Teaching Point-Group Symmetry with Three-Dimensional Models
ERIC Educational Resources Information Center
Flint, Edward B.
2011-01-01
Three tools for teaching symmetry in the context of an upper-level undergraduate or introductory graduate course on the chemical applications of group theory are presented. The first is a collection of objects that have the symmetries of all the low-symmetry and high-symmetry point groups and the point groups with rotational symmetries from 2-fold…
Parity-time symmetry broken by point-group symmetry
Fernández, Francisco M. Garcia, Javier
2014-04-15
We discuss a parity-time (PT) symmetric Hamiltonian with complex eigenvalues. It is based on the dimensionless Schrödinger equation for a particle in a square box with the PT-symmetric potential V(x, y) = iaxy. Perturbation theory clearly shows that some of the eigenvalues are complex for sufficiently small values of |a|. Point-group symmetry proves useful to guess if some of the eigenvalues may already be complex for all values of the coupling constant. We confirm those conclusions by means of an accurate numerical calculation based on the diagonalization method. On the other hand, the Schrödinger equation with the potential V(x, y) = iaxy{sup 2} exhibits real eigenvalues for sufficiently small values of |a|. Point group symmetry suggests that PT-symmetry may be broken in the former case and unbroken in the latter one.
Anticoherence of spin states with point-group symmetries
NASA Astrophysics Data System (ADS)
Baguette, D.; Damanet, F.; Giraud, O.; Martin, J.
2015-11-01
We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group-symmetric sets of points. We provide three different characterizations of anticoherence and establish a link between point symmetries, anticoherence, and classes of states equivalent through stochastic local operations with classical communication. We then investigate in detail the case of small numbers of qubits and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.
Anticoherence of spin states with point group symmetries
D. Baguette; F. Damanet; O. Giraud; J. Martin
2015-10-04
We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.
Crystallography of decahedral and icosahedral particles. II - High symmetry orientations
NASA Technical Reports Server (NTRS)
Yang, C. Y.; Yacaman, M. J.; Heinemann, K.
1979-01-01
Based on the exact crystal structure of decahedral and icosahedral particles, high energy electron diffraction patterns and image profiles have been derived for various high symmetry orientations of the particles with respect to the incident beam. These results form a basis for the identification of small metal particle structures with advanced methods of transmission electron microscopy.
Symmetry, stability, and elastic properties of icosahedral incommensurate crystals
Bak, P.
1985-11-01
The symmetry and stability of icosahedral incommensurate structures and generalized two-dimensional Penrose pentagonal structures are studied. The crystallographic properties of Penrose lattices are described by five-dimensional (5D) super space groups, and the icosahedral structures are described by 6D space groups, with or without improper translations. The density in real space is given as the density along a three-dimensional plane in this 6D space. The fivefold symmetry of the diffraction spectrum of Mn-Al alloys, which is inconsistent with three-dimensional translational invariance, reflects a fivefold rotation axis of the 6D space group. The six continuous degrees of freedom associated with the 6D space represent the usual three orthogonal rigid displacements of the crystal, plus three phase shifts associated with internal rearrangements, leading to three acoustic-phonon modes and three phason modes. There are two independent elastic constants, which is fewer than in any regular crystal, representing one-dimensional and five-dimensional irreducible strains, respectively. If the phase degrees of freedom are included, there are five generalized elastic constants. The stability of icosahedral structures and ''lyotropic'' Penrose structures can be understood from a phenomenological Landau theory. The ideal icosahedral crystal has perfect positional order, which is stable with respect to thermal fluctuations at low temperatures. The melting transition is first order.
Virus templated plasmonic nanoclusters with icosahedral symmetry via directed assembly
NASA Astrophysics Data System (ADS)
Ratna, Banahalli; Fontana, Jake; Dressick, Walter; Phelps, Jamie; Johnson, John; Sampson, Travian; Rendell, Ronald; Soto, Carissa
2015-03-01
Controlling the spatial and orientational order of plasmonic nanoparticles may lead to structures with novel electromagnetic properties and applications such as sub-wavelength imaging and ultra-sensitive chemical sensors. Here we report the directed assembly of three-dimensional, icosahedral plasmonic nanoclusters with resonances at visible wavelengths. We show using transmission electron microcopy and in situ dynamic light scattering the nanoclusters consist of twelve gold nanospheres attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. We measured the bulk absorbance from aqueous suspensions of nanoclusters and reproduced the major features of the spectrum using finite-element simulations. Furthermore, because the viruses are easily produced in gram quantities the directed assembly approach is capable of high-throughput, providing a strategy to realize large quantities for applications. NRL summer intern under the HBCU/MI Summer Research Program.
The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry
ERIC Educational Resources Information Center
Nottis, Katharyn E. K.; Kastner, Margaret E.
2005-01-01
Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four…
Cao, Wenwu
Allowed mesoscopic point group symmetries in domain average engineering of perovskite ferroelectric average engineering in proper ferroelectric systems arising from the cubic Pm3¯m symmetry perovskite4 Both solid solution systems have a perovskite structure. Poling along one of the pseudocubic axes
Virtual and Printed 3D Models for Teaching Crystal Symmetry and Point Groups
ERIC Educational Resources Information Center
Casas, Lluís; Estop, Euge`nia
2015-01-01
Both, virtual and printed 3D crystal models can help students and teachers deal with chemical education topics such as symmetry and point groups. In the present paper, two freely downloadable tools (interactive PDF files and a mobile app) are presented as examples of the application of 3D design to study point-symmetry. The use of 3D printing to…
Mechanical Deformation of Spherical Viruses with Icosahedral Symmetry
Vliegenthart, Gerard Adriaan; Gompper, Gerhard
2006-01-01
Virus capsids and crystalline surfactant vesicles are two examples of self-assembled shells in the nano- to micrometer size range. Virus capsids are particularly interesting since they have to sustain large internal pressures while encapsulating and protecting the viral DNA. We therefore study the mechanical properties of crystalline shells of icosahedral symmetry on a substrate under a uniaxial applied force by computer simulations. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number of elementary building blocks N (the capsomers in the case of viral shells), the Föppl-von Kármán number ? (which characterizes the relative importance of shear and bending elasticity), and the confining geometry. In particular, we show that whereas large shells are well described by continuum elasticity-theory, small shells of the size of typical viral capsids behave differently already for small deformations. Our results are essential to extract quantitative information about the elastic properties of viruses and vesicles from deformation experiments. PMID:16679375
Teaching Molecular Symmetry of Dihedral Point Groups by Drawing Useful 2D Projections
ERIC Educational Resources Information Center
Chen, Lan; Sun, Hongwei; Lai, Chengming
2015-01-01
There are two main difficulties in studying molecular symmetry of dihedral point groups. One is locating the C[subscript 2] axes perpendicular to the C[subscript n] axis, while the other is finding the s[subscript]d planes which pass through the C[subscript n] axis and bisect the angles formed by adjacent C[subscript 2] axes. In this paper, a…
Icosahedral (A5) Family Symmetry and the Golden Ratio Prediction for Solar Neutrino Mixing
Everett, Lisa L
2008-01-01
We investigate the possibility of using icosahedral symmetry as a family symmetry group in the lepton sector. The rotational icosahedral group, which is isomorphic to A5, the alternating group of five elements, provides a natural context in which to explore (among other possibilities) the intriguing hypothesis that the solar neutrino mixing angle is governed by the golden ratio. We present a basic toolbox for model-building using icosahedral symmetry, including explicit representation matrices and tensor product rules. As a simple application, we construct a minimal model at tree level in which the solar angle is related to the golden ratio, the atmospheric angle is maximal, and the reactor angle vanishes to leading order. The approach provides a rich setting in which to investigate the flavor puzzle of the Standard Model.
Virus-Templated Plasmonic Nanoclusters with Icosahedral Symmetry via Directed Self-Assembly
Fontana, Jake; Dressick, Walter J; Phelps, Jamie; Johnson, John E; Rendell, Ronald W; Sampson, Travian; Ratna, Banahalli R; Soto, Carissa M
2014-01-01
The assembly of plasmonic nanoparticles with precise spatial and orientational order may lead to structures with new electromagnetic properties at optical frequencies. The directed self-assembly method presented controls the interparticle-spacing and symmetry of the resulting nanometer-sized elements in solution. The self-assembly of three-dimensional (3D), icosahedral plasmonic nanosclusters (NCs) with resonances at visible wavelengths is demonstrated experimentally. The ideal NCs consist of twelve gold (Au) nanospheres (NSs) attached to thiol groups at predefined locations on the surface of a genetically engineered cowpea mosaic virus with icosahedral symmetry. In situ dynamic light scattering (DLS) measurements confirm the NSs assembly on the virus. Transmission electron micrographs (TEM) demonstrate the ability of the self-assembly method to control the nanoscopic symmetry of the bound NSs, which reflects the icosahedral symmetry of the virus. Both, TEM and DLS show that the NCs comprise of a distribution of capsids mostly covered (i.e., 6–12 NS/capsid) with NSs. 3D finite-element simulations of aqueous suspensions of NCs reproduce the experimental bulk absorbance measurements and major features of the spectra. Simulations results show that the fully assembled NCs give rise to a 10-fold surface-averaged enhancement of the local electromagnetic field. PMID:24733721
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.
Bodner, Mark; Bourret, Emmanuel; Patera, Jiri; Szajewska, Marzena
2015-05-01
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583-591, (2014), PLOS ONE, 10.1371/journal.pone.0084079] describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space {\\bb R}^3 as a mechanism of generating higher fullerenes from C60. The icosahedral symmetry of C60 can be seen as the junction of 17 orbits of a symmetric subgroup of order 4 of the icosahedral group of order 120. This subgroup is noted by A1 × A1, because it is isomorphic to the Weyl group of the semi-simple Lie algebra A1 × A1. Thirteen of the A1 × A1 orbits are rectangles and four are line segments. The orbits form a stack of parallel layers centered on the axis of C60 passing through the centers of two opposite edges between two hexagons on the surface of C60. These two edges are the only two line segment layers to appear on the surface shell. Among the 24 convex polytopes with shell formed by hexagons and 12 pentagons, having 84 vertices [Fowler & Manolopoulos (1992). Nature (London), 355, 428-430; Fowler & Manolopoulos (2007). An Atlas of Fullerenes. Dover Publications Inc.; Zhang et al. (1993). J. Chem. Phys. 98, 3095-3102], there are only two that can be identified with breaking of the H3 symmetry to A1 × A1. The remaining ones are just convex shells formed by regular hexagons and 12 pentagons without the involvement of the icosahedral symmetry. PMID:25921498
Kumar, Mohit
2013-01-01
Minor group human rhinoviruses bind low-density lipoprotein (LDL) receptors for endocytosis. Once they are inside endosomes, the acidic pH triggers their dissociation from the receptors and conversion into hydrophobic subviral A particles; these attach to the membrane and transfer their single-strand, positive-sense RNA genome into the cytosol. Here, we allowed human rhinovirus 2 (HRV2) A particles, produced in vitro by incubation at pH 5.4, to attach to liposomes; cryo-electron microscopy 3-dimensional single-particle image reconstruction revealed that they bind to the membrane around a 2-fold icosahedral symmetry axis. PMID:23946453
Crystallography of decahedral and icosahedral particles. I - Geometry of twinning
NASA Technical Reports Server (NTRS)
Yang, C. Y.
1979-01-01
The crystal structure of the tetrahedral twins in multiply-twinned particles with decahedral and icosahedral point group symmetries has been examined and correlated with the face-centered cubic structure. Details on the crystal structure as well as the geometrical relationships among twins in each particle are presented. These crystallographic facts serve as a basis for the interpretation of small particle images obtained with advanced methods of transmission electron microscopy.
Protruding knob-like proteins violate local symmetries in an icosahedral marine virus
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
Assembly of simple icosahedral viruses.
