would easily erase any primordial baryon asymmetry. We show that this situation can be saved by simply adding a new charged particle with its own asymmetry. The neutrality of the Universe, together with sphaleron processes, then ensures a survival of baryon asymmetry. Several topics on flavor structure of the supersymmetric grand unified theories are discussed. First, we show that the successful predictions for the Kobayashi-Maskawa mixing matrix elements, V{sub ub}/V{sub cb} = {radical}m{sub u}/m{sub c} and V{sub td}/V{sub ts} = {radical}m{sub d}/m{sub s}, are a consequence of a large class of models, rather than specific properties of a few models. Second, we discuss how the recent observation of the decay {beta} {yields} s{gamma} constrains the parameter space when the ratio of the vacuum expectation values of the two Higgs doublets, tan{Beta}, is large. Finally, we discuss the flavor structure of proton decay. We observe a surprising enhancement of the branching ratio for the muon mode in SO(10) models compared to the same mode in the SU(5) model.
Rare Isotopes and Fundamental Symmetries
NASA Astrophysics Data System (ADS)
Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy
2009-01-01
Experiments searching for new interactions in nuclear beta decay / Klaus P. Jungmann -- The beta-neutrino correlation in sodium-21 and other nuclei / P. A. Vetter ... [et al.] -- Nuclear structure and fundamental symmetries/ B. Alex Brown -- Schiff moments and nuclear structure / J. Engel -- Superallowed nuclear beta decay: recent results and their impact on V[symbol] / J. C. Hardy and I. S. Towner -- New calculation of the isospin-symmetry breaking correlation to superallowed Fermi beta decay / I. S. Towner and J. C. Hardy -- Precise measurement of the [symbol]H to [symbol]He mass difference / D. E. Pinegar ... [et al.] -- Limits on scalar currents from the 0+ to 0+ decay of [symbol]Ar and isospin breaking in [symbol]Cl and [symbol]Cl / A. Garcia -- Nuclear constraints on the weak nucleon-nucleon interaction / W. C. Haxton -- Atomic PNC theory: current status and future prospects / M. S. Safronova -- Parity-violating nucleon-nucleon interactions: what can we learn from nuclear anapole moments? / B. Desplanques -- Proposed experiment for the measurement of the anapole moment in francium / A. Perez Galvan ... [et al.] -- The Radon-EDM experiment / Tim Chupp for the Radon-EDM collaboration -- The lead radius Eexperiment (PREX) and parity violating measurements of neutron densities / C. J. Horowitz -- Nuclear structure aspects of Schiff moment and search for collective enhancements / Naftali Auerbach and Vladimir Zelevinsky -- The interpretation of atomic electric dipole moments: Schiff theorem and its corrections / C. -P. Liu -- T-violation and the search for a permanent electric dipole moment of the mercury atom / M. D. Swallows ... [et al.] -- The new concept for FRIB and its potential for fundamental interactions studies / Guy Savard -- Collinear laser spectroscopy and polarized exotic nuclei at NSCL / K. Minamisono -- Environmental dependence of masses and coupling constants / M. Pospelov.
Nonlocalization of Nonlocal Symmetry and Symmetry Reductions of the Burgers Equation
NASA Astrophysics Data System (ADS)
Jin, Yan; Jia, Man; Lou, Sen-Yue
2012-12-01
Symmetry reduction method is one of the best ways to find exact solutions. In this paper, we study the possibility of symmetry reductions of the well known Burgers equation including the nonlocal symmetry. The related new group invariant solutions are obtained. Especially, the interactions among solitons, Airy waves, and Kummer waves are explicitly given.
Teaching symmetry in the introductory physics curriculum
Hill, C. T.; Lederman, L. M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
Quantum Mechanical Observers and Time Reparametrization Symmetry
NASA Astrophysics Data System (ADS)
Konishi, Eiji
2012-07-01
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their nonunitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
Symmetry Properties of Potentiometric Titration Curves.
ERIC Educational Resources Information Center
Macca, Carlo; Bombi, G. Giorgio
1983-01-01
Demonstrates how the symmetry properties of titration curves can be efficiently and rigorously treated by means of a simple method, assisted by the use of logarithmic diagrams. Discusses the symmetry properties of several typical titration curves, comparing the graphical approach and an explicit mathematical treatment. (Author/JM)
Hidden flavor symmetries of SO(10) GUT
NASA Astrophysics Data System (ADS)
Bajc, Borut; Smirnov, Alexei Yu.
2016-08-01
The Yukawa interactions of the SO(10) GUT with fermions in 16-plets (as well as with singlets) have certain intrinsic ("built-in") symmetries which do not depend on the model parameters. Thus, the symmetric Yukawa interactions of the 10 and 126 dimensional Higgses have intrinsic discrete Z2 ×Z2 symmetries, while the antisymmetric Yukawa interactions of the 120 dimensional Higgs have a continuous SU(2) symmetry. The couplings of SO(10) singlet fermions with fermionic 16-plets have U(1) 3 symmetry. We consider a possibility that some elements of these intrinsic symmetries are the residual symmetries, which originate from the (spontaneous) breaking of a larger symmetry group Gf. Such an embedding leads to the determination of certain elements of the relative mixing matrix U between the matrices of Yukawa couplings Y10, Y126, Y120, and consequently, to restrictions of masses and mixings of quarks and leptons. We explore the consequences of such embedding using the symmetry group conditions. We show how unitarity emerges from group properties and obtain the conditions it imposes on the parameters of embedding. We find that in some cases the predicted values of elements of U are compatible with the existing data fits. In the supersymmetric version of SO(10) such results are renormalization group invariant.
Copper Keplerates: High-Symmetry Magnetic Molecules.
Palacios, Maria A; Moreno Pineda, Eufemio; Sanz, Sergio; Inglis, Ross; Pitak, Mateusz B; Coles, Simon J; Evangelisti, Marco; Nojiri, Hiroyuki; Heesing, Christian; Brechin, Euan K; Schnack, Jürgen; Winpenny, Richard E P
2016-01-01
Keplerates are molecules that contain metal polyhedra that describe both Platonic and Archimedean solids; new copper keplerates are reported, with physical studies indicating that even where very high molecular symmetry is found, the low-temperature physics does not necessarily reflect this symmetry. PMID:26530901
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
NASA Astrophysics Data System (ADS)
Kumar, Vijay
2009-02-01
We report results of ab initio pseudopotential calculations on the nanocoating of gold on an icosahedral Al13 cluster and the findings of icosahedrally symmetric endohedral Al@Al12Au20- and empty cage Al12Au202- compound fullerenes formed of metal atoms. Twelve Al atoms cap the pentagonal faces of a dodecahedral Au20 cage in which each Au atom has three Al atoms and three Au atoms as nearest neighbors. Mixing of Al13 and Au20 magic clusters leads to a large heat of formation of 0.55 eV/atom and high stability of the Al@Al12Au20 compound fullerene. The binding energies of Al12Au20 and Al@Al12Au20 are 3.017 and 3.007 eV/atom, respectively, which are much larger than 2.457 eV/atom for Au32 fullerene, leading to the possibility of their high abundance.
Extracting hidden symmetry from the energy spectrum
NASA Astrophysics Data System (ADS)
Yuzbashyan, Emil A.; Happer, William; Altshuler, Boris L.; Shastry, Sriram B.
2003-03-01
In this paper we revisit the problem of finding hidden symmetries in quantum mechanical systems. Our interest in this problem was renewed by nontrivial degeneracies of a simple spin Hamiltonian used to model spin relaxation in alkali-metal vapours. We consider this spin Hamiltonian in detail and use this example to outline a general approach to finding symmetries when eigenvalues and eigenstates of the Hamiltonian are known. We extract all nontrivial symmetries responsible for the degeneracy and show that the symmetry group of the Hamiltonian is SU(2). The symmetry operators have a simple meaning which becomes transparent in the limit of large spin. As an additional example we apply the method to the hydrogen atom.
On Gauging Symmetry of Modular Categories
NASA Astrophysics Data System (ADS)
Cui, Shawn X.; Galindo, César; Plavnik, Julia Yael; Wang, Zhenghan
2016-05-01
Topological order of a topological phase of matter in two spacial dimensions is encoded by a unitary modular (tensor) category (UMC). A group symmetry of the topological phase induces a group symmetry of its corresponding UMC. Gauging is a well-known theoretical tool to promote a global symmetry to a local gauge symmetry. We give a mathematical formulation of gauging in terms of higher category formalism. Roughly, given a UMC with a symmetry group G, gauging is a 2-step process: first extend the UMC to a G-crossed braided fusion category and then take the equivariantization of the resulting category. Gauging can tell whether or not two enriched topological phases of matter are different, and also provides a way to construct new UMCs out of old ones. We derive a formula for the {H^4} -obstruction, prove some properties of gauging, and carry out gauging for two concrete examples.
Tests of gravitational symmetries with radio pulsars
NASA Astrophysics Data System (ADS)
Shao, LiJing; Wex, Norbert
2016-09-01
Symmetries play important roles in modern theories of physical laws. In this paper, we review several experimental tests of important symmetries associated with the gravitational interaction, including the universality of free fall for self-gravitating bodies, time-shift symmetry in the gravitational constant, local position invariance and local Lorentz invariance of gravity, and spacetime translational symmetries. Recent experimental explorations for post-Newtonian gravity are discussed, of which, those from pulsar astronomy are highlighted. All of these tests, of very different aspects of gravity theories, at very different length scales, favor to very high precision the predictions of the strong equivalence principle (SEP) and, in particular, general relativity which embodies SEP completely. As the founding principles of gravity, these symmetries are motivated to be promoted to even stricter tests in future.
