Pauling, Linus
1989-01-01
A doubly icosahedral complex involves roughly spherical clusters of atoms with icosahedral point-group symmetry, which are themselves, in parallel orientation, icosahedrally packed. These complexes may form cubic crystallites; three structures of this sort have been identified. Analysis of electron diffraction photographs of the decagonal quasicrystal Al6Pd has led to its description as involving pentagonal twinning of an orthorhombic crystal with a = 51.6 Å, b = 37.6 Å, and c = 33.24 Å, with about 4202 atoms in the unit, comprising two 1980-atom doubly icosahedral complexes, each involving icosahedral packing of 45 44-atom icosahedral complexes (at 0 0 0 and 1/2 1/2 1/2) and 242 interstitial atoms. The complexes and clusters are oriented with one of their fivefold axes in the c-axis direction. Images PMID:16594092
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.
Liquid Crystal Phases Lacking Point Group Symmetry
NASA Astrophysics Data System (ADS)
Chattham, Nattaporn; Shao, Renfan; Maclennan, Joseph E.; Clark, Noel A.; Korblova, Eva; Walba, David M.
2001-03-01
In his 1974 monographs deGennes describes the smectic CG (SmC_G, G for general), a phase of two-dimensional fluid layers having rod-shaped molecules tilted with respect to the layer normal and ordered such that the principal axes of the optical dielectric tensor generally lie neither along the layer normal nor in the plane of the layer. Such layers are polar, with macroscopic polarization P oriented arbitrarily in the diagonal frame, and thus are not symmetric under any rotation or reflection or nontrivial combination thereof, i.e., belong to the class C1 in the Schoenfliess notation. Furthermore, since they lack mirror symmetry, they are chiral. Although deGennes was not optimistic about the prospect for finding such a phase, it appears once again, if a liquid crystal phase can be described, it can be found. Here we report the observation of C1 layers in a fluid smectic phase of bent core molecules. It is evident from freely suspended films that this molecular layer structure exhibits two spontaneous symmetry-breaking instabilities: polar molecular orientational ordering about the layer normal and molecular tilt. These combine to form a chiral layer structure with a handedness depending on the sign of tilt. This work is supported by NASA Grant NAG3-2457.
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.
From Molecular Point Group Symmetry to Space Group Symmetry.
ERIC Educational Resources Information Center
Hathaway, Brian
1979-01-01
Describes undergraduate chemistry curricula in which the student is asked to either build a model of one asymmetric unit in the unit cell and to indicate the positions of the symmetry-related units by putting in key atoms, or to identify on a prebuild model the asymetric and symmetry-related units. (BB)
Multi-Weyl topological semimetals stabilized by point group symmetry.
Fang, Chen; Gilbert, Matthew J; Dai, Xi; Bernevig, B Andrei
2012-06-29
We perform a complete classification of two-band k·p theories at band crossing points in 3D semimetals with n-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of new 3D topological semimetals characterized by C(4,6)-protected double-Weyl nodes with quadratic in-plane (along k(x,y)) dispersion or C(6)-protected triple-Weyl nodes with cubic in-plane dispersion. We apply this theory to the 3D ferromagnet HgCr(2)Se(4) and confirm it is a double-Weyl metal protected by C(4) symmetry. Furthermore, if the direction of the ferromagnetism is shifted away from the [001] axis to the [111] axis, the double-Weyl node splits into four single Weyl nodes, as dictated by the point group S(6) of that phase. Finally, we discuss experimentally relevant effects including the splitting of multi-Weyl nodes by applying a C(n) breaking strain and the surface Fermi arcs in these new semimetals. PMID:23005002
Symmetry, stability, and diffraction properties of icosahedral crystals
Bak, P.
1985-01-01
In a remarkable experiment on an Mn-Al alloy, Shechtman et al. observed a diffraction spectrum with icosahedral symmetry. This is inconsistent with discrete translational invariance since the symmetry includes a five-fold axis. In this paper, it is shown that the crystallography and diffraction pattern can be described by a six-dimensional space group. The crystal structure in 3d is obtained as a cut along a 3d hyperplane in a regular 6d crystal. Displacements of the 6d crystal along 6 orthogonal directions define 6 continuous symmetries for the icosahedral crystal, three of which are phase symmetries describing internal rearrangements of the atoms.
Symmetry, Point Groups, and Character Tables, Part 3, Character Tables and Their Significance
ERIC Educational Resources Information Center
Orchin, Milton; Jaffe, H. H.
1970-01-01
Presents the third of a series of articles on symmetry. Describes the symmetry properties of molecules in translatiional and rotational motion. Presents these dynamic symmetry properties in character tables for five point groups. Supplements the article with more rigorous material involving spectroscopic states, degenerate point groups and…
Symmetry, Point Groups, and Character Tables, Part 3, Character Tables and Their Significance
ERIC Educational Resources Information Center
Orchin, Milton; Jaffe, H. H.
1970-01-01
Presents the third of a series of articles on symmetry. Describes the symmetry properties of molecules in translatiional and rotational motion. Presents these dynamic symmetry properties in character tables for five point groups. Supplements the article with more rigorous material involving spectroscopic states, degenerate point groups and
Crystallography of decahedral and icosahedral particles. II - High symmetry orientations
NASA Technical Reports Server (NTRS)
Yang, C. Y.; Yacaman, M. J.; Heinemann, K.
1979-01-01
Based on the exact crystal structure of decahedral and icosahedral particles, high energy electron diffraction patterns and image profiles have been derived for various high symmetry orientations of the particles with respect to the incident beam. These results form a basis for the identification of small metal particle structures with advanced methods of transmission electron microscopy.
Symmetry based fast marching method for icosahedral virus segmentation
NASA Astrophysics Data System (ADS)
Shan, Guihua; Liu, Jun; Ye, Liang; Chi, Xuebin
2010-02-01
Segmentation of icosahedral virus density map from cryo-electron microscope (CryoEM) is a challenging task because virus structure is complex and density map is at low resolution. Fast marching method is widely used in segmentation, in which seed selection is essential for correct segmentation results. However, the selection of an appropriate seed is difficult. In this paper, we present the method of selecting the seed in fast marching algorithm by making use of the shape symmetry to improve the fast marching method for icosahedral virus segmentation. Based on the feature of icosahedron, we compute and get its symmetry axes inside the density map. With these symmetry axes, we specify the initial seeds with the local maxima value along symmetry axes. Further, the new data structures are presented, which can effectively reduce the memory cost when implement the fast marching algorithm. Experimental results show that the approach can obtain segmentation results of the density maps fast and accurately.
Breaking of Icosahedral Symmetry: C60 to C70
Bodner, Mark; Patera, Jiri; Szajewska, Marzena
2014-01-01
We describe the existence and structure of large fullerenes in terms of symmetry breaking of the molecule. Specifically, we describe the existence of in terms of breaking of the icosahedral symmetry of by the insertion into its middle of an additional decagon. The surface of is formed by 12 regular pentagons and 25 regular hexagons. All 105 edges of are of the same length. It should be noted that the structure of the molecules is described in exact coordinates relative to the non-orthogonal icosahedral bases. This symmetry breaking process can be readily applied, and could account for and describe other larger cage cluster fullerene molecules, as well as more complex higher structures such as nanotubes. PMID:24599292
Virus templated plasmonic nanoclusters with icosahedral symmetry via directed assembly
NASA Astrophysics Data System (ADS)
Ratna, Banahalli; Fontana, Jake; Dressick, Walter; Phelps, Jamie; Johnson, John; Sampson, Travian; Rendell, Ronald; Soto, Carissa
2015-03-01
Controlling the spatial and orientational order of plasmonic nanoparticles may lead to structures with novel electromagnetic properties and applications such as sub-wavelength imaging and ultra-sensitive chemical sensors. Here we report the directed assembly of three-dimensional, icosahedral plasmonic nanoclusters with resonances at visible wavelengths. We show using transmission electron microcopy and in situ dynamic light scattering the nanoclusters consist of twelve gold nanospheres attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. We measured the bulk absorbance from aqueous suspensions of nanoclusters and reproduced the major features of the spectrum using finite-element simulations. Furthermore, because the viruses are easily produced in gram quantities the directed assembly approach is capable of high-throughput, providing a strategy to realize large quantities for applications. NRL summer intern under the HBCU/MI Summer Research Program.
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
ERIC Educational Resources Information Center
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-01-01
Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four…
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
ERIC Educational Resources Information Center
Casas, Llus; Estop, Euge`nia
2015-01-01
Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
ERIC Educational Resources Information Center
Casas, 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…
On the Number of Generator Sets of the Non-Cubic Symmetry Point Groups.
ERIC Educational Resources Information Center
Kouyoumdjian, E. R.
1983-01-01
The generator set of a group is the subset of the set of elements of the group. The nature and use of generator sets is discussed, focusing on generator sets for the noncubic symmetry point groups containing one, two, and three symmetry elements. (JN)
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
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…
NASA Technical Reports Server (NTRS)
Shavitt, I.
1979-01-01
A procedure is described for the utilization of abelian point group symmetry in the graphical unitary group approach (GUGA) to calculations of correlated electronic wavefunctions. The procedure is based on a recursively computed set of symmetry dependent counting indices, and results in the separate numbering, without gaps, of the Gelfand states (configuration functions) belonging to each symmetry species
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.
Bodner, Mark; Bourret, Emmanuel; Patera, Jiri; Szajewska, Marzena
2015-05-01
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120. This subgroup is noted by A1 × A1, because it is isomorphic to the Weyl group of the semi-simple Lie algebra A1 × A1. Thirteen of the A1 × A1 orbits are rectangles and four are line segments. The orbits form a stack of parallel layers centered on the axis of C60 passing through the centers of two opposite edges between two hexagons on the surface of C60. These two edges are the only two line segment layers to appear on the surface shell. Among the 24 convex polytopes with shell formed by hexagons and 12 pentagons, having 84 vertices [Fowler & Manolopoulos (1992). Nature (London), 355, 428-430; Fowler & Manolopoulos (2007). An Atlas of Fullerenes. Dover Publications Inc.; Zhang et al. (1993). J. Chem. Phys. 98, 3095-3102], there are only two that can be identified with breaking of the H3 symmetry to A1 × A1. The remaining ones are just convex shells formed by regular hexagons and 12 pentagons without the involvement of the icosahedral symmetry. PMID:25921498
Kumar, Mohit
2013-01-01
Minor group human rhinoviruses bind low-density lipoprotein (LDL) receptors for endocytosis. Once they are inside endosomes, the acidic pH triggers their dissociation from the receptors and conversion into hydrophobic subviral A particles; these attach to the membrane and transfer their single-strand, positive-sense RNA genome into the cytosol. Here, we allowed human rhinovirus 2 (HRV2) A particles, produced in vitro by incubation at pH 5.4, to attach to liposomes; cryo-electron microscopy 3-dimensional single-particle image reconstruction revealed that they bind to the membrane around a 2-fold icosahedral symmetry axis. PMID:23946453
Symmetry properties of tetraammine platinum(II) with C2v and C4v point groups
Moghani, Ghorban Ali; Ashrafi, Ali Reza; Hamadanian, Masood
2005-01-01
Let G be a weighted graph with adjacency matrix A=[aij]. An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix D=[dij], where for i?j, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for different nuclei. Balasubramanian (1995) computed the Euclidean graphs and their automorphism groups for benzene, eclipsed and staggered forms of ethane and eclipsed and staggered forms of ferrocene. This paper describes a simple method, by means of which it is possible to calculate the automorphism group of weighted graphs. We apply this method to compute the symmetry of tetraammine platinum(II) with C2v and C4v point groups. PMID:15682509
Köppl, Christoph; Werner, Hans-Joachim
2015-04-28
Electron correlation methods based on symmetry-adapted canonical Hartree-Fock orbitals can be speeded up significantly in the well known group theoretical manner, using the fact that integrals vanish unless the integrand is totally symmetric. In contrast to this, local electron correlation methods cannot benefit from such simplifications, since the localized molecular orbitals (LMOs) generally do not transform according to irreducible representations of the underlying point group symmetry. Instead, groups of LMOs become symmetry-equivalent and this can be exploited to accelerate local calculations. We describe an implementation of such a symmetry treatment for density-fitted local Møller-Plesset perturbation theory, using various types of virtual orbitals: Projected atomic orbitals, orbital specific virtuals, and pair natural orbitals. The savings by the symmetry treatment are demonstrated by calculations for several large molecules having different point group symmetries. Benchmarks for the parallel execution efficiency of our method are also presented.
Phenomenological theory of icosahedral incommensurate (''quasiperiodic'') order in Mn-Al alloys
Bak, P.
1985-04-08
The crystal structure with icosahedral point-group symmetry and long-range orientational order observed by Shechtman et al. in Mn-Al alloys can be explained as a multiple-q density-wave structure with only one length scale. Its existence and stability can be understood from a simple Landau theory. The diffraction spots can be indexed by six- (or more-) dimensional space-group symmetries. Icosahedral incommensurate structures constitute natural extensions of smectic, rodlike, and cubic crystal structures.
NASA Astrophysics Data System (ADS)
Wiseman, Robin D.
1998-09-01
Previous results for the generation of linear, icosahedral, Jahn-Teller (JT) Hamiltonians with continuous group symmetries are extended. It is demonstrated that it is possible to define electronic generalized tensor operators on a direct sum electronic space such that a set of these operators is closed under commutation with another set of electronic generalized tensor operators which act as the generators of a continuous group. The normal modes carrying irreducible representations of the continuous group are then coupled `equally' to produce a JT Hamiltonian which is invariant under the operations of the continuous group. The continuous groups generated on the direct sum spaces 0305-4470/31/37/022/img1, 0305-4470/31/37/022/img2, 0305-4470/31/37/022/img3 and 0305-4470/31/37/022/img4 are discussed in detail. These additional continuous groups are of interest when the lowest JT states of certain icosahedral JT systems (such as some of those found in 0305-4470/31/37/022/img5) are modelled. The additional continuous group symmetry allows an analytic diagonalization of the linear JT matrix to be provided and thus facilitates an exact treatment of the vibronic ground state for these models.
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
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.
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
Mean Field Theories of Icosahedral Quasicrystals.
NASA Astrophysics Data System (ADS)
Troian, Sandra Marina
In 1984 Shechtman et al. discovered a metallic solid (Al(,86)Mn(,14)) with diffraction spots as sharp as those of crystals but with icosahedral point group symmetry, known to be incompatible with translational symmetry. One of the interesting crystallographic questions posed by the discovery of quasicrystals, as these materials are now called, is why does the atomic density assume an icosahedrally symmetric configuration in preference to conventional periodic crystalline forms. To address this question, we use a phenomenological approach based on the Landau theory of crystal formation (Landau, 1937) to ascertain whether any of the conventional elementary approaches to crystal formation might not contain metastable (or even stable) quasicrystalline solutions hitherto overlooked because of the almost universal prejudice that positional ordering must be periodic. Alexander and McTague (1978) touched on the possibility of icosahedrally symmetric structures using a (single order parameter) Landau free energy. We reexamine and extend their model and find that there are three distinct icosahedral stationary points to the free energy, although none of them is ever globally stable compared with more conventional competing structures like the body-centered cubic, hexagonal, or smectic. Which periodic form is favored depends on the temperature range investigated. We find that two of these stationary points are not even local minima of the free energy. We generalize this model by constructing a Landau theory for two or three-component systems, which appear to give a region of the phase diagram in which icosahedral quasicrystalline ordering is the state of lowest free energy. The quasicrystals are stabilized by special geometric ratios between the length scales characterizing the components. Three components are required to stabilize a two-dimensional quasicrystal but two components suffice to stabilize a three-dimensional one. We present results for two different ratios studied. We also rederive and generalize a model free energy presented by Kalugin et al. to show that their original conclusion of a metastable quasicrystal is invalidated by the inclusion of a local quartic term in the free energy. Lastly, we review three other mean field theories recently proposed to explain the existence of quasicrystals.
Icosahedral packing of RNA viral genomes.
Rudnick, Joseph; Bruinsma, Robijn
2005-01-28
Many spherelike RNA viruses package a portion of their genome in a manner that mirrors the icosahedral symmetry of the protein container, or capsid. Graph-theoretical constraints forbid exact realization of icosahedral symmetry. This paper explores the consequences of graph-theoretical constraints on quasi-icosahedral genome structures. A key result is the prediction that the genome organization is a Hamiltonian path or cycle and that the associated assembly scenario of such single-stranded spherelike RNA viruses resembles that of cylindrical RNA viruses, such as tobacco mosaic viruses. PMID:15698326
Point Group Determination of Calcium Tartrate by Etch Figure
NASA Astrophysics Data System (ADS)
Nakatani, Noriyuki
1991-11-01
Etch figures of gel-grown orthorhombic calcium tartrate tetrahydrate crystals have been examined in order to determine the point group symmetry. Making a thorough investigation of etch-figure characters on natural surfaces of rhombic dodecahedron crystals, we reached the firm conclusion that the point group is nonpolar 222.
Anisotropic packing and diffraction-peak shifts in icosahedral glasses
NASA Astrophysics Data System (ADS)
Goldman, Alan I.; Stephens, Peter W.
1988-02-01
We show that the anisotropic random packing of units with icosahedral symmetry produces diffraction patterns with distortions similar to recent electron and x-ray diffraction measurements. Using the Hendricks-Teller formalism discussed in an earlier paper, we show that the peak shifts predicted by the introduction of phason strain in an ideal quasilattice may also be described by this anisotropic, random-packing, icosahedral glass model.
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….
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).
Pauling, L
1990-01-01
An analysis of electron micrographs of Al5Mn quasicrystals obtained by rapidly cooling a molten alloy with composition Al17Mn and removing the Al matrix by electrosolution, revealing aggregates of 20 microcrystals at the corners of a pentagonal dodecahedron, supports the proposal that these microcrystals are cubic crystals twinned about an icosahedral seed, with each cubic microcrystal sharing a threefold axis and three symmetry planes with the seed. Images PMID:11607108
Icosahedral Structure of Aluminum-Lithium Aluminum-Copper and Aluminum-Copper Alloys
NASA Astrophysics Data System (ADS)
Guryan, Christopher Alan
1990-08-01
Icosahedral alloys are materials whose diffraction patterns display the symmetry of the icosahedron, which is incompatible with the translational symmetry of a crystal. This dissertation describes several diffraction experiments on icosahedral alloys. The incommensurability of icosahedrally symmetric structures leads to extra degrees of freedom in their description; we attempt to understand the unusual disorder of icosahedral phases linked to these extra degrees of freedom. In Chapter I we review the unique properties of icosahedral phases, and then present the results of diffraction experiments in the remaining five chapters. The first (Chapter II) is a crystallographic refinement of a crystalline phase, R Al_{5 cdot 6}Li_{2 cdot 9} Cu, related to icosahedral Al-Li-Cu. We find that this phase is a body centered cubic (BCC) packing of nearly -icosahedral clusters of atoms. Next we present in Chapter III the measurement of over 200 diffraction peaks from a single grain sample of icosahedral Al-Li-Cu. Both integrated intensity of diffraction peaks and their half width at half maximum (HWHM) are modeled as functions of both G _parallel (normal reciprocal space wavevector) and G_bot (the three extra degrees of freedom arising from the icosahedral structure). Chapter IV presents measurements of diffuse scattering in i-(AlLiCu). In Chapter V x-ray diffraction peaks of the icosahedral phase of Al-Cu-Ru are found to have no dependence of HWHM on G_bot , as had been the case of all other alloys previously studied. Finally Chapter VI describes diffraction measurements of icosahedral Al-Cu-Fe, from samples annealed at various temperatures. Annealing at 600^circ C introduces phason disorder into the alloy, while annealing at 700^circC removes it. This result is consistent with random tiling models of the icosahedral phase.
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…
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
Atomic clusters and atomic surfaces in icosahedral quasicrystals.
Quiquandon, Marianne; Portier, Richard; Gratias, Denis
2014-05-01
This paper presents the basic tools commonly used to describe the atomic structures of quasicrystals with a specific focus on the icosahedral phases. After a brief recall of the main properties of quasiperiodic objects, two simple physical rules are discussed that lead one to eventually obtain a surprisingly small number of atomic structures as ideal quasiperiodic models for real quasicrystals. This is due to the fact that the atomic surfaces (ASs) used to describe all known icosahedral phases are located on high-symmetry special points in six-dimensional space. The first rule is maximizing the density using simple polyhedral ASs that leads to two possible sets of ASs according to the value of the six-dimensional lattice parameter A between 0.63 and 0.79 nm. The second rule is maximizing the number of complete orbits of high symmetry to construct as large as possible atomic clusters similar to those observed in complex intermetallic structures and approximant phases. The practical use of these two rules together is demonstrated on two typical examples of icosahedral phases, i-AlMnSi and i-CdRE (RE = Gd, Ho, Tm). PMID:24815972
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.
NASA Astrophysics Data System (ADS)
Lošdorfer Božič, Anže; Podgornik, Rudolf
2013-02-01
Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by patchy charge distributions exhibiting certain point group symmetries. We derive a general form of the electrostatic interaction energy of two permeable, arbitrarily charged spherical shells in the Debye-Hückel approximation and apply it to the case of particles with icosahedral, octahedral, and tetrahedral inhomogeneous charge distributions. We analyze in detail how charge distribution symmetry modifies the interaction energy and find that local charge inhomogeneities reduce the repulsion of two overall equally charged particles, while sufficient orientational variation in the charge distribution can turn the minimum interaction energy into an attraction. Additionally, we show that larger patches and thus lower symmetries and wave numbers result in bigger attraction given the same variation.
Lošdorfer Božič, Anže; Podgornik, Rudolf
2013-02-21
Inhomogeneous charge distributions have important repercussions on electrostatic interactions in systems of charged particles but are often difficult to examine theoretically. We investigate how electrostatic interactions are influenced by patchy charge distributions exhibiting certain point group symmetries. We derive a general form of the electrostatic interaction energy of two permeable, arbitrarily charged spherical shells in the Debye-Hückel approximation and apply it to the case of particles with icosahedral, octahedral, and tetrahedral inhomogeneous charge distributions. We analyze in detail how charge distribution symmetry modifies the interaction energy and find that local charge inhomogeneities reduce the repulsion of two overall equally charged particles, while sufficient orientational variation in the charge distribution can turn the minimum interaction energy into an attraction. Additionally, we show that larger patches and thus lower symmetries and wave numbers result in bigger attraction given the same variation. PMID:23445030
Irreducible representations of some point groups which are isomorphic to some dihedral groups
NASA Astrophysics Data System (ADS)
Yahya, Zainab; Ali, Nor Muhainiah Mohd; Sarmin, Nor Haniza; Adnan, Noor Asma'Adny Mohd; Rahmat, Hamisan
2014-07-01
Let G be a finite group and M a vector space over K. A representation of G with representation space M is a homomorphism of G into GL(M), where GL(M) denotes the group of all invertible linear transformations of a vector space M onto itself. Furthermore, any representation of G is irreducible if the only subrepresentations of G are {0} and G. A point group is a group of symmetry operations all of which leave at least one point unmoved. There are some point groups which are isomorphic to dihedral groups. In this paper, the irreducible representations of some point groups which are isomorphic to some dihedral groups are given.
Two-Dimensional Crystals of Icosahedral Viruses at Liquid interfaces
NASA Astrophysics Data System (ADS)
Fukuto, Masafumi; Yang, Lin; Checco, Antonio; Kuzmenko, Ivan; Nguyen, Quyen; Mank, Nick; Wang, Qian
2012-02-01
Two-dimensional (2D) assembly of turnip yellow mosaic virus (TYMV) on cationic lipid monolayers is investigated at the air-water interface. TYMV, an icosahedral virus with a diameter of 28 nm, exhibits well-defined roughness, charge distribution, and hydrophilic/hydrophobic patches on its surface. The electrostatic attraction to the lipid-coated aqueous interface provides means to impose a specific virus orientation and hence reduce the number of possible inter-particle interactions. The 2D geometry is particularly advantageous in dissecting the role of anisotropy in aqueous-media assembly, which involves various types of similarly weak interactions. We show that the assembly approach used not only facilitates crystallization but also provides insights on how complex anisotropic interactions can be exploited to generate long-range order. Specifically, we report an in situ x-ray scattering observation of novel 2D crystal forms of TYMV that reflect the virus' icosahedral symmetry. The symmetry, shape, and surface heterogeneities of TYMV suggest a mechanism by which these crystals are stabilized by a combination of hydrophobic, electrostatic, and steric interactions.
Point Groups Based on Methane and Adamantane (Td) Skeletons.
ERIC Educational Resources Information Center
Fujita, Shinsaku
1986-01-01
Describes a procedure for constructing point groups based on the symmetric parent molecules of methane and adamantane. Intended for use in teaching concepts such as subgroups and cosets to beginners in group theory. (TW)
Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials
Mihalkovic, M. |; Zhu, W.; Henley, C.L.; Phillips, R.
1996-04-01
We have constructed and relaxed over 200 different finite structure models for the quasicrystal {ital i}-AlMn based on decorations of the {open_quote}{open_quote}canonical-cell tiling.{close_quote}{close_quote} We adopted {ital ab} {ital initio}-based pair potentials with strong Friedel oscillations, which reproduce the phase diagram of real Al-Mn intermetallic crystal structures fairly well. Our various decoration rules encompass cases with face-centered icosahedral (FCI) symmetry and with simple icosahedral (SI) symmetry, and include additional variations in the occupancy and/or chemistry of certain site types. Each decoration was applied to 11 distinct periodic approximants of the tiling. We found that (i) the relaxed atomic positions of each site type can be closely approximated by fixed positions on each tile type, even though the environments (beyond the first neighbor) are inequivalent. (ii) Models with simple icosahedral (SI) space-group symmetry were better than those with face-centered icosahedral (FCI) space-group symmetry. (iii) {open_quote}{open_quote}Loose{close_quote}{close_quote} decorations, containing voids almost large enough for an atom, were better than the {open_quote}{open_quote}dense{close_quote}{close_quote} decorations which were suggested by packing considerations. (iv) Our results depended on using the realistic potentials; {ital short}-range potentials favor the {open_quote}{open_quote}dense{close_quote}{close_quote} structures, and many details depend on the second or further oscillations in the potentials. (v) For our best model, there is relatively little variation of the energy when tiles are rearranged, i.e., a {ital random}-{ital tiling} {ital model} is a good zero-order description of the system. {copyright} {ital 1996 The American Physical Society.}
Surface structures of Al-Pd-Mn and Al-Cu-Fe icosahedral quasicrystals
Shen, Z.
1999-02-12
In this dissertation, the author reports on the surface structure of i-Al-Pd-Mn twofold, threefold, fivefold and i-Al-Cu-Fe fivefold surfaces. The LEED studies indicate the existence of two distinct stages in the regrowth of all four surfaces after Ar{sup +} sputtering. In the first stage, upon annealing at relatively low temperature: 500K--800K (depending on different surfaces), a cubic phase appears. The cubic LEED patterns transform irreversibly to unreconstructed quasicrystalline patterns upon annealing to higher temperatures, indicating that the cubic overlayers are metastable. Based upon the data for three chemically-identical, but symmetrically-inequivalent surfaces, a model is developed for the relation between the cubic overlayers and the quasicrystalline substrate. The model is based upon the related symmetries of cubic close-packed and icosahedral-packed materials. These results may be general among Al-rich, icosahedral materials. STM study of Al-Pd-Mn fivefold surface shows that terrace-step-kink structures start to form on the surface after annealing above 700K. Large, atomic ally-flat terraces were formed after annealing at 900K. Fine structures with fivefold icosahedral symmetry were found on those terraces. Data analysis and comparison of the STM images and structure model of icosahedral Al-Pd-Mn suggest that the fine structures in the STM images may be the pseudo Mackay (PMI) clusters which are the structure units of the structure model. Based upon his results, he can conclude that quasicrystalline structures are the stable structures of quasicrystal surfaces. In other words, quasicrystalline structures extend from the bulk to the surface. As a result of the effort reported in this dissertation, he believes that he has increased his understanding of the surface structure of icosahedral quasicrystals to a new level.
Beta cell device using icosahedral boride compounds
Aselage, Terrence L. (62 Avenida Del Sol, Cedar Crest, NM 87008); Emin, David (1502 Harvard Ct., NE., Albuquerque, NM 87106-3712)
2002-01-01
A beta cell for converting beta-particle energies into electrical energy having a semiconductor junction that incorporates an icosahedral boride compound selected from B.sub.12 As.sub.2, B.sub.12 P.sub.2, elemental boron having an .alpha.-rhombohedral structure, elemental boron having a .beta.-rhombohedral structure, and boron carbides of the chemical formula B.sub.12-x C.sub.3-x, where 0.15
Sharp diffraction maxima from an icosahedral glass
NASA Astrophysics Data System (ADS)
Stephens, P. W.; Goldman, A. I.