Almendral, José M
2013-01-01
Icosahedral viruses exhibit elegant pathways of capsid assembly and maturation regulated by symmetry principles. Assembly is a dynamic process driven by consecutive and genetically programmed morphogenetic interactions between protein subunits. The non-symmetric capsid subunits are gathered by hydrophobic contacts and non-covalent interactions in assembly intermediates, which serve as blocks to build a symmetric capsid. In some cases, non-symmetric interactions among intermediates are involved in assembly, highlighting the remarkable capacity of capsid proteins to fold into demanding conformations compatible with a closed protein shell. In this chapter, the morphogenesis of structurally simple icosahedral viruses, including representative members of the parvoviruses, picornaviruses or polyomaviruses as paradigms, is described in some detail. Icosahedral virus assembly may occur in different subcellular compartments and involve a panoplia of cellular and viral factors, chaperones, and protein modifications that, in general, are still poorly characterized. Mechanisms of viral genome encapsidation may imply direct interactions between the genome and the assembly intermediates, or active packaging into a preformed empty capsid. High stability of intermediates and proteolytic cleavages during viral maturation usually contribute to the overall irreversible character of the assembly process. These and other simple icosahedral viruses were pioneer models to understand basic principles of virus assembly, continue to be leading subjects of morphogenetic analyses, and have inspired ongoing studies on the assembly of larger viruses and cellular and synthetic macromolecular complexes. PMID:23737056
Growth of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Socolar, Joshua; Hann, Connor; Steinhardt, Paul
2015-03-01
The discovery of an icosahedral quasicrystal that formed naturally in a rock sample originating from a meteorite highlights fundamental questions about quasicrystal formation. ?The growth of a well-ordered quasicrystal through kinetics dominated by local energetics is known to be possible in principle for 2D systems: a Penrose tiling, for example, can be grown from a particular type of small seed by adding tiles only to surface sites where the tile type and orientation are unambiguously determined by already placed tiles that share a vertex. We consider the generalization of this result to icosahedral quasicrystal tilings comprised of Ammann rhombohedra. Numerical simulations strongly suggest that infinite, well-ordered, icosahedral quasicrystals can be generated. Unlike the 2D case, defects are generated outside the original seed, but the number of such defects appears to grow only linearly with the cluster radius. Analysis of the lift of the tiling to a 6D hypercubic lattice provides key insights into the growth mechanism.
About the atomic structures of icosahedral quasicrystals
NASA Astrophysics Data System (ADS)
Quiquandon, Marianne; Gratias, Denis
2014-01-01
This paper is a survey of the crystallographic methods that have been developed these last twenty five years to decipher the atomic structures of the icosahedral stable quasicrystals since their discovery in 1982 by D. Shechtman. After a brief recall of the notion of quasiperiodicity and the natural description of Z-modules in 3-dim as projection of regular lattices in N>3-dim spaces, we give the basic geometrical ingredients useful to describe icosahedral quasicrystals as irrational 3-dim cuts of ordinary crystals in 6-dim space. Atoms are described by atomic surfaces (ASs) that are bounded volumes in the internal (or perpendicular) 3-dim space and the intersections of which with the physical space are the actual atomic positions. The main part of the paper is devoted to finding the major properties of quasicrystalline icosahedral structures. As experimentally demonstrated, they can be described with a surprisingly few high symmetry ASs located at high symmetry special points in 6-dim space. The atomic structures are best described by aggregations and intersections of high symmetry compact interpenetrating atomic clusters. We show here that the experimentally relevant clusters are derived from one generic cluster made of two concentric triacontahedra scaled by ? and an external icosidodecahedron. Depending on which ones of the orbits of this cluster are eventually occupied by atoms, the actual atomic clusters are of type Bergman, Mackay, Tsai and others….
Janner, A
2011-11-01
The RNA viruses cowpea chlorotic mottle, satellite tobacco mosaic, pariacoto and MS2, already considered in part IV of this series of papers [Janner, A. (2011a), Acta Cryst. A67, 517-520], are investigated further, with the aim to arrive at a possible physical basis for their structural properties. The shell structure of the filled capsid is analyzed in terms of successive spherical boundaries of the sets of icosahedral equivalent chains. By inversion in the sphere enclosing the capsid, the internal boundaries are transformed into external ones, which are more easily visualized. This graphical procedure reveals the presence of regularly spaced shells with boundaries fitting with anti-nodal surfaces of the virus considered as an elastic resonator. The centers of gravity of the various chains occur in the nodal regions of eigenvibrations with wavelength ? = R(0)/K(0), where R(0) is the radius of the virus and K(0) takes one of the values 12, 6, 4, 3, depending on the mode. The resonator model is consistent with practically all spherical shell boundaries, whereas deviations are observed for the icosahedral axial modes, which apparently play a secondary role with respect to the spherical ones. Both the spherical and the axial anti-nodal surfaces fit very well with the packed structure of the viruses in the crystal which, accordingly, is expected to have eigenfrequencies related to those of the virus. These results open the way to a better understanding of the possibility of breaking the capsid using resonant forced oscillations excited, for example, by an applied elastic shock or by irradiation with femtosecond laser pulses, as already realised by K.-T. Tsen and co-workers. An alternative `plywood' model connected to the extreme elastic properties of the capsid is also considered. PMID:22011468
Entropy-driven formation of large icosahedral colloidal clusters by spherical confinement.
de Nijs, Bart; Dussi, Simone; Smallenburg, Frank; Meeldijk, Johannes D; Groenendijk, Dirk J; Filion, Laura; Imhof, Arnout; van Blaaderen, Alfons; Dijkstra, Marjolein
2015-01-01
Icosahedral symmetry, which is not compatible with truly long-range order, can be found in many systems, such as liquids, glasses, atomic clusters, quasicrystals and virus-capsids. To obtain arrangements with a high degree of icosahedral order from tens of particles or more, interparticle attractive interactions are considered to be essential. Here, we report that entropy and spherical confinement suffice for the formation of icosahedral clusters consisting of up to 100,000 particles. Specifically, by using real-space measurements on nanometre- and micrometre-sized colloids, as well as computer simulations, we show that tens of thousands of hard spheres compressed under spherical confinement spontaneously crystallize into icosahedral clusters that are entropically favoured over the bulk face-centred cubic crystal structure. Our findings provide insights into the interplay between confinement and crystallization and into how these are connected to the formation of icosahedral structures. PMID:25173580
A group theoretical approach to structural transitions of icosahedral quasicrystals and point arrays
Emilio Zappa; Eric C. Dykeman; Reidun Twarock
2015-12-07
In this paper we describe a group theoretical approach to the study of structural transitions of icosahedral quasicrystals and point arrays. We apply the concept of Schur rotations, originally proposed by Kramer, to the case of aperiodic structures with icosahedral symmetry; these rotations induce a rotation of the physical and orthogonal spaces invariant under the icosahedral group, and hence, via the cut-and-project method, a continuous transformation of the corresponding model sets. We prove that this approach allows for a characterisation of such transitions in a purely group theoretical framework, and provide explicit computations and specific examples. Moreover, we prove that this approach can be used in the case of finite point sets with icosahedral symmetry, which have a wide range of applications in carbon chemistry (fullerenes) and biology (viral capsids).
NASA Astrophysics Data System (ADS)
Blatov, V. A.; Ilyushin, G. D.
2012-12-01
A database of intermetallic compounds has been compiled using the TOPOS program package. This database includes 514 topological types, containing 12- and 13-atom icosahedral i clusters. An isolated group of 1649 i clusters is described by 14 point groups and their maximum symmetry D 3 d (bar 3 m) and T h ( m bar 3) is established, respectively, in 47 and 25 types of crystal structures. A structural analysis of the outer quasispherical shells showed that local 63-atom i configurations 1@12@50, which contain 50 atoms in the second layer, are implemented in 8 out of 19 cases. Examples of new topologically different types of 50-atom D50 deltahedra in the Samson phases ?-Mg23Al30 and ?-Mg2Al3 are presented. Four topologically different sites with coordination numbers of 5, 6, 6, or 7 are established in the ? shell and seven sites with coordination numbers of 5, 5, 6, 6, 6, 6, or 7 are found in the ? shell. The inner i clusters for the ?-Mg2Al3 structure (with the symmetry bar 3 m) and the ?-Mg23Al30 structure (with the symmetry bar 3) have a similar chemical composition, i.e., Mg7Al6 and Mg6Al7, and their 50-atom shells are chemically identical to 18Mg + 32Al. The configurations found supplement the series of known two-layer icosahedral Bergman and Mackay clusters in the form of deltahedra with 32- and 42-atom shells.
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.
Platonic solids back in the sky: Icosahedral inflation
Jonghee Kang; Alberto Nicolis
2015-09-09
We generalize the model of solid inflation to an anisotropic cosmic solid. Barring fine tunings, the observed isotropy of the cosmological background and of the scalar two-point function isolate the icosahedral group as the only possible symmetry group of such a solid. In such a case, higher-point correlation functions---starting with the three-point one---are naturally maximally anisotropic, which makes the standard detection strategies highly inefficient and calls for a dedicated analysis of CMB data. The tensor two-point function can also be highly anisotropic, but only in the presence of sizable higher-derivative couplings.
Platonic solids back in the sky: Icosahedral inflation
Kang, Jonghee
2015-01-01
We generalize the model of solid inflation to an anisotropic cosmic solid. Barring fine tunings, the observed isotropy of the cosmological background and of the scalar two-point function isolate the icosahedral group as the only possible symmetry group of such a solid. In such a case, higher-point correlation functions---starting with the three-point one---are naturally maximally anisotropic, which makes the standard detection strategies highly inefficient and calls for a dedicated analysis of CMB data. The tensor two-point function can also be highly anisotropic, but only in the presence of sizable higher-derivative couplings.
Irreducible representations of some point groups which are isomorphic to some dihedral groups
NASA Astrophysics Data System (ADS)
Yahya, Zainab; Ali, Nor Muhainiah Mohd; Sarmin, Nor Haniza; Adnan, Noor Asma'Adny Mohd; Rahmat, Hamisan
2014-07-01
Let G be a finite group and M a vector space over K. A representation of G with representation space M is a homomorphism of G into GL(M), where GL(M) denotes the group of all invertible linear transformations of a vector space M onto itself. Furthermore, any representation of G is irreducible if the only subrepresentations of G are {0} and G. A point group is a group of symmetry operations all of which leave at least one point unmoved. There are some point groups which are isomorphic to dihedral groups. In this paper, the irreducible representations of some point groups which are isomorphic to some dihedral groups are given.
Icosahedral Platinum Alloy Nanocrystals with Enhanced Electrocatalytic Activities
Chen, Sow-Hsin
to be built into the icosahedral (Ih) nanoparticle.3a For a regular icosahedral nanocrystal, it is made of 20 environment in an inert reducing gas may limit the oxidative etching of these twinned particles.9
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
Preparation and properties of icosahedral borides
Aselage, T.L.; Tallant, D.R.; Gieske, J.H.; Van Deusen, S.B.; Tissot, R.G.
1989-01-01
The electronic and thermal transport properties of refractory icosahedral boron-rich solids suggest the utilization of these unique solids as high-temperature semiconductors. Such applications will require high-quality, well-characterized materials. A variety of techniques have been used to prepare powders, ceramics, and single crystals of boron carbides and the icosahedral boron pnictides. X-ray diffraction, Raman spectroscopy, and ultrasound measurements have been used to probe boron carbide sample quality. Each of these measurements supports the structural model of boron carbides developed from analysis of transport data. Initial electrical conductivity (E{sub a} {approx} 0.17 eV) is consistent with a bipolaronic hopping mechanism. 43 refs., 6 figs., 1 tab.
Icosahedral DNA nanocapsules by modular assembly.
Bhatia, Dhiraj; Mehtab, Shabana; Krishnan, Ramya; Indi, Shantinath S; Basu, Atanu; Krishnan, Yamuna
2009-01-01
It's a trap! DNA polyhedra formed through molecular self-assembly may function as nanocapsules for the targeted delivery of encapsulated entities. This functional aspect was demonstrated for the most complex DNA-based platonic solid: During the stepwise amalgamation of discrete polyhedra to form icosahedra, gold nanoparticles (GNPs) were encapsulated from solution (see illustration and TEM image of icosahedral cages containing GNPs). PMID:19222079
Nonicosahedral Equilibrium Overlayers of Icosahedral Quasicrystals
NASA Astrophysics Data System (ADS)
Yurechko, M.; Grushko, B.; Ebert, Ph.
