Linus Pauling
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
Pauling, L
1989-12-01
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 Al(6)Pd has led to its description as involving pentagonal twinning of an orthorhombic crystal with a = 51.6 A, b = 37.6 A, and c = 33.24 A, 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. PMID:16594092
Close-packed structure and icosahedral symmetry
V. Paidar
1988-01-01
The structures of the pentagonal and icosahedral symmetry are derived on the basis of various arrangements of atomic tetrahedra and octahedra assuming minimal distortions and deformations. The icosahedral structures consist of two interpenetrating networks, one of which is composed of groups of four icosahedra and the other of bisected diamond-type bonds.
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M., E-mail: fernande@quimica.unlp.edu.ar; Garcia, Javier [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)] [INIFTA (UNLP, CCT La Plata-CONICET), División Química Teórica, Blvd. 113 S/N, Sucursal 4, Casilla de Correo 16, 1900 La Plata (Argentina)
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.
Do All Spherical Viruses Have Icosahedral Symmetry?
Eric Lewin Altschuler; Antonio Pérez--Garrido
2009-02-24
Recent high resolution structures for viral capsids with 12, 32 and 72 subunits ($T1$, $T3$ and $T7$ viruses) have confirmed theoretical predictions of an icosadeltahedral structure with 12 subunits having five nearest neighbors (pentamers) and $(10T+2)-12$ subunits having six nearest neighbor subunits (hexamers). Here we note that theoretical considerations of energy strain for $T4$, $T9$ $T16$ and $T25$ viruses by aligned pentamers and energy strain along with the sheer number of possible arrangement of pentamers as the number of subunits grows, and simulations for such numbers of subunits make an icosadeltahedral configuration either miraculously unlikely or indicate that there must be a principle of capsid assembly of unprecedented fidelity in Nature. We predict, for example, that high resolution data will show $T4$ capsids to have $D_{5h}$ not icosahedral symmetry.
Face-Transitive Polyhedra with Rectangular Faces and Icosahedral Symmetry
H. S. M. Coxeter; Branko Grünbaum
2001-01-01
We describe three hexacontahedra in which the faces are rectangles, all equivalent under symmetries of the icosahedral group and having all edges in the mirror planes of the symmetry group. Under the restriction that adjacent faces are not coplanar, these are the only possible polyhedra of this kind. 1. Introduction. In a recent paper (2) we described two face-transitive polyhedra
NSDL National Science Digital Library
Dexter Perkins
This exercise involves identifying symmetry in crystals and using that information to assign crystals to crystal systems and point groups. Students examine cardboard models and wooden blocks and fill their symmetry elements into a table. Then they figure out what what crystal system and point group each sample belongs to and fill in another table.
Perturbation theory by the moment method and point-group symmetry
Francisco M. Fernández
2014-09-14
We analyze earlier applications of perturbation theory by the moment method (also called inner product method) to anharmonic oscillators. For concreteness we focus on two-dimensional models with symmetry $C_{4v}$ and $C_{2v}$ and reveal the reason why some of those earlier treatments proved unsuitable for the calculation of the perturbation corrections for some excited states. Point-group symmetry enables one to predict which states require special treatment.
Comparison of Stretching Force Constants in Symmetry Coordinates between Td and C3v Point Groups
NASA Astrophysics Data System (ADS)
Julian, Maureen M.
1999-05-01
In this paper we consider what happens to the force constants of a silicate moiety (SiO4) when the length of one of its bonds is changed. This situation exists in the molecule O3SiObrSiO3, where Obr is the bridging oxygen atom connecting the two SiO3 moieties. The problem is to present a set of force constants such that when the structure of the more symmetric molecule is perturbed, the relevant force constants are also perturbed. Algebraic expressions are derived for the stretching force constants of SiO4 (tetrahedral point group Td) and ObrSiO3 (point group C3v) in symmetry coordinates. This paper is addressed to students and researchers in applied group theory who wish to compare force constants between similar molecules. We assume the reader has some familarity with the group theoretical methods presented by Wilson et al. (Wilson, E. B. Jr.; Decius, J. C.; Cross, P. C. Molecular Vibrations; Dover: New York, 1980). We cannot apply Wilson's method for obtaining symmetry coordinates from internal coordinates directly, as we demonstrate. Instead we must start with the irreducible representations of the symmetries of the moiety with the higher symmetry and then reduce them to the representations of the symmetries of the moiety with the lower symmetry. The symmetry coordinates are calculated for each species in order to factor the secular equation. The matrix representations of the generators of these point groups are a function of the specific symmetry coordinates. Finally, the symmetry coordinates are applied to the force constant matrix and the algebraic results are compared.
Virus-Templated Plasmonic Nanoclusters with Icosahedral Symmetry via Directed Self-Assembly
Fontana, Jake; Dressick, Walter J; Phelps, Jamie; Johnson, John E; Rendell, Ronald W; Sampson, Travian; Ratna, Banahalli R; Soto, Carissa M
2014-01-01
The assembly of plasmonic nanoparticles with precise spatial and orientational order may lead to structures with new electromagnetic properties at optical frequencies. The directed self-assembly method presented controls the interparticle-spacing and symmetry of the resulting nanometer-sized elements in solution. The self-assembly of three-dimensional (3D), icosahedral plasmonic nanosclusters (NCs) with resonances at visible wavelengths is demonstrated experimentally. The ideal NCs consist of twelve gold (Au) nanospheres (NSs) attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. In situ dynamic light scattering (DLS) measurements confirm the NSs assembly on the virus. Transmission electron micrographs (TEM) demonstrate the ability of the self-assembly method to control the nanoscopic symmetry of the bound NSs, which reflects the icosahedral symmetry of the virus. Both, TEM and DLS show that the NCs comprise of a distribution of capsids mostly covered (i.e., 6–12 NS/capsid) with NSs. 3D finite-element simulations of aqueous suspensions of NCs reproduce the experimental bulk absorbance measurements and major features of the spectra. Simulations results show that the fully assembled NCs give rise to a 10-fold surface-averaged enhancement of the local electromagnetic field. PMID:24733721
Models of fullerene molecules: Deliberately truncated face forms of icosahedral symmetry
Dilanyan, R.A.; Rybchenko, O.G.; Shekhtman, V.Sh. [Institute of Solid-State Physics, Moscow (Russian Federation)
1994-01-01
A method is proposed to describe fullerene molecules C{sub n} with the aid of noncrystallographic icosahedral m{bar 3}{bar 5} and 235 groups. It is shown that the truncation of face forms of icosahedral symmetry by a pentagonal dodecahedron yields the C{sub 60}, C{sub 80}, and C{sub 140} polyhedra. For these clusters, the radii of the spheres circumscribing the polyhedra, the numerical values of the coordinates of the atoms forming these molecules, and the parameters of the face-centered crystal (fcc) lattices formed by special packing of spheres were calculated. The X-ray diffraction patterns of the fullerene compounds C{sub 60}, C{sub 80}, and C{sub 140} were simulated. 4 refs., 2 figs., 2 tabs.
J. D. Baena; L. Jelinek; R. Marqués
2007-01-01
In this paper, a systematic approach to the design of bulk isotropic magnetic metamaterials is presented. The roles of the symmetries of both the constitutive element and the lattice are analyzed. For this purpose, it is assumed that the metamaterial is composed of cubic split ring resonators (SRRs) arranged in a cubic lattice. The minimum symmetries needed to ensure an
Baena, J D; Marques, R
2007-01-01
In this paper a systematic approach to the design of bulk isotropic magnetic metamaterials is presented. The role of the symmetries of both the constitutive element and the lattice are analyzed. For this purpose it is assumed that the metamaterial is composed by cubic SRR resonators, arranged in a cubic lattice. The minimum symmetries needed to ensure an isotropic behavior are analyzed, and some particular configurations are proposed. Besides, an equivalent circuit model is proposed for the considered cubic SRR resonators. Experiments are carried out in order to validate the proposed theory. We hope that this analysis will pave the way to the design of bulk metamaterials with strong isotropic magnetic response, including negative permeability and left-handed metamaterials.
Dislocations in icosahedral quasicrystals.
Feuerbacher, Michael
2012-10-21
Dislocations in quasicrystals, as a direct result of the lack of translational symmetry in these materials, possess various salient features. The Burgers vector of a dislocation in an icosahedral quasicrystal is a 6-dimensional vector, which reflects the fact that the dislocation, besides the phonon-type strain field analogous to dislocations in ordinary crystals, is associated inseparably with a further type of defect, the phasons. Phasons are critically involved in the formation and motion of dislocations in quasicrystals and govern the macroscopic plastic behaviour of these materials. In this article the properties of dislocations in icosahedral quasicrystals are comprehensively reviewed, starting from a continuum-mechanical description, via core-structure simulation, to their full experimental characterization. The experimental results presented address the icosahedral phases in the well explored systems Al-Pd-Mn and Zn-Mg-Dy. PMID:22760204
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
NASA Astrophysics Data System (ADS)
Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah
2014-07-01
Marine viruses play crucial roles in shaping the dynamics of oceanic microbial communities and in the carbon cycle on Earth. Here we report a 4.7-Å structure of a cyanobacterial virus, Syn5, by electron cryo-microscopy and modelling. A C? backbone trace of the major capsid protein (gp39) reveals a classic phage protein fold. In addition, two knob-like proteins protruding from the capsid surface are also observed. Using bioinformatics and structure analysis tools, these proteins are identified to correspond to gp55 and gp58 (each with two copies per asymmetric unit). The non 1:1 stoichiometric distribution of gp55/58 to gp39 breaks all expected local symmetries and leads to non-quasi-equivalence of the capsid subunits, suggesting a role in capsid stabilization. Such a structural arrangement has not yet been observed in any known virus structures.
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah
2014-01-01
Marine viruses play crucial roles in shaping the dynamics of oceanic microbial communities and in the carbon cycle on Earth. Here we report a 4.7-Å structure of a cyanobacterial virus, Syn5, by electron cryo-microscopy and modelling. A C? backbone trace of the major capsid protein (gp39) reveals a classic phage protein fold. In addition, two knob-like proteins protruding from the capsid surface are also observed. Using bioinformatics and structure analysis tools, these proteins are identified to correspond to gp55 and gp58 (each with two copies per asymmetric unit). The non 1:1 stoichiometric distribution of gp55/58 to gp39 breaks all expected local symmetries and leads to non-quasi-equivalence of the capsid subunits, suggesting a role in capsid stabilization. Such a structural arrangement has not yet been observed in any known virus structures. PMID:24985522
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.
Metallic phase with long-range orientational order and no translational symmetry
D. Shechtman; I. Blech; D. Gratias; J. W. Cahn
1984-01-01
A metallic solid (Al-14-at. pct.-Mn) with long-range orientational order, but with icosahedral point group symmetry, which is inconsistent with lattice translations, has been observed. Its diffraction spots are as sharp as those of crystals but cannot be indexed to any Bravais lattice. The solid is metastable and forms from the melt by a first-order transition.
Icosahedral quasiperiodic ground states?
NASA Astrophysics Data System (ADS)
Narasimhan, Subha; Jaric, Marko V.
1989-01-01
An icosahedral quasiperiodic zero-temperature phase with lower enthalpy than in Bravais and close-packed crystal structures has been found for a system of particles interacting via a square-well potential. This remains true after small changes in the potential, pressure, and even after small changes within a class of icosahedral structures. Above a certain critical pressure, the icosahedral phase transforms into the bcc Bravais crystal structure.
About the atomic structures of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Quiquandon, Marianne; Gratias, Denis
2014-01-01
This paper is a survey of the crystallographic methods that have been developed these last twenty five years to decipher the atomic structures of the icosahedral stable quasicrystals since their discovery in 1982 by D. Shechtman. After a brief recall of the notion of quasiperiodicity and the natural description of Z-modules in 3-dim as projection of regular lattices in N>3-dim spaces, we give the basic geometrical ingredients useful to describe icosahedral quasicrystals as irrational 3-dim cuts of ordinary crystals in 6-dim space. Atoms are described by atomic surfaces (ASs) that are bounded volumes in the internal (or perpendicular) 3-dim space and the intersections of which with the physical space are the actual atomic positions. The main part of the paper is devoted to finding the major properties of quasicrystalline icosahedral structures. As experimentally demonstrated, they can be described with a surprisingly few high symmetry ASs located at high symmetry special points in 6-dim space. The atomic structures are best described by aggregations and intersections of high symmetry compact interpenetrating atomic clusters. We show here that the experimentally relevant clusters are derived from one generic cluster made of two concentric triacontahedra scaled by ? and an external icosidodecahedron. Depending on which ones of the orbits of this cluster are eventually occupied by atoms, the actual atomic clusters are of type Bergman, Mackay, Tsai and others….
Egami, Takeshi [ORNL
2007-01-01
The possibility of icosahedral order in liquids and its role in glass transition is discussed in a broad context of statistical mechanics of liquid. It is pointed out that the structures of glasses and liquids are described both in terms of the topology of atomic bond networks as well as the local distortion of the atomic bonds. While topology plays a dominant role in covalent glasses, local distortion is likely to be more important for metallic glasses.
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.
Icosahedral packing of B12 icosahedra in boron suboxide (B6O)
Hervé Hubert; Bertrand Devouard; Laurence A. J. Garvie; Michael O'Keeffe; Peter R. Buseck; William T. Petuskey; Paul F. McMillan
1998-01-01
Objects with icosahedral symmetry (Ih) bear a special fascination; natural examples are rare, but include radiolaria and virus particles (virions). The discovery of C60, a molecule in the shape of a truncated icosahedron with Ih symmetry, has aroused widespread interest. In 1962, Mackay described a radiating packing of spheres in Ih symmetry, in which the centres of successive shells of
Topological Invariants in Point Group Symmetric Photonic Topological Insulators
Chen, Xiao-Dong; Chen, Wen-Jie; Wang, Jia-Rong; Dong, Jian-Wen
2014-01-01
We proposed a group-theory method to calculate topological invariant in bi-isotropic photonic crystals invariant under crystallographic point group symmetries. Spin Chern number has been evaluated by the eigenvalues of rotation operators at high symmetry k-points after the pseudo-spin polarized fields are retrieved. Topological characters of photonic edge states and photonic band gaps can be well predicted by total spin Chern number. Nontrivial phase transition is found in large magnetoelectric coupling due to the jump of total spin Chern number. Light transport is also issued at the {\\epsilon}/{\\mu} mismatching boundary between air and the bi-isotropic photonic crystal. This finding presents the relationship between group symmetry and photonic topological systems, which enables the design of photonic nontrivial states in a rational manner.
Statistical mechanics of pentagonal and icosahedral order in dense liquids
Subir Sachdev; David R. Nelson
1985-01-01
A Ginzburg-Landau model of short-range icosahedral order in bulk liquids, and of pentagonal order in two-dimensional fluids, is used to calculate density correlation functions in these systems. The theory predicts peaks in the structure factor, at positions determined by symmetries of ideal curved-space ``crystals.'' The peaks are broadened in a way which reflects the inability of icosahedra and pentagons to
Mechanical properties of icosahedral virus capsids
NASA Astrophysics Data System (ADS)
Vliegenthart, G. A.; Gompper, G.
2007-12-01
Virus capsids are self-assembled protein shells in the size range of 10 to 100 nanometers. The shells of DNA-viruses have to sustain large internal pressures while encapsulating and protecting the viral DNA. We employ computer simulations to study the mechanical properties of crystalline shells with icosahedral symmetry that serve as a model for virus capsids. The shells are positioned on a substrate and deformed by a uni-axial force excerted by a small bead. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number N of elementary building blocks (capsomers), and the Föppl-von Kármán number ? which characterizes the relative importance of shear and bending elasticity.
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…
Effects of scars on icosahedral crystalline shell stability under external pressure
NASA Astrophysics Data System (ADS)
Wan, Duanduan; Bowick, Mark J.; Sknepnek, Rastko
2015-03-01
We study how the stability of spherical crystalline shells under external pressure is influenced by the defect structure. In particular, we compare stability for shells with a minimal set of topologically required defects to shells with extended defect arrays (grain boundary "scars" with nonvanishing net disclination charge). We perform both Monte Carlo and conjugate gradient simulations to compare how shells with and without scars deform quasistatically under external hydrostatic pressure. We find that the critical pressure at which shells collapse is lowered for scarred configurations that break icosahedral symmetry and raised for scars that preserve icosahedral symmetry. The particular shapes which arise from breaking of an initial icosahedrally symmetric shell depend on the Föppl-von Kármán number.
NSDL National Science Digital Library
Dexter Perkins
This summary exercise involves crystal system and point group identification and stereo diagram construction. Students are presented with 5 blocks and for each block they must determine it's point group and crystal system, make stereo diagrams showing all symmetry and faces, and draw the blocks by hand or with SHAPE and label the Miller Indices.
Icosahedral packing of B12 icosahedra in boron suboxide (B6O)
NASA Astrophysics Data System (ADS)
Hubert, Hervé; Devouard, Bertrand; Garvie, Laurence A. J.; O'Keeffe, Michael; Buseck, Peter R.; Petuskey, William T.; McMillan, Paul F.
1998-01-01
Objects with icosahedral symmetry (Ih) bear a special fascination; natural examples are rare, but include radiolaria and virus particles (virions). The discovery of C60, a molecule in the shape of a truncated icosahedron with Ih symmetry, has aroused widespread interest. In 1962, Mackay described a radiating packing of spheres in Ih symmetry, in which the centres of successive shells of spheres lie on the surfaces of icosahedra. There has been extensive investigation of the conditions under which such packing might be realized in assemblies of atoms or of molecules such as C60 (ref. 5). Here we report the preparation, at high temperatures and pressures, of boron suboxide (B6O) in which the preferred form of the material is as macroscopic, near-perfect, regular icosahedra, similar to the multiply-twinned particles observed in some cubic materials. A major difference is that B6O has a rhombohedral structure that nearly exactly fits the geometrical requirements needed to obtain icosahedral twins. These icosahedral particles have a structure that can be described as a Mackay packing of icosahedral B12 units, and thus has long-ranged order without translational symmetry.
Statistical mechanics of pentagonal and icosahedral order in dense liquids
NASA Astrophysics Data System (ADS)
Sachdev, Subir; Nelson, David R.
1985-08-01
A Ginzburg-Landau model of short-range icosahedral order in bulk liquids, and of pentagonal order in two-dimensional fluids, is used to calculate density correlation functions in these systems. The theory predicts peaks in the structure factor, at positions determined by symmetries of ideal curved-space ``crystals.'' The peaks are broadened in a way which reflects the inability of icosahedra and pentagons to form a close-packed lattice in flat space. The results in three dimensions provide a good fit to experiments on vapor-deposited metal films and to computer simulations.
Alternative approaches to onion-like icosahedral fullerenes.
Janner, A
2014-03-01
The fullerenes of the C60 series (C60, C240, C540, C960, C1500, C2160 etc.) form onion-like shells with icosahedral Ih symmetry. Up to C2160, their geometry has been optimized by Dunlap & Zope from computations according to the analytic density-functional theory and shown by Wardman to obey structural constraints derived from an affine-extended Ih group. In this paper, these approaches are compared with models based on crystallographic scaling transformations. To start with, it is shown that the 56 symmetry-inequivalent computed carbon positions, approximated by the corresponding ones in the models, are mutually related by crystallographic scalings. This result is consistent with Wardman's remark that the affine-extension approach simultaneously models different shells of a carbon onion. From the regularities observed in the fullerene models derived from scaling, an icosahedral infinite C60 onion molecule is defined, with shells consisting of all successive fullerenes of the C60 series. The structural relations between the C60 onion and graphite lead to a one-parameter model with the same Euclidean symmetry P63mc as graphite and having a c/a = ?(2) ratio, where ? = 1.618… is the golden number. This ratio approximates (up to a 4% discrepancy) the value observed in graphite. A number of tables and figures illustrate successive steps of the present investigation. PMID:24572318
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.
NSDL National Science Digital Library
Dexter Perkins
This is an introduction to basic symmetry elements. Students make drawings that show good examples of rotation axes and mirror planes and inversion centers with and without a 2-fold axis. They describe real objects a mirror plane, an inversion center, and 2, 3, 4, and 6-fold axes in 3D. They think about symmetry in atomic structures and indicate which symmetry elements are present in ball and stick models of minerals. Then they count the different kinds of symmetry elements present in wooden blocks and real minerals.
Icosahedral Platinum Alloy Nanocrystals with Enhanced Electrocatalytic Activities
Chen, Sow-Hsin
surface capping agents play critical roles in stabilizing the icosahedral shape with {111} surfaces. Among and organic surface capping agents. Compositions are readily controllable for these icosahedral nanocrystals) icosahedral nanocrystals based on the gas reducing agent in liquid solution method. Both CO gas and organic
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
Hargittai, I.
1986-01-01
This book demonstrates the progress in the application of the symmetry concept. Highlights symmetry as a fundamental concept in science and as the best unifying idea crossing various branches of most human activities. In addition to its use in traditional symmetry-oriented fields, the concept has made headway in other areas such as reaction chemistry, musicology, nuclear physics, biology, cosmology, etc. This work, illustrated with over 400 drawings, brings together the most diverse fields from mathematics to psychology, the creative and performing arts and most branches of the sciences.
Petrology of Ti Point Group, Northland, New Zealand
R. F. Heming
1980-01-01
Lavas of the late Miocene Ti Point Group are found as scattered flow remnants, a dike, and a sill. Most are basalts with olivine phenocrysts set in a groundmass of clinopyroxene and plagioclase. One flow remnant is a glassy andesite and the relationship of this rock to the basalts is unknown. Together they are interpreted as the remains of a
Thermal stability of Al-Cu-Fe icosahedral alloys
NASA Astrophysics Data System (ADS)
Bessière, M.; Quivy, A.; Lefebvre, S.; Devaud-Rzepski, J.; Calvayrac, Y.
1991-12-01
A stable ideally quasiperiodic phase exists in a small range of concentration, close to the composition Al{62}Cu{25.5}Fe{12.5}. Reducing the iron content, or replacing small amounts of copper by aluminium, lead to icosahedral alloys which exhibit around 650 ^{circ}C structural transformations of unclear nature: in the X-ray powder diffraction pattern, the peak profiles become purely Lorentzian (Al{62.3}Cu{25.3}Fe{12.4}) or diffuse “side-bands” appear in the tails of the Bragg peaks (Al{63}Cu{24.5}Fe{12.5}). In the last case long annealing treatments eventually transform the Bragg peaks into diffuse peaks located at positions clearly off the ideal icosahedral symmetry. Small deviations from this composition range lead to Bragg peaks with shoulders whatever the heat-treatment may be; perfect icosahedral order is never obtained for these compositions (Al{63,25}Cu{24,5}Fe{12,25}, Al{64}Cu{24}Fe{12}, Al{63}Cu{25}Fe{12}). Une phase stable idéalement quasipériodique existe dans un petit domaine de concentration, au voisinage de la composition Al{62}Cu{25,5}Fe{12,5}. La diminution de la teneur en fer, ou le remplacement de faibles quantités de cuivre par de l'aluminium, conduisent à des alliages icosaédriques qui subissent vers 650 ^{circ}C des transformations structurales dont la nature n'est pas clairement identifiée: dans le diagramme de diffraction des rayons X sur poudre, les profils de raies deviennent purement Lorentziens (Al{62,3}Cu{25,3}Fe{12,4}) ou bien des raies diffuses apparaissent dans le pied des pics de Bragg (Al{63}Cu{24,5}Fe{12,5}). Dans ce dernier cas un long traitement de recuit transforme finalement les pics de Bragg en des pics diffus localisés à des positions clairement en dehors de celles correspondant à la symétrie icosaédrique idéale. De faibles écarts à ce domaine de compositions conduisent à des diagrammes de rayons X où les pics de Bragg sont épaulés quel que soit le traitement thermique ; l'ordre icosaédrique parfait n'est jamais obtenu pour ces compositions (Al{63,25}Cu{24,5}Fe{12,25}, Al{64}Cu{24}Fe{12}, Al{63}Cu{25}Fe{12}).
van den Worm, Sjoerd H E; Koning, Roman I; Warmenhoven, Hans J; Koerten, Henk K; van Duin, Jan
2006-11-01
We solved the structures of the single-stranded RNA bacteriophages Qbeta, PP7 and AP205 by cryo-electron microscopy. On the outside, the symmetrized electron density maps resemble the previously described cryo-electron microscopy structure of MS2. RNA density is present inside the capsids, suggesting that the genomic RNA of Qbeta, PP7 and AP205, analogous to MS2, contains many coat protein-binding sites in addition to the hairpin on which assembly and packaging are initiated. All four bacteriophages harbour the same overall arrangement of the RNA, which is a unique combination of both triangles and pentagons. This combination has not been found in other icosahedral viruses, in which the RNA structures are either triangular or pentagonal. Strikingly, the unique RNA packing of the Leviviridae appears to deploy the most efficient method of RNA storage by obeying icosahedral symmetry. PMID:16989861
Quantum transport through single and multilayer icosahedral fullerenes
NASA Astrophysics Data System (ADS)
Lovey, Daniel A.; Romero, Rodolfo H.
2013-10-01
We use a tight-binding Hamiltonian and Green functions methods to calculate the quantum transmission through single-wall fullerenes and bilayered and trilayered onions of icosahedral symmetry attached to metallic leads. The electronic structure of the onion-like fullerenes takes into account the curvature and finite size of the fullerenes layers as well as the strength of the intershell interactions depending on to the number of interacting atom pairs belonging to adjacent shells. Misalignment of the symmetry axes of the concentric iscosahedral shells produces breaking of the level degeneracies of the individual shells, giving rise some narrow quasi-continuum bands instead of the localized discrete peaks of the individual fullerenes. As a result, the transmission function for non symmetrical onions is rapidly varying functions of the Fermi energy. Furthermore, we found that most of the features of the transmission through the onions are due to the electronic structure of the outer shell with additional Fano-like antiresonances arising from coupling with or between the inner shells.
E. König; S. Kremer
1977-01-01
Computational methods are described for effecting complete ligand field calculations, inclusive of spin-orbit coupling, on the strong-field {(cN)Sl'SaSl'L;l'b} basis. Plotter routines which subsequently execute complet e energy diagrams of Tanabe-Sugano type are presented. The procedures operate for all dN configurations, N = 1, 2, ..., 9, and make full use of the point group symmetry of the system, G?SO(3). The
Confessions of an icosahedral virus crystallographer
Johnson, John E.
2013-01-01
This is a personal history of my structural studies of icosahedral viruses that evolved from crystallographic studies, to hybrid methods with electron cryo-microscopy and image reconstruction (cryoEM) and then developed further by incorporating a variety of physical methods to augment the high resolution crystallographic studies. It is not meant to be comprehensive, even for my own work, but hopefully provides some perspective on the growth of our understanding of these remarkable biologic assemblies. The goal is to provide a historical perspective for those new to the field and to emphasize the limitations of any one method, even those that provide atomic resolution information about viruses. PMID:23291268
Method of making an icosahedral boride structure
Hersee, Stephen D. (3712 Silver Ave. SE., Albuquerque, NM 87108); Wang, Ronghua (939 Buena Vista Dr., SE., Apt. F203, Albuquerque, NM 87106); Zubia, David (4409 Buckingham Dr., El Paso, TX 79902); Aselage, Terrance L. (62 Avenida Del Sol, Cedar Crest, NM 87008); Emin, David (1502 Harvard Ct. NE., Albuquerque, NM 87106)
2005-01-11
A method for fabricating thin films of an icosahedral boride on a silicon carbide (SiC) substrate is provided. Preferably the icosahedral boride layer is comprised of either boron phosphide (B.sub.12 P.sub.2) or boron arsenide (B.sub.12 As.sub.2). The provided method achieves improved film crystallinity and lowered impurity concentrations. In one aspect, an epitaxially grown layer of B.sub.12 P.sub.2 with a base layer or substrate of SiC is provided. In another aspect, an epitaxially grown layer of B.sub.12 As.sub.2 with a base layer or substrate of SiC is provided. In yet another aspect, thin films of B.sub.12 P.sub.2 or B.sub.12 As.sub.2 are formed on SiC using CVD or other vapor deposition means. If CVD techniques are employed, preferably the deposition temperature is above 1050.degree. C., more preferably in the range of 1100.degree. C. to 1400.degree. C., and still more preferably approximately 1150.degree. C.
Density waves theory of the capsid structure of small icosahedral viruses
V. L. Lorman; S. B. Rochal
2006-11-24
We apply Landau theory of crystallization to explain and to classify the capsid structures of small viruses with spherical topology and icosahedral symmetry. We develop an explicit method which predicts the positions of centers of mass for the proteins constituting viral capsid shell. Corresponding density distribution function which generates the positions has universal form without any fitting parameter. The theory describes in a uniform way both the structures satisfying the well-known Caspar and Klug geometrical model for capsid construction and those violating it. The quasiequivalence of protein environments in viral capsid and peculiarities of the assembly thermodynamics are also discussed.
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…
Dislocation reactions in icosahedral Al-Pd-Mn quasicrystals
Renhui Wang; Michael Feuerbacher; Markus Wollgarten; Knut Urban
1998-01-01
Possible dislocation reactions in face-centred icosahedral quasicrystals are considered from the geometric and energetic points of view. Some typical examples of the reactions between dislocations with different twofold Burgers vectors were confirmed experimentally in a plastically deformed Al-Pd-Mn icosahedral quasicrystal by identification of the Burgers vectors of dislocations in triple-node arrangements. Several examples were investigated in a transmission electron microscope
The RNA of turnip yellow mosaic virus exhibits icosahedral order
Larson, Steven B. [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States); Lucas, Robert W. [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States); Greenwood, Aaron [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States); McPherson, Alexander [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States)]. 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.
NASA Astrophysics Data System (ADS)
Harter, William G.; Li, Alvason Zhenhua
2013-06-01
Quantum revivals or "super-beats" are predicted to occur when angularly localized symmetric tops states are free to evolve. Similar types of dynamics are expected to involve spherical top superfine and superhyperfine level clusters that are labeled by induced representations of octahedral or tetrahedral symmetries for XY_4, XY_6, and related molecules. A considerably more complicated set of effects are expected for the icosahedral molecule C_ {60} and its related isotopomers. An important difference for icosahedral symmetry is that its superfine splitting ratios are most-irrational (Golden-ratio) fractions that preclude perfect Poincare recurrence of quantum phase while the octahedral splitting ratios are rational. William Harter and Justin Mitchell, International Journal of Molecular Science, 14, 714 (2013).
Dislocation motion in icosahedral quasicrystals at elevated temperatures: numerical simulation
G. D. Schaaf; J. Roth; H.-R. Trebin
2003-01-01
We have simulated shear deformation of an icosahedral model quasicrystal at elevated temperatures with molecular dynamics. The generation of a dislocation loop was studied with a new visualization technique and a critical stress almost as large as the theoretical shear strength was measured. Built-in dislocations started to move at a temperature-dependent critical stress lower by one order of magnitude. While
Icosahedral phase formation in rapidly quenched aluminum-ruthenium alloys
Anlage, Steven
Icosahedral phase formation in rapidly quenched aluminum- ruthenium alloys Steven M. Anlagea phases as a function of composition. We have chosen the aluminum-ruthenium alloy system because of aluminum and ruthenium were formed by inductively heating the elemental metals in an alumina crucible
Location coding on icosahedral aperture 3 hexagon discrete global grids
Kevin Sahr
2008-01-01
Discrete global grid systems (DGGSs) represent a relatively new, but increasingly popular, approach to the problem of representing geospatial location on computer systems. Despite growing interest amongst potential users in icosahedral aperture 3 hexagon DGGSs, the practical use of such systems has been hindered by a lack of efficient spatial indexing methods. In this paper we discuss the two primary
Racah Algebra for SU(2) in a Point Group Basis; Finite Subgroup Polynomial Bases for SU(3)
NASA Astrophysics Data System (ADS)
Desmier, Paul Edmond
1982-03-01
Integrity bases for tensors of type (GAMMA)(,r) whose components are polynomials in the components of tensors of type (GAMMA)(,5) ((GAMMA)(,6) for ('(d))O) are given explicitely for the double tetrahedral and octahedral point groups (('(d))T and ('(d))O), where the main axis of symmetry is trigonal. We formulate analytic basis states for the decomposition of SU(2) through the chain ('(d))T (R-HOOK) ('(d))C(,3) (R-HOOK) ('(d))C(,1) and use them to construct the Racah algebra. A method is given for deriving branching rules, in the form of generating functions, for the decomposition of representations of SU(3) into representations of its finite subgroups. Interpreted in terms of an integrity basis, the generating functions define analytic polynomial basis states for SU(3) which respect the finite subgroup.
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.
Cardone, Giovanni; Yan, Xiaodong; Sinkovits, Robert S; Tang, Jinghua; Baker, Timothy S
2013-09-01
Single particle analysis is a valuable tool in cryo-electron microscopy for determining the structure of biological complexes. However, the conformational state and the preparation of the sample are factors that play a critical role in the ultimate attainable resolution. In some cases extensive analysis at the microscope of a sample under different conditions is required to derive the optimal acquisition conditions. Currently this analysis is limited to raw micrographs, thus conveying only limited information on the structure of the complex. We are developing a computing system that generates a three-dimensional reconstruction from a single micrograph acquired under cryogenic and low dose conditions, and containing particles with icosahedral symmetry. The system provides the microscopist with immediate structural information from a sample while it is in the microscope and during the preliminary acquisition stage. The system is designed to run without user intervention on a multi-processor computing resource and integrates all the processing steps required for the analysis. Tests performed on experimental data sets show that the probability of obtaining a reliable reconstruction from one micrograph is primarily determined by the quality of the sample, with success rates close to 100% when sample conditions are optimal, and decreasing to about 60% when conditions are sub-optimal. The time required to generate a reconstruction depends significantly on the diameter of the particles, and in most instances takes about 1min. The proposed approach can provide valuable three-dimensional information, albeit at low resolution, on conformational states, epitope binding, and stoichiometry of icosahedral multi-protein complexes. PMID:23891839
Cardone, Giovanni; Yan, Xiaodong; Sinkovits, Robert S.; Tang, Jinghua; Baker, Timothy S.
2013-01-01
Single particle analysis is a valuable tool in cryo-electron microscopy for determining the structure of biological complexes. However, the conformational state and the preparation of the sample are factors that play a critical role in the ultimate attainable resolution. In some cases extensive analysis at the microscope of a sample under different conditions is required to derive the optimal acquisition conditions. Currently this analysis is limited to raw micrographs, thus conveying only limited information on the structure of the complex. We are developing a computing system that generates a three-dimensional reconstruction from a single micrograph acquired under cryogenic and low dose conditions, and containing particles with icosahedral symmetry. The system provides the microscopist with immediate structural information from a sample, while it is in the microscope and during the preliminary acquisition stage. The system is designed to run without user intervention on a multi-processor computing resource and integrates all the processing steps required for the analysis. Tests performed on experimental data sets show that the probability of obtaining a reliable reconstruction from one micrograph is primarily determined by the quality of the sample, with success rates close to 100% when sample conditions are optimal, and decreasing to about 60% when conditions are sub-optimal. The time required to generate a reconstruction depends significantly on the diameter of the particles, and in most instances takes about one minute. The proposed approach can provide valuable three-dimensional information, albeit at low resolution, on conformational states, epitope binding, and stoichiometry of icosahedral multi-protein complexes. PMID:23891839
Icosahedral and approximant phases in a Mg–Ga–Al–Zn alloy and their electrical resistivities
K. Edagawa; N. Naito; S. Takeuchi
1992-01-01
It has been found in a Mg Ga-Al-Zn alloy that an icosahedral phase produced by melt-spinning transforms to the 1\\/1 cubic approximant of the icosahedral phase at 653 K and successively to the 2\\/1 cubic approximant at around 668 K upon heating. Structural relations of the two approximant phases to the icosahedral phase are discussed, in the framework of the
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
Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles
Shevchenko, Vladimir Ya.; Madison, Alexey E.; Mackay, Alan L.
2007-01-01
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. PMID:17301478
Atomic force microscopy analysis of icosahedral virus RNA.