1986-03-01
Densely packed assemblies of icosahedra, such that icosahedral bond-orientational order is enforced throughout the sample, are considered. The peaks in the calculated diffraction patterns may be put in a one-to-one correspondence with the electron and X-ray diffraction patterns from icosahedral Al-Mn alloys, allowing the determination of the packing-unit size. It is shown that these maxima are not Bragg diffraction peaks, but have an intrinsic width, and may be understood as resulting from the interference between two or more characteristic lengths, as originally discussed by Hendricks and Teller (1942).
Experimental Evidence of Icosahedral and Decahedral Packing in One-Dimensional Nanostructures
Velázquez-Salazar, J. Jesús; Esparza, Rodrigo; Mejía-Rosales, Sergio Javier; Estrada-Salas, Rubén; Ponce, Arturo; Deepak, Francis Leonard; Castro-Guerrero, Carlos; José-Yacamán, Miguel
2011-01-01
The packing of spheres is a subject that has drawn the attention of mathematicians and philosophers for centuries, and that currently attracts the interest of the scientific community in several fields. At the nanoscale, the packing of atoms affect the chemical and structural properties of the material, and hence, its potential applications. This report describes the experimental formation of five-fold nanostructures by the packing of interpenetrated icosahedral and decahedral units. These nanowires, formed by the reaction of a mixture of metal salts (Au and Ag) in the presence of oleylamine, are obtained when the chemical composition is specifically Ag/Au=3/1. The experimental images of the icosahedral nanowires have a high likelihood with simulated electron micrographs of structures formed by two or three Boerdijk-Coxeter-Bernal helices roped on a single structure, whereas for the decahedral wires, simulations using a model of adjacent decahedra match the experimental structures. To our knowledge, this is the first report of the synthesis of nanowires formed by the packing of structures with five-fold symmetry. These icosahedral nanowire structures remind those of quasicrystals that can only be formed if at least two atomic species are present and in which icosahedral and decahedral packing has been found for bulk crystals. PMID:21790155
Stability of the X -Y phase of the two-dimensional C4 point group insulator
NASA Astrophysics Data System (ADS)
de Leeuw, Bart; Küppersbusch, Carolin; Juričić, Vladimir; Fritz, Lars
2015-06-01
Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this paper we consider an extension of the Bernevig-Hughes-Zhang model that describes a point group insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators but only if the Sz component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes, and the surface states localize, even if the crystalline symmetries are intact on average.
Structure and Stability of Aluminum-Copper Face-Centered Icosahedral Alloys
NASA Astrophysics Data System (ADS)
Shield, Jeffrey E.
The phases and microstructures in rapidly solidified Al-Cu-Ru alloys were investigated in this study. A chemically and topologically disordered icosahedral (i) phase grows dendritically from the liquid as the primary solidification product over the entire compositional region studied. The as-solidified i-phase is metastable and transforms to crystalline products at ~500^ circC. The i-phase was not found as a product of the exothermic transformation for any composition, indicating that it is not the low temperature stable phase in the Al-Cu-Ru system. A chemically and topologically ordered i-phase was found to be an equilibrium phase at temperatures above ~670^circ C and exists over a compositional region of several atomic percent. Once formed, this phase was easily retained at lower temperatures because of kinetic limitations of the transformation to the low temperature crystalline phase. Crystalline phases which from diffraction results appear structurally similar to the i-phase were also found in the Al-Cu-Ru system. These "approximant" phases aid in the determination of the atomic structure of i-phases by having common structural units. A simple cubic structure (a = 12.38 A, Pm3) containing a bcc network of icosahedral clusters was discovered. Comparisons of this phase with the i-phase indicated that strong similarities exist between the two structures. A rhombohedral approximant phase was also found. It exists as a transition state between the low-temperature crystalline phase and the high-temperature i-phase. This approximant phase also contains local icosahedral symmetry. The strong presence of icosahedral clusters in approximant phases in the Al-Cu-Ru system points to the distinct possibility that the i-phase is a quasiperiodic packing of icosahedral clusters of atoms.
3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Vaid, Thomas P.
2014-01-01
Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching…
3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Vaid, Thomas P.
2014-01-01
Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching
Topological Quantum Hashing with the Icosahedral Group
Burrello, Michele; Xu Haitan; Mussardo, Giuseppe; Wan Xin
2010-04-23
We study an efficient algorithm to hash any single-qubit gate into a braid of Fibonacci anyons represented by a product of icosahedral group elements. By representing the group elements by braid segments of different lengths, we introduce a series of pseudogroups. Joining these braid segments in a renormalization group fashion, we obtain a Gaussian unitary ensemble of random-matrix representations of braids. With braids of length O(log{sup 2}(1/{epsilon})), we can approximate all SU(2) matrices to an average error {epsilon} with a cost of O(log(1/{epsilon})) in time. The algorithm is applicable to generic quantum compiling.
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.
Stroh formalism for icosahedral quasicrystal and its application
NASA Astrophysics Data System (ADS)
Li, Lian He; Liu, Guan Ting
2012-02-01
The Stroh formalism for two-dimensional deformations of the icosahedral quasicrystal is studied, for which there are six pairs of complex eigenvalues. The closed-form expressions for the elastic displacement and stress fields induced by a dislocation in an icosahedral quasicrystal are obtained using the extended Stroh formalism. The effect of phonon-phason coupling elastic constant on mechanical behavior are also discussed.
Yang, Zheng; Bahar, Ivet; Widom, Michael
2009-06-01
Coarse-grained elastic network models elucidate the fluctuation dynamics of proteins around their native conformations. Low-frequency collective motions derived by simplified normal mode analysis are usually involved in biological function, and these motions often possess noteworthy symmetries related to the overall shape of the molecule. Here, insights into these motions and their frequencies are sought by considering continuum models with appropriate symmetry and boundary conditions to approximately represent the true atomistic molecular structure. We solve the elastic wave equations analytically for the case of spherical symmetry, yielding a symmetry-based classification of molecular motions together with explicit predictions for their vibrational frequencies. We address the case of icosahedral symmetry as a perturbation to the spherical case. Applications to lumazine synthase, satellite tobacco mosaic virus, and brome mosaic virus show that the spherical elastic model efficiently provides insights on collective motions that are otherwise obtained by detailed elastic network models. A major utility of the continuum models is the possibility of estimating macroscopic material properties such as the Young's modulus or Poisson's ratio for different types of viruses. PMID:19486668
Symmetry arguments in chemistry
Dunitz, Jack D.
1996-01-01
The use (and misuse) of symmetry arguments in constructing molecular models and in the interpretation of experimental observations bearing on molecular structure (spectroscopy, diffraction, etc.) is discussed. Examples include the development of point groups and space groups for describing the external and internal symmetry of crystals, the derivation of molecular symmetry by counting isomers (the benzene structure), molecular chirality, the connection between macroscopic and molecular chirality, pseudorotation, the symmetry group of nonrigid molecules, and the use of orbital symmetry arguments in discussing aspects of chemical reactivity. PMID:8962036
Analysis of phases in the structure determination of an icosahedral virus
Plevka, Pavel; Kaufmann, Brbel; Rossmann, Michael G.
2012-03-15
The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to the correct solution, opposite enantiomorph, Babinet inversion and opposite enantiomorph with Babinet inversion. These incorrect solutions can be seeded from structure factors belonging to reciprocal-space volumes that lie close to icosahedral NCS axes where the structure amplitudes tend to be large and the phases tend to be 0 or {pi}. Furthermore, the false solutions can spread more easily if there are large errors in defining the envelope designating the region in which NCS averaging is performed.
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.
The RNA of turnip yellow mosaic virus exhibits icosahedral order
Larson, Steven B.; Lucas, Robert W.; Greenwood, Aaron; McPherson, Alexander . E-mail: amcphers@uci.edu
2005-04-10
Difference electron density maps, based on structure factor amplitudes and experimental phases from crystals of wild-type turnip yellow mosaic virus and those of empty capsids prepared by freeze-thawing, show a large portion of the encapsidated RNA to have an icosahedral distribution. Four unique segments of base-paired, double-helical RNA, one to two turns in length, lie between 33-A and 101-A radius and are organized about either 2-fold or 5-fold icosahedral axes. In addition, single-stranded loops of RNA invade the pentameric and hexameric capsomeres where they contact the interior capsid surface. The remaining RNA, not seen in electron density maps, must serve as connecting links between these secondary structural elements and is likely icosahedrally disordered. The distribution of RNA observed crystallographically appears to be in agreement with models based on biochemical data and secondary structural analyses.
Symmetry Engineering of Graphene Plasmonic Crystals.
Yeung, Kitty Y M; Chee, Jingyee; Song, Yi; Kong, Jing; Ham, Donhee
2015-08-12
The dispersion relation of plasmons in graphene with a periodic lattice of apertures takes a band structure. Light incident on this plasmonic crystal excites only particular plasmonic modes in select bands. The selection rule is not only frequency/wavevector matching but also symmetry matching, where the symmetry of plasmonic modes originates from the point group symmetry of the lattice. We demonstrate versatile manipulation of light-plasmon coupling behaviors by engineering the symmetry of the graphene plasmonic crystal. PMID:26154440
Axial point groups: rank 1, 2, 3 and 4 property tensor tables.
Litvin, Daniel B
2015-05-01
The form of a physical property tensor of a quasi-one-dimensional material such as a nanotube or a polymer is determined from the material's axial point group. Tables of the form of rank 1, 2, 3 and 4 property tensors are presented for a wide variety of magnetic and non-magnetic tensor types invariant under each point group in all 31 infinite series of axial point groups. An application of these tables is given in the prediction of the net polarization and magnetic-field-induced polarization in a one-dimensional longitudinal conical magnetic structure in multiferroic hexaferrites. PMID:25921503
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 bioengineering for capsid drug delivery systems. This result also suggests that in addition to biochemical attachment restrictions, there are additional geometric constraints that should be adhered to when modifying protein capsids. PMID:27045511
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 bioengineering for capsid drug delivery systems. This result also suggests that in addition to biochemical attachment restrictions, there are additional geometric constraints that should be adhered to when modifying protein capsids. PMID:27045511
Crystallization, structural diversity and anisotropy effects in 2D arrays of icosahedral viruses†
Nguyen, Quyen L.; Vasilyev, Oleg; Mank, Nick; Washington-Hughes, Clorissa L.; Kuzmenko, Ivan; Checco, Antonio; Mao, Yimin; Wang, Qian; Yang, Lin
2016-01-01
We investigate two-dimensional (2D) assembly of the icosahedral turnip yellow mosaic virus (TYMV) under cationic lipid monolayers at the aqueous solution–vapor interface. The 2D crystallization of TYMV has been achieved by enhancing electrostatically induced interfacial adsorption, an approach recently demonstrated for another virus. In situ X-ray scattering reveals two close-packed 2D crystalline phases of TYMV that are distinct from the previously reported hexagonal and centered square ( 2×2) arrays of TYMV. One of the newly observed phases arises from either a dimeric double-square (2 × 1) or tetrameric square (2 × 2) unit cell. The other is a rhombic crystal with a lattice angle of 80°. The two observed crystal phases are substantially less dense (by over10%) than a 2D lattice of TYMV could be according to its known size and shape, indicating that local anisotropic interparticle interactions play a key role in stabilizing these crystals. TYMV’s anisotropy attributes and numerical analysis of 2D arrays of virus-shaped particles are used to derive a model for the rhombic crystal in which the particle orientation is consistent with the electrostatic lipid–TYMV attraction and the interparticle contacts exhibit steric complementarity. The interplay between particle anisotropy and packing is contrasted between the rhombic crystal model and the square ( 2×2) crystal. This study highlights how the high symmetry and subtle asphericity of icosahedral particles enrich the variety and complexity of ordered 2D structures that can be generated through self-assembly. PMID:26029772
Energy-Momentum Stability of Icosahedral Configurations of Point Vortices on a Sphere
NASA Astrophysics Data System (ADS)
Newton, Paul K.; Ostrovskyi, Vitalii
2012-08-01
We investigate the nonlinear stability of the icosahedral relative equilibrium configuration of point vortices on a sphere. The relative equilibrium problem is formulated as a problem of finding the nullspace of the configuration matrix that encodes the geometry of the icosahedron, as in Jamaloodeen and Newton (Proc. Royal Soc. A, Math. Phys. Eng. Sci. 462(2075):3277, 2006). The seven-dimensional nullspace of the configuration matrix, A, associated with the icosahedral geometry gives rise to a basis set of vortex strengths for which the icosahedron stays in relative formation, and we use these values to form the augmented Hamiltonian governing the stability. We choose the basis set made up of (i) one element with equal strength vortices on every vertex of the icosahedron (the uniform icosahedron); (ii) six elements made up of equal and opposite antipodal pairs. We start by proving nonlinear stability of the antipodal vortex pair (by direct methods). Following the methods laid out in Simo et al. (Arch. Ration. Mech. Anal. 115(1):15-59, 1991) and Pekarsky and Marsden (J. Math. Phys. 39(11):5894-5907, 1998) and more generally in Marsden and Ratiu (Introduction to Mechanics and Symmetry, 1999), we then combine our knowledge of the nullspace structure of A with the structure of the underlying Hamiltonian, and analyze the stability of the icosahedron using the energy-momentum method. Because the parameter space is large, we focus on the physically motivated and important case obtained by combining the basis elements into (i) the uniform icosahedron; (ii) a von Kármán vortex street configuration of equal and opposite staggered, evenly spaced latitudinal rows equidistant from the equator (Chamoun et al. in Phys. Fluids 21:116603, 2009), and (iii) the North Pole-South Pole equal and opposite vortex pair. Stability boundaries in a three-parameter space are calculated for linear combinations of these grouped basis configurations.
Encapsulation of a polymer by an icosahedral virus
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
NASA Astrophysics Data System (ADS)
Ting, Tan Yee; Idrus, Nor'ashiqin Mohd.; Masri, Rohaidah; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat
2014-06-01
Torsion free crystallographic groups, called Bieberbach groups, appear as fundamental groups of compact, connected, flat Riemannian manifolds and have many interesting properties. New properties of the group can be obtained by, not limited to, exploring the groups and by computing their homological functors such as nonabelian tensor squares, the central subgroup of nonabelian tensor squares, the kernel of the mapping of nonabelian tensor squares of a group to the group and many more. In this paper, the homological functor, J(G) of a centerless torsion free crystallographic group of dimension five with a nonabelian point group which is a dihedral point group is computed using commutator calculus.
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.
NASA Astrophysics Data System (ADS)
Kurtuldu, Güven; Rappaz, Michel
2015-06-01
Recently, we have shown that minute Cr additions (typically 0.1 wt%) to Al-Zn alloys solidified in a uniform temperature field lead to the formation of fine equiaxed fcc Al grains [1]. Furthermore, these grains exhibit an unexpectedly large number of twin, or neartwin, relationships with their nearest neighbors and some of them even show a 5-fold symmetry multi-twin relationship with a common (110) direction. Similar observations have been made for yellow gold alloys (Au-12.5wt%Cu-12.5wt%Ag) inoculated with very small amounts of Ir (5-200 ppm) [2]. These results become fully consistent when one considers that the primary fcc phase forms on facets of icosahedral quasicrystals (iQC's), either by heteroepitaxy solidification or by peritectic transformation, with the following relationship: <111>fcc || 3-fold symmetry iQC axes, <110>fcc ⊥ 2-fold symmetry iQC axes. The present study contributes to a better understanding of the frequency of twin boundary formation by the nucleation of fcc phase from an iQC template. A simple stereological model for the formation of equiaxed grains on such iQC templates has been derived. It is based on a 3D Voronoi tessellation of randomly distributed and oriented iQC template centers. Each iQC nucleation template site is the origin of 20 fcc grains with the heteroepitaxy relationships mentioned above on the 20 facets of the iQC. Therefore, the neighboring grains having a common iQC nucleation site contributes to the twin boundary frequency, while those coming from different iQC sites have random grain boundary orientations. The twin boundary frequency of the grains nucleated from iQC templates seen in 2D metallographic sections is compared with that measured in EBSD reconstructed grain structures.
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.
The NQR and NMR studies of icosahedral borides
NASA Astrophysics Data System (ADS)
Lee, Donghoon; Bray, Philip J.; Aselage, Terry L.
1999-06-01
Boron NMR and NQR studies have been performed on three icosahedral borides: icons/Journals/Common/alpha" ALT="alpha" ALIGN="TOP"/>- and icons/Journals/Common/beta" ALT="beta" ALIGN="TOP"/>-rhombohedral boron and boron carbide (B12C3). Two 11B NMR peaks, separated by significant chemical shifts in the range from 130 ppm to 280 ppm, were clearly observed for all of the icosahedral borides that were not enriched in the 10B isotope. A single peak, however, was found for the 10B enriched boron carbide powder (90.6 at.% enrichment.) Moreover, the peak separation in the 11B NMR spectrum for the unenriched icons/Journals/Common/beta" ALT="beta" ALIGN="TOP"/>-boron was reduced when the sample was crushed into a fine powder. In addition to NMR responses, four strong NQR responses were observed for boron carbides from different manufacturers. Two resonance signals, observed at 513 kHz and 2769 kHz, correspond to one of the icosahedral boron sites and the boron in the CBC chain, respectively. The other two NQR responses, having frequencies of 361 and 380 kHz, are either 10B responses for the chain site or 11B responses for the other boron sites in the icosahedra. The NQR responses are not only consistent with the previous NMR studies performed independently by Silver and Bray (1959 J. Chem. Phys. 31 247) and by Hynes and Alexander (1971 J. Chem. Phys. 54 5296, 1972 J. Chem. Phys. Erratum 56), but also provide much higher accuracy for the values of the quadrupolar parameters.
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.
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.
Dynamic and Kinetic Assembly Studies of an Icosahedral Virus Capsid
NASA Astrophysics Data System (ADS)
Lee, Kelly
2011-03-01
Hepatitis B virus has an icosahedrally symmetrical core particle (capsid), composed of either 90 or 120 copies of a dimeric protein building block. We are using time-resolved, solution small-angle X-ray scattering and single-molecule fluorescence microscopy to probe the core particle assembly reaction at the ensemble and individual assembly levels. Our experiments to date reveal the assembly process to be highly cooperative with minimal population of stable intermediate species. Solution conditions, particularly salt concentration, appears to influence the partitioning of assembly products into the two sizes of shells. Funding from NIH R00-GM080352 and University of Washington.
Melting of bcc Transition Metals and Icosahedral Clustering
Ross, M; Boehler, R; Japel, S
2006-05-26
In contrast to polyvalent metals, transition metals have low melting slopes(dT/dP) that are due to partially filled d-bands that allow for a lowering of liquid phase energy through s-d electron transfer and the formation of local structures. In the case of bcc transition metals we show the apparent discrepancy of DAC melting measurements with shock melting of Mo can be understood by reexamining the shock data for V and Ta and introducing the presence of an icosahedral short range order (ISRO) melt phase.
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.
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.
Phylogeny of capsid proteins of small icosahedral RNA plant viruses.
Dolja, V V; Koonin, E V
1991-07-01
Statistically significant alignment was generated between the amino acid sequences of the (putative) shell (S) domains of the capsid proteins of small RNA plant viruses with icosahedral capsids in the tombusvirus, carmovirus, dianthovirus, sobemovirus and luteovirus groups. Inspection of the alignment showed good correspondence between the experimentally defined beta-strands and alpha-helices of the capsid proteins of tomato bushy stunt, southern bean mosaic and turnip crinkle viruses, allowing prediction of the secondary structure elements in proteins with unresolved tertiary structure. It is concluded that this set of viral capsid proteins forms a tight evolutionary cluster. Comparison of the alignment of the proteins of this family with the sequences of other capsid proteins of icosahedral RNA viruses revealed more distant similarities to the satellites of tobacco necrosis, panicum mosaic, tobacco mosaic and maize white line mosaic viruses, as well as to nepo- and comoviruses. The tentative phylogenetic tree derived from the capsid protein alignment separated into three main lineages: (I) carmo-, tombus- and dianthoviruses, (II) southern bean mosaic, tobacco necrosis and maize chlorotic mottle viruses, and (III) luteoviruses. Comparison of this tree topology with the tentative evolutionary schemes for the respective virus RNA-dependent RNA polymerases suggested that gene shuffling is the universal trend in the evolution of small RNA plant virus genomes. PMID:1856686
The Formation and Structure of Aluminum-Copper - (lithium, Magnesium) Icosahedral Alloys.
NASA Astrophysics Data System (ADS)
Shen, Yong
Quasicrystals have orientational order but lack periodic translational order. Sharp electron diffraction spots imply that they differ from amorphous materials. On the other hand, the aperiodic array of diffraction spots is inconsistent with conventional crystallography, which allows only two-, three-, four-, or sixfold symmetry axes. The discovery of the first icosahedral quasicrystal in a rapidly solidified Al-Mn alloy has created a flurry of activities in studying their structure and thermodynamics. AlCuLi icosahedral phase (i-phase) is the first stable quasicrystalline phase; and centimeter size quasicrystals can be obtained. Thus, AlCuLi i-phase is a model system for understanding the structure and thermodynamics of quasicrystalline materials. The research I have done consists of three parts: (1) Structural studies using high resolution x-ray diffraction. We found that Al(Cu) were decorated at the edge centers and vertices of two types of Penrose tiles, which are the basic units of Penrose tiling. Our results are the first successful determination of the atomic position in quasicrystalline materials, and prove that the Penrose tiling is a better description of quasicrystalline materials than other structural models. (2) Structural studies using pulsed neutron scattering. The dominant contribution to the AlCuLi x-ray spectrum comes from Al and Cu atoms since Li is a weak scatterer. However, the scattering length of the Li atom in neutron diffraction is comparable to that of Al(Cu). Furthermore, Li and Mg have opposite signs in scattering length. Thus, isomorphic substitution of Li by Mg results in contrast variation in neutron diffraction spectra, which demonstrates how Li atoms affect the diffraction. Using the pair distribution function analysis, we convincingly reveal the role of Li atoms in the structure. (3) Stability and formation. We investigate the formation of i-phase by varying preparation condition and stoichiometry. By using differential scanning calorimetry and x-ray diffraction, we established the thermodynamic relationship between the i-phase and the related crystalline phase.
Marzec, C J; Day, L A
1993-01-01
The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found. Images FIGURE 5 FIGURE 6 FIGURE 8 FIGURE 9 PMID:8312492
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...
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.
Icosahedron and icosahedral order in rapidly solidified A1-Ni-Mo alloys
Niikura, A.; Tsai, A.P.; Inoue, A.; Masumoto, T. . Inst. for Materials Research)
1992-09-01
The quasicrystalline state characterized by long range icosahedral order was firstly reported by Shechtman et al. Icosahedral bond-orientational order has ben observed in a molecular dynamics simulation of an under-cooled Lennard-Jones liquid. A correlation between the structure factors of metallic glasses and the icosahedral solid was also noted. Al[sub 12]Mo(or Al[sub 12]W) is a compound with a structure consisting of a bcc array of Al icosahedron centered by Mo(or W); thus it contains 13 atoms per primitive unit cell and local icosahedral packing which is in favor of the formation of an icosahedral phase in a quenched state. Meanwhile Ni is known as a promotion element for the creation of an Al based amorphous alloy. The authors have observed that the icosahedral phase is created in AlNiMo alloys and transited to an amorphous phase with increasing Ni. Transformation from amorphous via i-phase and finally to Al[sub 12]Mo was observed in Al[sub 85Ni][sub 10Mo][sub 5]. In this paper, the authors focus on the icosahedron and icosahedral order in correlation with composition in the Al-Ni-Mo system.
Hu, Wen; Yi, Jianhong; Zheng, Biju; Wang, Limin
2013-06-01
Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti₁.₆V₀.₄Ni)₁₀₀₋xScx (x=0.5–6) quaternary icosahedral quasicrystals have been successfully synthesized via arc-melting and subsequent melt-spinning techniques, and then their electrochemical performance toward hydrogen is explored. When the molar ratio of Sc addition is under 1%, a maximum discharge capacity of about 270 mA h g⁻¹ can be delivered. With further increasing Sc amount to 6%, good cycling stability as well as significantly retarded self-discharge rate (capacity retention 94% after 24 h relaxation) is observed. But meanwhile, the discharge capacities fall into 250-240 mA h g⁻¹, and the electrocatalytic activity improvement is highly demanded. - Graphical abstract: Quasicrystalline Ti–V–Ni–Sc hydrogen storage materials: Sc addition into Ti₁.₆V₀.₄Ni alloy forms the icosahedral phase (see picture). With optimal Sc dosage, the anodic cycling stability and self-discharge property are greatly enhanced. - Highlights: • Crystalline disallowed 5-fold symmetry is present in (Ti₁.₆V₀.₄Ni)₁₀₀₋xScx alloys. • Ti-based metastable quasicrystalline alloys can store hydrogen electrochemically. • A maximum discharge capacity of 270 mA h g⁻¹ can be delivered. • Advantageous cycle stability and self-discharge property benefit from Sc addition. • Ti and V dissolution is suppressed by an oxide layer resulting from Sc corrosion.
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
Dynamico, an Icosahedral Dynamical Core Designed for Consistency and Versatility
NASA Astrophysics Data System (ADS)
Dubos, T.
2014-12-01
The design of the icosahedral-hexagonal dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations (HPE) in a Lagrangian vertical coordinate, and the HPE in a hybrid mass-based vertical coordinate. In line with more general lines of thought known as physics-preserving discretizations and discrete differential geometry, kinematics and dynamics are separated as strictly as possible. This separation means that the transport of mass, scalars and potential temperature uses no information regarding the specific momentum equation being solved. This disregarded information includes the equation of state as well as any metric information, and is used only for certain terms of the momentum budget, written in Hamiltonian, vector-invariant form. The common Hamiltonian structure of the various equations of motion (Tort and Dubos, 2014 ; Dubos and Tort, 2014) is exploited to formulate energy-conserving spatial discretizations in a unified way. Furthermore most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. This design permits to consider several extensions in the near future, especially to deep-atmosphere, moist and non-hydrostatic equations. Representative academic three-dimensional benchmarks are run and analyzed, showing correctness of the model (Figure : time-zonal statistics from Held and Suarez (1994) simulations). Hopefully preliminary full-physics results will be presented as well. References : T. Dubos and M. Tort, "Equations of atmospheric motion in non-Eulerian vertical coordinates : vector-invariant form and Hamiltonian formulation", accepted by Mon. Wea. Rev. M. Tort and T. Dubos, "Usual approximations to the equations of atmospheric motion : a variational perspective" accepted by J. Atmos. Sci T. Dubos et al., "DYNAMICO, an icosahedral hydrostatic dynamical core designed for consistency and versatility", in preparation.
NASA Astrophysics Data System (ADS)
Mohammad, Siti Afiqah; Ali, Nor Muhainiah Mohd; Sarmin, Nor Haniza; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah
2014-06-01
A Bieberbach group is a torsion free crystallographic group, which is an extension of a free abelian group of finite rank by a finite point group, while homological functors of a group include nonabelian tensor square, exterior square and Schur Multiplier. In this paper, some homological functors of a Bieberbach group of dimension four with dihedral point group of order eight are computed.
Difference in Icosahedral Short-Range Order in Early and Late Transition Metal Liquids
NASA Technical Reports Server (NTRS)
Lee, G. W.; Gangopadbyay, A. K.; Kelton, K. F.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.
2004-01-01
New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in-situ synchrotron x-ray diffraction measurements of electrostatically-levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid. although this has been predicted by theoretical studies on atomic clusters.
Difference in Icosahedral Short-Range Order in Early and Late Transition Metals Liquids
NASA Technical Reports Server (NTRS)
Lee, G. W.; Gangopadhyay, A. K.; Kelton, K. F.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.
2003-01-01
New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in-situ synchrotron x-ray diffraction measurements of electrostatically-levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid, although this has been predicted by theoretical studies on atomic clusters.
Formation of microstructure of icosahedral phase in rapidly solidified aluminum-chromium alloys
Rosen, G.I.; Shechtman, D.
1994-01-01
Rapid solidification of Al-Cr alloys resulted in the nucleation and growth of icosahedral phase in the 14--36 wt% Cr range. The highest volume fraction of this phase was obtained between 21--26 wt% Cr. It was found that the different alloy compositions contain a variety of morphologies and microstructures which also depend on location regarding the cross section of the ribbon. The icosahedral phase is not stoichiometric and its maximum Cr content is between 26--30 wt% Cr. In the higher alloy compositions the stable intermetallic {epsilon} phase grows epitaxial on the icosahedral phase with a distinctive orientation relationship.