2005-12-01
We demonstrate that icosahedral Al-Pd-Mn quasicrystals can have nonicosahedrally ordered thermodynamic equilibrium overlayers. The formation of orthorhombic or decagonal equilibrium surface structures is determined by the phase equilibrium of the ternary alloy at given composition and temperature as well as by the surface acting as nucleation site. Nonequilibrium steady-state orthorhombic and hexagonal structures can also be derived with the same methodology when taking preferential evaporation into account. The results describe consistently all presently observed surface structures.
Structure factor for an icosahedral quasicrystal within a statistical approach.
Strzalka, Radoslaw; Buganski, Ireneusz; Wolny, Janusz
2015-05-01
This paper describes a detailed derivation of a structural model for an icosahedral quasicrystal based on a primitive icosahedral tiling (three-dimensional Penrose tiling) within a statistical approach. The average unit cell concept, where all calculations are performed in three-dimensional physical space, is used as an alternative to higher-dimensional analysis. Comprehensive analytical derivation of the structure factor for a primitive icosahedral lattice with monoatomic decoration (atoms placed in the nodes of the lattice only) presents in detail the idea of the statistical approach to icosahedral quasicrystal structure modelling and confirms its full agreement with the higher-dimensional description. The arbitrary decoration scheme is also discussed. The complete structure-factor formula for arbitrarily decorated icosahedral tiling is derived and its correctness is proved. This paper shows in detail the concept of a statistical approach applied to the problem of icosahedral quasicrystal modelling. PMID:25921496
Stability of the X -Y phase of the two-dimensional C4 point group insulator
NASA Astrophysics Data System (ADS)
de Leeuw, Bart; Küppersbusch, Carolin; Juri?i?, Vladimir; Fritz, Lars
2015-06-01
Noninteracting insulating electronic states of matter can be classified according to their symmetries in terms of topological invariants which can be related to effective surface theories. These effective surface theories are in turn topologically protected against the effects of disorder. Topological crystalline insulators are, on the other hand, trivial in the sense of the above classification but still possess surface modes. In this paper we consider an extension of the Bernevig-Hughes-Zhang model that describes a point group insulator. We explicitly show that the surface properties of this state can be as robust as in topologically nontrivial insulators but only if the Sz component of the spin is conserved. However, in the presence of Rashba spin-orbit coupling this protection vanishes, and the surface states localize, even if the crystalline symmetries are intact on average.
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.
3 nj-symbols and harmonic superposition coefficients: an icosahedral abacus
NASA Astrophysics Data System (ADS)
Aquilanti, Vincenzo; Coletti, Cecilia
2001-08-01
Angular momentum recoupling coefficients of angular momentum theory and matrix elements for basis set transformation of hyperspherical harmonics enjoy properties and sum rules crucial for applications but complicated without the guidance of graphical techniques. These coefficients being related to Racah's polynomials, the graphs also apply to polynomials of the hypergeometric family, their q-analogues and their `elliptic' extensions. A useful `abacus' exploiting the connections with presentations of icosahedral and related symmetries is introduced. Particular and limiting cases, such as those of the semiclassical type, allow a unified view of properties of angular and hyperangular momentum algebra, including relationships among vector coupling coefficients and rotation matrix elements.
Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal.
Cui, C; Nugent, P J; Shimoda, M; Ledieu, J; Fournée, V; Tsai, A P; McGrath, R; Sharma, H R
2014-01-01
The structure of the twofold surface of the icosahedral (i-)Ag-In-Yb quasicrystal has been investigated using low energy electron diffraction (LEED) and scanning tunneling microscopy (STM). The LEED confirms that the surface exhibits quasicrystalline long range order with the twofold rotational symmetry expected from the bulk. STM images reveal a step-terrace structure with terrace size comparable to that of the other high symmetry surfaces of the same quasicrystal. The distribution of step heights and high resolution STM images of terraces suggest that the surface terminates at bulk planes that intersect the center of rhombic triacontahedral clusters, the building blocks of the system, as in the case of the threefold and fivefold surfaces of the system. These planes are rich in Yb and In. No facets are observed on the surface, suggesting that the twofold surface is as stable as the other high symmetry surfaces. PMID:24263167
On The Structure of Al-Pd-Mn Icosahedral Phase
NASA Astrophysics Data System (ADS)
Tamura, Nobumichi; Robertson, J. Lee; Moss, Simon C.
1998-03-01
The purpose of this work is to obtain an improvement of the existing models for icosahedral quasicrystals, by combining the results obtained from a 6D-dimensional approach with those obtained by a 3D refinement of a hypothetical approximant structure with respect to the observed intensities of the icosahedral phase. We applied this method to a set of integrated intensities of 832 X-ray, and 260 neutron independent reflections of the icosahedral Al-Pd-Mn quasicrystal. Section maps of the 6D electron density function display faceted atomic surfaces with rather complex shapes. Moreover, these atomic surfaces appear to be slightly bent with components in the physical space. Refinements by simulated annealing of hypothetical approximants show that their structures are essentially based on well-defined icosahedral clusters related to the Mackay clusters. The radii of the icosahedral polyhedra forming the clusters are slightly different from those obtained with "flat" atomic surfaces, and lead to more realistic interatomic distances than those provided by geometric models of icosahedral phases. We show that the bending of the atomic surfaces is directly connected to the accommodation of interatomic distances between different kinds of atoms.
3D Printed Molecules and Extended Solid Models for Teaching Symmetry and Point Groups
ERIC Educational Resources Information Center
Scalfani, Vincent F.; Vaid, Thomas P.
2014-01-01
Tangible models help students and researchers visualize chemical structures in three dimensions (3D). 3D printing offers a unique and straightforward approach to fabricate plastic 3D models of molecules and extended solids. In this article, we prepared a series of digital 3D design files of molecular structures that will be useful for teaching…
Icosahedral Gold Cage Clusters: M@Au??? (M = V, Nb, and Ta)
Zhai, Hua JIN.; Li, Jun; Wang, Lai S.
2004-11-01
We report the observation and characterization of a series of stable bimetallic 18-valence-electron clusters containing a highly symmetric 12-atom icosahedral Au cage with an encapsulated central heteroatom of group VB transition metals, M-Au??? (M = V, Nb, Ta). Electronic and structural properties of these clusters were probed by anion photoelectron spectroscopy and theoretical calculations. Characteristics of the M-Au??? species include their remarkably high binding energies and relatively simple spectral features, which reflect their high symmetry and stability. The adiabatic electronic binding energies of M-Au??? were measured to be 3.70 ? 0.03, 3.77 ? 0.03, and 3.76 ? 0.03 eV for M = V, Nb, and Ta, respectively. Comparison of density functional calculations with experimental data established the highly symmetric icosahedral structures for the 18-electron cluster anions, which may be promising building blocks for cluster-assembled nanomaterials in the form of stoichiometric [M-Au???]X? salts.
Pease, Leonard F; Tsai, De-Hao; Brorson, Kurt A; Guha, Suvajyoti; Zachariah, Michael R; Tarlov, Michael J
2011-03-01
We present a rapid and quantitative method to physically characterize the structure and stability of viruses. Electrospray differential mobility analysis (ES-DMA) is used to determine the size of capsomers (i.e., hexons) and complete capsids. We demonstrate how to convert the measured mobility size into the icosahedral dimensions of a virus, which for PR772 become 68.4 nm for vertex-to-vertex, 54.4 nm for facet-to-facet, and 58.2 nm for edge-to-edge lengths, in reasonable agreement with dimensions from transmission electron microscopy for other members of the family Tectiviridae (e.g., PRD1). These results indicate ES-DMA's mobility diameter most closely approximates the edge-to-edge length. Using PR772's edge length (36.0 nm) and the size of the major capsid hexon (?8.4 nm) from ES-DMA with icosahedral geometry, PR772's T = 25 symmetry is confirmed and the number of proteins in the capsid shell is determined. We also demonstrate the use of ES-DMA to monitor the temporal disintegration of PR772, the thermal degradation of PP7, and the appearance of degradation products, essential to viral stability assays. These results lay groundwork essential for the use of ES-DMA for a variety of applications including monitoring of vaccine and gene therapy vector products, confirmation of viral inactivation, and theoretical studies of self-assembling macromolecular structures. PMID:21302934
NASA Astrophysics Data System (ADS)
Vail, Benjamin; Aris, Damian; Scarlete, Mihai
The present study proposes an algorithm for point-group analysis (PGA) of the vibrational activity of molecules, adapted for the efficient utilization of the linear packages incorporated into currently available symbolic computation engines (SCE), such as Maple, Mathcad, or Mathematica. By the creation of this algorithm, we have addressed the need for a numerically friendly environment, outside the "locked" procedures within molecular modeling packages, which will preserve its flexibility, transparency, and maneuverability, regardless of the complexity of the calculation. The format of the character tables of the point groups significant to chemical species has been adapted to ensure automatic numerization, and consistent input of the alphanumeric data from the existent character tables into the SCE templates designed to perform the PGA. The two proposed templates address two complementary objectives: (i) a totally transparent and interactive file has been designed to allow access to all intermediate results at all levels of the procedure for easy implementation of potential additional modules of special interest 1-5, and (ii) for fast output and routine calculations of the IR/Raman vibrational activity of molecules based on their point groups, a totally automatic file with a highly simplified input interface has been designed. The numerical interface conveniently replaces the usual graphic user interface that is common to most commercial molecular modeling software packages, requiring minimum input determination. The structure for both templates is based on the use of the digitized forms for the character tables, for the symmetry operations, and for symmetry elements, all saved in dedicated libraries uploaded to the numerical database of the SCE.
Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles
Shevchenko, Vladimir Ya. Madison, Alexey E.; Mackay, Alan L.
2007-03-01
In icosahedral carbon nanoparticles, the diamond-like core can undergo a reversible topological transition into and coexist coherently with the onion shells. The general approach for describing and designing complex hierarchical icosahedral structures is discussed. Structural models of icosahedral carbon nanoparticles in which the local arrangement of atoms is virtually identical to that in diamond are derived. It is shown that icosahedral diamond-like particles can be transformed into onion-like shell structures (and vice versa) by the consecutive smoothing (puckering) of atomic networks without disturbance of their topological integrity. The possibility of coherent coexistence of icosahedral diamond-like core with onion shells is shown.
Melting and Equilibrium Shape of Icosahedral Gold Nanoparticles
Teitel, Stephen L.
Melting and Equilibrium Shape of Icosahedral Gold Nanoparticles Yanting Wang a , S. Teitel a} surfaces have shown that, unlike the {100} and {110} surfaces which melt below the bulk melting temperature how the high stability of the {111} facets effects the melting and equilibrium shape
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
Reconstructing an icosahedral virus from single-particle diffraction experiments
NASA Astrophysics Data System (ADS)
Saldin, D. K.; Poon, H.-C.; Schwander, P.; Uddin, M.; Schmidt, M.
2011-08-01
The first experimental data from single-particle scattering experiments from free electron lasers (FELs) are now becoming available. The first such experiments are being performed on relatively large objects such as viruses, which produce relatively low-resolution, low-noise diffraction patterns in so-called ``diffract-and-destroy'' experiments. We describe a very simple test on the angular correlations of measured diffraction data to determine if the scattering is from an icosahedral particle. If this is confirmed, the efficient algorithm proposed can then combine diffraction data from multiple shots of particles in random unknown orientations to generate a full 3D image of the icosahedral particle. We demonstrate this with a simulation for the satellite tobacco necrosis virus (STNV), the atomic coordinates of whose asymmetric unit is given in Protein Data Bank entry 2BUK.
Dynamics and stability of icosahedral Fe-Pt nanoparticles.