Kuznetsov, Yurii G; Daijogo, Sarah; Zhou, Jiashu; Semler, Bert L; McPherson, A
2005-03-18
Single-stranded genomic RNAs from four icosahedral viruses (poliovirus, turnip yellow mosaic virus (TYMV), brome mosaic virus (BMV), and satellite tobacco mosaic virus (STMV)) along with the RNA from the helical tobacco mosaic virus (TMV) were extracted using phenol/chloroform. The RNAs were imaged using atomic force microscopy (AFM) under dynamic conditions in which the RNA was observed to unfold. RNAs from the four icosahedral viruses initially exhibited highly condensed, uniform spherical shapes with diameters consistent with those expected from the interiors of their respective capsids. Upon incubation at 26 degrees C, poliovirus RNA gradually transformed into chains of globular domains having the appearance of thick, irregularly segmented fibers. These ultimately unwound further to reveal segmented portions of the fibers connected by single strands of RNA of 0.5-1 nm thickness. Virtually the same transformations were shown by TYMV and BMV RNA, and with heating, the RNA from STMV. Upon cooling, the chains of domains of poliovirus RNA and STMV RNA condensed and re-formed their original spherical shapes. TMV RNAs initially appeared as single-stranded threads of 0.5-1.0 nm diameter but took on the structure of the multidomain chains upon further incubation at room temperature. These ultimately condensed into short, thick chains of larger domains. Our observations suggest that classical extraction of RNA from icosahedral virions produces little effect on overall conformation. As tertiary structure is lost however, it is evident that secondary structural elements are arranged in a sequential, linear fashion along the polynucleotide chain. At least in the case of poliovirus and STMV, the process of tertiary structure re-formation from the linear chain of secondary structural domains proceeds in the absence of protein. RNA base sequence, therefore, may be sufficient to encode the conformation of the encapsidated RNA even in the absence of coat proteins. PMID:15733916
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.
Alok Singh; A. P Tsai
1998-01-01
Solidification behaviour of lead particles embedded in icosahedral and decagonal quasicrystalline matrix has been studied. Differential scanning calorimetry traces for the icosahedral matrix show a sharp lead melting peak but a very flat solidification exotherm with several peaks, while lead in the decagonal matrix shows sharp melting and solidification peaks. Transmission electron microscopy shows that lead particles are faceted on
A Global Ocean Model Based on Icosahedral-Hexagonal Grids With a Hybrid Vertical Coordinate
T. D. Ringler; J. Baumgardner; D. A. Randall
2003-01-01
This talk will present results from a new ocean general circulation model (OGCM). The ocean model uses an icosahedral-hexagonal grid to tile the surface of the sphere and hybrid (floating) coordinates to discretize the vertical depth of the ocean. The use of icosahedral-hexagonal grids leads to a highly uniform and isotropic discretization of the sphere and eliminates problematic grid singularities
Competition between face-centered cubic and icosahedral cluster structures R. S. Berry
Berry, R. Stephen
Competition between face-centered cubic and icosahedral cluster structures R. S. Berry UniversityÂ1090 September 1997 The binding energy of atoms in icosahedral and face-centered-cubic clusters is calculated interactions form close-packed crystal structures, which include hexagonal and face-centered cubic fcc
Non-hermitean hamiltonians with unitary and antiunitary symmetry
Francisco M. Fernández; Javier Garcia
2014-04-26
We analyze 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 analyze their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry $C_{2v}$ 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.
Symmetries, Symmetry Breaking, Gauge Symmetries
Strocchi, Franco
2015-01-01
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field ...
Unusual properties of icosahedral boron-rich solids
Emin, David [Department of Physics and Astronomy, 800 Yale Boulevard NE (MSC 07 4220), University of New Mexico, Albuquerque, NM 87131 (United States)]. E-mail: emin@unm.edu
2006-09-15
Icosahedral boron-rich solids are materials containing boron-rich units in which atoms reside at an icosahedron's 12 vertices. These materials are known for their exceptional bonding and the unusual structures that result. This article describes how the unusual bonding generates other distinctive and useful effects. In particular, radiation-induced atomic vacancies and interstitials spontaneously recombine to produce the 'self-healing' that underlies these materials' extraordinary radiation tolerance. Furthermore, boron carbides, a group of icosahedral boron-rich solids, possess unusual electronic, magnetic and thermal properties. For example, the charge carriers, holes, localize as singlet pairs on icosahedra. The unusual origin of this localization is indicated by the absence of a concomitant photo-ionization. The thermally assisted hopping of singlet pairs between icosahedra produces Seebeck coefficients that are unexpectedly large and only weakly dependent on carrier concentration. These properties are exploited in devices: (1) long-lived high-power high-capacity beta-voltaic cells (2) very high temperature thermoelectrics and (3) solid-state neutron detectors. - Graphical abstract: Very high-resolution transmission electron microscopy shows no damage to B{sub 12}P{sub 2} after an intense bombardment (10{sup 18} electrons/cm{sup 2} s) by 400 keV electrons to a net dose of about 10{sup 23} electrons/cm{sup 2}.
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.
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.
A new icosahedral quasicrystal in rapidly solidified FeTi2
NASA Astrophysics Data System (ADS)
Dong, C.; Hei, Z. K.; Wang, L. B.; Song, Q. H.; Wu, Y. K.
1986-08-01
The observation (by TEM) of a new icosahedral quasi-crystal in a rapidly solidified FeTi2 alloy is reported. Of the 96 atoms constituting a unit cell of the c(FeTi2) structure one half of the atoms are packed into FeTi2 icosahedral groups, with the smaller Fe atoms at the center and the Ti atoms at the vertices of the icosahedron; half are packed into pentagonal prisms, with Ti atoms at their centers. The occurrence of this kind of icosahedral phase is discussed in the framework of crystal chemistry.
Point-group sensitive orientation mapping of non-centrosymmetric crystals
NASA Astrophysics Data System (ADS)
Winkelmann, Aimo; Nolze, Gert
2015-02-01
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.
Symmetries, Symmetry Breaking, Gauge Symmetries
Franco Strocchi
2015-02-23
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which account for the $\\theta$ vacua.
Evolution of icosahedral clusters during the rapid solidification of liquid TiAl alloy
NASA Astrophysics Data System (ADS)
Xie, Zhuo-Cheng; Gao, Ting-Hong; Guo, Xiao-Tian; Qin, Xin-Mao; Xie, Quan
2014-05-01
The evolution characteristics of icosahedral clusters during the rapid solidification of TiAl alloy under different cooling rates are investigated based on molecular dynamics simulations. The short-range order structural properties of liquid and amorphous TiAl alloy are analyzed by several structural characterization methods. It is found that the cooling rate plays a key role during the evolution of icosahedral clusters and has significant effect on the glass transition temperature. Simultaneously, the medium-range order structural evolutions are described in detail by quantitative method and visualization technology during the rapid solidification. The results reveal that the medium-range order icosahedral clusters have good structural stability and configural continuity during the rapid cooling process. Furthermore, the icosahedral structures have significant improvements with decreasing cooling rate. The structures block the crystal nucleation and improve the glass forming ability of supercooled liquid.
Design and manufacture of an icosahedral virus model for educational use
Stach, Laurie A. (Laurie Anna)
2005-01-01
A model of an icosahedral virus was designed and manufactured. Much consideration was given to the design of different aspects of the part. though there were many uncertainties about some parameters that disallowed precise ...
Magnetic Properties of an Icosahedral Phase of Ga-Mg-Zn Alloy
Kaichi Saito; Susumu Matsuo; Tsutomu Ishimasa
1993-01-01
Magnetic properties of two kinds of Ga-Mg-Zn alloy samples were studied. One is Ga20Mg40Zn40 icosahedral phase which was thermally stable below about 615 K, the other is Ga18.5Mg41.5Zn40 alloy which exhibited amorphous-like X-ray diffraction pattern with no sharp peaks. The icosahedral phase showed a linear relationship between the magnetic susceptibility and the square of temperature. The improvement of the specimen
Formation of large-scale icosahedral clusters in a simple liquid approaching the glass transition
F. H. M Zetterling; M. Dzugutov; S. I Simdyankin
2001-01-01
A number of singularities observed in super-cooled liquids approaching the glass transition point are commonly interpreted as indicating spatial heterogeneity. This conjecture assumes that the whole volume is decomposed into structurally distinct domains. In simple super-cooled liquids, the assumed domain structure is usually associated with icosahedral clustering; however, no evidence for growing length scale of icosahedral ordering in a super-cooled
Finite size specimens with cracks of icosahedral Al—Pd—Mn quasicrystals
NASA Astrophysics Data System (ADS)
Yang, Lian-Zhi; Ricoeur, Andreas; He, Fan-Min; Gao, Yang
2014-05-01
Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral Al—Pd—Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon—phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral Al—Pd—Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon—phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of phonon—phason coupling effect on the icosahedral Al—Pd—Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.
Viruses and Fullerenes - Symmetry as a Common Thread?
Dechant, Pierre-Philippe; Keef, Tom; Twarock, Reidun
2014-01-01
We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational principle in virus structure and assembly. We adapt this group theoretic framework here to the physical requirements dictated by carbon chemistry, and show that we can derive mathematical models for carbon onions within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in Nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.
Viruses and Fullerenes - Symmetry as a Common Thread?
Pierre-Philippe Dechant; Jess Wardman; Tom Keef; Reidun Twarock
2014-02-18
We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational principle in virus structure and assembly. We adapt this group theoretic framework here to the physical requirements dictated by carbon chemistry, and show that we can derive mathematical models for carbon onions within this affine symmetry approach. This suggests the applicability of affine symmetry in a wider context in Nature, as well as offering a novel perspective on the geometric principles underpinning carbon chemistry.
NASA Astrophysics Data System (ADS)
Rappaz, Michel; Kurtuldu, Güven
2015-02-01
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 < 110rangle 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.
Semiconducting icosahedral boron arsenide crystal growth for neutron detection
NASA Astrophysics Data System (ADS)
Whiteley, C. E.; Zhang, Y.; Gong, Y.; Bakalova, S.; Mayo, A.; Edgar, J. H.; Kuball, M.
2011-03-01
Semiconducting icosahedral boron arsenide, B12As2, is an excellent candidate for neutron detectors, thermoelectric converters, and radioisotope batteries, for which high quality single crystals are required. Thus, the present study was undertaken to grow B12As2 crystals by precipitation from metal solutions (nickel) saturated with elemental boron (or B12As2 powder) and arsenic in a sealed quartz ampoule. B12As2 crystals of 10-15 mm were produced when a homogeneous mixture of the three elements was held at 1150 °C for 48-72 h and slowly cooled (3.5 °C/h). The crystals varied in color and transparency from black and opaque to clear and transparent. X-ray topography (XRT), and elemental analysis by energy dispersive X-ray spectroscopy (EDS) confirmed that the crystals had the expected rhombohedral structure and chemical stoichiometry. The concentrations of residual impurities (nickel, carbon, etc.) were low, as measured by Raman spectroscopy and secondary ion mass spectrometry (SIMS). Additionally, low etch-pit densities (4.4×107 cm-2) were observed after etching in molten KOH at 500 °C. Thus, the flux growth method is viable for growing large, high-quality B12As2 crystals.
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...
Formation of F- and P-Type Icosahedral Quasicrystals in the Zn Mg Ho Alloy System*
NASA Astrophysics Data System (ADS)
Shimizu, Takayuki; Ishimasa, Tsutomu
1998-10-01
Two types of icosahedral quasicrystals, F- and P-types, formed at 563°C in the Zn60Mg40-xHox alloy depending on Ho content. In the composition range of 6?x?10, F-type icosahedral quasicrystal formed as a major phase in these alloys. The intensity of superlattice reflections which occurred due to F-type ordering became weaker in the alloys with lower Ho content. At x=5, P-type icosahedral quasicrystal formed, coexisting with MgZn2-type Laves phase at 563°C and 503°C. Some electron diffraction patterns of the P-type icosahedral quasicrystal exhibited diffuse scattering intensity at positions corresponding to F-type superlattice reflections. By annealing at 403°C, a mixture of the P-type icosahedral quasicrystal and the MgZn2-type phase changed to a mixture of the F-type quasicrystal and a decagonal quasicrystal. The former state was reversibly obtained by additional annealing at 503°C. These experimental results support the interpretation that the three types of quasicrystals form as a thermodynamically stable state in the Zn Mg Ho alloy system.
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.
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@B??@A2?? (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
Projective symmetry of partons in the Kitaev honeycomb model
NASA Astrophysics Data System (ADS)
Mellado, Paula; Petrova, Olga; Tchernyshyov, Oleg
2015-01-01
Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of the Kitaev honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities do not reflect the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.
NASA Astrophysics Data System (ADS)
Alqannas, Haifa S.; Lakin, Andrew J.; Farrow, Joseph A.; Dunn, Janette L.
2013-10-01
We will consider the role played by electron-vibration and electron-electron interactions, through Jahn-Teller (JT) and Coulomb interactions, respectively, in icosahedral systems in which triplet electronic states are coupled to hg-type vibrations. Starting from the electronic terms that arise from consideration of Coulomb interactions, we introduce JT couplings both within the terms and between nondegenerate terms. We show how the symmetry of the JT distortion can change when extra electrons are added, and give the conditions under which JT distortions can be suppressed entirely when the Coulomb interactions are sufficiently large. The relevance of our results to anions of the fullerene molecule C60 are briefly discussed, and existing experimental measurements are used to estimate values for the quadratic JT coupling constants for these anions.
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...
The local atomic quasicrystal structure of the icosahedral Mg25Y11Zn64 alloy
S. Brühne; E. Uhrig; C. Gross; W. Assmus; A. S. Masadeh; S. J. L. Billinge
2005-01-01
A local and medium range atomic structure model for the face centred icosahedral (fci) Mg25Y11Zn64 alloy has been established in a sphere of r = 27 Å. The model was refined by least squares techniques using the atomic pair distribution (PDF) function obtained from synchrotron powder diffraction. Three hierarchies of the atomic arrangement can be found: (i) five types of
The local atomic quasicrystal structure of the icosahedral Mg25Y11Zn64 alloy
S Brühne; E Uhrig; C Gross; W Assmus; A S Masadeh
A local and medium range atomic structure model for the face centred icosahedral (fci) Mg25Y11Zn64 alloy has been established in a sphere of r = 27 Å. The model was refined by least squares techniques using the atomic pair distribution (PDF) function obtained from synchrotron powder diffraction. Three hierarchies of the atomic arrangement can be found: (i) five types of
Nucleation and Growth of Icosahedral Boron Suboxide Clusters at High Pressure
NASA Astrophysics Data System (ADS)
McMillan, Paul F.; Hubert, Hervé; Chizmeshya, Andrew; Petuskey, William T.; Garvie, Lawrence A. J.; Devouard, Bertrand
1999-10-01
The stoichiometry of boron suboxide (B6O1-?) synthesized from mixtures of boron and boron oxide (B2O3) at high pressure lies closer to the nominal composition (?=0) than materials obtained at atmospheric pressure. The materials obtained in the high pressure syntheses in the presence of molten B2O3 also have a higher degree of crystallinity than for sintered powders. For syntheses at temperatures of 1700-1800°C at pressures between 4 and approximately 5.5 GPa, the well-crystallized particles are dominated by icosahedral multiply-twinned particles up to approximately 40 ?m in diameter. This unusual morphology is obtained by Mackay packing, i.e., by assembly of successive shells of icosahedral B12 units around a central icosahedral nucleus to give a multiply twinned particle in which each of the 20 elements has the Roverline3m space group of the rhombohedral ?-B structure. We examine the thermodynamic and kinetic factors associated with the development of this morphology during high pressure growth and use ab initio calculations to investigate the energetic driving forces for initiation of the Mackay packing around the central icosahedral nucleus.
An icosahedral algal virus has a complex unique vertex decorated by a spike
Baker, Timothy S.
bursaria Chlorella virus-1 is an icosahedrally shaped, 1,900-Å-diameter virus that infects unicellular cryoelectron microscopy reconstruction Paramecium bursaria Chlorella virus-1 cell entry specialized vertex protein Paramecium bursaria Chlorella virus-1 (PBCV-1) belongs to the genus Chlorovirus
Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.
2006-07-31
Relatively minor perturbations to a crystal structure can in some cases result in apparently large changes in symmetry. Changes in space group or even lattice can be induced by heavy metal or halide soaking (Dauter et al, 2001), flash freezing (Skrzypczak-Jankun et al, 1996), and Se-Met substitution (Poulsen et al, 2001). Relations between various space groups and lattices can provide insight in the underlying structural causes for the symmetry or lattice transformations. Furthermore, these relations can be useful in understanding twinning and how to efficiently solve two different but related crystal structures. Although (pseudo) symmetric properties of a certain combination of unit cell parameters and a space group are immediately obvious (such as a pseudo four-fold axis if a is approximately equal to b in an orthorhombic space group), other relations (e.g. Lehtio, et al, 2005) that are less obvious might be crucial to the understanding and detection of certain idiosyncrasies of experimental data. We have developed a set of tools that allows straightforward exploration of possible metric symmetry relations given unit cell parameters and a space group. The new iotbx.explore{_}metric{_}symmetry command produces an overview of the various relations between several possible point groups for a given lattice. Methods for finding relations between a pair of unit cells are also available. The tools described in this newsletter are part of the CCTBX libraries, which are included in the latest (versions July 2006 and up) PHENIX and CCI Apps distributions.
NASA Astrophysics Data System (ADS)
Takagiwa, Yoshiki; Kimura, Kaoru
2014-08-01
In this article, we review the characteristic features of icosahedral cluster solids, metallic-covalent bonding conversion (MCBC), and the thermoelectric properties of Al-based icosahedral quasicrystals and approximants. MCBC is clearly distinguishable from and closely related to the well-known metal-insulator transition. This unique bonding conversion has been experimentally verified in 1/1-AlReSi and 1/0-Al12Re approximants by the maximum entropy method and Rietveld refinement for powder x-ray diffraction data, and is caused by a central atom inside the icosahedral clusters. This helps to understand pseudogap formation in the vicinity of the Fermi energy and establish a guiding principle for tuning the thermoelectric properties. From the electron density distribution analysis, rigid heavy clusters weakly bonded with glue atoms are observed in the 1/1-AlReSi approximant crystal, whose physical properties are close to icosahedral Al-Pd-TM (TM: Re, Mn) quasicrystals. They are considered to be an intermediate state among the three typical solids: metals, covalently bonded networks (semiconductor), and molecular solids. Using the above picture and detailed effective mass analysis, we propose a guiding principle of weakly bonded rigid heavy clusters to increase the thermoelectric figure of merit (ZT) by optimizing the bond strengths of intra- and inter-icosahedral clusters. Through element substitutions that mainly weaken the inter-cluster bonds, a dramatic increase of ZT from less than 0.01 to 0.26 was achieved. To further increase ZT, materials should form a real gap to obtain a higher Seebeck coefficient.
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
NASA Astrophysics Data System (ADS)
Tanaka, Hajime
2003-08-01
It is well known that bulk metallic glass formers have a tendency to show local icosahedral chemical ordering. We argue that the frustration between this short-range bond ordering and the long-range crystalline ordering controls the fragility and the glass-forming ability of these liquids. Our model suggests that a system having a stronger tendency to show local icosahedral ordering should be less fragile and a better glass former. This scenario also naturally explains the close relationship among the degree of local icosahedral ordering in liquid, glass formability, and quasicrystal formability.
Hu, Wen [Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan (China); State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, CAS, Changchun 130022, Jilin (China); Yi, Jianhong; Zheng, Biju [Faculty of Materials Science and Engineering, Kunming University of Science and Technology, Kunming 650093, Yunnan (China); Wang, Limin, E-mail: lmwang@ciac.jl.cn [State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of Applied Chemistry, CAS, Changchun 130022, Jilin (China)
2013-06-15
Thanks to the revolutionary discovery of 5-fold symmetry contributed by Shechtman, quasicrystal is now recognized as another solid-state existing form. As the second largest class of quasicrystals, titanium-based icosahedral quasicrystals are very promising for hydrogen storage applications owing to their inherent abundant interstitial sites and favorable hydrogen-metal chemistry. In this context, (Ti{sub 1.6}V{sub 0.4}Ni){sub 100?x}Sc{sub x} (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{sup ?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{sup ?1}, and the electrocatalytic activity improvement is highly demanded. - Graphical abstract: Quasicrystalline Ti–V–Ni–Sc hydrogen storage materials: Sc addition into Ti{sub 1.6}V{sub 0.4}Ni alloy forms the icosahedral phase (see picture). With optimal Sc dosage, the anodic cycling stability and self-discharge property are greatly enhanced. - Highlights: • Crystalline disallowed 5-fold symmetry is present in (Ti{sub 1.6}V{sub 0.4}Ni){sub 100?x}Sc{sub x} alloys. • Ti-based metastable quasicrystalline alloys can store hydrogen electrochemically. • A maximum discharge capacity of 270 mA h g{sup ?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.
Shan-Ying Wang; Jing-Zhi Yu; Hiroshi Mizuseki; Qiang Sun; Chong-Yu Wang; Yoshiyuki Kawazoe
2004-01-01
The energetics and local spin magnetic moment of a single 3,4d impurity (Sc-Ni, Y-Pd) encapsulated in an icosahedral Au12 cage have been studied theoretically by using a real-space first-principles cluster method with generalized gradient approximation for exchange-correlation functional. The relativistic effect is considered by scalar relativistic pseudopotentials. All doped clusters show unexpected large relative binding energies compared with icosahedral Au13
Adsorption sites on icosahedral quasicrystal surfaces: dark stars and white flowers.
Unal, Bari?; Jenks, C J; Thiel, P A
2009-02-01
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. PMID:21817296
An icosahedral algal virus has a complex unique vertex decorated by a spike.
Cherrier, Mickaël V; Kostyuchenko, Victor A; Xiao, Chuan; Bowman, Valorie D; Battisti, Anthony J; Yan, Xiaodong; Chipman, Paul R; Baker, Timothy S; Van Etten, James L; Rossmann, Michael G
2009-07-01
Paramecium bursaria Chlorella virus-1 is an icosahedrally shaped, 1,900-A-diameter virus that infects unicellular eukaryotic green algae. A 5-fold symmetric, 3D reconstruction using cryoelectron microscopy images has now shown that the quasiicosahedral virus has a unique vertex, with a pocket on the inside and a spike structure on the outside of the capsid. The pocket might contain enzymes for use in the initial stages of infection. The unique vertex consists of virally coded proteins, some of which have been identified. Comparison of shape, size, and location of the spike with similar features in bacteriophages T4 and P22 suggests that the spike might be a cell-puncturing device. Similar asymmetric features may have been missed in previous analyses of many other viruses that had been assumed to be perfectly icosahedral. PMID:19541619
Analytical models of icosahedral shells for 3D optical imaging of viruses
Jafarpour, Aliakbar
2014-01-01
A modulated icosahedral shell with an inclusion is a concise description of many viruses, including recently-discovered large double-stranded DNA ones. Many X-ray scattering patterns of such viruses show major polygonal fringes, which can be reproduced in image reconstruction with a homogeneous icosahedral shell. A key question regarding a low-resolution reconstruction is how to introduce further changes to the 3D profile in an efficient way with only a few parameters. Here, we derive and compile different analytical models of such an object with consideration of practical optical setups and typical structures of such viruses. The benefits of such models include 1) inherent filtering and suppressing different numerical errors of a discrete grid, 2) providing a concise and meaningful set of descriptors for feature extraction in high-throughput classification/sorting and higher-resolution cumulative reconstructions, 3) disentangling (physical) resolution from (numerical) discretization step and having a vector ...
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.
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
Structure of a high-order icosahedral approximant phase in Mg-Ga-Al-Zn system
K. Edagawa; K. Suzuki; M. Ichihara; S. Takeuchi; A. Kamiya; U. Mizutani
1991-01-01
The melt-spun Mg39·5Ga16·4 A14·1Zn40·0 ribbon consists entirely of micrograins of an icosahedral phase (I-phase). The calorimetric and X-ray diffraction studies have shown that the I-phase undergoes an exothermic transformation to an approximant crystalline phase at 630 K on heating at a rate of 20 K min. Detailed structural analysis of the crystalline phase has revealed that the phase corresponds to
Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy
Grigorieff, Nikolaus; Harrison, Stephen C.
2011-01-01
Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfill predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3 – 4 Å resolution. This review summarizes technical developments, both in instrumentation and in computation, that have led to the new structures, which advance our understanding of virus assembly and cell entry. PMID:21333526
H. Kubokawa; M. Fujiwara; T. Nasuno; M. Satoh
2010-01-01
The dynamical characteristics of the tropical tropopause layer (TTL) are investigated using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) run on the Earth Simulator under an aqua planet condition. Two experiments are performed: one with a 3.5 km horizontal spacing and a three-dimensional snapshot output and another with a 7 km horizontal spacing and 3-hourly averages for 1 month. The number
Precipitates in a Mg–Zn–Y alloy reinforced by an icosahedral quasicrystalline phase
I. J. Kim; D. H. Bae; D. H. Kim
2003-01-01
The precipitation behavior under various heat treatment conditions in the as-cast and hot-rolled Mg–Zn–Y alloy has been investigated. While MgZn2 precipitates are distributed in the ?-Mg matrix at 190°C, in the temperature range of 350–420°C, polygon-shaped icosahedral phase (I-phase) precipitates are mainly formed. The precipitated I-phase is mostly found to be localized near the eutectic region in the as-cast ingot,
Brien, Valerie; Dauscher, Anne; Machizaud, Francis [Laboratoire de Science et Genie des Materiaux et de Metallurgie, UMR CNRS-INPL 7584, Parc de Saurupt, ENSMN, F-54042 Nancy Cedex (France); Laboratoire de Physique des Materiaux, UMR CNRS-INPL-UHP 7556, Parc de Saurupt, ENSMN, F-54042 Nancy Cedex (France); Laboratoire de Science et Genie des Materiaux et de Metallurgie, UMR CNRS-INPL 7584, Parc de Saurupt, ENSMN, F-54042 Nancy Cedex (France)
2006-08-15
The optical reflectivity of Al-based and Ti-based quasicrystalline and approximant samples were investigated versus the quality of their structural morphology using optical reflectometry, x-ray diffraction, and transmission electron microscopy. The different structural morphologies were obtained using three different preparation processes: sintering, pulsed laser deposition, and reactive cathodic magnetron sputtering. The work demonstrates that the canonical behavior of icosahedral state in specular reflectivity is extremely sensitive to different and very fine aspects of the microstructure: sizes of grains smaller than 50 nm, slight local diffuse disorder, and shifts away from the icosahedral crystallographic structure (approximants). The work explains why the optical properties of the same kind of quasicrystals found in literature sometimes reveal a different behavior from one author to another. The study then confirms the work of some authors and definitely shows that the canonical behavior of icosahedral state in specular reflectivity over the 30 000-50 000 cm{sup -1} domain is characterized by a decreasing function made of steps. It also shows that this behavior can be interpreted thanks to the cluster hierarchy of the model of Janot [Phys. Rev. B 53, 181 (1996)].
Computational self-assembly of a one-component icosahedral quasicrystal.
Engel, Michael; Damasceno, Pablo F; Phillips, Carolyn L; Glotzer, Sharon C
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems. PMID:25485986
Computational self-assembly of a one-component icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Engel, Michael; Damasceno, Pablo F.; Phillips, Carolyn L.; Glotzer, Sharon C.
2015-01-01
Icosahedral quasicrystals (IQCs) are a form of matter that is ordered but not periodic in any direction. All reported IQCs are intermetallic compounds and either of face-centred-icosahedral or primitive-icosahedral type, and the positions of their atoms have been resolved from diffraction data. However, unlike axially symmetric quasicrystals, IQCs have not been observed in non-atomic (that is, micellar or nanoparticle) systems, where real-space information would be directly available. Here, we show that an IQC can be assembled by means of molecular dynamics simulations from a one-component system of particles interacting via a tunable, isotropic pair potential extending only to the third-neighbour shell. The IQC is body-centred, self-assembles from a fluid phase, and in parameter space neighbours clathrates and other tetrahedrally bonded crystals. Our findings elucidate the structure and dynamics of the IQC, and suggest routes to search for it and design it in soft matter and nanoscale systems.
Lowe, M; Yadav, T P; Fournée, V; Ledieu, J; McGrath, R; Sharma, H R
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol. PMID:25747095
NASA Astrophysics Data System (ADS)
Lowe, M.; Yadav, T. P.; Fournée, V.; Ledieu, J.; McGrath, R.; Sharma, H. R.
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
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…
J. Bordé; Ch. J. Bordé; C. Salomon; A. van Lerberghe; M. Ouhayoun; C. D. Cantrell
1980-01-01
It is shown that the mixing of vibration-rotation states by nuclear hyperfine interactions causes crossover resonances to appear in infrared saturation spectra. Examples are displayed in the nu3 band of SF6 and obtain the tensor centrifugal-distortion constant t044 and the tensor spin-rotation constant cd. The value of t044 (5.7 Hz) obtained is in excellent agreement with the theoretical value. A
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
Icosahedral packing of polymer-tethered nanospheres and stabilization of the Gyroid Phase
NSDL National Science Digital Library
Iacovella, Christopher R.
2006-05-17
We present results of molecular simulations that predict the phases formed by the selfassembly of model nanospheres functionalized with a single polymer “tether”. Microphase separation of the immiscible tethers and nanospheres induces the formation of the double gyroid, perforated lamella and crystalline bilayer phases. Confinement effects promote the formation of icosahedral arrangements of nanoparticles that help to stabilize the gyroid and perforated lamella phases. We also present a new metric for determining the local arrangement of particles in liquid and solid configurations.
Preprint, link to published version can be found below.
NASA Astrophysics Data System (ADS)
Belin-Ferré, Esther; Fournée, Vincent; Dubois, Jean Marie
2000-09-01
This paper concentrates on a comparison of Al 3p occupied densities of states in crystalline and quasicrystalline Al-Cu-Fe intermetallics. This comparison is made quantitative by computing the two first moments of this partial distribution, which correspond to the partial contribution of Al atoms to the cohesive energy of the material and to the orbital overlap modulated by the coordination number, respectively. From these data, we conclude that the icosahedral quasicrystal and its approximants represent a region of specifically enhanced stability in the Al-Cu-Fe phase diagram. We assign this effect to the specific role played by Al 3p states in the Hume-Rothery mechanism. We confirm the occurrence of a stronger hybridization between Al 3p and Fe 3d states in the icosahedral structure whereas we point out a weaker interaction with Cu 3d states in the icosahedral compounds as compared to stable approximants.
Shen, Y.T.; Kim, T.H.; Gangopadhyay, A.K.; Kelton, K.F.; (WSU)
2009-06-05
One explanation for the glass transition is a geometrical frustration owing to the development of non-space-filling short-range order (icosahedral, tetrahedral). However, experimental demonstrations of this are lacking. Here, the first quantitative measurements of the time-dependent nucleation rate in a Zr59Ti3Cu20Ni8Al10 bulk metallic glass are combined with the first measurements of the evolution of the supercooled liquid structure to near the glass transition temperature to provide strong support for an icosahedral-order-based frustration model for the glass transition in Zr-based glasses.
Cluster packing geometry for Al-based F-type icosahedral alloys
Nobuhisa Fujita; Hikari Takano; Akiji Yamamoto; An-Pang Tsai
2013-01-29
This paper presents a new highly stable periodic approximant to the Al-based F-type icosahedral quasicrystals, i-Al-Pd-TM (TM=transition metals). The structure of this intermetallic Al-Pd-Cr-Fe compound is determined ab initio using single-crystal X-ray diffraction, where the space group is identified to be Pa-3 and the lattice constant 40.5 angstrom. The structure is well described as a dense packing of clusters of two kinds, which are known in the literature as the pseudo-Mackay type and the Bergman type clusters. The clusters are centered at the vertices of a canonical cell tiling, in which the parity of each vertex determines the kind of the associated cluster. Adjacent clusters can be markedly interpenetrated, while the structure requires no glue atoms to fill in the gaps between the clusters. It is shown that the crystal can be designated as a 2x2x2 superstructure of the ordinary cubic 3/2 rational approximant. The superlattice ordering is shown to be of a different kind from the P-type superlattice ordering previously reported in i-Al-Pd-Mn. The present results will greatly improve the understanding of atomic structures of F-type icosahedral quasicrystals and their approximants.
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
NASA Astrophysics Data System (ADS)
Rípodas, P.; Gassmann, A.; Förstner, J.; Majewski, D.; Giorgetta, M.; Korn, P.; Kornblueh, L.; Wan, H.; Zängl, G.; Bonaventura, L.; Heinze, T.
2009-06-01
The Icosahedral Shallow Water Model (ICOSWM) has been a first step in the development of the ICON (acronym for ICOsahedral Nonhydrostatic) models. ICON is a joint project of the Max Planck Institute for Meteorology in Hamburg (MPI-M) and Deutscher Wetterdienst (DWD) for the development of new unified general circulation models for climate modeling and numerical weather forecasting on global or regional domains. A short description of ICOSWM is given. Standard test cases are used to test the performance of ICOSWM. The National Center for Atmospheric Research (NCAR) Spectral Transform Shallow Water Model (STSWM) has been used as reference for test cases without an analytical solution. The sensitivity of the model results to different model parameters is studied. The kinetic energy spectra are calculated and compared to the STSWM spectra. A comparison to the shallow water version of the current operational model GME at DWD is presented. In the framework of the ICON project an hydrostatic dynamical core has been developed, and a local grid refinement option and a non-hydrostatic dynamical core are under development. The results presented in this paper use the ICOSWM version at the end of 2008 and are a benchmark for the new options implemented in the development of these models.
NASA Astrophysics Data System (ADS)
Rípodas, P.; Gassmann, A.; Förstner, J.; Majewski, D.; Giorgetta, M.; Korn, P.; Kornblueh, L.; Wan, H.; Zängl, G.; Bonaventura, L.; Heinze, T.
2009-12-01
The Icosahedral Shallow Water Model (ICOSWM) has been a first step in the development of the ICON (acronym for ICOsahedral Nonhydrostatic) models. ICON is a joint project of the Max Planck Institute for Meteorology in Hamburg (MPI-M) and Deutscher Wetterdienst (DWD) for the development of new unified general circulation models for climate modeling and numerical weather forecasting on global or regional domains. A short description of ICOSWM is given. Standard test cases are used to test the performance of ICOSWM. The National Center for Atmospheric Research (NCAR) Spectral Transform Shallow Water Model (STSWM) has been used as reference for test cases without an analytical solution. The sensitivity of the model results to different model parameters is studied. The kinetic energy spectra are calculated and compared to the STSWM spectra. A comparison to the shallow water version of the current operational model GME at DWD is presented. The results presented in this paper use the ICOSWM version at the end of 2008 and are a benchmark for the new options implemented in the development of the ICON project.
Infectious bursal disease virus is an icosahedral polyploid dsRNA virus
Luque, Daniel; Rivas, Germán; Alfonso, Carlos; Carrascosa, José L.; Rodríguez, José F.; Castón, José R.
2009-01-01
Viruses are a paradigm of the economy of genome resources, reflected in their multiplication strategy and for their own structure. Although there is enormous structural diversity, the viral genome is always enclosed within a proteinaceous coat, and most virus species are haploid; the only exception to this rule are the highly pleomorphic enveloped viruses. We performed an in-depth characterization of infectious bursal disease virus (IBDV), a non-enveloped icosahedral dsRNA virus with a bisegmented genome. Up to 6 natural populations can be purified, which share a similar protein composition but show higher sedimentation coefficients as particle density increases. Stoichiometry analysis of their genome indicated that these biophysical differences correlate with the copy number of dsRNA segments inside the viral capsid. This is a demonstration of a functional polyploid icosahedral dsRNA virus. We show that IBDV particles with greater genome copy number have higher infectivity rates. Our results show an unprecedented replicative strategy for dsRNA viruses and suggest that birnaviruses are living viral entities encompassing numerous functional and structural characteristics of positive and negative ssRNA viruses. PMID:19164552
Zirnbauer, Martin R
2010-01-01
Physical systems exhibiting stochastic or chaotic behavior are often amenable to treatment by random matrix models. In deciding on a good choice of model, random matrix physics is constrained and guided by symmetry considerations. The notion of 'symmetry class' (not to be confused with 'universality class') expresses the relevance of symmetries as an organizational principle. Dyson, in his 1962 paper referred to as the Threefold Way, gave the prime classification of random matrix ensembles based on a quantum mechanical setting with symmetries. In this article we review Dyson's Threefold Way from a modern perspective. We then describe a minimal extension of Dyson's setting to incorporate the physics of chiral Dirac fermions and disordered superconductors. In this minimally extended setting, where Hilbert space is replaced by Fock space equipped with the anti-unitary operation of particle-hole conjugation, symmetry classes are in one-to-one correspondence with the large families of Riemannian symmetric spaces.