Symmetries in geology and geophysics
Turcotte, Donald L.; Newman, William I.
1996-01-01
Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth’s topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters. PMID:11607719
Chiral symmetries associated with angular momentum
NASA Astrophysics Data System (ADS)
Bhattacharya, M.; Kleinert, M.
2014-03-01
In quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this paper we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss these simple, useful and beautiful symmetries at all. The first time a student encounters them is when the Dirac equation is discussed in a course on relativistic quantum mechanics, or when particle-hole symmetry is studied in the context of superconductivity. In this paper, we will show how chiral symmetries can be simply elucidated using the theory of angular momentum, which is taught in virtually all introductory quantum mechanics courses.
Guo, Yiming; Stacey, Timothy E; Fredrickson, Daniel C
2014-05-19
The crystal structures of intermetallic phases offer a wealth of geometrical features (helices, multishelled clusters, and host-guest motifs) whose formation has yet to be explained or predicted by chemical theory. A recently developed extension of the acid-base concept to metallic systems, the μ3-acidity model, provides an avenue for developing this understanding for intermetallics formed from transition metals. In this Article, we illustrate how this approach can be used to understand one of the most striking geometrical entities to emerge in intermetallic chemistry, the Mackay cluster of icosahedral quasicrystals. We present μ3-acidity analyses, based on DFT-calibrated Hückel calculations, for a series of Sc-Ir intermetallics: ScIr (CsCl-type), Sc2Ir (Ti2Ni-type), Sc11Ir4, and the Mackay cluster containing phases Sc57Ir13 and Sc44Ir7. We begin by illustrating that a μ3-acidity model correctly predicts that each of these phases is stable relative to disproportionation into their neighboring compounds when a common set of Hückel parameters and d-orbital occupancies is used. Next, we explain these results by developing a relationship between the distance distribution of homoatomic contacts within an atom's coordination sphere and the μ3-neutralization it experiences. For a given average homoatomic distance, the role of heteroatomic contacts is higher when the distribution of homoatomic contacts is narrower. This effect is key to the strength of the acid-base neutralization of the Sc-rich phases, where the Sc atoms find a scarcity of Ir atoms from which to obtain neutralization. Under these circumstances, Sc-Ir contacts should be maximized, whereas the number and distance variations of the Sc-Sc contacts should be minimized. These expectations are borne out by the observed crystal structures. In particular, the Mackay clusters of Sc57Ir13 and Sc44Ir7, in which a central Ir atom is icosahedrally coordinated by a pentagonal dodecahedral array of face-sharing Sc
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-10-01
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain "anomalous" SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H4(G ,U (1 )) , which also precisely labels the set of 3D SPT phases, with symmetry group G . An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U (1 )2 ] topological order with a reduced symmetry Z2×Z2⊂SO (3 ) , which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
Natural quasicrystal with decagonal symmetry.
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S; Andronicos, Christopher L; Distler, Vadim V; Eddy, Michael P; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J; Steinhardt, William M; Yudovskaya, Marina; Steinhardt, Paul J
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W.
2014-12-15
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+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.
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Law-Hine, Didier; Zeghal, Mehdi; Bressanelli, Stéphane; Constantin, Doru; Tresset, Guillaume
2016-08-10
Viruses are astonishing edifices in which hundreds of molecular building blocks fit into the final structure with pinpoint accuracy. We established a robust kinetic model accounting for the in vitro self-assembly of a capsid shell derived from an icosahedral plant virus by using time-resolved small-angle X-ray scattering (TR-SAXS) data at high spatiotemporal resolution. By implementing an analytical model of a spherical patch into a global fitting algorithm, we managed to identify a major intermediate species along the self-assembly pathway. With a series of data collected at different protein concentrations, we showed that free dimers self-assembled into a capsid through an intermediate resembling a half-capsid. The typical lifetime of the intermediate was a few seconds and yet the presence of so large an oligomer was not reported before. The progress in instrumental detection along with the development of powerful algorithms for data processing contribute to shedding light on nonequilibrium processes in highly complex systems such as viruses. PMID:27444997
Huang, Huogen; Chen, Liang
2015-08-17
Ti-Zr-Ni quasicrystals have been demonstrated to store a large number of hydrogen atoms, which implies strong potential application in hydrogen energy field for them. However, the desorption of hydrogen atoms in the quasicrystals is quite difficult, with the indication of high desorption temperature and slow desorption rate. The shortage limits their use in the field to a large extent. But this kind of quasicrystals might be used in nuclear fusion energy field, because tritium as a coral fuel for nuclear fusion needs tight storage. However, equilibrium pressure at room temperature of Ti-Zr-Ni quasicrystals, important for their application in fusion energy field, has not been clear yet. In this work, we designed a gas-solid reaction system with the pressure resolution of 10{sup −8}Pa and carried out hydrogen desorption investigation at different temperatures on Ti{sub 36}Zr{sub 40}Ni{sub 20}Pd{sub 4} icosahedral quasicrystal. Based on three Pressure-Composition-Temperature desorption curves, we speculate according to Van’t Hoff theory about hydrogen storage that its equilibrium pressure at room temperature could be at the magnitude of 10{sup −6}Pa, displaying good stability of hydrogen in the quasicrystal and also implying application prospects in fusion energy field for quasicrystals of this type.
Miyazaki, Naoyuki; Higashiura, Akifumi; Higashiura, Tomoko; Akita, Fusamichi; Hibino, Hiroyuki; Omura, Toshihiro; Nakagawa, Atsushi; Iwasaki, Kenji
2016-02-01
The minor outer capsid protein P2 of Rice dwarf virus (RDV), a member of the genus Phytoreovirus in the family Reoviridae, is essential for viral cell entry. Here, we clarified the structure of P2 and the interactions to host insect cells. Negative stain electron microscopy (EM) showed that P2 proteins are monomeric and flexible L-shaped filamentous structures of ∼20 nm in length. Cryo-EM structure revealed the spatial arrangement of P2 in the capsid, which was prescribed by the characteristic virion structure. The P2 proteins were visualized as partial rod-shaped structures of ∼10 nm in length in the cryo-EM map and accommodated in crevasses on the viral surface around icosahedral 5-fold axes with hydrophobic interactions. The remaining disordered region of P2 assumed to be extended to the radial direction towards exterior. Electron tomography clearly showed that RDV particles were away from the cellular membrane at a uniform distance and several spike-like densities, probably corresponding to P2, connecting a viral particle to the host cellular membrane during cell entry. By combining the in vitro and in vivo structural information, we could gain new insights into the detailed mechanism of the cell entry of RDV. PMID:26374901
Jakse, N.; Pasturel, A.
2015-08-28
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al{sub 80}Ni{sub 20} alloy upon cooling. Our results evidence a huge increase of local icosahedral ordering (ISRO) in the undercooled regime which is more developed around Ni than Al atoms. We show that ISRO has a strong impact on self-diffusion coefficients of both species and is at the origin of their crossover from Arrhenius to non-Arrhenius behavior around a crossover temperature T{sub X} = 1000 K, located in the undercooled region. We also clearly identify that this temperature corresponds to the development of dynamic heterogeneities and to the breakdown of the Stokes-Einstein relation. At temperatures below this crossover, we find that the behavior of the diffusion and relaxation dynamics is mostly incompatible with predictions of the mode-coupling theory. Finally, an analysis of the van Hove function indicates that the crossover temperature T{sub X} marks the onset of a change in the diffusion mechanism from a normal flow to an activated process with hopping. From these results, the glass-forming ability of the alloy is discussed.
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.
Discrete symmetries and de Sitter spacetime
Cotăescu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the α-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Electromagnetic Radiation under Explicit Symmetry Breaking
NASA Astrophysics Data System (ADS)
Sinha, Dhiraj; Amaratunga, Gehan A. J.
2015-04-01
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna.
\\cal{PT} -symmetry in Rydberg atoms
NASA Astrophysics Data System (ADS)
Ziauddin; Chuang, You-Lin; Lee, Ray-Kuang
2016-07-01
We propose a scheme to realize parity-time ( {PT} )-symmetry in an ensemble of strongly interacting Rydberg atoms, which act as superatoms due to the dipole blockade mechanism. We show that Rydberg-dressed 87Rb atoms in a four-level inverted Y-type configuration is highly efficient to generate the refractive index for a probe field, with a symmetric (antisymmetric) profile spatially in the corresponding real (imaginary) part. Comparing with earlier investigations, the present scheme provides a versatile platform to control the system from {PT} -symmetry to non-PT -symmetry via different external parameters, i.e., coupling field detuning, probe field intensity and control field intensity.
Polytopes vibrations within Coxeter group symmetries
NASA Astrophysics Data System (ADS)
Chadzitaskos, Goce; Patera, Jiıř´; Szajewska, Marzena
2016-05-01
We are considering polytopes with exact reflection symmetry group G in the real 3-dimensional Euclidean space R3. By changing one simple element of the polytope (position of one vertex or length of an edge), one can retain the exact symmetry of the polytope by simultaneously changing other corresponding elements of the polytope. A simple method of using the symmetry of polytopes in order to determine several resonant frequencies is presented. Knowledge of these frequencies, or at least their ratios can be used for control of some principal changes of the polytopes.