Jochym, Pawe? T; ?a?ewski, Jan; Sternik, Ma?gorzata; Piekarz, Przemys?aw
2015-11-14
The structure, dynamics and stability of Fe-Pt nanoparticles have been investigated using DFT-based techniques: total energy calculations and molecular dynamics. The investigated systems included multi-shell and disordered nanoparticles of iron and platinum. The study concerns icosahedral particles with the magic number of atoms (55): iron-terminated Fe43Pt12, platinum-terminated Fe12Pt43, and disordered Fe27Pt28. Additionally, the Fe6Pt7 cluster has been investigated to probe the behaviour of extremely small Fe-Pt particles. Molecular dynamics simulations have been performed for a few temperatures between T = 150-1000 K. The calculations revealed high structural instability of the Fe-terminated nanoparticles and a strong stabilising effect of the Pt-termination in the shell-type icosahedral particles. The platinum termination prevented disordering of the particle even at T = 1000 K indicating very high melting temperatures of these Fe-Pt icosahedral structures. The analysis of evolution of the radial distribution function has shown a significant tendency of Pt atoms to move to the outside layer of the particles - even in the platinum deficient cases. PMID:25757479
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.
APS/123-QED Signature of nearly icosahedral structures in liquid and supercooled liquid metals and
Widom, Michael
APS/123-QED Signature of nearly icosahedral structures in liquid and supercooled liquid metals appear here I. INTRODUCTION Turnbull [1{3] established that metallic liquids can be supercooled) A growing body of experiments display indirect evidence of icosahedral structures in supercooled liquid
PHYSICAL REVIE% 8 VOLUME 34, NUMBER 2 Icosahedral order in glass: Acoustic properties
Widom, Michael
properties of real glass in fiat space. This paper addresses the acoustic and vibrational propertiesPHYSICAL REVIE% 8 VOLUME 34, NUMBER 2 Icosahedral order in glass: Acoustic properties 15 JULY 1986 of continuum elastic theory in S3, and of a hypothetical perfect icosahedral crystal in I . Isotropy of elastic
Symmetry, Fullerenes, Nanotechnology and Other Stuff Virginia Tech
Zhigilei, Leonid V.
Symmetry, Fullerenes, Nanotechnology and Other Stuff H. C. Dorn Virginia Tech Alpha helix Protein, and Curl (1984-5) Large Fullerenes Laser Apparatus C60, Fullerenes, BuckyBalls! 0.2 m 0.7 nm #12;Dr. Richard Smalley, Nobel Laureate,1996 Leukemia Victim, October 2005 Fullerenes (Buckyballs) Icosahedral (Ih
Dynamic and Kinetic Assembly Studies of an Icosahedral Virus Capsid
NASA Astrophysics Data System (ADS)
Lee, Kelly
2011-03-01
Hepatitis B virus has an icosahedrally symmetrical core particle (capsid), composed of either 90 or 120 copies of a dimeric protein building block. We are using time-resolved, solution small-angle X-ray scattering and single-molecule fluorescence microscopy to probe the core particle assembly reaction at the ensemble and individual assembly levels. Our experiments to date reveal the assembly process to be highly cooperative with minimal population of stable intermediate species. Solution conditions, particularly salt concentration, appears to influence the partitioning of assembly products into the two sizes of shells. Funding from NIH R00-GM080352 and University of Washington.
Melting of bcc Transition Metals and Icosahedral Clustering
Ross, M; Boehler, R; Japel, S
2006-05-26
In contrast to polyvalent metals, transition metals have low melting slopes(dT/dP) that are due to partially filled d-bands that allow for a lowering of liquid phase energy through s-d electron transfer and the formation of local structures. In the case of bcc transition metals we show the apparent discrepancy of DAC melting measurements with shock melting of Mo can be understood by reexamining the shock data for V and Ta and introducing the presence of an icosahedral short range order (ISRO) melt phase.
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
NASA Astrophysics Data System (ADS)
Kurtuldu, Güven; Rappaz, Michel
2015-06-01
Recently, we have shown that minute Cr additions (typically 0.1 wt%) to Al-Zn alloys solidified in a uniform temperature field lead to the formation of fine equiaxed fcc Al grains [1]. Furthermore, these grains exhibit an unexpectedly large number of twin, or neartwin, relationships with their nearest neighbors and some of them even show a 5-fold symmetry multi-twin relationship with a common (110) direction. Similar observations have been made for yellow gold alloys (Au-12.5wt%Cu-12.5wt%Ag) inoculated with very small amounts of Ir (5-200 ppm) [2]. These results become fully consistent when one considers that the primary fcc phase forms on facets of icosahedral quasicrystals (iQC's), either by heteroepitaxy solidification or by peritectic transformation, with the following relationship: <111>fcc || 3-fold symmetry iQC axes, <110>fcc ? 2-fold symmetry iQC axes. The present study contributes to a better understanding of the frequency of twin boundary formation by the nucleation of fcc phase from an iQC template. A simple stereological model for the formation of equiaxed grains on such iQC templates has been derived. It is based on a 3D Voronoi tessellation of randomly distributed and oriented iQC template centers. Each iQC nucleation template site is the origin of 20 fcc grains with the heteroepitaxy relationships mentioned above on the 20 facets of the iQC. Therefore, the neighboring grains having a common iQC nucleation site contributes to the twin boundary frequency, while those coming from different iQC sites have random grain boundary orientations. The twin boundary frequency of the grains nucleated from iQC templates seen in 2D metallographic sections is compared with that measured in EBSD reconstructed grain structures.
Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations
NASA Astrophysics Data System (ADS)
Satoh, M.; Matsuno, T.; Tomita, H.; Miura, H.; Nasuno, T.; Iga, S.
2008-03-01
A new type of ultra-high resolution atmospheric global circulation model is developed. The new model is designed to perform "cloud resolving simulations" by directly calculating deep convection and meso-scale circulations, which play key roles not only in the tropical circulations but in the global circulations of the atmosphere. Since cores of deep convection have a few km in horizontal size, they have not directly been resolved by existing atmospheric general circulation models (AGCMs). In order to drastically enhance horizontal resolution, a new framework of a global atmospheric model is required; we adopted nonhydrostatic governing equations and icosahedral grids to the new model, and call it Nonhydrostatic ICosahedral Atmospheric Model (NICAM). In this article, we review governing equations and numerical techniques employed, and present the results from the unique 3.5-km mesh global experiments—with O(10 9) computational nodes—using realistic topography and land/ocean surface thermal forcing. The results show realistic behaviors of multi-scale convective systems in the tropics, which have not been captured by AGCMs. We also argue future perspective of the roles of the new model in the next generation atmospheric sciences.
NASA Astrophysics Data System (ADS)
Sargolzaei, Mahdi; Lotfizadeh, Neda
2011-04-01
We have demonstrated the electronic structures and magnetic properties of single 3d transition metal (TM) atoms encapsulated in noble metal clusters with icosahedral symmetry in the framework of relativistic density functional theory. Orbital polarization corrections have been used to obtain an upper-estimation for orbital magnetic moments of all individual 3d atoms. The relativistic corrections are marginally affected the spin magnetic moments, whereas they induce significant orbital magnetism in TM@X12 icosahedra. It is found that a superatomic picture has to be taken into account in order to explain the spin and orbital magnetism induced in TM@X12 icosahedron based on the Hund’s rules.
Marzec, C J; Day, L A
1993-01-01
The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found. Images FIGURE 5 FIGURE 6 FIGURE 8 FIGURE 9 PMID:8312492
Neutron-diffraction study of icosahedral Al-Cu-Fe single quasicrystals
NASA Astrophysics Data System (ADS)
Cornier-Quiquandon, M.; Quivy, A.; Lefebvre, S.; Elkaim, E.; Heger, G.; Katz, A.; Gratias, D.
1991-08-01
This paper reports neutron-diffraction results on a single icosahedral quasicrystal of Al-Cu-Fe. The basic properties of the structure have been extracted using six-dimensional (6D) Patterson analysis from 219 independent orbits of reflections. Described in 6D space, the structure has hyperspace group F?m35 and is defined by the three atomic surfaces located at special points with full icosahedral symmetry of the F lattice. These points are the two inequivalent nodes of the underlying primitive lattice plus one of the two inequivalent body centers, the remaining one being empty. The atomic surfaces are embedded in perpendicular space and are well approximated by polyhedra bounded by two-fold planes. These are a large triacontahedron located at the origin, a triacontahedron of the same size truncated along the five-fold directions at the other node, and a small polyhedron bounded by twofold planes at the occupied body center. Although no speculation has been made for distributing the atomic species within these atomic surfaces, the raw reliability factor between experimental and calculated diffraction intensities is already 0.20 with no fitting parameters and the density is found only 2.9% lower than the experimental one. The model presented here can be considered as a zero-order structure to be used for subsequent modeling. The atomic surfaces generate no unacceptably short distances between atoms. Both interatomic distances and coordination numbers of the three first shells are in good agreement with the most recent extended x-ray-absorption fine-structure results. The atomic surfaces are connected together by 3D pieces embedded in the parallel space. They define a partition of the 6D space in hyperprisms, which can be decomposed in direct products of 3D facets located in perpendicular and parallel spaces similar to the oblique cell decomposition of the 3D Penrose tiling. Phasons can propagate along the five-fold and two-fold directions by atomic jumps of 0.1705 and 0.179 nm, respectively.
Icosahedral capsid formation by capsomers and short polyions
NASA Astrophysics Data System (ADS)
Zhang, Ran; Linse, Per
2013-04-01
Kinetical and structural aspects of the capsomer-polyion co-assembly into icosahedral viruses have been simulated by molecular dynamics using a coarse-grained model comprising cationic capsomers and short anionic polyions. Conditions were found at which the presence of polyions of a minimum length was necessary for capsomer formation. The largest yield of correctly formed capsids was obtained at which the driving force for capsid formation was relatively weak. Relatively stronger driving forces, i.e., stronger capsomer-capsomer short-range attraction and/or stronger electrostatic interaction, lead to larger fraction of kinetically trapped structures and aberrant capsids. The intermediate formation was investigated and different evolving scenarios were found by just varying the polyion length.
Jin, Renxi; Liu, Chong; Zhao, Shuo; Das, Anindita; Xing, Hongzhu; Gayathri, Chakicherla; Xing, Yan; Rosi, Nathaniel L; Gil, Roberto R; Jin, Rongchao
2015-08-25
The [Au37(PPh3)10(SR)10X2](+) nanocluster (where SR = thiolate and X = Cl/Br) was theoretically predicted in 2007, but since then, there has been no experimental success in the synthesis and structure determination. Herein, we report a kinetically controlled, selective synthesis of [Au37(PPh3)10(SC2H4Ph)10X2](+) (counterion: Cl(-) or Br(-)) with its crystal structure characterized by X-ray crystallography. This nanocluster shows a rod-like structure assembled from three icosahedral Au13 units in a linear fashion, consistent with the earlier prediction. The optical absorption and the electrochemical and catalytic properties are investigated. The successful synthesis of this new nanocluster allows us to gain insight into the size, structure, and property evolution of gold nanoclusters that are based upon the assembly of icosahedral units (i.e., cluster of clusters). Some interesting trends are identified in the evolution from the monoicosahedral [Au13(PPh3)10X2](3+) to the bi-icosahedral [Au25(PPh3)10(SC2H4Ph)5X2](2+) and to the tri-icosahedral [Au37(PPh3)10(SC2H4Ph)10X2](+) nanocluster, which also points to the possibility of achieving even longer rod nanoclusters based upon assembly of icosahedral building blocks. PMID:26214221
Metal-organic framework materials based on icosahedral boranes and carboranes
Mirkin, Chad A.; Hupp, Joseph T.; Farha, Omar K.; Spokoyny, Alexander M.; Mulfort, Karen L.
2010-11-02
Disclosed herein are metal-organic frameworks of metals and boron rich ligands, such as carboranes and icosahedral boranes. Methods of synthesizing and using these materials in gas uptake are disclosed.
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 ...
Structure of Al-Li-Cu icosahedral crystals and Penrose tiling
Shen, Y.; Poon, S.J.; Dmowski, W.; Egami, T.; Shiflet, G.J.