Valset, K; Tafto, J
2011-06-01
We classify the point symmetries at the different points in the Brillouin zone for the 17 two-dimensional space groups and the symmetries of the Bloch waves for the 10 two-dimensional crystallographic point groups. Simple examples involving breakdown of Friedels law, Gjonnes-Moodie lines, and reflection and refraction at interfaces are presented. PMID:20832173
Performance Analysis of high-order remap-type advection scheme on icosahedral-hexagonal grid
NASA Astrophysics Data System (ADS)
Mittal, Rashmi; Dubey, Sarvesh; Saxena, Vaibhav; Meurdesoif, Yann
2014-05-01
A comparative performance analysis on computational cost of second order advection schemes FF-CSLAM (Flux form conservative semi-Lagrangian multi-tracer transport scheme) and it's two simplifications on Icosahedral grid has been presented. Tracer transport is one of the main building blocks in atmospheric models and hence their performance greatly determines the overall performance of the model. FF-CSLAM falls in the category of arbitrary Lagrangian Eulerian (ALE) scheme. It exploits the finite volume formulation and therefore it is inherently conservative. Flux-area through edges are approximated with great circle arcs in an upwind fashion. Bi-quadratic sub-grid scale reconstructions using weighted least-squares method is employed to approximate trace field. Area integrals on the overlapped region of flux-area and static Eulerian meshes are evaluated via line-integrals. A brief description of implementation of FF-CSLAM on icosahedral -hexagonal meshes along with and its numerical accuracy in terms of standard test cases will be presented. A comparative analysis of the computational overhead is necessary to assess the suitability of FF-CSLAM for massively parallel and multi-threading computer architectures in comparison to other advection schemes implemented on icosahedral grids. The main focus of this work is to present the implementation of the shared memory parallelization and to describe the memory access pattern of the numerical scheme. FF-CSLAM is a remap-type advection scheme, thus extra calculation are done in comparison to the other advection schemes. The additional computations are associated with the search required to find the overlap area between the area swept through the edge and the underlining grid. But the experiments shows that the associated computational overhead is minimal for multi-tracer transport. It will be shown that for the Courant Number less than one, FF-CSLAM, the computations are not expensive. Since the grid cells are arranged in rectangular array just like cubed-sphere or lat-lon grids, the schemes computational performance is similar to that of the similar schemes on geodesic grids.
Symmetry-protected entangling boundary zero modes in crystalline topological insulators
NASA Astrophysics Data System (ADS)
Chang, Po-Yao; Mudry, Christopher; Ryu, Shinsei
2014-09-01
Crystalline topological insulators owe their topological character to the protection that certain boundary states acquire because of certain point-group symmetries. We first show that a Hermitian operator obeying supersymmetric quantum mechanisms (SUSY QM) delivers the entanglement spectrum. We then show that such an entanglement spectrum that is compatible with a certain point-group symmetry obeys a certain local spectral symmetry. The latter result is applied to the stability analysis of four fermionic non-interacting Hamiltonians, the last of which describes graphene with a Kekule distortion. All examples have the remarkable property that their entanglement spectra inherit a local spectral symmetry from either an inversion or reflection symmetry that guarantees the stability of gapless boundary entangling states, even though all examples fail to support protected gapless boundary states at their physical boundaries.
P. Danielewicz
2006-07-15
Examination of symmetry energy is carried out on the basis of an elementary binding-energy formula. Constraints are obtained on the energy value at the normal nuclear density and on the density dependence of the energy at subnormal densities.
DYNAMICO, an icosahedral hydrostatic dynamical core designed for consistency and versatility
NASA Astrophysics Data System (ADS)
Dubos, T.; Dubey, S.; Tort, M.; Mittal, R.; Meurdesoif, Y.; Hourdin, F.
2015-02-01
The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-03-18
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 ?m in diameter and adenine-thymine (AT)-rich genomes of up to 1.25 Mb encoding a thousand proteins. Like their Mimivirus prototype discovered 10 y ago, they entirely replicate within cytoplasmic virion factories. In contrast, the recently discovered Pandoraviruses exhibit larger amphora-shaped virions 1 ?m in length and guanine-cytosine-rich genomes up to 2.8 Mb long encoding up to 2,500 proteins. Their replication involves the host nucleus. Whereas the Megaviridae share some general features with the previously described icosahedral large DNA viruses, the Pandoraviruses appear unrelated to them. Here we report the discovery of a third type of giant virus combining an even larger pandoravirus-like particle 1.5 ?m in length with a surprisingly smaller 600 kb AT-rich genome, a gene content more similar to Iridoviruses and Marseillevirus, and a fully cytoplasmic replication reminiscent of the Megaviridae. This suggests that pandoravirus-like particles may be associated with a variety of virus families more diverse than previously envisioned. This giant virus, named Pithovirus sibericum, was isolated from a >30,000-y-old radiocarbon-dated sample when we initiated a survey of the virome of Siberian permafrost. The revival of such an ancestral amoeba-infecting virus used as a safe indicator of the possible presence of pathogenic DNA viruses, suggests that the thawing of permafrost either from global warming or industrial exploitation of circumpolar regions might not be exempt from future threats to human or animal health. PMID:24591590
Bodner, George M.
Icosahedral Carborane Derivatives Inorganic Chemistry, Vol. 13,No. IO,I 9 74 2321 Table 11 benzenesulfonate, 10531-13-2;malononitrile, 109-77-3. ' Contribution No. 2504 from the Department of Chemistry
Symmetry classification of bond order parameters in cuprates
NASA Astrophysics Data System (ADS)
Zeyher, Roland
2015-02-01
We study bond order parameters for generalized t -J models on a square lattice. Using the plane-wave limit the considered order parameters form basis functions for irreducible representations of the symmetry transformations of the point group and of time reversal. We show that, for instability wave vectors along the diagonals, all possible basis functions either are fine tuned (i.e., obey restrictions beyond the requirements of symmetry) or break time-reversal symmetry and thus describe flux states. For instability wave vectors along the crystalline axes, corresponding to the observed case in underdoped cuprates, there are only three representations with A1,B1, and E symmetry which do not break time-reversal symmetry in the general case. We suggest that one of them has recently been observed in resonant elastic x-ray scattering.
Pauling, L. (Linus Pauling Institute of Science and Medicine, Palo Alto, CA (USA))
1988-07-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, noise) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals.
Is space-time symmetry a suitable generalization of parity-time symmetry?
Paolo Amore; Francisco M. Fernández; Javier Garcia
2014-05-20
We discuss space-time symmetric Hamiltonian operators of the form $% H=H_{0}+igH^{\\prime}$, where $H_{0}$ is Hermitian and $g$ real. $H_{0}$ is invariant under the unitary operations of a point group $G$ while $H^{\\prime}$ is invariant under transformation by elements of a subgroup $G^{\\prime}$ 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 $% 0complex eigenvalues for $g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.
First-principles study of the electronic structures of icosahedral TiN (N=13,19,43,55) clusters.
Wang, Shan-Ying; Yu, Jing-Zhi; Mizuseki, Hiroshi; Yan, Jia-An; Kawazoe, Yoshiyuki; Wang, Chong-Yu
2004-05-01
We have studied the electronic structures of icosahedral Ti(N) clusters (N=13, 19, 43, and 55) by using a real-space first-principles cluster method with generalized gradient approximation for exchange-correlation potential. The hexagonal close-packed and fcc close-packed clusters have been studied additionally for comparisons. It is found that the icosahedral structures are the most stable ones except for Ti(43), where fcc close-packed structure is favorable in energy. We present and discuss the variation of bond length, the features of the highest occupied molecular orbitals and the lowest unoccupied molecular orbital, the evolution of density of states, and the magnetic moment in detail. The results are in good agreement with the predictions from the collision-induced dissociation and size-selected anion photoelectron spectroscopy experiments. PMID:15267771
Chern, I-Liang
1994-08-01
Two versions of a control volume method on a symmetrized icosahedral grid are proposed for solving the shallow-water equations on a sphere. One version expresses of the equations in the 3-D Cartersian coordinate system, while the other expresses the equations in the northern/southern polar sterographic coordinate systems. The pole problem is avoided because of these expressions in both versions and the quasi-homogenity of the icosahedral grid. Truncation errors and convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence tests of the numerical gradient and divergent operators associated with this method are studied. A convergence test for a steady zonal flow is demonstrated. Several simulations of Rossby-Haurwitz waves with various numbers are also performed.
Atomic model of anti-phase boundaries in a face-centred icosahedral Zn Mg Dy quasicrystal
Jianbo Wang; Wenge Yang; Renhui Wang
2003-01-01
An atomic model in the physical space for an anti-phase boundary (APB) in the ordered face-centred icosahedral Zn-Mg-Dy quasicrystal phase is presented, based on a six-dimensional model suggested by Ishimasa and Shimizu (2000 Mater. Sci. Eng. A 294-296 232, Ishimasa 2001 private communication). The physical space atomic positions of the defected structure were used for the calculation of the corresponding
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…
Finite Symmetry Transformation Groups and Exact Solutions of Konopelchenko-Dubrovsky Equation
NASA Astrophysics Data System (ADS)
Zhang, Huan-Ping; Li, Biao; Chen, Yong
2009-09-01
Based on the general direct method developed by Lou et al. [J. Phys. A: Math. Gen. 38 (2005) L129], the symmetry group theorem is obtained, from that both the Lie point groups and the non-Lie symmetry groups of the Konopelchenko-Dubrovsky (KD) equation are obtained. From the theorem, some exact solutions of KD equation are derived from a simple travelling wave solution and a multi-soliton solution.
Improved smoothness and homogeneity of icosahedral grids using the spring dynamics method
NASA Astrophysics Data System (ADS)
Iga, Shin-ichi; Tomita, Hirofumi
2014-02-01
An icosahedral grid that has both high smoothness and homogeneity is proposed. The grid-generation method is based on the combination of the spring dynamics (SPR) method with zero natural spring length (SPR0) and transformation by a smooth analytic function around the 12 vertices of an icosahedron. As a preliminary step, we first showed that the grid interval of the grid generated by SPR0 was inversely proportional to a Lambert conformal conic projection map factor, with a map angle of 300° around the vertices. Then, the transformation function was analytically determined, such that the resolution for the azimuthal direction became constant. In order to estimate cost-efficiency of numerical simulation with the newly proposed grid, we introduced an index defined as the ratio between the minimum grid interval and the squared maximum grid interval. It showed a 2.5% improvement from a recursive grid, and a 0.3-12% improvement from the best cases of the original SPR grid proposed by Tomita et al. (2002) [23] [hereafter, T02] dependent on global resolution. We also re-examined the original SPR method and found that the natural spring length proposed in T02 should be shortened to avoid instability when the global resolution is higher than grid-level 8. Finally, we examined the grids using advection/shallow water simulations.
Proteomic Analysis of Sulfolobus solfataricus During Sulfolobus Turreted Icosahedral Virus Infection
Maaty, Walid S.; Selvig, Kyla; Ryder, Stephanie; Tarlykov, Pavel; Hilmer, Jonathan K.; Heinemann, Joshua; Steffens, Joseph; Snyder, Jamie C.; Ortmann, Alice C.; Movahed, Navid; Spicka, Kevin; Chetia, Lakshindra; Grieco, Paul A.; Dratz, Edward A.; Douglas, Trevor; Young, Mark J.; Bothner, Brian
2012-01-01
Where there is life, there are viruses. The impact of viruses on evolution, global nutrient cycling, and disease has driven research on their cellular and molecular biology. Knowledge exists for a wide range of viruses, however, a major exception are viruses with archaeal hosts. Archaeal virus-host systems are of great interest because they have similarities to both eukaryotic and bacterial systems and often live in extreme environments. Here we report the first proteomics-based experiments on archaeal host response to viral infection. Sulfolobus Turreted Icosahedral Virus (STIV) infection of Sulfolobus solfataricus P2 was studied using 1D and 2D differential gel electrophoresis (DIGE) to measure abundance and redox changes. Cysteine reactivity was measured using novel fluorescent zwitterionic chemical probes that, together with abundance changes, suggest that virus and host are both vying for control of redox status in the cells. Proteins from nearly 50% of the predicted viral open reading frames were found along with a new STIV protein with a homolog in STIV2. This study provides insight to features of viral replication novel to the archaea, makes strong connections to well described mechanisms used by eukaryotic viruses such as ESCRT-III mediated transport, and emphasizes the complementary nature of different omics approaches. PMID:22217245
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.
None
2011-02-24
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of “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 “renormalizab
Pauling, L. (Linus Pauling Institute of Science and Medicine, Palo Alto, CA (USA))
1988-11-01
A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals.
Shackelford, Scott A; Belletire, John L; Boatz, Jerry A; Schneider, Stefan; Wheaton, Amanda K; Wight, Brett A; Ammon, Herman L; Peryshkov, Dmitry V; Strauss, Steven H
2010-06-18
Thirteen bridged triazolium and imidazolium dicationic salts, which uniquely pair closo-icosahedral perfluoroborane [B(12)F(12)](2-), borane [B(12)H(12)](2-), or carborane [CB(11)H(12)](-) anionic species with unsaturated bridged heterocyclium dications, were synthesized using an aqueous benchtop method. This considerably extends the scope of a reported aqueous synthesis of binary [heterocyclium](2)[B(12)H(12)] and [heterocyclium][CB(11)H(12)] salts. Also, the one-step preparation of five new precursor bridged heterocyclium dicationic dihalide salts using conventional procedures and in one case a microwave-assisted method is described. PMID:20499850
Plasticity of single-grain icosahedral Al-Pd-Mn quasi-crystals deformed at room temperature
Mompiou, F.; Caillard, D
2004-07-12
Transmission electron microscopy observations have been performed on icosahedral Al-Pd-Mn quasi-crystal samples deformed at 20 deg. C under a high confining pressure. They reveal a large density of wavy walls from which several climbing dislocations are emitted. Near-screw dislocations have been found at the wall terminations with a Burgers vector contained in the wall plane. Careful plane determinations and dislocation analyses are not consistent with a glide and cross-slip mechanism. The results can be better interpreted as a deformation by cracks in mode III followed by a re-healing process.
Icosahedral short-range order in amorphous Cu80Si20 by ab initio molecular dynamics simulation study
Wu, S.; Kramer, Matthew J.; Fang, Xiaowei; Wang, Shy-Guey; Wang, Cai-Zhuang; Ho, Kai-Ming; Ding, Z.J.; Chen, L.Y.
2012-04-26
Short-range order in liquid and amorphous structures of Cu80Si20 is studied by ab initio molecular dynamics simulations. We performed the simulations at 1140 and 300 K respectively to investigate the local structure change from liquid to amorphous. The result of structure factor in comparison with experimental data indicates that our simulation of amorphous Cu80Si20 is reliable. By using the bond-angle distribution function, Honeycutt–Andersen index, Voronoi tessellation method, and the atomistic cluster alignment method, the icosahedral short-range order in the system is revealed. Strong Cu–Si interaction was also observed.
Baker, T. S.; Olson, N. H.; Fuller, S. D.
1999-01-01
Viruses are cellular parasites. The linkage between viral and host functions makes the study of a viral life cycle an important key to cellular functions. A deeper understanding of many aspects of viral life cycles has emerged from coordinated molecular and structural studies carried out with a wide range of viral pathogens. Structural studies of viruses by means of cryo-electron microscopy and three-dimensional image reconstruction methods have grown explosively in the last decade. Here we review the use of cryo-electron microscopy for the determination of the structures of a number of icosahedral viruses. These studies span more than 20 virus families. Representative examples illustrate the use of moderate- to low-resolution (7- to 35-?) structural analyses to illuminate functional aspects of viral life cycles including host recognition, viral attachment, entry, genome release, viral transcription, translation, proassembly, maturation, release, and transmission, as well as mechanisms of host defense. The success of cryo-electron microscopy in combination with three-dimensional image reconstruction for icosahedral viruses provides a firm foundation for future explorations of more-complex viral pathogens, including the vast number that are nonspherical or nonsymmetrical. PMID:10585969
NASA Astrophysics Data System (ADS)
Nakayama, Ryu-suke; Takeuchi, Tsunehiro
2015-01-01
In this study, a new thermal rectifier working at high temperatures above 300 K was developed using Al61.5Cu26.5Fe12 icosahedral quasicrystal and Ag2Te. The thermal conductivity of Al61.5Cu26.5Fe12 increased drastically with temperature and, at 1000 K, reached a value nine times larger than that at 300 K. The thermal conductivity of Ag2Te showed a sudden decrease at around 400 K, and the thermal conductivity at 423 K became 60% smaller than that at 300 K. By making a composite consisting of Al61.5Cu26.5Fe12 icosahedral quasicrystal and Ag2Te, we succeeded in obtaining a large thermal rectification ratio (TRR) of | J large|/| J small| = 1.63 using two heat reservoirs maintained at T H = 543 K and T L = 300 K. The obtained TRR value is the largest among those ever reported for bulk thermal rectifiers.
Zheng Yang; Ivet Bahar; Michael Widom
2009-01-01
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
A Reflective Symmetry Descriptor
Michael M. Kazhdan; Bernard Chazelle; David P. Dobkin; Adam Finkelstein; Thomas A. Funkhouser
2002-01-01
Computing reflective symmetries of 2D and 3D shapes is a classi- cal problem in computer vision and computational geometry. Most prior work has focused on finding the main axes of symmetry, or determining that none ex- ists. In this paper, we introduce a new reflective symmetry descriptor that repre- sents a measure of reflective symmetry for an arbitrary 3D voxel
Tricas, Hugo; Colon, Marta; Ellis, David; Macgregor, Stuart A; McKay, David; Rosair, Georgina M; Welch, Alan J; Glukhov, Ivan V; Rossi, Fulvio; Laschi, Franco; Zanello, Piero
2011-04-28
The icosahedral carboranes 1-C(6)F(5)-2-Ph-1,2-closo-C(2)B(10)H(10) (1), 1-(4'-F(3)CC(6)H(4))-2-Ph-1,2-closo-C(2)B(10)H(10) (2), 1,2-(4'-F(3)CC(6)H(4))(2)-1,2-closo-C(2)B(10)H(10) (3), 1-(4'-H(3)CC(6)F(4))-2-Ph-1,2-closo-C(2)B(10)H(10) (4), 1-(4'-F(3)CC(6)F(4))-2-Ph-1,2-closo-C(2)B(10)H(10) (5), 1,2-(4'-F(3)CC(6)F(4))(2)-1,2-closo-C(2)B(10)H(10) (6), 1,7-(4'-F(3)CC(6)F(4))(2)-1,7-closo-C(2)B(10)H(10) (7) and 1,12-(4'-F(3)CC(6)F(4))(2)-1,12-closo-C(2)B(10)H(10) (8), with fluorinated aryl substituents on cage carbon atoms, have been prepared in good to high yields and characterised by microanalysis, (1)H, (11)B and (19)F NMR spectroscopies, mass spectrometry, single-crystal X-ray diffraction and (spectro)electrochemistry. By analysis of , the weighted average (11)B chemical shift, a ranking order for the ortho carboranes 1-6 is established based on the combined electron-withdrawing properties of the C-substituents, and is in perfect agreement with that established independently by electrochemical study. In a parallel computational study the effects of a wide range of different substituents on the redox properties of carboranes have been probed by comparison of ?E values, where ?E is the energy gap between the DFT-optimised [7,9-R(2)-7,9-nido-C(2)B(10)](2-) anion and its DFT-optimised basket-shaped first oxidation product. The overall conclusion from the NMR spectroscopic, electrochemical and computational studies is that strongly electron withdrawing substituents significantly stabilise [7,9-nido-C(2)B(10)](2-) dianions with respect to oxidation, and that the best practical substituent is 4-F(3)CC(6)F(4). Thus attention focussed on the reduction of 1,2-(4'-F(3)CC(6)F(4))(2)-1,2-closo-C(2)B(10)H(10), compound 6. The sequence 6/[6](-)/[6](2-) appears reversible on the cyclic voltammetric timescale but on the longer timescale of macroelectrolysis the radical anion is only partially stable. EPR study of the electrogenerated monoanions from the ortho-carboranes 1-6 confirms the cage-centred nature of the redox processes. In contrast, the reduction of the meta- and para-carboranes 7 and 8, respectively, appears to be centred on the aromatic substituents, a conclusion supported by the results of DFT calculation of the LUMOs of compounds 6-8. Bulk 2-electron reduction of 6 affords a dianion which is remarkably stable to reoxidation, surviving for several hours in the open laboratory in the absence of halogenated solvents. PMID:21390395
D. R. Pooler
1980-01-01
For pt.I see J. Phys. A (GB), vol.11, no.6, p.1045 (1978). Using cubic systems as illustrative examples the author derives and extends previous results on the invariances of Jahn-Teller systems using a more direct method. The theory is more general in being applicable to all simple-phase real-character physical symmetry groups. It is shown how various continuous groups can be generated
Symmetry conditions for nonreciprocal light propagation in magnetic crystals
NASA Astrophysics Data System (ADS)
Szaller, Dávid; Bordács, Sándor; Kézsmárki, István
2013-01-01
Recent studies demonstrated the violation of reciprocity in optical processes in low-symmetry magnetic crystals. In these crystals the speed of light can be different for counterpropagating beams. Correspondingly, they can show strong directional anisotropies such as direction dependent absorption also called directional dichroism [Bordács , Nat. Phys.10.1038/nphys2387 8, 734 (2012); Saito , J. Phys. Soc. Jpn.10.1143/JPSJ.77.013705 77, 013705 (2008)]. Based on symmetry considerations, we identify the magnetic point groups of materials which can host such directional anisotropies and also provide a list of possible candidate materials to observe these phenomena. In most of these cases, the symmetry of the crystal allows directional anisotropy not only for optical processes but also for the propagation of beams of particles and scalar waves. We also predict new types of directional optical anisotropies—besides the toroidal-moment-induced optical magnetoelectric effect and the magnetochiral dichroism investigated so far—and specify the magnetic point groups of crystals where they can emerge.
Snyder, Jamie C.; Brumfield, Susan K.; Peng, Nan; She, Qunxin; Young, Mark J.
2011-01-01
Host cells infected by Sulfolobus turreted icosahedral virus (STIV) have been shown to produce unusual pyramid-like structures on the cell surface. These structures represent a virus-induced lysis mechanism that is present in Archaea and appears to be distinct from the holin/endolysin system described for DNA bacteriophages. This study investigated the STIV gene products required for pyramid formation in its host Sulfolobus solfataricus. Overexpression of STIV open reading frame (ORF) c92 in S. solfataricus alone is sufficient to produce the pyramid-like lysis structures in cells. Gene disruption of c92 within STIV demonstrates that c92 is an essential protein for virus replication. Immunolocalization of c92 shows that the protein is localized to the cellular membranes forming the pyramid-like structures. PMID:21525343
Sharma, H. R., E-mail: H.R.Sharma@liv.ac.uk; Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R. [Surface Science Research Centre and Department of Physics, The University of Liverpool, Liverpool L69 3BX (United Kingdom)] [Surface Science Research Centre and Department of Physics, The University of Liverpool, Liverpool L69 3BX (United Kingdom); McLeod, I.; Dhanak, V. R. [Department of Physics and the Stephenson Institute for Renewable Energy, The University of Liverpool, Liverpool L69 3BX (United Kingdom)] [Department of Physics and the Stephenson Institute for Renewable Energy, The University of Liverpool, Liverpool L69 3BX (United Kingdom); Shimoda, M. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan)] [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Tsai, A. P. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan) [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577 (Japan)
2014-05-07
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C{sub 60} on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C{sub 60} molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C{sub 60} molecules atop the Pb islands approaches zero, regardless of the overall C{sub 60} coverage.
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
How does symmetry impact the flexibility of proteins?
Schulze, Bernd; Sljoka, Adnan; Whiteley, Walter
2014-01-01
It is well known that (i) the flexibility and rigidity of proteins are central to their function, (ii) a number of oligomers with several copies of individual protein chains assemble with symmetry in the native state and (iii) added symmetry sometimes leads to added flexibility in structures. We observe that the most common symmetry classes of protein oligomers are also the symmetry classes that lead to increased flexibility in certain three-dimensional structures—and investigate the possible significance of this coincidence. This builds on the well-developed theory of generic rigidity of body–bar frameworks, which permits an analysis of the rigidity and flexibility of molecular structures such as proteins via fast combinatorial algorithms. In particular, we outline some very simple counting rules and possible algorithmic extensions that allow us to predict continuous symmetry-preserving motions in body–bar frameworks that possess non-trivial point-group symmetry. For simplicity, we focus on dimers, which typically assemble with twofold rotational axes, and often have allosteric function that requires motions to link distant sites on the two protein chains. PMID:24379431
Pseudo-fivefold diffraction symmetries in tetrahedral packing.
Lee, Stephen; Henderson, Ryan; Kaminsky, Corey; Nelson, Zachary; Nguyen, Jeffers; Settje, Nick F; Schmidt, Joshua Teal; Feng, Ji
2013-07-29
We review the way in which atomic tetrahedra composed of metallic elements pack naturally into fused icosahedra. Orthorhombic, hexagonal, and cubic intermetallic crystals based on this packing are all shown to be united in having pseudo-fivefold rotational diffraction symmetry. A unified geometric model involving the 600-cell is presented: the model accounts for the observed pseudo-fivefold symmetries among the different Bravais lattice types. The model accounts for vertex-, edge-, polygon-, and cell-centered fused-icosahedral clusters. Vertex-centered and edge-centered types correspond to the well-known pseudo-fivefold symmetries in Ih and D5h quasicrystalline approximants. The concept of a tetrahedrally-packed reciprocal space cluster is introduced, the vectors between sites in this cluster corresponding to the principal diffraction peaks of fused-icosahedrally-packed crystals. This reciprocal-space cluster is a direct result of the pseudosymmetry and, just as the real-space clusters, can be rationalized by the 600-cell. The reciprocal space cluster provides insights for the Jones model of metal stability. For tetrahedrally-packed crystals, Jones zone faces prove to be pseudosymmetric with one another. Lower and upper electron per atom bounds calculated for this pseudosymmetry-based Jones model are shown to accord with the observed electron counts for a variety of Group 10-12 tetrahedrally-packed structures, among which are the four known Cu/Cd intermetallic compounds: CdCu2, Cd3Cu4, Cu5Cd8, and Cu3Cd10. The rationale behind the Jones lower and upper bounds is reviewed. The crystal structure of Zn11Au15Cd23, an example of a 1:1 MacKay cubic quasicrystalline approximant based solely on Groups 10-12 elements is presented. This compound crystallizes in Im3 (space group no. 204) with a = 13.842(2)?Å. The structure was solved with R1 = 3.53?%, I > 2?; = 5.33?%, all data with 1282/0/38 data/restraints/parameters. PMID:23780731
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.
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.
Geometric intrinsic symmetries
Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl; Szulerecka, A.; Pedrak, A. [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)] [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)
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.
NSDL National Science Digital Library
Exploratorium
2010-01-01
In this activity, learners use pattern blocks and mirrors to explore symmetry. Learners work in pairs and build mirror images of each other's designs. In doing so, learners will examine principles of symmetry and reflection.
Roelof Bijker
2005-09-02
The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and Lie algebras, and Noether's theorem. In the second part, some applications of symmetries in physics are discussed, ranging from isospin and flavor symmetry to more recent developments involving the interacting boson model and its extension to supersymmetries in nuclear physics.
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…
A. B. Balantekin
2009-10-09
Three facets of symmetries in neutrino physics are briefly reviewed: i) The SO(5) symmetry of the neutrino mass and and its connection to the see-saw mechanism; ii) Flavor SU(N) symmetries of dense, self-interacting neutrino gases in astrophysical settings; iii) The neutrino mixing angle theta13 and possible CP-violation in the neutrino sector.
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)
Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
T. Duguet
2014-11-03
We extend coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference coupled cluster theory and projected Hartree-Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy {\\it and} norm kernels for which naturally terminating coupled-cluster expansions could be eventually obtained. The present work focuses on $SU(2)$ but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to $U(1)$ symmetry associated with particle number conservation. This is relevant to Bogoliubov coupled cluster theory that was recently formulated and applied to singly open-shell nuclei.
Symmetry broken and restored coupled-cluster theory: I. Rotational symmetry and angular momentum
NASA Astrophysics Data System (ADS)
Duguet, T.
2015-02-01
We extend coupled-cluster (CC) theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of near-degenerate finite quantum systems with an open-shell character. As such, the newly developed many-body formalism offers a wealth of potential applications and further extensions dedicated to the ab initio description of, e.g., doubly open-shell atomic nuclei and molecule dissociation. The formalism, which encompasses both single-reference CC theory and projected Hartree–Fock theory as particular cases, permits the computation of usual sets of connected diagrams while consistently incorporating static correlations through the highly non-perturbative restoration of rotational symmetry. Interestingly, the yrast spectroscopy of the system, i.e. the lowest energy associated with each angular momentum, is accessed within a single calculation. A key difficulty presently overcome relates to the necessity to handle generalized energy and norm kernels for which naturally terminating CC expansions could be eventually obtained. The present work focuses on SU(2) but can be extended to any (locally) compact Lie group and to discrete groups, such as most point groups. In particular, the formalism will be soon generalized to U(1) symmetry associated with particle number conservation. This is relevant to Bogoliubov CC theory that was recently applied to singly open-shell nuclei.
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.
Chiral symmetry breaking in hidden local symmetry
S Y Furui; R. Kobayashi; M. Nakagawa
1995-01-01
Summary Chiral breaking for baryon and meson interaction is formulated in the framework of the hidden local symmetric theory of the\\u000a non-linear sigma model on the manifoldU(3)L×U(3)R\\/U(3)V. The chiral symmetry-breaking term transforms as (3,3*) underU(3)L×U(3)R at the first order. Several low-energy theorems are derived for the electromagnetic interaction of baryon. The symmetry-breaking\\u000a term preservesSU(2)×U(1) symmetry; we have confirmed that the Sakurai
Julian M. Rosalie; Hidetoshi Somekawa; Alok Singh; Toshiji Mukai
2011-01-01
Intermetallic precipitates formed in heat-treated and aged Mg-Zn and Mg-Zn-Y alloys have been investigated via electron microscopy. Coarse spheroidal precipitates formed on deformation twin boundaries contained domains belonging to either the MgZn2 hexagonal Laves phase or the monoclinic Mg4Zn7 phase. Both phases are structurally related to the quasi-crystalline phase formed in Mg-Zn-Y alloys, containing icosahedrally coordinated zinc atoms arranged as
R. Wang; M. X. Dai
1993-01-01
Dislocations in an Al62Cu25.5Fe12.5 face-centered icosahedral quasicrystal were studied by means of the contrast experiment and defocus convergent-beam electron diffraction technique. The indices of the six-dimensional Burgers vector of the dislocations were determined to be 1\\/2[1 -1 1 -1 0 0]. The projection b|| of this six-dimensional Burgers vector in the three-dimensional physical space is exactly parallel to a twofold
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.
Maniraj, M [UGC-DAE Confortium for Scientific Research; Rai, Abhishek [UGC-DAE Confortium for Scientific Research; Barman, S R [UGC-DAE Confortium for Scientific Research; Krajci, M [Slovak Academy of Sciences; Schlagel, Deborah L [Ames Laboratory; Lograsso, Thomas A [Ames Laboratory; Horn, K [Fritz-Haber-Institut der Max-Planck-Gesellschaft
2014-09-01
We study the unoccupied region of the electronic structure of the fivefold symmetric surface of an icosahedral (i) Al-Pd-Mn quasicrystal. A feature that exhibits parabolic dispersion with an effective mass of (1.15±0.1)me and tracks the change in the work function is assigned to an image potential resonance because our density functional calculation shows an absence of band gap in the respective energy region. We show that Sn grows pseudomorphically on i?Al?Pd?Mn as predicted by density functional theory calculations, and the energy of the image potential resonance tracks the change in the work function with Sn coverage. The image potential resonance appears much weaker in the spectrum from the related crystalline Al-Pd-Mn surface, demonstrating that its strength is related to the compatibility of the quasiperiodic wave functions in i?Al?Pd?Mn with the free-electron-like image potential states. Our investigation of the energy region immediately above EF provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
NASA Astrophysics Data System (ADS)
Maniraj, M.; Rai, Abhishek; Barman, S. R.; Kraj?í, M.; Schlagel, D. L.; Lograsso, T. A.; Horn, K.
2014-09-01
We study the unoccupied region of the electronic structure of the fivefold symmetric surface of an icosahedral (i) Al-Pd-Mn quasicrystal. A feature that exhibits parabolic dispersion with an effective mass of (1.15±0.1)me and tracks the change in the work function is assigned to an image potential resonance because our density functional calculation shows an absence of band gap in the respective energy region. We show that Sn grows pseudomorphically on i-Al-Pd-Mn as predicted by density functional theory calculations, and the energy of the image potential resonance tracks the change in the work function with Sn coverage. The image potential resonance appears much weaker in the spectrum from the related crystalline Al-Pd-Mn surface, demonstrating that its strength is related to the compatibility of the quasiperiodic wave functions in i-Al-Pd-Mn with the free-electron-like image potential states. Our investigation of the energy region immediately above EF provides unambiguous evidence for the presence of a pseudogap, in agreement with our density functional theory calculations.
Four-index integral transformation exploiting symmetry
NASA Astrophysics Data System (ADS)
Yamamoto, Shigeyoshi; Nagashima, Umpei
2005-02-01
We present a Fortran implementation of four-index integral transformation in the LCAO-MO (linear combination of atomic orbitals-molecular orbitals) framework that exploits symmetry. Electron correlation calculations, such as configuration interaction (CI) calculations, usually require electron repulsion integrals to be transformed to a molecular orbital basis from a basis using atomic orbitals. In large molecular systems it is vital to exploit the sparsity of integrals in making this transformation. By exploiting symmetry, the sparsity of integrals is fully utilized, the size of intermediate file is minimized, and the computational cost is reduced. The present algorithm is simple and can readily be added to existing quantum chemistry program packages. Program summaryTitle of program: SYM4TR (symmetry adapted 4-index integral transformation) Catalogue identifier: ADUW Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADUW Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Computers: IBM/AIX, HP Alpha server/Tru64, PC's/Linux Program language used: Fortran 95 Number of lines in distributed program, including test data, etc.: 4519 No. of bytes in distributed program, including test data, etc.: 32 095 Distributed format: tar gzip file Nature of physical problem: Molecular orbital calculations including electron correlation effects usually require electron repulsion integrals to be transformed from an atomic orbital (AO) basis to a molecular orbital (MO) basis. By exploiting the sparsity of molecular integrals, the computational cost and memory needed for the transformation are minimized. Method of solution: The sparsity of molecular integrals is exploited. The program treats only nonzero integrals. The length of running indices in DO loops is reduced using the block-diagonal form of the MO coefficient matrix. In the present program, the point group is limited to D 2h and its subgroups.
Roy Maartens; David Taylor
1997-12-11
We define affine transport lifts on the tangent bundle by associating a transport rule for tangent vectors with a vector field on the base manifold. The aim is to develop tools for the study of kinetic/ dynamical symmetries in relativistic particle motion. The transport lift unifies and generalises the various existing lifted vector fields, with clear geometric interpretations. We find the affine dynamical symmetries of free particle motion, and compare this to previous results and to the alternative concept of "matter symmetry".
NASA Astrophysics Data System (ADS)
Babi, D.; Klein, D. J.; Sah, C. H.
1993-08-01
All fullerene isomers with up to 70 atoms have been generated and their symmetry analyzed. A safe and efficient algorithm for determination of symmetrically equivalent vertices, edges and faces in the corresponding molecular graph is outlined. The automorphism group determined in this way represents the maximal symmetry which the pertinent molecule can have. All analyzed isomers are classified by their symmetry, and the results are tabulated.
Detection of symmetry and anti-symmetry.
Mancini, Sandra; Sally, Sharon L; Gurnsey, Rick
2005-07-01
To assess the role of second-order channels in symmetry perception we measured the effects of check size, spatial frequency content, eccentricity and grey scale range on the detection of symmetrical and anti-symmetrical patterns. Thresholds for symmetrical stimuli were only moderately affected by these manipulations. Anti-symmetrical stimuli composed of large black and white checks elicited low thresholds. However, anti-symmetry became essentially undetectable at small check sizes. Removing low frequencies from large-check-size, anti-symmetrical stimuli had little effect on thresholds whereas removing high frequencies had a pronounced effect. Moving the stimuli from fixation to 8 degrees eccentricity caused a dramatic increase in thresholds for anti-symmetrical stimuli but not symmetrical stimuli. When the grey scale range was increased anti-symmetry was undetectable at any check size whereas symmetry was easily seen at all. We argue that these results and others in the literature suggest that anti-symmetry is only detected under conditions favourable to selective attention. PMID:15845246
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.