Jin, Renxi; Liu, Chong; Zhao, Shuo; Das, Anindita; Xing, Hongzhu; Gayathri, Chakicherla; Xing, Yan; Rosi, Nathaniel L; Gil, Roberto R; Jin, Rongchao
2015-08-25
The [Au37(PPh3)10(SR)10X2](+) nanocluster (where SR = thiolate and X = Cl/Br) was theoretically predicted in 2007, but since then, there has been no experimental success in the synthesis and structure determination. Herein, we report a kinetically controlled, selective synthesis of [Au37(PPh3)10(SC2H4Ph)10X2](+) (counterion: Cl(-) or Br(-)) with its crystal structure characterized by X-ray crystallography. This nanocluster shows a rod-like structure assembled from three icosahedral Au13 units in a linear fashion, consistent with the earlier prediction. The optical absorption and the electrochemical and catalytic properties are investigated. The successful synthesis of this new nanocluster allows us to gain insight into the size, structure, and property evolution of gold nanoclusters that are based upon the assembly of icosahedral units (i.e., cluster of clusters). Some interesting trends are identified in the evolution from the monoicosahedral [Au13(PPh3)10X2](3+) to the bi-icosahedral [Au25(PPh3)10(SC2H4Ph)5X2](2+) and to the tri-icosahedral [Au37(PPh3)10(SC2H4Ph)10X2](+) nanocluster, which also points to the possibility of achieving even longer rod nanoclusters based upon assembly of icosahedral building blocks. PMID:26214221
Metal-organic framework materials based on icosahedral boranes and carboranes
Mirkin, Chad A.; Hupp, Joseph T.; Farha, Omar K.; Spokoyny, Alexander M.; Mulfort, Karen L.
2010-11-02
Disclosed herein are metal-organic frameworks of metals and boron rich ligands, such as carboranes and icosahedral boranes. Methods of synthesizing and using these materials in gas uptake are disclosed.
Van Hove singularities of some icosahedral boron-rich solids by differential reflectivity spectra
NASA Astrophysics Data System (ADS)
Werheit, Helmut
2015-09-01
Differential reflectivity spectra of some icosahedral boron rich solids, β-rhombohedral boron, boron carbide and YB66-type crystals, were measured. The derivatives yield the van Hove singularities, which are compared with results obtained by other experimental methods.
A face-sharing bi-icosahedral model for Al₂₃⁻.
Koyasu, K; Tsukuda, T
2014-10-21
A face-sharing bi-icosahedral motif is proposed as a candidate structure of the magic cluster, Al23(-), on the basis of DFT calculations. The structure can be viewed as a quasi-molecule made of two Al13 (D3d) superatoms with an open electronic configuration via constructive overlap of 1F and 2P superatomic orbitals. A face-sharing tri-icosahedral motif is also predicted for Al33(-). PMID:25199061
Structure and Decoration of the Icosahedral and Rhombohedral Phases in AlCuFe Alloys
NASA Astrophysics Data System (ADS)
Le Lann, A.; Devaud, J.
1995-01-01
Structural models for AlCuFe icosahedral and rhombohedral phases are obtained by decomposition, in perpendicular space, of the atomic surfaces into cells of identical local environment. The models are described in 3D real space and compared to the corresponding H.R.E.M. images obtained on structurally perfect icosahedral and rhombohedral phases. The specificity of their aperiodic structure and chemical decoration is outlined.
Speckle in the diffraction patterns of Hendricks-Teller and icosahedral glass models
NASA Astrophysics Data System (ADS)
Garg, Anupam; Levine, Dov
1988-05-01
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.
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.
ERIC Educational Resources Information Center
Jittam, Piyachat; Ruenwongsa, Pintip; Panijpan, Bhinyo
2008-01-01
We have found it an effective way of teaching symmetry in the context of stereoselectivity, to use common everyday objects with the same point groups as the substrates involved. This has helped students to distinguish between those symmetry elements which allow for stereospecificity and those which preclude it. Two symmetry elements, the simple
ERIC Educational Resources Information Center
Jittam, Piyachat; Ruenwongsa, Pintip; Panijpan, Bhinyo
2008-01-01
We have found it an effective way of teaching symmetry in the context of stereoselectivity, to use common everyday objects with the same point groups as the substrates involved. This has helped students to distinguish between those symmetry elements which allow for stereospecificity and those which preclude it. Two symmetry elements, the simple…
NASA Astrophysics Data System (ADS)
Rappaz, Michel; Kurtuldu, Güven
2015-08-01
We have recently shown that minute solute element additions to liquid metallic alloys can strongly influence the nucleation of the fcc phase and act as a grain refinement method. Electron back-scattered diffraction observations revealed a concomitant increase in the percentage of nearest neighbor (nn) grains that are in a twin relationship. Furthermore, multiple-twinned (MT) nn grain configurations with a fivefold symmetry around a common direction have been identified, an occurrence that can be explained when the symmetry of the icosahedron is accounted for. It was then conjectured that a new nucleation mechanism occurs in two steps: first, the formation of small icosahedral quasicrystals in the melt, followed by heteroepitaxy of the fcc phase on facets of these quasicrystals. In the present contribution, based on thermodynamics arguments, it is proposed that the first step occurs by spinodal decomposition of the liquid, in a manner similar to Guinier-Preston zones formation in solid state precipitation, while the second step is a transformation of these quasicrystal precursors into MT-fcc nanocrystals once the driving force for this transformation is sufficient to overcome the fcc-liquid interfacial energy and the elastic strains associated with MT-fcc nanoparticles. This explanation sets up guidelines for finding solute elements and composition ranges that favor this grain refinement mechanism.
Icosahedral quasicrystal structure determination: Al-Cu-Li
Qiu, S.Y.
1992-01-01
This dissertation reports the theoretical study of the determination of quasicrystal atomic structures. A new method is developed for phasing the quasicrystal diffraction data (neutron, X-ray diffraction). A mathematical model is built which explicitly relates quasicrystals to their related periodic crystals. A test of the method is made on a simple theoretical system, the icosahedral quasiperiodic Ammann tiling decorated with point scatterers (Dirac [sigma] scattering potential) on vertices. A success is achieved in reconstructing the phases of the quasicrystal. The method is applied to a real quasicrystal system, the icosahedral quasicrystal i(Al[sub .570]Cu[sub .108]Li[sub .322]), where single-grain X-ray as well as neutron diffraction data are available, and the structure of the related large-unit-cell crystal of R(Al[sub .564]Cu[sub .116]Li[sub .320]), is well known. The reconstructed phases give the density of scatterers, which can then be used in the analysis of the atomic structure, and provide a guide to the final structure modeling. The validity of the method is evaluated with respect to the non-negativity of the resulting electron densities. In order to identify the negativity due to the intensity cut-off, the negativity is evaluated as a function of the cut-off and compared with the exact and reconstructed quasiperiodic Ammann tilings as well as with the experimental and model crystal data of R(Al[sub .564]Cu[sub .116]Li[sub .320]). It is concluded that the negativity of the reconstructed quasiperiodic electron density of i(Al[sub .570]Cu[sub .108]Li[sub .322]) is consistent with a cut-off effect. Modeling of the i(Al[sub .570]Cu[sub .108]Li[sub .322]) atomic structure in six-dimensional hyperspace is discussed. It is assumed that atomic surfaces can be modeled by polyhedra which can be described by a finite number of parameters. The authors successfully generated a model which agrees with the experimental data.
Local growth rules and kinetics for ordered icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Socolar, Joshua; Hann, Connor; Steinhardt, Paul
Icosahedral quasicrystals (IQCs) with extremely high degrees of translational order have been produced in the lab and found in naturally occurring minerals. While the existence of IQCs is well established, questions remain about how IQCs form. We address the question of whether it is possible in principle for nucleation and growth dominated by local growth rules and kinetics to produce a perfectly ordered IQC. We find that it is possible to produce an IQC with a vanishing density of defects through a local growth algorithm for sequential, face-to-face addition of tiles of two different shapes to a growing cluster. The choice of how to add a tile at any selected vertex on the surface is based only on short-range information about tiles that share the vertex. The process is analogous to the Onoda growth rule for 2D Penrose tilings, but new subtleties emerge in three dimensions. The geometric features underlying this algorithm can inform analyses of experimental systems and numerical models that generate highly ordered quasicrystals.
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.
Schein, Stan; Gayed, James Maurice
2014-02-25
The three known classes of convex polyhedron with equal edge lengths and polyhedral symmetry--tetrahedral, octahedral, and icosahedral--are the 5 Platonic polyhedra, the 13 Archimedean polyhedra--including the truncated icosahedron or soccer ball--and the 2 rhombic polyhedra reported by Johannes Kepler in 1611. (Some carbon fullerenes, inorganic cages, icosahedral viruses, geodesic structures, and protein complexes resemble these fundamental shapes.) Here we add a fourth class, "Goldberg polyhedra," which are also convex and equilateral. We begin by decorating each of the triangular facets of a tetrahedron, an octahedron, or an icosahedron with the T vertices and connecting edges of a "Goldberg triangle." We obtain the unique set of internal angles in each planar face of each polyhedron by solving a system of n equations and n variables, where the equations set the dihedral angle discrepancy about different types of edge to zero, and the variables are a subset of the internal angles in 6gons. Like the faces in Kepler's rhombic polyhedra, the 6gon faces in Goldberg polyhedra are equilateral and planar but not equiangular. We show that there is just a single tetrahedral Goldberg polyhedron, a single octahedral one, and a systematic, countable infinity of icosahedral ones, one for each Goldberg triangle. Unlike carbon fullerenes and faceted viruses, the icosahedral Goldberg polyhedra are nearly spherical. The reasoning and techniques presented here will enable discovery of still more classes of convex equilateral polyhedra with polyhedral symmetry. PMID:24516137
NASA Astrophysics Data System (ADS)
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.
Comparative Study of Non-Enveloped Icosahedral Viruses Size
Nikitin, Nikolai; Trifonova, Ekaterina; Evtushenko, Evgeniy; Kirpichnikov, Mikhail; Atabekov, Joseph; Karpova, Olga
2015-01-01
Now, as before, transmission electron microscopy (TEM) is a widely used technique for the determination of virions size. In some studies, dynamic light scattering (DLS) has also been applied for this purpose. Data obtained by different authors and using different methods could vary significantly. The process of TEM sample preparation involves drying on the substrate, which can cause virions to undergo morphology changes. Therefore, other techniques should be used for measurements of virions size in liquid, (i.e. under conditions closer to native). DLS and nanoparticle tracking analysis (NTA) provide supplementary data about the virions hydrodynamic diameter and aggregation state in liquid. In contrast to DLS, NTA data have a higher resolution and also are less sensitive to minor admixtures. In the present work, the size of non-enveloped icosahedral viruses of different nature was analyzed by TEM, DLS and NTA: the viruses used were the encephalomyocarditis virus (animal virus), and cauliflower mosaic virus, brome mosaic virus and bean mild mosaic virus (plant viruses). The same, freshly purified, samples of each virus were used for analysis using the different techniques. The results were compared with earlier published data and description databases. DLS data about the hydrodynamic diameter of bean mild mosaic virus, and NTA data for all examined viruses, were obtained for the first time. For all virus samples, the values of size obtained by TEM were less than virions sizes determined by DLS and NTA. The contribution of the electrical double layer (EDL) in virions hydrodynamic diameter was evaluated. DLS and NTA data adjusted for EDL thickness were in better agreement with TEM results. PMID:26545232
Comparative Study of Non-Enveloped Icosahedral Viruses Size.
Nikitin, Nikolai; Trifonova, Ekaterina; Evtushenko, Evgeniy; Kirpichnikov, Mikhail; Atabekov, Joseph; Karpova, Olga
2015-01-01
Now, as before, transmission electron microscopy (TEM) is a widely used technique for the determination of virions size. In some studies, dynamic light scattering (DLS) has also been applied for this purpose. Data obtained by different authors and using different methods could vary significantly. The process of TEM sample preparation involves drying on the substrate, which can cause virions to undergo morphology changes. Therefore, other techniques should be used for measurements of virions size in liquid, (i.e. under conditions closer to native). DLS and nanoparticle tracking analysis (NTA) provide supplementary data about the virions hydrodynamic diameter and aggregation state in liquid. In contrast to DLS, NTA data have a higher resolution and also are less sensitive to minor admixtures. In the present work, the size of non-enveloped icosahedral viruses of different nature was analyzed by TEM, DLS and NTA: the viruses used were the encephalomyocarditis virus (animal virus), and cauliflower mosaic virus, brome mosaic virus and bean mild mosaic virus (plant viruses). The same, freshly purified, samples of each virus were used for analysis using the different techniques. The results were compared with earlier published data and description databases. DLS data about the hydrodynamic diameter of bean mild mosaic virus, and NTA data for all examined viruses, were obtained for the first time. For all virus samples, the values of size obtained by TEM were less than virions sizes determined by DLS and NTA. The contribution of the electrical double layer (EDL) in virions hydrodynamic diameter was evaluated. DLS and NTA data adjusted for EDL thickness were in better agreement with TEM results. PMID:26545232
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 Astrophysics Data System (ADS)
Hu, Wen; Yi, Jianhong; Zheng, Biju; Wang, Limin
2013-06-01
Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti1.6V0.4Ni)100-xScx (x=0.5-6) quaternary icosahedral quasicrystals have been successfully synthesized via arc-melting and subsequent melt-spinning techniques, and then their electrochemical performance toward hydrogen is explored. When the molar ratio of Sc addition is under 1%, a maximum discharge capacity of about 270 mA h g-1 can be delivered. With further increasing Sc amount to 6%, good cycling stability as well as significantly retarded self-discharge rate (capacity retention 94% after 24 h relaxation) is observed. But meanwhile, the discharge capacities fall into 250-240 mA h g-1, and the electrocatalytic activity improvement is highly demanded.
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.
Symmetry, stability, and dynamics of multidomain and multicomponent protein systems
Blundell, Tom L.; Srinivasan, N.
1996-01-01
Symmetry is commonly observed in many biological systems. Here we discuss representative examples of the role of symmetry in structural molecular biology. Point group symmetries are observed in many protein oligomers whose three-dimensional atomic structures have been elucidated by x-ray crystallography. Approximate symmetry also occurs in multidomain proteins. Symmetry often confers stability on the molecular system and results in economical usage of basic components to build the macromolecular structure. Symmetry is also associated with cooperativity. Mild perturbation from perfect symmetry may be essential in some systems for dynamic functions. PMID:8962033
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 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.
2003-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si[3], for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron x-ray and high flux neutron facilities, this is shown here.
NASA Technical Reports Server (NTRS)
Kelton, K. F.; Gangopadhyay, A. K.; Lee, G. W.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.; Robinson, M. B.; Schenk, T.; Simonet, V.; Holland-Moritz, D.; Curreri, Peter A. (Technical Monitor)
2002-01-01
Over fifty years ago, David Turnbull showed that the temperature of many metallic liquids could be decreased far below their equilibrium melting temperature before crystallization occurred. To explain those surprising results, Charles Frank hypothesized that the local structures of undercooled metallic liquids are different from those of crystal phases, containing a significant degree of icosahedral order that is incompatible with extended periodicity. Such structural differences must create a barrier to the formation crystal phases, explaining the observed undercooling behavior. If true, the nucleation from the liquid of phases with extended icosahedral order should be easier. Icosahedral order is often favored in small clusters, as observed recently in liquid-like clusters of pure Pb on the (111) surface of Si(3), for example. However, it has never been shown that an increasing preference for icosahedral phase formation can be directly linked with the development of icosahedral order in the undercooled liquid. Owing to the combination of very recent advances in levitation techniques and the availability of synchrotron X-ray and high flux neutron facilities.
Pauling, Linus
1989-01-01
The twofold-axis electron-diffraction photographs of icosahedral quasicrystals are of three kinds, reflecting three different structures of the cubic crystals that by icosahedral twinning form the quasicrystals. The first kind, represented by Al13Cu4Fe3, contains two very large icosahedral complexes, each of about 4680 atoms, in the body-centered arrangement, with six smaller icosahedral complexes (104 atoms each) in the principal interstices. The second kind, represented by Al5Mn, contains four of the very large complexes in the face-centered arrangement (cubic close packing), with four of the smaller clusters in the interstices. The third kind, represented by Al6CuLi3, contains eight icosahedral complexes, each of about 1350 atoms, in the β-W arrangement. The supporting evidence for these cubic structures is discussed as well as other evidence showing that the simple quasicrystal theory, which states that quasicrystals do not involve any translational identity operations, has to be modified. Images PMID:16594078
Growth and characterization of single grain icosahedral AlCuFe quasicrystals
NASA Astrophysics Data System (ADS)
Kelso, N.; Canfield, P. C.; Bud'Ko, S. L.
2002-03-01
In this talk we will review the growth of Al-rich quasicrystals from metallic solutions. In particular we will discuss the growth of single grains of icosahedral AlCuFe from the ternary melt. Whereas the growths of single grain decagonal phase AlNiCo and icosahedral phase AlPdMn from metallic solutions are rather simple, the growth of sizable single grains of icosahedral phase AlCuFe presents a more difficult problem, but single grains as large as several cubic mm can be produced. Structural data from electron microscopy as well as thermodynamic and transport data will be presented and discussed. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. W-7405-Eng-82. This work was supported by the Director for Energy Research, Office of Basic Energy Sciences.
NASA Astrophysics Data System (ADS)
Mainzer, Klaus
Symmetry and complexity in early culture and philosophy -- Symmetry and complexity in mathematics -- Symmetry and complexity in physical sciences -- Symmetry and complexity in chemical sciences -- Symmetry and complexity in life sciences -- Symmetry and complexity in economic and social sciences -- Symmetry and complexity in computer science -- Symmetry and complexity in philosophy and arts.
Structural symmetry and protein function.
Goodsell, D S; Olson, A J
2000-01-01
The majority of soluble and membrane-bound proteins in modern cells are symmetrical oligomeric complexes with two or more subunits. The evolutionary selection of symmetrical oligomeric complexes is driven by functional, genetic, and physicochemical needs. Large proteins are selected for specific morphological functions, such as formation of rings, containers, and filaments, and for cooperative functions, such as allosteric regulation and multivalent binding. Large proteins are also more stable against denaturation and have a reduced surface area exposed to solvent when compared with many individual, smaller proteins. Large proteins are constructed as oligomers for reasons of error control in synthesis, coding efficiency, and regulation of assembly. Symmetrical oligomers are favored because of stability and finite control of assembly. Several functions limit symmetry, such as interaction with DNA or membranes, and directional motion. Symmetry is broken or modified in many forms: quasisymmetry, in which identical subunits adopt similar but different conformations; pleomorphism, in which identical subunits form different complexes; pseudosymmetry, in which different molecules form approximately symmetrical complexes; and symmetry mismatch, in which oligomers of different symmetries interact along their respective symmetry axes. Asymmetry is also observed at several levels. Nearly all complexes show local asymmetry at the level of side chain conformation. Several complexes have reciprocating mechanisms in which the complex is asymmetric, but, over time, all subunits cycle through the same set of conformations. Global asymmetry is only rarely observed. Evolution of oligomeric complexes may favor the formation of dimers over complexes with higher cyclic symmetry, through a mechanism of prepositioned pairs of interacting residues. However, examples have been found for all of the crystallographic point groups, demonstrating that functional need can drive the evolution of any symmetry. PMID:10940245
Surface preparation and characterization of the icosahedral Al-Pd-Mn-Ga quasicrystal
Heinzig, Mark; Jenks, Cynthia J.; Van Hove, Michel; Fisher, Ian; Canfield, Paul; Thiel, Patricia A.
2002-01-08
Auger electron spectroscopy and low-energy electron diffraction (LEED) provide basic information about the structure and composition of the fivefold surface of the quaternary quasicrystal, icosahedral Al67Pd4Mn21Ga8. Surface preparation techniques established previously for two of the icosahedral ternary alloys, Al-Pd-Mn and Al-Cu-Fe, appear to be similarly effective for Al-Pd-Mn-Ga. After annealing in the range 600-950 K, the surface concentration of Ga is constant and low. After annealing in the range 900-950 K, a good LEED pattern is obtained. LEED indicates that Ga changes the surface structure significantly.
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.
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.
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...
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.
Dynamic Paper Constructions for Easier Visualization of Molecular Symmetry
ERIC Educational Resources Information Center
Sein, Lawrence T., Jr.
2010-01-01
A system for construction of simple poster-board models is described. The models dynamically demonstrate the symmetry operations of proper rotation, improper rotation, reflection, and inversion for the chemically important point groups D[subscript 3h], D[subscript 4h], D[subscript 5h], D[subscript 6h], T[subscript d], and O[subscript h]. The…
Web-Supported Chemistry Education: Design of an Online Tutorial for Learning Molecular Symmetry
ERIC Educational Resources Information Center
Korkmaz, Ali; Harwood, William S.
2004-01-01
This paper describes our use of the ADDIE protocol to design and develop an interactive tutorial for students learning molecular symmetry operations and point groups. The tutorial provides a 3-D environment where students can examine molecules, structures, and symmetry elements. Most such tutorials are connected to courses or instructors in…
Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ′}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ′} is invariant under transformation by elements of a subgroup G{sup ′} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
Correlation of Atomic Cluster Symmetry and Glass-Forming Ability of Metallic Glass
Xi Xuekui; Li Lilong; Wu Yue; Zhang Bo; Wang Weihua
2007-08-31
Local structures play a crucial role in glass formation and properties. In addition to topological short-range order, the geometric property of site symmetry is another important but less known characteristic of local structures. It is shown that the observed sharp increase of glass forming ability of Ce{sub 70-x}Al{sub 10}Cu{sub 20}Co{sub x} upon Co addition is correlated with a dramatic increase of Al site symmetry, as reflected by decreasing quadrupole frequency measured by {sup 27}Al NMR. The result is consistent with the structure model of Al-centered icosahedral clusters as the predominant structural building blocks.
None
2011-10-06
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ?renormalizable?. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged ?vector? particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of ?massless? modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a ?massive? SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic ?vector? field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are ?scalar?? fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a ?renormalizable? theory. From our analysis of the preserved gauge symmetry, we suggested in 1966 that this is indeed the case, in contradistinction to the aforementioned earlier theories of charged massive vector fields. The full proof of ?renormalizability? is subtle and was achieved in the impressive work of ?t Hooft and Veltman. One gains some insight into the subtleties by making explicit the equivalence of Higgs? approach with ours. - To a large extend, the LHC was build to detect the massive SBS scalar boson, i.e. the fluctuations of the scalar field. More elaborate realizations of the mechanism without elementary scalars are possible, but their experimental confirmation may (or may not) be outside the scope of present available technology. - The mechanism of Brout, Englert and Higgs unified in the same theoretical framework short- and long-range forces. It became the cornerstone of the electroweak theory and opened the way to a modern view on unified laws of nature.
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.
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.
Icosahedral ordering in liquid iron studied via x-ray scattering and Monte Carlo simulations
NASA Astrophysics Data System (ADS)
Inui, Masanori; Maruyama, Kenji; Kajihara, Yukio; Nakada, Masaru
2009-11-01
X-ray diffraction measurements were carried out for liquid iron near the melting temperature and atomic configurations were constructed from the structure factor S(Q) obtained, by reverse Monte Carlo modeling and Monte Carlo simulation with the effective pair potential deduced by the inverse method. The bond-orientational order parameter Ŵ6 calculated from the atomic configurations obtained from both simulations indicates a pronounced icosahedral ordering, and the fraction of nearly icosahedral configurations is estimated to be approximately 14% in liquid iron. These experimentally obtained results seem consistent with recent results of ab initio molecular-dynamics simulation for liquid iron [P. Ganesh and M. Widom, Phys. Rev. B 77, 014205 (2008)].
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.
Growth of Au on Pt icosahedral nanoparticles revealed by low-dose in situ TEM.
Wu, Jianbo; Gao, Wenpei; Wen, Jianguo; Miller, Dean J; Lu, Ping; Zuo, Jian-Min; Yang, Hong
2015-04-01
A growth mode was revealed by an in situ TEM study of nucleation and growth of Au on Pt icosahedral nanoparticles. Quantitative analysis of growth kinetics was carried out based on real-time TEM data, which shows the process involves: (1) deposition of Au on corner sites of Pt icosahedral nanoparticles, (2) diffusion of Au from corners to terraces and edges, and (3) subsequent layer-by-layer growth of Au on Au surfaces to form Pt@Au core-shell nanoparticles. The in situ TEM results indicate diffusion of Au from corner islands to terraces and edges is a kinetically controlled growth, as evidenced by a measurement of diffusion coefficients for these growth processes. We demonstrated that in situ electron microscopy is a valuable tool for quantitative study of nucleation and growth kinetics and can provide new insight into the design and precise control of heterogeneous nanostructures. PMID:25723499
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.
Reply to ``Comment on `Low-temperature lattice excitation of icosahedral Al-Mn-Pd quasicrystals' ''
NASA Astrophysics Data System (ADS)
Li, Cuilian; Liu, Youyan
2002-01-01
In response to the comment by Wang and Qin, we have rewritten our equation (22) following the coordinate system of Ding et al. [J. Wuhan Univ. (Nature Science Edition) 3, 23 (1992)]. According to the thermodynamic stability condition and the experiment of Capitan et al., we have chosen the new parameters of the phason elastic constants. Based on this, we have recalculated the coefficients of the expressions on the vibrational denty of states and the specific heat of the icosahedral Al-Mn-Pd quasicrystal. Our results are still in agreement with the experimental data measured by Wälti et al. [Phys. Rev. B 57, 10 504 (1998)]. It demonstrates that our method is useful for dealing with the low-temperature vibrational excitation of icosahedral quasicrystals.
Electron momentum distribution of icosahedral Cd84Yb16 studied by Compton scattering
NASA Astrophysics Data System (ADS)
Okada, J. T.; Watanabe, Y.; Nanao, S.; Tamura, R.; Takeuchi, S.; Yokoyama, Y.; Hiraoka, N.; Itou, M.; Sakurai, Y.
2003-10-01
The electron momentum distribution in icosahedral Cd84Yb16 has been studied using the high-resolution Compton scattering technique with a momentum resolution of 0.16 a.u. The experimental valence-electron Compton profile is decomposed into two components: an inverted parabolalike one and a broad Gaussian-like one. We have found that the Fermi sphere, deduced from the number of electrons under the inverted parabolalike component, just coincides with the quasi-Brillouin zones constructed from the intense (211111) and (221001) reciprocal points. The Gaussian-like part is attributed to the electron occupation of the Yb 5d states. These facts are taken as signature that both the Hume-Rothery mechanism and the sp-d hybridization mechanism contribute to the formation of the pseudogap, stabilizing the icosahedral phase of Cd84Yb16.
NASA Astrophysics Data System (ADS)
Lowe, M.; Yadav, T. P.; Fournée, V.; Ledieu, J.; McGrath, R.; Sharma, H. R.
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
Lowe, M; Yadav, T P; Fourne, V; Ledieu, J; McGrath, R; Sharma, H R
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol. PMID:25747095
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.
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.
Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole
NASA Astrophysics Data System (ADS)
Li, Lian-He
2013-11-01
The generalized 2D problem of icosahedral quasicrystals containing an elliptic hole is considered by using the extended Stroh formalism. The closed-form solutions for the displacements and stresses are obtained under general loading conditions. The solution of the Griffith crack problem as a special case of the results is also observed. The stress intensity factor and strain energy release rate are given. The effect of the phonon—phason coupling elastic constant on the mechanical behavior is also discussed.
A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, Jin
2013-11-01
The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM uses innovations in model formulation similar to its hydrostatic version of the Flow-following Icosahedral Model (FIM) developed by Earth System Research Laboratory (ESRL) which has been tested and accepted for future use by the National Weather Service as part of their operational global prediction ensemble. Innovations from the FIM used in the NIM include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, et al., 2010), * All differentials evaluated as finite-volume integrals around the cells, *Icosahedral grid optimization (Wang and Lee, 2011) NIM extends the two-dimensional finite-volume operators used in FIM into the three-dimensional finite-volume solvers designed to improve pressure gradient calculation and orographic precipitation over complex terrain. The NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as warm bubble, density current, internal gravity wave, and mountain waves. Physical parameterizations have been incorporated into the NIM dynamic core and successfully tested with multimonth aqua-planet simulations. Recent results from NIM simulations will be presented at the Symposium.
NASA Astrophysics Data System (ADS)
Tsai, An Pang
2008-04-01
We review the stability of various icosahedral quasicrystals (iQc) from a metallurgical viewpoint. The stability of stable iQcs is well interpreted in terms of Hume-Rothery rules, i.e. atomic size factor and valence electron concentration, e/a. For metastable iQcs, we discuss the role of phason disorder introduced by rapid solidification, in structural stability and its interplay with chemical order and composition. Invited paper.
Computational self-assembly of a one-component icosahedral quasicrystal.
Engel, Michael; Damasceno, Pablo F; Phillips, Carolyn L; Glotzer, Sharon C
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems. PMID:25485986
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
NASA Astrophysics Data System (ADS)
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.
Solution growth of a binary icosahedral quasicrystal of Sc[subscript 12]Zn[subscript 88
Canfield, P.C.; Caudle, M.L.; Ho, C.-S.; Kreyssig, A.; Nandi, S.; Kim, M.G.; Lin, X.; Kracher, A.; Dennis, K.W.; McCallum, R.W.; Goldman, A.I.