Dark Matter from Binary Tetrahedral Flavor Symmetry
NASA Astrophysics Data System (ADS)
Eby, David; Frampton, Paul
2012-03-01
Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.
Critical Symmetry and Supersymmetry in Nuclei
Iachello, Francesco
2006-04-26
The role of dynamic symmetries and supersymmetries in nuclei is reviewed. The concept of critical symmetry, appropriate to describe bosonic systems (even-even nuclei) at the critical point of a phase transition, is introduced, and the symmetry, E(5), at the critical point of spherical to {gamma}-unstable shape phase transition, is discussed. The recently introduced concept of critical supersymmetry, appropriate to describe mixed systems of bosons and fermions (odd-even nuclei) at the critical point of a phase transition is presented. The case of a j=3/2 particle at the critical point of spherical to {gamma}-unstable transition, called E(5/4), is discussed.
Mirror Symmetry for Quasi-Homogeneous Singularities
NASA Astrophysics Data System (ADS)
Rathnakumara, Himal; Jarvis, Tyler
2008-10-01
I will present an introduction to mirror symmetry in the context of string theory. Then I will describe an instance of mirror symmetry for singularties defined by quasi-homogeneous polynomials in weighted projective spaces. Milnor rings and the FJRW (Fan-Jarvis-Ruan-Witten) rings associated with these singularities and their relation to the Landua-Ginzburg A model and the Landua-Ginzburg B model will be explained. Results of the calculations for certain singularities for which the mirror symmetry conjecture has been verified will be presented.
Inversion symmetry protected topological insulators and superconductors
NASA Astrophysics Data System (ADS)
Lee, Dung-Hai; Lu, Yuan-Ming
2015-03-01
Three dimensional topological insulator represents a class of novel quantum phases hosting robust gapless boundary excitations, which is protected by global symmetries such as time reversal, charge conservation and spin rotational symmetry. In this work we systematically study another class of topological phases of weakly interacting electrons protected by spatial inversion symmetry, which generally don't support stable gapless boundary states. We classify these inversion-symmetric topological insulators and superconductors in the framework of K-theory, and construct their lattice models. We also discuss quantized response functions of these inversion-protected topological phases, which serve as their experimental signatures.
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuriĭ Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals.
Mei, Jun; Chen, Zeguo; Wu, Ying
2016-01-01
We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound. PMID:27587311
Pseudo-time-reversal symmetry and topological edge states in two-dimensional acoustic crystals
Mei, Jun; Chen, Zeguo; Wu, Ying
2016-01-01
We propose a simple two-dimensional acoustic crystal to realize topologically protected edge states for acoustic waves. The acoustic crystal is composed of a triangular array of core-shell cylinders embedded in a water host. By utilizing the point group symmetry of two doubly degenerate eigenstates at the Γ point, we can construct pseudo-time-reversal symmetry as well as pseudo-spin states in this classical system. We develop an effective Hamiltonian for the associated dispersion bands around the Brillouin zone center, and find the inherent link between the band inversion and the topological phase transition. With numerical simulations, we unambiguously demonstrate the unidirectional propagation of acoustic edge states along the interface between a topologically nontrivial acoustic crystal and a trivial one, and the robustness of the edge states against defects with sharp bends. Our work provides a new design paradigm for manipulating and transporting acoustic waves in a topologically protected manner. Technological applications and devices based on our design are expected in various frequency ranges of interest, spanning from infrasound to ultrasound. PMID:27587311
Symmetry energy of warm nuclear systems
NASA Astrophysics Data System (ADS)
Agrawal, B. K.; De, J. N.; Samaddar, S. K.; Centelles, M.; Viñas, X.
2014-02-01
The temperature dependence of the symmetry energy and symmetry free energy coefficients of infinite nuclear matter and of finite nuclei is investigated. For infinite matter, both these coefficients are found to have a weaker dependence on temperature at densities close to saturation; at low but homogeneous densities, the temperature dependence becomes stronger. For finite systems, different definitions of symmetry energy coefficients are encountered in the literature yielding different values. A resolution to this problem is suggested from a global liquid-drop-inspired fit of the energies and free energies of a host of nuclei covering the entire periodic table. The hot nucleus is modeled in a subtracted finite-temperature Thomas-Fermi framework, with dynamical surface phonon coupling to nucleonic motion plugged in. Contrary to infinite nuclear matter, a substantial change in the symmetry energy coefficients is observed for finite nuclei with temperature.
RNA quaternary structure and global symmetry.
Jones, Christopher P; Ferré-D'Amaré, Adrian R
2015-04-01
Many proteins associate into symmetric multisubunit complexes. Structural analyses suggested that, by contrast, virtually all RNAs with complex 3D structures function as asymmetric monomers. Recent crystal structures revealed that several biological RNAs exhibit global symmetry at the level of their tertiary and quaternary structures. Here we survey known examples of global RNA symmetry, including the true quaternary symmetry of the bacteriophage ϕ29 prohead RNA (pRNA) and the internal pseudosymmetry of the single-chain flavin mononucleotide (FMN), glycine, and cyclic di-AMP (c-di-AMP) riboswitches. For these RNAs, global symmetry stabilizes the RNA fold, coordinates ligand-RNA interactions, and facilitates association with symmetric binding partners. PMID:25778613
Spatial Symmetries of the Local Densities
Rohozinski, S.; Dobaczewski, J.; Nazarewicz, Witold
2010-01-01
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Matrix Models, Emergent Spacetime and Symmetry Breaking
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2009-12-15
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
RNA quaternary structure and global symmetry
Jones, Christopher P.; Ferré-D'Amaré, Adrian R.
2015-01-01
Many proteins associate into symmetric multisubunit complexes. Structural analyses suggested that, in contrast, virtually all RNAs with complex three-dimensional structures function as asymmetric monomers. Recent crystal structures revealed that several biological RNAs exhibit global symmetry at the level of their tertiary and quaternary structures. Here, we survey known examples of global RNA symmetry, including the true quaternary symmetry of the bacteriophage ϕ29 prohead RNA (pRNA), and the internal pseudosymmetry of the single-chain flavin mononucleotide (FMN), glycine, and cyclic diadenosine monophosphate (c-di-AMP) riboswitches. For these RNAs, global symmetry stabilizes the RNA fold, coordinates ligand-RNA interactions, and facilitates association with symmetric binding partners. PMID:25778613
Spontaneous chiral symmetry breaking in metamaterials
NASA Astrophysics Data System (ADS)
Liu, Mingkai; Powell, David A.; Shadrivov, Ilya V.; Lapine, Mikhail; Kivshar, Yuri S.
2014-07-01
Spontaneous chiral symmetry breaking underpins a variety of areas such as subatomic physics and biochemistry, and leads to an impressive range of fundamental phenomena. Here we show that this prominent effect is now available in artificial electromagnetic systems, enabled by the advent of magnetoelastic metamaterials where a mechanical degree of freedom leads to a rich variety of strong nonlinear effects such as bistability and self-oscillations. We report spontaneous symmetry breaking in torsional chiral magnetoelastic structures where two or more meta-molecules with opposite handedness are electromagnetically coupled, modifying the system stability. Importantly, we show that chiral symmetry breaking can be found in the stationary response of the system, and the effect is successfully demonstrated in a microwave pump-probe experiment. Such symmetry breaking can lead to a giant nonlinear polarization change, energy localization and mode splitting, which provides a new possibility for creating an artificial phase transition in metamaterials, analogous to that in ferrimagnetic domains.
Modelling Symmetry Classes 233 and 432.
ERIC Educational Resources Information Center
Dutch, Steven I.
1986-01-01
Offers instructions and geometrical data for constructing solids of the enantiomorphous symmetry classes 233 and 432. Provides background information for each class and highlights symmetrical relationships and construction patterns. (ML)
Space and time from translation symmetry
Schwarz, A.
2010-01-15
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Matrix Models, Emergent Spacetime and Symmetry Breaking
NASA Astrophysics Data System (ADS)
Grosse, Harald; Lizzi, Fedele; Steinacker, Harold
2009-12-01
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
Personal recollections on chiral symmetry breaking
NASA Astrophysics Data System (ADS)
Kobayashi, Makoto
2016-07-01
The author's work on the mass of pseudoscalar mesons is briefly reviewed. The emergence of the study of CP violation in the renormalizable gauge theory from consideration of chiral symmetry in the quark model is discussed.
Shift symmetry and inflation in supergravity
Brax, Philippe; Martin, Jerome
2005-07-15
We consider models of inflation in supergravity with a shift symmetry. We focus on models with one modulus and one inflaton field. The presence of this symmetry guarantees the existence of a flat direction for the inflaton field. Mildly breaking the shift symmetry using a superpotential which depends not only on the modulus, but also on the inflaton field allows one to lift the inflaton flat direction. Along the inflaton direction, the {eta} problem is alleviated. Combining the KKLT mechanism for modulus stabilization and a shift symmetry breaking superpotential of the chaotic inflation type, we find models reminiscent of 'mutated hybrid inflation' where the inflationary trajectory is curved in the modulus-inflaton plane. We analyze the phenomenology of these models and stress their differences with both chaotic and hybrid inflation.