1987-04-06
We report synchrotron x-ray powder-diffraction measurements of the Al-Li-Cu icosahedral phase. Our results are found to be in agreement with the computed diffraction intensities of the three-dimensional Penrose tiling when Al and Cu atoms are randomly positioned at the vertices and edge centers of the unit cells. Comparison is also made with a similarly decorated icosahedral structure constructed by dense packing of icosahedra. The agreement is less satisfactory.
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 ...
Non-Hermitian Hamiltonians with unitary and antiunitary symmetries
Fernández, Francisco M. Garcia, Javier
2014-03-15
We analyse several non-Hermitian Hamiltonians with antiunitary symmetry from the point of view of their point-group symmetry. It enables us to predict the degeneracy of the energy levels and to reduce the dimension of the matrices necessary for the diagonalization of the Hamiltonian in a given basis set. We can also classify the solutions according to the irreducible representations of the point group and thus analyse their properties separately. One of the main results of this paper is that some PT-symmetric Hamiltonians with point-group symmetry C{sub 2v} exhibit complex eigenvalues for all values of a potential parameter. In such cases the PT phase transition takes place at the trivial Hermitian limit which suggests that the phenomenon is not robust. Point-group symmetry enables us to explain such anomalous behaviour and to choose a suitable antiunitary operator for the PT symmetry. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •PT-symmetric multidimensional oscillators appear to show PT phase transitions. •This transition was conjectured to be a high-energy phenomenon. •We show that point group symmetry is useful for predicting broken PT symmetry in multidimensional oscillators. •PT-symmetric oscillators with C{sub 2v} symmetry exhibit phase transitions at the trivial Hermitian limit.
NASA Astrophysics Data System (ADS)
Cai, Tanhong
2001-07-01
We investigate the atomic structure of fivefold surface of icosahedral (i-) Al-Cu-Fe quasicrystal using scanning tunneling microscopy (STM) under ultra high vacuum (UHV). Annealing the sputtered surface at appropriate temperature produces a step-terrace structure on the surface. Our STM analysis indicates that the terraces are separated with primarily two stepheights in the ratio of t=5+1 /2 , a characteristic ratio in quasiperiodic structures. The measurements agree with the results from dynamical low energy electron diffraction (LEED) calculations. The spatial distribution of stepheights along the fivefold axis does not follow the quasiperiodic Fibonacci sequence. The existence of such stacking defects in the bulk structure is confirmed with the screw dislocations often observed in the STM scans. The first atomic resolution STM images on this type of material are obtained. The flat terraces are dominated with "ten-petal flower-like" motif, locally arranged with fivefold symmetry. Similar structural features can be identified in the atomically-dense planes generated from one of the available bulk structure models. Based on these results, we conclude that the fivefold i-AlCuFe surface corresponds to a two-dimensional cut of the bulk material. After examining the clean surface, we investigate the nucleation and growth of aluminium metallic thin films on the quasicrystalline i-Al-Cu-Fe fivefold surface. Upon deposition at room temperature, aluminium adatoms nucleate as pentagonal "starfish" with uniform size and in the same orientation. The same structure features are observed for different fluxes at low coverages. Based on the experimental results and the available bulk structure model, we identify the specific nucleation sites on the substrate and develop a model for the formation of the pentagonal starfish.
NASA Astrophysics Data System (ADS)
Rappaz, Michel; Kurtuldu, Güven
2015-08-01
We have recently shown that minute solute element additions to liquid metallic alloys can strongly influence the nucleation of the fcc phase and act as a grain refinement method. Electron back-scattered diffraction observations revealed a concomitant increase in the percentage of nearest neighbor (nn) grains that are in a twin relationship. Furthermore, multiple-twinned (MT) nn grain configurations with a fivefold symmetry around a common direction have been identified, an occurrence that can be explained when the symmetry of the icosahedron is accounted for. It was then conjectured that a new nucleation mechanism occurs in two steps: first, the formation of small icosahedral quasicrystals in the melt, followed by heteroepitaxy of the fcc phase on facets of these quasicrystals. In the present contribution, based on thermodynamics arguments, it is proposed that the first step occurs by spinodal decomposition of the liquid, in a manner similar to Guinier-Preston zones formation in solid state precipitation, while the second step is a transformation of these quasicrystal precursors into MT-fcc nanocrystals once the driving force for this transformation is sufficient to overcome the fcc-liquid interfacial energy and the elastic strains associated with MT-fcc nanoparticles. This explanation sets up guidelines for finding solute elements and composition ranges that favor this grain refinement mechanism.
Symmetries, Symmetry Breaking, Gauge Symmetries
Franco Strocchi
2015-07-02
The concepts of symmetry, symmetry breaking and gauge symmetries are discussed, their operational meaning being displayed by the observables {\\em and} the (physical) states. For infinitely extended systems the states fall into physically disjoint {\\em phases} characterized by their behavior at infinity or boundary conditions, encoded in the ground state, which provide the cause of symmetry breaking without contradicting Curie Principle. Global gauge symmetries, not seen by the observables, are nevertheless displayed by detectable properties of the states (superselected quantum numbers and parastatistics). Local gauge symmetries are not seen also by the physical states; they appear only in non-positive representations of field algebras. Their role at the Lagrangian level is merely to ensure the validity on the physical states of local Gauss laws, obeyed by the currents which generate the corresponding global gauge symmetries; they are responsible for most distinctive physical properties of gauge quantum field theories. The topological invariants of a local gauge group define superselected quantum numbers, which account for the $\\theta$ vacua.
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.
Design of Three-shell Icosahedral Matryoshka Clusters A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd, Mn)
Huang, Xiaoming; Zhao, Jijun; Su, Yan; Chen, Zhongfang; King, R. Bruce
2014-01-01
We propose a series of icosahedral matryoshka clusters of A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd), which possess large HOMO-LUMO gaps (1.29 to 1.54?eV) and low formation energies (0.06 to 0.21?eV/atom). A global minimum search using a genetic algorithm and density functional theory calculations confirms that such onion-like three-shell structures are the ground states for these A21B12 binary clusters. All of these icosahedral matryoshka clusters, including two previously found ones, i.e., [As@Ni12@As20]3? and [Sn@Cu12@Sn20]12?, follow the 108-electron rule, which originates from the high Ih symmetry and consequently the splitting of superatom orbitals of high angular momentum. More interestingly, two magnetic matryoshka clusters, i.e., Sn@Mn12@Sn20 and Pb@Mn12@Pb20, are designed, which combine a large magnetic moment of 28 µB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices. PMID:25376938
Design of Three-shell Icosahedral Matryoshka Clusters A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd, Mn)
NASA Astrophysics Data System (ADS)
Huang, Xiaoming; Zhao, Jijun; Su, Yan; Chen, Zhongfang; King, R. Bruce
2014-11-01
We propose a series of icosahedral matryoshka clusters of A@B12@A20 (A = Sn, Pb; B = Mg, Zn, Cd), which possess large HOMO-LUMO gaps (1.29 to 1.54 eV) and low formation energies (0.06 to 0.21 eV/atom). A global minimum search using a genetic algorithm and density functional theory calculations confirms that such onion-like three-shell structures are the ground states for these A21B12 binary clusters. All of these icosahedral matryoshka clusters, including two previously found ones, i.e., [As@Ni12@As20]3- and [Sn@Cu12@Sn20]12-, follow the 108-electron rule, which originates from the high Ih symmetry and consequently the splitting of superatom orbitals of high angular momentum. More interestingly, two magnetic matryoshka clusters, i.e., Sn@Mn12@Sn20 and Pb@Mn12@Pb20, are designed, which combine a large magnetic moment of 28 µB, a moderate HOMO-LUMO gap, and weak inter-cluster interaction energy, making them ideal building blocks in novel magnetic materials and devices.
Comparative Study of Non-Enveloped Icosahedral Viruses Size
Nikitin, Nikolai; Trifonova, Ekaterina; Evtushenko, Evgeniy; Kirpichnikov, Mikhail; Atabekov, Joseph; Karpova, Olga
2015-01-01
Now, as before, transmission electron microscopy (TEM) is a widely used technique for the determination of virions size. In some studies, dynamic light scattering (DLS) has also been applied for this purpose. Data obtained by different authors and using different methods could vary significantly. The process of TEM sample preparation involves drying on the substrate, which can cause virions to undergo morphology changes. Therefore, other techniques should be used for measurements of virions size in liquid, (i.e. under conditions closer to native). DLS and nanoparticle tracking analysis (NTA) provide supplementary data about the virions hydrodynamic diameter and aggregation state in liquid. In contrast to DLS, NTA data have a higher resolution and also are less sensitive to minor admixtures. In the present work, the size of non-enveloped icosahedral viruses of different nature was analyzed by TEM, DLS and NTA: the viruses used were the encephalomyocarditis virus (animal virus), and cauliflower mosaic virus, brome mosaic virus and bean mild mosaic virus (plant viruses). The same, freshly purified, samples of each virus were used for analysis using the different techniques. The results were compared with earlier published data and description databases. DLS data about the hydrodynamic diameter of bean mild mosaic virus, and NTA data for all examined viruses, were obtained for the first time. For all virus samples, the values of size obtained by TEM were less than virions sizes determined by DLS and NTA. The contribution of the electrical double layer (EDL) in virions hydrodynamic diameter was evaluated. DLS and NTA data adjusted for EDL thickness were in better agreement with TEM results. PMID:26545232
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...
Precipitation of Nanoscale Icosahedral Quasicrystalline Phase in Amorphous Hf70Cu20Pd10 Alloy
NASA Astrophysics Data System (ADS)
Li, Chunfei; Inoue, Akihisa
2000-12-01
An amorphous Hf70Cu20Pd10 ternary alloy was prepared and its crystallization process was studied. The crystallization proceeds through two exothermic reactions. Annealing of the specimen at a temperature lower than the onset point of the low-temperature exothermic reaction resulted in the precipitation of an icosahedral quasicrystalline phase. Further annealing at the same temperature caused the phase transformation to Hf2Cu crystalline phase, indicating the metastable character of the icosahedral quasicrystalline phase. In comparison with the crystallization process of other Hf-based amorphous alloys, the effect of Pd addition on the precipitation of the icosahedral quasicrystalline phase was discussed from the point of view of atomic radius.
Luo; Hashimoto
2000-10-01
A new ordered structure W' with a lattice parameter (a = 2.05 nm) about three times as large as that of the fundamental face-centered cubic W phase (a = 0.6848 nm) has been found in the Mg-Zn-Y system by means of transmission electron microscopy. The W' and W phases have the cube-to-cube orientation relationship. Moreover, the strong electron diffraction spots of the W' phase showed pseudoicosahedral symmetry, implying that it is a crystalline approximant of the Mg-Zn-Y icosahedral quasicrystal. In the high-resolution electron microscopic images of the W' phase, Penrose tiles of pentagons and boats with an edge length of a(p) = 0.481 nm can be identified. A binary tile of crown subunit has also been deduced from such a tiling. Translation domains of the W' phase have also been observed and the translation vectors at the domain boundary are: a(p), tau x a(p) and (1 + tau) x a(p), respectively, where (1 + tau) x a(p) equals to the edge length a(r) of the big obtuse rhombus of the W' phase and tau = (1 + square root of 5)/2, is the golden ratio. PMID:10831292
Competition between face-centered cubic and icosahedral cluster structures R. S. Berry
Berry, R. Stephen
Competition between face-centered cubic and icosahedral cluster structures R. S. Berry University analysis of the competition between these structures. In this paper we carry out this analysis using the competition between structures by us- ing a ``phase diagram'' see Ref. 13 on which we plot the Morse
Critical scaling of medium-range icosahedral ordering in glass transition of metallic liquids
Z. W. Wu; F. X. Li; C. W. Huo; M. Z. Li; W. H. Wang; K. X. Liu
2015-10-25
The temperature evolution of medium-range icosahedral ordering formed by connected icosahedral short-range order (ISRO) in metallic glass-forming liquids was investigated via molecular dynamics simulations. It is found that the size distribution of the clusters formed by ISRO via volume-sharing at various temperatures in supercooled region collapses together, following a very good scaling law $n(S,T) {\\sim} S^{-{\\tau}}f(S/|1-Tc/T|^{-1/{\\sigma}})$ with {\\tau} and {\\sigma} scaling exponents. Tc is found to coincide with the glass transition temperature Tg. This indicates that glass transition may be regarded as a critical phenomenon associated with the critical scaling behavior of medium-range icosahedral ordering. Furthermore, it is revealed that with the formation of the medium-range icosahedral order and more ISROs packed together, the atomic configurations of ISROs are optimized from distorted ones toward perfect ones. This significantly lowers the energies of ISROs and introduces great geometric frustration simultaneously. Both factors make key impacts on the drastic dynamic slowdown in liquids during cooling. These findings provide direct structure-property relationship for understanding the nature of glass transition.
cond-mat/04xxxxxx Canonical cell model of Cadmium-based icosahedral alloys
Widom, Michael
cond-mat/04xxxxxx Canonical cell model of Cadmium-based icosahedral alloys M. Mihalkovic and M) Cadmium-based quasicrystals (Cd-Ca and Cd-Yb) were the first binary alloys discovered to form thermodynamically stable quasicrystals. As a binary alloy, and with a strong size difference be- tween atomic
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...