2010-07-23
We report the discovery of a binary icosahedral phase in a Sc-Zn alloy obtained through solution-growth, producing millimeter-sized, facetted, single grain quasicrystals that exhibit different growth morphologies, pentagonal dodecahedra, and rhombic triacontahedra, under only marginally different growth conditions. These two morphologies manifest different degrees of quasicrystalline order. The discovery of i-Sc{sub 12}Zn{sub 88} suggests that a re-examination of binary phase diagrams at compositions close to crystalline approximant structures may reveal other binary quasicrystalline phases.
Dynamical x-ray diffraction from an icosahedral Al-Pd-Mn quasicrystal
Kycia, S.
1996-04-23
Primary extinction effects in diffraction from single grains of Al-Pd- Mn, and presumably many other FCI alloys, may be significant and should be corrected for prior to use of diffraction data in structural determinations. Probes based on dynamical diffraction effects, such as x-ray standing wave fluorescence, multiple beam interference, and x-ray transmission topographs, may now be used to study the bulk and surface structure of some quasicrystals. The observation of dynamical diffraction from icosahedral Al-Pd-Mn is a striking confirmation of the fact that quasicrystals can present a degree of structural perfection comparable to that found in the best periodic intermetallic crystals.
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 electron microscope (TEM) images of viral particles before and after USP laser irradiation, the locations of weak structural links on the capsid of MNV-1 were revealed. This important information will greatly aid our understanding of the structure of non-enveloped, icosahedral viruses. We envision that this non-invasive, efficient viral eradication method will find applications in the disinfection of pharmaceuticals, biologicals and blood products in the near future. PMID:24495489
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.
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
A mass conservative semi-implicit scheme for the shallow water equations on an icosahedral grid
NASA Astrophysics Data System (ADS)
Bonaventura, L.
2003-04-01
A mass conservative, semi-implicit discretization for the vector invariant formulation of the shallow water equations on the sphere is introduced. These equations are discretized on a quasi-uniform, geodesic, icosahedral Voronoi-Delaunay grid (see e.g. [Heikes and Randall, 1995]) with a C-grid variable arrangement, according to the approach introduced in [Casulli and Walters, 2000]. A finite volume discretization is employed for the continuity equation in conservation law form, using as control volumes either the hexagonal/pentagonal or the dual triangular cells. The momentum equation is discretized with an extension of the approach introduced in [Lin and Rood, 1997] to semi-implicit time discretization on the icosahedral grid. Various possible treatments of the Coriolis force terms will be compared. Results obtained in standard shallow water test cases will be presented, along with an analysis of the discretization properties regarding conservation of energy and potential vorticity. This work is being carried out within the preliminary phase of the ICON research project, which involves, along with Max Planck Institut für Meteorologie Hamburg and the Deutscher Wetterdienst, PIK Potsdam, Freie Universität Berlin, Universität Bonn, Technische Universität München and various other research institutions (see the web page at the project site icon.enes.org). The aim of this project is the development of a unified nonhydrostatic model for global and regional climate simulation and weather forecasting.
NASA Astrophysics Data System (ADS)
Doronin, Yu. S.; Vakula, V. L.; Kamarchuk, G. V.; Tkachenko, A. A.; Samovarov, V. N.
2016-02-01
We propose a new approach to analyzing the cathodoluminescence spectra of free argon nanoclusters, forming in a supersonic jet flowing into vacuum. Based on this approach, we conduct an analysis of the intensities of the luminescence bands of neutral and charged excimer complexes (Ar2)* and (Ar+4)*, measured for clusters with an average size ranging from 500 to 8900 atoms per cluster, and a diameter of 32-87 Å. It is shown that the concentration of the substance condensed into clusters, which determines the integrated intensity of the bands, is proportional to the logarithm of the average size of the clusters in the jet. An analysis of the normalized intensities of the (Ar2)* and (Ar+4)* bands for crystalline clusters with an fcc structure allowed us to establish that the luminescence of neutral (Ar2)* molecules comes from within the volume of the cluster, while the charged complexes (Ar+4)* emit from the subsurface layer. We highlighted an area of cluster dimensions at which the jet is dominated by quasi-crystalline clusters with an icosahedral structure, and it is shown that the transition from icosahedral clusters to fcc structures occurs when the average size of the cluster in the jet is N ¯ = (1000-1800) atoms/cluster.
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
The Structure of the NTPase That Powers DNA Packaging into Sulfolobus Turreted Icosahedral Virus 2
Happonen, Lotta J.; Oksanen, Esko; Liljeroos, Lassi; Goldman, Adrian; Kajander, Tommi
2013-01-01
Biochemical reactions powered by ATP hydrolysis are fundamental for the movement of molecules and cellular structures. One such reaction is the encapsidation of the double-stranded DNA (dsDNA) genome of an icosahedrally symmetric virus into a preformed procapsid with the help of a genome-translocating NTPase. Such NTPases have been characterized in detail from both RNA and tailed DNA viruses. We present four crystal structures and the biochemical activity of a thermophilic NTPase, B204, from the nontailed, membrane-containing, hyperthermoacidophilic archaeal dsDNA virus Sulfolobus turreted icosahedral virus 2. These are the first structures of a genome-packaging NTPase from a nontailed, dsDNA virus with an archaeal host. The four structures highlight the catalytic cycle of B204, pinpointing the molecular movement between substrate-bound (open) and empty (closed) active sites. The protein is shown to bind both single-stranded and double-stranded nucleic acids and to have an optimum activity at 80°C and pH 4.5. The overall fold of B204 places it in the FtsK-HerA superfamily of P-loop ATPases, whose cellular and viral members have been suggested to share a DNA-translocating mechanism. PMID:23698307
Hierarchy of bond stiffnesses within icosahedral-based gold clusters protected by thiolates
NASA Astrophysics Data System (ADS)
Yamazoe, Seiji; Takano, Shinjiro; Kurashige, Wataru; Yokoyama, Toshihiko; Nitta, Kiyofumi; Negishi, Yuichi; Tsukuda, Tatsuya
2016-01-01
Unique thermal properties of metal clusters are believed to originate from the hierarchy of the bonding. However, an atomic-level understanding of how the bond stiffnesses are affected by the atomic packing of a metal cluster and the interfacial structure with the surrounding environment has not been attained to date. Here we elucidate the hierarchy in the bond stiffness in thiolate-protected, icosahedral-based gold clusters Au25(SC2H4Ph)18, Au38(SC2H4Ph)24 and Au144(SC2H4Ph)60 by analysing Au L3-edge extended X-ray absorption fine structure data. The Au-Au bonds have different stiffnesses depending on their lengths. The long Au-Au bonds, which are more flexible than those in the bulk metal, are located at the icosahedral-based gold core surface. The short Au-Au bonds, which are stiffer than those in the bulk metal, are mainly distributed along the radial direction and form a cyclic structural backbone with the rigid Au-SR oligomers.
Some investigations of symmetry and extremal properties of molecular electron momentum densities
NASA Astrophysics Data System (ADS)
Gadre, Shridhar R.; Limaye, Ajay C.; Kulkarni, Sudhir A.
1991-06-01
It is known that the molecular electron momentum density γ(p) is inversion symmetric. In this article, the generalized repercussions of this fact on the symmetries of γ(p) are discussed. A comprehensive study of the symmetry transformation from positional to momentum density due to the introduction of inversion operator i in the symmetry point group of a molecular system (in r space) has been presented. The symmetry enhancement in C3v and Td point groups is brought out via the respective electron momentum density contour maps. Further, the extremal properties of γ(p) have been studied for CH4, H2O, HCN, NH3, C2H2, C2H4, C2H6, and CO molecules. The local maxima are observed at p=0 and elsewhere, whereas the minima and saddle points are invariably found to be at p=0 for the molecules studied here.
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.
The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, J. L.; MacDonald, A. E.
2014-12-01
A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP. Physical parameterizations such as those used by GFS have been incorporated into NIM dynamic core and successfully tested with multi-months aqua-planet simulations as well as real data simulations. NIM has been implemented on GPUs and CPUs. Efficiency tests show GPU significantly speeds up model calculations.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Neutrinos and flavor symmetries
Tanimoto, Morimitsu
2015-07-15
We discuss the recent progress of flavor models with the non-Abelian discrete symmetry in the lepton sector focusing on the θ{sub 13} and CP violating phase. In both direct approach and indirect approach of the flavor symmetry, the non-vanishing θ{sub 13} is predictable. The flavor symmetry with the generalised CP symmetry can also predicts the CP violating phase. We show the phenomenological analyses of neutrino mixing for the typical flavor models.
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…
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or
Chiral symmetry and chiral-symmetry breaking
Peskin, M.E.
1982-12-01
These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)
NASA Astrophysics Data System (ADS)
Saida, Junji; Inoue, Akihisa
2001-01-01
It is found that an icosahedral quasicrystalline phase is formed in the Zr-Al-Ni-Cu glassy alloy by addition of Nb, Ta or V elements. The icosahedral phase was confirmed as a primary precipitation phase in the melt-spun Zr65Al7.5Ni10Cu12.5X5 (X=Nb, Ta or V) glassy alloys with a two-stage crystallization process after the distinct glass transition. The onset temperature of the transformation from glass to icosahedral phase is 705 K for Nb, 710 K for Ta and 702 K for V at the heating rate of 0.67 Ks-1. The size of the icosahedral particles is in the range of 10 to 50 nm. The second crystallization reaction results in the formation of Zr2Cu + Zr2Ni + Zr3Al2 phases through a sharp exothermic reaction. The formation of a nano scale icosahedral phase in the Zr-Al-Ni-Cu glassy alloy by addition of Nb, Ta or V, as well as noble metals, indicates that the increase of the nucleation rate contributes to the precipitation of the icosahedral phase, leading to the concept that the icosahedral short-range order exists in the glassy state in the Zr-Al-Ni-Cu alloy.
Thermal Conductivity and Seebeck Coefficients of Icosahedral Boron Arsenide Films on Silicon Carbide
Y Gong; Y Zhang; M Dudley; Y Zhang; J Edgar; P Heard; M Kuball
2011-12-31
The thermal conductivity of icosahedral boron arsenide (B{sub 12}As{sub 2}) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3{omega} technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 {micro}V/K and 136 {micro}V/K for samples grown at 1350 C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Terrace-dependent nucleation of small Ag clusters on a five-fold icosahedral quasicrystal surface
Unal, B.; Evans, J.W.; Lograsso, T.A.; Ross, A.R.; Jenks, C.J.; Thiel, P.A.
2007-07-21
Nucleation of Ag islands on the five-fold surface of icosahedral Al-Pd-Mn is influenced strongly by trap sites. Submonolayers of Ag prepared by deposition at 365 K and with a flux of 1 x 10{sup -3} monolayers/s exhibit a variation in Ag island densities across different terraces. Comparisons with previous work and with rate equation analysis indicate that trap sites are not saturated under these experimental conditions and that the difference in island densities is not necessarily due to variation in trap densities. While it could have a number of different origins, our results point to a terrace-dependent value of the effective diffusion barrier for Ag adatoms.
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
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.
Zhang, Xing; Zhou, Z. Hong; Baker, Timothy S.
2014-01-01
In cryo-electron microscopy and single particle analysis, data acquisition and image processing are generally carried out in sequential steps and computation of a three-dimensional reconstruction only begins once all the micrographs have been acquired. We are developing an integrated system for processing images of icosahedral particles during microscopy to provide reconstructed density maps in real-time at the highest possible resolution. The system is designed as a combination of pipelines to run in parallel on a computer cluster and analyzes micrographs as they are acquired, handling automatically all the processing steps from defocus estimation and particle picking to origin/orientation determination. An ab-initio model is determined independently from the first micrographs collected, and new models are generated as more particles become available. As a proof of concept, we simulated data acquisition sessions using three sets of micrographs of good to excellent quality that were previously recorded from different icosahedral viruses. Results show that the processing of single micrographs can keep pace with an acquisition rate of about two images per minute. The reconstructed density map improves steadily during the image acquisition phase and its quality at the end of data collection is only moderately inferior to that obtained by expert users who processed semi-automatically all the micrographs after the acquisition. The current prototype demonstrates the advantages of integrating three-dimensional image processing with microscopy, which include an ability to monitor acquisition in terms of the final structure and to predict how much data and microscope resources are needed to achieve a desired resolution. PMID:24613762
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-01-01
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 μm in diameter and adenine–thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 μm in length and guanine–cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 μm in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590
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.
Symmetries in BF and HAADF STEM image calculations.
Watanabe, K; Asano, E; Yamazaki, T; Kikuchi, Y; Hashimoto, I
2004-12-01
Reductions in bright-field (BF) scanning transmission electron microscopy (STEM) and high-angle annular dark-field (HAADF) STEM image calculations with the aid of Bloch wave symmetry are discussed under assumptions that an absorption potential is written by a local potential and a zero-order Laue zone lies parallel to the crystal surface. Translational symmetry allows us to take only partial incident beams in the first Brillouin zone instead of enormous number of partial incident beams in a large convergent disk. Two dimensional point group confines partial incident beams to an irreducible area in addition to factoring a dispersion matrix into noninteracting submatrices on a high symmetry line using the projection operator. The drastic reductions in computing time and memory enable us to readily calculate various BF STEM and HAADF STEM images. The validity and accuracy are demonstrated in comparisons with high resolution experimental BF STEM and HAADF STEM images. PMID:15556696
Baryogenesis from symmetry principle
NASA Astrophysics Data System (ADS)
Fong, Chee Sheng
2016-01-01
In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario and also to identify the different roles played by the symmetry. This formalism is then applied to the standard model and its supersymmetric extension, which constitute two important foundations for constructing models of baryogenesis.
Pauling, Linus
1988-01-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, “noise”) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals. PMID:16593948
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.
Jaakkola, Salla T.; Penttinen, Reetta K.; Vilén, Silja T.; Jalasvuori, Matti; Rönnholm, Gunilla; Bamford, Jaana K. H.; Bamford, Dennis H.
2012-01-01
Studies on viral capsid architectures and coat protein folds have revealed the evolutionary lineages of viruses branching to all three domains of life. A widespread group of icosahedral tailless viruses, the PRD1-adenovirus lineage, was the first to be established. A double β-barrel fold for a single major capsid protein is characteristic of these viruses. Similar viruses carrying genes coding for two major capsid proteins with a more complex structure, such as Thermus phage P23-77 and haloarchaeal virus SH1, have been isolated. Here, we studied the host range, life cycle, biochemical composition, and genomic sequence of a new isolate, Haloarcula hispanica icosahedral virus 2 (HHIV-2), which resembles SH1 despite being isolated from a different location. Comparative analysis of these viruses revealed that their overall architectures are very similar except that the genes for the receptor recognition vertex complexes are unrelated even though these viruses infect the same hosts. PMID:22357274
Zlotnick, A; Palmer, I; Kaufman, J D; Stahl, S J; Steven, A C; Wingfield, P T
1999-03-01
The icosahedral nucleocapsid of human hepatitis B virus is a homopolymer of the dimeric capsid protein also known as hepatitis B core antigen or HBcAg. Purified capsid protein obtained from an Escherichia coli expression system was reassembled into a mixture of T = 3 and T = 4 icosahedral particles consisting of 90 and 120 dimers, respectively. The two types of capsid were separated on a preparative scale by centrifugation through a sucrose gradient. In addition to this heterogeneity, the capsid protein has three cysteines, one of which has a great propensity for forming disulfide bonds between the two subunits, forming a dimer. To eliminate heterogeneity arising from oxidation, alanines were substituted for the cysteines. T = 3 and T = 4 capsids crystallized under similar conditions. Crystals of T = 3 capsids diffracted to approximately 8 A resolution; crystals of T = 4 capsids diffracted to 4 A resolution. PMID:10089479
Nogi, Naoyuki . E-mail: nnogi@tkg.att.ne.jp; Tanaka, Satoru
2006-09-15
Computational calculations of Becke's three-parameter hybrid method using the LYP correlation functional (B3LYP) have been performed on (B{sub 12}H{sub 12}){sup 2-} dodecaborane anions with different boron isotopic compositions. This was done in order to investigate isotopic dependence of vibrational spectral properties of B{sub 12} icosahedra, and for comparison of the optical vibrational properties of the icosahedral molecule with the characteristics of inter- or intra-icosahedral optical phonon vibrational modes in boron-rich crystals. - Graphical abstract: Calculated Raman spectra of the {l_brace}({sup 10}B{sub 6} {sup 11}B{sub 6})(H{sub 6}T{sub 6}){r_brace}{sup 2} anion (f)-(g) with same isotope ratio. Tritium, T atoms were arranged in the {sup 10}B atoms with a rhombohedral arrangement (f) and an equatorial (g)
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-02-13
It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures-and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body-bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body-bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains. PMID:24379431
Jaatinen, S T; Happonen, L J; Laurinmäki, P; Butcher, S J; Bamford, D H
2008-09-15
Icosahedral dsDNA viruses isolated from hot springs and proposed to belong to the Tectiviridae family infect the gram-negative thermophilic Thermus thermophilus bacterium. Seven such viruses were obtained from the Promega Corporation collection. The structural protein patterns of three of these viruses, growing to a high titer, appeared very similar but not identical. The most stable virus, P23-77, was chosen for more detailed studies. Analysis of highly purified P23-77 by thin layer chromatography for neutral lipids showed lipid association with the virion. Cryo-EM based three-dimensional image reconstruction of P23-77 to 1.4 nm resolution revealed an icosahedrally-ordered protein coat, with spikes on the vertices, and an internal membrane. The capsid architecture of P23-77 is most similar to that of the archaeal virus SH1. These findings further complicate the grouping of icosahedrally-symmetric viruses containing an inner membrane. We propose a single superfamily or order with members in several viral families. PMID:18657283
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
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.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged
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.
Prevelige, P E; Thomas, D; King, J
1993-01-01
The polymerization of protein subunits into precursor shells empty of DNA is a critical process in the assembly of double-stranded DNA viruses. For the well-characterized icosahedral procapsid of phage P22, coat and scaffolding protein subunits do not assemble separately but, upon mixing, copolymerize into double-shelled procapsids in vitro. The polymerization reaction displays the characteristics of a nucleation limited reaction: a paucity of intermediate assembly states, a critical concentration, and kinetics displaying a lag phase. Partially formed shell intermediates were directly visualized during the growth phase by electron microscopy of the reaction mixture. The morphology of these intermediates suggests that assembly is a highly directed process. The initial rate of this reaction depends on the fifth power of the coat subunit concentration and the second or third power of the scaffolding concentration, suggesting that pentamer of coat protein and dimers or trimers of scaffolding protein, respectively, participate in the rate-limiting step. Images FIGURE 4 PMID:8471727
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.
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.
Lee, Kelly K; Tang, Jinghua; Taylor, Derek; Bothner, Brian; Johnson, John E
2004-07-01
Nudaurelia omega capensis virus (N omega V) capsids were previously characterized in two morphological forms, a T=4, 485-A-diameter round particle with large pores and a tightly sealed 395-A icosahedrally shaped particle with the same quasi-symmetric surface lattice. The large particle converts to the smaller particle when the pH is lowered from 7.6 to 5, and this activates an autocatalytic cleavage of the viral subunit at residue 570. Here we report that both 1-anilino-8 naphthalene sulfonate (ANS) and the covalent attachment of the thiol-reactive fluorophore, maleimide-ANS (MIANS), inhibit the structural transition and proteolysis at the lower pH. When ANS is exhaustively washed from the particles, the maturation proceeds normally; however, MIANS-modified particles are still inhibited after the same washing treatment, indicating that covalent attachment targets MIANS to a critical location for inhibition. Characterization of the low-pH MIANS product by electron cryo-microscopy (cryo-EM) and image reconstruction demonstrated a morphology intermediate between the two forms previously characterized. A pseudoatomic model of the intermediate configuration was generated by rigid body refinement of the X-ray structure of the subunits (previously determined in the assembled capsid) into the cryo-EM density, allowing a quantitative description of the inhibited intermediate and a hypothesis for the mechanism of the inhibition. PMID:15194797
Lee, Kelly K.; Tang, Jinghua; Taylor, Derek; Bothner, Brian; Johnson, John E.
2004-01-01
Nudaurelia ? capensis virus (N?V) capsids were previously characterized in two morphological forms, a T=4, 485--diameter round particle with large pores and a tightly sealed 395- icosahedrally shaped particle with the same quasi-symmetric surface lattice. The large particle converts to the smaller particle when the pH is lowered from 7.6 to 5, and this activates an autocatalytic cleavage of the viral subunit at residue 570. Here we report that both 1-anilino-8 naphthalene sulfonate (ANS) and the covalent attachment of the thiol-reactive fluorophore, maleimide-ANS (MIANS), inhibit the structural transition and proteolysis at the lower pH. When ANS is exhaustively washed from the particles, the maturation proceeds normally; however, MIANS-modified particles are still inhibited after the same washing treatment, indicating that covalent attachment targets MIANS to a critical location for inhibition. Characterization of the low-pH MIANS product by electron cryo-microscopy (cryo-EM) and image reconstruction demonstrated a morphology intermediate between the two forms previously characterized. A pseudoatomic model of the intermediate configuration was generated by rigid body refinement of the X-ray structure of the subunits (previously determined in the assembled capsid) into the cryo-EM density, allowing a quantitative description of the inhibited intermediate and a hypothesis for the mechanism of the inhibition. PMID:15194797
Icosahedral quasicrystals in Zn-T-Sc (T = Mn, Fe, Co or Ni) alloys
NASA Astrophysics Data System (ADS)
Maezawa, Ryo; Kashimoto, Shiro; Ishimasa, Tsutomu
2004-04-01
Starting from the Zn17Sc3 cubic approximant, new quasicrystal alloys were sought by replacement of Zn with transition elements T. In the cases when T = Mn, Fe, Co and Ni, new icosahedral quasicrystals are formed in as-cast alloys as major phases at alloy compositions of Zn75T10Sc15. All these quasicrystals belong to a primitive type and have six-dimensional lattice parameters a6D ranging from 7.044 to 7.107 Å. They have valence electron concentrations e/a ranging from 2.01 to 2.14, and almost the same ratios between the edge length aR of the Penrose tile and the averaged atomic diameter
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.
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.
NASA Astrophysics Data System (ADS)
Lam, C. S.
2007-11-01
Neutrino mixing is studied from a symmetry perspective, both bottom-up and top-down. In the bottom-up approach, we start from the tri-bimaximal mixing, or one of its three partial patterns, and construct a list of horizontal symmetry groups capable of reproducing the mixing without adjustment of parameters. This list, labeled by an integer n ⩾ 3, is explicitly calculated for n = 3. In the top-down approach, we start from any finite group possessing a three-dimensional irreducible representation and an order-2 element, give a recipe to determine what mixing pattern it contains, and how to construct a dynamical model to reveal a particular mixing. Finally, we point out that if quark mixing is controlled by symmetry in this way, then there is an exciting possibility to determine most of the CKM mixing parameters by symmetry alone.
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.
Pauling, Linus
1988-01-01
Single-grain precession x-ray diffraction photographs of Al6CuLi3 have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 Å, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the β-W arrangement. In this compound two of the clusters consist of 104 atoms and six consist of 136 atoms, with 24 atoms shared. The same structure is assigned to the C-phase, Al37Cu3Li21Mg3, and to GaMg2Zn3. A theory of icosahedral quasicrystals and amorphous metals is described. PMID:16593929
Superconductivity and symmetry breaking
NASA Astrophysics Data System (ADS)
Sarasua, L. G.
2012-02-01
In the present work we consider the relation between superconductivity and spontaneous gauge symmetry breaking (SGBS). We show that ODLRO does not require in principle SBGS, even in the presence of particle number fluctuations, by examining exact solutions of a fermionic pairing model. The criteria become equivalent if a symmetry breaking field is allowed, which can be attributed to the interaction with the environment. However, superconducting states without SBGS are not forbidden.
Pauling, Linus
1988-01-01
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
NASA Astrophysics Data System (ADS)
Lee, G. W.; Gangopadhyay, A. K.; Croat, T. K.; Rathz, T. J.; Hyers, R. W.; Rogers, J. R.; Kelton, K. F.
2005-11-01
Comprehensive undercooling experiments on a large number of simple crystalline, polytetrahedral, and icosahedral quasicrystalline phase forming compositions in Ti-Zr-Ni alloys have been carried out using electrostatic levitation (ESL) techniques for containerless processing. Consistent with Frank’s hypothesis, a direct correlation was found between the reduced undercooling [ ΔTr=(Tl-Tr)/Tl , where Tr and Tl are the nucleation and liquidus temperatures, respectively] and the icosahedral short-range order in the solid. The reduced undercooling is less for liquids that form the icosahedral quasicrystal ( i phase) than for those that form the hcp C14 Laves polytetrahedral phase. For many compositions near 21at.% Ni, the primary nucleation of a metastable i phase instead of a stable C14 Laves phase demonstrates that the interfacial free energy between the liquid and the i phase is smaller than between the liquid and the C14 Laves phase, indicating icosahedral local order in the undercooled liquid. This is in agreement with a classical-nucleation-theory-based estimate of the interfacial free energy and the work of formation of the critical cluster from the undercooling data. Taken together with high-energy x-ray diffraction studies of the undercooled liquid, these results demonstrate that the local structure of liquids in Ti-Zr-Ni alloys is icosahedral, as postulated by Frank over a half century ago.
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.
Disorder and complexity in the atomic structure of the perfect icosahedral alloy of Al-Pd-Mn
de Boissieu, M.; Stephens, P. ); Boudard, M.; Janot, C. ); Chapman, D.L. ); Audier, M. )
1994-05-30
The atomic structure of the perfect Al-Pd-Mn icosahedral phase has been studied on single grain samples. Using anomalous x-ray diffraction close to the Pd edge, the partial structure factor [ital F][sub Pd] has been extracted. In the six-dimensional description of its structure, we find that the atomic surface cannot be described by an object with a sharp boundary. A phason Debye-Waller term has been introduced to fully account for the data. It is interpreted as resulting from random phason disorder and nonsphericity of the atomic surfaces.
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.
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)
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 =|
Seeing Science through Symmetry
NASA Astrophysics Data System (ADS)
Gould, L. I.
Seeing Through Symmetry is a course that introduces non-science majors to the pervasive influence of symmetry in science. The concept of symmetry is usedboth as a link between subjects (such as physics, biology, mathematics, music, poetry, and art) and as a method within a subject. This is done through the development and use of interactive multimedia learning environments to stimulate learning. Computer-based labs enable the student to further explore the concept by being gently led from the arts to science. This talk is an update that includes some of the latest changes to the course. Explanations are given on methodology and how a variety of interactive multimedia tools contribute to both the lecture and lab portion of the course (created in 1991 and taught almost every semester since then, including one in Sweden).
NASA Astrophysics Data System (ADS)
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
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)
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, ?, ? and ? particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction onlythis is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would have to be rather clever to recognize that the particle interactions were rotationally invariant. Nambu and Goldstone showed that the spontaneous breakdown of a (continuous) symmetry implied the existence of massless scalar particles, referred to as Nambu Goldstone bosons, or simply Goldstone bosons. Meanwhile Anderson, in his study of (non-relativistic) superconductivity, showed that the exclusion of magnetic flux (Meissner effect) corresponds to a finite range for the electromagnetic field and hence to a `massive photon'. In a relativistic context Englert, Brout, Guralnik and more particularly Higgs showed that a spontaneous breaking of a gauge symmetry resulted in a massive, instead of a massless, gauge particle and no Goldstone particle; in the jargon of the day, the massless gauge particle had `eaten' the massless Goldstone boson and become massive; exactly Anderson's observation. It is this phenomenon which has been invoked so successfully to explain the masses of the W and Z bosons of weak interactions. Spontaneous symmetry breaking, therefore, has played a major role in the development of the Standard Model of particle physics, and it has also proved an important tool in condensed matter physics, for example in the understanding of phase transitions. At the same time, however, in the understanding of most (or all) particle physicists, and perhaps also condensed matter physicists, the notion of spontaneous symmetry breaking has been inexorably linked to that of a degenerate vacuum. This is the background and the starting point for Strocchi's book. Recognizing the power and importance of the concept of spontaneous symmetry breaking in theoretical physics, he defines it in a more refined and general way than usual. `Despite the many popular accounts', he writes, `the phenomenon of spontaneous symmetry breaking is deep and subtle and it is not without [reason] that it has been fully understood only in recent times.' Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the existence of non-symmetric ground states and the infinite extension of the system. The book is divided into two parts, treating respectively the classical and quantum regimes. In classical field theory the symmetry breaking is explained in terms of the occurrence of disjoint sectors, or different phases, of a physical system. In the quantum regime the mechanism is characterized by a symmetry breaking order parameter, for which non-perturbative criteria are discussed, following the work of Wightman, in contrast to the usual Goldstone perturbative strategy. Strocchi's main interest is in condensed matter, rather than particle, physics, and the topics he covers include spin systems, Fermi and Bose gases and finite temperature field theory. The book is based on lectures given over a number of years. It is written in a pleasing style at a level suitable for graduate students in theoretical physics. While mathematically proper, it is not forbidding for a physics readership; the author is always aware this subject is a branch of physics. It should make profitable reading for many theoretical physicists.