Compact stars and the symmetry energy
NASA Astrophysics Data System (ADS)
Providência, Constana; Cavagnoli, Rafael; Menezes, Debora P.; Panda, Prafulla K.; Rabhi, Aziz
2013-02-01
The effect of the symmetry energy on some properties of compact stars which contain strange degrees of freedom is discussed. Both the onset of hyperons or kaon condensation will be considered. The hyperon-meson couplings are chosen according to experimental values of the hyperon nuclear matter potentials and possible uncertainties are considered. It is shown that a softer symmetry energy affects the onset of strangeness, namely neutral (negatively charged) strange particles set on at larger (smaller) densities, and gives rise to a smaller strangeness fraction as a function of density. A softer symmetry energy will possibily give rise to maximum mass configurations with larger masses. Hyperon-meson couplings have a strong effect on the mass of the star. It is shown that, for stars with masses above 1 Msolar, the radius of the star varies linearly with the symmetry energy slope L.
Symmetry and the Cosmic Microwave Background
NASA Technical Reports Server (NTRS)
Wollock, Edward J.
2012-01-01
A brief historical introduction to the development of observational astronomy and cosmology will be presented. The close relationship between the properties of light, symmetry, and our understanding the contents of our universe will be explored.
Composite fermions and broken symmetries in graphene.
Amet, F; Bestwick, A J; Williams, J R; Balicas, L; Watanabe, K; Taniguchi, T; Goldhaber-Gordon, D
2015-01-01
The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields. PMID:25562690
Composite fermions and broken symmetries in graphene
NASA Astrophysics Data System (ADS)
Amet, F.; Bestwick, A. J.; Williams, J. R.; Balicas, L.; Watanabe, K.; Taniguchi, T.; Goldhaber-Gordon, D.
2015-01-01
The electronic properties of graphene are described by a Dirac Hamiltonian with a four-fold symmetry of spin and valley. This symmetry may yield novel fractional quantum Hall (FQH) states at high magnetic field depending on the relative strength of symmetry-breaking interactions. However, observing such states in transport remains challenging in graphene, as they are easily destroyed by disorder. In this work, we observe in the first two Landau levels the two-flux composite-fermion sequences of FQH states between each integer filling factor. In particular, the odd-numerator fractions appear between filling factors 1 and 2, suggesting a broken-valley symmetry, consistent with our observation of a gap at charge neutrality and zero field. Contrary to our expectations, the evolution of gaps in a parallel magnetic field suggests that states in the first Landau level are not spin-polarized even up to very large out-of-plane fields.
Nanostructure symmetry: Relevance for physics and computing
Dupertuis, Marc-André; Oberli, D. Y.; Karlsson, K. F.; Dalessi, S.; Gallinet, B.; Svendsen, G.
2014-03-31
We review the research done in recent years in our group on the effects of nanostructure symmetry, and outline its relevance both for nanostructure physics and for computations of their electronic and optical properties. The exemples of C3v and C2v quantum dots are used. A number of surprises and non-trivial aspects are outlined, and a few symmetry-based tools for computing and analysis are shortly presented.
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
Symmetry breaking of quasihelical stellarator equilibria
Weening, R.H. )
1993-04-01
A mean-field Ohm's law is used to determine the effects of the bootstrap current on quasihelically symmetric stellarator equilibria. The Ohm's law leads to the conclusion that the effects of the bootstrap current break the quasihelical stellarator symmetry at second order in an inverse aspect ratio expansion of the magnetic field strength. The level of symmetry breaking suggests that good approximations to quasihelical stellarator fusion reactors may not be attainable.
Leptogenesis with Friedberg-Lee Symmetry
NASA Astrophysics Data System (ADS)
Araki, Takeshi; Geng, C. Q.
We consider the µ - τ symmetric Friedberg-Lee (FL) symmetry for the neutrino sector and show that a specific FL translation leads to the tribimaximal mixing pattern of the Maki-Nakagawa-Sakata (MNS) matrix. We also apply the symmetry to the type-I seesaw framework and address the baryon asymmetry of the universe through the leptogenesis mechanism. We try to establish a relation between the net baryon asymmetry and CP phases included in the MNS matrix.
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
Cicogna, G.; Pegoraro, F.
2015-02-15
We identify and discuss a family of azimuthally symmetric, incompressible, magnetohydrodynamic plasma equilibria with poloidal and toroidal flows in terms of solutions of the Generalized Grad Shafranov (GGS) equation. These solutions are derived by exploiting the incompressibility assumption, in order to rewrite the GGS equation in terms of a different dependent variable, and the continuous Lie symmetry properties of the resulting equation and, in particular, a special type of “weak” symmetries.
Noether symmetries in the phase space
NASA Astrophysics Data System (ADS)
Díaz, Bogar; Galindo-Linares, Elizabeth; Ramírez-Romero, Cupatitzio; Silva-Ortigoza, Gilberto; Suárez-Xique, Román; Torres del Castillo, Gerardo F.; Velázquez, Mercedes
2014-09-01
The constants of motion of a mechanical system with a finite number of degrees of freedom are related to the variational symmetries of a Lagrangian constructed from the Hamiltonian of the original system. The configuration space for this Lagrangian is the phase space of the original system. The symmetries considered in this manner include transformations of the time and may not be canonical in the standard sense.
Symmetry energy in cold dense matter
NASA Astrophysics Data System (ADS)
Jeong, Kie Sang; Lee, Su Houng
2016-01-01
We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.
Fluency Expresses Implicit Knowledge of Tonal Symmetry
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences. PMID:26869960
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
Fluency Expresses Implicit Knowledge of Tonal Symmetry.
Ling, Xiaoli; Li, Fengying; Qiao, Fuqiang; Guo, Xiuyan; Dienes, Zoltan
2016-01-01
The purposes of the present study were twofold. First, we sought to establish whether tonal symmetry produces processing fluency. Second, we sought to explore whether symmetry and chunk strength express themselves differently in fluency, as an indication of different mechanisms being involved for sub- and supra-finite state processing. Across two experiments, participants were asked to listen to and memorize artificial poetry showing a mirror symmetry (an inversion, i.e., a type of cross serial dependency); after this training phase, people completed a four-choice RT task in which they were presented with new artificial poetry. Participants were required to identify the stimulus displayed. We found that symmetry sped up responding to the second half of strings, indicating a fluency effect. Furthermore, there was a dissociation between fluency effects arising from symmetry vs. chunk strength, with stronger fluency effects for symmetry rather than chunks in the second half of strings. Taken together, we conjecture a divide between finite state and supra-finite state mechanisms in learning grammatical sequences. PMID:26869960
Exploring symmetry in near-vacuum hohlraums
NASA Astrophysics Data System (ADS)
Berzak Hopkins, L.; Le Pape, S.; Divol, L.; Meezan, N.; MacKinnon, A.; Ho, D. D.; Jones, O.; Khan, S.; Ma, T.; Milovich, J.; Pak, A.; Ross, J. S.; Thomas, C.; Turnbull, D.; Amendt, P.; Wilks, S.; Zylstra, A.; Rinderknecht, H.; Sio, H.; Petrasso, R.
2015-11-01
Recent experiments with near-vacuum hohlraums, which utilize a minimal but non-zero helium fill, have demonstrated performance improvements relative to conventional gas-filled (0.96 - 1.6 mg/cc helium) hohlraums: minimal backscatter, reduced capsule drive degradation, and minimal suprathermal electron generation. Because this is a low laser-plasma interaction platform, implosion symmetry is controlled via pulse-shaping adjustments to laser power balance. Extending this platform to high-yield designs with high-density carbon capsules requires achieving adequate symmetry control throughout the pulse. In simulations, laser propagation is degraded suddenly by hohlraum wall expansion interacting with ablated capsule material. Nominal radiation-hydrodynamics simulations have not yet proven predictive on symmetry of the final hotspot, and experiments show more prolate symmetry than preshot calculations. Recent efforts have focused on understanding the discrepancy between simulated and measured symmetry and on alternate designs for symmetry control through varying cone fraction, trade-offs between laser power and energy, and modifications to case-to-capsule ratio. Work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344.
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.