Twisted symmetries and integrable systems
G. Cicogna; G. Gaeta
2010-02-07
Symmetry properties are at the basis of integrability. In recent years, it appeared that so called "twisted symmetries" are as effective as standard symmetries in many respects (integrating ODEs, finding special solutions to PDEs). Here we discuss how twisted symmetries can be used to detect integrability of Lagrangian systems which are not integrable via standard symmetries.
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.
NSDL National Science Digital Library
Children's Museum of Houston
2011-01-01
In this hands-on activity, learners make New Year's Eve party hats out of wrapping paper. Learners use symmetry and measurement to cut out shapes they need to assemble the hats. In a related video, Mr. O and his assistants explain how to make the party hats using rotational symmetry. Learners can watch this video before creating their hats.
A. A. Kirillov; A. A. Korotkevich; S. G. Rubin
2012-10-16
The mechanism of symmetry formation is discussed in the framework of multidimensional gravity. It is shown that this process is strictly connected to the entropy decrease of compact space. The existence of low energy symmetries is not postulated from the beginning. They could be absent during the inflationary stage under certain conditions discussed in the paper.
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…
NSDL National Science Digital Library
2007-01-01
In this simulation, you will learn about axial symmetry and the difference between the axes. Just drag and drop the shapes onto the grid and choose between the different axes of symmetry to see the effect it has on the various shapes.
On the symmetry breaking phenomenon
Petre Birtea; Mircea Puta; Tudor S. Ratiu; Ruazvan Micu Tudoran
2006-01-01
We investigate the problem of symmetry breaking in the framework of dynamical systems with symmetry on a smooth manifold. Two cases will be analyzed: general and Hamiltonian dynamical systems. We give sufficient conditions for symmetry breaking in both cases.
NASA Astrophysics Data System (ADS)
Keunen, R.; Cathcart, N.; Kitaev, V.
2014-06-01
A size- and shape-selective synthesis of pentagonally twinned silver icosahedral nanoparticles (AgIhNPs), one of the five platonic solid morphologies, has been developed by integrating three key factors: nuclei templating by copper, photochemical development using violet LED light and chemical oxidative etching. The presence of copper is essential for AgIhNP shape selection via the promotion of icosahedral nuclei in precursor NPs. Violet light (401-410 nm) is crucial to promote plasmonic selection of near-spherical AgIhNPs. Oxidative etching with hydrogen peroxide and photochemical reduction with citrate establishes a red-ox equilibrium for the photochemical selection of AgIhNPs. The addition of chloride ions improves size- and shape-selectivity. Finally, the demonstration of 1-D growth of AgIhNPs to pentagonal pins initiated at AgIhNP pentagonal-twinned defects highlights a universal role of twinned defects for the formation of anisotropic nanoparticles.A size- and shape-selective synthesis of pentagonally twinned silver icosahedral nanoparticles (AgIhNPs), one of the five platonic solid morphologies, has been developed by integrating three key factors: nuclei templating by copper, photochemical development using violet LED light and chemical oxidative etching. The presence of copper is essential for AgIhNP shape selection via the promotion of icosahedral nuclei in precursor NPs. Violet light (401-410 nm) is crucial to promote plasmonic selection of near-spherical AgIhNPs. Oxidative etching with hydrogen peroxide and photochemical reduction with citrate establishes a red-ox equilibrium for the photochemical selection of AgIhNPs. The addition of chloride ions improves size- and shape-selectivity. Finally, the demonstration of 1-D growth of AgIhNPs to pentagonal pins initiated at AgIhNP pentagonal-twinned defects highlights a universal role of twinned defects for the formation of anisotropic nanoparticles. Electronic supplementary information (ESI) available: Additional information on the synthesis series. See DOI: 10.1039/c4nr01477d
John H. Schwarz
1995-03-20
A brief review of the status of duality symmetries in string theory is presented. The evidence is accumulating rapidly that an enormous group of duality symmetries, including perturbative T dualities and non-perturbative S-dualities, underlies string theory. It is my hope that an understanding of these symmetries will suggest the right way to formulate non-perturbative string theory. Whether or not this hope is realized, it has already been demonstrated that this line of inquiry leads to powerful new tools for understanding gauge theories and new evidence for the uniqueness of string theory, as well as deep mathematical results.
Lang, C. B.; Schroeck, Mario [Institut fuer Physik, FB Theoretische Physik, Universitaet Graz, A-8010 Graz (Austria)
2011-10-15
In quantum chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of {rho} and a{sub 1} approach each other) while confining properties persist.
Nested polytopes with non-crystallographic symmetry as projected orbits of extended Coxeter groups
Motiejus Valiunas; Emilio Zappa; Briony Thomas; Reidun Twarock
2015-01-27
We construct nested polytopes with non-crystallographic symmetry from the orbits of groups containing a non-crystallographic Coxeter group $W$ via projection. For this, we embed $W$ into the point group $\\mathcal{P}$ of a higher dimensional lattice, and study the orbits of the subgroups of $\\mathcal{P}$ which contain $W$. The projection of these orbits into a lower dimensional subspace invariant under $W$ consists of nested shell arrangements with non-crystallographic symmetry. We study the properties of these structures and classify them in the case of extensions of $W$, i.e. subgroups of $\\mathcal{P}$ that contain $W$ as a normal subgroup. Geometrically, the convex hulls of these orbits represent nested polytopes with non-crystallographic symmetry. These have interesting applications in physics (quasicrystals), biology (viruses) and carbon chemistry (fullerenes).
NSDL National Science Digital Library
McIntosh, Harold V. (Harold Varner), 1929-
This online text is an exhaustive description of the role of symmetry in the degeneracy of a single-particle bound state system in quantum mechanics. Both non-relativistic and relativistic examples are studied.
Polymer quantization and Symmetries
Ghanashyam Date; Nirmalya Kajuri
2013-02-24
Polymer quantization was discovered during the construction of Loop Quantum Cosmology. For the simplest quantum theory of one degree of freedom, the implications for dynamics were studied for the harmonic oscillator as well as some other potentials. For more degrees of freedom, the possibility of continuous, kinematic symmetries arises. While these are realised on the Hilbert space of polymer quantum mechanics, their infinitesimal versions are not supported. For an invariant Hamiltonian, these symmetry realizations imply infinite degeneracy suggesting that the symmetry should be spontaneously or explicitly broken. The estimation of symmetry violations in some cases have been analysed before. Here we explore the alternative of shifting the arena to the distributional states. We discuss both the polymer quantum mechanics case as well as polymer quantized scalar field.
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.
Finite group symmetry breaking
G. Gaeta
2005-10-02
Finite group symmetry is commonplace in Physics, in particular through crystallographic groups occurring in condensed matter physics -- but also through the inversions (C,P,T and their combinations) occurring in high energy physics and field theory. The breaking of finite groups symmetry has thus been thoroughly studied, and general approaches exist to investigate it. In Landau theory, the state of a system is described by a finite dimensional variable (the {\\it order parameter}), and physical states correspond to minima of a potential, invariant under a group. In this article we describe the basics of symmetry breaking analysis for systems described by a symmetric polynomial; in particular we discuss generic symmetry breakings, i.e. those determined by the symmetry properties themselves and independent on the details of the polynomial describing a concrete system. We also discuss how the plethora of invariant polynomials can be to some extent reduced by means of changes of coordinates, i.e. how one can reduce to consider certain types of polynomials with no loss of generality. Finally, we will give some indications on extension of this theory, i.e. on how one deals with symmetry breakings for more general groups and/or more general physical systems.
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.
Keunen, R; Cathcart, N; Kitaev, V
2014-07-21
A size- and shape-selective synthesis of pentagonally twinned silver icosahedral nanoparticles (AgIhNPs), one of the five platonic solid morphologies, has been developed by integrating three key factors: nuclei templating by copper, photochemical development using violet LED light and chemical oxidative etching. The presence of copper is essential for AgIhNP shape selection via the promotion of icosahedral nuclei in precursor NPs. Violet light (401-410 nm) is crucial to promote plasmonic selection of near-spherical AgIhNPs. Oxidative etching with hydrogen peroxide and photochemical reduction with citrate establishes a red-ox equilibrium for the photochemical selection of AgIhNPs. The addition of chloride ions improves size- and shape-selectivity. Finally, the demonstration of 1-D growth of AgIhNPs to pentagonal pins initiated at AgIhNP pentagonal-twinned defects highlights a universal role of twinned defects for the formation of anisotropic nanoparticles. PMID:24910249
NASA Astrophysics Data System (ADS)
Dolinšek, J.; Vrtnik, S.; Klanjšek, M.; Jagli?i?, Z.; Smontara, A.; Smiljani?, I.; Biluši?, A.; Yokoyama, Y.; Inoue, A.; Landauro, C. V.
2007-08-01
In order to test for the true intrinsic properties of icosahedral i-Al-Cu-Fe quasicrystals, we performed investigations of magnetism, electrical resistivity, thermoelectric power, and thermal conductivity on a single-crystalline Al64Cu23Fe13 quasicrystal grown by the Czochralski technique. This sample shows superior quasicrystallinity, an almost phason-free structure, and excellent thermal stability. Magnetic measurements revealed that the sample is best classified as a weak paramagnet. Electrical resistivity exhibits a negative temperature coefficient with ?4K=3950??cm and R=?4K/?300K=1.8 , whereas the thermopower exhibits a sign reversal at T=278K . Simultaneous analysis of the resistivity and thermopower using spectral-conductivity model showed that the Fermi energy is located at the minimum of the pseudogap in the spectral conductivity ?(?) . Thermal conductivity is anomalously low for an alloy of metallic elements. Comparing the physical properties of the investigated single-crystalline Al64Cu23Fe13 quasicrystal to literature reports on polycrystalline i-Al-Cu-Fe material, we conclude that there are no systematic differences between the high-quality single-crystalline and polycrystalline i-Al-Cu-Fe quasicrystals, except for the hindering of long-range transport by grain boundaries in the polycrystalline material. The so far reported physical properties of i-Al-Cu-Fe appear to be intrinsic to this family of icosahedral quasicrystals, regardless of the form of the material.
Tarumi, Ryuichi
2013-01-01
We investigated free-vibration acoustic resonance (FVAR) of two-dimensional St Venant–Kirchhoff-type hyperelastic materials and revealed the existence and structure of colour symmetry embedded therein. The hyperelastic material is isotropic and frame indifferent and includes geometrical nonlinearity in its constitutive equation. The FVAR state is formulated using the principle of stationary action with a subsidiary condition. Numerical analysis based on the Ritz method revealed the existence of four types of nonlinear FVAR modes associated with the irreducible representations of a linearized system. Projection operation revealed that the FVAR modes can be classified on the basis of a single colour (black or white) and three types of bicolour (black and white) magnetic point groups: , , and . These results demonstrate that colour symmetry naturally arises in the finite amplitude nonlinear FVAR modes, and its vibrational symmetries are explained in terms of magnetic point groups rather than the irreducible representations that have been used for linearized systems. We also predicted a grey colour nonlinear FVAR mode which cannot be derived from a linearized system. PMID:24204182
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).
Pseudospin Dynamical Symmetry in Nuclei
NASA Astrophysics Data System (ADS)
Ginocchio, Joseph N.
2015-02-01
Pseudospin symmetry has been useful in understanding atomic nuclei. We review the arguments that this symmetry is a relativistic symmetry. The condition for this symmetry is that the sum of the vector and scalar potentials in the Dirac Hamiltonian is a constant. We give the generators of pseudospin symmetry. We review some of the predictions that follow from this insight into the relativistic origins of pseudospin symmetry. Since in nuclei the sum of the scalar and vector potentials is not zero but is small, we discuss preliminary investigations into the conditions on the potentials to produce partial dynamic pseudospin symmetry. Finally we show that approximate pseudospin symmetry in nuclei predicts approximate spin symmetry in anti-nucleon scattering from nuclei.
Kallosh, R.; Linde, A.; Linde, D.; Susskind, L. [Department of Physics, Stanford University, Stanford, California 94305-4060 (United States)] [Department of Physics, Stanford University, Stanford, California 94305-4060 (United States); [California Institute of Technology, Pasadena, California 91125 (United States)
1995-07-15
There exists a widely held notion that gravitational effects can strongly violate global symmetries. If this is correct, it may lead to many important consequences. We argue, in particular, that nonperturbative gravitational effects in the axion theory lead to a strong violation of {ital CP} invariance unless they are suppressed by an extremely small factor {ital g}{approx_lt}10{sup {minus}82}. One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar axion field as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tensor field. We show, however, that this gauge symmetry does not protect the axion mass from quantum corrections. The amplitude of gravitational effects violating global symmetries could be strongly suppressed by {ital e}{sup {minus}{ital S}}, where {ital S} is the action of a wormhole which may absorb the global charge. Unfortunately, in a wide variety of theories based on the Einstein theory of gravity the action appears to be fairly small, {ital S}{similar_to}10. However, we find that the existence of wormholes and the value of their action are extremely sensitive to the structure of space on the nearly Planckian scale. We consider several examples (Kaluza-Klein theory, conformal anomaly, {ital R}{sup 2} terms) which show that modifications of the Einstein theory on the length scale {ital l}{approx_lt}10{ital M}{sub {ital P}}{sup {minus}1} may strongly suppress violation of global symmetries. We find also that in string theory there exists an additional suppression of topology change by the factor {ital e}{sup {minus}8{pi}2}/{ital g}{sup 2}. This effect is strong enough to save the axion theory for the natural values of the stringy gauge coupling constant.
Skewed Rotation Symmetry Group Detection
Seungkyu Lee; Yanxi Liu
2010-01-01
Abstract—We present a novel and effective algorithm for affinely skewed,rotation symmetry,group detection from real-world images. We define a complete,skewed,rotation symmetry,detection problem,as discovering,five independent,properties of a skewed,rotation symmetry,group: (1) the center of rotation; (2) the affine deformation; (3) the type of the symmetry,group; (4) the cardinality of the symmetry,group; and (5) the supporting,region of the symmetry,group in the image. We propose,a
Poincaré gauge symmetries, hamiltonian symmetries and trivial gauge transformations
Rabin Banerjee; Debraj Roy
2011-12-20
We resolve a problem of finding the Poincare symmetries from hamiltonian gauge symmetries constructed through a canonical procedure of handling constrained systems. Through the use of Noether identities corresponding to the symmetries, we motivate a procedure of finding the map between the hamiltonian and Poincare gauge parameters. Using this map, we show that the Poincare and hamiltonian gauge symmetries are equivalent, modulo trivial gauge transformations.
Skewed rotation symmetry group detection.
Lee, Seungkyu; Liu, Yanxi
2010-09-01
We present a novel and effective algorithm for affinely skewed rotation symmetry group detection from real-world images. We define a complete skewed rotation symmetry detection problem as discovering five independent properties of a skewed rotation symmetry group: 1) the center of rotation, 2) the affine deformation, 3) the type of the symmetry group, 4) the cardinality of the symmetry group, and 5) the supporting region of the symmetry group in the image. We propose a frieze-expansion (FE) method that transforms rotation symmetry group detection into a simple, 1D translation symmetry detection problem. We define and construct a pair of rotational symmetry saliency maps, complemented by a local feature method. Frequency analysis, using Discrete Fourier Transform (DFT), is applied to the frieze-expansion patterns (FEPs) to uncover the types (cyclic, dihedral, and O2), the cardinalities, and the corresponding supporting regions, concentric or otherwise, of multiple rotation symmetry groups in an image. The phase information of the FEP is used to rectify affinely skewed rotation symmetry groups. Our result advances the state of the art in symmetry detection by offering a unique combination of region-based, feature-based, and frequency-based approaches. Experimental results on 170 synthetic and natural images demonstrate superior performance of our rotation symmetry detection algorithm over existing methods. PMID:20634559
Tessellations: Geometry and Symmetry
NSDL National Science Digital Library
2011-05-23
This lesson is designed to develop students' understanding of polygons and symmetry by exploring tessellations and their geometric properties. This lesson provides links to discussions and activities related to tessellations as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.
NSDL National Science Digital Library
2014-09-19
In this math activity, learners experiment with the concept of symmetry. Learners use mirrors to identify which pictures, letters, and shapes are symmetrical and then complete the missing halves for images. This activity guide contains a material list, sample questions to ask, literary connections, extensions, and alignment to local and national standards.
BOOK REVIEW: Symmetry Breaking
NASA Astrophysics Data System (ADS)
Ryder, L. H.
2005-11-01
One of the most fruitful and enduring advances in theoretical physics during the last half century has been the development of the role played by symmetries. One needs only to consider SU(3) and the classification of elementary particles, the Yang Mills enlargement of Maxwell's electrodynamics to the symmetry group SU(2), and indeed the tremendous activity surrounding the discovery of parity violation in the weak interactions in the late 1950s. This last example is one of a broken symmetry, though the symmetry in question is a discrete one. It was clear to Gell-Mann, who first clarified the role of SU(3) in particle physics, that this symmetry was not exact. If it had been, it would have been much easier to discover; for example, the proton, neutron, ?, ? and ? particles would all have had the same mass. For many years the SU(3) symmetry breaking was assigned a mathematical form, but the importance of this formulation fell away when the quark model began to be taken seriously; the reason the SU(3) symmetry was not exact was simply that the (three, in those days) quarks had different masses. At the same time, and in a different context, symmetry breaking of a different type was being investigated. This went by the name of `spontaneous symmetry breaking' and its characteristic was that the ground state of a given system was not invariant under the symmetry transformation, though the interactions (the Hamiltonian, in effect) was. A classic example is ferromagnetism. In a ferromagnet the atomic spins are aligned in one direction only—this is the ground state of the system. It is clearly not invariant under a rotation, for that would change the ground state into a (similar but) different one, with the spins aligned in a different direction; this is the phenomenon of a degenerate vacuum. The contribution of the spin interaction, s1.s2, to the Hamiltonian, however, is actually invariant under rotations. As Coleman remarked, a little man living in a ferromagnet would have to be rather clever to recognize that the particle interactions were rotationally invariant. Nambu and Goldstone showed that the spontaneous breakdown of a (continuous) symmetry implied the existence of massless scalar particles, referred to as Nambu Goldstone bosons, or simply Goldstone bosons. Meanwhile Anderson, in his study of (non-relativistic) superconductivity, showed that the exclusion of magnetic flux (Meissner effect) corresponds to a finite range for the electromagnetic field and hence to a `massive photon'. In a relativistic context Englert, Brout, Guralnik and more particularly Higgs showed that a spontaneous breaking of a gauge symmetry resulted in a massive, instead of a massless, gauge particle and no Goldstone particle; in the jargon of the day, the massless gauge particle had `eaten' the massless Goldstone boson and become massive; exactly Anderson's observation. It is this phenomenon which has been invoked so successfully to explain the masses of the W and Z bosons of weak interactions. Spontaneous symmetry breaking, therefore, has played a major role in the development of the Standard Model of particle physics, and it has also proved an important tool in condensed matter physics, for example in the understanding of phase transitions. At the same time, however, in the understanding of most (or all) particle physicists, and perhaps also condensed matter physicists, the notion of spontaneous symmetry breaking has been inexorably linked to that of a degenerate vacuum. This is the background and the starting point for Strocchi's book. Recognizing the power and importance of the concept of spontaneous symmetry breaking in theoretical physics, he defines it in a more refined and general way than usual. `Despite the many popular accounts', he writes, `the phenomenon of spontaneous symmetry breaking is deep and subtle and it is not without [reason] that it has been fully understood only in recent times.' Strocchi's main emphasis is on the fact that the loss of symmetric behaviour requires both the existence of non-symmetric ground states and the
Gauging without Initial Symmetry
Alexei Kotov; Thomas Strobl
2014-04-10
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 Sigma, the original functional is extended appropriately by additional Lie(G)-valued 1-form gauge fields so as to lift the symmetry to Maps(Sigma,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 v_a on the target M satisfying the extended Killing equation v_{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.
Shackelford, Scott A; Belletire, John L; Boatz, Jerry A; Schneider, Stefan; Wheaton, Amanda K; Wight, Brett A; Hudgens, Leslie M; Ammon, Herman L; Strauss, Steven H
2009-06-18
Ten new salts that pair triazolium and imidazolium cations with closo-icosahedral anions [B(12)H(12)](2-) and [CB(11)H(12)](-) were synthesized in water solvent using an open-air, benchtop method. These unreported [Heterocyclium](2)[B(12)H(12)] and [Heterocyclium][CB(11)H(12)] salts extend reports of [Imidazolium][CB(11)H(12)] and [Pyridinium][CB(11)H(12)] salts that were synthesized in anhydrous organic solvents under an inert atmosphere with glovebox or Schlenk techniques. Spectroscopic data, melting points, and densities are reported for each salt. Single-crystal X-ray structures are provided for the five new [B(12)H(12)](2-) salts. PMID:19441856
Dai, Tie; Schutgens, Nick A J; Goto, Daisuke; Shi, Guangyu; Nakajima, Teruyuki
2014-12-01
A new global aerosol assimilation system adopting a more complex icosahedral grid configuration is developed. Sensitivity tests for the assimilation system are performed utilizing satellite retrieved aerosol optical depth (AOD) from the Moderate Resolution Imaging Spectroradiometer (MODIS), and the results over Eastern Asia are analyzed. The assimilated results are validated through independent Aerosol Robotic Network (AERONET) observations. Our results reveal that the ensemble and local patch sizes have little effect on the assimilation performance, whereas the ensemble perturbation method has the largest effect. Assimilation leads to significantly positive effect on the simulated AOD field, improving agreement with all of the 12 AERONET sites over the Eastern Asia based on both the correlation coefficient and the root mean square difference (assimilation efficiency). Meanwhile, better agreement of the Ångström Exponent (AE) field is achieved for 8 of the 12 sites due to the assimilation of AOD only. PMID:25017412
Persson, K.; Schneider, G.; Jordan, D. B.; Viitanen, P. V.; Sandalova, T.
1999-01-01
Lumazine synthase catalyzes the penultimate step in the synthesis of riboflavin in plants, fungi, and microorganisms. The enzyme displays two quaternary structures, the pentameric forms in yeast and fungi and the 60-meric icosahedral capsids in plants and bacteria. To elucidate the structural features that might be responsible for differences in assembly, we have determined the crystal structures of lumazine synthase, complexed with the inhibitor 5-nitroso-6-ribitylamino-2,4-pyrimidinedione, from spinach and the fungus Magnaporthe grisea to 3.3 and 3.1 A resolution, respectively. The overall structure of the subunit and the mode of inhibitor binding are very similar in these enzyme species. The core of the subunit consists of a four-stranded parallel beta-sheet sandwiched between two helices on one side and three helices on the other. The packing of the five subunits in the pentameric M. grisea lumazine synthase is very similar to the packing in the pentameric substructures in the icosahedral capsid of the plant enzyme. Two structural features can be correlated to the differences in assembly. In the plant enzyme, the N-terminal beta-strand interacts with the beta-sheet of the adjacent subunit, thus extending the sheet from four to five strands. In fungal lumazine synthase, an insertion of two residues after strand beta1 results in a completely different orientation of this part of the polypeptide chain and this conformational difference prevents proper packing of the subunits at the trimer interface in the icosahedron. In the spinach enzyme, the beta-hairpin connecting helices alpha4 and alpha5 participates in the packing at the trimer interface of the icosahedron. Another insertion of two residues at this position of the polypeptide chain in the fungal enzyme disrupts the hydrogen bonding in the hairpin, and the resulting change in conformation of this loop also interferes with proper intrasubunit contacts at the trimer interface. PMID:10595538
Hadler, Amelia B; Harris, Nicholas A; Fredrickson, Daniel C
2013-11-20
Despite significant progress in the structural characterization of the quasicrystalline state, the chemical origins of long- and short-range icosahedral order remain mysterious and a subject of debate. In this Article, we present the crystal structure of a new complex intermetallic phase, Ca10Cd27Cu2 (mC234.24), whose geometrical features offer clues to the driving forces underlying the icosahedral clusters that occur in Bergman-type quasicrystals. Ca10Cd27Cu2 adopts a C-centered monoclinic superstructure of the 1/1 Bergman approximant structure, in which [110] layers of Bergman clusters in the 1/1 structure are separated through the insertion of additional atoms (accompanied by substantial positional disorder). An examination of the coordination environments of Ca and Cu (in the ordered regions) reveals that the structure can be viewed as a combination of coordination polyhedra present in the nearest binary phases in the Ca-Cd-Cu compositional space. A notable feature is the separation of Ca-Cd and Cu-Cd interactions, with Bergman clusters emerging as Ca-Cd Friauf polyhedra (derived from the MgZn2-type CaCd2 phase) encapsulate a Cu-Cd icosahedron similar to those appearing in Cu2Cd5. DFT chemical pressure calculations on nearby binary phases point to the importance of this segregation of Ca-Cd and Cu-Cd interactions. The mismatch in atomic size between Cu and Cd leads to an inability to satisfy Ca-Cu and Ca-Cd interactions simultaneously in the Friauf polyhedra of the nearby Laves phase CaCd2. The relegation of the Cu atoms to icosahedra prevents this frustration while nucleating the formation of Bergman clusters. PMID:24147875
NASA Astrophysics Data System (ADS)
Henderson, T. B.; Benjamin, S.; Bleck, R.; Brown, J.; Sun, S.; Bao, J.; Sahm, S.; Grell, G. A.; Fiorino, M.
2010-12-01
NOAA/ESRL has developed a new global model over the past few years, with real-time predictions out to 7+ days since February 2008. In this presentation, we will focus on improvements to the FIM since June 2009, including those in physics, vertical coordinate, and inline chemistry with treatment of volcanic ash. After a very brief review of the numerical characteristics of the FIM model [isentropic-sigma-hybrid vertical coordinate, finite-volume (FV) transport, icosahedral horizontal grid], we will include comparison of forecast skill between the FIM model and NCEP’s GFS model. Recent improvements in the vertical coordinate have enhanced robustness of the FIM in flow features, especially in the stratosphere and lower mesosphere. A new physical parameterization package from the GFS (implemented in NCEP GFS in late July 2010) has also been successfully implemented within the FIM (results to be shown). NOAA/ESRL has also extended the FIM to an inline-chemistry version with 16 aerosol types, including 4 size bins for volcanic ash. This FIM-chem-ash version resulted from the incorporation of a version of the WRF-chem package within the FIM framework, with transport of all aerosols within the FIM isentropic-FV-icosahedral framework. The FIM-chem-ash model was implemented in response to the April 2010 volcanic eruption of Eyjafjallajokull in Iceland. Future plans for the FIM will be described, including incorporation of its dynamic core within NCEP’s Global Ensemble Forecast System, and application of FIM-chem-ash for NOAA research issues.
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…
Helical symmetry in linear systems
Bicak, Jiri [Institute of Theoretical Physics, Faculty of Mathematics Physics, Charles University, Prague (Czech Republic); Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany); Schmidt, Bernd G. [Max-Planck-Institut fuer Gravitationsphysik, Albert-Einstein-Institut, Am Muehlenberg 1, D-14476 Golm (Germany)
2007-11-15
We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman-Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.
On the symmetry breaking phenomenon
Petre Birtea; Mircea Puta; Tudor S. Ratiu; MICU TUDORAN
2006-01-01
We investigate the problem of symmetry breaking in the framework of dynamical\\u000asystems with symmetry on a smooth manifold. Two cases will be analyzed: general\\u000aand Hamiltonian dynamical systems. We give sufficient conditions for symmetry\\u000abreaking in both cases.
Symmetry Energy in Nuclear Surface
Pawel Danielewicz; Jenny Lee
2008-12-25
Interplay between the dependence of symmetry energy on density and the variation of nucleonic densities across nuclear surface is discussed. That interplay gives rise to the mass dependence of the symmetry coefficient in an energy formula. Charge symmetry of the nuclear interactions allows to introduce isoscalar and isovector densities that are approximately independent of the magnitude of neutron-proton asymmetry.
Helical Symmetry in Linear Systems
Jiri Bicak; Bernd G. Schmidt
2008-03-28
We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman--Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.
Breaking Generator Symmetry George Katsirelos
Walsh, Toby
Breaking Generator Symmetry George Katsirelos NICTA Sydney, Australia george problematic. One solution is to focus on just sym- metries that generate the symmetry group. Whilst there are special cases where breaking just the symmetries in a generating set is complete, there are also cases
Reflections on Symmetry and Proof
ERIC Educational Resources Information Center
Merrotsy, Peter
2008-01-01
The concept of symmetry is fundamental to mathematics. Arguments and proofs based on symmetry are often aesthetically pleasing because they are subtle and succinct and non-standard. This article uses notions of symmetry to approach the solutions to a broad range of mathematical problems. It responds to Krutetskii's criteria for mathematical…
Group analysis and renormgroup symmetries
Vladimir F. Kovalev; Veniamin V. Pustovalov; Dmitrii V. Shirkov
1998-01-01
An original regular approach to constructing special type symmetries for boundary value problems, namely renormgroup symmetries, is presented. Different methods of calculating these symmetries based on modern group analysis are described. An application of the approach to boundary value problems is demonstrated with the help of a simple mathematical model.
a Broken Symmetry Ontology: Quantum Mechanics as a Broken Symmetry.
NASA Astrophysics Data System (ADS)
Buschmann, Jonathan Edgar
We propose 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, we are led to consider non-heterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows us to find a generalized principle of symmetry and a generalized symmetry--conservation formalisms. In particular, we clarify the role of Noether's theorem in field theory. We show 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, we account for the interpretational problem and the essential incompleteness of quantum mechanics. We propose that the broken symmetry underlying this ontological domain is broken dilation invariance.
NSDL National Science Digital Library
2007-12-12
This website provides 30 suggested activities in Symmetry and Tessellations using resources available across the World Wide Web. The author, Jill Britton, has complied this collection of links to coordinate with the chapters and activities from her publication, Investigating Patterns: Symmetry and Tessellations (Grades 5-8). The activities begin with What is Mathematics? and move on to cover topics such as Pythagoras? observations of music, patterns on Ukrainian Easter eggs, and tessellating art. She provides a short comment on each of the websites and the links are arranged by activity topic. Links at the bottom of the website will take visitors to other collections of links relating to more pattern-related activities.
Strong Electroweak Symmetry Breaking
Grinstein, Benjamin
2011-01-01
Models of spontaneous breaking of electroweak symmetry by a strong interaction do not have fine tuning/hierarchy problem. They are conceptually elegant and use the only mechanism of spontaneous breaking of a gauge symmetry that is known to occur in nature. The simplest model, minimal technicolor with extended technicolor interactions, is appealing because one can calculate by scaling up from QCD. But it is ruled out on many counts: inappropriately low quark and lepton masses (or excessive FCNC), bad electroweak data fits, light scalar and vector states, etc. However, nature may not choose the minimal model and then we are stuck: except possibly through lattice simulations, we are unable to compute and test the models. In the LHC era it therefore makes sense to abandon specific models (of strong EW breaking) and concentrate on generic features that may indicate discovery. The Technicolor Straw Man is not a model but a parametrized search strategy inspired by a remarkable generic feature of walking technicolor,...
Dark discrete gauge symmetries
Batell, Brian [Perimeter Institute for Theoretical Physics, Waterloo, ON, N2J 2W9 (Canada)
2011-02-01
We investigate scenarios in which dark matter is stabilized by an Abelian Z{sub N} discrete gauge symmetry. Models are surveyed according to symmetries and matter content. Multicomponent dark matter arises when N is not prime and Z{sub N} contains one or more subgroups. The dark sector interacts with the visible sector through the renormalizable kinetic mixing and Higgs portal operators, and we highlight the basic phenomenology in these scenarios. In particular, multiple species of dark matter can lead to an unconventional nuclear recoil spectrum in direct detection experiments, while the presence of new light states in the dark sector can dramatically affect the decays of the Higgs at the Tevatron and LHC, thus providing a window into the gauge origin of the stability of dark matter.
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.
Invariants of broken discrete symmetries.
Kalozoumis, P A; Morfonios, C; Diakonos, F K; Schmelcher, P
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries. PMID:25126903
Invariants of Broken Discrete Symmetries
NASA Astrophysics Data System (ADS)
Kalozoumis, P. A.; Morfonios, C.; Diakonos, F. K.; Schmelcher, P.
2014-08-01
The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
Bertrand Zavidovique; Vito Di Gesù
2005-01-01
\\u000a In this paper we concentrate on a measure of symmetry. Given a transform S, the kernel SK of a pattern is defined as the maximal included symmetric sub-set of this pattern. A first algorithm is outlined to exhibit\\u000a this kernel. The maximum being taken over all directions, the problem arises to know which center to use. Then the optimal\\u000a direction
Davood Momeni; Ratbay Myrzakulov
2014-10-04
The symmetry issue for Galileons has been studied. In particular we address scaling (conformal) and Noether symmetrized Galileons. We have been proven a series of theorems about the form of Noether conserved charge (current) for irregular (not quadratic) dynamical systems. Special attentions have been made on Galileons. We have been proven that for Galileons always is possible to find a way to "symmetrized" Galileo's field .
Hidden Symmetry Subgroup Problems
Thomas Decker; Gábor Ivanyos; Miklos Santha; Pawel Wocjan
2012-01-18
We advocate a new approach of addressing hidden structure problems and finding efficient quantum algorithms. We introduce and investigate the Hidden Symmetry Subgroup Problem (HSSP), which is a generalization of the well-studied Hidden Subgroup Problem (HSP). Given a group acting on a set and an oracle whose level sets define a partition of the set, the task is to recover the subgroup of symmetries of this partition inside the group. The HSSP provides a unifying framework that, besides the HSP, encompasses a wide range of algebraic oracle problems, including quadratic hidden polynomial problems. While the HSSP can have provably exponential quantum query complexity, we obtain efficient quantum algorithms for various interesting cases. To achieve this, we present a general method for reducing the HSSP to the HSP, which works efficiently in several cases related to symmetries of polynomials. The HSSP therefore connects in a rather surprising way certain hidden polynomial problems with the HSP. Using this connection, we obtain the first efficient quantum algorithm for the hidden polynomial problem for multivariate quadratic polynomials over fields of constant characteristic. We also apply the new methods to polynomial function graph problems and present an efficient quantum procedure for constant degree multivariate polynomials over any field. This result improves in several ways the currently known algorithms.
Symmetries in Physics: Philosophical Reflections
Katherine Brading; Elena Castellani
2003-01-19
This is the introductive paper to the volume "Symmetries in Physics: Philosophical Reflections", Cambridge University Press, 2003. We begin with a brief description of the historical roots and emergence of the concept of symmetry that is at work in modern physics. Then, in section 2, we mention the different varieties of symmetry that fall under this general umbrella, outlining the ways in which they were introduced into physics. We also distinguish between two different uses of symmetry: symmetry principles versus symmetry arguments. In section 3 we make some remarks of a general nature concerning the status and significance of symmetries in physics. Finally, in section 4, we outline the structure of the book and the contents of each part.
Holographic Heavy Quark Symmetry
Koji Hashimoto; Noriaki Ogawa; Yasuhiro Yamaguchi
2014-12-27
We investigate the heavy quark spin symmetry, i.e. the mass degeneracy of pseudo-scalar and vector quarkonia at heavy quark limit, by using the gauge/gravity correspondence. We allow generic D3-like geometry with a flavor D7-brane, to avoid supersymmetric mass degeneracy. For geometries admitting physical QCD-like properties, we find that the mass degeneracy is generically achieved in a good accuracy, up to a few percent mass splitting. We also compute spectra of excited quarkonia states, and discuss comparisons with experiments and quark-model calculations.
Zhen Chao Dong; John D. Corbett
1995-01-01
We report examples of how tuning with cation sizes can allow the isolation of remarkable cluster units not known in the binary alloys, the centered icosahedral polyanions of TlââÂ¹Â°â» in NaâAâTlââ (A = K, Rb, Cs), and TlââÂ¹Â¹â» in NaâKâTlââ. The important effects of centering and cation size on the bonding and stability are discussed. We also correlate the structures
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.