Weakly broken galileon symmetry
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar 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.
Baker, T. S.; Olson, N. H.; Fuller, S. D.
1999-01-01
Viruses are cellular parasites. The linkage between viral and host functions makes the study of a viral life cycle an important key to cellular functions. A deeper understanding of many aspects of viral life cycles has emerged from coordinated molecular and structural studies carried out with a wide range of viral pathogens. Structural studies of viruses by means of cryo-electron microscopy and three-dimensional image reconstruction methods have grown explosively in the last decade. Here we review the use of cryo-electron microscopy for the determination of the structures of a number of icosahedral viruses. These studies span more than 20 virus families. Representative examples illustrate the use of moderate- to low-resolution (7- to 35-Å) structural analyses to illuminate functional aspects of viral life cycles including host recognition, viral attachment, entry, genome release, viral transcription, translation, proassembly, maturation, release, and transmission, as well as mechanisms of host defense. The success of cryo-electron microscopy in combination with three-dimensional image reconstruction for icosahedral viruses provides a firm foundation for future explorations of more-complex viral pathogens, including the vast number that are nonspherical or nonsymmetrical. PMID:10585969
Larson, Eric T; Reiter, Dirk; Young, Mark; Lawrence, C Martin
2006-08-01
Sulfolobus turreted icosahedral virus (STIV) was the first icosahedral virus characterized from an archaeal host. It infects Sulfolobus species that thrive in the acidic hot springs (pH 2.9 to 3.9 and 72 to 92 degrees C) of Yellowstone National Park. The overall capsid architecture and the structure of its major capsid protein are very similar to those of the bacteriophage PRD1 and eukaryotic viruses Paramecium bursaria Chlorella virus 1 and adenovirus, suggesting a viral lineage that predates the three domains of life. The 17,663-base-pair, circular, double-stranded DNA genome contains 36 potential open reading frames, whose sequences generally show little similarity to other genes in the sequence databases. However, functional and evolutionary information may be suggested by a protein's three-dimensional structure. To this end, we have undertaken structural studies of the STIV proteome. Here we report our work on A197, the product of an STIV open reading frame. The structure of A197 reveals a GT-A fold that is common to many members of the glycosyltransferase superfamily. A197 possesses a canonical DXD motif and a putative catalytic base that are hallmarks of this family of enzymes, strongly suggesting a glycosyltransferase activity for A197. Potential roles for the putative glycosyltransferase activity of A197 and their evolutionary implications are discussed. PMID:16840342
Kalko, S G; Cachau, R E; Silva, A M
1992-01-01
An analysis of the crystallographically determined structures of the icosahedral protein coats of Tomato Bushy Stunt Virus, Southern Bean Mosaic Virus, Satellite Tobacco Necrosis Virus, Human Rhinovirus 14 and Mengovirus around their fivefold axes is presented. Accessibilities surfaces, electrostatic energy profile calculations, ion-protein interaction energy calculations, free energy perturbation methods and comparisons with structures of chelating agents are used in this study. It is concluded that the structures built around the viral fivefold axes would be adequate for ion binding and transport. Relative ion preferences are derived for the binding sites, using free energy perturbation methods, which are consistent with the experimental data when available. In the cases where crystallographic studies determined the existence of ions on the fivefold axes, our results indicate that they would correspond to ions in crystallization or purification buffers. The environment of the fivefold axes are rich in polar residues in all icosahedral viral structures whose atomic coordinates are available, including some that are not being analyzed in detail in this work. The fivefold channel-like structures have most of the basic properties expected for real ion channels including a funnel at the entrance, a polar internal environment with frequent alternation of acidic and basic residues, ion binding sites, the capability to induce ion dehydration and ion transit from the external viral surface to the binding sites. Images FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7 PMID:1384743
Nanoscale icosahedral packing in amorphous Mg50Ni50: An ab initio study
NASA Astrophysics Data System (ADS)
Tetik, Erkan; Durandurdu, Murat; Karadağ, Faruk
2012-10-01
We present the atomic structure of amorphous Mg50Ni50 alloy based on an ab initio molecular-dynamics method. Our simulation reveals that Ni atoms form predominantly perfect or defective icosahedrons and a non-negligible amount of low coordinated prism-like structures. An ordered icosahedrons packing with a hexagonal symmetry is also observed in the model. The physical origin of a low activation energy for the crystallization and better hydrogenation in amorphous Mg50Ni50 is discussed.
NASA Astrophysics Data System (ADS)
Li, Lian He; You Fan, Tian
2006-11-01
The plane elasticity equations of two-dimensional quasicrystals of point group 10 are reduced to a single partial differential equation with eighth order by introducing a stress potential function. Further, we develop the complex variable function method for classical elasticity theory to that of the quasicrystals. The complex representations of stress and displacement components of phonon and phason fields in the quasicrystals are given. With the help of conformal transformation, an exact solution for the elliptic notch of the quasicrystals is presented. The solution of the Griffith crack problem as a special case of the results is also observed. This work shows that the stress potential and complex variable function methods are powerful for solving the complicated boundary value problems of higher order partial differential equations originating from quasicrystal elasticity.
Symmetry constraint for foreground extraction.
Fu, Huazhu; Cao, Xiaochun; Tu, Zhuowen; Lin, Dongdai
2014-05-01
Symmetry as an intrinsic shape property is often observed in natural objects. In this paper, we discuss how explicitly taking into account the symmetry constraint can enhance the quality of foreground object extraction. In our method, a symmetry foreground map is used to represent the symmetry structure of the image, which includes the symmetry matching magnitude and the foreground location prior. Then, the symmetry constraint model is built by introducing this symmetry structure into the graph-based segmentation function. Finally, the segmentation result is obtained via graph cuts. Our method encourages objects with symmetric parts to be consistently extracted. Moreover, our symmetry constraint model is applicable to weak symmetric objects under the part-based framework. Quantitative and qualitative experimental results on benchmark datasets demonstrate the advantages of our approach in extracting the foreground. Our method also shows improved results in segmenting objects with weak, complex symmetry properties. PMID:23797312
ERIC Educational Resources Information Center
Renshaw, Barbara S.
1986-01-01
Trademark designs provide a familiar yet innovative way for students to look at a number of mathematical concepts. How line and rotational symmetry can be presented using trademarks is the focus of this article. The emphasis is on the design of bulletin boards. (MNS)
Dynamical (super) symmetry breaking
Murayama, Hitoshi
2000-10-03
Dynamical Symmetry Breaking (DSB) is a concept theoristsrely on very often in the discussions of strong dynamics, model building,and hierarchy problems. In this talk, I will discuss why this is such apermeating concept among theorists and how they are used in understandingphysics. I also briefly review recent progress in using dynamicalsymmetry breaking to construct models of supersymmetry breaking andfermion masses.
Introduction to chiral symmetry
Koch, V.
1996-01-08
These lectures are an attempt to a pedagogical introduction into the elementary concepts of chiral symmetry in nuclear physics. Effective chiral models such as the linear and nonlinear sigma model will be discussed as well as the essential ideas of chiral perturbation theory. Some applications to the physics of ultrarelativistic heavy ion collisions will be presented.
ERIC Educational Resources Information Center
Seidel, Judith Day
1998-01-01
Presents activities that demonstrate how technology can help students discover the mathematics in nature. Claims that these experiences can clarify students' vision of the symmetry of beauty that fills the world beyond the computer. Concludes that the use of flexible software tools helps students explore how a shape is affected when they change…
Binary tetrahedral flavor symmetry
NASA Astrophysics Data System (ADS)
Eby, David A.
A study of the T' Model and its variants utilizing Binary Tetrahedral Flavor Symmetry. We begin with a description of the historical context and motivations for this theory, together with some conceptual background for added clarity, and an account of our theory's inception in previous works. Our model endeavors to bridge two categories of particles, leptons and quarks, a unification made possible by the inclusion of additional Higgs particles, shared between the two fermion sectors and creating a single coherent system. This is achieved through the use of the Binary Tetrahedral symmetry group and an investigation of the Tribimaximal symmetry evidenced by neutrinos. Our work details perturbations and extensions of this T' Model as we apply our framework to neutrino mixing, quark mixing, unification, and dark matter. Where possible, we evaluate model predictions against experimental results and find excellent matching with the atmospheric and reactor neutrino mixing angles, an accurate prediction of the Cabibbo angle, and a dark matter candidate that remains outside the limits of current tests. Additionally, we include mention of a number of unanswered questions and remaining areas of interest for future study. Taken together, we believe these results speak to the promising potential of finite groups and flavor symmetries to act as an approximation of nature.
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.
On group Fourier analysis and symmetry preserving discretizations of PDEs
NASA Astrophysics Data System (ADS)
Munthe-Kaas, H. Z.
2006-05-01
In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie group- and exponential-time integrators for differential equations, we will in the first part of the paper present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetric PDEs, where the discretization preserves the 120 symmetries of the icosahedral group. This motivates the study of spectral element discretizations based on triangular subdivisions. In the second part of the paper, we introduce novel applications of multivariate non-separable Chebyshev polynomials in the construction of spectral element bases on triangular and simplicial sub-domains. These generalized Chebyshev polynomials are intimately connected to the theory of root systems and Weyl groups (used in the classification of semi-simple Lie algebras), and these polynomials share most of the remarkable properties of the classical Chebyshev polynomials, such as near-optimal Lebesgue constants for the interpolation error, the existence of FFT-based algorithms for computing interpolants and pseudo-spectral differentiation and existence of Gaussian integration rules. The two parts of the paper can be read independently.
Symmetry in Logos and Hubcaps.
ERIC Educational Resources Information Center
Gallian, Joseph A.
1990-01-01
Described is a way to illustrate cyclic and dihedral groups through symmetry using corporate logos and hubcaps. Examples of the different kinds of symmetry groups are explained in terms of Leonardo's Theorem. (KR)
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…
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.
Cluster Symmetries and Dynamics
NASA Astrophysics Data System (ADS)
Freer, Martin
2016-03-01
Many light nuclei display behaviour that indicates that rather than behaving as an A-body systems, the protons and neutrons condense into clusters. The α-particle is the most obvious example of such clustering. This contribution examines the role of such α-clustering on the structure, symmetries and dynamics of the nuclei 8Be, 12C and 16O, recent experimental measurements and future perspectives.
Sharma, H. R. Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.; Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577
2014-05-07
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C{sub 60} on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C{sub 60} molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C{sub 60} molecules atop the Pb islands approaches zero, regardless of the overall C{sub 60} coverage.
Sharma, H R; Smerdon, J A; Nugent, P J; Ribeiro, A; McLeod, I; Dhanak, V R; Shimoda, M; Tsai, A P; McGrath, R
2014-05-01
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage. PMID:24811658
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
Boissieu, M. de; Francoual, S.; Kaneko, Y.; Ishimasa, T.
2005-09-02
We report on the absolute scale measurement of the x-ray diffuse scattering in the ZnMgSc icosahedral quasicrystal and its periodic approximant. Whereas the diffuse scattering in the approximant is purely accounted for by thermal diffuse scattering, an additional signal is observed in the quasicrystal. It is related to phason fluctuations as indicated by its Q{sub per}{sup 2} dependence. Moreover, when compared to previous measurements carried out on the i-AlPdMn phase, we find that the amount of diffuse scattering is smaller in the i-ZnMgSc phase, in agreement with larger phason elastic constants in this phase. This is confirmed by the observation of a large number of weak Bragg peaks having a high Q{sub per} reciprocal space component.
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.
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.
Applications of chiral symmetry
NASA Astrophysics Data System (ADS)
Davoudiasl, Hooman
We study some applications of the chiral symmetry of quantum chromodynamics in treating phenomena involving hadrons at low energies, where perturbative methods are not valid. We begin by introducing the concepts of global symmetry breaking and the consequent generation of Goldstone bosons. It is shown how these concepts are realized through chiral symmetry breaking and provide an understanding of some of the features of strong interactions at low energies. This leads us to the chiral perturbation theory effective Lagrangian for the low energy interactions of the light pseudo-scalars. We use this effective Lagrangian, and the considerations that led to it, as the basis of our approach in studying three different problems. First, we find the rates for the τ lepton decays /tau /to V/pi/nu/sb/tau, where V stands for /rho,/ K*, or ω, and extract the magnitude of the ρomega/pi coupling, /vert g2(/rho)/vert = 0.6. Next, we use this coupling to find the decay rate for D0/to /bar K*0/pi/sp- e+/nu/sb/varepsilon, in a certain kinematic regime. This rate depends on the DD*/pi coupling and our results can provide an extraction of this coupling, given data on this decay. The third problem we address is that of finding solutions that represent the qualitative behavior of the disoriented chiral condensate in the non- linear sigma model at [/cal O](p4). We show that these solutions do not become singular at short distances where the [/cal O](p2) solutions begin to diverge.
Symmetry and perturbation theory
NASA Astrophysics Data System (ADS)
Gaeta, Giuseppe
A co-chain map for the G invariant De Rham complex -- New examples of trihamiltonian structures linking different Lenard chains -- Wave propagation in an elastic medium: GDS equations -- Parametric excitation in nonlinear dynamics -- Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 -- The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems -- Shadowing chains of collision orbits for the elliptic 3-body problem -- Similarity reductions of an optical model -- Fold, transcritical and pitchfork singularities for time-reversible systems -- Homographic three-body motions with positive and negative masses -- Remarks on conformal Killing tensors and separation of variables -- A regularity theory for optimal partition problems -- Lambda and mu-symmetries -- Potential symmetries and linearization of some evolution equations -- Periodic solutions for zero mass nonlinear wave equations -- Fundamental covariants in the invariant theory of Killing tensors -- Global geometry of 3-body trajectories with vanishing angular momentum -- The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension -- On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure -- An explicit solution of the (quantum) elliptic Calogero-Sutherland model -- An application of the Melnikov integral to a restricted three body problem -- Reductions of integrable equations and automorphic Lie algebras -- Geometric reduction of Poisson operators -- Closed manifolds admitting metrics with the same geodesics -- A transcritical-flip bifurcation in a model for a robot-arm -- Alignment and the classification of Lorentz-signature tensors -- Renormalization group symmetry and gas dynamics -- Refined computation of hypernormal forms -- New order reductions for Euler-Lagrange equations -- Regularity of pseudogroup orbits -- Relaxation times to equilibrium in Fermi-Pasta-Ulam system -- Energy cascade in Fermi-Pasta-Ulam models -- On Birkhoff method for integrable lagrangian systems -- Symmetry of singularities and orbit spaces of compact linear groups -- Symmetric solutions in molecular potentials -- Variational approach to soliton generation and stability analysis of multidimensional nonlinear Schrodinger equation -- Differential invariants for infinite-dimensional algebras.
Absence of helical surface states in bulk semimetals with broken inversion symmetry
NASA Astrophysics Data System (ADS)
Ortix, Carmine; Venderbos, Jörn W. F.; Hayn, Roland; van den Brink, Jeroen
2014-03-01
Whereas the concept of topological band structures was developed originally for insulators with a bulk band gap, it has become increasingly clear that the prime consequences of a nontrivial topology—spin-momentum locking of surface states—can also be encountered in gapless systems. We show that point-group symmetries allow for helical semimetals, i.e., semimetals with Dirac-like topological surface states, to exist. The presence of this state, however, critically depends on the presence of crystal inversion symmetry. Using the paradigmatic example of mercury chalcogenides HgX (X = Te, Se, S), we show that an infinitesimally small broken inversion symmetry (BIS) renders the helical semimetallic state unstable. The BIS is also very important in the fully gapped topological insulating regime, renormalizing the surface Dirac cones in an anisotropic manner. As a consequence, the handedness of the Dirac cones can be flipped by a biaxial stress field.
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.
Symmetry-adapted digital modeling I. Axial symmetric proteins.
Janner, A
2016-05-01
Considered are axial symmetric proteins exemplified by the octameric mitochondrial creatine kinase, the Pyr RNA-binding attenuation protein, the D-aminopeptidase and the cyclophilin A-cyclosporin complex, with tetragonal (422), trigonal (32), pentagonal (52) and pentagonal (52) point-group symmetry, respectively. One starts from the protein enclosing form, which is characterized by vertices at points of a lattice (the form lattice) whose dimension depends on the point group. This allows the indexing of Cα's at extreme radial positions. The indexing is extended to additional residues on the basis of a finer lattice, the digital modeling lattice Λ, which includes the form lattice as a sublattice. This leads to a coarse-grained description of the protein. In the crystallographic point-group case, the planar indices are obtained from a projection of atomic positions along the rotation axis, taken as the z axis. The planar indices of a Cα are then those of the nearest projected lattice point. In the non-crystallographic case, low indices are an additional requirement. The coarse-grained bead follows from the condition imposed on the residues selected to have a z coordinate within a band of value δ above and below the height of lattice points. The choice of δ permits a variation of the coarse-grained bead model. For example, the value δ = 0.5 leads to a fine-grained indexing of the full set of residues, whereas with δ = 0.25 one gets a coarse-grained model which includes only about half of these residues. Within this procedure, the indexing of the Cα only depends on the choice of the digital modeling lattice and not on the value of δ. The characteristics which distinguish the present approach from other coarse-grained models of proteins on lattices are summarized at the end. PMID:27126107
Jach, T.; Zhang, Y.; Colella, R.; de Boissieu, M.; Boudard, M.; Goldman, A.I.; Lograsso, T.A.; Delaney, D.W.; Kycia, S.
1999-04-01
We have observed dynamical diffraction in the
Na9K16TI~25: A New Phase Containing Naked Icosahedral Cluster Fragments Ti99-
Li, Bin; Corbett, John D.
2007-12-05
The phase Na{sub 9}K{sub 16}Tl{sub 25.25(2)} was synthesized by fusion of the elements in sealed Ta containers followed by quenching and annealing at 250 C. The structure established by single crystal X-ray diffraction means (P6{sub 3}/m, Z = 2, a = 19.376(3) {angstrom}, c = 11.480(2) {angstrom}) features Tl{sub 9}{sup 9-} clusters. These are well separated by cations that bridge between, faces, edges, and vertices of the clusters; sodium appears to be essential in this role. This is the third compound known to contain Tl{sub 9} clusters, but here two of nine sites are partially occupied, which can be interpreted as a 70:30 mixture of Tl{sub 9} and Tl{sub 7} units in the same cavity. This Tl{sub 9} example also displays lower symmetry (C{sub s}) but requires the same 2n skeletal electrons. EHTB electronic structure calculations indicate that the Fermi level intersects a finite densities-of-states (DOS), and only some bonds are optimized at E{sub F}, giving some insight regarding the site of Tl deficiency. Direct geometric relationships are found among Tl{sub 13}, Tl{sub 9}, Tl{sub 7} and Tl{sub 5} clusters through systematic removal of vertices.
Symmetry 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.
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.
Lo, Pok Man; Swanson, Eric S.
2011-03-15
Schwinger-Dyson equations are used to study spontaneous chiral and parity symmetry breaking of three-dimensional quantum electrodynamics with two-component fermions. This theory admits a topological photon mass that explicitly breaks parity symmetry and generates a fermion mass. We show for the first time that it is possible to spontaneously break both parity and chiral symmetry. We also find that chiral symmetry is restored at a critical number of fermion flavors in our truncation scheme. Finally, the Coleman-Hill theorem is used to demonstrate that the results are reasonably accurate.
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.
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.
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.
Wang, Xue; Figueroa-Cosme, Legna; Yang, Xuan; Luo, Ming; Liu, Jingyue; Xie, Zhaoxiong; Xia, Younan
2016-02-10
Engineering the surface structure of noble-metal nanocrystals offers an effective route to the development of catalysts or electrocatalysts with greatly enhanced activity. Here, we report the synthesis of Pt-based icosahedral nanocages whose surface is enclosed by both {111} facets and twin boundaries while the wall thickness can be made as thin as six atomic layers. The nanocages are derived from Pd@Pt4.5L icosahedra by selectively etching away the Pd in the core. During etching, the multiply twinned structure can be fully retained whereas the Pt atoms in the wall reconstruct to eliminate the corrugated structure built in the original Pt shell. The Pt-based icosahedral nanocages show a specific activity of 3.50 mA cm(-2) toward the oxygen reduction reaction, much greater than those of the Pt-based octahedral nanocages (1.98 mA cm(-2)) and a state-of-the-art commercial Pt/C catalyst (0.35 mA cm(-2)). After 5000 cycles of accelerated durability test, the mass activity of the Pt-based icosahedral nanocages drops from 1.28 to 0.76 A mg(-1)Pt, which is still about four times greater than that of the original Pt/C catalyst (0.19 A mg(-1)Pt). PMID:26760681
Monocular symmetry in binocular vision.
Erkelens, Casper J; van Ee, Raymond
2007-01-01
Human vision is highly sensitive to bilateral symmetry in 2-D images. It is, however, not clear yet whether this visual sensitivity relates to symmetry of 3-D objects or whether it relates to symmetry of the 2-D image itself. We used a stereoscopically presented stimulus and a 3-D bisection task that enable us to dissociate object symmetry from image symmetry. The bisection stimulus consisted of three parallel lines, of which two lines were located in one depth plane and the third line in another. Bisection judgments were different for horizontal and vertical lines, which can be explained by taking into account the distinct viewpoints of the left and right eyes for either of the visible sides of the 3-D object. Image symmetry from a monocular vantage point predicts 3-D bisection better than object symmetry. We conclude that observers use either of the two monocular 2-D images separately but not a single cyclopean view-nicely dovetailing with what they do when they assess both 3-D visual direction and 3-D shape-to assess 3-D symmetry. PMID:17461689
ERIC Educational Resources Information Center
Hancock, Karen
2007-01-01
In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
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.
Sterile neutrinos and global symmetries
Sayre, J.; Wiesenfeldt, S.; Willenbrock, S.
2005-07-01
We use an effective-field-theory approach to construct models with naturally light sterile neutrinos, due to either exact or accidental global symmetries. The most attractive models we find are based on gauge symmetries, either discrete or continuous. We give examples of simple models based on Z{sub N}, U(1){sup '}, and SU(2){sup '}.
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.
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.
Hyperbolic-symmetry vector fields.
Gao, Xu-Zhen; Pan, Yue; Cai, Meng-Qiang; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2015-12-14
We present and construct a new kind of orthogonal coordinate system, hyperbolic coordinate system. We present and design a new kind of local linearly polarized vector fields, which is defined as the hyperbolic-symmetry vector fields because the points with the same polarization form a series of hyperbolae. We experimentally demonstrate the generation of such a kind of hyperbolic-symmetry vector optical fields. In particular, we also study the modified hyperbolic-symmetry vector optical fields with the twofold and fourfold symmetric states of polarization when introducing the mirror symmetry. The tight focusing behaviors of these vector fields are also investigated. In addition, we also fabricate micro-structures on the K9 glass surfaces by several tightly focused (modified) hyperbolic-symmetry vector fields patterns, which demonstrate that the simulated tightly focused fields are in good agreement with the fabricated micro-structures. PMID:26699014
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
NASA Astrophysics Data System (ADS)
Jakse, N.; Pasturel, A.
2015-08-01
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al80Ni20 alloy upon cooling. Our results evidence a huge increase of local icosahedral ordering (ISRO) in the undercooled regime which is more developed around Ni than Al atoms. We show that ISRO has a strong impact on self-diffusion coefficients of both species and is at the origin of their crossover from Arrhenius to non-Arrhenius behavior around a crossover temperature TX = 1000 K, located in the undercooled region. We also clearly identify that this temperature corresponds to the development of dynamic heterogeneities and to the breakdown of the Stokes-Einstein relation. At temperatures below this crossover, we find that the behavior of the diffusion and relaxation dynamics is mostly incompatible with predictions of the mode-coupling theory. Finally, an analysis of the van Hove function indicates that the crossover temperature TX marks the onset of a change in the diffusion mechanism from a normal flow to an activated process with hopping. From these results, the glass-forming ability of the alloy is discussed.
Jakse, N; Pasturel, A
2015-08-28
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al80Ni20 alloy upon cooling. Our results evidence a huge increase of local icosahedral ordering (ISRO) in the undercooled regime which is more developed around Ni than Al atoms. We show that ISRO has a strong impact on self-diffusion coefficients of both species and is at the origin of their crossover from Arrhenius to non-Arrhenius behavior around a crossover temperature TX = 1000 K, located in the undercooled region. We also clearly identify that this temperature corresponds to the development of dynamic heterogeneities and to the breakdown of the Stokes-Einstein relation. At temperatures below this crossover, we find that the behavior of the diffusion and relaxation dynamics is mostly incompatible with predictions of the mode-coupling theory. Finally, an analysis of the van Hove function indicates that the crossover temperature TX marks the onset of a change in the diffusion mechanism from a normal flow to an activated process with hopping. From these results, the glass-forming ability of the alloy is discussed. PMID:26328857
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.
Brumfield, Susan K.; Ortmann, Alice C.; Ruigrok, Vincent; Suci, Peter; Douglas, Trevor; Young, Mark J.
2009-01-01
Little is known about the replication cycle of archaeal viruses. We have investigated the ultrastructural changes of Sulfolobus solfataricus P2 associated with infection by Sulfolobus turreted icosahedral virus (STIV). A time course of a near synchronous STIV infection was analyzed using both scanning and transmission electron microscopy. Assembly of STIV particles, including particles lacking DNA, was observed within cells, and fully assembled STIV particles were visible by 30 h postinfection (hpi). STIV was determined to be a lytic virus, causing cell disruption beginning at 30 hpi. Prior to cell lysis, virus infection resulted in the formation of pyramid-like projections from the cell surface. These projections, which have not been documented in any other host-virus system, appeared to be caused by the protrusion of the cell membrane beyond the bordering S-layer. These structures are thought to be sites at which progeny virus particles are released from infected cells. Based on these observations of lysis, a plaque assay was developed for STIV. From these studies we propose an overall assembly model for STIV. PMID:19357174
Jalasvuori, Matti; Jaatinen, Silja T.; Laurinavičius, Simonas; Ahola-Iivarinen, Elina; Kalkkinen, Nisse; Bamford, Dennis H.; Bamford, Jaana K. H.
2009-01-01
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 ∼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
New building blocks in the 2/1 crystalline approximant of a Bergman-type icosahedral quasicrystal
Lin, Qisheng; Corbett, John D.
2006-01-01
The refined x-ray crystal structure of the phase Mg27Al10.7(2)Zn47.3(2) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsulates an Al2 dimer. This phase exhibits the same long-range order as recently established for the Tsai-type Sc–Mg–Zn 2/1 approximant crystal, with substantial geometric and atomic distribution differences between the two only in the short range orders. This common feature suggests that Bergman- and Tsai-type quasicrystals may be more similar than earlier conceived. Factors germane to the formation of, and the differences between, Bergman- vs. Tsai-type 1/1 and 2/1 approximate structures are considered, including notably different distributions of the more electropositive elements. PMID:16950873
Symmetries of Dynamically Equivalent Theories
NASA Astrophysics Data System (ADS)
Gitman, D. M.; Tyutin, I. V.
2006-03-01
A natural and very important development of constrained system theory is a detail study of the relation between the constraint structure in the Hamiltonian formulation with specific features of the theory in the Lagrangian formulation, especially the relation between the constraint structure with the symmetries of the Lagrangian action. An important preliminary step in this direction is a strict demonstration, and this is the aim of the present article, that the symmetry structures of the Hamiltonian action and of the Lagrangian action are the same. This proved, it is sufficient to consider the symmetry structure of the Hamiltonian action. The latter problem is, in some sense, simpler because the Hamiltonian action is a first-order action. At the same time, the study of the symmetry of the Hamiltonian action naturally involves Hamiltonian constraints as basic objects. One can see that the Lagrangian and Hamiltonian actions are dynamically equivalent. This is why, in the present article, we consider from the very beginning a more general problem: how the symmetry structures of dynamically equivalent actions are related. First, we present some necessary notions and relations concerning infinitesimal symmetries in general, as well as a strict definition of dynamically equivalent actions. Finally, we demonstrate that there exists an isomorphism between classes of equivalent symmetries of dynamically equivalent actions.
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
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
Mamone, Salvatore; Johnson, Mark R; Ollivier, Jacques; Rols, Stphane; Levitt, Malcolm H; Horsewill, Anthony J
2016-01-21
The fine structure of the rotational ground state of molecular ortho-hydrogen confined inside the fullerene cage C60 is investigated by inelastic neutron scattering (INS). The INS line corresponding to transitions between the three sub-levels comprising the ortho ground state to the non-degenerate para ground state was studied as a function of temperature down to 60 mK in neutron energy gain. The experiments show that at ambient pressure the three ortho sub-levels are split into a low energy non-degenerate level and a high energy doubly degenerate level separated by 0.135 0.010 meV. This observation is consistent with hydrogen molecules being located at sites with axial symmetry superseding the icosahedral symmetry of isolated rigid C60 cages in the solid phase. To gain insight into the role of inter-cage interactions in determining the symmetry breaking potential, the effects of hydrostatic pressure on the fine structure of the line was also investigated. The analysis of the INS spectra shows that the potential and the energy levels of H2 are sensitive to the orientation of neighbouring cages, consistent with the low-temperature crystalline phase of C60. PMID:26687060
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).