ERIC Educational Resources Information Center
Jittam, Piyachat; Ruenwongsa, Pintip; Panijpan, Bhinyo
2008-01-01
We have found it an effective way of teaching symmetry in the context of stereoselectivity, to use common everyday objects with the same point groups as the substrates involved. This has helped students to distinguish between those symmetry elements which allow for stereospecificity and those which preclude it. Two symmetry elements, the simple…
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
Symmetry, Landau theory and polytope models of glass
NASA Astrophysics Data System (ADS)
Nelson, David R.; Widom, Michael
1984-08-01
Order in supercooled liquids and metallic glasses is related to a regular icosahedral "crystal" consisting of 120 particles inscribed on the surface of a sphere in four dimensions. Hyperspherical harmonics and the discrete symmetry group of this four-dimensional platonic solid can be used to construct an order parameter for glasses in three-dimensional flat space. A uniformly frustrated Landau expansion in this order parameter suggests a ground state with a regular array of wedge disclination lines. Homotopy theory is used to classify all topologically stable defects. A generalization of Bloch's theorem for electronic states in flat space solids allows explicit diagonalization of tight binding models defined on the curved-space icosahedral crystal.
Dual-phase glassy/nanoscale icosahedral phase materials in Cu–Zr–Ti–Pd system alloys
Louzguine-Luzgin, Dmitri V.; Churyumov, A.Yu.
2014-10-15
The present work is devoted to an investigation of the formation kinetics, stability and homogeneity area of the nanoscale icosahedral phase formed on heating in the dual-phase glassy/quasicrystalline phase Cu–Zr–Ti–Pd alloys. The data obtained indicate that the Cu–Zr–Ti–Pd icosahedral phase is not a Cu-rich part of the compositional homogeneity area of the Zr–Cu–Pd one. Moreover, Ti, as well as Pd, is found to be an important element stabilizing quasicrystalline phase in the Cu–Zr–Ti–Pd alloys. The formation criteria for Cu- and Zr/Hf-based icosahedral phases are discussed based on the quasilattice constant to average atomic diameter ratio. Deviation from a certain ratio leads to destabilization of the icosahedral phase. By using the isothermal calorimetry traces transformation kinetics above and below the glass-transition region was analyzed. Some difference in the transformation kinetics above and below the glass-transition region allows us to suggest that possible structure changes occur upon glass-transition. - Highlights: • Formation kinetics, stability and homogeneity area of nanoscale icosahedral phase • Cu–Zr–Ti–Pd icosahedral phase is not a Cu-rich part of Zr–Cu–Pd one. • Ti, as well as Pd, is an important element stabilizing quasicrystalline phase. • Difference in transformation kinetics above and below glass-transition region.
Symmetry in the basic sciences
NASA Astrophysics Data System (ADS)
Toole, Joseph E.; Jensen, David W.; Rogers, Mark E.; Chernek, Paul J.; Erstfeld, Thomas E.
1989-04-01
The basic mathematical theory behind plane symmetry groups is presented. This theory is then applied in classifying the symmetry of bounded figures, frieze patterns and wallpaper patterns. Recently developed algorithms are included to help analyze complex designs. Symmetry operations relevant to 3-D crystallography are discussed. In particular, the seven crystal systems that classify the 32 crystallographic point groups are described. These are then used to construct the Bravais lattices. The role is investigated of symmetry in biological forms. Specifically, work on growth and form of molluscan shells is reviewed with an attempt to explain the consequences of that growth and form to the natural history of the Chambered Nautilus and its ancestors. The central role symmetry has increasingly played in physics is looked at by examining the Principle of Least Action and the invariance of the Lagrangian under a transformation. Noether's Theorem guarantees that a conservation law is associated with each of these symmetries. Examples include the conservation of energy, linear momentum, and angular momentum, as well as the purely quantum mechanical symmetry of invariance under an exchange operation. A brief look at gauge theories is the final example of how symmetry has become a guiding principle in the formulation of new theories.
Adsorption sites on icosahedral quasicrystal surfaces: Dark stars and white flowers
Unal, B.; Jenks, C.J.; Thiel, P.A.
2009-01-12
From other work, two preferred sites have been suggested for metals and semimetals adsorbed on the fivefold surfaces of icosahedral, Al-based quasicrystals. Because of their appearance in scanning tunneling microscopy (STM) images, these sites are known as dark stars and white flowers. In this paper, we analyze four bulk structural models in physical space to determine the types, chemical decorations, and densities of the dark star - and, to a lesser extent, the white flower - adsorption sites for the fivefold planes of icosahedral Al-Pd-Mn. We find that the chemical decorations of these sites are heterogeneous, even within a single model. Both features are also structurally heterogeneous, according to STM measurements, and the structural variation is consistent with the bulk structure models. Finally, from the models, the density of dark stars in the planes correlates with the step height. This may explain previous experimental observations of different properties for different terraces.
Scanning Tunneling Microscopy Studies of Surface Structures of Icosahedral Al-Cu-Fe Quasicrystals
Tanhong Cai
2002-12-31
Three papers are included in this dissertation. The first paper: ''Structural aspects of the fivefold quasicrystalline Al-Cu-Fe surface from STM and dynamical LEED studies'', is in press with ''Surface Science''. The second paper: ''An STM study of the atomic structure of the icosahedral Al-Cu-Fe fivefold surface'' is submitted to ''Physical Review B, Rapid Communication''. The third paper: ''Pseudomorphic starfish: arrangement of extrinsic metal atoms on a quasicrystalline substrate'' is submitted to ''Nature''. Following the third paper are general conclusions and appendices that document the published paper ''Structural aspects of the three-fold surface of icosahedral Al-Pd-Mn'' (appearing in volume 461, issue 1-3 of ''Surface Science'' on page L521-L527, 2000), the design as well as the specifications of the aluminum evaporator used in the aluminum deposition study in this dissertation, an extended discussion of the aluminum deposition on the quasicrystalline surface, and the STM database.
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)
Dai, Mingxing; Wang, Renhui
1990-01-01
Higher-order Laue zone (HOLZ) line patterns of an Al 76Si 4Mn 20 quasi- crystalline icosahedral phase (I phase) have been obtained experimentally with a large angular range by connecting a series of conventional convergent-beam electron diffraction patterns. The computer simulated HOLZ line patterns covering the whole orientation triangle of the I phase, which were calculated by using cut and projection method and the simple quasilattice model, show principle agreement with the experimental ones.
Is space-time symmetry a suitable generalization of parity-time symmetry?
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier
2014-11-15
We discuss space-time symmetric Hamiltonian operators of the form H=H{sub 0}+igH{sup ?}, where H{sub 0} is Hermitian and g real. H{sub 0} is invariant under the unitary operations of a point group G while H{sup ?} is invariant under transformation by elements of a subgroup G{sup ?} of G. If G exhibits irreducible representations of dimension greater than unity, then it is possible that H has complex eigenvalues for sufficiently small nonzero values of g. In the particular case that H is parity-time symmetric then it appears to exhibit real eigenvalues for all 0
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
NASA Astrophysics Data System (ADS)
Lowe, M.; Yadav, T. P.; Fournée, V.; Ledieu, J.; McGrath, R.; Sharma, H. R.
2015-03-01
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe3O4 rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
Lowe, M.; McGrath, R.; Sharma, H. R.; Yadav, T. P.; Fournée, V.; Ledieu, J.
2015-03-07
The use of quasicrystals as precursors to catalysts for the steam reforming of methanol is potentially one of the most important applications of these new materials. To develop application as a technology requires a detailed understanding of the microscopic behavior of the catalyst. Here, we report the effect of leaching treatments on the surface microstructure, chemical composition, and valence band of the icosahedral (i-) Al-Cu-Fe quasicrystal in an attempt to prepare a model catalyst. The high symmetry fivefold surface of a single grain i-Al-Cu-Fe quasicrystal was leached with NaOH solution for varying times, and the resulting surface was characterized by x-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), scanning electron microscopy (SEM), and atomic force microscopy (AFM). The leaching treatments preferentially remove Al producing a capping layer consisting of Fe and Cu oxides. The subsurface layer contains elemental Fe and Cu in addition to the oxides. The quasicrystalline bulk structure beneath remains unchanged. The subsurface gradually becomes Fe{sub 3}O{sub 4} rich with increasing leaching time. The surface after leaching exhibits micron sized dodecahedral cavities due to preferential leaching along the fivefold axis. Nanoparticles of the transition metals and their oxides are precipitated on the surface after leaching. The size of the nanoparticles is estimated by high resolution transmission microscopy to be 5-20 nm, which is in agreement with the AFM results. Selected area electron diffraction (SAED) confirms the crystalline nature of the nanoparticles. SAED further reveals the formation of an interface between the high atomic density lattice planes of nanoparticles and the quasicrystal. These results provide an important insight into the preparation of model catalysts of nanoparticles for steam reforming of methanol.
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
High Pressure X-ray Diffraction Study on Icosahedral Boron Arsenide (B12As2)
J Wu; H Zhu; D Hou; C Ji; C Whiteley; J Edgar; Y Ma
2011-12-31
The high pressure properties of icosahedral boron arsenide (B12As2) were studied by in situ X-ray diffraction measurements at pressures up to 25.5 GPa at room temperature. B12As2 retains its rhombohedral structure; no phase transition was observed in the pressure range. The bulk modulus was determined to be 216 GPa with the pressure derivative 2.2. Anisotropy was observed in the compressibility of B12As2-c-axis was 16.2% more compressible than a-axis. The boron icosahedron plays a dominant role in the compressibility of boron-rich compounds.
STM study of the atomic structure of the icosahedral Al-Cu-Fe fivefold surface
NASA Astrophysics Data System (ADS)
Cai, T.; Fournée, V.; Lograsso, T.; Ross, A.; Thiel, P. A.
2002-04-01
We use scanning tunneling microscopy (STM) to investigate the atomic structure of the icosahedral (i-) Al-Cu-Fe fivefold surface in ultra high vacuum (UHV). Studies show that large, atomically flat terraces feature many ten-petal ``flowers'' with internal structure. The observed flower patterns can be associated with features on Al rich dense atomic planes generated from two-dimensional cuts of bulk models based on x-ray and neutron diffraction experiments. The results confirm that the fivefold surface of i-Al-Cu-Fe corresponds to a bulk-terminated plane.
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.
Translational symmetry Rotational symmetry
Lee, Carl
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Medium-range icosahedral order in quasicrystal-forming Zr{sub 2}Pd binary metallic glass
Huang Li; Fang, X. W.; Wang, C. Z.; Ho, K. M.; Kramer, M. J.; Ding, Z. J.