Spontaneous Symmetry Breaking in Nonrelativistic Systems
NASA Astrophysics Data System (ADS)
Watanabe, Haruki
The subject of condensed matter physics is very rich --- there are an infinite number of parameters producing a diversity of exciting phenomena. As a theorist, my goal is to distill general principles out of this complexity --- to construct theories that can coherently explain many known examples altogether. This thesis is composed of several attempts to develop such theories in topics related to spontaneously symmetry breaking. A remarkable feature of many-body interacting systems is that although they are described by equations respecting various symmetries, they may spontaneously organize into a state that explicitly breaks symmetries. Examples are numerous: various types of crystalline and magnetic orders, Bose-Einstein condensates of cold atoms, superfluids of liquid helium, chiral symmetry in QCD, neutron stars, and cosmic inflation. These systems with spontaneously broken continuous symmetries have gapless excitations, so called Nambu-Goldstone bosons (NGBs). Although the properties of NGBs are well understood in Lorentz-invariant systems, surprisingly, some basic properties of NGBs such as their number and dispersion in nonrelativistic systems have not been discussed from a general perspective. In the first part of this thesis, we solve this issue by developing and analyzing an effective Lagrangian that coherently captures the low-energy, long-distance physics of many different symmetry-breaking states all at once. Next, we examine whether these NGBs originating from spontaneous symmetry breaking remain to be well-defined excitations inside a metal, where low-energy electrons near Fermi surface can collide with them. Our result is a one equation criterion that specifies whether the interactions between electrons and NGBs can be ignored, or whether it completely changes their character. In the latter case, unusual phases of matter such as non-Fermi liquids may arise; in that case, NGBs are overdamped and cannot form particle-like excitations in spite of the
Unal, Baris
2008-01-01
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
Perception of Mirror Symmetry in Autism Spectrum Disorders
ERIC Educational Resources Information Center
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…
De Jong, W; Ahlquist, P
1992-08-01
For many plant RNA viruses, multiple viral gene products, including noncapsid movement proteins and capsid proteins, contribute to the spread of infection within plants. The extent to which these factors interact to support infection spread is not known, but, for movement protein mutants of certain viruses, the inability of coinoculated "helper" viruses to complement defective movement has suggested a possible requirement for coadaptation between noncapsid movement proteins and other virus factors. To test directly for required coadaptation, the 3a movement protein gene of cowpea chlorotic mottle virus, an icosahedral bromovirus, was replaced with the nonhomologous 30-kDa movement protein gene of sunn-hemp mosaic virus, a rod-shaped, cowpea-adapted tobamovirus. The resulting hybrid virus is competent for systemic infection of cowpea, with systemic infection dependent upon expression of the 30-kDa gene. In view of the dramatic differences between cowpea chlorotic mottle virus and sunn-hemp mosaic virus in genetic organization and particle morphology, the ability of the hybrid to systemically infect cowpea implies that the tobamovirus 30-kDa movement protein functions independently of sequence-specific interactions with other viral components or sequences. Similarly, the required contribution of bromovirus capsid protein to infection movement appears to be independent of specific interaction with the natural 3a movement protein. In addition to other implications concerning movement protein and coat protein function, the results are consistent with the possibility that two or more distinguishable transfer processes may be involved in crossing different tissue barriers to achieve full systemic spread of infection. PMID:1495969
Lin, Qisheng; Corbett, John D
2008-09-01
Two crystalline approximants (ACs) and their corresponding icosahedral quasicrystal (i-QC) are obtained in the Ca-Au-Ga system through conventional solid-state exploratory syntheses. Single crystal structural analyses reveal that the 1/1 AC, Ca 3Au x Ga 19- x ( x = approximately 9.3-12.1) [ Im3, a = 14.6941(6)-14.7594(6) A], has the empty cubes in the prototypic YCd 6 (= Y 3Cd 18) now fully occupied by Ga, resulting in a 3:19 stoichiometry. In parallel, the distorted cubes in the 2/1 AC, Ca 13Au 57.1Ga 23.4 [ Pa3, a = 23.9377(8) A] are fully or fractionally occupied by Ga. The valence electron count per atom ( e/ a) for the 2/1 AC (1.64) is smaller than that over the 1/1 AC composition range (1.76-2.02), and the e/ a of the Ca 15.2Au 50.3Ga 34.5 i-QC, 1.84, is somewhat distant from typical values for Tsai-type i-QCs ( approximately 2.0). Comparisons of the gallium results with the corresponding In phases suggest that the structural differences result mainly from size rather than electronic factors. The 1/1 and 2/1 appear to be thermodynamically stable on slow cooling, as usual, whereas the i-QC isolated by quenching decomposes on heating at approximately 660 degrees C, mainly into 2/1 AC and Ca 3(Au,Ga) 11. Calculations of the electronic structure of 1/1 AC suggest that the Fermi sphere-Brillouin zone interactions remain important for the Ca-Au-Ga i-QC. PMID:18672875
Zheng, Qiang; Wagner, Frank R; Ormeci, Alim; Prots, Yurii; Burkhardt, Ulrich; Schmidt, Marcus; Schnelle, Walter; Grin, Yuri; Leithe-Jasper, Andreas
2015-11-01
Two ternary borides MNi9 B8 (M=Al, Ga) were synthesized by thermal treatment of mixtures of the elements. Single-crystal X-ray diffraction data reveal AlNi9 B8 and GaNi9 B8 crystallizing in a new type of structure within the space group Cmcm and the lattice parameters a=7.0896(3) Å, b=8.1181(3) Å, c=10.6497(4) Å and a=7.0897(5) Å, b=8.1579(4) Å, c=10.6648(7) Å, respectively. The boron atoms build up two-dimensional layers, which consist of puckered [B16 ] rings with two tailing B atoms, whereas the M atoms reside in distorted vertices-condensed [Ni12 ] icosahedra, which form a three-dimensional framework interpenetrated by boron porphyrin-reminiscent layers. An unusual local arrangement resembling a giant metallo-porphyrin entity is formed by the [B16 ] rings, which, due to their large annular size of approximately 8 Å, chelate four of the twelve icosahedral Ni atoms. An analysis of the chemical bonding by means of the electron localizability approach reveals strong covalent B-B interactions and weak Ni-Ni interactions. Multi-center dative B-Ni interaction occurs between the Al-Ni framework and the boron layers. In agreement with the chemical bonding analysis and band structure calculations, AlNi9 B8 is a Pauli-paramagnetic metal. PMID:26418894
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Residual symmetries of the gravitational field
NASA Astrophysics Data System (ADS)
Ayón-Beato, Eloy; Velázquez-Rodríguez, Gerardo
2016-02-01
We develop a geometric criterion that unambiguously characterizes the residual symmetries of a gravitational Ansatz. It also provides a systematic and effective computational procedure for finding all the residual symmetries of any gravitational Ansatz. We apply the criterion to several examples starting with the Collinson Ansatz for circular stationary axisymmetric spacetimes. We reproduce the residual symmetries already known for this Ansatz including their conformal symmetry, for which we identify the corresponding infinite generators spanning the two related copies of the Witt algebra. We also consider the noncircular generalization of this Ansatz and show how the noncircular contributions on the one hand break the conformal invariance and on the other hand enhance the standard translation symmetries of the circular Killing vectors to supertranslations depending on the direction along which the circularity is lost. As another application of the method, the well-known relation defining conjugate gravitational potentials introduced by Chandrasekhar, which makes possible the derivation of the Kerr black hole from a trivial solution of the Ernst equations, is deduced as a special point of the general residual symmetry of the Papapetrou Ansatz. In this derivation we emphasize how the election of Weyl coordinates, which determines the Papapetrou Ansatz, breaks also the conformal freedom of the stationary axisymmetric spacetimes. Additionally, we study AdS waves for any dimension generalizing the residual symmetries already known for lower dimensions and exhibiting a very complex infinite-dimensional Lie algebra containing three families: two of them span the semidirect sum of the Witt algebra and scalar supertranslations and the third generates vector supertranslations. Independently of this complexity we manage to comprehend the true meaning of the infinite connected group as the precise diffeomorphisms subgroup allowing to locally deform the AdS background into Ad
The small step toward asymmetry: Aesthetic judgment of broken symmetries.
Gartus, Andreas; Leder, Helmut
2013-01-01
Symmetry and complexity both affect the aesthetic judgment of abstract patterns. However, although beauty tends to be associated with symmetry, there are indications that small asymmetries can also be beautiful. We investigated the influence of small deviations from symmetry on people's aesthetic liking for abstract patterns. Breaking symmetry not only decreased patterns' symmetry but also increased their complexity. While an increase of complexity normally results in a higher liking, we found that even a small decrease of symmetry has a strong effect, such that patterns with slightly broken symmetries were significantly less liked than fully symmetric ones. PMID:24349695
Relativistic symmetries in nuclear single-particle spectra
NASA Astrophysics Data System (ADS)
Guo, Jian-You; Liang, Hao Zhao; Meng, Jie; Zhou, Shan-Gui
Symmetry is a fundamental concept in quantum physics. The quasi-degeneracy between single-particle orbitals (n, l, j = l + 1/2) and (n -1, l + 2, j = l + 3/2) indicates a hidden symmetry in atomic nuclei, the so-called pseudospin symmetry. Since the pseudospin symmetry was recognized as a relativistic symmetry in 1990s, many special features, including the spin symmetry for anti-nucleons, and many new concepts have been introduced. In this Chapter, we will illustrate the schematic picture of spin and pseudospin symmetries, derive the basic formalism, highlight the recent progress from several different aspects, and discuss selected open issues in this topic.
Group Parametrized Tunneling and Local Symmetry Conditions
NASA Astrophysics Data System (ADS)
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar γ ^i {bar g}_i of operators in dual symmetry group bar G. The coefficients bar γ ^i are parameters that define a complete set of allowed paths for any H with G-symmetry and are related thru spectral decomposition of G to eigensolutions of H. Quantum G vs.bar G duality generalizes lab -vs. -body and state -vs. -particle. The number of relevant bar γ ^i-parameters is reduced if a system tends to stick in states of a local symmetry subgroup LsubsetG so the H spectrum forms level clusters labeled by induced representations d(ℓ)(L)\\uparrowG. A cluster-(ℓ) has one E(epsilon)-level labeled by G species (epsilon) for each L species (ℓ) in Depsilon(G)downarrowL by Frobenius reciprocity. Then we apply local symmetry conditions to each irrep Depsilon(bar γ ^i {bar g}_i) that has already been reduced with respect to local symmetry L. This amounts to setting each off-diagonal component Dj,kepsilon(H) to zero. Local symmetry conditions may tell which bar γ ^i-parameters are redundant or zero and directly determine d(ℓ)\\uparrowG tunneling matrix eigenvalues that give E(epsilon)-levels as well as eigenvectors. Otherwise one may need to choose a particular localizing subgroup chain LsubsetL_1subsetL_2...G and further reduce the number of path parameters to facilitate spectral fitting. J.T. Hougen, 2009 MSS RJ01, {J Mol Spect 123, 197 (1987) W.G. Harter and
Statistical palaeomagnetic field modelling and symmetry considerations
NASA Astrophysics Data System (ADS)
Hulot, G.; Bouligand, C.