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.
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.
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.
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.
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
Janner, A
2011-03-01
The relation between serotype differentiation and crystallographic symmetry, revealed by the contact fingerprint diagrams investigated in Part II [Janner (2010). Acta Cryst. A66, 312-326] for the human rhinovirus, is extended to the Picornaviridae family. The approach, outlined in Part I [Janner (2010). Acta Cryst. A66, 301-311] and Part II for biomacromolecules packed in a crystal and based on concepts such as packing lattice, kissing points and crystal-packing parameters, can directly be applied to the picornaviruses. In particular, the contact fingerprint diagrams of 20 different virus strains have been derived. In these cases, as for the rhinovirus, these diagrams are serotype/strain specific, justifying the name fingerprint. The molecular basis for the serotype variability, and the associated conservation requirements, is usually analysed by considering antigenic sites, where capsid residues bind with antibodies, and receptor sites, where other residues bind with molecular receptors of the host cell membrane. Both the antigenic variation and the receptor conservation allow repeated infection of the host cells of the given animals. The graphical description of these sites is usually done by footprints and roadmap diagrams, mapping properties of the capsid surface and using the icosahedral symmetry of the capsid. The alternative fingerprint diagrammatic description, based on the crystal symmetry, adopted in Part II for the contact sites, where a capsid is bound to the next one in the crystal packing, is extended to the antigenic and receptor binding sites. Again, the antigenic/receptor fingerprints are specific, at least for the nine picornaviruses investigated so far, despite the more than a factor of ten larger coarse graining with respect to the corresponding footprint and roadmap diagrams. The latter are based on a grid spacing of about 2 Å, whereas the spacing implied by the packing-lattice approximation adopted in fingerprints varies typically from 20 to 50 Å. The fingerprint diagrams are accordingly simpler (because approximated), but nevertheless still serotype specific, despite the complex character of the interactions involved. PMID:21325720
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 .
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.
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.
Soft theorems from anomalous symmetries
NASA Astrophysics Data System (ADS)
Huang, Yu-tin; Wen, Congkao
2015-12-01
We discuss constraints imposed by soft limits for effective field theories arising from symmetry breaking. In particular, we consider those associated with anomalous conformal symmetry as well as duality symmetries in supergravity. We verify these soft theorems for the dilaton effective action relevant for the a-theorem, as well as the one-loop effective action for N=4 supergravity. Using the universality of leading transcendental coefficients in the α' expansion of string theory amplitudes, we study the matrix elements of operator R 4 with half maximal supersymmetry. We construct the non-linear completion of R 4 that satisfies both single and double soft theorems up to seven points. This supports the existence of duality invariant completion of R 4.
Symmetries, Lie Algebras and Representations
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph
2003-10-01
Preface; 1. Symmetries and conservation laws; 2. Basic examples; 3. The Lie algebra su(3) and hadron symmetries; 4. Formalization: algebras and Lie algebras; 5. Representations; 6. The Cartan-Weyl basis; 7. Simple and affine Lie algebras; 8. Real Lie algebras and real forms; 9. Lie groups; 10. Symmetries of the root system. The Weyl group; 11. Automorphisms of Lie algebras; 12. Loop algebras and central extensions; 13. Highest weight representations; 14. Verma modules, Casimirs, and the character formula; 15. Tensor products of representations; 16. Clebsch-Gordan coefficients and tensor operators; 17. Invariant tensors; 18. Subalgebras and branching rules; 19. Young tableaux and the symmetric group; 20. Spinors, Clifford algebras, and supersymmetry; 21. Representations on function spaces; 22. Hopf algebras and representation rings; Epilogue; References; Index.
Nonholonomic Mechanical Systems with Symmetry
NASA Astrophysics Data System (ADS)
Bloch, Anthony M.; Krishnaprasad, P. S.; Marsden, Jerrold E.; Murray, Richard M.
1996-12-01
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control-theoretical applications. The basic methodology is that of geometric mechanics applied to the Lagrange-d'Alembert formulation, generalizing the use of connections and momentum maps associated with a given symmetry group to this case. We begin by formulating the mechanics of nonholonomic systems using an Ehresmann connection to model the constraints, and show how the curvature of this connection enters into Lagrange's equations. Unlike the situation with standard configuration-space constraints, the presence of symmetries in the nonholonomic case may or may not lead to conservation laws. However, the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables. This momentum equation, which plays an important role in control problems, involves parallel transport operators and is computed explicitly in coordinates. An alternative description using a body reference frame relates part of the momentum equation to the components of the Euler-Poincar equations along those symmetry directions consistent with the constraints. One of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not. An example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard, a modified version of the skateboard which uses momentum coupling for locomotion generation. We construct a synthesis of the mechanical connection and the Ehresmann connection defining the constraints, obtaining an important new object we call the nonholonomic connection. When the nonholonomic connection is a principal connection for the given symmetry group, we show how to perform Lagrangian reduction in the presence of nonholonomic constraints, generalizing previous results which only held in special cases. Several detailed examples are given to illustrate the theory.
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.
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.
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).
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Chiral symmetry on the lattice
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model.
NASA Astrophysics Data System (ADS)
Tsuji, Masaharu; Nakamura, Nozomi; Tang, Xinling; Uto, Keiko; Matsunaga, Mika
2014-11-01
We previously reported that trapezoid, plate-like and mono- or bi-tetrahedral Ag-flag structures are evolved from side facets of Ag-nanorod (NR) seeds when AgNO3 was reduced in N,N-dimethylformamide (DMF) in the presence of polyvinylpyrrolidone (PVP). In this study, we examined what shapes are grown by further growth of bitetrahedral flags based on TEM and SEM observations. For this purpose, we initially studied effects of the reaction temperature, concentrations of PVP, and molecular weights of PVP for the shape evolution of flag types of Ag nanostructures from Ag-NR seeds. Results show that shape and size of flags can be controlled by changing these parameters and reaction times. Under an appropriate experimental condition, we found that decahedral and icosahedral flags and their intermediates having {1 1 1} facets were finally grown by stepwise growth of tetrahedral units, although yield of perfect decahedral and icosahedral flags were low because of occurrence of homogenous nucleation at high AgNO3 concentration.
Effective field theory for spacetime symmetry breaking
NASA Astrophysics Data System (ADS)
Hidaka, Yoshimasa; Noumi, Toshifumi; Shiu, Gary
2015-08-01
We discuss the effective field theory for spacetime symmetry breaking from the local symmetry point of view. By gauging spacetime symmetries, the identification of Nambu-Goldstone (NG) fields and the construction of the effective action are performed based on the breaking pattern of diffeomorphism, local Lorentz, and (an)isotropic Weyl symmetries as well as the internal symmetries including possible central extensions in nonrelativistic systems. Such a local picture distinguishes, e.g., whether the symmetry breaking condensations have spins and provides a correct identification of the physical NG fields, while the standard coset construction based on global symmetry breaking does not. We illustrate that the local picture becomes important in particular when we take into account massive modes associated with symmetry breaking, the masses of which are not necessarily high. We also revisit the coset construction for spacetime symmetry breaking. Based on the relation between the Maurer-Cartan one form and connections for spacetime symmetries, we classify the physical meanings of the inverse-Higgs constraints by the coordinate dimension of broken symmetries. Inverse Higgs constraints for spacetime symmetries with a higher dimension remove the redundant NG fields, whereas those for dimensionless symmetries can be further classified by the local symmetry breaking pattern.
Classification of Arnold-Beltrami flows and their hidden symmetries
NASA Astrophysics Data System (ADS)
Fré, P.; Sorin, A. S.
2015-07-01
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds 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 exhaustive classification of all generalized ABC- flows and of their hidden symmetries. We make several conceptual comments about the need of a field-theory yielding Beltrami equation as a field equation and/or an instanton equation and on the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that are different from the non-linear one proposed by Arnold and possibly make contact with M-theory and the geometry of flux-compactifications.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
On extended symmetries for the Galileon
NASA Astrophysics Data System (ADS)
Noller, Johannes; Sivanesan, Vishagan; von Strauss, Mikael
2015-09-01
We investigate a large class of infinitesimal, but fully nonlinear in the field, transformations of the Galileon and search for extended symmetries. The transformations involve powers of the coordinates x and the field π up to any finite order N . Up to quadratic order the structure of these symmetry transformations is the unique generalization of both the infinitesimal version of the standard Galileon shift symmetry as well as a recently discovered infinitesimal extension of this symmetry. The only higher-order extensions of this symmetry we recover are ("Galileon dual" versions of) symmetries of the standard kinetic term.
A Futures Curriculum for Symmetry.
ERIC Educational Resources Information Center
Dickmann, Leonore W.
The paper describes a model to aid curriculum developers as they design futures curricula. The objective is to demonstrate how curricula can be holistic in perspective and balanced in provision for student future-focused role image as well as subject matter. The model, based on symmetry (within the individual and the curriculum), has seven facets:…
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.
Kohn's theorem and Galilean symmetry
NASA Astrophysics Data System (ADS)
Zhang, P.-M.; Horvathy, P. A.
2011-08-01
The relation between the separability of a system of charged particles in a uniform magnetic field and Galilean symmetry is revisited using Duval's “Bargmann framework”. If the charge-to-mass ratios of the particles are identical, ea/ma=ɛ for all particles, then the Bargmann space of the magnetic system is isometric to that of an anisotropic harmonic oscillator. Assuming that the particles interact through a potential which only depends on their relative distances, the system splits into one representing the center of mass plus a decoupled internal part, and can be mapped further into an isolated system using Niederer's transformation. Conversely, the manifest Galilean boost symmetry of the isolated system can be “imported” to the oscillator and to the magnetic systems, respectively, to yield the symmetry used by Gibbons and Pope to prove the separability. For vanishing interaction potential the isolated system is free and our procedure endows all our systems with a hidden Schrödinger symmetry, augmented with independent internal rotations. All these properties follow from the cohomological structure of the Galilei group, as explained by Souriau's “décomposition barycentrique”.
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.
Exploiting Symmetry on Parallel Architectures.
NASA Astrophysics Data System (ADS)
Stiller, Lewis Benjamin
1995-01-01
This thesis describes techniques for the design of parallel programs that solve well-structured problems with inherent symmetry. Part I demonstrates the reduction of such problems to generalized matrix multiplication by a group-equivariant matrix. Fast techniques for this multiplication are described, including factorization, orbit decomposition, and Fourier transforms over finite groups. Our algorithms entail interaction between two symmetry groups: one arising at the software level from the problem's symmetry and the other arising at the hardware level from the processors' communication network. Part II illustrates the applicability of our symmetry -exploitation techniques by presenting a series of case studies of the design and implementation of parallel programs. First, a parallel program that solves chess endgames by factorization of an associated dihedral group-equivariant matrix is described. This code runs faster than previous serial programs, and discovered it a number of results. Second, parallel algorithms for Fourier transforms for finite groups are developed, and preliminary parallel implementations for group transforms of dihedral and of symmetric groups are described. Applications in learning, vision, pattern recognition, and statistics are proposed. Third, parallel implementations solving several computational science problems are described, including the direct n-body problem, convolutions arising from molecular biology, and some communication primitives such as broadcast and reduce. Some of our implementations ran orders of magnitude faster than previous techniques, and were used in the investigation of various physical phenomena.
Simple current symmetries in RCFT
NASA Astrophysics Data System (ADS)
Bantay, P.
2005-01-01
The question ``Which abelian permutation groups arise as group of simple currents in Rational Conformal Field Theory?'' is investigated using the formalism of weighted permutation actions. After a review of the relevant properties of simple current symmetries, the general theory of WPA-s and admissibility conditions are described, and classification results are illustrated by a couple of examples.
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)
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
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.
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…
The Geometry of Reflectance Symmetries.
Tan, Ping; Quan, Long; Zickler, Todd
2011-12-01
Different materials reflect light in different ways, and this reflectance interacts with shape, lighting, and viewpoint to determine an object's image. Common materials exhibit diverse reflectance effects, and this is a significant source of difficulty for image analysis. One strategy for dealing with this diversity is to build computational tools that exploit reflectance symmetries, such as reciprocity and isotropy, that are exhibited by broad classes of materials. By building tools that exploit these symmetries, one can create vision systems that are more likely to succeed in real-world, non-Lambertian environments. In this paper, we develop a framework for representing and exploiting reflectance symmetries. We analyze the conditions for distinct surface points to have local view and lighting conditions that are equivalent under these symmetries, and we represent these conditions in terms of the geometric structure they induce on the Gaussian sphere and its abstraction, the projective plane. We also study the behavior of these structures under perturbations of surface shape and explore applications to both calibrated and uncalibrated photometric stereo. PMID:21339528
Spin and symmetry adaptation of the variational two-electron reduced-density-matrix method
Gidofalvi, Gergely; Mazziotti, David A.
2005-11-15
The variational two-electron reduced-density-matrix (2-RDM) method computes the ground-state energy and 2-RDM of an atom or molecule without calculation of the many-electron wave function. Recently, the computational efficiency of the 2-RDM method has been significantly enhanced through the use of a first-order algorithm for semidefinite programming [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. In this paper we develop a spin- and symmetry-adapted formulation of the method that further improves its efficiency by incorporating both the spin and spatial symmetries of many-electron atoms and molecules. While previous work on density-matrix symmetry focused on only one form of the 2-RDM, the variational method employs three different forms of the 2-RDM, known as the D, Q, and G matrices, to restrict the 2-RDM to be approximately N-representable, that is representable by an N-electron wave function. We apply spin symmetries to the three forms of the 2-RDM, each of which breaks into four diagonal spin-blocks, namely one singlet and three triplet blocks. If the molecules have point-group symmetry, each of the 2-RDMs may be further subdivided into smaller diagonal blocks according to the spatial symmetry of the basis functions. The subdivision of the 2-RDMs into diagonal blocks generates significant computational savings in both floating-point operations and memory storage. Calculations illustrate the computational savings. Spin adaptation also enforces the correct expectation value of the S{sup 2} operator, which in earlier work is applied as a separate constraint.
Quantum group and quantum symmetry
NASA Astrophysics Data System (ADS)
Chang, Zhe
1995-11-01
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum group is primarily introduced as a systematic method for solving the Yang-Baxter equation. Quantum group theory is presented within the framework of quantum double through quantizing Lie bi-algebra. Both the highest weight and the cyclic representations are investigated for the quantum group and emphasis is laid on the new features of representations for q being a root of unity. Quantum symmetries are explored in selected topics of modern physics. For a Hamiltonian system the quantum symmetry is an enlarged symmetry that maintains invariance of equations of motion and allows a deformation of the Hamiltonian and symplectic form. The configuration space of the integrable lattice model is analyzed in terms of the representation theory of quantum group. By means of constructing the Young operators of quantum group, the Schrödinger equation of the model is transformed to be a set of coupled linear equations that can be solved by the standard method. Quantum symmetry of the minimal model and the WZNW model in conformal field theory is a hidden symmetry expressed in terms of screened vertex operators, and has a deep interplay with the Virasoro algebra. In quantum group approach a complete description for vibrating and rotating diatomic molecules is given. The exact selection rules and wave functions are obtained. The Taylor expansion of the analytic formulas of the approach reproduces the famous Dunham expansion.
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.
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.
Notes on generalized global symmetries in QFT
NASA Astrophysics Data System (ADS)
Sharpe, Eric
2015-11-01
It was recently argued that quantum field theories possess one-form and higher-form symmetries, labelled `generalized global symmetries.' In this paper, we describe how those higher-form symmetries can be understood mathematically as special cases of more general 2-groups and higher groups, and discuss examples of quantum field theories admitting actions of more general higher groups than merely one-form and higher-form symmetries. We discuss analogues of topological defects for some of these higher symmetry groups, relating some of them to ordinary topological defects. We also discuss topological defects in cases in which the moduli `space' (technically, a stack) admits an action of a higher symmetry group. Finally, we outline a proposal for how certain anomalies might potentially be understood as describing a transmutation of an ordinary group symmetry of the classical theory into a 2-group or higher group symmetry of the quantum theory, which we link to WZW models and bosonization.
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.
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.
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.
Symmetries in Lagrangian Field Theory
NASA Astrophysics Data System (ADS)
Búa, Lucia; Bucataru, Ioan; León, Manuel de; Salgado, Modesto; Vilariño, Silvia
2015-06-01
By generalising the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that purpose we consider the first-order jet bundles J1π of a fiber bundle π : E → ℝk where ℝk is the space of independent variables. Generalized symmetries of the Lagrangian are introduced and the corresponding Noether theorem is proved.
The New Charge Symmetry Breaking
Stephenson, E. J.
2007-06-13
For few body systems, the treatment of charge symmetry breaking (CSB) that is based on meson-exchange models is being replaced by effective field theories whose CSB originates in the down-up quark mass difference and quark electromagnetic effects. In parallel, two new observations of CSB in {pi}0 production (the fore-aft asymmetry in n+p{yields}d+{pi}0 and the total cross section for d+d{yields}4He+{pi}0) provide applicable data.
Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ≥Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator 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 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;3:13945. PMID:24802391
Symmetry groups of single-wall nanotubes.
De Las Peñas, Ma Louise Antonette N; Loyola, Mark L; Basilio, Antonio M; Santoso, Eko Budi
2014-01-01
This work investigates the symmetry properties of single-wall carbon nanotubes and their structural analogs, which are nanotubes consisting of different kinds of atoms. The symmetry group of a nanotube is studied by looking at symmetries and color fixing symmetries associated with a coloring of the tiling by hexagons in the Euclidean plane which, when rolled, gives rise to a geometric model of the nanotube. The approach is also applied to nanotubes with non-hexagonal symmetry arising from other isogonal tilings of the plane. PMID:24419167
Bakalova, S.; Gong, Y; Cobet, C; Esser, N; Zhang, Y; Edgar, J; Zhang, Y; Dudley, M; Kuball, M
2010-01-01
An experimental and theoretical study on the dielectric-response function of icosahedral B{sub 12}As{sub 2} in the spectral region between 1.24 and 9.8 eV is presented. Comprehensive experimental information on the energy band structure from the analysis of features in the optical dispersion was complemented by spin-orbit first-principles calculations. The lowest indirect band gap width is 3.2 eV; the two lowest direct interband transitions are at 3.46 and 3.9 eV. High-energy critical points are assigned to specific electron transitions in the Brillouin zone and their dimensionality was determined. The static dielectric constant of B{sub 12}As{sub 2} is uniaxially anisotropic with values of 7.84 and 9.02 for polarization perpendicular and parallel to the trigonal axis. Hole and electron effective masses are derived from the band dispersions.
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.
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.
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
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
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
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.
Spontaneous violation of mirror symmetry
NASA Astrophysics Data System (ADS)
Dyatlov, I. T.
2015-11-01
A model of the violation of symmetry is considered for a system that can spontaneously choose between nearly identical states that differ only in the weak-interaction properties ( R ↔ L). This mirror symmetrymakes it possible to reproduce the observed qualitative properties of the quark and lepton mixing matrices. In this case, the lepton mixing matrix is indicative of an inverse character of the spectrum of Standard Model neutrinos and their Dirac nature. Despite the Dirac properties of the neutrinos, leptonnumber- changing processes of the e - + μ + → e + + μ - type are possible here, but they may involve exclusively leptons.
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.
Dynamical symmetries in noncommutative theories
Amorim, Ricardo
2008-11-15
In the present work we study dynamical space-time symmetries in noncommutative relativistic theories by using the minimal canonical extension of the Doplicher, Fredenhagen, and Roberts algebra. Our formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity {theta}{sup {mu}}{sup {nu}}. In this framework we consider theories that are invariant under the Poincare group P or under its extension P{sup '}, when translations in the extra dimensions are permitted. The Noether's formalism adapted to such extended x+{theta} space-time is employed.
Reflection symmetry-integrated image segmentation.
Sun, Yu; Bhanu, Bir
2012-09-01
This paper presents a new symmetry-integrated region-based image segmentation method. The method is developed to obtain improved image segmentation by exploiting image symmetry. It is realized by constructing a symmetry token that can be flexibly embedded into segmentation cues. Interesting points are initially extracted from an image by the SIFT operator and they are further refined for detecting the global bilateral symmetry. A symmetry affinity matrix is then computed using the symmetry axis and it is used explicitly as a constraint in a region growing algorithm in order to refine the symmetry of the segmented regions. A multi-objective genetic search finds the segmentation result with the highest performance for both segmentation and symmetry, which is close to the global optimum. The method has been investigated experimentally in challenging natural images and images containing man-made objects. It is shown that the proposed method outperforms current segmentation methods both with and without exploiting symmetry. A thorough experimental analysis indicates that symmetry plays an important role as a segmentation cue, in conjunction with other attributes like color and texture. PMID:22201051
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards this end, we will show the possible link between the features in Saturn's magnetic field and dynamics in the semi-conducting region of Saturn.
Gauge symmetries, topology, and quantisation
NASA Astrophysics Data System (ADS)
Balachandran, A. P.
1994-10-01
The following two loosely connected sets of topics are reviewed in these lecture notes: 1) Gauge invariance, its treatment in field theories and its implications for internal symmetries and edge states such as those in the quantum Hall effect. 2) Quantisation on multiply connected spaces and a topological proof the spin-statistics theorem which avoids quantum field theory and relativity. Under 1), after explaining the meaning of gauge invariance and the theory of constraints, we discuss boundary conditions on gauge transformations and the definition of internal symmetries in gauge field theories. We then show how the edge states in the quantum Hall effect can be derived from the Chern-Simons action using the preceding ideas. Under 2), after explaining the significance of fibre bundles for quantum physics, we review quantisation on multiply connected spaces in detail, explaining also mathematical ideas such as those of the universal covering space and the fundamental group. These ideas are then used to prove the aforementioned topological spin-statistics theorem.
Superconformal symmetry, NMSSM, and inflation
NASA Astrophysics Data System (ADS)
Ferrara, Sergio; Kallosh, Renata; Linde, Andrei; Marrani, Alessio; van Proeyen, Antoine
2011-01-01
We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincaré supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant. The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coupling. This can be achieved by introducing the nonminimal scalar-curvature coupling, and by taking into account interactions with a hidden sector. In this approach, the smallness of the mass parameters in the NMSSM may be traced back to the original superconformal invariance. This allows one to address the μ problem and the cosmological domain wall problem in this model, and to implement chaotic inflation in the NMSSM. We discuss the gravitino problem in the NMSSM inflation, as well as the possibility to obtain a broad class of new versions of chaotic inflation in supergravity.
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.
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.
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.
Radiation Symmetry of NIF Hohlraums
NASA Astrophysics Data System (ADS)
Jones, O. S.; Suter, L. J.; Pollaine, S. M.; Haan, S. W.
1997-11-01
We have used the three-dimensional, view-factor radiation transport code, Gertie (G. Zimmerman, D. Munroe, R. Kirkpatrick, and D. Bailey.), to analyze the symmetry of indirect drive ignition experiments on the National Ignition Facility (NIF). These calculations directly consider vacuum radiation only. Plasma effects enter indirectly through specification of the time-dependent albedos and effective dimensions of the hohlraum and capsule. These specifications come from seperate simulations with the radiation hydrodynamics code Lasnex. First, we examine the intrinsic azimuthal asymmetry of NIF's full 192 beam configuration using highly refined grids. Next, we quantify the sensitivity of the overall symmetry to systematic effects such as laser power imbalance and beam pointing errors. The power balance analysis includes the effects of correlations due to shared amplifiers among pairs of beam quads. Finally, we estimate the degree of radiation asymmetries that may exist during the NIF activation phase. The NIF activation plan (M. Lane, B. Van Wontergrun, LLNL, private communication, 1997.) will allow target physics experiments as banks of beams come online. This set of calculations provides an idea of the degree of asymmetry that will exist during various phases of NIF activation, and thus allows us to assess how we might best use these early experiments.
Symmetry Energy of Dilute Warm Nuclear Matter
Natowitz, J. B.; Hagel, K.; Kowalski, S.; Qin, L.; Shlomo, S.; Wada, R.; Roepke, G.; Typel, S.; Blaschke, D.; Bonasera, A.; Klaehn, T.; Wolter, H. H.
2010-05-21
The symmetry energy of nuclear matter is a fundamental ingredient in the investigation of exotic nuclei, heavy-ion collisions, and astrophysical phenomena. New data from heavy-ion collisions can be used to extract the free symmetry energy and the internal symmetry energy at subsaturation densities and temperatures below 10 MeV. Conventional theoretical calculations of the symmetry energy based on mean-field approaches fail to give the correct low-temperature, low-density limit that is governed by correlations, in particular, by the appearance of bound states. A recently developed quantum-statistical approach that takes the formation of clusters into account predicts symmetry energies that are in very good agreement with the experimental data. A consistent description of the symmetry energy is given that joins the correct low-density limit with quasiparticle approaches valid near the saturation density.
Quantum Deformations of Einstein's Relativistic Symmetries
Lukierski, Jerzy
2006-11-03
We shall outline two ways of introducing the modification of Einstein's relativistic symmetries of special relativity theory -- the Poincare symmetries. The most complete way of introducing the modifications is via the noncocommutative Hopf-algebraic structure describing quantum symmetries. Two types of quantum relativistic symmetries are described, one with constant commutator of quantum Minkowski space coordinates ({theta}{mu}{nu}-deformation) and second with Lie-algebraic structure of quantum space-time, introducing so-called {kappa}-deformation. The third fundamental constant of Nature - fundamental mass {kappa} or length {lambda} - appears naturally in proposed quantum relativistic symmetry scheme. The deformed Minkowski space is described as the representation space (Hopf-module) of deformed Poincare algebra. Some possible perspectives of quantum-deformed relativistic symmetries will be outlined.
Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry
2011-01-01
Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry. PMID:21958045
Nonlocal dynamics and infinite nonrelativistic conformal symmetries
NASA Astrophysics Data System (ADS)
Andrzejewski, K.; Bolonek-Lasoń, K.
2016-03-01
We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite-dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the nonrelativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model, and on the quantum level, it leads to the centrally extended Virasoro algebra.
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
Spin-orbit-free topological insulators without time-reversal symmetry.
Alexandradinata, A; Fang, Chen; Gilbert, Matthew J; Bernevig, B Andrei
2014-09-12
We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n=3,4, and 6 of the C_{nv} groups, we find the first-known 3D topological insulators without spin-orbit coupling, and with surface modes that are protected only by point groups; i.e., the relevant symmetries are purely crystalline and do not include time reversal. To describe these C_{nv} systems, we introduce the notions of (a) a halved mirror chirality, an integer invariant which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent Chern number, the traditional Thouless-Kohmoto-Nightingale-den Nijs invariant generalized to bent 2D manifolds. We find that a Weyl semimetallic phase intermediates two gapped phases with distinct halved chiralities. In addition to electronic systems without spin-orbit coupling, our findings also apply to intrinsically spinless systems such as photonic crystals and ultracold atoms. PMID:25259991
Interpretation of symmetry experiments on Omega
NASA Astrophysics Data System (ADS)
Lours, Laurence; Bastian, Josiane; Monteil, Marie-Christine; Philippe, Franck; Jadaud, Jean-Paul
2006-10-01
The interpretation of the symmetry experiments performed on Omega in 2005 with 3 cone LMJ-like irradiation is presented here. The goal of this campaign was the characterization of the irradiation symmetry by X-ray imaging of the D2Ar capsule. Images of backlit implosion (as done in earlier campaigns with foam balls) and core emission were obtained on the same shot, and can be compared to FCI2 simulations. This set of shots comfirms former results with foam balls of a good symmetry control with 3 cones in empty hohlraums. The influence of the hohlraum shape on symmetry is also studied by comparison of cylindrical hohlraums vs rugby ones.
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.
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.
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 were also two colleagues who would have liked to participate but were unable to do so (M Horn and A Solomon); we agreed to incorporate their manuscripts into the Proceedings. We would like to thank the staff of Collegium Mehrerau for their hospitality. Once more special thanks to the Schenk Family for their continuing friendship and generous support. The informal evening meetings in these stimulating surroundings probably contributed as much to the scientific success as the lectures during the day and many personal contacts were made. Last, but not least, we would like to thank Yvette again for her unremitting support. Dieter Schuch and Michael Ramek Frankfurt am Main and Graz, July 2012 Conference photograph
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.