Guo, Yiming; Stacey, Timothy E; Fredrickson, Daniel C
2014-05-19
The crystal structures of intermetallic phases offer a wealth of geometrical features (helices, multishelled clusters, and host-guest motifs) whose formation has yet to be explained or predicted by chemical theory. A recently developed extension of the acid-base concept to metallic systems, the ?3-acidity model, provides an avenue for developing this understanding for intermetallics formed from transition metals. In this Article, we illustrate how this approach can be used to understand one of the most striking geometrical entities to emerge in intermetallic chemistry, the Mackay cluster of icosahedral quasicrystals. We present ?3-acidity analyses, based on DFT-calibrated Hückel calculations, for a series of Sc-Ir intermetallics: ScIr (CsCl-type), Sc2Ir (Ti2Ni-type), Sc11Ir4, and the Mackay cluster containing phases Sc57Ir13 and Sc44Ir7. We begin by illustrating that a ?3-acidity model correctly predicts that each of these phases is stable relative to disproportionation into their neighboring compounds when a common set of Hückel parameters and d-orbital occupancies is used. Next, we explain these results by developing a relationship between the distance distribution of homoatomic contacts within an atom's coordination sphere and the ?3-neutralization it experiences. For a given average homoatomic distance, the role of heteroatomic contacts is higher when the distribution of homoatomic contacts is narrower. This effect is key to the strength of the acid-base neutralization of the Sc-rich phases, where the Sc atoms find a scarcity of Ir atoms from which to obtain neutralization. Under these circumstances, Sc-Ir contacts should be maximized, whereas the number and distance variations of the Sc-Sc contacts should be minimized. These expectations are borne out by the observed crystal structures. In particular, the Mackay clusters of Sc57Ir13 and Sc44Ir7, in which a central Ir atom is icosahedrally coordinated by a pentagonal dodecahedral array of face-sharing Sc octahedra, represent a natural way of merging the competing needs for enhancing Sc-Ir interactions while diminishing those between the Sc atoms. PMID:24801239
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.
Tsurumaru, Toyohiro [Mitsubishi Electric Corporation, Information Technology R and D Center, 5-1-1 Ofuna, Kamakura-shi, Kanagawa, 247-8501 Japan (Japan)
2010-01-15
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C{sub 4}, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of 'rank two' can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
NASA Technical Reports Server (NTRS)
Rosensteel, George
1995-01-01
Riemann ellipsoids model rotating galaxies when the galactic velocity field is a linear function of the Cartesian coordinates of the galactic masses. In nuclear physics, the kinetic energy in the linear velocity field approximation is known as the collective kinetic energy. But, the linear approximation neglects intrinsic degrees of freedom associated with nonlinear velocity fields. To remove this limitation, the theory of symplectic dynamical symmetry is developed for classical systems. A classical phase space for a self-gravitating symplectic system is a co-adjoint orbit of the noncompact group SP(3,R). The degenerate co-adjoint orbit is the 12 dimensional homogeneous space Sp(3,R)/U(3), where the maximal compact subgroup U(3) is the symmetry group of the harmonic oscillator. The Hamiltonian equations of motion on each orbit form a Lax system X = (X,F), where X and F are elements of the symplectic Lie algebra. The elements of the matrix X are the generators of the symplectic Lie algebra, viz., the one-body collective quadratic functions of the positions and momenta of the galactic masses. The matrix F is composed from the self-gravitating potential energy, the angular velocity, and the hydostatic pressure. Solutions to the hamiltonian dynamical system on Sp(3,R)/U(3) are given by symplectic isospectral deformations. The Casimirs of Sp(3,R), equal to the traces of powers of X, are conserved quantities.
NASA Astrophysics Data System (ADS)
Tsurumaru, Toyohiro
2010-01-01
This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of “rank two” can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.
Symmetry principles for string theory
Evans, M; Evans, Mark; Giannakis, Ioannis
1994-01-01
The gauge symmetries that underlie string theory arise from inner automorphisms of the algebra of observables of the associated conformal field theory. In this way it is possible to study broken and unbroken symmetries on the same footing, and exhibit an infinite-dimensional supersymmetry algebra that includes space-time diffeomorphisms and an infinite number of spontaneously broken level-mixing symmetries. We review progress in this area, culminating in the identification of a weighted tensor algebra as a subalgebra of the full symmetry. We also briefly describe outstanding problems. Talk presented at the Gursey memorial conference, Istanbul, Turkey, June, 1994.
Bowtie nanoantennas with symmetry breaking
NASA Astrophysics Data System (ADS)
Chen, Ji; Zhang, Zhaoyu
2015-01-01
Surface plasmon resonances of optical bowtie nanoantennas with symmetry breaking are studied numerically using the finite-element method. Beginning with both x-axial and y-axial symmetry, bowtie structures are reshaped by varying two parameters (edge lengths and bow angles) to create various symmetries to achieve controllable resonant modes and gap enhancement in the visible and infrared wavelength range. The four edges' coupling is the main factor contributing to the final fundamental resonances. Double fundamental resonances can be achieved in bowtie structures with x-axial or y-axial symmetry. These properties can guide both the engineering and the fabrication of plasmonic nanoantennas.
Lo, Pok Man; Swanson, Eric S. [Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 (United States)
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.
The Degrees of Symmetry functions
Hector Rabal; Nelly Cap
2014-12-18
We propose a generalization of the concept of symmetry as a continuous function of the reference center or line location. We suggest that this concept can be applied to many closed systems and exploring its time evolution. When the function changes along time it is an indication that external factors are acting on the system.The change in the symmetry function along time can be thought as a current in the symmetry degree and its time behavior a measure of the effect of the external agent. Keywords: Symmetry, conservation laws, degree of parity.
Effect of temperature and substitution on Cope rearrangement: a symmetry perspective.
Tuvi-Arad, Inbal; Rozgonyi, Tamás; Stirling, András
2013-12-01
Many reactions feature symmetry variation along the reaction path on the potential energy surface. The interconversion of the point group symmetry of the stationary points can be characteristic of these processes. Increasing the temperature, however, leads to the loss of symmetry in its traditional yes-no language. We find that in such cases the instantaneous distance of the molecular structure from its symmetric counterpart is a suitable collective variable that can describe the reaction process. We show that this quantity, the continuous symmetry measure (CSM), has a positive linear relationship with temperature, implying that even highly symmetric molecules should be considered as asymmetric above 0 K. Using ab initio molecular dynamics, we simulate the temperature-induced Cope rearrangements of several fluxional molecules and employ different CSMs to follow the reaction progress. We use this methodology to demonstrate the validity of important concepts governing these reactions: Woodward-Hoffmann rules and TS aromaticity. Statistical analysis of the CSM distributions reveals that ligands connected to the carbon frame have profound effect on the reaction course. In particular, our results show that lower temperatures tend to enhance the differences between the TS-stabilizing effect of the substituents. PMID:24246010
Conformal symmetry and unification
Pawlowski, Marek [Soltan Institute for Nuclear Studies, Warsaw (Poland)
1998-12-15
The Weyl-Weinberg-Salam model is presented. It is based on the local conformal gauge symmetry. The model identifies the Higgs scalar field in SM with the Penrose-Chernikov-Tagirov scalar field of the conformal theory of gravity. Higgs mechanism for generation of particle masses is replaced by the originated in Weyl's ideas conformal gauge scale fixing. Scalar field is no longer a dynamical field of the model and does not lead to quantum particle-like excitations that could be observed in HE experiments. Cosmological constant is naturally generated by the scalar quadric term. Weyl vector bosons can be present in the theory and can mix with photon--Z-boson system.
Giampiero Esposito; Giuseppe Marmo
2005-11-21
The concepts of symmetry and symmetry groups are at the heart of several developments in modern theoretical and mathematical physics. The present paper is devoted to a number of selected topics within this framework: Euclidean and rotation groups; the properties of fullerenes in physical chemistry; Galilei, Lorentz and Poincare groups; conformal transformations and the Laplace equation; quantum groups and Sklyanin algebras. For example, graphite can be vaporized by laser irradiation, producing a remarkably stable cluster consisting of 60 carbon atoms. The corresponding theoretical model considers a truncated icosahedron, i.e. a polygon with 60 vertices and 32 faces, 12 of which are pentagonal and 20 hexagonal. The Carbon 60 molecule obtained when a carbon atom is placed at each vertex of this structure has all valences satisfied by two single bonds and one double bond. In other words, a structure in which a pentagon is completely surrounded by hexagons is stable. Thus, a cage in which all 12 pentagons are completely surrounded by hexagons has optimum stability. On a more formal side, the exactly solvable models of quantum and statistical physics can be studied with the help of the quantum inverse problem method. The problem of enumerating the discrete quantum systems which can be solved by the quantum inverse problem method reduces to the problem of enumerating the operator-valued functions that satisfy an equation involving a fixed solution of the quantum Yang--Baxter equation. Two basic equations exist which provide a systematic procedure for obtaining completely integrable lattice approximations to various continuous completely integrable systems. This analysis leads in turn to the discovery of Sklyanin algebras.
NSDL National Science Digital Library
2011-01-01
This website provides text, images, animations, and interactive Java applets to teach bilateral and rotational symmetry. Learners are given drawing and painting challenges as well as recreational activities such as making a virtual kaleidoscope. Clicking on the first button 'Best Symmetry Animation' takes students through the entire sequence.
Nonclassical symmetry and Riemann invariants
Souichi Murata
2005-01-26
In this paper it is shown that Riemann invariants are invariant under nonclassical symmetries of a hyperbolic system. As a specific example, we study the one-dimensional shallow water equations on the flat and present another type invariance under nonclassical symmetries.
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.)
Nonlocal symmetries of evolution equations
Renat Zhdanov
2009-01-01
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution equations in one spatial variable invariant under Lie algebras of the dimension up to three. As a result, we construct the broad families of new nonlinear evolution equations
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.
Geometrical spin symmetry and spin
Pestov, I. B., E-mail: pestov@theor.jinr.ru [Joint Institute for Nuclear Research (Russian Federation)
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.
Symmetry planes of Paleozoic crinoids
Lane, N. G.; Webster, G. D.
1967-11-30
, illustrated by Galateacrinus (after Moore, 1962). 2. Homocrinid (E-EC) symmetry plane (after Ubaghs, 1953). 3. Heterocrinid (D-AB) symmetry plane (after Ubaghs, 1953). 4 -5. Infrabasal, basal, and radial circlets of Permian flex- ible crinoids, Tram pidocrinus... at top and bottom of figures mark A-CD plane, dotted lines E-BC, or in Fig. 3, the D-AB plane; figures 1-5 are dorsal (aboral) views of adults, radials black.] 16 The University of Kansas Paleontological Contributions—Paper 25 explanation of the symmetry...
Alcoba, Diego R; Oña, Ofelia B; Torres, Juan J; Lain, Luis; Torre, Alicia
2013-01-01
High accuracy energies of low-lying excited states, in molecular systems, have been determined by means of a procedure which combines the G-particle-hole Hypervirial (GHV) equation method [Alcoba et al. Int. J. Quantum Chem. 109:3178 (2009)] and the Hermitian Operator (HO) one [Bouten et al. Nucl. Phys. A 202:127 (1973)]. This paper reports a suitable strategy to introduce the point group symmetry within the framework of the combined GHV-HO method, what leads to an improvement of the computational efficiency. The resulting symmetry-adapted formulation has been applied to illustrate the computer timings and the hardware requirements in selected chemical systems of several geometries.
Higgs family symmetry and supersymmetry
Patt, Brian Lawrence
2006-01-01
In this thesis we investigate building models of family symmetry that give the Higgs fields family structure. We construct several models, starting with 2 generation models then moving onto 3 generation models. These models ...
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.
Nonholonomic mechanical systems with symmetry
Anthony M. Bloch; P. S. Krishnaprasad; Jerrold E. Marsden; Richard M. Murray
1996-01-01
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
Duality symmetry and Kerker conditions.
Zambrana-Puyalto, X; Fernandez-Corbaton, I; Juan, M L; Vidal, X; Molina-Terriza, G
2013-06-01
We unveil the relationship between two anomalous scattering processes known as Kerker conditions and the duality symmetry of Maxwell equations. We generalize these conditions and show that they can be applied to any particle with cylindrical symmetry, not only to spherical particles as the original Kerker conditions were derived for. We also explain the role of the optical helicity in these scattering processes. Our results find applications in the field of metamaterials, where new materials with directional scattering are being explored. PMID:23722768
Nonlocal symmetries of evolution equations
Renat Zhdanov
2010-01-01
We suggest the method for group classification of evolution equations admitting nonlocal symmetries which are associated with\\u000a a given evolution equation possessing nontrivial Lie symmetry. We apply this method to second-order evolution equations in\\u000a one spatial variable invariant under Lie algebras of the dimension up to three. As a result, we construct the broad families\\u000a of new nonlinear evolution equations
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
Bonus symmetry in conformal field theory
Kenneth Intriligator
1990-01-01
Conformal field theories typically have an enlarged symmetry over that of the chiral algebra. These enlarged symmetries simplify the analysis of a theory by linking representations that would appear independent based on considerations of the smaller symmetry of the chiral algebra. It will be shown that this bonus symmetry occurs whenever a primary field g has a fusion rule with
Symmetry energy from nuclear multifragmentation
NASA Astrophysics Data System (ADS)
Mallik, Swagata; Chaudhuri, Gargi
2013-01-01
The ratio of symmetry energy coefficient to temperature Csym/T is extracted from different prescriptions using the isotopic as well as the isobaric yield distributions obtained in different projectile fragmentation reactions. It is found that the values extracted from our theoretical calculation agree with those extracted from the experimental data but they differ very much from the input value of the symmetry energy used. The best possible way to deduce the value of the symmetry energy coefficient is to use the fragment yield at the breakup stage of the reaction and it is better to use the grand canonical model for the fragmentation analysis. This is because the formulas that are used for the deduction of the symmetry energy coefficient are all derived in the framework of the grand canonical ensemble, which is valid only at the breakup (equilibrium) condition. The yield of “cold” fragments, either from the theoretical models or from experiments, when used for extraction of the symmetry energy coefficient using these prescriptions, might lead to the wrong conclusion.
Collective states and symmetry rearrangement
Chu, H.Y. [Univ. of Illinois, Urbana, IL (United States). Dept. of Physics; Khanna, F.C. [Univ. of Alberta, Edmonton, Alberta (Canada). Dept. of Physics]|[TRIUMF, Vancouver, British Columbia (Canada)
1996-06-30
Collective states provide an important feature of the low-lying excitations in nuclei. Very often these states are inter-mingled with single particle excitations and surface vibrations of the finite nuclei. Here the authors wish to explore the collective states from the general viewpoint of symmetry rearrangement which has been studied extensively by Prof. Umezawa and his collaborators who showed, in a brilliant way, how the Goldstone bosons emerge and how they play the role in restoring the original symmetry operations. The authors have shown here an important relationship between the isovector collective states and symmetry rearrangement in nuclei. The interplay of strong and electromagnetic interactions leads to a finite energy gap for the isomagnons. The role of isomagnons in the low energy excitations has important consequences for {beta}-decay and it is anticipated in the excitation and decay of the matter in a heavy-ion collision. They have calculated the full response function of the Isobaric Analog State (IAS) at zero temperature and the finite temperature response function is analyzed at small T and long wavelength. The present approach of symmetry rearrangement and collective states has established a unified approach to the isovector collective states in nuclei and to collective states in all many-particle systems. This was the conjecture of Hiroomi Umezawa when a study was initially started of symmetry rearrangement in nuclear systems in analogy to his previous studies in condensed matter systems. The authors believe that they have established, at least partially, the vision of Hiroomi Umezawa.
Symmetry energy from nuclear multifragmentation
Swagata Mallik; Gargi Chaudhuri
2013-01-23
The ratio of symmetry energy coefficient to temperature $C_{sym}/T$ is extracted from different prescriptions using the isotopic as well as the isobaric yield distributions obtained in different projectile fragmentation reactions. It is found that the values extracted from our theoretical calculation agree with those extracted from the experimental data but they differ very much from the input value of the symmetry energy used. The best possible way to deduce the value of the symmetry energy coefficient is to use the fragment yield at the breakup stage of the reaction and it is better to use the grand canonical model for the fragmentation analysis. This is because the formulas that are used for the deduction of the symmetry energy coefficient are all derived in the framework of the grand canonical ensemble which is valid only at the break-up (equilibrium) condition. The yield of "cold" fragments either from the theoretical models or from experiments when used for extraction of the symmetry energy coefficient using these prescriptions might lead to the wrong conclusion.
Fearful symmetry in aposematic plants.
Lev-Yadun, Simcha
2011-11-01
Symmetry has been proposed to increase the efficiency of visual aposematic displays in animals, and I suggest that it may also be true for many aposematic spiny or poisonous plants. For instance, in the very spiny plant taxa cacti, Aloe sp., Agave sp. and Euphorbia sp., which have been proposed to be aposematic because of their colorful spine system, the shoots, and in cacti, the spiny fruits as well, are usually radially symmetric. Moreover, in the radial symmetric shoots of Agave and Aloe their individual spiny leaves are also bilaterally symmetric. Spiny or poisonous fruits of various other taxa, the symmetric spiny leaf rosettes and flowering spiny heads of many Near Eastern species of the Asteraceae and other taxa, and poisonous colorful flowers in taxa that were proposed to be aposematic are also symmetric. Thus, in plants, like in animals, symmetry seems to be commonly associated with visual aposematism and probably contributes to its effectiveness. Symmetry may stem from developmental constraints, or like in flowers, have other signaling functions. However, because of the better perception of symmetry by animals it may exploit inherited modes of animal sensing that probably result in paying more attention to symmetric shapes. All these possible alternatives do not negate the probable deterring role of symmetry in plant aposematism. PMID:22067106
Optical metamaterials with quasicrystalline symmetry: Symmetry-induced optical isotropy
NASA Astrophysics Data System (ADS)
Kruk, Sergey S.; Helgert, Christian; Decker, Manuel; Staude, Isabelle; Menzel, Christoph; Etrich, Christoph; Rockstuhl, Carsten; Jagadish, Chennupati; Pertsch, Thomas; Neshev, Dragomir N.; Kivshar, Yuri S.
2013-11-01
We apply the concept of quasicrystals to metamaterials and experimentally demonstrate metasurfaces with isotropic properties and high resonance strength. By comparing quasicrystalline, periodic, and amorphous metasurfaces we quantify the impact of symmetry on their properties. This is achieved by studying the eigenpolarizations’ ellipticity and circular dichroism induced by mutual coupling of the meta-atoms. The advantage of the quasicrystalline in comparison to a periodic arrangement originates from the ability to reach a higher rotational symmetry in k space, therefore opening a route towards isotropic metasurfaces.
Chiral Symmetry Breaking in Graphene
Gordon W. Semenoff
2011-08-19
The question of whether the Coulomb interaction is strong enough to break the sublattice symmetry of un-doped graphene is discussed. We formulate a strong coupling expansion where the ground state of the Coulomb Hamiltonian is found exactly and the kinetic hopping Hamiltonian is treated as a perturbation. We argue that many of the properties of the resulting system would be shared by graphene with a Hubbard model interaction. In particular, the best candidate sublattice symmetry breaking ground state is an antiferromagnetic Mott insulator. We discuss the results of some numerical simulations which indicate that the Coulomb interaction is indeed subcritical. We also point out the curious fact that, if the electron did not have spin degeneracy, the tendency to break chiral symmetry would be much greater and even relatively weak Coulomb interactions would likely gap the spectrum.
New symmetries of massless QED
NASA Astrophysics Data System (ADS)
He, Temple; Mitra, Prahar; Porfyriadis, Achilleas P.; Strominger, Andrew
2014-10-01
An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function on the conformal sphere at future null infinity ([InlineMediaObject not available: see fulltext.]) but are independent of the retarded time. The value of ? at past null infinity ([InlineMediaObject not available: see fulltext.]) is determined from that on [InlineMediaObject not available: see fulltext.] by the condition that it take the same value at either end of any light ray crossing Minkowski space. The ? ? constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.
Annular symmetry nonlinear frequency converters
NASA Astrophysics Data System (ADS)
Kasimov, Dror; Arie, Ady; Winebrand, Emil; Rosenman, Gil; Bruner, Ariel; Shaier, Pnina; Eger, David
2006-10-01
We present a new type of two-dimensional nonlinear structure for quasi-phase matching. This structure has continuous rotational symmetry, and in contrary to the commonly used periodic structures, is not lattice shaped and has no translation symmetry. It is shown that this annular symmetry structure possesses interesting phase matching attributes that are significantly different than those of periodic structures. In particular, it enables simultaneous phase-matched frequency doubling of the same pump into several different directions. Moreover, it has extremely wide phase-mismatch tolerance, since a change in the phase matching conditions does not change the second harmonic power, but only changes its propagation direction. Several structures were fabricated using either the indirect e-beam method in LiNbO3 or the electric field poling method in stoichiometric LiTaO3, and their conversion efficiencies, as well as angular and thermal dependencies, were characterized by second harmonic generation.
Flavored Peccei-Quinn symmetry
NASA Astrophysics Data System (ADS)
Ahn, Y. H.
2015-03-01
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a ? - ? power law in the lepton sector, such that relatively large 13 mixing angle with bilarge ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong charge parity (C P ) problem, in a way that no domain wall problem occurs, based on A4×U (1 )X symmetry in a supersymmetric framework. Here we refer to the global U (1 )X symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry." In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under U (1 )X, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected to each other. So the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around the 1 012 GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay, and the axion. We examine the model predictions, arisen from the ? - ? power law, on leptonic C P violation, neutrinoless double beta decay, and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass ma?2.53 ×1 0-5 eV and the axion coupling to photon ga ? ??1.33 ×1 0-15 GeV-1 . And subsequently the square of the ratio between them is shown to be one or two orders of magnitude lower than that of the conventional axion model.
Kastner, Ruth E. [Department of Philosophy, University of Maryland, College Park, MD 20742 (United States)
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.
Chiral symmetry in quarkyonic matter
Kojo, T., E-mail: torujj@quark.phy.bnl.gov [Brookhaven National Laboratory, RIKEN BNL Research Center (United States)
2012-05-15
The 1/N{sub c} expansion classifies nuclear matter, deconfined quark matter, and Quarkyonic matter in low temperature region. We investigate the realization of chiral symmetry in Quarkyonic matter by taking into account condensations of chiral particle-hole pairs. It is argued that chiral symmetry and parity are locally violated by the formation of chiral spirals, <{psi}-bar exp (2i{mu}{sub q} z{gamma}{sup 0} {gamma}{sup z}){psi}> . An extension to multiple chiral spirals is also briefly discussed.
Monster symmetry and extremal CFTs
NASA Astrophysics Data System (ADS)
Gaiotto, Davide
2012-11-01
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in AdS 3. We prove that no c = 48 extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
Monster symmetry and Extremal CFTs
Davide Gaiotto
2008-01-07
We test some recent conjectures about extremal selfdual CFTs, which are the candidate holographic duals of pure gravity in $AdS_3$. We prove that no $c=48$ extremal selfdual CFT or SCFT may possess Monster symmetry. Furthermore, we disprove a recent argument against the existence of extremal selfdual CFTs of large central charge.
The Geometry of Reflectance Symmetries.
Tan, Ping; Quan, Long; Zickler, Todd
2011-02-17
Different materials reflect light in different ways, and this reflectance interacts with shape, lighting, and viewpoint to determine an object's image. Common materials exhibit diverse reflectance effects, and this is a significant source of difficulty for image analysis. One strategy for dealing with this diversity is to build computational tools that exploit reflectance symmetries, such as reciprocity and isotropy, that are exhibited by broad classes of materials. By building tools that exploit these symmetries, one can create vision systems that are more likely to succeed in real-world, non-Lambertian environments. In this paper, we develop a framework for representing and exploiting reflectance symmetries. We analyze the conditions for distinct surface points to have local view and lighting conditions that are equivalent under these symmetries, and we represent these conditions in terms of the geometric structure they induce on the Gaussian sphere and its abstraction, the projective plane. We also study the behavior of these structures under perturbations of surface shape and explore applications to both calibrated and un-calibrated photometric stereo. PMID:21339528
Basic logic: reflection, symmetry, visibility.
Sambin, Giovanni
Basic logic: reflection, symmetry, visibility. Giovanni Sambin - Giulia Battilotti - Claudia Faggian Abstract We introduce a sequent calculus B for a new logic, named basic logic. The aim of basic logic is to find a structure in the space of logics. Classical, intuitionistic, quantum and non
SYMMETRY AND HETEROGENEITY IN HIGH
of a superconducting condensate to resist to the attacks of high temperature. Solution to this problem of fundamental physics is needed for the design of room temperature superconductors, for controlling the decoherenceSYMMETRY AND HETEROGENEITY IN HIGH TEMPERATURE SUPERCONDUCTORS #12;#12;Kluwer Academic Publishers
From symmetries to number theory
Tempesta, P., E-mail: p.tempesta@fis.ucm.e [Universidad Complutense, Departamento de Fisica Teorica II, Facultad de Fisicas (Spain)
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
Baryon and chiral symmetry breaking
Gorsky, A. [Institute for Theoretical and Experimental Physics (ITEP), Moscow, Russia and Moscow Institute of Physics and Technology (MIPT), Dolgoprudny (Russian Federation); Krikun, A. [NORDITA, KTH Royal Institute of Technology and Stockholm University Stockholm, Sweden and Institute for Theoretical and Experimental Physics (ITEP), Moscow (Russian Federation)
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.
Fundamental Symmetries and Conservation Laws
NASA Astrophysics Data System (ADS)
Haxton, W. C.
2009-08-01
I discuss recent progress in low-energy tests of symmetries and conservation laws, including parity nonconservation in atoms and nuclei, electric dipole moment tests of time-reversal invariance, ?-decay correlation studies, and decays violating separate (family) and total lepton number.
Tetraquark Spectroscopy: A Symmetry Analysis
J. Vijande; A. Valcarce
2009-12-18
We present a detailed analysis of the symmetry properties of a four-quark wave function and its solution by means of a variational approach for simple Hamiltonians. We discuss several examples in the light and heavy-light meson sector.
Symmetry for Periodic Railway Timetables
Christian Liebchen
2004-01-01
Periodic timetabling for railway networks is usually modeled by the Periodic Event Scheduling Problem (PESP). This model permits to express many requirements that practitioners impose on periodic railway timetables. We discuss a requirement practitioners are asking for, but which, so far, has not been the topic of mathematical studies: the concept of symmetry. Several motivations why symmetric timetables might seem
Honours Project Symmetry Classifications of
Aslaksen, Helmer
's periodic tilings in Table 1 (see appendix). Firstly, it aims to provide the readers an overview in Table 1 (appendix). Therefore, finally, given an Escher's periodic tiling the reader would be ableHonours Project Symmetry Classifications of Periodic Tilings Â Escher's drawings Name: Kavitha d
Testing Lorentz symmetry with atoms and Light
Neil Russell
2011-09-04
This article reports on the Fifth Meeting on CPT and Lorentz Symmetry, CPT'10, held at the end of June 2010 in Bloomington, Indiana, USA. The focus is on recent tests of Lorentz symmetry using atomic and optical physics.
Embedded Representations and Quasi-Dynamical Symmetry
D. J. Rowe
2011-06-08
This presentation explains why models with a dynamical symmetry often work extraordinarily well even in the presence of large symmetry breaking interactions. A model may be a caricature of a more realistic system with a "quasi-dynamical" symmetry. The existence of quasi-dynamical symmetry in physical systems and its significance for understanding collective dynamics in complex nuclei is explained in terms of the precise mathematical concept of an "embedded representation". Examples are given which exhibit quasi-dynamical symmetry to a remarkably high degree. Understanding this unusual symmetry and why it occurs, is important for recognizing why dynamical symmetries appear to be much moreprevalent than they would otherwise have any right to be and for interpreting the implications of a model's successes. We indicate when quasi-dynamical symmetry is expected to apply and present a challenge as to how best to make use of this potentially powerful algebraic structure.
Stillness in Motion The Essence of Symmetry
Lee, Carl
October 2014 11 / 39 #12;Chemistry (Carvone) Carl Lee Symmetry October 2014 12 / 39 #12;Chemistry (Carvone) Motion: Reflection across a plane Carl Lee Symmetry October 2014 13 / 39 #12;Chemistry (Carvone
Symmetry descriptors and 3D shape matching
Michael M. Kazhdan; Thomas A. Funkhouser; Szymon Rusinkiewicz
2004-01-01
In this paper, we present the Symmetry Descriptors of a 3D model. This is a collection of spherical functions that describes the measure of a model's rotational and reflective symmetry with respect to every axis passing through the center of mass. We show that Symmetry Descriptors can be computed efficiently using fast signal processing techniques, and demonstrate the empirical value
Symmetry Properties of Second Order Hyperpolarizabilities
J. W. Wu
1994-01-01
Time-reversal symmetry property of a second order nonlinear optical hyperpolarizability is examined in terms of the Manley-Rowe power relation to find relationship to the overall permutation symmetry. An extended symmetry relation is discovered reducing the independent number of the hyperpolarizability tensor components describing the second order nonlinear optical processes. Experimental implications are discussed.
Man Sik Park Symmetry and Separability In
Man Sik Park Symmetry and Separability In Spatial-Temporal Processes Man Sik Park, Montserrat Fuentes Symmetry and Separability In Spatial-Temporal Processes 1 #12;Man Sik Park Motivation Â· In general-pollution data. Symmetry and Separability In Spatial-Temporal Processes 2 #12;Man Sik Park Research Objectives 1
Detecting Symmetry and Symmetric Constellations of Features
Gareth Loyand; Jan-olof Eklundh
2006-01-01
A novel and efficient method is presented for grouping feature points on the basis of their underlying symmetry and characterising the symmetries present in an image. We show how symmetric pairs of features can be efficiently detected, how the symmetry bonding each pair is extracted and evaluated, and how these can be grouped into symmetric constellations that specify the domi-
Flavored Peccei-Quinn symmetry
Y. H. Ahn
2015-02-10
In an attempt to uncover any underlying physics in the standard model (SM), we suggest a $\\mu$--$\\tau$ power law in the lepton sector, such that relatively large 13 mixing angle with bi-large ones can be derived. On the basis of this, we propose a neat and economical model for both the fermion mass hierarchy problem of the SM and a solution to the strong CP problem, in a way that no domain wall problem occurs, based on $A_{4}\\times U(1)_{X}$ symmetry in a supersymmetric framework. Here we refer to the global $U(1)_X$ symmetry that can explain the above problems as "flavored Peccei-Quinn symmetry". In the model, a direct coupling of the SM gauge singlet flavon fields responsible for spontaneous symmetry breaking to ordinary quarks and leptons, both of which are charged under $U(1)_X$, comes to pass through Yukawa interactions, and all vacuum expectation values breaking the symmetries are connected each other. So, the scale of Peccei-Quinn symmetry breaking is shown to be roughly located around $10^{12}$ GeV section through its connection to the fermion masses. The model predictions are shown to lie on the testable regions in the very near future through on-going experiments for neutrino oscillation, neutrinoless double beta decay and axion. We examine the model predictions, arisen from the $\\mu$--$\\tau$ power law, on leptonic $CP$ violation, neutrinoless double beta decay and atmospheric mixing angle, and show that the fermion mass and mixing hierarchies are in good agreement with the present data. Interestingly, we show the model predictions on the axion mass $m_a\\simeq2.53\\times10^{-5}$ eV and the axion coupling to photon $g_{a\\gamma\\gamma}\\simeq1.33\\times10^{-15}~{\\rm GeV}^{-1}$. And subsequently the square of the ratio between them is shown to be 1 or 2 orders of magnitude lower than that of the conventional axion model.
CP symmetry in optical systems
Dana, Brenda; Malomed, Boris A
2015-01-01
We introduce a model of a dual-core optical waveguide with opposite signs of the group-velocity-dispersion (GVD) 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 ($\\mathcal{CP}$) symmetry, while the addition of the intra-core cubic nonlinearity breaks the symmetry. By means of direct simulations and analytical approximations, it is demonstrated that the linear system generates expanding Gaussian states, while the nonlinear one gives rise to broad oscillating solitons, as well as a general family of stable stationary gap solitons.
Symmetry restoration and quantumness reestablishment
NASA Astrophysics Data System (ADS)
Zeng, Guo-Mo; Wu, Lian-Ao; Xing, Hai-Jun
2014-09-01
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.
Adding CP to flavour symmetries
Varzielas, I de Medeiros
2015-01-01
I propose the use of CP-odd invariants, which are independent of basis and valid for any choice of CP transformation, as a powerful approach to study CP in the presence of flavour symmetries. As examples of the approach I focus on Lagrangians invariant under $\\Delta(27)$. I comment on the consequences of adding a specific CP symmetry to a Lagrangian and distinguish cases where several $\\Delta(27)$ singlets are present depending on how they couple to the triplets. One of the examples included is a very simple toy model with explicit CP violation with calculable phases, which is referred to as explicit geometrical CP violation by comparison with previously known cases of (spontaneous) geometrical CP violation.
Symmetry restoration and quantumness reestablishment
Guo-Mo Zeng; Lian-Ao Wu; Hai-Jun Xing
2014-09-18
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies.
Quantum diffeomorphisms and conformal symmetry
NASA Astrophysics Data System (ADS)
Antoniadis, Ignatios; Mazur, Pawel O.; Mottola, Emil
1997-04-01
We analyze the constraints of general coordinate invariance for quantum theories possessing conformal symmetry in four dimensions. The character of these constraints simplifies enormously on the Einstein universe R×S3. The SO(4,2) global conformal symmetry algebra of this space determines uniquely a finite shift in the Hamiltonian constraint from its classical value. In other words, the global Wheeler-De Witt equation is modified at the quantum level in a well-defined way in this case. We argue that the higher moments of T00 should not be imposed on the physical states a priori either, but only the weaker condition
Symmetry restoration and quantumness reestablishment.
Zeng, Guo-Mo; Wu, Lian-Ao; Xing, Hai-Jun
2014-01-01
A realistic quantum many-body system, characterized by a generic microscopic Hamiltonian, is accessible only through approximation methods. The mean field theories, as the simplest practices of approximation methods, commonly serve as a powerful tool, but unfortunately often violate the symmetry of the Hamiltonian. The conventional BCS theory, as an excellent mean field approach, violates the particle number conservation and completely erases quantumness characterized by concurrence and quantum discord between different modes. We restore the symmetry by using the projected BCS theory and the exact numerical solution and find that the lost quantumness is synchronously reestablished. We show that while entanglement remains unchanged with the particle numbers, quantum discord behaves as an extensive quantity with respect to the system size. Surprisingly, discord is hardly dependent on the interaction strengths. The new feature of discord offers promising applications in modern quantum technologies. PMID:25231796
Interfacial Fermi Loops from Interfacial Symmetries
NASA Astrophysics Data System (ADS)
Takahashi, Ryuji; Murakami, Shuichi
2014-12-01
We propose a concept of interfacial symmetries such as interfacial particle-hole symmetry and interfacial time-reversal symmetry, which appear in interfaces between two regions related to each other by particle-hole or time-reversal transformations. These symmetries result in novel dispersion of interface states. In particular, for the interfacial particle-hole symmetry, the gap closes along a loop ("Fermi loop") at the interface. We numerically demonstrate this for the Fu-Kane-Mele tight-binding model. We show that the Fermi loop originates from a sign change of a Pfaffian of a product between the Hamiltonian and a constant matrix.
The New Charge Symmetry Breaking
NASA Astrophysics Data System (ADS)
Stephenson, E. J.
2007-06-01
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 ?0 production (the fore-aft asymmetry in n+p?d+?0 and the total cross section for d+d?4He+?0) provide applicable data.
Charge Symmetry Breaking and QCD
NASA Astrophysics Data System (ADS)
Miller, Gerald A.; Opper, Allena K.; Stephenson, Edward J.
2006-11-01
Charge symmetry breaking (CSB) in the strong interaction occurs because of the difference between the masses of the up and down quarks. The use of effective field theories allows us to follow this influence of confined quarks in hadronic and nuclear systems. We review the progress in observing and understanding CSB, with particular attention to the recent successful observations of CSB in measurements involving the production of a single neutral pion, and to the related theoretical progress.
Mirror symmetry for abelian varieties
Vasily Golyshev; Valery Lunts; Dmitri Orlov
2001-01-01
We work out the notion of mirror symmetry for abelian varieties and study its properties. Our construction are based on the correspondence between two $Q$--algebraic groups. One is the Hodge (or special Mumford--Tate) group. The second group $\\\\bar{Spin(A)}$ is defined as follows: the group of autoequivalences of the bounded derived category of coherent sheaves acts on the total cohomology $H(A,Q)$
Symmetry analysis of talus bone
Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.