2005-06-01
In the present paper, we address symmetry issues in the context of the so-called giant gaussian process (GGP) modelling approach, currently used to statistically analyse the present and past magnetic field of the Earth at times of stable polarity. We first recall the principle of GGP modelling, and for the first time derive the complete and exact constraints a GGP model should satisfy if it is to satisfy statistical spherical, axisymmetrical or equatorially symmetric properties. We note that as often correctly claimed by the authors, many simplifying assumptions used so far to ease the GGP modelling amount to make symmetry assumptions, but not always exactly so, because previous studies did not recognize that symmetry assumptions do not systematically require a lack of cross-correlations between Gauss coefficients. We further note that GGP models obtained so far for the field over the past 5Myr clearly reveal some spherical symmetry breaking properties in both the mean and the fluctuating field (as defined by the covariance matrix of the model) and some equatorial symmetry breaking properties in the mean field. Non-zonal terms found in the mean field of some models and mismatches between variances defining the fluctuating field (in models however not defined in a consistent way) would further suggest that axial symmetry also is broken. The meaning of this is discussed. Spherical symmetry breaking trivially testifies for the influence of the rotation of the Earth on the geodynamo (a long-recognized fact). Axial symmetry breaking, if confirmed, could hardly be attributed to anything else but some influence of the core-mantle boundary (CMB) conditions on the geodynamo (also a well-known fact). By contrast, equatorial symmetry breaking (in particular the persistence of an axial mean quadrupole) may not trivially be considered as evidence of some influence of CMB conditions. To establish this, one would need to better investigate whether or not this axial quadrupole has
The symmetries of the Carroll superparticle
NASA Astrophysics Data System (ADS)
Bergshoeff, Eric; Gomis, Joaquim; Parra, Lorena
2016-05-01
Motivated by recent applications of Carroll symmetries we investigate, using the method of nonlinear realizations, the geometry of flat and curved (AdS) Carroll space and the symmetries of a particle moving in such a space both in the bosonic as well as in the supersymmetric case. In the bosonic case we find that the Carroll particle possesses an infinite-dimensional symmetry which only in the flat case includes dilatations. The duality between the Bargmann and Carroll algebra, relevant for the flat case, does not extend to the curved case. In the supersymmetric case we study the dynamics of the { N }=1 AdS Carroll superparticle. Only in the flat limit we find that the action is invariant under an infinite-dimensional symmetry that includes a supersymmetric extension of the Lifshitz Carroll algebra with dynamical exponent z = 0. We also discuss in the flat case the extension to { N }=2 supersymmetry and show that the flat { N }=2 superparticle is equivalent to the (non-moving) { N }=1 superparticle and that therefore it is not BPS unlike its Galilei counterpart. This is due to the fact that in this case kappa-symmetry eliminates the linearized supersymmetry. In an appendix we discuss the { N }=2 curved case in three-dimensions only and show that there are two { N }=2 theories that are physically different.
Weyl-gauge symmetry of graphene
Iorio, Alfredo
2011-05-15
Research Highlights: > Graphene action's Weyl symmetry identifies shapes for which the DOS is invariant. > Electrons on graphene might experience a general-relativistic-like spacetime. > Rich mathematical structures, such as the Liouville's equation, naturally arise. - Abstract: The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.
Reflections on the concept of symmetry
NASA Astrophysics Data System (ADS)
Lorenz, Kuno
2005-10-01
The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, "being symmetric" in general usage is synonymous with "being harmonious", and in technical usage, as in Euclid's Elements, it is synonymous with "commensurable". Due to the second meaning, which is close to the etymology of συ´μμɛτρoς, "with measure" has likewise to be read as "being [in] rational [ratios]" and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.
Symmetry in social exchange and health
NASA Astrophysics Data System (ADS)
Siegrist, Johannes
2005-10-01
Symmetry is a relevant concept in sociological theories of exchange. It is rooted in the evolutionary old norm of social reciprocity and is particularly important in social contracts. Symmetry breaking through violation of the norm of reciprocity generates strain in micro-social systems and, above all, in victims of non-symmetric exchange. In this contribution, adverse healthconsequences of symmetry breaking in contractual social exchange are analysed, with a main focus on the employment contract. Scientific evidence is derived from prospective epidemiological studies testing the model of effort-reward imbalance at work. Overall, a twofold elevated risk of incident disease is observed in employed men and women who are exposed to non-symmetric exchange. Health risks include coronary heart disease, depression and alcohol dependence, among others. Preliminary results suggest similar effects on health produced by symmetry breaking in other types of social relationships (e.g. partnership, parental roles). These findings underline the importance of symmetry in contractual social exchange for health and well-being.
Symmetry-protected topological phases in noninteracting fermion systems
NASA Astrophysics Data System (ADS)
Wen, Xiao-Gang
2012-02-01
Symmetry-protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For noninteracting fermion systems with time reversal (T̂), charge conjugation (Ĉ), and/or U(1) (N̂) symmetries, the total symmetry group can depend on the relations between those symmetry operations, such as T̂N̂T̂-1=N̂ or T̂N̂T̂-1=-N̂. As a result, the SPT phases of those fermion systems with different symmetry groups have different classifications. In this paper, we use Kitaev's K-theory approach to classify the gapped free-fermion phases for those possible symmetry groups. In particular, we can view the U(1) as a spin rotation. We find that superconductors with the Sz spin-rotation symmetry are classified by Z in even dimensions, while superconductors with the time reversal plus the Sz spin-rotation symmetries are classified by Z in odd dimensions. We show that all 10 classes of gapped free-fermion phases can be realized by electron systems with certain symmetries. We also point out that, to properly describe the symmetry of a fermionic system, we need to specify its full symmetry group that includes the fermion number parity transformation (-)N̂. The full symmetry group is actually a projective symmetry group.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ℤn symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/ℤ2N and T6/ℤ2 × ℤ2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ℤ2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ℤ3 charge.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Facial symmetry assessment based on geometric features
NASA Astrophysics Data System (ADS)
Xu, Guoping; Cao, Hanqiang
2015-12-01
Face image symmetry is an important factor affecting the accuracy of automatic face recognition. Selecting high symmetrical face image could improve the performance of the recognition. In this paper, we proposed a novel facial symmetry evaluation scheme based on geometric features, including centroid, singular value, in-plane rotation angle of face and the structural similarity index (SSIM). First, we calculate the value of the four features according to the corresponding formula. Then, we use fuzzy logic algorithm to integrate the value of the four features into a single number which represents the facial symmetry. The proposed method is efficient and can adapt to different recognition methods. Experimental results demonstrate its effectiveness in improving the robustness of face detection and recognition.
Approximate gauge symmetry of composite vector bosons
NASA Astrophysics Data System (ADS)
Suzuki, Mahiko
2010-08-01
It can be shown in a solvable field theory model that the couplings of the composite vector bosons made of a fermion pair approach the gauge couplings in the limit of strong binding. Although this phenomenon may appear accidental and special to the vector bosons made of a fermion pair, we extend it to the case of bosons being constituents and find that the same phenomenon occurs in a more intriguing way. The functional formalism not only facilitates computation but also provides us with a better insight into the generating mechanism of approximate gauge symmetry, in particular, how the strong binding and global current conservation conspire to generate such an approximate symmetry. Remarks are made on its possible relevance or irrelevance to electroweak and higher symmetries.
Breaking the Symmetry in Molecular Nanorings
2016-01-01
Because of their unique electronic properties, cyclic molecular structures ranging from benzene to natural light-harvesting complexes have received much attention. Rigid π-conjugated templated porphyrin nanorings serve as excellent model systems here because they possess well-defined structures that can readily be controlled and because they support highly delocalized excitations. In this study, we have deliberately modified a series of six-porphyrin nanorings to examine the impact of lowering the rotational symmetry on their photophysical properties. We reveal that as symmetry distortions increase in severity along the series of structures, spectral changes and an enhancement of radiative emission strength occur, which derive from a transfer of oscillator strength into the lowest (k = 0) state. We find that concomitantly, the degeneracy of the dipole-allowed first excited (k = ±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906
How center vortices break chiral symmetry
NASA Astrophysics Data System (ADS)
Faber, Manfried; Höllwieser, Roman
2016-01-01
We investigate the chiral properties of near-zero modes for thick classical center vortices in SU(2) lattice gauge theory as examples of the phenomena which may arise in a vortex vacuum. In particular we analyze the creation of near-zero modes from would-be zero modes of various topological charge contributions from center vortices. We show that classical colorful spherical vortex and instanton ensembles have almost identical Dirac spectra and the low-lying eigenmodes from spherical vortices show all characteristic properties for chiral symmetry breaking. We further show that also vortex intersections are able to give rise to a finite density of near-zero modes, leading to chiral symmetry breaking via the Banks-Casher formula. We discuss the mechanism by which center vortex fluxes contribute to chiral symmetry breaking.