NASA Astrophysics Data System (ADS)
Gu, Pei-Hong
2012-07-01
We propose a novel SU (3)c × SU (2)L × SU (2)R × U(1) B - L left-right symmetric model where the standard model fermion and Higgs fields are SU (2)L doublets or SU (2) singlets while their mirror partners are SU (2)R doublets or SU (2) singlets. The scalar fields also include a real singlet for dark matter and two SU (2) triplets for seesaw. The mixing between the standard model and mirror fermions is forbidden by a Z2 × Z2‧ discrete symmetry. The mirror charged fermions can decay into their standard model partners with the dark-matter scalar while the mirror neutrinos can decay into the mirror charged fermions through the right-handed gauge interactions. Our model can have new implications on the strong CP problem, leptogenesis, collider phenomenology and dark matter detection.
Haemodynamic flow: symmetry and synthesis.
Dewey, C Forbes
2002-01-01
This paper is presented as a summary and synthesis of the presentations at the conference entitled "Breaking Symmetry in Haemodynamics". As the accompanying papers will attest, there has been enormous progress in understanding the effects of fluid flow on the arterial endothelium and the consequential effects on the vessel wall. It is now clearly understood that the focal lesions found in atherosclerotic arteries are the product of asymmetrical flow and the resulting disturbed flow that occurs near arterial bifurcations and other selected points around the human vasculature. The flow in large vessels can now be determined accurately with MR and in vitro cast models. Although theory allows arterial flow to be characterized by asymmetry in time and space, our understanding of the processes that act to translate this asymmetry into pathology is becoming much more symmetric, or complete. The new frontiers of research in arterial flow are now translating to smaller scales, at the cellular level and below. PMID:12122278
Permutation symmetry for theta functions
Carlson, B.C.
2011-01-21
This paper does for combinations of theta functions most of what Carlson (2004) [1] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral R{sub F} of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas.
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
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.
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.
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.
Unal, Baris
2008-12-01
The present work in this dissertation mainly focuses on the clean fivefold surfaces of i-Al-Pd-Mn quasicrystals as well as the nucleation and growth of Ag films on these surfaces. In addition, Ag film growth on NiAl(110) has been explored in the frame of this dissertation. First, we have investigated the equilibration of a fivefold surface of icosahedral Al-Pd-Mn quasicrystal at 900-915 K and 925-950 K, using Omicron variable temperature scanning tunneling microscope (STM). Annealing at low temperatures resulted in many voids on some terraces while the others were almost void-free. After annealing at 925-950K, void-rich terraces became much rarer. Our STM images suggest that through growth and coalescence of the voids, a different termination becomes exposed on host terraces. All of these observations in our study indicate that even after the quasicrystalline terrace-step structure appears, it evolves with time and temperature. More specifically, based on the STM observations, we conclude that during the annealing a wide range of energetically similar layers nucleate as surface terminations, however, with increasing temperature (and time) this distribution gets narrower via elimination of the metastable void-rich terraces. Next, we have examined the bulk structural models of icosahedral Al-Pd-Mn quasicrystal in terms of the densities, compositions and interplanar spacings for the fivefold planes that might represent physical surface terminations. In our analyses, we mainly have focused on four deterministic models which have no partial or mixed occupancy but we have made some comparisons with an undeterministic model. We have compared the models with each other and also with the available experimental data including STM, LEED-IV, XPD and LEIS. In all deterministic models, there are two different families of layers (a pair of planes), and the nondeterministic model contains similar group of planes. These two families differ in terms of the chemical decoration of their top planes. Hence, we name them as Pd+(with Pd) and Pd-(without Pd). Based on their planer structure and the step height, it can be said that these two families can be viable surface terminations. However, besides the Pd content, these two sets differ in terms of relative densities of their top planes as well as the gap separating the layer from the nearest atomic plane. The experimental data and other arguments lead to the conclusion that the Pd- family is favored over the Pd+. This has an important implication on the interpretation of local motifs seen in the high resolution STM images. In other words, the dark stars are not formed by cut-Bergmans rather they are formed by cut-Mackays.
Cortines, Juliana R.; Motwani, Tina; Vyas, Aashay A.
2014-01-01
ABSTRACT Icosahedral virus assembly requires a series of concerted and highly specific protein-protein interactions to produce a proper capsid. In bacteriophage P22, only coat protein (gp5) and scaffolding protein (gp8) are needed to assemble a procapsid-like particle, both in vivo and in vitro. In scaffolding protein's coat binding domain, residue R293 is required for procapsid assembly, while residue K296 is important but not essential. Here, we investigate the interaction of scaffolding protein with acidic residues in the N-arm of coat protein, since this interaction has been shown to be electrostatic. Through site-directed mutagenesis of genes 5 and 8, we show that changing coat protein N-arm residue 14 from aspartic acid to alanine causes a lethal phenotype. Coat protein residue D14 is shown by cross-linking to interact with scaffolding protein residue R293 and, thus, is intimately involved in proper procapsid assembly. To a lesser extent, coat protein N-arm residue E18 is also implicated in the interaction with scaffolding protein and is involved in capsid size determination, since a cysteine mutation at this site generated petite capsids. The final acidic residue in the N-arm that was tested, E15, is shown to only weakly interact with scaffolding protein's coat binding domain. This work supports growing evidence that surface charge density may be the driving force of virus capsid protein interactions. IMPORTANCE Bacteriophage P22 infects Salmonella enterica serovar Typhimurium and is a model for icosahedral viral capsid assembly. In this system, coat protein interacts with an internal scaffolding protein, triggering the assembly of an intermediate called a procapsid. Previously, we determined that there is a single amino acid in scaffolding protein required for P22 procapsid assembly, although others modulate affinity. Here, we identify partners in coat protein. We show experimentally that relatively weak interactions between coat and scaffolding proteins are capable of driving correctly shaped and sized procapsids and that the lack of these proper protein-protein interfaces leads to aberrant structures. The present work represents an important contribution supporting the hypothesis that virus capsid assembly is governed by seemingly simple interactions. The highly specific nature of the subunit interfaces suggests that these could be good targets for antivirals. PMID:24600011
Thyrhaug, Erling; Sørensen, Thomas Just; Gryczynski, Ignacy; Gryczynski, Zygmunt; Laursen, Bo W
2013-03-14
To fully exploit the capabilities of fluorescence probes in modern experiments, where advanced instrumentation is used to probe complex environments, other photophysical properties than emission color and emission intensity are monitored. Each dye property can be addressed individually as well as collectively to provide in-depth information unavailable from the standard intensity measurements. Dyes with long emission lifetimes and strongly polarized transitions enable the monitoring of lifetime changes as well as emission polarization (anisotropy). Thus experiments can be designed to follow slow dynamics. The UV and visible electronic transitions of a series of red-emitting dyes based on the triangulenium motif are investigated. We resolve overlapping features in the spectra and assign the orientation of the transition moments to the molecular axes. The result is the complete Jablonski diagram for the UV and visible spectral region. The symmetries of the studied dyes are shown to have a large influence on the optical response, and they are clearly separated into two groups of symmetry by their photophysical properties. The C(2v) symmetric dyes, azadioxatriangulenium (ADOTA(+)) and diazaoxatriangulenium (DAOTA(+)), have high emission anisotropies, fluorescence lifetimes around 20 ns, and fluorescence quantum yields of ∼50%. The trioxatriangulenium (TOTA(+)) and triazatriangulenium (TATA(+)) dyes-nominally of D(3h) symmetry-have fluorescence lifetimes around 10 ns lifetimes and fluorescence quantum yields of 10-15%. However, the D(3h) symmetry is shown to be lowered to a point group, where the axes transform uniquely such that the degeneracy of the E' states is lifted. PMID:23391292
NASA Astrophysics Data System (ADS)
Fan, Jiji
The Standard Model provides a successful description of presently known particle phenomena up to scale of hundreds of GeV. Still, the Standard Model is a work in progress and could be extended to describe physics at higher energies, for instance, the TeV scale which will be explored soon at the Large Hadron Collider. In this thesis, we present several projects exploring possible new physics beyond Standard Model and their collider signatures. The first part is dedicated to a particular supersymmetric scenario characterized by cascade decays with copious lepton production. The scenario has striking signatures that can be probed by the Large Hadron Collider even in the 10 TeV run with as little as 200 pb-1 of data, provided the squark masses are about 1 TeV. Its spectrum arises in several well-motivated models and its signatures are long-lived sleptons, numerous isolated leptons, abundant Higgs production, rather energetic jets, and no missing energy. The Higgs can be discovered in the h ? bb mode via the 4 leptons+4 jets channel because the leptons accompanying Higgs production suppress the background. We present a low-scale gaugino mediation model that realizes the scenario and reconstruct the spectrum via several clean channels. The second part explores scenarios where the electroweak symmetry breaking sector is nearly scale invariant and consequently gives rise to a light CP even scalar particle. We study the couplings of the light scalar to the Standard Model particles that can arise from the explicit breaking of scale invariance focusing on the possible differences with the minimal Standard Model. The couplings of the light scalar to light fermions, as well as to the massless gauge bosons, can be significantly enhanced. We find possible new discovery channels due to the decays of the conformal scalar into e +e- and mu+mu - pairs as well as new production channels via, light quark annihilation. In the third part, we present a calculable 'node! of electroweak symmetry breaking in which the Higgs doublet emerges from the meta-stable supersymmetry breaking sector as a pseudo Nambu-Goldstone boson. The Higgs boson mass is further protected by the little Higgs mechanism, and naturally suppressed by a two-loop factor from the supersymmetry breaking scale of 10 TeV. The last part discusses one Lorentz violation scheme where the spacetime symmetry is a subgroup of the full Lorentz group and atomic experiment constraints on this scheme.
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.
Symmetry is less than meets the eye.
Apthorp, Deborah; Bell, Jason
2015-03-30
Symmetry is a ubiquitous feature in the visual environment and can be detected by a variety of species, ranging from insects through to humans [1,2]. Here we show it can also bias estimates of basic scene properties. Mirror (reflective) symmetry can be detected in as little as 50 ms, in both natural and artificial visual scenes, and even when embedded within cluttered backgrounds [1]. In terms of its biological relevance, symmetry is a key determinant in mate selection; the degree of symmetry in a face is positively associated with perceived healthiness and attractiveness ratings [3]. In short, symmetry processing mechanisms are an important part of the neural machinery of vision. We reveal that the importance of symmetry extends beyond the processing of shape and objects. Mirror symmetry biases our perception of scene content, with symmetrical patterns appearing to have fewer components than their asymmetric counterparts. This demonstrates an interaction between two fundamental dimensions of visual analysis: symmetry [1] and number [4]. We propose that this numerical underestimation results from a processing bias away from the redundant information within mirror symmetrical displays, extending existing theories regarding redundancy in visual analysis [5,6]. PMID:25829006
PT-symmetry in honeycomb photonic lattices
Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We apply gain and loss to honeycomb photonic lattices and show that the dispersion relation is identical to tachyons--particles with imaginary mass that travel faster than the speed of light. This is accompanied by -symmetry breaking in this structure. We further show that the -symmetry can be restored by deforming the lattice.
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.
Topological symmetry breaking by quantum wormholes
Mignemi, S.; Moss, I. )
1993-10-15
In multiply connected spacetimes which contain quantum wormholes it may be possible to break gauge symmetries without the usual Higgs fields. In a simple model, symmetry breaking is favored by the quantum effects of Dirac Fermions and leads to vector boson masses related to the wormhole separation.
Fourier type transforms on Lie symmetry groups
NASA Astrophysics Data System (ADS)
Craddock, Mark
2015-09-01
In this paper, we construct operators on a Lie symmetry group which may be regarded as Fourier transforms. Essentially, we integrate solutions generated by Lie symmetries against suitable test functions. We show that this idea leads to a powerful method for solving Cauchy problems for parabolic and hyperbolic equations in two and higher dimensions. We also discuss applications to the elliptic case.
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)
Hojman symmetry in f(T) theory
NASA Astrophysics Data System (ADS)
Wei, Hao; Zhou, Ya-Nan; Li, Hong-Yu; Zou, Xiao-Bo
2015-11-01
Today, f(T) theory has been one of the popular modified gravity theories to explain the accelerated expansion of the universe without invoking dark energy. In this work, we consider the so-called Hojman symmetry in f(T) theory. Unlike Noether conservation theorem, the symmetry vectors and the corresponding conserved quantities in Hojman conservation theorem can be obtained by using directly the equations of motion, rather than Lagrangian or Hamiltonian. We find that Hojman symmetry can exist in f(T) theory, and the corresponding exact cosmological solutions are obtained. We find that the functional form of f(T) is restricted to be the power-law or hypergeometric type, while the universe experiences a power-law or hyperbolic expansion. These results are different from the ones obtained by using Noether symmetry in f(T) theory. Therefore, it is reasonable to find exact cosmological solutions via Hojman symmetry.
Ermakov's Superintegrable Toy and Nonlocal Symmetries
NASA Astrophysics Data System (ADS)
Leach, P. G. L.; Karasu Kalkanli, A.; Nucci, M. C.; Andriopoulos, K.
2005-11-01
We investigate the symmetry properties of a pair of Ermakov equations. The system is superintegrable and yet possesses only three Lie point symmetries with the algebra sl(2, R). The number of point symmetries is insufficient and the algebra unsuitable for the complete specification of the system. We use the method of reduction of order to reduce the nonlinear fourth-order system to a third-order system comprising a linear second-order equation and a conservation law. We obtain the representation of the complete symmetry group from this system. Four of the required symmetries are nonlocal and the algebra is the direct sum of a one-dimensional Abelian algebra with the semidirect sum of a two-dimensional solvable algebra with a two-dimensional Abelian algebra. The problem illustrates the difficulties which can arise in very elementary systems. Our treatment demonstrates the existence of possible routes to overcome these problems in a systematic fashion.
Natural Electroweak Breaking from a Mirror Symmetry
Chacko, Z.; Goh, Hock-Seng; Harnik, Roni
2006-06-16
We present ''twin Higgs models,'' simple realizations of the Higgs boson as a pseudo Goldstone boson that protect the weak scale from radiative corrections up to scales of order 5-10 TeV. In the ultraviolet these theories have a discrete symmetry which interchanges each standard model particle with a corresponding particle which transforms under a twin or a mirror standard model gauge group. In addition, the Higgs sector respects an approximate global symmetry. When this global symmetry is broken, the discrete symmetry tightly constrains the form of corrections to the pseudo Goldstone Higgs potential, allowing natural electroweak symmetry breaking. Precision electroweak constraints are satisfied by construction. These models demonstrate that, contrary to the conventional wisdom, stabilizing the weak scale does not require new light particles charged under the standard model gauge groups.
Shukla, A. K.; Dhaka, R. S.; Biswas, C.; Banik, S.; Barman, S. R.; Horn, K.; Ebert, Ph.; Urban, K.
2006-02-01
We report x-ray photoelectron spectroscopy (XPS) study of Na and K adlayers on icosahedral Al{sub 70.5}Pd{sub 21}Mn{sub 8.5} (i-Al-Pd-Mn) quasicrystal. The Na 1s core-level exhibits a continuous linear shift of 0.8 eV towards lower binding energies (BE) with increasing coverage up to one monolayer (ML) saturation coverage. In the case of K/i-Al-Pd-Mn, a similar linear shift in the K 2p spectra towards lower BE is observed. In both cases, the plasmon related loss features are observed only above 1 ML. The substrate core-level peaks, such as Al 2p, do not exhibit any shift with the adlayer deposition up to the highest coverage. Based on these experimental observations and previous studies of alkali metal growth on metals, we conclude that below 1 ML, both Na and K form a dispersed phase on i-Al-Pd-Mn and there is hardly any charge transfer to the substrate. The variation of the adlayer and substrate core-level intensities with coverage indicates layer by layer growth.
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.
Doronin, Yu. S.; Libin, M. Yu.; Samovarov, V. N.; Vakula, V. L.
2011-08-15
Supersonic-jet luminescence spectroscopy was applied to study vibronic transitions in icosahedral N{sub 2} and Ar-N{sub 2} clusters having from 100 to 400 particles per cluster. In the case of mixed Ar-N{sub 2} clusters, the w {sup 1}{Delta}{sub u}{yields} X {sup 1}{Sigma}{sub g}{sup +} transitions were observed to occur in single N{sub 2} molecules in an Ar environment, in very much the same way as in Ar-N{sub 2} bulk samples. In N{sub 2} clusters, however, a band series was detected which, to our knowledge, was never observed earlier. In the spectra of Ar-N{sub 2} clusters, this series coexisted with the ''bulk''w {sup 1}{Delta}{sub u}{yields} X{sup 1}{Sigma}{sub g}{sup +} transitions. Our analysis demonstrated that the series should be assigned to emission of van der Waals (N{sub 2}){sub 2} dimers from inside clusters. Earlier, such dimers were only observed in molecular beams and gaseous nitrogen; this paper reports their observation in the solid phase of nitrogen. Our results can be of interest from the viewpoint of producing polymeric nitrogen since (N{sub 2}){sub 2} dimers can be considered to be a starting species for its synthesis.
Ambrose, Rebecca L.; Lander, Gabriel C.; Maaty, Walid S.; Bothner, Brian; Johnson, John E.; Johnson, Karyn N.
2009-01-01
The vinegar fly, Drosophila melanogaster, is a popular model for the study of invertebrate antiviral immune responses. Several picorna-like viruses are commonly found in both wild and laboratory populations of D. melanogaster. The best-studied and most pathogenic of these is the dicistrovirus Drosophila C virus. Among the uncharacterized small RNA viruses of D. melanogaster, Drosophila A virus (DAV) is the least pathogenic. Historically, DAV has been labelled as a picorna-like virus based on its particle size and the content of its RNA genome. Here, we describe the characterization of both the genome and the virion structure of DAV. Unexpectedly, the DAV genome was shown to encode a circular permutation in the palm-domain motifs of the RNA-dependent RNA polymerase. This arrangement has only been described previously for a subset of viruses from the double-stranded RNA virus family Birnaviridae and the T=4 single-stranded RNA virus family Tetraviridae. The 8? (0.8?nm) DAV virion structure computed from cryo-electron microscopy and image reconstruction indicates that the virus structural protein forms two discrete domains within the capsid. The inner domain is formed from a clear T=3 lattice with similarity to the ?-sandwich domain of tomato bushy stunt virus, whilst the outer domain is not ordered icosahedrally, but forms a cage-like structure that surrounds the core domain. Taken together, this indicates that DAV is highly divergent from previously described viruses. PMID:19474243
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
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster-session, topics ranging from theoretical chemistry and molecular physics via fundamental problems in quantum theory to thermodynamics, nonlinear dynamics, soliton theory and finally cosmology, were examined and lively discussed. Nearly all the talks can also be viewed on the conference website. The majority of participants contributed to these Proceedings but some were unable to do so as their results were either previously submitted or published elsewhere. We refer to: · Quesne C 2013, J. Math. Phys. 54, 102102. · Spera M 2013, (Nankai Series in Pure, Applied Mathematics and Theoretical Physics): 11 Symmetries and Groups in Contemporary Physics: pp. 593-598 Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics Tianjin, China, 20 - 26 August 2012 (World Scientific, Singapore) · Snobl L and Winternitz P 2014, Classification and Identification of Lie Algebras, CRM Monograph Series 33 (Montreal) ISBN-10: 0-8218-4355-9, ISBN-13: 978-0-8218-4355-0 (http://www.ams.org/bookstore?fn=20&arg1=crmmseries&ikey=CRMM-33). Our personal thanks to Daniel and family! Endless support from the Schenk Family who, among other things, sponsored (yet again) the entire conference dinner (including wines and banquet hall) meant that some costs could be alleviated. We could therefore assist various colleagues from economically-weak countries, despite the lack of external funding. A financial deficit meant we would have had to forego the Conference Proceedings, published in previous years by IOP. After long deliberations, and with donations from Gerhard Berssenbrügge, Dr. Dr. Stephan Hauk and Dr. Volker Weisswange, this could be facilitated. We are very grateful to these private donors for their generous and wholehearted support. The staff of Collegium Mehrerau is also to be thanked for their hospitality. Finally, our sincere thanks to Yvette not only for her preparatory work and support during the conference, but also for her persistent interest and help in producing the Proceedings within a reasonable time. Dieter Schuch, Frankfurt am Main, Germany Michael Ramek, Graz, Austria August 2014
Natural quasicrystal with decagonal symmetry
NASA Astrophysics Data System (ADS)
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-03-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) <= 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula.
Structural symmetry in evolutionary games.
McAvoy, Alex; Hauert, Christoph
2015-10-01
In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time, for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be 'evolutionarily equivalent' in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term 'homogeneous' should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry. PMID:26423436
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120 K to 1200 K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ≤ 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
PREFACE: Symmetries in Science 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 Proceedings though some were unable to do so as their results were either previously submitted or published elsewhere. In order to make these contributions also available to readers of the Proceedings, we now list the respective references as follow: Albertsson C, Hlavatý L and Šnobl L 2008 On the Poisson-Lie T-plurality of boundary conditions J. Math. Phys. 49 032301-23, arXiv:0706.0820; Bender C M, Brody D C and Hook D W 2008 Quantum effects in classical systems having complex energy J. Phys. A: Math. Theor. 41 352003 (15 pp); Kanellopoulos V, Kleber M and Kramer T 2009 Use of Lambert's theorem for the n-dimensional Coulomb problem Phys. Rev. A 80 012101; Kramer P 2010 Platonic topology and CMB fluctuations: homotopy anisotropy and multipole selection rules Class. Quantum Grav. 27 095013 (27 pp), arXiv:0909.2758v1; Quesne C 2009 Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics SIGMA 5 084 (24 pp). On the other hand, some colleagues planning on attending the meeting had to forfeit their participation due to unforeseeable circumstances. As they had prepared their contributions particularly for our symposium, we have also allowed their input. The articles of Kibler, Leach, Reinisch and Wolf have therefore been included though the authors were absent. Marcos Moshinsky and Yuriĭ Smirnov, two long-standing colleagues and friends who attended the symposium on multiple occasions passed away in the year before the conference. A memorial service was held at the chapel of the Mehrerau during the meeting. The commemorative words from Father Vinzenz were based on information from our own experience, from an article by Alejandro Frank in Letras Libres Junio 2009, p.54 (a monthly literary magazine published by Editorial Vuelta, in Spanish) and articles from "TESTIMONIOS, Marcos Moshinsky: 80 años de vida y 60 años de trabajo científico" 2001 Frank A and Wolf K B eds. Two contributions dedicated especially in their memory are also included in these Proceedings. It was especially rewarding and greatly appreciated that symposium-founder Bruno Gruber attended all the sessions and that Dr. Hubert Regner, a distinguished official of the provincial administration and ardent supporter of the symposia for over twenty years, honoured us with a visit and an encouraging address to the participants. We wish to express our sincere gratitude to the local community, particularly the Schenk Family and the staff of Collegium Mehrerau for the selfless friendship, generosity and kind hospitality they offered our gathering. It made a lasting impression on participants and guests alike and provided an excellent basis for fruitful scientific discussions and personal interactions. This and the positive resonance from participants have encouraged us to take the experiment a step further to "Symmetries in Science 2011"! Thanks also to Yvette for continuous and reliable support. The conference and proceedings would probably not have materialized without her. Frankfurt am Main and Graz, June 2010 Dieter Schuch Michael Ramek Conference photograph
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
Symmetry and range limits in importance indices.
Seifan, Tal; Seifan, Merav
2015-10-01
Recently, Mingo has analyzed the properties of I imp, an importance index, and demonstrated that its range is not symmetrical. While agreeing with this comment, we believe that more light needs to be shed on the issue of symmetry in relation to such indices. Importance indices are calculated using three values: performance of the organism in the absence and in the presence of neighbors and maximum performance of the organism in ideal conditions. Because of this structure, importance indices can hardly ever achieve symmetry along the whole range of potential performances. We discuss the limitation of the symmetry range for different symmetry types and for both additive and multiplicative indices. We conclude that importance indices, as other interactions indices, are practical tools for interpreting ecological outcomes, especially while comparing between studies. Nevertheless, the current structure of importance indices prevents symmetry along their whole range. While the lack of "perfect" symmetry may call for the development of more sophisticated importance metrics, the current indices are still helpful for the understanding of biological systems and should not be discarded before better alternatives are well established. To prevent potential confusion, we suggest that ecologists present the relevant index symmetry range in addition to their results, thus minimizing the probability of misinterpretation. PMID:26668718
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
Sufficient symmetry conditions for Topological Quantum Order
Nussinov, Zohar; Ortiz, Gerardo
2009-01-01
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn–Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order. PMID:19805113
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.
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.
Replica-symmetry breaking in neural networks
NASA Astrophysics Data System (ADS)
Dotsenko, V. S.; Tirozzi, B.
1992-06-01
Replica-symmetry breaking is studied in fully connected neural networks with modified pseudo-inverse interactions. The interaction matrix has an intermediate form between the Hebb learning rule and the pseudo-inverse one. At low temperature there is a region of parameters where the replica-symmetric solution is stable while its entropy is negative. It indicates the existence of the alternative solution in which the replica symmetry is broken. A one-stop replica-symmetry breaking solution is found and its properties are analyzed.
Nonanomalous discrete R symmetry decrees three generations.
Evans, Jason L; Ibe, Masahiro; Kehayias, John; Yanagida, Tsutomu T
2012-11-01
We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R symmetry larger than R parity, provided that the supersymmetric standard model can be minimally embedded into a grand unified theory. This connects an explanation for the number of generations with seemingly unrelated problems such as supersymmetry breaking, proton decay, the μ problem, and the cosmological constant through a discrete R symmetry. We also show that three generations is uniquely required by a nonanomalous discrete R symmetry in classes of grand unified theories such as the ones based on (semi)simple gauge groups. PMID:23215270
Electromagnetic radiation under explicit symmetry breaking.
Sinha, Dhiraj; Amaratunga, Gehan A J
2015-04-10
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna. PMID:25910163
Exploring Symmetry to Assist Alzheimer's Disease Diagnosis
NASA Astrophysics Data System (ADS)
Illán, I. A.; Górriz, J. M.; Ramírez, J.; Salas-Gonzalez, D.; López, M.; Padilla, P.; Chaves, R.; Segovia, F.; Puntonet, C. G.
Alzheimer's disease (AD) is a progressive neurodegenerative disorder first affecting memory functions and then gradually affecting all cognitive functions with behavioral impairments and eventually causing death. Functional brain imaging as Single-Photon Emission Computed Tomography (SPECT) is commonly used to guide the clinician's diagnosis. The essential left-right symmetry of human brains is shown to play a key role in coding and recognition. In the present work we explore the implications of this symmetry in AD diagnosis, showing that recognition may be enhanced when considering this latent symmetry.
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.
Shift-symmetries at higher order
NASA Astrophysics Data System (ADS)
Abel, Steven; Stewart, Richard J.
2016-02-01
The fate of shift-symmetries in effective string models is considered beyond tree-level. Such symmetries have been proposed in the past as a way to maintain a hierarchically small Higgs mass and also play a role in schemes of cosmological relaxation. It is argued that on general grounds one expects shift-symmetries to be restored in the limit of certain asymmetric compactifications, to all orders in perturbation theory. This behaviour is verified by explicit computation of the Kähler potential to one-loop order.
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.
Timelike infinity and asymptotic symmetry
NASA Astrophysics Data System (ADS)
Gen, Uchida; Shiromizu, Tetsuya
1998-12-01
By extending Ashtekar and Romano's definition of spacelike infinity to the timelike direction, a new definition of asymptotic flatness at timelike infinity for an isolated system with a source is proposed. The treatment provides unit spacelike three-hyperboloid timelike infinity and avoids the introduction of the troublesome differentiability conditions which were necessary in the previous works on asymptotically flat space-times at timelike infinity. Asymptotic flatness is characterized by the falloff rate of the energy-momentum tensor at timelike infinity, which makes it easier to understand physically what space-times are investigated. The notion of the order of the asymptotic flatness is naturally introduced from the rate. The definition gives a systematized picture of hierarchy in the asymptotic structure, which was not clear in the previous works. It is found that if the energy-momentum tensor falls off at a rate faster than ˜t-2, the space-time is asymptotically flat and asymptotically stationary in the sense that the Lie derivative of the metric with respect to ∂t falls off at the rate ˜t-2. It also admits an asymptotic symmetry group similar to the Poincaré group. If the energy-momentum tensor falls off at a rate faster than ˜t-3, the four-momentum of a space-time may be defined. On the other hand, angular momentum is defined only for space-times in which the energy-momentum tensor falls off at a rate faster than ˜t-4.
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.
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.
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.
Permutation Symmetry Determines the Discrete Wigner Function
NASA Astrophysics Data System (ADS)
Zhu, Huangjun
2016-01-01
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry transformation. We prove that, in the discrete scenario, this permutation symmetry is equivalent to the symmetry group being a unitary 2 design. Such a highly symmetric representation can only appear in odd prime power dimensions besides dimensions 2 and 8. It suffices to single out a unique discrete Wigner function among all possible quasiprobability representations. In the course of our study, we show that this discrete Wigner function is uniquely determined by Clifford covariance, while no Wigner function is Clifford covariant in any even prime power dimension.
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 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.
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.