2011-06-06
Medium-range order in Zr{sub 2}Pd metallic glass was studied using a combination of x-ray diffraction experiment and atomistic simulations. We show that, in contrast to earlier experimental interpretations, the icosahedral-like polyhedron is centered around Pd, rather than Zr. Furthermore, we find that the ordered icosahedral packing around Pd extends to the third shell in the way similar to that in the Bergman-type clusters. The existence of Bergman-type clusters sheds interesting light into the formation of nanoquasicrystal phase during crystallization process of Zr{sub 2}Pd metallic glass.
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…
Symmetry and equivalence restrictions in electronic structure calculations
NASA Technical Reports Server (NTRS)
Bauschlicher, Charles W., Jr.; Taylor, Peter R.
1988-01-01
A simple method for obtaining MCSCF orbitals and CI natural orbitals adapted to degenerate point groups, with full symmetry and equivalnece restrictions, is described. Among several advantages accruing from this method are the ability to perform atomic SCF calculations on states for which the SCF energy expression cannot be written in terms of Coulomb and exchange integrals over real orbitals, and the generation of symmetry-adapted atomic natural orbitals for use in a recently proposed method for basis set contraction.
The architecture and chemical stability of the archaeal Sulfolobus turreted icosahedral virus.
Khayat, Reza; Fu, Chi-yu; Ortmann, Alice C; Young, Mark J; Johnson, John E
2010-09-01
Viruses utilize a diverse array of mechanisms to deliver their genomes into hosts. While great strides have been made in understanding the genome delivery of eukaryotic and prokaryotic viruses, little is known about archaeal virus genome delivery and the associated particle changes. The Sulfolobus turreted icosahedral virus (STIV) is a double-stranded DNA (dsDNA) archaeal virus that contains a host-derived membrane sandwiched between the genome and the proteinaceous capsid shell. Using cryo-electron microscopy (cryo-EM) and different biochemical treatments, we identified three viral morphologies that may correspond to biochemical disassembly states of STIV. One of these morphologies was subtly different from the previously published 27-A-resolution electron density that was interpreted with the crystal structure of the major capsid protein (MCP). However, these particles could be analyzed at 12.5-A resolution by cryo-EM. Comparing these two structures, we identified the location of multiple proteins forming the large turret-like appendages at the icosahedral vertices, observed heterogeneous glycosylation of the capsid shell, and identified mobile MCP C-terminal arms responsible for tethering and releasing the underlying viral membrane to and from the capsid shell. Collectively, our studies allow us to propose a fusogenic mechanism of genome delivery by STIV, in which the dismantled capsid shell allows for the fusion of the viral and host membranes and the internalization of the viral genome. PMID:20592081
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
A mass conservative semi-implicit scheme for the shallow water equations on an icosahedral grid
NASA Astrophysics Data System (ADS)
Bonaventura, L.
2003-04-01
A mass conservative, semi-implicit discretization for the vector invariant formulation of the shallow water equations on the sphere is introduced. These equations are discretized on a quasi-uniform, geodesic, icosahedral Voronoi-Delaunay grid (see e.g. [Heikes and Randall, 1995]) with a C-grid variable arrangement, according to the approach introduced in [Casulli and Walters, 2000]. A finite volume discretization is employed for the continuity equation in conservation law form, using as control volumes either the hexagonal/pentagonal or the dual triangular cells. The momentum equation is discretized with an extension of the approach introduced in [Lin and Rood, 1997] to semi-implicit time discretization on the icosahedral grid. Various possible treatments of the Coriolis force terms will be compared. Results obtained in standard shallow water test cases will be presented, along with an analysis of the discretization properties regarding conservation of energy and potential vorticity. This work is being carried out within the preliminary phase of the ICON research project, which involves, along with Max Planck Institut für Meteorologie Hamburg and the Deutscher Wetterdienst, PIK Potsdam, Freie Universität Berlin, Universität Bonn, Technische Universität München and various other research institutions (see the web page at the project site icon.enes.org). The aim of this project is the development of a unified nonhydrostatic model for global and regional climate simulation and weather forecasting.
NASA Astrophysics Data System (ADS)
Kelton, Kenneth
2005-03-01
Over a half-century ago, Charles Frank argued that metallic liquids could be undercooled because of developing icosahedral short-range order (ISRO) in the liquid that is incompatible with the translational periodicity of crystal phases. Our recent high-energy x-ray diffraction and nucleation undercooling studies of electrostatically levitated droplets of a Ti-Zr-Ni liquid produced the first experimental proof of this hypothesis. In addition to coupling to the nucleation barrier for the ordered phase, the icosahedral order can significantly influence the thermophysical properties of the liquid. A sharp decrease in the specific heat that is correlated with the growing ISRO indicates a rapidly decreasing configurational entropy in the liquid, at temperatures far above the glass transition temperature. Surprisingly, our studies demonstrate that ISRO is evident even above the liquidus temperature in the Ti-Zr-Ni liquid as well as in liquid Ni. It is significantly distorted in liquid Ti, consistent with an increasing importance of the covalent character of the 3-d bonding, which frustrates the development of ISRO. Supported by NASA under contract NAG8-1682, and by the National Science Foundation under grant DMR 03-07410.
NASA Astrophysics Data System (ADS)
Cummings, F. R.; Muller, T. F. G.; Malgas, G. F.; Arendse, C. J.
2015-10-01
Potentiostatic anodization of commercially pure, 50 ?m-thick titanium (Ti) foil was performed in aqueous, phosphate electrolytes at increasing experimental timeframes at a fixed applied potential for the synthesis of titania nanotube arrays (TNAs). High resolution scanning electron microscopy images, combined with energy dispersive spectroscopy and x-ray diffraction spectra reveal that anodization of the Ti foil in a 1 M NaF+0.5 M H3PO4 electrolyte for 4 h yields a titanate surface with pore diameters ranging between 100 and 500 nm. The presence of rods on the Ti foil surface with lengths exceeding 20 ?m and containing high concentrations of phosphor on the exterior was also detected at these conditions, along with micro-sized coral reef-like titanate balls. We propose that the formation of these structures play a major role during the anodization process and impedes nanotube growth during the anodization process. High spatially resolved scanning transmission electron microscopy-electron energy loss spectroscopy (STEM-EELS) performed along the length of a single anodized TiO2 nanotube reveals a gradual evolution of the nanotube crystallinity, from a rutile-rich bottom to a predominantly anatase TiO2 structure along its length.
The Three-Dimensional Finite-Volume Non-Hydrostatic Icosahedral Model (NIM)
NASA Astrophysics Data System (ADS)
Lee, J. L.; MacDonald, A. E.
2014-12-01
A multi-scales Non-hydrostatic Icosahedral Model (NIM) has been developed at Earth System Research Laboratory (ESRL) to meet NOAA's future prediction mission ranging from mesoscale short-range, high-impact weather forecasts to longer-term intra-seasonal climate prediction. NIM formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM is designed to utilize the state-of-art computing architecture such as Graphic Processing Units (GPU) processors to run globally at kilometer scale resolution to explicitly resolve convective storms and complex terrains. The novel features of NIM numerical design include: 1.1. A local coordinate system upon which finite-volume integrations are undertaken. The use of a local Cartesian coordinate greatly simplifies the mathematic formulation of the finite-volume operators and leads to the finite-volume integration along straight lines on the plane, rather than along curved lines on the spherical surface. 1.2. A general indirect addressing scheme developed for modeling on irregular grid. It arranges the icosahedral grid with a one-dimensional vector loop structure, table specified memory order, and an indirect addressing scheme that yields very compact code despite the complexities of this grid. 1.3. Use of three-dimensional finite-volume integration over control volumes constructed on the height coordinates. Three-dimensional finite-volume integration accurately represents the Newton Third Law over terrain and improves pressure gradient force over complex terrain. 1.4. Use of the Runge-Kutta 4th order conservative and positive-definite transport scheme 1.5. NIM dynamical solver has been implemented on CPU as well as GPU. As one of the potential candidates for NWS next generation models, NIM dynamical core has been successfully verified with various benchmark test cases including those proposed by DCMIP. Physical parameterizations such as those used by GFS have been incorporated into NIM dynamic core and successfully tested with multi-months aqua-planet simulations as well as real data simulations. NIM has been implemented on GPUs and CPUs. Efficiency tests show GPU significantly speeds up model calculations.
Terrace-dependent nucleation of small Ag clusters on a five-fold icosahedral quasicrystal surface
Unal, B.; Evans, J.W.; Lograsso, T.A.; Ross, A.R.; Jenks, C.J.; Thiel, P.A.
2007-07-21
Nucleation of Ag islands on the five-fold surface of icosahedral Al-Pd-Mn is influenced strongly by trap sites. Submonolayers of Ag prepared by deposition at 365 K and with a flux of 1 x 10{sup -3} monolayers/s exhibit a variation in Ag island densities across different terraces. Comparisons with previous work and with rate equation analysis indicate that trap sites are not saturated under these experimental conditions and that the difference in island densities is not necessarily due to variation in trap densities. While it could have a number of different origins, our results point to a terrace-dependent value of the effective diffusion barrier for Ag adatoms.
Defining criteria for oligomannose immunogens for HIV using icosahedral virus capsid scaffolds.
Astronomo, Rena D; Kaltgrad, Eiton; Udit, Andrew K; Wang, Sheng-Kai; Doores, Katie J; Huang, Cheng-Yuan; Pantophlet, Ralph; Paulson, James C; Wong, Chi-Huey; Finn, M G; Burton, Dennis R
2010-04-23
The broadly neutralizing antibody 2G12 recognizes a conserved cluster of high-mannose glycans on the surface envelope spike of HIV, suggesting that the "glycan shield" defense of the virus can be breached and may, under the right circumstances, serve as a vaccine target. In an attempt to recreate features of the glycan shield semisynthetically, oligomannosides were coupled to surface lysines on the icosahedral capsids of bacteriophage Q beta and cowpea mosaic virus (CPMV). The Q beta glycoconjugates, but not CPMV, presented oligomannose clusters that bind the antibody 2G12 with high affinity. However, antibodies against these 2G12 epitopes were not detected in immunized rabbits. Rather, alternative oligomannose epitopes on the conjugates were immunodominant and elicited high titers of anti-mannose antibodies that do not crossreact with the HIV envelope. The results presented reveal important design considerations for a carbohydrate-based vaccine component for HIV. PMID:20416507
Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel
2014-01-01
The largest known DNA viruses infect Acanthamoeba and belong to two markedly different families. The Megaviridae exhibit pseudo-icosahedral virions up to 0.7 ?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
DYNAMICO-1.0, an icosahedral hydrostatic dynamical core designed for consistency and versatility
NASA Astrophysics Data System (ADS)
Dubos, T.; Dubey, S.; Tort, M.; Mittal, R.; Meurdesoif, Y.; Hourdin, F.
2015-10-01
The design of the icosahedral dynamical core DYNAMICO is presented. DYNAMICO solves the multi-layer rotating shallow-water equations, a compressible variant of the same equivalent to a discretization of the hydrostatic primitive equations in a Lagrangian vertical coordinate, and the primitive equations in a hybrid mass-based vertical coordinate. The common Hamiltonian structure of these sets of equations is exploited to formulate energy-conserving spatial discretizations in a unified way. The horizontal mesh is a quasi-uniform icosahedral C-grid obtained by subdivision of a regular icosahedron. Control volumes for mass, tracers and entropy/potential temperature are the hexagonal cells of the Voronoi mesh to avoid the fast numerical modes of the triangular C-grid. The horizontal discretization is that of Ringler et al. (2010), whose discrete quasi-Hamiltonian structure is identified. The prognostic variables are arranged vertically on a Lorenz grid with all thermodynamical variables collocated with mass. The vertical discretization is obtained from the three-dimensional Hamiltonian formulation. Tracers are transported using a second-order finite-volume scheme with slope limiting for positivity. Explicit Runge-Kutta time integration is used for dynamics, and forward-in-time integration with horizontal/vertical splitting is used for tracers. Most of the model code is common to the three sets of equations solved, making it easier to develop and validate each piece of the model separately. Representative three-dimensional test cases are run and analyzed, showing correctness of the model. The design permits to consider several extensions in the near future, from higher-order transport to more general dynamics, especially deep-atmosphere and non-hydrostatic equations.