2014-01-01
Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45. PMID:24802391
Relativity symmetries and Lie algebra contractions
NASA Astrophysics Data System (ADS)
Cho, Dai-Ning; Kong, Otto C. W.
2014-12-01
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m , n) symmetry as an isometry on an m + n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m , n) preserving a symmetry of the same type at dimension m + n - 1, e.g. a G(m , n - 1) , together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2 , 4) , which is the particular case for our interest on the physics side as the proposed relativity symmetry for 'quantum spacetime'. The contractions from G(1 , 3) may be relevant to real physics.
Enhanced Facial Symmetry Assessment in Orthodontists.
Jackson, Tate H; Clark, Kait; Mitroff, Stephen R
2013-01-01
Assessing facial symmetry is an evolutionarily important process, which suggests that individual differences in this ability should exist. As existing data are inconclusive, the current study explored whether a group trained in facial symmetry assessment, orthodontists, possessed enhanced abilities. Symmetry assessment was measured using face and non-face stimuli among orthodontic residents and two control groups: university participants with no symmetry training and airport security luggage screeners, a group previously shown to possess expert visual search skills unrelated to facial symmetry. Orthodontic residents were more accurate at assessing symmetry in both upright and inverted faces compared to both control groups, but not for non-face stimuli. These differences are not likely due to motivational biases or a speed-accuracy tradeoff-orthodontic residents were slower than the university participants but not the security screeners. Understanding such individual differences in facial symmetry assessment may inform the perception of facial attractiveness. PMID:24319342
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
Generalized CP and ?(96) family symmetry
NASA Astrophysics Data System (ADS)
Ding, Gui-Jun; King, Stephen F.
2014-05-01
We perform a comprehensive study of the ?(96) family symmetry combined with the generalized CP symmetry HCP. We investigate the lepton mixing parameters which can be obtained from the original symmetry ?(96)?HCP breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely G? and Gl subgroups in the neutrino and the charged lepton sector, respectively, and the remnant CP symmetries from the breaking of HCP are HCP? and HCPl, respectively, where all cases correspond to a preserved symmetry smaller than the full Klein symmetry, as in the semidirect approach, leading to predictions which depend on a single undetermined real parameter, which may be fitted to the reactor angle for example. We discuss 26 possible cases, including a global ?2 determination of the best fit parameters and the correlations between mixing parameters, in each case.
Symmetry and general symmetry groups of the coupled Kadomtsev-Petviashvili equation
NASA Astrophysics Data System (ADS)
Wang, Jia; Li, Biao
2009-06-01
In this paper, the Lie symmetry algebra of the coupled Kadomtsev-Petviashvili (cKP) equation is obtained by the classical Lie group method and this algebra is shown to have a Kac-Moody-Virasoro loop algebra structure. Then the general symmetry groups of the cKP equation is also obtained by the symmetry group direct method which is proposed by Lou et al. From the general symmetry groups, the Lie symmetry group can be recovered and a group of discrete transformations can be derived simultaneously. Lastly, from a known simple solution of the cKP equation, we can easily obtain two new solutions by the general symmetry groups.
History of electroweak symmetry breaking
T. W. B. Kibble
2015-02-22
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Effective Operators and Extended Symmetry
J. -M. Frère; M. Tytgat; J. M. Moreno; J. Orloff
1993-07-30
In this note we expand on our previous study of the implications of LEP1 results for future colliders. We extend the effective operator-based analysis of De R\\'ujula et al. to a larger symmetry group, and show at which cost their expectations can be relaxed. Of particular interest to experiment is a rephrasing of our previous results in terms of the Renard et al. parametrization for the gauge boson self-couplings (slightly extended to include $\\delta g_{\\gamma}$). We suggest the use of a ($\\delta g_{\\gamma}$, $\\delta g_{Z}$) plot to confront the expectations of various models.
History of electroweak symmetry breaking
Kibble, T W B
2015-01-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
M. Dine; Z. Sun
2005-06-28
In the landscape, states with $R$ symmetries at the classical level form a distinct branch, with a potentially interesting phenomenology. Some preliminary analyses suggested that the population of these states would be significantly suppressed. We survey orientifolds of IIB theories compactified on Calabi-Yau spaces based on vanishing polynomials in weighted projective spaces, and find that the suppression is quite substantial. On the other hand, we find that a $Z_2$ R-parity is a common feature in the landscape. We discuss whether the cosmological constant and proton decay or cosmology might select the low energy branch. We include also some remarks on split supersymmetry.
Gauge theories of spacetime symmetries
Friedemann Brandt
2001-09-13
Gauge theories of conformal spacetime symmetries are presented which merge features of Yang-Mills theory and general relativity in a new way. The models are local but nonpolynomial in the gauge fields, with a nonpolynomial structure that can be elegantly written in terms of a metric (or vielbein) composed of the gauge fields. General relativity itself emerges from the construction as a gauge theory of spacetime translations. The role of the models within a general classification of consistent interactions of gauge fields is discussed as well.
Spacetime symmetries and varying scalars
Ralf Lehnert
2005-08-29
This talk discusses the relation between spacetime-dependent scalars, such as couplings or fields, and the violation of Lorentz symmetry. A specific cosmological supergravity model demonstrates how scalar fields can acquire time-dependent expectation values. Within this cosmological background, excitations of these scalars are governed by a Lorentz-breaking dispersion relation. The model also contains couplings of the scalars to the electrodynamics sector leading to the time dependence of both the fine-structure parameter alpha and the theta angle. Through these couplings, the variation of the scalars is also associated with Lorentz- and CPT-violating effects in electromagnetism.
Symmetry and Dirac points in graphene spectrum
Gregory Berkolaiko; Andrew Comech
2014-12-28
Existence and stability of Dirac points in the dispersion relation of operators periodic with respect to the hexagonal lattice is investigated for different sets of additional symmetries. The following symmetries are considered: rotation by $2\\pi/3$ and inversion, rotation by $2\\pi/3$ and horizontal reflection, inversion or reflection with weakly broken rotation symmetry, and the case where no Dirac points arise: rotation by $2\\pi/3$ and vertical reflection. All proofs are based on symmetry considerations and are elementary in nature. In particular, existence of degeneracies in the spectrum is proved by a transplantation argument (which is deduced from the (co)representation of the relevant symmetry group). The conical shape of the dispersion relation is obtained from its invariance under rotation by $2\\pi/3$. Persistence of conical points when the rotation symmetry is weakly broken is proved using a geometric phase in one case and parity of the eigenfunctions in the other.
Onsager symmetry for inhomogeneous magnetized plasmas
Nambu, M. [Department of Applied Physics, Faculty of Engineering, Kyushu University, Ropponmatsu, Fukuoka 810 (Japan)] [Department of Applied Physics, Faculty of Engineering, Kyushu University, Ropponmatsu, Fukuoka 810 (Japan)
1996-12-01
The symmetry properties of the linear dielectric function for an inhomogeneous magnetized plasma are studied based on the local mode approximation as well as on the modified local mode approximation. In the local mode approximation applied to the electrostatic or electromagnetic waves, the dielectric tensor lacks both the Hermitian symmetry and the symmetry of the Onsager relations. The lack of the symmetry properties arises because Fourier decomposition into plane waves is not a correct method for an inhomogeneous medium. The modified local mode approximation completely recovers the symmetry properties for the electromagnetic waves. However, it still lacks the symmetry properties for the electrostatic waves, due to the diamagnetic current. Some of the controversies previously given for an inhomogeneous plasma are also discussed. {copyright} {ital 1996 American Institute of Physics.}
Galileo Symmetries in Polymer Particle Representation
Dah-Wei Chiou
2007-04-10
To illustrate the conceptual problems for the low-energy symmetries in the continuum of spacetime emerging from the discrete quantum geometry, Galileo symmetries are investigated in the polymer particle representation of a non-relativistic particle as a simple toy model. The complete Galileo transformations (translation, rotation and Galileo boost) are naturally defined in the polymer particle Hilbert space and Galileo symmetries are recovered with highly suppressed deviations in the low-energy regime from the underlying polymer particle description.
Additional Symmetries of Supersymmetric KP Hierarchies
Sonia Stanciu
1994-03-31
We investigate the additional symmetries of several supersymmetric KP hierarchies: the SKP hierarchy of Manin and Radul, the $\\hbox{SKP}_2$ hierarchy, and the Jacobian SKP hierarchy. In all three cases we find that the algebra of symmetries is isomorphic to the algebra of superdifferential operators, or equivalently $\\SW_{1+\\infty}$. These results seem to suggest that despite their realization depending on the dynamics, the additional symmetries are kinematical in nature.
Contact Symmetries and Hamiltonian Thermodynamics
A. Bravetti; C. S. Lopez-Monsalvo; F. Nettel
2015-02-22
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 analyze 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.
Introduction to Electroweak Symmetry Breaking
Dawson,S.
2008-10-02
The Standard Model (SM) is the backbone of elementary particle physics-not only does it provide a consistent framework for studying the interactions of quark and leptons, but it also gives predictions which have been extensively tested experimentally. In these notes, I review the electroweak sector of the Standard Model, discuss the calculation of electroweak radiative corrections to observables, and summarize the status of SM Higgs boson searches. Despite the impressive experimental successes, however, the electroweak theory is not completely satisfactory and the mechanism of electroweak symmetry breaking is untested. I will discuss the logic behind the oft-repeated statement: 'There must be new physics at the TeV scale'. These lectures reflect my strongly held belief that upcoming results from the LHC will fundamentally change our understanding of electroweak symmetry breaking. In these lectures, I review the status of the electroweak sector of the Standard Model, with an emphasis on the importance of radiative corrections and searches for the Standard Model Higgs boson. A discussion of the special role of the TeV energy scale in electroweak physics is included.
Spinor Structure and Internal Symmetries
V. V. Varlamov
2015-03-26
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 Poincar\\'{e} 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.
NASA Astrophysics Data System (ADS)
Heeck, Julian
2014-12-01
The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B- L)-violating processes leads us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g?, the Stückelberg mass MZ?, and the kinetic mixing angle ?. The new force could manifest itself at any scale, and we collect and derive bounds on g? over the entire testable range MZ? = 0-1013 eV, also of interest for the more popular case of spontaneously broken B-L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV
Julian Heeck
2014-11-10
The difference between baryon number B and lepton number L is the only anomaly-free global symmetry of the Standard Model, easily promoted to a local symmetry by introducing three right-handed neutrinos, which automatically make neutrinos massive. The non-observation of any (B-L)-violating processes leads us to scrutinize the case of unbroken gauged B-L; besides Dirac neutrinos, the model contains only three parameters, the gauge coupling strength g', the Stueckelberg mass $M_{Z'}$, and the kinetic mixing angle $\\chi$. The new force could manifest itself at any scale, and we collect and derive bounds on g' over the entire testable range $M_{Z'}$ = 0 - $10^{13}$ eV, also of interest for the more popular case of spontaneously broken B-L or other new light forces. We show in particular that successful Big Bang nucleosynthesis provides strong bounds for masses 10 eV < $M_{Z'}$ < 10 GeV due to resonant enhancement of the rate $\\bar{f} f \\leftrightarrow \\bar{\
Local unitary symmetries and entanglement invariants
NASA Astrophysics Data System (ADS)
Johansson, Markus
2014-11-01
We investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the connection between this stratification and the ring of entanglement invariants and the corresponding geometric description in terms of algebraic varieties. On a stratum of a non-trivial symmetry group the invariants of the symmetry preserving operations gives a sufficient description of entanglement. Finding these invariants is often a simpler problem than finding the invariants of the local unitary group. The conditions, as given by the Luna–Richardson theorem, for when the ring of such invariants is isomorphic to the ring of local unitary invariants on the stratum are discussed. As an example we consider symmetry groups that can be diagonalized by local unitary operations and for which the group action on each qubit is non-trivial. On the stratum of such a symmetry the entanglement can be described in terms of a canonical form and the invariants of the symmetry preserving operations. This canonical form and the invariants are directly determined by the symmetry group. Further, we briefly discuss how some recently proposed entanglement classification schemes capture symmetry properties.
Symmetry energy in nuclear density functional theory
W. Nazarewicz; P. -G. Reinhard; W. Satula; D. Vretenar
2013-07-22
The nuclear symmetry energy represents a response to the neutron-proton asymmetry. In this survey we discuss various aspects of symmetry energy in the framework of nuclear density functional theory, considering both non-relativistic and relativistic self-consistent mean-field realizations side-by-side. Key observables pertaining to bulk nucleonic matter and finite nuclei are reviewed. Constraints on the symmetry energy and correlations between observables and symmetry-energy parameters, using statistical covariance analysis, are investigated. Perspectives for future work are outlined in the context of ongoing experimental efforts.
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
Graphic Design: Using Symmetry to Create Corporate Logos
NSDL National Science Digital Library
PBS TeacherSource - Math
1995-01-01
This activity teaches students to describe three types of symmetry, to categorize symmetric figures based on type of symmetry, and to create figures using different type of symmetry. The activities use familiar logos and signs to show how symmetry is used in the world of design, and to help differentiate between the different kinds of symmetry used in these examples.
Symmetry and Relativity : From Classical Mechanics to Modern Particle Physics
Paris-Sud XI, UniversitÃ© de
Symmetry and Relativity : From Classical Mechanics to Modern Particle Physics Z.J. Ajaltouni symmetries in Classical Physics (section 2). Â· Relativistic Symmetries in Quantum Mechanics (section 3 of Relativity and Symmetry. 2 Relativity and Symmetries in Classical Physics 2.1 Classical Mechanics One
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
Electroweak Symmetry Breaking via QCD
NASA Astrophysics Data System (ADS)
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-01
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.
Symmetries in collective neutrino oscillations
Huaiyu Duan; George M. Fuller; Yong-Zhong Qian
2009-07-31
We discuss the relationship between a symmetry in the neutrino flavour evolution equations and neutrino flavour oscillations in the collective precession mode. This collective precession mode can give rise to spectral swaps (splits) when conditions can be approximated as homogeneous and isotropic. Multi-angle numerical simulations of supernova neutrino flavour transformation show that when this approximation breaks down, non-collective neutrino oscillation modes decohere kinematically, but the collective precession mode still is expected to stand out. We provide a criterion for significant flavour transformation to occur if neutrinos participate in a collective precession mode. This criterion can be used to understand the suppression of collective neutrino oscillations in anisotropic environments in the presence of a high matter density. This criterion is also useful in understanding the breakdown of the collective precession mode when neutrino densities are small.
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
Jisuke Kubo; Kher Sham Lim; Manfred Lindner
2014-09-01
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 $\\lesssim m_S\\lesssim $ 3 TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at LHC. If the colored boson is electrically charged, the branching fraction of the Higgs decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of non-perturbative EW scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem.
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 Schuc
Rosenthal, Peter B
2015-04-19
Elucidation of the structure of biological macromolecules and larger assemblies has been essential to understanding the roles they play in living processes. Methods for three-dimensional structure determination of biological assemblies from images recorded in the electron microscope were therefore a key development. In his paper published in Philosophical Transactions B in 1971, Crowther described new computational procedures applied to the first three-dimensional reconstruction of an icosahedral virus from images of virus particles preserved in negative stain. The method for determining the relative orientation of randomly oriented particles and combining their images for reconstruction exploited the high symmetry of the virus particle. Computational methods for image analysis have since been extended to include biological assemblies without symmetry. Further experimental advances, combined with image analysis, have led to the method of cryomicroscopy, which is now used by structural biologists to study the structure and dynamics of biological machines and assemblies in atomic detail. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750240
Rosenthal, Peter B.
2015-01-01
Elucidation of the structure of biological macromolecules and larger assemblies has been essential to understanding the roles they play in living processes. Methods for three-dimensional structure determination of biological assemblies from images recorded in the electron microscope were therefore a key development. In his paper published in Philosophical Transactions B in 1971, Crowther described new computational procedures applied to the first three-dimensional reconstruction of an icosahedral virus from images of virus particles preserved in negative stain. The method for determining the relative orientation of randomly oriented particles and combining their images for reconstruction exploited the high symmetry of the virus particle. Computational methods for image analysis have since been extended to include biological assemblies without symmetry. Further experimental advances, combined with image analysis, have led to the method of cryomicroscopy, which is now used by structural biologists to study the structure and dynamics of biological machines and assemblies in atomic detail. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society. PMID:25750240
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.
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.
Covariant quantum mechanics and quantum symmetries
JanyÂ?ka, Josef
Covariant quantum mechanics and quantum symmetries Josef JanyÅ¸ska 1 , Marco Modugno 2 , Dirk Saller: quantum mechanics, classical mechanics, general relativity, infinitesimal symmetries. 2000 MSC: 81P99, 81Q Introduction 2 2 Covariant quantum mechanics 5 2.1 Classical background
SYMMETRY-BASED COMPLETION Thiago Pereira1
, IMPA 2 Computer Science, Cornell 3 Matmidia, PUCÂRio Keywords: Image completion, Inpainting, Symmetry be consis- tent with the image as a whole. This implies two steps in the inpainting pipeline: analysis of the image for inpainting (see Figure 7). More precisely, we estimate the image's symmetries and complete
Testing for ellipsoidal symmetry: A comparison study
Lyudmila Sakhanenko
2008-01-01
The focus of this paper is the methodology for testing ellipsoidal symmetry, which was recently proposed by Koltchinskii and Sakhanenko [Koltchinskii, V., Sakhanenko, L. 2000. Testing for ellipsoidal symmetry of a multivariate distribution. In: Giné, E., Mason, D., Wellner, J. (Eds.), High Dimensional Probability II. In: Progress in Probability, Birkhäuser, Boston, pp. 493–510]. It is a class of omnibus bootstrap
Affordance and Symmetry in User Interfaces
Paul A. Cairns; Harold W. Thimbleby
2008-01-01
A ordance, consistency, flow, user model, and mode are examples of terms in HCI that, while attractive, do not have clear operational definitions. Using the mathematical concept of symmetry, this paper shows it is possible to suggest a clear operational definition for significant aspects of a ordance, forming a precise concept of symmetry-a ordance. In doing so, it becomes clear
On contact symmetries of evolution equations
Qing Huang; Renat Zhdanov; Changzheng Qu
2013-01-10
In this paper, we develop an algebraic approach to classifying contact symmetries of the second-order nonlinear evolution equations. Up to contact isomorphisms, all inequivalent PDEs admitting semi-simple algebras, solvable algebras of dimension $n\\leq4$, and algebras having nontrivial Levi factors, belonging to the class under consideration, and corresponding contact symmetries they admitted are listed.
Symmetry in critical random Boolean network dynamics
NASA Astrophysics Data System (ADS)
Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.
On systems having Poincaré and Galileo symmetry
NASA Astrophysics Data System (ADS)
Holland, Peter
2014-12-01
Using the wave equation in d ? 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincaré and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d = 1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d > 1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwell's equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Marius de Leeuw; Takuya Matsumoto; Sanefumi Moriyama; Vidas Regelskis; Alessandro Torrielli
2012-04-11
We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.
Secret symmetries in AdS\\/CFT
Marius de Leeuw; Takuya Matsumoto; Sanefumi Moriyama; Vidas Regelskis; Alessandro Torrielli
2012-01-01
We discuss special quantum group (secret) symmetries of the integrable system associated with the AdS\\/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.
de Leeuw, Marius; Moriyama, Sanefumi; Regelskis, Vidas; Torrielli, Alessandro
2012-01-01
We discuss special quantum group (secret) symmetries of the integrable system associated to the AdS/CFT correspondence. These symmetries have by now been observed in a variety of forms, including the spectral problem, the boundary scattering problem, n-point amplitudes, the pure-spinor formulation and quantum affine deformations.
Bilateral symmetry breaking in nonlinear circular cylinders
Lu, Ya Yan
nonlinear Fabry-Perot interferometer: an analytical study," Opt. Lett. 15, 14121414 (1990). 5. C. Par.P. Torres, J. Boyce, and R.Y. Chiao, "Bilateral symmetry breaking in a nonlinear Fabry-Perot cavity. Baets, "Symmetry breaking with coupled Fano resonances," Opt. Express 16, 30693076 (2008). 12. K
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)
Broken chiral symmetry on a null plane
Beane, Silas R., E-mail: silas@physics.unh.edu
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.
The role of symmetry in nuclear physics
NASA Astrophysics Data System (ADS)
Iachello, Francesco
2015-02-01
The role of discrete symmetries in nuclear physics is briefly reviewed within the context of the algebraic cluster model (ACM). The symmetries D3 (triangle) for 3? and Td (tetrahedron) for 4? are discussed and evidence shown for their occurrence in 12C (D3) and 16O (Td).
Symmetry is less than meets the eye.
Apthorp, Deborah; Bell, Jason
2015-03-30
Symmetry is a ubiquitous feature in the visual environment and can be detected by a variety of species, ranging from insects through to humans [1,2]. Here we show it can also bias estimates of basic scene properties. Mirror (reflective) symmetry can be detected in as little as 50 ms, in both natural and artificial visual scenes, and even when embedded within cluttered backgrounds [1]. In terms of its biological relevance, symmetry is a key determinant in mate selection; the degree of symmetry in a face is positively associated with perceived healthiness and attractiveness ratings [3]. In short, symmetry processing mechanisms are an important part of the neural machinery of vision. We reveal that the importance of symmetry extends beyond the processing of shape and objects. Mirror symmetry biases our perception of scene content, with symmetrical patterns appearing to have fewer components than their asymmetric counterparts. This demonstrates an interaction between two fundamental dimensions of visual analysis: symmetry [1] and number [4]. We propose that this numerical underestimation results from a processing bias away from the redundant information within mirror symmetrical displays, extending existing theories regarding redundancy in visual analysis [5,6]. PMID:25829006
Broken Symmetries and Bare Coupling Constants
Murray Gell-Mann; Fredrik Zachariasen
1961-01-01
There are known cases of symmetry laws valid for one kind of interaction but broken by another. Each symmetry is then supposed to be exact for bare masses and coupling constants but only approximate for the renormalized quantities, like neutron and proton masses. We ask how the equality of unrenormalized constants can be rephrased as a statement about measurable quantities.
Symmetry in critical random Boolean network dynamics.
Hossein, Shabnam; Reichl, Matthew D; Bassler, Kevin E
2014-04-01
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems. PMID:24827294
Teaching symmetry in the introductory physics curriculum
Hill, C. T. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Lederman, L. M. [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
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.
Spontaneous Reflection Symmetry Breaking in LCs?
Walba, David
The SmC has this as well (not mentioned). Brand, H. R.; Cladis, P. E.; Pleiner, H. "Symmetry and defects). Brand, H. R.; Cladis, P. E.; Pleiner, H. "Symmetry and defects in the CM phase of polymeric liquid? O O O O H N N O #12;Is the H-Bonded Dimer Antiferro? Not! The switching is actually dielectric #12
On systems having Poincaré and Galileo symmetry
Peter Holland
2014-11-13
Using the wave equation in d > or = 1 space dimensions it is illustrated how dynamical equations may be simultaneously Poincar\\'e and Galileo covariant with respect to different sets of independent variables. This provides a method to obtain dynamics-dependent representations of the kinematical symmetries. When the field is a displacement function both symmetries have a physical interpretation. For d = 1 the Lorentz structure is utilized to reveal hitherto unnoticed features of the non-relativistic Chaplygin gas, including a relativistic structure with a limiting case that exhibits the Carroll group, and field-dependent symmetries and associated Noether charges. The Lorentz transformations of the potentials naturally associated with the Chaplygin system are given. These results prompt the search for further symmetries and it is shown that the Chaplygin equations support a nonlinear superposition principle. A known spacetime mixing symmetry is shown to decompose into label-time and superposition symmetries. It is shown that a quantum mechanical system in a stationary state behaves as a Chaplygin gas. The extension to d > 1 is used to illustrate how the physical significance of the dual symmetries is contingent on the context by showing that Maxwells equations exhibit an exact Galileo covariant formulation where Lorentz and gauge transformations are represented by field-dependent symmetries. A natural conceptual and formal framework is provided by the Lagrangian and Eulerian pictures of continuum mechanics.
Symmetries of the Burgers Turbulence without Pressure
Timo Aukusti Laine
2013-02-03
We investigate local symmetries of the Burgers turbulence driven by an external random force. By using a path integral formalism, we show that the Jacobian has physics in it; local symmetries and an anomaly. We also study a local invariance of the effective action and show it is related to Kolmogorov's second law of self-similarity.
CP Symmetry in Particle Introduction Results
?umer, Slobodan
/19Physics in Ljubljana, FMF, July 2011 j j y y #12;Introduction Why CP (A)Symmetry? Introduction Results B) In the Universe today particles completely dominate over B. Golob 2/19Physics in Ljubljana, FMF, July 2011 Why all, FMF, July 2011 + - K-CP #12;Introduction Why CP (A)Symmetry? Introduction Results B
Symmetry-adapted excited states for the T{sub 1u}(direct-product)h{sub g} Jahn-Teller system
Qiu, Q. C.; Dunn, J. L.; Bates, C. A.
2001-08-15
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 T{sub 1u}(direct-product)h{sub g} JT system for the case of D{sub 5d} 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{sub 60}{sup -} molecule.
Symmetries, weak symmetries, and related solutions of the Grad-Shafranov equation
Cicogna, G. [Dipartimento di Fisica, 'E.Fermi' dell'Universita di Pisa, INFN, Sez. di Pisa, Largo B.Pontecorvo 3, I-56127 Pisa (Italy); Pegoraro, F.; Ceccherini, F. [Dipartimento di Fisica, 'E.Fermi' dell'Universita di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa (Italy)
2010-10-15
We discuss a new family of solutions of the Grad-Shafranov (GS) equation that describes D-shaped toroidal plasma equilibria with sharp gradients at the plasma edge. These solutions have been derived by exploiting the continuous Lie symmetry properties of the GS equation and in particular a special type of 'weak' symmetries. In addition, we review the continuous Lie symmetry properties of the GS equation and present a short but exhaustive survey of the possible choices for the arbitrary flux functions that yield GS equations admitting some continuous Lie symmetry. Particular solutions related to these symmetries are also discussed.
Symmetry-protected adiabatic quantum transistors
Dominic J. Williamson; Stephen D. Bartlett
2014-08-14
Adiabatic quantum transistors allow quantum logic gates to be performed by applying a large field to a quantum many-body system prepared in its ground state, without the need for local control. The basic operation of such a device can be viewed as driving a spin chain from a symmetry protected phase to a trivial phase, and this perspective offers an avenue to generalise the adiabatic quantum transistor and to design several improvements. The performance of quantum logic gates is shown to depend only on universal symmetry properties of a symmetry-protected phase rather than fine tuned parent Hamiltonians, and it is possible to implement a universal set of logic gates in this way by combining several different types of symmetry protected matter. Such symmetry-protected adiabatic quantum transistors are argued to be robust to a range of relevant noise processes.
Noether theorem for mu-symmetries
G. Cicogna; G. Gaeta
2007-08-23
We give a version of Noether theorem adapted to the framework of mu-symmetries; this extends to such case recent work by Muriel, Romero and Olver in the framework of lambda-symmetries, and connects mu-symmetries of a Lagrangian to a suitably modified conservation law. In some cases this "mu-conservation law'' actually reduces to a standard one; we also note a relation between mu-symmetries and conditional invariants. We also consider the case where the variational principle is itself formulated as requiring vanishing variation under mu-prolonged variation fields, leading to modified Euler-Lagrange equations. In this setting mu-symmetries of the Lagrangian correspond to standard conservation laws as in the standard Noether theorem. We finally propose some applications and examples.
Heterotic effective action and duality symmetries revisited
NASA Astrophysics Data System (ADS)
Hohm, Olaf; Sen, Ashoke; Zwiebach, Barton
2015-02-01
The dimensional reduction of heterotic supergravity with gauge fields truncated to the Cartan subalgebra exhibits a continuous O( d, d + 16; ?) global symmetry, related to the O( d, d + 16; ?) T-duality of heterotic strings on a d-torus. The O( d, d + 16; ?) symmetry is not present, however, if the supergravity reduction is done including the full set of E 8 × E 8 or SO(32) gauge fields. We analyze which duality symmetries are realized to all orders in ? ' in the proper effective field theories for the massless string states. We find a universal O( d, d; ?) symmetry, also predicted by double field theory. We confirm this by giving a novel formulation of the dimensionally reduced supergravity in terms of O( d, d) multiplets, and we discuss cases of symmetry enhancement.
Symmetry breaking patterns in 3HDM
NASA Astrophysics Data System (ADS)
Ivanov, I. P.; Nishi, C. C.
2015-01-01
An attractive feature of New Physics models with multiple Higgs fields is that they are equipped with discrete symmetry groups in the Higgs and flavour sectors. These symmetry groups are often broken at the global minimum of the Higgs potential, either completely or to a proper subgroup, with certain phenomenological consequences. Here, we systematically explore these symmetry breaking patterns in the scalar sector of the three-Higgs-doublet model (3HDM). We use the full list of discrete symmetry groups allowed in 3HDM, and for each group we find all possible ways it can break by the Higgs vacuum expectation value alignment. We also discuss the interplay between these symmetry groups and various forms of CP -violation in the scalar sector of 3HDM. Not only do our results solve the problem for 3HDM, but they also hint at several general features in multi-scalar sectors.
Heavy Diquark Symmetry Constraints for Strong Decays
B. Eakins; W. Roberts
2012-10-31
The Heavy Diquark Symmetry (HDS) of Doubly Heavy Baryons (DHBs) provides new insights into the spectroscopy of these hadrons. We derive the consequences of this symmetry for the mass spectra and the decay widths of DHBs. We compare these symmetry constraints to results from a nonrelativistic quark model for the mass spectra and results from the $^3P_0$ model for strong decays. The quark model we implement was not constructed with these symmetries and contains interactions which explicitly break HDS. Nevertheless, these symmetries emerge. We argue that the $^3P_0$ model and any other model for strong transitions which employs a spectator assumption explicitly respects HDS. We also explore the possibility of treating the strange quark as a heavy quark and apply these ideas to $\\Xi$, $\\Xi_c$, and $\\Xi_b$ baryons.
Enhanced Gauge Symmetry in M-Theory
K. Davis
1996-08-16
In this article we examine some points in the moduli space of M-Theory at which there arise enhanced gauge symmetries. In particular, we examine the ``trivial" points of enhanced gauge symmetry in the moduli space of M-Theory on $S^{ 1 } \\times S^{ 1 } / { \\bf Z }_{ 2 }$ as well as the points of enhanced gauge symmetry in the moduli space of M-Theory on $ K3 $ and those in the moduli space of M-Theory on $T^{5}/{\\bf Z}_{2} \\times S^{1}$. Also, we employ the above enhanced gauge symmetries to derive the existence of some points of enhanced gauge symmetry in the moduli space of the Type IIA string theory.
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. PMID:16803369
Discrete symmetries and models of flavor mixing
NASA Astrophysics Data System (ADS)
Smirnov, Alexei Yu
2011-12-01
Evidences of a discrete symmetry behind the pattern of lepton mixing are analyzed. The program of "symmetry building" is outlined. Generic features and problems of realization of this program in consistent gauge models are formulated. The key issues include the flavor symmetry breaking, connection of mixing and masses, ad hoc prescription of flavor charges, "missing" representations, existence of new particles, possible accidental character of the TBM mixing. Various ways are considered to extend the leptonic symmetries to the quark sector and to reconcile them with Grand Unification. In this connection the quark-lepton complementarity could be a viable alternative to TBM. Observational consequences of the symmetries and future experimental tests of their existence are discussed.
Stallings, W C; Abdel-Meguid, S S; Lim, L W; Shieh, H S; Dayringer, H E; Leimgruber, N K; Stegeman, R A; Anderson, K S; Sikorski, J A; Padgette, S R; Kishore, G M
1991-01-01
5-enol-Pyruvylshikimate-3-phosphate synthase (EPSP synthase; phosphoenolpyruvate:3-phosphoshikimate 1-carboxyvinyltransferase, EC 2.5.1.19) is an enzyme on the pathway toward the synthesis of aromatic amino acids in plants, fungi, and bacteria and is the target of the broad-spectrum herbicide glyphosate. The three-dimensional structure of the enzyme from Escherichia coli has been determined by crystallographic techniques. The polypeptide backbone chain was traced by examination of an electron density map calculated at 3-A resolution. The two-domain structure has a distinctive fold and appears to be formed by 6-fold replication of a protein folding unit comprising two parallel helices and a four-stranded sheet. Each domain is formed from three of these units, which are related by an approximate threefold symmetry axis; in each domain three of the helices are completely buried by a surface formed from the three beta-sheets and solvent-accessible faces of the other three helices. The domains are related by an approximate dyad, but in the present crystals the molecule does not display pseudo-symmetry related to the symmetry of point group 32 because its approximate threefold axes are almost normal. A possible relation between the three-dimensional structure of the protein and the linear sequence of its gene will be described. The topological threefold symmetry and orientation of each of the two observed globular domains may direct the binding of substrates and inhibitors by a helix macrodipole effect and implies that the active site is located near the interdomain crossover segments. The structure also suggests a rationale for the glyphosate tolerance conferred by sequence alterations. Images PMID:11607190
PREFACE: Symmetries in Science XIV
NASA Astrophysics Data System (ADS)
Schuch, Dieter; Ramek, Michael
2010-04-01
Symmetries Logo This volume of the proceedings "Symmetries in Science XIV" is dedicated to the memory of our colleagues and dear friends Marcos Moshinsky and Yuri? Smirnov who regularly participated in these Symposia and were a great inspiration to many. We shall miss them. Dieter Schuch and Michael Ramek The international symposium "Symmetries in Science XIV" held at Collegium Mehrerau in Bregenz, Austria from July 19-24, 2009, attended by 32 scientists from 11 countries, was an experiment, performed by theoreticians. Aim of this experiment was to find out if the desire to revive or even continue this conference series was stronger than the very restricted pecuniary boundary conditions. It obviously was! After its establishment by Bruno Gruber in 1979, the biennial series settled in the very stimulating atmosphere of the monastery Mehrerau, which provided the ideal environment for a limited number of invited participants to exchange ideas, without parallel sessions, and pursue deeper discussions (at the latest in the evening at "Gasthof Lamm"). When the conference series terminated in 2003, former participants were quite disappointed. Meeting again at several (larger) conferences in subsequent years, there were repeated expressions of "the lack of a Bregenz-type meeting in our field nowadays" and the question of a possible "revitalization", even without external funding. After some hesitation, but also driven by our own desire to reinstate the series, we consulted Bruno who not only approved wholeheartedly but also offered his full support. It all finally led to the symposium in July 2009. The atmosphere was really like in the "good old days" and the interesting and thought-provoking presentations culminated in the publication of these Proceedings. We are grateful to Carl Bender for establishing contact with IOP making it possible for us to publish these Proceedings in the Journal of Physics Conference Series. A majority of the participants contributed to these Proceedings though some were unable to do so as their results were either previously submitted or published elsewhere. In order to make these contributions also available to readers of the Proceedings, we now list the respective references as follow: Albertsson C, Hlavatý L and Šnobl L 2008 On the Poisson-Lie T-plurality of boundary conditions J. Math. Phys. 49 032301-23, arXiv:0706.0820; Bender C M, Brody D C and Hook D W 2008 Quantum effects in classical systems having complex energy J. Phys. A: Math. Theor. 41 352003 (15 pp); Kanellopoulos V, Kleber M and Kramer T 2009 Use of Lambert's theorem for the n-dimensional Coulomb problem Phys. Rev. A 80 012101; Kramer P 2010 Platonic topology and CMB fluctuations: homotopy anisotropy and multipole selection rules Class. Quantum Grav. 27 095013 (27 pp), arXiv:0909.2758v1; Quesne C 2009 Solvable rational potentials and exceptional orthogonal polynomials in supersymmetric quantum mechanics SIGMA 5 084 (24 pp). On the other hand, some colleagues planning on attending the meeting had to forfeit their participation due to unforeseeable circumstances. As they had prepared their contributions particularly for our symposium, we have also allowed their input. The articles of Kibler, Leach, Reinisch and Wolf have therefore been included though the authors were absent. Marcos Moshinsky and Yuri? Smirnov, two long-standing colleagues and friends who attended the symposium on multiple occasions passed away in the year before the conference. A memorial service was held at the chapel of the Mehrerau during the meeting. The commemorative words from Father Vinzenz were based on information from our own experience, from an article by Alejandro Frank in Letras Libres Junio 2009, p.54 (a monthly literary magazine published by Editorial Vuelta, in Spanish) and articles from "TESTIMONIOS, Marcos Moshinsky: 80 años de vida y 60 años de trabajo científico" 2001 Frank A and Wolf K B eds. Two contributions dedicated especially in their memory are also included in thes
Geometry of Majorana neutrino and new symmetries
G. G. Volkov
2006-07-30
Experimental observation of Majorana fermion matter gives a new impetus to the understanding of the Lorentz symmetry and its extension, the geometrical properties of the ambient space-time structure, matter--antimatter symmetry and some new ways to understand the baryo-genesis problem in cosmology. Based on the primordial Majorana fermion matter assumption, we discuss a possibility to solve the baryo-genesis problem through the the Majorana-Diraco genesis in which we have a chance to understand creation of Q(em) charge and its conservation in our D=1+3 Universe after the Big Bang. In the Majorana-Diraco genesis approach there appears a possibility to check the proton and electron non-stability on the very low energy scale. In particle physics and in our space-time geometry, the Majorana nature of the neutrino can be related to new types of symmetries which are lying beyond the binary Cartan-Killing-Lie algebras/superalgebras. This can just support a conjecture about the non-completeness of the SM in terms of binary Cartan--Killing--Lie symmetries/supersymmetries. As one of the very important applications of such new ternary symmetries could be related with explanation of the nature of the three families and three colour symmetry. The Majorana neutrino can directly indicate the existence of a new extra-dimensional geometry and thanks to new ternary space-time symmetries, could lead at high energies to the unextraordinary phenomenological consequences.