NASA Astrophysics Data System (ADS)
Agashe, Kaustubh; Contino, Roberto; Da Rold, Leandro; Pomarol, Alex
2006-09-01
We show that a subgroup of the custodial symmetry O (3) that protects Δρ from radiative corrections can also protect the Zbbbar coupling. This allows one to build models of electroweak symmetry breaking, such as higgsless, little Higgs or 5D composite Higgs models, that are safe from corrections to Z → bbbar. We show that when this symmetry protects Zbbbar it cannot simultaneously protect Zttbar and Wtbbar. Therefore one can expect to measure sizable deviations from the SM predictions of these couplings at future collider experiments. We also show under what circumstances ZbRbbarR can receive corrections in the right direction to explain the anomaly in the LEP/SLD forward-backward asymmetry AFBb.
Spontaneous Symmetry Breaking in Interdependent Networked Game
NASA Astrophysics Data System (ADS)
Jin, Qing; Wang, Lin; Xia, Cheng-Yi; Wang, Zhen
2014-02-01
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value αC, the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds αC, spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method.
Symmetry-related decompositions of uncertainty
NASA Astrophysics Data System (ADS)
Viana, Marlos
2012-10-01
In statistics, the sample mean and variance are intimately related to the symmetries of the full symmetric group describing all possible permutations of assignments of observations to sampling units. While those symmetries yield exactly two invariant subspaces (in a sense to be defined in the text) in correspondence to those summary statistics, the invariant subspaces associated with specific subgroups of the full symmetric group may then lead to much detailed decompositions of the experimental uncertainty. In the present chapter we discuss the symmetry-related summaries of data arising from dihedral experiments, specifically in the context of multinomial models for frequency counts in symbolic sequences. Special examples are given to dihedral summaries that can be potentially interpreted as measures of (molecular) chirality or handedness.
Mutual information and spontaneous symmetry breaking
NASA Astrophysics Data System (ADS)
Hamma, A.; Giampaolo, S. M.; Illuminati, F.
2016-01-01
We show that the metastable, symmetry-breaking ground states of quantum many-body Hamiltonians have vanishing quantum mutual information between macroscopically separated regions and are thus the most classical ones among all possible quantum ground states. This statement is obvious only when the symmetry-breaking ground states are simple product states, e.g., at the factorization point. On the other hand, symmetry-breaking states are in general entangled along the entire ordered phase, and to show that they actually feature the least macroscopic correlations compared to their symmetric superpositions is highly nontrivial. We prove this result in general, by considering the quantum mutual information based on the two-Rényi entanglement entropy and using a locality result stemming from quasiadiabatic continuation. Moreover, in the paradigmatic case of the exactly solvable one-dimensional quantum X Y model, we further verify the general result by considering also the quantum mutual information based on the von Neumann entanglement entropy.
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which - apart from their rather specific expressions in terms of w(z) - are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
Topological phases with generalized global symmetries
NASA Astrophysics Data System (ADS)
Yoshida, Beni
2016-04-01
We present simple lattice realizations of symmetry-protected topological phases with q -form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d +1 ) -colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Nontriviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models, and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Anomalous Abelian symmetry in the standard model
Ramond, P.
1995-12-31
The observed hierarchy of quark and lepton masses can be parametrized by nonrenormalizable operators with dimensions determined by an anomalous Abelian family symmetry, a gauge extension to the minimal supersymmetric standard model. Such an Abelian symmetry is generic to compactified superstring theories, with its anomalies compensated by the Green-Schwarz mechanism. If we assume these two symmetries to be the same, we find the electroweak mixing angle to be sin {sup 2}{theta}{sub {omega}} = 3/8 at the string scale, just by setting the ratio of the product of down quark to charged lepton masses equal to one at the string scale. This assumes no GUT structure. The generality of the result suggests a superstring origin for the standard model. We generalize our analysis to massive neutrinos, and mixings in the lepton sector.
Workshop on electroweak symmetry breaking: proceedings
Hinchliffe, I.
1984-10-01
A theoretical workshop on electroweak symmetry breaking at the Superconducting Supercollider was held at Lawrence Berkeley Laboratory, June 4-22, 1984. The purpose of the workshop was to focus theoretical attention on the ways in which experimentation at the SSC could reveal manifestations of the phenomenon responsible for electroweak symmetry breaking. This issue represents, at present, the most compelling scientific argument for the need to explore the energy region to be made accessible by the SSC, and a major aim of the workshop was to involve a broad cross section of particle theorists in the ongoing process of sharpening the requirements for both accelerator and detector design that will ensure detection and identification of meaningful signals, whatever form the electroweak symmetry breaking phenomenon should actually take. Separate entries were prepared for the data base for the papers presented.
A torus bifurcation theorem with symmetry
NASA Technical Reports Server (NTRS)
Vangils, S. A.; Golubitsky, M.
1989-01-01
Hopf bifurcation in the presence of symmetry, in situations where the normal form equations decouple into phase/amplitude equations is described. A theorem showing that in general such degeneracies are expected to lead to secondary torus bifurcations is proved. By applying this theorem to the case of degenerate Hopf bifurcation with triangular symmetry it is proved that in codimension two there exist regions of parameter space where two branches of asymptotically stable two-tori coexist but where no stable periodic solutions are present. Although a theory was not derived for degenerate Hopf bifurcations in the presence of symmetry, examples are presented that would have to be accounted for by any such general theory.
Conservation Laws, Symmetries, and Elementary Particles
NASA Astrophysics Data System (ADS)
Hoekzema, Dick; Schooten, Gert; van den Berg, Ed; Lijnse, Piet
2005-05-01
The following student text on conservation laws, symmetries, and elementary particles was developed in a Dutch project for teaching modern physics to the top stream of the sixth year of secondary education (age 17-18). In a series of 35 lessons of 45-50 minutes each, students study particle-wave duality, the Heisenberg principle, probability models for properties of particles, the particle in a box, and applications, elementary particles, and astrophysics (http://www.phys.uu.nl/˜wwwpmn). In this paper we focus on particle physics and the key concepts of this chapter are: transformation, reaction equation, conservation laws, and symmetry. For recent literature regarding the teaching of symmetries and/or elementary particles, we refer to articles by Hill & Lederman, Pascolini & Pietroni,2 Kalmus,3 O'Connell,4 and Hanley.5
Mixed-Symmetry States in ^93Nb
NASA Astrophysics Data System (ADS)
McKay, C. J.; Bandyopadhyay, D.; Lesher, S. R.; Mynk, M.; Orce, J.; McEllistrem, M. T.; Yates, S. W.
2003-10-01
The neutron-proton version of the interacting boson model predicts the existence of mixed-symmetry collective excitations. In an even-even nucleus the 2^+_ms state has the distinctive signature of a strong M1 transition to the first 2^+ state and a weak E2 transiton to the ground state. Previous investigations of the N=52 isotones ^92Zr, ^94Mo and ^96Ru have have led to the identification of mixed-symmetry states. It is expected that odd-A nuclei will also display states with mixed-symmetry character. Therefore, excitation function and angular distibution measurements have been performed on ^93Nb, the lone stable odd-A N=52 isotone, using the (n,n^'γ) reaction at the University of Kentucky. Lifetimes were determined with the Doppler-shift attenuation method. This work was supported by the U.S. National Science Foundation under grant No. PHY-0098813
Symmetry transforms for ideal magnetohydrodynamics equilibria.
Bogoyavlenskij, Oleg I
2002-11-01
A method for constructing ideal magnetohydrodynamics (MHD) equilibria is introduced. The method consists of the application of symmetry transforms to any known MHD equilibrium [ O. I. Bogoyavlenskij, Phys. Rev. E. 62, 8616, (2000)]. The transforms break the geometrical symmetries of the field-aligned solutions and produce continuous families of the nonsymmetric MHD equilibria. The method of symmetry transforms also allows to obtain MHD equilibria with current sheets and exact solutions with noncollinear vector fields B and V. A model of the nonsymmetric astrophysical jets outside of their accretion disks is developed. The total magnetic and kinetic energy of the jet is finite in any layer c(1)
Nature's statistical symmetries, a characterization by wavelets.
Davis, A. B.
2001-01-01
Wavelets are the mathematical equivalent of a microscope, a means of looking at more or less detail in data. By applying wavelet transforms to remote sensing data (satellite images, atmospheric profiles, etc.), we can discover symmetries in Nature's ways of changing in lime and displaying a highly variable environment at any given time. These symmetries are not exact but statistical. The most intriguing one is 'scale-invariance' which describes how spatial statistics collected over a wide range of scales (using wave1m)follow simple power laws with respect to the scale parameter. The geometrical counterparts of statistical scale-invariance are the random fractals so often observed in Nature. This wavelet-based exploration of natural symmetry will be illustrated with clouds,
Electric-magnetic symmetry and Noether's theorem
NASA Astrophysics Data System (ADS)
Cameron, Robert P.; Barnett, Stephen M.