R parity violation from discrete R symmetries
NASA Astrophysics Data System (ADS)
Chen, Mu-Chun; Ratz, Michael; Takhistov, Volodymyr
2015-02-01
We consider supersymmetric extensions of the standard model in which the usual R or matter parity gets replaced by another R or non-R discrete symmetry that explains the observed longevity of the nucleon and solves the μ problem of MSSM. In order to identify suitable symmetries, we develop a novel method of deriving the maximal ZN(R) symmetry that satisfies a given set of constraints. We identify R parity violating (RPV) and conserving models that are consistent with precision gauge unification and also comment on their compatibility with a unified gauge symmetry such as the Pati-Salam group. Finally, we provide a counter-example to the statement found in the recent literature that the lepton number violating RPV scenarios must have μ term and the bilinear κLHu operator of comparable magnitude.
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.
Permutation Symmetry Determines the Discrete Wigner Function.
Zhu, Huangjun
2016-01-29
The Wigner function provides a useful quasiprobability representation of quantum mechanics, with applications in various branches of physics. Many nice properties of the Wigner function are intimately connected with the high symmetry of the underlying operator basis composed of phase point operators: any pair of phase point operators can be transformed to any other pair by a unitary symmetry transformation. We prove that, in the discrete scenario, this permutation symmetry is equivalent to the symmetry group being a unitary 2 design. Such a highly symmetric representation can only appear in odd prime power dimensions besides dimensions 2 and 8. It suffices to single out a unique discrete Wigner function among all possible quasiprobability representations. In the course of our study, we show that this discrete Wigner function is uniquely determined by Clifford covariance, while no Wigner function is Clifford covariant in any even prime power dimension. PMID:26871314
Symmetry reduction of quasi-free states
Torre, C. G.
2009-06-15
Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is noncompact, the group averaging prescription relies on technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein-Gordon field on Minkowski spacetime by a noncompact subgroup of the Poincare group consisting of a 1-parameter family of boosts, a 1-parameter family of spatial translations and a set of discrete translations. We show that the symmetry-reduced CCR algebra and vacuum state correspond to that used by each of Berger, Husain, and Pierri for the polarized Gowdy T{sup 3} quantum gravity model.
Infinite symmetry in the quantum Hall effect
NASA Astrophysics Data System (ADS)
Lütken, C. A.
2014-04-01
The new states of matter and concomitant quantum critical phenomena revealed by the quantum Hall effect appear to be accompanied by an emergent modular symmetry. The extreme rigidity of this infinite symmetry makes it easy to falsify, but two decades of experiments have failed to do so, and the location of quantum critical points predicted by the symmetry is in increasingly accurate agreement with scaling experiments. The symmetry severely constrains the structure of the effective quantum field theory that encodes the low energy limit of quantum electrodynamics of 1010 charges in two dirty dimensions. If this is a non-linear σ-model the target space is a torus, rather than the more familiar sphere. One of the simplest toroidal models gives a critical (correlation length) exponent that agrees with the value obtained from numerical simulations of the quantum Hall effect.
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.
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
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.
Symmetries and reduction in nonholonomic mechanics
NASA Astrophysics Data System (ADS)
Borisov, Alexey V.; Mamaev, Ivan S.
2015-09-01
This paper is a review of the problem of the constructive reduction of nonholonomic systems with symmetries. The connection of reduction with the presence of the simplest tensor invariants (first integrals and symmetry fields) is shown. All theoretical constructions are illustrated by examples encountered in applications. In addition, the paper contains a short historical and critical sketch covering the contribution of various researchers to this problem.
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.
Phil Anderson and Gauge Symmetry Breaking
NASA Astrophysics Data System (ADS)
Witten, Edward
In this article, I describe the celebrated paper that Phil Anderson wrote in 1962 with early contributions to the idea of gauge symmetry breaking in particle physics. To set the stage, I describe the work of Julian Schwinger to which Anderson was responding, and also some of Anderson's own work on superconductivity that provided part of the context. After describing Anderson's work I describe the later work of others, leading to the modern understanding of gauge symmetry breaking in weak interactions...
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.
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.
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.
Relabeling symmetries in hydrodynamics and magnetohydrodynamics
Padhye, N.; Morrison, P.J.
1996-04-01
Lagrangian symmetries and concomitant generalized Bianchi identities associated with the relabeling of fluid elements are found for hydrodynamics and magnetohydrodynamics (MHD). In hydrodynamics relabeling results in Ertel`s theorem of conservation of potential vorticity, while in MHD it yields the conservation of cross helicity. The symmetries of the reduction from Lagrangian (material) to Eulerian variables are used to construct the Casimir invariants of the Hamiltonian formalism.
Squeezing lepton pairs out of broken symmetries
NASA Astrophysics Data System (ADS)
Dutt-Mazumder, A. K.; Gale, C.; Majumder, A.; Teodorescu, O.
2002-04-01
We discuss two possible signatures of symmetry breaking that can appear in dilepton spectra, as measured in relativistic heavy ion collisions. The first involves scalar-vector meson mixing and is related to the breaking of Lorentz symmetry by a hot medium. The second is related to the breaking of Furry's theorem by a charged quark-gluon plasma. Those signals will be accessible to upcoming measurements to be performed at the GSI, RHIC, and the LHC. .
Symmetry calculation for molecules and transition states.
Vandewiele, Nick M; Van de Vijver, Ruben; Van Geem, Kevin M; Reyniers, Marie-Franoise; Marin, Guy B
2015-01-30
The symmetry of molecules and transition states of elementary reactions is an essential property with important implications for computational chemistry. The automated identification of symmetry by computers is a very useful tool for many applications, but often relies on the availability of three-dimensional coordinates of the atoms in the molecule and hence becomes less useful when these coordinates are a priori unavailable. This article presents a new algorithm that identifies symmetry of molecules and transition states based on an augmented graph representation of the corresponding structures, in which both topology and the presence of stereocenters are accounted for. The automorphism group order of the graph associated with the molecule or transition state is used as a starting point. A novel concept of label-stereoisomers, that is, stereoisomers that arise after labeling homomorph substituents in the original molecule so that they become distinguishable, is introduced and used to obtain the symmetry number. The algorithm is characterized by its generic nature and avoids the use of heuristic rules that would limit the applicability. The calculated symmetry numbers are in agreement with expected values for a large and diverse set of structures, ranging from asymmetric, small molecules such as fluorochlorobromomethane to highly symmetric structures found in drug discovery assays. The new algorithm opens up new possibilities for the fast screening of the degree of symmetry of large sets of molecules. PMID:25421576
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.
Symmetry-improved CJT effective action
NASA Astrophysics Data System (ADS)
Pilaftsis, Apostolos; Teresi, Daniele
2013-09-01
The formalism introduced by Cornwall, Jackiw and Tomboulis (CJT) provides a systematic approach to consistently resumming non-perturbative effects in Quantum Thermal Field Theory. One major limitation of the CJT effective action is that its loopwise expansion introduces residual violations of possible global symmetries, thus giving rise to massive Goldstone bosons in the spontaneously broken phase of the theory. In this paper we develop a novel symmetry-improved CJT formalism for consistently encoding global symmetries in a loopwise expansion. In our formalism, the extremal solutions of the fields and propagators to a loopwise truncated CJT effective action are subject to additional constraints given by the Ward Identities due to global symmetries. By considering a simple O(2) scalar model, we show that, unlike other methods, our approach satisfies a number of important field-theoretic properties. In particular, we find that the Goldstone boson resulting from spontaneous symmetry breaking of O(2) is massless and the phase transition is a second-order one, already in the Hartree-Fock approximation. After taking the sunset diagrams into account, we show how our approach properly describes the threshold properties of the massless Goldstone boson and the Higgs particle in the loops. Finally, assuming minimal modifications to the Hartree-Fock approximated CJT effective action, we calculate the corresponding symmetry-improved CJT effective potential and discuss the conditions for its uniqueness for scalar-field values away from its minimum.
Symmetry in Flowers: Diversity and Evolution.
Endress
1999-11-01
This article traces research on floral symmetry back to its beginnings. It brings together recent advances from different fields that converge in floral symmetry and new unpublished material on diversity and development of floral symmetry. During floral development, symmetry may change: monosymmetric flowers may have a polysymmetric early phase; polysymmetric flowers may have a monosymmetric or even asymmetric early phase; more than one symmetry change is also possible. In Lamiales s.l. (comprising the model plant Antirrhinum, where the cycloidea gene produces monosymmetric flowers with the adaxial side of the androecium reduced), taxa also occur in which the androecium is reduced on both sides, adaxial and abaxial. As a trend in asymmetric flowers, enantiomorphy (with two mirror-image morphs) at the level of individuals seems to occur only in groups in which the flowers are predominantly of a relatively simple construction. In contrast, one morph is fixed at the level of species or higher taxa in groups with more complicated flowers. This is indicated by the apparent lack of enantiomorphy in corolla contortion in asterids but its predominance in rosids with contort flowers, or by the apparent lack of enantiomorphy in the pollination organs of asymmetric flowers in Faboideae but its presence in asymmetric flowers in Caesalpinioideae. To study the evolution of the diverse symmetry patterns, a concerted approach from different fields including molecular developmental genetics, pollination biology, and comparative diversity research is necessary. PMID:10572019
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.
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
Spontaneous Breaking of Symmetry in Moyal Spacetime with Twisted Poincare Symmetry
Govindarajan, T. R.
2009-12-15
After briefly reviewing the gauge symmetry in Moyal spacetimes, we analyse aspects of symmetry breaking within a quantisation program preserving the twisted Poincare symmetry. We develop the LSZ approach for Moyal spacetimes and derive a mapping for scattering amplitudes on these spacetimes from the corresponding ones on the commutative spacetime. This map applies in the presence of spontaneous breakdown of symmetries as well. We also derive Goldstone's theorem on Moyal spacetime. The formalism developed here can be directly applied to the twisted standard model.
NASA Astrophysics Data System (ADS)
Dai, Tie; Shi, Guangyu; Nakajima, Teruyuki
2015-06-01
Aerosol optical properties are simulated using the Spectral Radiation Transport Model for Aerosol Species (SPRINTARS) coupled with the Non-hydrostatic ICosahedral Atmospheric Model (NICAM). The 3-year global mean all-sky aerosol optical thickness (AOT) at 550 nm, the Ångström Exponent (AE) based on AOTs at 440 and 870 nm, and the single scattering albedo (SSA) at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Aerosol Robotic Network (AERONET). The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the opposite is found over regions dominated by hydrophobic aerosol.
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
NASA Astrophysics Data System (ADS)
Lv, Bin-Jiang; Peng, Jian; Chu, Zhong
2015-09-01
The effect of Icosahedral phase (I-phase) on hot deformation behavior, dynamic recrystallization (DRX) evolution, and hot workability of Mg-2.0Zn-0.3Zr-0.2Y alloy has been investigated in the temperature range of 300-500 °C and strain rate range of 0.001-1 s-1 using Gleeble 3500D thermo-mechanical simulator. Based on regression analysis for Arrhenius-type equation of flow behavior, the average activation energy of deformation was determined as Q = 277.8 kJ/mol. The model of DRX evolution is . The DRX model agreed well with the microstructure evolution of the alloy at all deformation conditions. At lower strain rates (0.001-0.01 s-1), continuous DRX (CDRX) is the main DRX mechanism that occurred near the original grain boundaries. Twin-dynamic recrystallization (TDRX) began to occur at lower deformation temperatures and higher strain rates (0.1-1 s-1). At a deformation temperature range of 250 to 350 °C and a strain rate of 1 s-1, the main DRX mechanism is TDRX, and the density of twins decreased, and CDRX began to occur near the original grain boundaries. When the deformation temperature increased to 400 °C, TDRX disappeared and CDRX occurred near original grain boundaries and I-phase particles. According to the flow stress behavior and DRX model, the processing maps have exhibited the optimum deformation conditions to be 450 °C and the strain rate range of 0.01-0.001 s-1.
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 assumed symmetry breaking. In the last part of this thesis, we investigate the possibility of spontaneously breaking of Hamiltonian itself. The homogeneity of time is one of the most fundamental symmetries of nature, underlying the conservation of the energy. The question is whether this symmetry can be spontaneously broken, as suggested recently by Wilczek, in analogy with ordinary crystals. Contrary to his proposal that attracted a significant attention and stimulated many further studies, we prove a no-go theorem that rules out spontaneously breaking of time translation, in the ground state or in the canonical ensemble of a general Hamiltonian.
Haruyama, O.; Miyazawa, T.; Saida, J.; Inoue, A.
2001-08-06
The glass-to-icosahedral phase transformation in Zr{sub 70}Pd{sub 20}Ni{sub 10} and Zr{sub 65}Al{sub 7.5}Cu{sub 7.5}Ni{sub 10}Ag{sub 10} glasses was examined by the electrical resistivity measurement performed with a heating rate of 0.67 K/s. The resistivity increased with the promotion of icosahedral precipitation in Zr{sub 70}Pd{sub 20}Ni{sub 10} glass. On the other hand, Zr{sub 65}Al{sub 7.5}Cu{sub 7.5}Ni{sub 10}Ag{sub 10} glass exhibited the decrement of the resistivity according to the evolution of icosahedral phase. The latter was qualitatively explained by the drop of the resistivity of supercooled liquid phase due to the transfer of oxide atoms into the icosahedral phase. Also, the low temperature resistivity experiment showed that the conductivity of glassy and icosahedral phases might obey the weak localization model of conduction electrons. {copyright} 2001 American Institute of Physics.
Perception of Mirror Symmetry in Autism Spectrum Disorders
ERIC Educational Resources Information Center
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals
Perception of Mirror Symmetry in Autism Spectrum Disorders
ERIC Educational Resources Information Center
Falter, Christine M.; Bailey, Anthony J.
2012-01-01
Gestalt grouping in autism spectrum disorders (ASD) is selectively impaired for certain organization principles but for not others. Symmetry is a fundamental Gestalt principle characterizing many biological shapes. Sensitivity to symmetry was tested using the Picture Symmetry Test, which requires finding symmetry lines on pictures. Individuals…
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 AdS waves.
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.
Statistical palaeomagnetic field modelling and symmetry considerations
NASA Astrophysics Data System (ADS)
Hulot, G.; Bouligand, C.
2005-06-01
In the present paper, we address symmetry issues in the context of the so-called giant gaussian process (GGP) modelling approach, currently used to statistically analyse the present and past magnetic field of the Earth at times of stable polarity. We first recall the principle of GGP modelling, and for the first time derive the complete and exact constraints a GGP model should satisfy if it is to satisfy statistical spherical, axisymmetrical or equatorially symmetric properties. We note that as often correctly claimed by the authors, many simplifying assumptions used so far to ease the GGP modelling amount to make symmetry assumptions, but not always exactly so, because previous studies did not recognize that symmetry assumptions do not systematically require a lack of cross-correlations between Gauss coefficients. We further note that GGP models obtained so far for the field over the past 5Myr clearly reveal some spherical symmetry breaking properties in both the mean and the fluctuating field (as defined by the covariance matrix of the model) and some equatorial symmetry breaking properties in the mean field. Non-zonal terms found in the mean field of some models and mismatches between variances defining the fluctuating field (in models however not defined in a consistent way) would further suggest that axial symmetry also is broken. The meaning of this is discussed. Spherical symmetry breaking trivially testifies for the influence of the rotation of the Earth on the geodynamo (a long-recognized fact). Axial symmetry breaking, if confirmed, could hardly be attributed to anything else but some influence of the core-mantle boundary (CMB) conditions on the geodynamo (also a well-known fact). By contrast, equatorial symmetry breaking (in particular the persistence of an axial mean quadrupole) may not trivially be considered as evidence of some influence of CMB conditions. To establish this, one would need to better investigate whether or not this axial quadrupole has systematically reversed its polarity with the axial dipole in the past and whether dynamo simulations run under equatorial symmetric CMB conditions display additional transitions (mirror transitions, which we describe) only allowed in such instances. This remains to be fully investigated.
Group Parametrized Tunneling and Local Symmetry Conditions
NASA Astrophysics Data System (ADS)
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar 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 J. C. Mitchell, 2009 MSS RJ05 (See also following talk.) R.P. Feynman, R. B. Leighton, M. Sands, Lectures on Physics Vol.3 (Addison Wesley 1964) p.9-1 W.G. Harter, Principles of Symmetry, Dynamics, and Spectroscopy, (Wiley Interscience, 1993) p.265
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.
Resurrection of a Symmetry in Nucleon-Nucleus Scattering
Ginocchio, J.N.
1999-06-01
We reexamine a symmetry in nucleon-nucleus scattering that previously had been proclaimed to be dead. We show that this symmetry is the continuum analog of pseudospin symmetry, a relativistic symmetry which manifests itself in the spectra of nuclei. Using experimental data only, we show that pseudospin symmetry in nucleon-nucleus scattering is not dead but only modestly broken for 800thinspthinspMeV proton scattering on nuclei. {copyright} {ital 1999} {ital The American Physical Society}
Symmetry in social exchange and health
NASA Astrophysics Data System (ADS)
Siegrist, Johannes
2005-10-01
Symmetry is a relevant concept in sociological theories of exchange. It is rooted in the evolutionary old norm of social reciprocity and is particularly important in social contracts. Symmetry breaking through violation of the norm of reciprocity generates strain in micro-social systems and, above all, in victims of non-symmetric exchange. In this contribution, adverse healthconsequences of symmetry breaking in contractual social exchange are analysed, with a main focus on the employment contract. Scientific evidence is derived from prospective epidemiological studies testing the model of effort-reward imbalance at work. Overall, a twofold elevated risk of incident disease is observed in employed men and women who are exposed to non-symmetric exchange. Health risks include coronary heart disease, depression and alcohol dependence, among others. Preliminary results suggest similar effects on health produced by symmetry breaking in other types of social relationships (e.g. partnership, parental roles). These findings underline the importance of symmetry in contractual social exchange for health and well-being.
Discrete R symmetries and low energy supersymmetry
Dine, Michael; Kehayias, John
2010-09-01
If nature exhibits low energy supersymmetry, discrete (non-Z{sub 2}) R symmetries may well play an important role. In this paper, we explore such symmetries. We generalize gaugino condensation, constructing large classes of models which are classically scale invariant, and which spontaneously break discrete R symmetries (but not supersymmetry). The order parameters for the breaking include chiral singlets. These simplify the construction of models with metastable dynamical supersymmetry breaking. We explain that in gauge mediation, the problem of the cosmological constant makes ''retrofitting'' particularly natural--almost imperative. We describe new classes of models, with interesting scales for supersymmetry breaking, and which allow simple solutions of the {mu} problem. We argue that models exhibiting such R symmetries can readily solve not only the problem of dimension four operators and proton decay, but also dimension five operators. On the other hand, in theories of ''gravity mediation,'' the breaking of an R symmetry is typically of order M{sub p}; R parity is required to suppress dimension four B and L violating operators, and dimension five operators remain problematic.
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.
Student understanding of Symmetry and Gauss's law
NASA Astrophysics Data System (ADS)
Singh, Chandralekha
2005-09-01
Helping students learn why Gauss's law can or cannot be easily applied to determine the strength of the electric field at various points for a particular charge distribution, and then helping them learn to determine the shape of the Gaussian surfaces if sufficient symmetry exists can develop their reasoning and problem solving skills. We investigate the difficulties that students in calculus-based introductory physics courses have with the concepts of symmetry, electric field and electric flux that are pivotal to Gauss's law of electricity. Determination of the electric field using Gauss's law requires discerning the symmetry of a particular charge distribution and being able to predict the direction of the electric field everywhere if a high symmetry exists. It requires a good grasp of how to add the electric field vectors using the principle of superposition, and the concepts of area vector and electric flux. We administered free response and multiple-choice questions and conducted interviews with individual students using a think-aloud protocol to elucidate the difficulties students have with the concepts of symmetry, electric field and electric flux. Here we discuss student responses to some questions on a multiple-choice test administered to them. The test can be used both as a teaching and assessment tool.
Abe, Yasumi
2008-06-15
The space-time symmetry of noncommutative quantum field theories with a deformed quantization is described by the twisted Poincare algebra, while that of standard commutative quantum field theories is described by the Poincare algebra. Based on the equivalence of the deformed theory with a commutative field theory, the correspondence between the twisted Poincare symmetry of the deformed theory and the Poincare symmetry of a commutative theory is established. As a by-product, we obtain the conserved charge associated with the twisted Poincare transformation to make the twisted Poincare symmetry evident in the deformed theory. Our result implies that the equivalence between the commutative theory and the deformed theory holds in a deeper level, i.e., it holds not only in correlation functions but also in (different types of) symmetries.
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.
Dark matter stability without new symmetries
NASA Astrophysics Data System (ADS)
Catà, Oscar; Ibarra, Alejandro
2014-09-01
The stability of dark matter is normally achieved by imposing extra symmetries beyond those of the Standard Model of particle physics. In this paper we present a framework where the dark matter stability emerges as a consequence of the Standard Model symmetries. The dark matter particle is an antisymmetric tensor field (analogous to the one used for spin-1 mesons in QCD), singlet under the Standard Model gauge group. The Lagrangian possesses an accidental Z2 symmetry which makes the dark matter stable on cosmological time scales. Interactions with the Standard Model fields proceed through the Higgs portal, which allows the observed dark matter abundance to be generated via thermal freeze-out. We also discuss the prospects for observing this dark matter particle in direct detection experiments.
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.
Cylindrical polarization symmetry for nondestructive nanocharacterization
NASA Astrophysics Data System (ADS)
Zhan, Qiwen
2003-07-01
Recently there is an increasing interest in laser beams with radial symmetry in polarization. Due to the cylindrical symmetry in polarization, these beams have unique focusing properties, which may find wide applications in a variety of nanometer scale applications, including high-resolution metrology, high-density data storage, and multi-functional optical microtool. In this paper, simple method of generating cylindrically polarized beams is presented and their potential applications to nondestructive nano-characterization are discussed. A high resolution surface plasmon microscope and a surface plasmon enhanced apertureless near-field scanning optical microscope are proposed. An automatic scanning microellipsometer that uses the cylindrical symmetry to enhance the signal-to-noise-ratio in high-spatial-resolution ellipsometric measurement will also be presented.
PT-Symmetry-Breaking Chaos in Optomechanics.
Lü, Xin-You; Jing, Hui; Ma, Jin-Yong; Wu, Ying
2015-06-26
We demonstrate PT-symmetry-breaking chaos in an optomechanical system, which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in the PT-symmetry-breaking phase. Moreover, this chaos is switchable by tuning the system parameters so that a PT-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser-triggered chaos and its potential applications in secret communication. PMID:26197125
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)
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.
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
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
Yang-Mills origin of gravitational symmetries.
Anastasiou, A; Borsten, L; Duff, M J; Hughes, L J; Nagy, S
2014-12-01
By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized approximation, the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance, and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincaré symmetry. As a concrete example, we focus on the new minimal (12+12) off shell version of simple four-dimensional supergravity obtained by tensoring the off shell Yang-Mills multiplets (4+4, N_{L}=1) and (3+0, N_{R}=0). PMID:25526117
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.
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.
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.
Automorphic Lie algebras with dihedral symmetry
NASA Astrophysics Data System (ADS)
Knibbeler, V.; Lombardo, S.; Sanders, J. A.
2014-09-01
The concept of automorphic Lie algebras arises in the context of reduction groups introduced in the early 1980s in the field of integrable systems. automorphic Lie algebras are obtained by imposing a discrete group symmetry on a current algebra of Krichever-Novikov type. Past work shows remarkable uniformity between algebras associated to different reduction groups. For example, if the base Lie algebra is \\mathfrak{s}{{\\mathfrak{l}}_{2}}({C}) and the poles of the automorphic Lie algebra are restricted to an exceptional orbit of the symmetry group, changing the reduction group does not affect the Lie algebra structure. In this research we fix the reduction group to be the dihedral group and vary the orbit of poles as well as the group action on the base Lie algebra. We find a uniform description of automorphic Lie algebras with dihedral symmetry, valid for poles at exceptional and generic orbits.
Symmetry-related decompositions of uncertainty
NASA Astrophysics Data System (ADS)
Viana, Marlos
2012-10-01
In statistics, the sample mean and variance are intimately related to the symmetries of the full symmetric group describing all possible permutations of assignments of observations to sampling units. While those symmetries yield exactly two invariant subspaces (in a sense to be defined in the text) in correspondence to those summary statistics, the invariant subspaces associated with specific subgroups of the full symmetric group may then lead to much detailed decompositions of the experimental uncertainty. In the present chapter we discuss the symmetry-related summaries of data arising from dihedral experiments, specifically in the context of multinomial models for frequency counts in symbolic sequences. Special examples are given to dihedral summaries that can be potentially interpreted as measures of (molecular) chirality or handedness.
Arbitrary lattice symmetries via block copolymer nanomeshes
NASA Astrophysics Data System (ADS)
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-06-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes.
Workshop on electroweak symmetry breaking: proceedings
Hinchliffe, I.
1984-10-01
A theoretical workshop on electroweak symmetry breaking at the Superconducting Supercollider was held at Lawrence Berkeley Laboratory, June 4-22, 1984. The purpose of the workshop was to focus theoretical attention on the ways in which experimentation at the SSC could reveal manifestations of the phenomenon responsible for electroweak symmetry breaking. This issue represents, at present, the most compelling scientific argument for the need to explore the energy region to be made accessible by the SSC, and a major aim of the workshop was to involve a broad cross section of particle theorists in the ongoing process of sharpening the requirements for both accelerator and detector design that will ensure detection and identification of meaningful signals, whatever form the electroweak symmetry breaking phenomenon should actually take. Separate entries were prepared for the data base for the papers presented.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Gravitino dark matter and flavor symmetries
NASA Astrophysics Data System (ADS)
Monteux, Angelo; Carlson, Eric; Cornell, Jonathan M.
2014-08-01
In supersymmetric theories without R-parity, the gravitino can play the role of a decaying Dark Matter candidate without the problem of late NLSP decays affecting Big Bang Nucleosynthesis. In this work, we elaborate on recently discussed limits on R- parity violating couplings from decays to antideuterons and discuss the implications for two classes of flavor symmetries: horizontal symmetries, and Minimal Flavor Violation. In most of the parameter space the antideuteron constraints on R-parity violating couplings are stronger than low-energy baryon-number-violating processes. Even in the absence of flavor symmetries, we find strong new limits on couplings involving third-generation fields, and discuss the implications for LHC phenomenology. For TeV scale superpartners, we find that the allowed MFV parameter space is a corner with gravitino masses smaller than (10) GeV and small tan β.
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
Increased Sensitivity to Mirror Symmetry in Autism
Perreault, Audrey; Gurnsey, Rick; Dawson, Michelle; Mottron, Laurent; Bertone, Armando
2011-01-01
Can autistic people see the forest for the trees? Ongoing uncertainty about the integrity and role of global processing in autism gives special importance to the question of how autistic individuals group local stimulus attributes into meaningful spatial patterns. We investigated visual grouping in autism by measuring sensitivity to mirror symmetry, a highly-salient perceptual image attribute preceding object recognition. Autistic and non-autistic individuals were asked to detect mirror symmetry oriented along vertical, oblique, and horizontal axes. Both groups performed best when the axis was vertical, but across all randomly-presented axis orientations, autistics were significantly more sensitive to symmetry than non-autistics. We suggest that under some circumstances, autistic individuals can take advantage of parallel access to local and global information. In other words, autistics may sometimes see the forest and the trees, and may therefore extract from noisy environments genuine regularities which elude non-autistic observers. PMID:21559337
Spontaneous symmetry breaking in gauge theories.
Kibble, T W B
2015-01-13
The aim of this historical article is to describe the development of the idea of spontaneous symmetry breaking in gauge theories as seen from my perspective as a member of Abdus Salam's group at Imperial College London, UK. Beginning with an account of particle physics in the years after the Second World War, I describe early attempts at constructing a unified theory of weak and electromagnetic interactions, the obstacles encountered and how they were eventually overcome with the mass-generating mechanism incorporating the idea of spontaneous symmetry breaking, one of whose features is the now-famous Higgs boson. PMID:26949798
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.
High order symmetry interference lithography based nanoimprint
NASA Astrophysics Data System (ADS)
Letailleur, Alban A.; Nomenyo, Komla; Mc Murtry, Stefan; Barthel, Etienne; Sndergrd, Elin; Lrondel, Gilles
2011-01-01
We report on soft nanoimprint lithography using masters obtained by high order symmetry interference lithography. The use of high order symmetry leads to the formation of three-dimensional structures with features smaller than 40 nm. Masters were realized in silicon in a two-step process without transfer layer. Pure silicon masters allow mechanical stability and potential surface functionalization. We further demonstrate the ability of these masters as mold for nanoimprint lithography. High fidelity replication in hybrid sol-gel and pure silica with conservation of both minute features and long distance organization is observed over large areas.
Hopf bifurcation in the presence of symmetry
NASA Technical Reports Server (NTRS)
Golubitsky, M.; Stewart, I.
1985-01-01
Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.
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).