Graphene, Lattice QFT and Symmetries
L. B Drissi; E. H Saidi; M. Bousmina
2011-03-07
Borrowing ideas from tight binding model, we propose a board class of Lattice QFT models that are classified by the ADE Lie algebras. In the case of su(N) series, we show that the couplings between the quantum states living at the first nearest neighbor sites of the lattice $\\mathcal{L}_{su(N)}$ are governed by the complex fundamental representations \\underline{${{\\mathbf{N}}}$} and $\\bar{{\\mathbf{N}}}$ of $su(N)$; and the second nearest neighbor interactions are described by its adjoint $\\underline{\\mathbf{N}} \\otimes \\bar{\\mathbf{N}}$. The lattice models associated with the leading su(2), su(3) and su(4) cases are explicitly studied and their fermionic field realizations are given. It is also shown that the su(2) and su(3) models describe respectively the electronic properties of the acetylene chain and the graphene. It is established as well that the energy dispersion of the first nearest neighbor couplings is completely determined by the $A_{N}$ roots $ \\mathbf{\\alpha}$ through the typical dependence $N/2+\\sum_{roots}\\cos(\\mathbf{k}.\\alpha) $ with $\\mathbf{k}$ the wave vector. Other features such as DE extension and other applications are also discussed. Keywords: Tight Binding Model, Graphene, Lattice QFT, ADE Symmetries.
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.
Symmetry and twinning in boltwoodite
Strunz, H.; Tennyson, C.
1981-11-01
The authors give the results of an x-ray diffraction and chemical analysis of boltwoodite from Namibia. Chemical analysis revealed that as well as potassium there was a considerable amount of sodium; thus one may speak of sodium boltwoodite with the molecular ratio K/sub 2/O:Na/sub 2/O = 2 : 1. The potassium and sodium are partly replaced by H/sub 3/O. The idealized formula is (K,Na)/sub 2-x/(H/sub 2/O)/sub x/ x (UO/sub 2/SiO/sub 4/) x H/sub 2/O; the symmetry is monoclinic, the space group being C/sup 2//sub 2h/ = P2/sub 1//m, with a = 6.65 A, b = 7.07 A, c = 7.11 A, ..beta.. = 105/sup 0/30', Z = 2. The acicular crystals are elongated along (010) with a very pronounced cleavage in 001. The cleavage plane is (101). The mineral bears a very marked resemblance to kasolite.
Natural quasicrystal with decagonal symmetry
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S.; Andronicos, Christopher L.; Distler, Vadim V.; Eddy, Michael P.; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J.; Steinhardt, William M.; Yudovskaya, Marina; Steinhardt, Paul J.
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120?K to 1200?K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ? 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
Natural quasicrystal with decagonal symmetry.
Bindi, Luca; Yao, Nan; Lin, Chaney; Hollister, Lincoln S; Andronicos, Christopher L; Distler, Vadim V; Eddy, Michael P; Kostin, Alexander; Kryachko, Valery; MacPherson, Glenn J; Steinhardt, William M; Yudovskaya, Marina; Steinhardt, Paul J
2015-01-01
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al71Ni24Fe5, was discovered in the Khatyrka meteorite, a recently described CV3 carbonaceous chondrite. Icosahedrite, Al63Cu24Fe13, the first natural quasicrystal to be identified, was found in the same meteorite. The new quasicrystal was found associated with steinhardtite (Al38Ni32Fe30), Fe-poor steinhardtite (Al50Ni40Fe10), Al-bearing trevorite (NiFe2O4) and Al-bearing taenite (FeNi). Laboratory studies of decagonal Al71Ni24Fe5 have shown that it is stable over a narrow range of temperatures, 1120?K to 1200?K at standard pressure, providing support for our earlier conclusion that the Khatyrka meteorite reached heterogeneous high temperatures [1100 < T(K) ? 1500] and then rapidly cooled after being heated during an impact-induced shock that occurred in outer space 4.5 Gya. The occurrences of metallic Al alloyed with Cu, Ni, and Fe raises new questions regarding conditions that can be achieved in the early solar nebula. PMID:25765857
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.
Spacetime symmetries of the quantum Hall effect
NASA Astrophysics Data System (ADS)
Geracie, Michael; Son, Dam Thanh; Wu, Chaolun; Wu, Shao-Feng
2015-02-01
We study the symmetries of nonrelativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the nonrelativistic diffeomorphism invariance studied in previous work is enhanced to a full spacetime symmetry, allowing us to derive a number of Ward identities. These symmetries are smooth in the massless limit of the lowest Landau level. We develop a formalism for Newton-Cartan geometry with torsion to write these Ward identities in a covariant form. Previous results on the connection between Hall viscosity and Hall conductivity are reproduced.
Indirect Drive ICF Symmetry Experiments on Omega
NASA Astrophysics Data System (ADS)
Turner, R. E.; Landen, O. L.; Amendt, P. A.; Decker, C. D.; Glendinning, S. G.; Hammel, B. A.; Kalantar, D. H.; Seka, W.; Morse, S.; Pien, G.; Murphy, T.; Delamater, N.
1997-11-01
We report results of measurements of the symmetry of the soft x-ray drive from cylindrical hohlraum experiments on the OMEGA laser. Techniques used included measuring the symmetry of x-ray self-emission from implosions; x-ray backlighting of implosion targets; and following the shock-compressed boundary in foam-ball surrogate targets. The pointing and timing of 10 (out of 30 used) of Omega's beams was varied, to demonstrate time-dependent control of drive symmetry. We will present experimental details of these experiments.
Quantum spherical spins with local symmetry
NASA Astrophysics Data System (ADS)
Gomes, Pedro R. S.; Bienzobaz, P. F.
2015-02-01
We construct a quantum system of spherical spins with a continuous local symmetry. The model is exactly soluble in the thermodynamic limit and exhibits a number of interesting properties. We show that the local symmetry is spontaneously broken at finite as well as zero temperatures, implying the existence of classical and quantum phase transitions with a nontrivial critical behavior. The dynamical generation of gauge fields and the equivalence with the CP(N-1 ) model in the limit N ?? are investigated. The dynamical generation of gauge fields is a consequence of the restoration of the local symmetry.
Symmetry orbits of supergravity black holes
NASA Astrophysics Data System (ADS)
Stelle, K. S.
2015-01-01
Black-hole solutions of supergravity theories form families that realize the deep nonlinear "duality" symmetries of these theories. They form orbits under the action of these symmetry groups, with extremal (i.e., BPS) solutions at the limits of such orbits. An important technique for analyzing such solution families uses timelike dimensional reduction and exchanges the stationary black-hole problem for a nonlinear sigma-model problem. We characterize families of extremal or BPS solutions by nilpotent orbits under the duality symmetries, based on a trigraded or pentagraded decomposition of the corresponding duality-group algebra.
Lorentz Symmetry Breaking in Quantum Electrodynamics
D. M. Oliveira
2010-07-24
In this dissertation, we study the implications generated by the Lorentz breaking symmetry in quantum electrodynamics. We analyze fermions interacting with an electromagnetic field in the contexts of quantum mechanics and make radiative corrections. In quantum mechanics, the terms of the Lorentz breaking symmetry were treated as perturbations to the Dirac equation, and their expected values were obtained in a vacuum. In the radiative corrections, the Lorentz breaking symmetry was introduced in this interaction for the Chern-Simons like term could be induced in (3 +1) dimensions. We also discussed the consequences generated by this term on the propagation speeds of classic photons.
Symmetry of Differential Equations and Quantum Theory
NASA Astrophysics Data System (ADS)
Yerchuck, Dmitri; Dovlatova, Alla; Alexandrov, Andrey
2014-03-01
The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered in the frame of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to EM-field funcions, incoming in given equations, can be set up into the correspondence the Quaternion (twice-Hermitian) matrices by their quantization.
Spacetime Symmetries of the Quantum Hall Effect
Michael Geracie; Dam Thanh Son; Chaolun Wu; Shao-Feng Wu
2014-09-06
We study the symmetries of non-relativistic systems with an emphasis on applications to the fractional quantum Hall effect. A source for the energy current of a Galilean system is introduced and the non-relativistic diffeomorphism invariance studied in previous work is enhanced to a full spacetime symmetry, allowing us to derive a number of Ward identities. These symmetries are smooth in the massless limit of the lowest Landau level. We develop a formalism for Newton-Cartan geometry with torsion to write these Ward identities in a covariant form. Previous results on the connection between Hall viscosity and Hall conductivity are reproduced.
NASA Astrophysics Data System (ADS)
Enyashin, A. N.; Ivanovskii, A. L.
2011-08-01
The structural, elastic, and electronic properties of a series of icosahedral phases, such as boron subcarbides B12C3 and B13C2, subnitride B12N2, and suboxide B12O2, have been studied in the framework of the SCC-DFTB method. It has been found that the B12C2 and B13C2 phases manifest metal-like properties, while B12C3 and B12O2 are semiconductors. The estimates have shown that the insertion of 2 p atoms (C, N, or O) into intericosahedral pores of elemental boron can cause both a decrease in its elastic modulus (an increase in the compressibility of B12N2) and a sharp increase in the modulus B (in subcarbides B12C3 and B12BCC). On the other hand, the insertion of 2 p atoms into ?-B12 will favor an increase in its hardness (suboxide B12O2 will have a maximum hardness).
Dynamical symmetries in contemporary nuclear structure applications
NASA Astrophysics Data System (ADS)
Georgieva, A. I.; Ivanov, M. I.; Drenska, S. L.; Sviratcheva, K. D.; Draayer, J. P.
2010-12-01
In terms of group theory—the language of symmetries, the concept of spontaneous symmetry breaking is represented in terms of chains of group-subgroup structures that define the dynamical symmetry of the system under consideration. This framework enables exact analytic solutions of the associated eigenvalue problems. We review two types of applications of dynamical symmetries in contemporary theoretical nuclear structure physics: first for a classification of the many-body systems under consideration, with respect to an important characteristic of their behavior; and second for the creation of exactly solvable algebraic models that describe specific aspects of this behavior. This is illustrated with the boson and fermion realizations of symplectic structures. In the first case with an application of the sp(4, R) classification scheme of even-even nuclei within the major nuclear shells and next with of the sp(4) microscopic model for the description of isovector pairing correlations.
W symmetry in conformal field theory
Peter Bouwknegt; Kareljan Schoutens
1993-01-01
We review various aspects of W algebra symmetry in two-dimensional conformal field theory and string theory. We pay particular attention to the construction of W algebras through the quantum Drinfeld-Sokolov reduction and through the coset construction.
Dynamical electroweak symmetry breaking on the lattice
Keegan, Liam Roger George
2011-11-23
The LHC is expected to fid new physics beyond the Standard Model (BSM). Technicolor models are a class of BSM models which involve a new strongly interacting sector responsible for electroweak symmetry breaking (EWSB). ...
Noether symmetries and the Swinging Atwood Machine
NASA Astrophysics Data System (ADS)
Moreira, I. C.; Almeida, M. A.
1991-07-01
In this work we apply the Noether theorem with generalised symmetries for discussing the integrability of the Swinging Atwood Machine (SAM) model. We analyse also the limitations of this procedure and compare it with the Yoshida method.
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.
Symmetry: attractive not only to females
Hansen, L. T. T.; Amundsen, T.; Forsgren, E.
1999-01-01
Fluctuating asymmetry in bilateral traits has been proposed to reflect aspects of individual quality, and has hence been suggested to act as a cue in mate choice. Since sexual selection generally acts more strongly on males, numerous studies have focused on female preferences for symmetrical partners, while very little is known about potential male symmetry preferences. In the present experiment, we tested whether bluethroat males are sensitive to symmetry in an artificial ornament. Using different combinations of blue and orange leg bands, females were made symmetrical or asymmetrical. In outdoor aviaries placed in breeding habitat, males were allowed to choose between a symmetrical and an asymmetrical female. We found that males associated more with symmetrical than asymmetrical females, indicating a preference for symmetry. The magnitude of the symmetry preference of bluethroat males was similar to that of females of the same species.
On a symmetry relating gravity with antigravity
Quiros, Israel
2014-01-01
I investigate the impact of a "would be" fundamental symmetry of the laws of nature under the interchange of gravity and antigravity, on the understanding of negative energies in general relativity. For this purpose a toy model that is based on Einstein-Hilbert gravity with two minimally coupled self-interacting scalar fields is explored, where the second (exotic) scalar field with negative energy density may be regarded, alternatively, as an antigravitating field with positive energy. Spontaneous breakdown of reflection symmetry is then considered in order to discuss the implications the proposed "would be" fundamental symmetry might have for the vanishing of the cosmological constant. A possible connection of the gravity-antigravity symmetry with the so called quintom field is also explored.
On a symmetry relating gravity with antigravity
Israel Quiros
2014-10-02
I investigate the impact of a "would be" fundamental symmetry of the laws of nature under the interchange of gravity and antigravity, on the understanding of negative energies in general relativity. For this purpose a toy model that is based on Einstein-Hilbert gravity with two minimally coupled self-interacting scalar fields is explored, where the second (exotic) scalar field with negative energy density may be regarded, alternatively, as an antigravitating field with positive energy. Spontaneous breakdown of reflection symmetry is then considered in order to discuss the implications the proposed "would be" fundamental symmetry might have for the vanishing of the cosmological constant. A possible connection of the gravity-antigravity symmetry with the so called quintom field is also explored.
Space and time from translation symmetry
Schwarz, A. [Department of Mathematics, University of California-Davis, California 95616-8633 (United States)
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.
Spatial Symmetries of the Local Densities
Rohozinski, S. [Warsaw University; Dobaczewski, J. [Warsaw University; Nazarewicz, Witold [ORNL
2010-01-01
Spatial symmetries of the densities appearing in the nuclear Density Functional Theory are discussed. General forms of the local densities are derived by using methods of construction of isotropic tensor fields. The spherical and axial cases are considered.
Breaking so(4) symmetry without degeneracy lift
Pallares-Rivera, A; Kirchbach, M
2013-01-01
On the example of the quantum motion on S3, perturbed by the trigonometric Scarf potential (Scarf I) with one quantized and one continuous parameter, we argue that the breakdown by external scales of a Lie-algebraic symmetry of a quantum system must not necessarily amount to a lift of the degeneracies in the spectrum. To be specific, we show that though the spectrum under discussion carries hydrogen-like degeneracies, the corresponding wave functions do not transform according to so(4) carrier spaces but are finite linear combinations of so(4) representation functions describing carrier spaces of different dimensionality. Alternatively, these decompositions are also expansions in powers of the symmetry breaking scale, and allow to quantitatively describe the order to which the symmetry is violated. We conclude on the general possibility to break perturbatively an intact Lie algebraic symmetry, so(4) in our case, by external scales, such as the continuous parameter of Scarf I, and without leaving trace in the ...
Symmetries and Systematics of Doubly Heavy Hadrons
B. Eakins; W. Roberts
2012-04-12
We discuss the extension of the superflavor symmetry of doubly heavy baryons to states which contain an excited heavy diquark, and we examine some of the consequences of this symmetry for the spectra of doubly heavy baryons and heavy mesons. We explore the ramifications of a proposed symmetry that relates heavy diquarks to doubly heavy mesons. We present a method for determining how the excitation energy of a system containing two heavy quarks will scale as one changes the strength of the interactions and the reduced mass of the system. We use this to derive consequences of the heavy diquark-doubly heavy meson symmetry. We compare these consequences to the results of a quark model as well as the experimental data for doubly and singly heavy mesons. We also discuss the possibility of treating the strange quark as a heavy quark and apply the ideas developed here to strange hadrons.
Enhanced breaking of heavy quark spin symmetry
Guo, Feng-Kun; Shen, Cheng-Ping
2014-01-01
Heavy quark spin symmetry is useful to make predictions on ratios of decay or production rates of systems involving heavy quarks. The breaking of spin symmetry is generally of the order of $O({\\Lambda_{\\rm QCD}/m_Q})$, with $\\Lambda_{\\rm QCD}$ the scale of QCD and $m_Q$ the heavy quark mass. In this paper, we propose a new mechanism to enhance the spin symmetry breaking. Taking the decays of the $\\Upsilon(10860)$ into the $\\chi_{bJ}\\omega\\, (J=0,1,2)$ as an example, we show that a small $S$- and $D$-wave mixing can induce a significant breaking of the spin symmetry relations for the ratios of the branching fractions of these decays, owing to an enhancement of the decays of the $D$-wave component due to nearby coupled channels.
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.
On discrete symmetries and relic radiation anisotropy
M. V. Altaisky; N. E. Kaputkina
2014-06-17
It is argued that large scale angle correlations of the Cosmic Microwave Background Radiation (CMBR) temperature fluctuations measured by Wilkinson Microwave Anisotropy Probe (WMAP) mission may have a trace of discrete symmetries of quantum gravity
NSDL National Science Digital Library
2009-09-24
These 4 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to line and rotational symmetry. Supporting documents, materials, and progress indicators are included.
Symmetry systematics of pressure - induced phase transitions
Satish C. Gupta; R. Chidambaram
1994-01-01
Most pressure induced phase transitions are diffusionless. Because of this, there exists a one-to-one correspondence between the positions of atoms in the parent and the product phases, which, therefore, show interesting symmetry relationships. In this paper, we have used these for discussing a symmetry classification of pressure induced phase transitions into four categories: iso-symmetric, group-subgroup, intersection group, and order-disorder transitions.
Asymptotic symmetries in an optical lattice
G. Gaeta
2005-10-02
It was recently remarked by Lutz [{\\it Phys. Rev. A} {\\bf 67} (2003), 051402(R)] that the equation for the marginal Wigner distribution in an optical lattice admits a scale-free distribution corresponding to Tsallis statistics. Here we show that this distribution is invariant under an asymptotic symmetry of the equation, hence that this scale-free behavior can be understood in terms of symmetry analysis.
On Continuous Flavour Symmetries for Neutrinos
Merlo, Luca
2015-01-01
Flavour symmetries are fundamental tools in the search for an explanation to the flavour puzzle: fermion mass hierarchies, the neutrino mass ordering, the differences between the mixing matrices in the quark and lepton sector, can all find an explanation in models where the fermion generations undergo specific geometric relations. An overview on the implementation of continuous symmetries in the flavour sector is presented here, focussing on the lepton sector.
Aspects of Dynamical Chiral Symmetry Breaking
C. D. Roberts
2003-01-21
Dynamical chiral symmetry breaking is a nonperturbative phenomenon that may be studied using QCD's gap equation. Model-independent results can be obtained with a nonperturbative and symmetry preserving truncation. The gap equation yields the massive dressed-quark propagator, which has a spectral representation when considered as a function of the current-quark mass. This enables an explication of the connection between the infrared limit of the QCD Dirac operator's spectrum and the quark condensate appearing in the operator product expansion.
Family symmetries and the SUSY flavour problem
I. de Medeiros Varzielas; G. G. Ross
2006-12-19
We re-examine the constraints on continuous family symmetries coming from flavour changing neutral current limits on the D-term contributions to squark and slepton masses. We show that, for a restricted choice of the familon sector, continuous family symmetries are consistent with even the most conservative limits both for the case of gauge mediated supersymmetry breaking and the case of gravity mediated supersymmetry breaking.
Symmetry breaking of quasihelical stellarator equilibria
Weening, R.H. (Department of Physics, College of William and Mary, Williamsburg, Virginia 23185 (United States))
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.
Nanostructure symmetry: Relevance for physics and computing
Dupertuis, Marc-André; Oberli, D. Y. [Laboratory for Physics of Nanostructure, EPF Lausanne (Switzerland); Karlsson, K. F. [Department of Physics, Chemistry, and Biology (IFM), Linköping University (Sweden); Dalessi, S. [Computational Biology Group, Department of Medical Genetics, University of Lausanne (Switzerland); Gallinet, B. [Nanophotonics and Metrology Laboratory, EPF Lausanne (Switzerland); Svendsen, G. [Dept. of Electronics and Telecom., Norwegian University of Science and Technology, Trondheim (Norway)
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.
S_Kernel: A New Symmetry Measure
Vito Di Gesù; Bertrand Zavidovique
2005-01-01
\\u000a Symmetry is an important feature in vision. Several detectors or transforms have been proposed. In this paper we concentrate\\u000a on a measure of symmetry. Given a transform S, the kernel SK of a pattern is defined as the maximal included symmetric sub-set of this pattern. It is easily proven that, in any direction,\\u000a the optimal axis corresponds to the maximal
Magnetohydrodynamic equilibria with incompressible flows: Symmetry approach
NASA Astrophysics Data System (ADS)
Cicogna, G.; Pegoraro, F.
2015-02-01
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.
Local Conformal Symmetry: the Missing Symmetry Component for Space and Time
Gerard T. Hooft
2015-03-17
Local conformal symmetry is usually considered to be an approximate symmetry of nature, which is explicitly and badly broken. Arguments are brought forward here why it has to be turned into an exact symmetry that is spontaneously broken. As in the B.E.H. mechanism in Yang-Mills theories, we then will have a mechanism for disclosing the small-distance structure of the gravitational force. The symmetry could be as fundamental as Lorentz invariance, and guide us towards a complete understanding of physics at the Planck scale.
Surface topography and rotational symmetry breaking.
Basu, Rajratan; Nemitz, Ian R; Song, Qingxiang; Lemieux, Robert P; Rosenblatt, Charles
2012-07-01
The surface electroclinic effect, which is a rotation of the molecular director in the substrate plane proportional to an electric field E applied normal to the substrate, requires both a chiral environment and C(2) (or lower) rotational symmetry about E. The two symmetries typically are created in tandem by manipulating the surface topography, a process that conflates their effects. Here we use a pair of rubbed polymer-coated substrates in a twist geometry to obtain our main result, viz., that the strengths of two symmetries, in this case the rub-induced breaking of C(?) rotational symmetry and chiral symmetry, can be separated and quantified. Experimentally we observe that the strength of the reduced rotational symmetry arising from the rub-induced scratches, which is proportional to the electroclinic response, scales linearly with the induced topographical rms roughness and increases with increasing rubbing strength of the polymer. Our results also suggest that the azimuthal anchoring strength coefficient is relatively insensitive to the strength of the rubbing. PMID:23005441
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco, E-mail: f.cefala@unibas.ch, E-mail: stefan.antusch@unibas.ch [Department of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel (Switzerland)
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
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…
Group-theoretical framework for potential symmetries of evolution equations
Qing Huang; Changzheng Qu; Renat Zhdanov
2011-01-01
We develop algebraic approach to the problem of classification of potential symmetries of nonlinear evolution equations. It is essentially based on the recently discovered fact [R. Zhdanov, J. Math. Phys. 50, 053522 (2009)], that any such symmetry is mapped into a contact symmetry. The approach enables using the classical results on classification of contact symmetries of nonlinear evolution equations by
Jordan, David
The group of symmetries of a square This applet demonstrates symmetries of a square, in particular and with labels indicating the symmetries applied so far. Two composites may be compared using separate squares. Navigation Â· The dropdown menu for selecting symmetries is labelled Group element. Â· The which square? button
Tennant, Raymond F.
Symmetry: Culture and Science Issue on Symmetry and Islamic Art 2009 Page 1 Medieval Islamic, Spain contains many excellent examples of these Islamic constructions (Figure 2). Figure 1: Strapwork, and Penrose and Girih Tiles R. Tennant Symmetry: Culture and Science 2009 Issue on Symmetry and Islamic Art
Scalar Field Theories with Polynomial Shift Symmetries
Tom Griffin; Kevin T. Grosvenor; Petr Horava; Ziqi Yan
2014-12-02
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.
Energy bands: Chern numbers and symmetry
Iwai, T., E-mail: iwai@amp.i.kyoto-u.ac.jp [Kyoto University, 606-8501 Kyoto (Japan); Zhilinskii, B., E-mail: zhilin@univ-littoral.fr [Kyoto University, 606-8501 Kyoto (Japan); Universite du Littoral Cote d'Opale, 59140 Dunkerque (France)
2011-12-15
Energy bands formed by rotation-vibrational states of molecules in the presence of symmetry and their qualitative modifications under variation of some control parameters are studied within the semi-quantum model. Rotational variables are treated as classical whereas a finite set of vibrational states is considered as quantum. In the two-state approximation the system is described in terms of a fiber bundle with the base space being a two-dimensional sphere, the classical phase space for rotational variables. Generically this rank 2 complex vector bundle can be decomposed into two complex line bundles characterized by a topological invariant, the first Chern class. A general method of explicit calculation of Chern classes and of their possible modifications under variation of control parameters in the presence of symmetry is suggested. The construction of iso-Chern diagrams which split the space of control parameters into connected domains with fixed Chern numbers is suggested. A detailed analysis of the rovibrational model Hamiltonian for a D{sub 3} invariant molecule possessing two vibrational states transforming according to the two-dimensional irreducible representation is done to illustrate non-trivial restrictions imposed by symmetry on possible values of Chern classes. - Highlights: > Complex line bundles associated with eigenvalues of 2x2 Hermitian matrix Hamiltonians. > Hamiltonians are defined on the 2-sphere and invariant under symmetry groups. > Symmetry permits only some special integers as Chern numbers. > For SO(2) symmetry, the possible values are 0, {+-}K, where K is an index of the representation. > For D{sub 3} symmetry, the possible values are {+-}2, {+-}4 within our model Hamiltonians.
Applications of Symmetry Methods to the Theory of Plasma Physics
Giampaolo Cicogna; Francesco Ceccherini; Francesco Pegoraro
2006-02-03
The theory of plasma physics offers a number of nontrivial examples of partial differential equations, which can be successfully treated with symmetry methods. We propose three different examples which may illustrate the reciprocal advantage of this "interaction" between plasma physics and symmetry techniques. The examples include, in particular, the complete symmetry analysis of system of two PDE's, with the determination of some conditional and partial symmetries, the construction of group-invariant solutions, and the symmetry classification of a nonlinear PDE.
Euler integral symmetries for the confluent Heun equation and symmetries of the Painlevé equation PV
NASA Astrophysics Data System (ADS)
Kazakov, A. Ya.; Slavyanov, S. Yu.
2014-05-01
Euler integral symmetries relate solutions of ordinary linear differential equations and generate integral representations of the solutions in several cases or relations between solutions of constrained equations. These relations lead to the corresponding symmetries of the monodromy matrices for the differential equations. We discuss Euler symmetries in the case of the deformed confluent Heun equation, which is in turn related to the Painlevé equation PV. The existence of symmetries of the linear equations leads to the corresponding symmetries of the Painlevé equation of the Okamoto type. The choice of the system of linear equations that reduces to the deformed confluent Heun equation is the starting point for the constructions. The basic technical problem is to choose the bijective relation between the system parameters and the parameters of the deformed confluent Heun equation. The solution of this problem is quite large, and we use the algebraic computing system Maple for this.
Symmetry, full symmetry groups, and some exact solutions to a generalized Davey-Stewartson system
NASA Astrophysics Data System (ADS)
Li, Biao; Ye, Wang-Chuan; Chen, Yong
2008-10-01
The Lie symmetry algebra of a generalized Davey-Stewartson (GDS) system is obtained. The general element of this algebra depends on eight arbitrary functions of time, which has a Kac-Moody-Virasoro loop algebra structure and is isomorphic to that of the standard integrable Davey-Stewartson equations under certain conditions imposed on parameters and arbitrary functions. Then based on the symmetry group direct method proposed by Lou and Ma [J. Phys. A 38, L129 (2005)] the full symmetry groups of the GDS system are obtained. From the full symmetry groups, both the Lie symmetry group and a group of discrete transformations can be obtained. Finally, some exact solutions involving sech-sech2-sech2 and tanh-tanh2-tanh2 type solitary wave solutions are presented by a generalized subequation expansion method.
Reflections on the concept of symmetry
NASA Astrophysics Data System (ADS)
Lorenz, Kuno
2005-10-01
The concept of symmetry is omnipresent, although originally, in Greek antiquity, distinctly different from the modern logical notion. In logic a binary relation R is called symmetric if xRy implies yRx. In Greek, "being symmetric" in general usage is synonymous with "being harmonious", and in technical usage, as in Euclid's Elements, it is synonymous with "commensurable". Due to the second meaning, which is close to the etymology of ??´?????o?, "with measure" has likewise to be read as "being [in] rational [ratios]" and displays the origin of the concept of rationality of establishing a proportion. Heraclitus can be read as a master of such connections. Exercising rationality is a case of simultaneously finding and inventing symmetries. On that basis a proposal is made of how to relate the modern logical notion of symmetry, a second-order concept, on the one hand with modern first-order usages of the term symmetric in geometry and other fields, and on the other hand with the notion of balance that derives from the ancient usage of symmetric. It is argued that symmetries as states of balance exist only in theory, in practice they function as norms vis-à-vis broken symmetries.
Bilateral symmetry analysis of breast MRI
NASA Astrophysics Data System (ADS)
Alterson, Robert; Plewes, Donald B.
2003-10-01
Mammographic interpretation often uses symmetry between left and right breasts to indicate the site of potential tumour masses. This approach has not been applied to breast images obtained from MRI. We present an automatic technique for breast symmetry detection based on feature extraction techniques which does not require any efforts to co-register breast MRI data. The approach applies computer-vision techniques to detect natural biological symmetries in breast MR scans based on three objective measures of similarity: multiresolution non-orthogonal wavelet representation, three-dimensional intensity distributions and co-occurrence matrices. Statistical distributions that are invariant to feature localization are computed for each of the extracted image features. These distributions are later compared against each other to account for perceptual similarity. Studies based on 51 normal MRI scans of randomly selected patients showed that the sensitivity of symmetry detection rate approached 94%. The symmetry analysis procedure presented in this paper can be applied as an aid in detecting breast tissue changes arising from disease.
Symmetry breaking between SASI spiral modes
NASA Astrophysics Data System (ADS)
Kazeroni, R.; Guilet, J.; Foglizzo, T.
2014-12-01
The accretion shock formed during the collapse of massive stars is subject to the Standing Accretion Shock Instability (SASI). Spiral modes of SASI can redistribute angular momentum and spin-up a neutron star born from a non-rotating progenitor. If the asymmetries in the progenitor are initially small, two counter-rotating spiral modes with similar amplitudes emerge. In the non-linear regime of SASI, the symmetry between these modes may be broken and a strong spiral mode dominates the dynamics. We study here the timescale for symmetry breaking in order to evaluate the favorable conditions leading to angular momentum redistribution by the SASI. We perform 2D numerical simulations of a simplified setup in cylindrical geometry. These simulations show that a symmetry breaking occurs only if the initial radius of the shock wave is large enough compared to the radius of the neutron star. Furthermore, in the regime where symmetry breaking occurs, we observe stochastic variations, which require a statistical approach. A path towards an analytical description of the timescale for symmetry breaking is proposed.
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.
Conformal correlators of mixed-symmetry tensors
Miguel S. Costa; Tobias Hansen
2015-01-19
We generalize the embedding formalism for conformal field theories to the case of general operators with mixed symmetry. The index-free notation encoding symmetric tensors as polynomials in an auxiliary polarization vector is extended to mixed-symmetry tensors by introducing a new commuting or anticommuting polarization vector for each row or column in the Young diagram that describes the index symmetries of the tensor. We determine the tensor structures that are allowed in n-point conformal correlation functions and give an algorithm for counting them in terms of tensor product coefficients. A simple derivation of the unitarity bound for arbitrary mixed-symmetry tensors is obtained by considering the conservation condition in embedding space. We show, with an example, how the new formalism can be used to compute conformal blocks of arbitrary external fields for the exchange of any conformal primary and its descendants. The matching between the number of tensor structures in conformal field theory correlators of operators in d dimensions and massive scattering amplitudes in d+1 dimensions is also seen to carry over to mixed-symmetry tensors.
Conformal Symmetry for General Black Holes
Mirjam Cveti?; Finn Larsen
2011-06-16
We show that the warp factor of a generic asymptotically flat black hole in five dimensions can be adjusted such that a conformal symmetry emerges. The construction preserves all near horizon properties of the black holes, such as the thermodynamic potentials and the entropy. We interpret the geometry with modified asymptotic behavior as the "bare" black hole, with the ambient flat space removed. Our warp factor subtraction generalizes hidden conformal symmetry and applies whether or not rotation is significant. We also find a relation to standard AdS/CFT correspondence by embedding the black holes in six dimensions. The asymptotic conformal symmetry guarantees a dual CFT description of the general rotating black holes.
Supersymmetric defect models and mirror symmetry
NASA Astrophysics Data System (ADS)
Hook, Anson; Kachru, Shamit; Torroba, Gonzalo
2013-11-01
We study supersymmetric field theories in three space-time dimensions doped by various configurations of electric charges or magnetic fluxes. These are supersymmetric avatars of impurity models. In the presence of additional sources such configurations are shown to preserve half of the supersymmetries. Mirror symmetry relates the two sets of configurations. We discuss the implications for impurity models in 3d = 4 QED with a single charged hypermultiplet (and its mirror, the theory of a free hypermultiplet) as well as 3d = 2 QED with one flavor and its dual, a supersymmetric Wilson-Fisher fixed point. Mirror symmetry allows us to find backreacted solutions for arbitrary arrays of defects in the IR limit of = 4 QED. Our analysis, complemented with appropriate string theory brane constructions, sheds light on various aspects of mirror symmetry, the map between particles and vortices and the emergence of ground state entropy in QED at finite density.
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny [Institute for Theoretical Physics, ETH Zurich, CH-8093 Zurich (Switzerland); Svistunov, Boris [Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003 (United States); Russian Research Center 'Kurchatov Institute', 123182 Moscow (Russian Federation)
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.
Conservation Laws, Symmetries, and Elementary Particles
NASA Astrophysics Data System (ADS)
Hoekzema, Dick; Schooten, Gert; van den Berg, Ed; Lijnse, Piet
2005-05-01
The following student text on conservation laws, symmetries, and elementary particles was developed in a Dutch project for teaching modern physics to the top stream of the sixth year of secondary education (age 17-18). In a series of 35 lessons of 45-50 minutes each, students study particle-wave duality, the Heisenberg principle, probability models for properties of particles, the particle in a box, and applications, elementary particles, and astrophysics (http://www.phys.uu.nl/˜wwwpmn). In this paper we focus on particle physics and the key concepts of this chapter are: transformation, reaction equation, conservation laws, and symmetry. For recent literature regarding the teaching of symmetries and/or elementary particles, we refer to articles by Hill & Lederman, Pascolini & Pietroni,2 Kalmus,3 O'Connell,4 and Hanley.5
Viable axion from gauged flavor symmetries
Berenstein, David; Perkins, Erik [Department of Physics, University of California, Santa Barbara, California 93106 (United States)
2010-11-15
We consider a string-inspired nonsupersymmetric extension of the standard model with gauged anomalous U(1) flavor symmetries. Consistency requires the Green-Schwarz (GS) mechanism to cancel mixed anomalies. The additional required scalars provide Stueckelberg masses for the Z{sup '} particles associated to the gauged flavor symmetry, so they decouple at low energies. Our models also include a complex scalar field {phi} to generate Froggatt-Nielsen mass terms for light particles, giving a partial solution to the fermion mass problem. A residual approximate (anomalous) global symmetry survives at low energies. The associated pseudo-Goldstone mode is the phase of the {phi} scalar field, and it becomes the dominant contribution to the physical axion. An effective field theory analysis that includes neutrino masses gives a prediction for the axion decay constant. We find a simple model where the axion decay constant is in the center of the allowed window.