2012-12-01
In the absence of charges, Maxwell's equations are highly symmetrical. In particular, they place the electric and magnetic fields on equal footing. In light of this electric-magnetic symmetry, we introduce a variational description of the free electromagnetic field that is based upon the acknowledgement of both electric and magnetic potentials. We use our description, together with Noether's theorem, to demonstrate that electric-magnetic symmetry is, in essence, an expression of the conservation of optical helicity. The symmetry associated with the conservation of Lipkin's zilches is also identified. We conclude by considering, with care, the subtle separation of the rotation and boost angular momenta of the field into their ‘spin’ and ‘orbital’ contributions.
New Algorithms For Automated Symmetry Recognition
NASA Astrophysics Data System (ADS)
Paul, Jody; Kilgore, Tammy Elaine; Klinger, Allen
1988-02-01
In this paper we present new methods for computer-based symmetry identification that combine elements of group theory and pattern recognition. Detection of symmetry has diverse applications including: the reduction of image data to a manageable subset with minimal information loss, the interpretation of sensor data,1 such as the x-ray diffraction patterns which sparked the recent discovery of a new "quasicrystal" phase of solid matter,2 and music analysis and composition.3,4,5 Our algorithms are expressed as parallel operations on the data using the matrix representation and manipulation features of the APL programming language. We demonstrate the operation of programs that characterize symmetric and nearly-symmetric patterns by determining the degree of invariance with respect to candidate symmetry transformations. The results are completely general; they may be applied to pattern data of arbitrary dimension and from any source.
Breaking the Symmetry in Molecular Nanorings.
Gong, Juliane Q; Favereau, Ludovic; Anderson, Harry L; Herz, Laura M
2016-01-21
Because of their unique electronic properties, cyclic molecular structures ranging from benzene to natural light-harvesting complexes have received much attention. Rigid π-conjugated templated porphyrin nanorings serve as excellent model systems here because they possess well-defined structures that can readily be controlled and because they support highly delocalized excitations. In this study, we have deliberately modified a series of six-porphyrin nanorings to examine the impact of lowering the rotational symmetry on their photophysical properties. We reveal that as symmetry distortions increase in severity along the series of structures, spectral changes and an enhancement of radiative emission strength occur, which derive from a transfer of oscillator strength into the lowest (k = 0) state. We find that concomitantly, the degeneracy of the dipole-allowed first excited (k = ±1) state is lifted, leading to an ultrafast polarization switching effect in the emission from strongly symmetry-broken nanorings. PMID:26735906
Preserving Symmetry in Preconditioned Krylov Subspace Methods
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Chow, E.; Saad, Y.; Yeung, M. C.
1996-01-01
We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M. In the symmetric case, one can recover symmetry by using M-inner products in the conjugate gradient (CG) algorithm. This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the new algorithms are mathematically equivalent to split preconditioning, but do not require M to be factored. Better robustness in a specific sense can also be observed. When combined with truncated versions of iterative methods, tests show that this is more effective than the common practice of forfeiting near-symmetry altogether.
Symmetry and Resonance in Periodic FPU Chains
NASA Astrophysics Data System (ADS)
Rink, Bob
The symmetry and resonance properties of the Fermi Pasta Ulam chain with periodic boundary conditions are exploited to construct a near-identity transformation bringing this Hamiltonian system into a particularly simple form. This ``Birkhoff-Gustavson normal form'' retains the symmetries of the original system and we show that in most cases this allows us to view the periodic FPU Hamiltonian as a perturbation of a nondegenerate Liouville integrable Hamiltonian. According to the KAM theorem this proves the existence of many invariant tori on which motion is quasiperiodic. Experiments confirm this qualitative behaviour. We note that one can not expect this in lower-order resonant Hamiltonian systems. So the periodic FPU chain is an exception and its special features are caused by a combination of special resonances and symmetries.
NASA Astrophysics Data System (ADS)
Gasparini, Maria Alice
2005-11-01
Experimental projects using spherical antennas to detect gravitational waves are nowadays a concrete reality. The main purpose of this paper is to give a possible way of interpreting output data from such a system. Responses of the five fundamental quadrupole modes and of the six resonators in truncated icosahedral gravitational wave antenna (TIGA) collocations are shown as a function of the incoming direction of the incident wave. Then, for a source lying in the galactic plane, sidereal time and galactic longitude dependence is given. Thus, once a candidate source of gravitational waves is considered, we can exactly predict the resonators’ response as a function of time.
Quregisters, Symmetry Groups and Clifford Algebras
NASA Astrophysics Data System (ADS)
Cervantes, D.; Morales-Luna, G.
2016-03-01
Natural one-to-one and two-to-one homomorphisms from SO(3) into SU(2) are built conventionally, and the collection of qubits, is identified with a subgroup of SU(2). This construction is suitable to be extended to corresponding tensor powers. The notions of qubits, quregisters and qugates are translated into the language of symmetry groups. The corresponding elements to entangled states in the tensor product of Hilbert spaces reflect entanglement properties as well, and in this way a notion of entanglement is realised in the tensor product of symmetry groups.
Parity-time symmetry under magnetic flux
NASA Astrophysics Data System (ADS)
Jin, L.; Song, Z.
2016-06-01
We study a parity-time-(PT -) symmetric ring lattice, with one pair of balanced gain and loss located at opposite positions. The system remains PT -symmetric when threaded by a magnetic flux; however, the PT symmetry is sensitive to the magnetic flux in the presence of a large balanced gain and loss, or in a large system. We find a threshold gain or loss above which any nontrivial magnetic flux breaks the PT symmetry. We obtain the maximally tolerable magnetic flux for the exact PT -symmetric phase, which is approximately linearly dependent on a weak gain or loss.
Symmetry-constrained electron vortex propagation
NASA Astrophysics Data System (ADS)
Clark, L.; Guzzinati, G.; Béché, A.; Lubk, A.; Verbeeck, J.
2016-06-01
Electron vortex beams hold great promise for development in transmission electron microscopy but have yet to be widely adopted. This is partly due to the complex set of interactions that occur between a beam carrying orbital angular momentum (OAM) and a sample. Herein, the system is simplified to focus on the interaction between geometrical symmetries, OAM, and topology. We present multiple simulations alongside experimental data to study the behavior of a variety of electron vortex beams after interacting with apertures of different symmetries and investigate the effect on their OAM and vortex structure, both in the far field and under free-space propagation.
Dual technicolor with hidden local symmetry
Belitsky, A. V.
2010-08-15
We consider a dual description of the technicolor-like gauge theory within the D4/D8-brane configuration with varying confinement and electroweak symmetry breaking scales. Constructing an effective truncated model valid below a certain cutoff, we identify the particle spectrum with Kaluza-Klein modes of the model in a manner consistent with the hidden local symmetry. Integrating out heavy states, we find that the low-energy action receives nontrivial corrections stemming from the mixing between standard model and heavy gauge bosons, which results in reduction of oblique parameters.
Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Hořava, Petr; Yan, Ziqi
2015-12-01
Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion ω ˜kn (n =2 ,3 ,… ), whose naturalness is protected by polynomial shift symmetries. Here, we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of n changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem.
Weak Lie symmetry and extended Lie algebra
Goenner, Hubert
2013-04-15
The concept of weak Lie motion (weak Lie symmetry) is introduced. Applications given exhibit a reduction of the usual symmetry, e.g., in the case of the rotation group. In this context, a particular generalization of Lie algebras is found ('extended Lie algebras') which turns out to be an involutive distribution or a simple example for a tangent Lie algebroid. Riemannian and Lorentz metrics can be introduced on such an algebroid through an extended Cartan-Killing form. Transformation groups from non-relativistic mechanics and quantum mechanics lead to such tangent Lie algebroids and to Lorentz geometries constructed on them (1-dimensional gravitational fields).
Dynamical systems and σ-symmetries
NASA Astrophysics Data System (ADS)
Cicogna, G.; Gaeta, G.; Walcher, S.
2013-06-01
A deformation of the standard prolongation operation, defined on sets of vector fields in involution rather than on single ones, was recently introduced and christened ‘σ-prolongation’ correspondingly, one has ‘σ-symmetries’ of differential equations. These can be used to reduce the equations under study, but the general reduction procedure under σ-symmetries fails for equations of order 1. In this paper, we discuss how σ-symmetries can be used to reduce dynamical systems, i.e. sets of first-order ODEs in the form \\dot{x}^a = f^a (x).
Non-standard symmetries and quantum anomalies
Visinescu, Anca; Visinescu, Mihai
2008-08-31
Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.
Symmetry breaking in individual plasmonic nanoparticles
Wang, Hui; Wu, Yanpeng; Lassiter, Britt; Nehl, Colleen L.; Hafner, Jason H.; Nordlander, Peter; Halas, Naomi J.
2006-01-01
The plasmon resonances of a concentric metallic nanoshell arise from the hybridization of primitive plasmon modes of the same angular momentum on its inner and outer surfaces. For a nanoshell with an offset core, the reduction in symmetry relaxes these selection rules, allowing for an admixture of dipolar components in all plasmon modes of the particle. This metallodielectric nanostructure with reduced symmetry exhibits a core offset-dependent multipeaked spectrum, seen in single-particle spectroscopic measurements, and exhibits significantly larger local-field enhancements on its external surface than the equivalent concentric spherical nanostructure. PMID:16829573