Assessment of joint symmetry in arthritis.
Cresswell, Lynne; Farewell, Vern
2011-04-30
We evaluate three methods for the assessment of symmetry in the joints affected by an arthritic disease. The first two methods, based on published methodology, are limited by their assumptions. We introduce a third method that enables a more comprehensive investigation. In common with previous methods, this method examines tabulations of observed data for evidence of symmetry. Expected values for the table cells are simulated under an assumption of independent joint disease, whilst allowing for differences between patients, and joint locations, in terms of their susceptibility to disease symptoms. Departures of observed from expected values are assessed via a Pearson-type goodness-of-fit test and are examined for consistency with symmetry. We illustrate the three methods using data on the damage accrued in the hand joints of patients registered at the University of Toronto Psoriatic Arthritis clinic. PMID:21284011
Preserving Symmetry in Preconditioned Krylov Subspace Methods
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Chow, E.; Saad, Y.; Yeung, M. C.
1996-01-01
We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M. In the symmetric case, one can recover symmetry by using M-inner products in the conjugate gradient (CG) algorithm. This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the new algorithms are mathematically equivalent to split preconditioning, but do not require M to be factored. Better robustness in a specific sense can also be observed. When combined with truncated versions of iterative methods, tests show that this is more effective than the common practice of forfeiting near-symmetry altogether.
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.
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.
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 ?.
Symmetry, ordering and arranging compulsive behaviour.
Radomsky, A S; Rachman, S
2004-08-01
Compulsive ordering and arranging, and a preoccupation with symmetry are features of obsessive-compulsive disorder (OCD) that have not been examined experimentally. Three connected studies were conducted to examine this phenomenon: a self-report measure of this behaviour was developed and validated, participants were asked to engage in tasks designed to assess preferences for order, and to assess the interference of disorderly surroundings in the completion of a stressful activity. The self-report measure has sound psychometric properties and validity. Participants with a strong preference for order were made more anxious by having to complete a difficult task in a disorganized environment. Participants without this preference did not show this effect. The results are discussed in terms of the phenomenology of compulsive ordering and arranging, and its relationships with both OCD and normal human behaviour. It is suggested that compulsive ordering and a drive for symmetry are extreme manifestations of the common preference for order and symmetry. PMID:15178465
Twin and Mirror Symmetries from Presymmetry
Ernesto A. Matute
2011-11-11
We argue that presymmetry, a hidden predynamical electroweak quark-lepton symmetry that explains the fractional charges and triplication of families, must be extended beyond the Standard Model as to have a residual presymmetry that embraces partner particles and includes the strong sector, so accounting for the twin or mirror partners proposed to alleviate the naturalness problem of the weak scale. It leads to the full duplication of fermions and gauge bosons of the Standard Model independently of the ultraviolet completion of the theory, even if the Higgs particle is discarded by experiment, which adds robustness to twin and mirror symmetries. The established connection is so strongly motivated that the search for twin or mirror matter becomes the possible test of presymmetry. If the physics beyond the Standard Model repairs its left-right asymmetry, mirror symmetry should be the one realized in nature.
Workshop on electroweak symmetry breaking: proceedings
Hinchliffe, I. (ed.)
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.
``Statistical'' symmetry with applications to phase transitions
NASA Astrophysics Data System (ADS)
Birman, Joseph L.; Trebin, H.-R.
1985-01-01
Hermann proposed that mesomorphic media should be classified by assigning certain "statistical symmetry groups" to each possible partially ordered array. Two translational groups introduced were called superordinate and subordinate. We find that the average density in such a partially ordered medium has the superordinate symmetry ?1, while the pair correlation function has the subordinate symmetry ?2. A complete listing is made of all compatible combinations of ?1 and ?2 in two and three dimensions. This leads to more possible symmetries than Hermann obtained, e.g., also to nonstoichiometric crystals. The order parameter space for the systems is found to be the quotient space ?1/?2. In most cases it is identical to the order parameter space of low-dimensional XY spin systems. The Landau free energy is expanded as functional of the two-particle correlation function K; the translation group is found to be ?1×?2. A Landau mean-field theory can then be carried out by expanding the system free energy into a series of invariants of the active irreducible representations of K and mapping the free energy onto that for an XY planar spin system. We predict novel critical behavior for transitions between mesomorphic phases and "go nogo" selection rules for continuous transitions. We give the structure factors for X-ray scattering so changes in all such phase transitions are observable. The statistical symmetry groups, which describe point and translational symmetries of the mesophases, are classified. Proposals are made to include quasi-long-range or topological order in the classification scheme.
Local unitary symmetries of hypergraph states
NASA Astrophysics Data System (ADS)
Lyons, David W.; Upchurch, Daniel J.; Walck, Scott N.; Yetter, Chase D.
2015-03-01
Hypergraph states are multiqubit states whose combinatorial description and entanglement properties generalize the well-studied class of graph states. Graph states are important in applications such as measurement-based quantum computation and quantum error correction. The study of hypergraph states, with their richer multipartite entanglement and other nonlocal properties, has a promising outlook for new insight into multipartite entanglement. We present results analyzing local unitary symmetries of hypergraph states, including both continuous and discrete families of symmetries. In particular, we show how entanglement types can be detected and distinguished by certain configurations in the hypergraphs from which hypergraph states are constructed.
Extracting Symmetry Energy from Projectile Spectator Fragmentation
NASA Astrophysics Data System (ADS)
Kumar, Sanjeev
2013-11-01
In order to extract the symmetry energy, the Zbound (the sum of charge number for fragments having Z ? 2) dependence of multiplicity of neutrons (Mn) from the projectile spectator fragmentation of 124Sn and 124La at 600 MeV/nucleon within isospin quantum molecular dynamics (IQMD) model is compared with the experimental findings of ALADIN2000 collaboration.12 The findings favor the soft symmetry energy with soft equation of state. For all the projectiles (124Sn, 124 La, 107 Sn), the peak Mn obey the universal behavior around Zbound/ZProjectile ? 0.7 with different value of Mn ? 12, 9, 7, respectively.
Algebraic Models: Coordinates, Scales, and Dynamical Symmetries
Michael W. N. Ibrahim
2000-05-15
We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle Schr\\"odinger hamiltonian which, for low energy states, gives equivalent results to a bosonic algebraic model to leading order in $N$. The process is used to study the associated geometries of the dynamical symmetries of U(3). By demanding that the inner product be preserved in the Schr\\"odinger picture we conclude that different dynamical symmetries correspond to different scales.
Block type symmetry of bigraded Toda hierarchy
NASA Astrophysics Data System (ADS)
Li, Chuanzhong; He, Jingsong; Su, Yucai
2012-01-01
In this paper, we define Orlov-Schulman's operators ML, MR, and then use them to construct the additional symmetries of the bigraded Toda hierarchy. We further show that these additional symmetries form an interesting infinite-dimensional Lie algebra known as a Block type Lie algebra, whose structure theory and representation theory have recently received much attention in the literature. By acting on two different spaces under the weak W-constraints, we find in particular two representations of this Block type Lie algebra.
On the dynamic viscous permeability tensor symmetry.
Perrot, Camille; Chevillotte, Fabien; Panneton, Raymond; Allard, Jean-François; Lafarge, Denis
2008-10-01
Based on a direct generalization of a proof given by Torquato for symmetry property in static regime, this express letter clarifies the reasons why the dynamic permeability tensor is symmetric for spatially periodic structures having symmetrical axes which do not coincide with orthogonal pairs being perpendicular to the axis of three-, four-, and sixfold symmetry. This somewhat nonintuitive property is illustrated by providing detailed numerical examples for a hexagonal lattice of solid cylinders in the asymptotic and frequency dependent regimes. It may be practically useful for numerical implementation validation and/or convergence assessment. PMID:19062788
A simple test for spacetime symmetry
NASA Astrophysics Data System (ADS)
Houri, Tsuyoshi; Yasui, Yukinori
2015-03-01
This paper presents a simple method for investigating spacetime symmetry for a given metric. The method makes use of the curvature conditions that are obtained from the Killing equations. We use the solutions of the curvature conditions to compute an upper bound on the number of Killing vector fields, as well as Killing–Yano (KY) tensors and closed conformal KY tensors. We also use them in the integration of the Killing equations. By means of the method, we thoroughly investigate KY symmetry of type D vacuum solutions such as the Kerr metric in four dimensions. The method is also applied to a large variety of physical metrics in four and five dimensions.
PT-symmetry in macroscopic magnetic structures
J. M. Lee; T. Kottos; B. Shapiro
2014-08-14
We introduce the notion of PT-symmetry in magnetic nanostructures and show that they can support a new type of non-Hermitian dynamics. Using the simplest possible set-up consisting of two coupled ferromagnetic films, one with loss and another one with a balanced amount of gain, we demonstrate the existence of a spontaneous PT-symmetry breaking point where both the eigenfrequencies and eigenvectors are degenerate. Below this point the frequency spectrum is real indicating stable dynamics while above this point it is complex signaling unstable dynamics.
Study of Spinor Symmetries in Nuclear Structure
NASA Astrophysics Data System (ADS)
Kuyucak, Serdar
One of the possible spinor symmetries of the interacting boson-fermion model is studied. The interacting boson -fermion model is a direct extension of the interacting boson model of nuclear collective states, where the fermion degrees of freedom of the odd nucleon are coupled to the boson core. Since in this model nuclei are treated as a mixed system of bosons and fermions, in order to discuss its symmetries the ordinary concept of symmetry is extended to spinor symmetries. In this work, we discuss the spinor symmetry, Spin(6), which arises when the bosons have SO(6) symmetry and the fermions occupy a single particle orbital with j = 3/2 which is described by an SU(4) symmetry. The states are classified according to the irreducible representations of the group chain Spin(6)(R-HOOK)Spin(5)(R-HOOK)Spin(3)(R -HOOK)Spin(2). An energy formula is derived assuming that the Hamiltonian can be written in terms of the Casimir operators of this group chain. The Spin(6) wave functions are constructed by expanding them into product of the boson SO(6) and fermion SU(4) wave functions. Using these wave functions we obtain closed expressions for electromagnetic (E0, M1, E2) transition rates, static moments and (one and two) nucleon transfer reaction intensities. Comparison of the calculations with the experimental data on iridium and gold isotopes shows that the Spin(6) symmetry scheme forms a reasonable zeroth order approximation in describing properties of these nuclei. Improvements over the results is possible by (i) incorporating other single particle orbitals (j = 1/2, 5/2, 7/2) to the dominant j = 3/2 orbital, (ii) mixing the boson SU(3) limit to the SO(6) limit. Although, in general, these effects must be dealt with numerical computations, the cases of mixing of the j = 1/2 orbital and the boson SU(3) limit can be studied in perturbation theory. We also report the results of the perturbation calculations of the above effects.
Holonomy and Symmetry in M-theory
Chris Hull
2003-05-07
Supersymmetric solutions of 11-dimensional supergravity can be classified according to the holonomy of the supercovariant derivative arising in the Killing spinor condition. It is shown that the holonomy must be contained in $\\SL(32,\\R)$. The holonomies of solutions with flux are discussed and examples are analysed. In extending to M-theory, account has to be taken of the phenomenon of ` supersymmetry without supersymmetry'. It is argued that including the fermionic degrees of freedom in M-theory requires a formulation with a local $\\SL(32,\\R)$ symmetry, analogous to the need for local Lorentz symmetry in coupling spinors to gravity.
Holographic metals and insulators with helical symmetry
NASA Astrophysics Data System (ADS)
Donos, Aristomenis; Goutéraux, Blaise; Kiritsis, Elias
2014-09-01
Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in Einstein-Maxwell-Dilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming AdS 5 UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current.
Chimera Death: Symmetry Breaking in Dynamical Networks
Anna Zakharova; Marie Kapeller; Eckehard Schöll
2014-02-03
For a network of generic oscillators with nonlocal topology and symmetry-breaking coupling we establish novel partially coherent inhomogeneous spatial patterns, which combine the features of chimera states (coexisting incongruous coherent and incoherent domains) and oscillation death (oscillation suppression), which we call chimera death. We show that due to the interplay of nonlocality and breaking of rotational symmetry by the coupling two distinct scenarios from oscillatory behavior to a stationary state regime are possible: a transition from an amplitude chimera to chimera death via in-phase synchronized oscillations, and a direct abrupt transition for larger coupling strength.
Holographic Metals and Insulators with Helical Symmetry
Aristomenis Donos; Blaise Goutéraux; Elias Kiritsis
2014-09-17
Homogeneous, zero temperature scaling solutions with Bianchi VII spatial geometry are constructed in Einstein-Maxwell-Dilaton theory. They correspond to quantum critical saddle points with helical symmetry at finite density. Assuming $AdS_{5}$ UV asymptotics, the small frequency/(temperature) dependence of the AC/(DC) electric conductivity along the director of the helix are computed. A large class of insulating and conducting anisotropic phases is found, as well as isotropic, metallic phases. Conduction can be dominated by dissipation due to weak breaking of translation symmetry or by a quantum critical current.
Second Order Symmetries of the Conformal Laplacian
NASA Astrophysics Data System (ADS)
Michel, Jean-Philippe; Radoux, Fabian; Šilhan, Josef
2014-02-01
Let (M,g) be an arbitrary pseudo-Riemannian manifold of dimension at least 3. We determine the form of all the conformal symmetries of the conformal (or Yamabe) Laplacian on (M,g), which are given by differential operators of second order. They are constructed from conformal Killing 2-tensors satisfying a natural and conformally invariant condition. As a consequence, we get also the classification of the second order symmetries of the conformal Laplacian. Our results generalize the ones of Eastwood and Carter, which hold on conformally flat and Einstein manifolds respectively. We illustrate our results on two families of examples in dimension three.
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
NASA Astrophysics Data System (ADS)
Weichselbaum, Andreas
2012-12-01
A general framework for non-abelian symmetries is presented for matrix-product and tensor-network states in the presence of well-defined orthonormal local as well as effective basis sets. The two crucial ingredients, the Clebsch-Gordan algebra for multiplet spaces as well as the Wigner-Eckart theorem for operators, are accounted for in a natural, well-organized, and computationally straightforward way. The unifying tensor-representation for quantum symmetry spaces, dubbed QSpace, is particularly suitable to deal with standard renormalization group algorithms such as the numerical renormalization group (NRG), the density matrix renormalization group (DMRG), or also more general tensor networks such as the multi-scale entanglement renormalization ansatz (MERA). In this paper, the focus is on the application of the non-abelian framework within the NRG. A detailed analysis is presented for a fully screened spin- 3/2 three-channel Anderson impurity model in the presence of conservation of total spin, particle-hole symmetry, and SU(3) channel symmetry. The same system is analyzed using several alternative symmetry scenarios based on combinations of U(1, SU(2, SU(2, SU(3, as well as the enveloping symplectic Sp(6) symmetry. These are compared in detail, including their respective dramatic gain in numerical efficiency. In the Appendix, finally, an extensive introduction to non-abelian symmetries is given for practical applications, together with simple self-contained numerical procedures to obtain Clebsch-Gordan coefficients and irreducible operators sets. The resulting QSpace tensors can deal with any set of abelian symmetries together with arbitrary non-abelian symmetries with compact, i.e. finite-dimensional, semi-simple Lie algebras.
From Old Symmetries to New Symmetries: Quarks, Leptons and B-L
Rabindra N. Mohapatra
2014-09-29
The Baryon-Lepton difference ($B-L$) is increasingly emerging as a possible new symmetry of the weak interactions of quarks and leptons as a way to understand the small neutrino masses. There is the possibility that current and future searches at colliders and in low energy rare processes may provide evidence for this symmetry. This paper provides a brief overview of the early developments that led to B-L as a possible symmetry beyond the standard model, and also discusses some recent developments.
Optical symmetry in liquid crystal displays
Frank Cuypers; Alexis De Vos
1989-01-01
Some authors include in their articles polar plots showing the directional dependence of either transmission or contrast ratio of a liquid crystal display (LCD). In some cases those plots have a symmetry axis; here we explain when and why it occurs.
Carbon Nanotubes: From Symmetry to Applications
NASA Astrophysics Data System (ADS)
Damnjanovi?, M.
In this chapter, we show how the concept of symmetry gives theoretical explanation of the properties, which made carbon nanotubes (NTs) one of the most interesting materials of nanotechnology. First, in Sect. 3.1, we consider basic facts on single-wall carbon nanotubes (SWCNTs), including their configuration and symmetry. Then, we discuss double-wall nanotubes.Next, Sect. 3.2 is devoted to elementary symmetry-based physical properties. More precisely, we explain the energy spectrum of electrons and phonons, showing that as the consequence of the symmetry, energies must be arranged in the so-called bands. Elementary properties of these band structures may be a priory discussed, yielding easily famous conducting law, showing strong dependence of conductivity on the type of nanotube. Conserved quantum numbers enable us to extract selection rules for various physical processes. This way, radial breathing mode appears to be very important for the characterization of the samples by Raman spectroscopy. Also, optical properties are derived.Finally, in Sect. 3.3, mutual interaction between the walls of double-wall nanotubes is discussed. It is explained why this interaction is very weak, which is used to propose nanomachines with almost superslippery parts.
Weyl-Gauge Symmetry of Graphene
Alfredo Iorio
2011-01-19
The conformal invariance of the low energy limit theory governing the electronic properties of graphene is explored. In particular, it is noted that the massless Dirac theory in point enjoys local Weyl symmetry, a very large symmetry. Exploiting this symmetry in the two spatial dimensions and in the associated three dimensional spacetime, we find the geometric constraints that correspond to specific shapes of the graphene sheet for which the electronic density of states is the same as that for planar graphene, provided the measurements are made in accordance to the inner reference frame of the electronic system. These results rely on the (surprising) general relativistic-like behavior of the graphene system arising from the combination of its well known special relativistic-like behavior with the less explored Weyl symmetry. Mathematical structures, such as the Virasoro algebra and the Liouville equation, naturally arise in this three-dimensional context and can be related to specific profiles of the graphene sheet. Speculations on possible applications of three-dimensional gravity are also proposed.
Sargent and the unbearable lightness of symmetry
Esther-Mirjam Sent
1998-01-01
Influenced by changes in his environment in the early 1980s, Thomas Sargent tried to serve his interest in finding conceptual integrity of theory and method by using rational expectations to link general equilibrium theory and vector autoregressions. Dead ends loomed large on Sargent's horizon when he tried to fit the a priori bias towards symmetry in general equilibrium theory into
Movement Symmetries and the Mammalian Vestibular System
NASA Astrophysics Data System (ADS)
McCollum, Gin; Boyle, Richard
2000-03-01
Unity of movement requires vertebrates to have an ability to symmetrize along the midline. For example, human erect stance involves symmetry with respect to gravity. The mammalian vestibular system provides a mechanism for maintaining symmetries, which is also open to influence and adaptation by the rest of the organism. The vestibular system includes the inner ear endorgans and central nuclei, along with projections to oculomotor, cerebellar, thalamic, and spinal motor centers. The vestibular endorgans - the semicircular canals and the otoliths - use sensory hairs to register inertia. The vestibular endorgans are right-left symmetric and the semicircular canals form an approximately orthogonal coordinate system for angular motion. Primary afferent axons project from the endorgans to the vestibular nuclei (and a few other places). The vestibular nuclei integrate vestibular, visual, and somatosensory signals, along with a proposed copy of the voluntary motor command and signals from other central structures. The relationship between the canals and the otoliths gives rise to symmetries among neurons, in the organization among the several vestibular nuclei, and in the projections from the vestibular nuclei. These symmetries organize the space of body movements so that functional relationships are maintained in spite of the many free variables of body movement. They also provide a foundation for adaptive reinterpretation of the relationship between canal and otolith signals, for example in freefall.
Gender Symmetry, Sexism, and Intimate Partner Violence
ERIC Educational Resources Information Center
Allen, Christopher T.; Swan, Suzanne C.; Raghavan, Chitra
2009-01-01
This study of a predominantly Hispanic sample of 92 male and 140 female college students examines both gender symmetry in intimate partner violence (IPV) and inconsistent relationships found in previous studies between sexist attitudes and IPV. Results indicate that although comparable numbers of men and women perpetrate and are victimized in…
Dual string with U(1) colour symmetry
M. Ademollo; L. Brink; A. D'Adda; R. D'Auria; E. Napolitano; S. Sciuto; E. del Giudice; P. di Vecchia; S. Ferrara; F. Gliozzi; R. Musto; R. Pettorino; J. H. Schwarz
1976-01-01
The string model with a U(1) colour symmetry is analyzed in detail. It is shown that the critical dimension of this model is D = 2. There are no tachyons in the U(1) string. Moreover the massless ground state is the only physical particle of the spectrum. All other states are decoupled because of the gauge conditions. The n-point amplitudes
cover image Symmetry-breaking transitions
Loss, Daniel
: coping with uncertainty Andreas Winter 641 Statistical physics: Physicists get social Luciano Pietronero of the class Alison Wright review article 645 high-temperature superconductivity in iron-based materials a symmetry breaking transition Roman Yusupov, Tomaz Mertelj, Viktor V. Kabanov, Serguei Brazovskii, Primoz
Electroweak Symmetry Breaking from Monopole Condensation
Csaki, Csaba [Institute for High Energy Phenomenology, Newman Laboratory of Elementary Particle Physics, Cornell University, Ithaca, New York 14853 (United States); Shirman, Yuri [Department of Physics, University of California, Irvine, California 92697 (United States); Terning, John [Department of Physics, University of California, Davis, California 95616 (United States) and Physics Department, Theory Unit, CERN, Geneva (Switzerland)
2011-01-28
We argue that the electroweak symmetry of the standard model (SM) could be broken via condensation of magnetic monopole bilinears. We present an extension of the SM where this could indeed happen, and where the heavy top mass is also a consequence of the magnetic interactions.
Symmetries and retracts of quantum logics
Kallus, M.; Trnkova, V.
1987-01-01
The authors prove that there are arbitrarily many quantum logics, none of which is similar to a part of another and each of which has the group of all symmetries isomorphic to a given abstract group. Moreover, each of them contains a given logic with atomic blocks as its sublogic.
Recent Results in Symmetry Breaking Justin Pearson
Flener, Pierre
Recent Results in Symmetry Breaking Justin Pearson Uppsala University May 27, 2009 Justin Pearson Andrews), Pascal Van Hentenryck (Brown), Tom Kelsey (St Andrws), Steve Linton (St Andrews), Justin Pearson (Uppsala), Colva M. Roney-Dougal (St Andrews), Meinolf Sellmann (Brown), and Magnus Â°Agren (Uppsala) Justin
Dynamics of Symmetry Breaking and Tachyonic Preheating
Gary Felder; Juan García-Bellido; Patrick B. Greene; Lev Kofman; Andrei Linde; Igor Tkachev
2001-01-01
We reconsider the old problem of the dynamics of spontaneous symmetry breaking (SSB) using 3D lattice simulations. We develop a theory of tachyonic preheating, which occurs due to the spinodal instability of the scalar field. Tachyonic preheating is so efficient that SSB typically completes within a single oscillation as the field rolls towards the minimum of its effective potential. We
Simulating 32 Bit Architectures Using Introspective Symmetries
Sue Shee; Leroy Brisk; Terry Ackee
Unified pseudorandom communication have led to many significant advances, including erasure cod- ing and Smalltalk. this technique might seem unex- pected but has ample historical precendence. Given the current status of interposable symmetries, math- ematicians urgently desire the understanding of link- level acknowledgements, which embodies the struc- tured principles of cyberinformatics. In order to an- swer this problem, we disprove
Permutation symmetry of the scattering equations
NASA Astrophysics Data System (ADS)
Lam, C. S.
2015-02-01
Closed formulas for tree amplitudes of n -particle scatterings of gluon, graviton, and massless scalar particles have been proposed by Cachazo, He, and Yuan. They depend on (n -3 ) quantities ?? which satisfy a set of coupled scattering equations, with momentum dot products as input coefficients. These equations are known to have (n -3 )! solutions; hence, each ?? is believed to satisfy a single polynomial equation of degree (n -3 )!. In this article, we derive the transformation properties of ?? under momentum permutation and verify them with known solutions at low n , and with exact solutions at any n for special momentum configurations. For momentum configurations not invariant under a certain momentum permutation, new solutions can be obtained for the permuted configuration from these symmetry relations. These symmetry relations for ?? lead to symmetry relations for the (n -3 )!+1 coefficients of the single-variable polynomials, whose correctness are checked with the known cases at low n . The extent to which the coefficient symmetry relations can determine the coefficients is discussed.
Landau-Ginzburg Mirror Symmetry Conjecture
He, Weiqiang; Shen, Yefeng; Webb, Rachel
2015-01-01
We prove the Landau-Ginzburg mirror symmetry conjecture between invertible quasi-homogeneous polynomial singularities at all genera. That is, we show that the FJRW theory (LG A-model) of such a polynomial is equivalent to the Saito-Givental theory (LG B-model) of the mirror polynomial.
Landau-Ginzburg Mirror Symmetry Conjecture
Weiqiang He; Si Li; Yefeng Shen; Rachel Webb
2015-03-05
We prove the Landau-Ginzburg mirror symmetry conjecture between invertible quasi-homogeneous polynomial singularities at all genera. That is, we show that the FJRW theory (LG A-model) of such a polynomial is equivalent to the Saito-Givental theory (LG B-model) of the mirror polynomial.
SFT Symmetry, Mathematics (Experimental): 5212.48.
ERIC Educational Resources Information Center
Dade County Public Schools, Miami, FL.
This is the third in a series of four guidebooks on minimum course content designed to develop geometric concepts intuitively, using the "slides, flips, and turns" approach developed by the University of Illinois, Committee on School Mathematics. Topics include the development of the concept of symmetry, triangles and quadrilateral…
Unified flavor symmetry from warped dimensions
NASA Astrophysics Data System (ADS)
Frank, Mariana; Hamzaoui, Cherif; Pourtolami, Nima; Toharia, Manuel
2015-03-01
In a model of warped extra-dimensions with all matter fields in the bulk, we propose a scenario which explains all the masses and mixings of the SM fermions. In this scenario, the same flavor symmetric structure is imposed on all the fermions of the Standard Model (SM), including neutrinos. Due to the exponential sensitivity on bulk fermion masses, a small breaking of this symmetry can be greatly enhanced and produce seemingly un-symmetric hierarchical masses and small mixing angles among the charged fermion zero-modes (SM quarks and charged leptons), thus washing out visible effects of the symmetry. If the Dirac neutrinos are sufficiently localized towards the UV boundary, and the Higgs field leaking into the bulk, the neutrino mass hierarchy and flavor structure will still be largely dominated and reflect the fundamental flavor structure, whereas localization of the quark sector would reflect the effects of the flavor symmetry breaking sector. We explore these features in an example based on which a family permutation symmetry is imposed in both quark and lepton sectors.
The Symmetry Group of the Permutahedron
ERIC Educational Resources Information Center
Crisman, Karl-Dieter
2011-01-01
Although it can be visualized fairly easily and its symmetry group is easy to calculate, the permutahedron is a somewhat neglected combinatorial object. We propose it as a useful case study in abstract algebra. It supplies concrete examples of group actions, the difference between right and left actions, and how geometry and algebra can work…
Influence of Structural Symmetry on Protein Dynamics
Matsunaga, Yasuhiro; Koike, Ryotaro; Ota, Motonori; Tame, Jeremy R. H.; Kidera, Akinori
2012-01-01
Structural symmetry in homooligomeric proteins has intrigued many researchers over the past several decades. However, the implication of protein symmetry is still not well understood. In this study, we performed molecular dynamics (MD) simulations of two forms of trp RNA binding attenuation protein (TRAP), the wild-type 11-mer and an engineered 12-mer, having two different levels of circular symmetry. The results of the simulations showed that the inter-subunit fluctuations in the 11-mer TRAP were significantly smaller than the fluctuations in the 12-mer TRAP while the internal fluctuations were larger in the 11-mer than in the 12-mer. These differences in thermal fluctuations were interpreted by normal mode analysis and group theory. For the 12-mer TRAP, the wave nodes of the normal modes existed at the flexible interface between the subunits, while the 11-mer TRAP had its nodes within the subunits. The principal components derived from the MD simulations showed similar mode structures. These results demonstrated that the structural symmetry was an important determinant of protein dynamics in circularly symmetric homooligomeric proteins. PMID:23189176
Folded Fashions: Symmetry in Clothing Design.
ERIC Educational Resources Information Center
Evered, Lisa J.
1992-01-01
Fashion design is a field perceived as both a female and male domain that utilizes mathematics. Presents creative activities to teach the concept of symmetry as applied in fashion designs in the style of the famous French designer Madeleine Vionnet. (MDH)
SYMMETRIES OF TODA EQUATIONS Pantelis A. Damianou
Pantelis, Damianou
to generate nonlinear Poisson brackets for the Toda Lattice. In essence, it is an example of a system whichV, are discussed in Chen, Lee and Lin [4] and in Fokas [9]. General theory of master symmetries is dis- cussed: They preserve constants of motion, Hamiltonian vector fields and they generate a hierarchy of Poisson brackets
Geometry and symmetries in lattice spinor gravity
Wetterich, C., E-mail: c.wetterich@thphys.uni-heidelberg.de
2012-09-15
Lattice spinor gravity is a proposal for regularized quantum gravity based on fermionic degrees of freedom. In our lattice model the local Lorentz symmetry is generalized to complex transformation parameters. The difference between space and time is not put in a priori, and the euclidean and the Minkowski quantum field theory are unified in one functional integral. The metric and its signature arise as a result of the dynamics, corresponding to a given ground state or cosmological solution. Geometrical objects as the vierbein, spin connection or the metric are expectation values of collective fields built from an even number of fermions. The quantum effective action for the metric is invariant under general coordinate transformations in the continuum limit. The action of our model is found to be also invariant under gauge transformations. We observe a 'geometrical entanglement' of gauge- and Lorentz-transformations due to geometrical objects transforming non-trivially under both types of symmetry transformations. - Highlights: Black-Right-Pointing-Pointer We formulate the geometrical aspects of a proposal for a lattice regularized model of quantum gravity. Black-Right-Pointing-Pointer The vierbein shows an entanglement between Lorentz symmetry and gauge symmetry. Black-Right-Pointing-Pointer Euclidean and Minkowski signatures of the collective metric and the vierbein are described within the same functional integral.
Breaking Value Symmetry NICTA and UNSW
Walsh, Toby
.walsh@nicta.com.au Abstract Symmetry is an important factor in solving many constraint satisfaction problems. One common type have identical machines to schedule, identical jobs to process, or equiva- lently skilled personnel. For n = 12, the problem corresponds to arranging the half-notes of a scale so that all musical in
Breaking Value Symmetry # NICTA and UNSW
Walsh, Toby
.walsh@nicta.com.au Abstract Symmetry is an important factor in solving many constraint satisfaction problems. One common type have identical machines to schedule, identical jobs to process, or equiva lently skilled personnel. For n = 12, the problem corresponds to arranging the halfnotes of a scale so that all musical in
Weak Interactions with Lepton-Hadron Symmetry
S. L. Glashow; J. Iliopoulos; L. Maiani
1970-01-01
We propose a model of weak interactions in which the currents are constructed out of four basic quark fields and interact with a charged massive vector boson. We show, to all orders in perturbation theory, that the leading divergences do not violate any strong-interaction symmetry and the next to the leading divergences respect all observed weak-interaction selection rules. The model
Symmetry: Art and Science Tihany Congress, 2004
OF FOAMS W. DRENCKHAN AND D. WEAIRE Abstract: 10 15 lines. Art and science present two faces of human, biology, architecture and arts. 1 INTRODUCTION Books such as "Structure in Nature is a Strategy for DesignSymmetry: Art and Science Tihany Congress, 2004 SOME CONFLUENCES OF ART AND SCIENCE IN THE PHYSICS
Dynamical symmetry in the quadratic Zeeman effect
C. W. Clark; K. T. Taylor
1981-01-01
Zimmerman, Kash, and Kleppner (1980) postulated a hidden symmetry in atomic hydrogen in a uniform magnetic field. The present paper demonstrates that the quasi-constant of the motion in the system can be simply related to the asymptotic form of the quantum mechanical wavefunction. Accurate wavefunctions for the states of the series are computed, and evaluated by summing the weighted individual
THE SYMMETRY OF OPTIMALLY DENSE PACKINGS
with packings of regular pentagons in the Euclidean plane, E 2 . First we recall that by a ``packing'' pTHE SYMMETRY OF OPTIMALLY DENSE PACKINGS by Charles Radin * Mathematics Department, University was the densest packings of simple bodies, for instance spheres or polyhedra, in Euclidean or hyperbolic spaces
The symmetry properties of planetary magnetic fields
Raedler, K.H. (Zentral Inst. fuer Astrophysik, Potsdam-Babelsberg (East Germany)); Ness, N.F. (Univ. of Delaware, Newark (United States))
1990-03-01
This paper provides a comparative study of the geometrical structures of the magnetic fields of Earth, Jupiter, Saturn, and Uranus, starting from the traditional multipolar representations of these fields. For Earth, Jupiter, and Saturn the centered dipole, quadrupole, and octupole contributions are included, while at Uranus, only the dipole and quadrupole contributoins are considered. The magnetic fields are analyzed by decomposing them into those parts which have simple symmetry properties with respect to the rotation axis and the equatorial plane. It is found that there are a number of common features of the magnetic fields of Earth and Jupiter. Compared to Earth and Jupiter, the Saturnian field exhibits not only a high degree of symmetry about the rotation axis, by now rather well known, but also a high degree of antisymmetry about the equatorial plane. The Uranian field shows strong deviations from both such symmetries. Nevertheless, there remain features common to all four planets. The implications of these results for dynamo models are discussed. With a vgiew to Cowling's theorem the symmetry of the fields is investigated with respect to not only the rotation axis but also to other axes intersecting the plaentary center. Surprisingly, the high degree of asymmetry of the Uranian field that is observed with respect to the rotation axis reduces considerably to being compare to that for Earth or Jupiter when the appropriate axis is employed.
Gauge Symmetry Breaking in a Throat Geometry
Jacek Pawe?czyk
2008-02-04
We analyze behaviour of D3-branes in BGMPZ throat geometry. We show that although single brane has some of the moduli stabilized multi-brane system tends to expand and form a bound state. Such a system loses non-abelian gauge symmetry.
Einstein-Yang-Mills theory: Asymptotic symmetries
NASA Astrophysics Data System (ADS)
Barnich, Glenn; Lambert, Pierre-Henry
2013-11-01
Asymptotic symmetries of the Einstein-Yang-Mills system with or without cosmological constant are explicitly worked out in a unified manner. In agreement with a recent conjecture, one finds a Virasoro-Kac-Moody type algebra not only in three dimensions but also in the four-dimensional asymptotically flat case.
Multipartite invariant states. II. Orthogonal symmetry
Chruscinski, Dariusz; Kossakowski, Andrzej [Institute of Physics, Nicolaus Copernicus University, GrudziaPdzka 5/7, 87-100 Torun (Poland)
2006-06-15
We construct a class of multipartite states possessing orthogonal symmetry. This new class contains multipartite states which are invariant under the action of local unitary operations introduced in our preceding paper [Phys. Rev. A 73, 062314 (2006)]. We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
Asymmetric Twin Representation: the Transfer Matrix Symmetry
Anastasia Doikou
2007-01-10
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic -- independent of the choice of model -- open transfer matrix with a trivial left boundary. In addition it is shown that the boundary quantum algebra is the centralizer of the $B$ type Hecke algebra. We then focus on the asymmetric twin representation of the boundary Temperley-Lieb algebra. More precisely, by exploiting exchange relations dictated by the reflection equation we show that the transfer matrix with trivial boundary conditions enjoys the recognized ${\\cal U}_{q}(sl_2) \\otimes {\\cal U}_{{\\mathrm i}}(sl_2)$ symmetry. When a non-diagonal boundary is implemented the symmetry as expected is reduced, however again certain familiar boundary non-local charges turn out to commute with the corresponding transfer matrix.