Yan, Xiaodong; Cardone, Giovanni; Zhang, Xing; Zhou, Z Hong; Baker, Timothy S
2014-04-01
In cryo-electron microscopy and single particle analysis, data acquisition and image processing are generally carried out in sequential steps and computation of a three-dimensional reconstruction only begins once all the micrographs have been acquired. We are developing an integrated system for processing images of icosahedral particles during microscopy to provide reconstructed density maps in real-time at the highest possible resolution. The system is designed as a combination of pipelines to run in parallel on a computer cluster and analyzes micrographs as they are acquired, handling automatically all the processing steps from defocus estimation and particle picking to origin/orientation determination. An ab initio model is determined independently from the first micrographs collected, and new models are generated as more particles become available. As a proof of concept, we simulated data acquisition sessions using three sets of micrographs of good to excellent quality that were previously recorded from different icosahedral viruses. Results show that the processing of single micrographs can keep pace with an acquisition rate of about two images per minute. The reconstructed density map improves steadily during the image acquisition phase and its quality at the end of data collection is only moderately inferior to that obtained by expert users who processed semi-automatically all the micrographs after the acquisition. The current prototype demonstrates the advantages of integrating three-dimensional image processing with microscopy, which include an ability to monitor acquisition in terms of the final structure and to predict how much data and microscope resources are needed to achieve a desired resolution. PMID:24613762
Pauling, L. )
1988-07-01
Analysis of the measured values of Q for the weak peaks (small maxima, usually considered to be background fluctuations, noise) on the x-ray powder diffraction curves for 17 rapidly quenched alloys leads directly to the conclusion that they are formed by an 820-atom or 1012-atom primitive cubic structure that by icosahedral twinning produces the so-called icosahedral quasi-crystals.
NASA Astrophysics Data System (ADS)
Dewar, R. L.; Hudson, S. R.
1998-01-01
A simple and general definition of stellarator symmetry is presented and its relation to previous definitions discussed. It is shown that the field-line flow in systems possessing stellarator symmetry is time-reversal invariant if the the toroidal angle is regarded as “time”.
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.
Stagno, Vincenzo; Bindi, Luca; Shibazaki, Yuki; Tange, Yoshinori; Higo, Yuji; Mao, H-K; Steinhardt, Paul J; Fei, Yingwei
2014-01-01
The first natural-occurring quasicrystal, icosahedrite, was recently discovered in the Khatyrka meteorite, a new CV3 carbonaceous chondrite. Its finding raised fundamental questions regarding the effects of pressure and temperature on the kinetic and thermodynamic stability of the quasicrystal structure relative to possible isochemical crystalline or amorphous phases. Although several studies showed the stability at ambient temperature of synthetic icosahedral AlCuFe up to ~35?GPa, the simultaneous effect of temperature and pressure relevant for the formation of icosahedrite has been never investigated so far. Here we present in situ synchrotron X-ray diffraction experiments on synthetic icosahedral AlCuFe using multianvil device to explore possible temperature-induced phase transformations at pressures of 5?GPa and temperature up to 1773?K. Results show the structural stability of i-AlCuFe phase with a negligible effect of pressure on the volumetric thermal expansion properties. In addition, the structural analysis of the recovered sample excludes the transformation of AlCuFe quasicrystalline phase to possible approximant phases, which is in contrast with previous predictions at ambient pressure. Results from this study extend our knowledge on the stability of icosahedral AlCuFe at higher temperature and pressure than previously examined, and provide a new constraint on the stability of icosahedrite. PMID:25070248
Spectral signatures of high-symmetry quantum dots and effects of symmetry breaking
NASA Astrophysics Data System (ADS)
Karlsson, K. F.; Oberli, D. Y.; Dupertuis, M. A.; Troncale, V.; Byszewski, M.; Pelucchi, E.; Rudra, A.; Holtz, P. O.; Kapon, E.
2015-10-01
High symmetry epitaxial quantum dots (QDs) with three or more symmetry planes provide a very promising route for the generation of entangled photons for quantum information applications. The great challenge to fabricate nanoscopic high symmetry QDs is further complicated by the lack of structural characterization techniques able to resolve small symmetry breaking. In this work, we present an approach for identifying and analyzing the signatures of symmetry breaking in the optical spectra of QDs. Exciton complexes in InGaAs/AlGaAs QDs grown along the [111]B crystalline axis in inverted tetrahedral pyramids are studied by polarization resolved photoluminescence spectroscopy combined with lattice temperature dependence, excitation power dependence and temporal photon correlation measurements. By combining such a systematic experimental approach with a simple theoretical approach based on a point-group symmetry analysis of the polarized emission patterns of each exciton complex, we demonstrate that it is possible to achieve a strict and coherent identification of all the observable spectral patterns of numerous exciton complexes and a quantitative determination of the fine structure splittings of their quantum states. This analysis is found to be particularly powerful for selecting QDs with the highest degree of symmetry (C3v and {D}3h) for potential applications of these QDs as polarization entangled photon sources. We exhibit the optical spectra when evolving towards asymmetrical QDs, and show the higher sensitivity of certain exciton complexes to symmetry breaking.
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.
Speculation of equilibrium pressure of Ti36Zr40Ni20Pd4 icosahedral quasicrystal
NASA Astrophysics Data System (ADS)
Huang, Huogen; Chen, Liang
2015-08-01
Ti-Zr-Ni quasicrystals have been demonstrated to store a large number of hydrogen atoms, which implies strong potential application in hydrogen energy field for them. However, the desorption of hydrogen atoms in the quasicrystals is quite difficult, with the indication of high desorption temperature and slow desorption rate. The shortage limits their use in the field to a large extent. But this kind of quasicrystals might be used in nuclear fusion energy field, because tritium as a coral fuel for nuclear fusion needs tight storage. However, equilibrium pressure at room temperature of Ti-Zr-Ni quasicrystals, important for their application in fusion energy field, has not been clear yet. In this work, we designed a gas-solid reaction system with the pressure resolution of 10-8Pa and carried out hydrogen desorption investigation at different temperatures on Ti36Zr40Ni20Pd4 icosahedral quasicrystal. Based on three Pressure-Composition-Temperature desorption curves, we speculate according to Van't Hoff theory about hydrogen storage that its equilibrium pressure at room temperature could be at the magnitude of 10-6Pa, displaying good stability of hydrogen in the quasicrystal and also implying application prospects in fusion energy field for quasicrystals of this type.
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.
Thermal conductivity and Seebeck coefficients of icosahedral boron arsenide films on silicon carbide
Gong, Y.; Kuball, M.; Zhang, Y.; Dudley, M.; Zhang, Y.; Edgar, J. H.; Heard, P. J.
2010-10-15
The thermal conductivity of icosahedral boron arsenide (B{sub 12}As{sub 2}) films grown on (0001) 6H-SiC substrates by chemical vapor deposition was studied by the 3{omega} technique. The room temperature thermal conductivity decreased from 27.0 to 15.3 W/m K as the growth temperature was decreased from 1450 to 1275 deg. C. This is mainly attributed to the differences in the impurity concentration and microstructure, determined from secondary ion mass spectrometry and high resolution transmission electron microscopy, respectively. Callaway's theory was applied to calculate the temperature-dependent thermal conductivity, and the results are in good agreement with the experimental data. Seebeck coefficients were determined as 107 {mu}V/K and 136 {mu}V/K for samples grown at 1350 deg. C with AsH{sub 3}/B{sub 2}H{sub 6} flow ratio equals to 1:1 and 3:5, respectively.
Pauling, L. )
1988-11-01
A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tiling-six-dimensional-projection theory, is described. Values of the primitive-cubic lattice constant for several quasicrystals are evaluated from x-ray and neutron diffraction data. The fact that the low-angle diffraction maxima can be indexed with cubic unit cells provides additional support for the twinned-cubic-crystal theory of icosahedral quasicrystals.
Vibrational properties and specific heat of core-shell Ag-Au icosahedral nanoparticles.
Sauceda, Huziel E; Garzón, Ignacio L
2015-11-14
The vibrational density of states (VDOS) of metal nanoparticles can be a fingerprint of their geometrical structure and determine their low-temperature thermal properties. Theoretical and experimental methods are available nowadays to calculate and measure it over a size range of 1-4 nm. In this work, we present theoretical results regarding the VDOS of Ag-Au icosahedral nanoparticles with a core-shell structure in that size range (147-923 atoms). The results are obtained by changing the size and type of atoms in the core-shell structure. For all sizes investigated, a smooth and monotonic variation of the VDOSs from Ag to Au is obtained by increasing the number of core Au atoms, and vice versa. Nevertheless, the Ag561Au362 nanoparticle, with a Ag core, shows an anomalous enhancement at low frequencies. An analysis of the calculated VDOSs indicates that as a general trend the low-frequency region is mainly due to the shell contribution, whereas at high frequencies the core effect would be dominant. A linear variation with size is obtained for the period of quasi-breathing mode (QBM), in agreement with the behaviour obtained for pure Ag and Au nanoparticles. A non-monotonic variation is obtained for the QBM frequency as a function of the Ag concentration for all nanoparticles investigated. The calculated specific heat at low temperatures of the Ag-Au nanoparticles is smaller (larger) than the corresponding one calculated for the pure Au (Ag) nanoparticles of same size. Nevertheless, the enhancement of VDOS at low frequencies of the Ag561Au362 nanoparticle with a Ag core induced larger values of specific heat than those of the pure Au923 nanoparticle in the temperature range of 5-15 K. PMID:25697903
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…
Precipitation of icosahedral quasicrystalline phase in Hf65Al7.5Ni10Cu12.5Pd5 metallic glass
NASA Astrophysics Data System (ADS)
Li, Chunfei; Saida, Junji; Matsushita, Mitsuhide; Inoue, Akihisa
2000-07-01
An icosahedral quasicrystalline phase was found in a Hf65Al7.5Ni10Cu12.5Pd5 metallic glass annealed in the supercooled liquid region. Upon annealing at high temperature, the quasicrystalline phase was found to decompose to regular crystalline phases, indicating that it is a metastable phase. The present alloy was compared with the previously reported Zr- and Ti-based alloys with the formation of icosahedral quasicrystalline phases. Hf, Zr, and Ti belong to the same 4A column in the element periodical table. Based on the above comparison, conditions in terms of atomic radius and alloy composition which favor the formation of icosahedral quasicrystalline phase in 4A element based alloys, were suggested.
Tai, K. P.; Gao, N.; Dai, X. D.; Li, J. H.; Lai, W. S.; Liu, B. X.
2006-08-28
Metallic glasses are obtained in an immiscible Nb-Ag system by ion beam mixing and an atomic configuration in the amorphous structure is discovered, i.e., an icositetrahedral ordering, which, together with an icosahedral ordering also observed in the Nb-Ag metallic glasses and in some previously reported systems, helps in formulating a structural spectrum of the amorphous solids. The experimental characterization and atomistic modeling with an ab initio derived Nb-Ag potential demonstrate the significance of structural heredity, i.e., the crystalline structures of the constituent metals play a decisive role in determining the atomic structure of the metallic glasses in the system.
None
2011-10-06
- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not ?renormalizable?. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged ?vector? particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of ?massless? modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a ?massive? SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic ?vector? field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are ?scalar?? fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a ?renormalizable? theory. From our analysi
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 Technical Reports Server (NTRS)
Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)
1994-01-01
The efficient implementation of method for electron correlation in molecular 4-component calculations demands that symmetry be exploited where possible. Algorithms for the construction of matrices and the transformation of integrals over symmetry-adapted basis functions, where the point group is restricted to D(sub 2h) and subgroups, will be presented. The merits of keeping the primitive integrals in the scalar basis will be compared with those of transforming them to the 2-spinor basis.
NASA Astrophysics Data System (ADS)
Buchmuller, Wilfried; Dierigl, Markus; Ruehle, Fabian; Schweizer, Julian
2015-11-01
We consider six-dimensional supergravity with gauge group SO (10) × U(1)A, compactified on the orbifold T2 /Z2. Three quark-lepton generations arise as zero modes of a bulk 16-plet due to magnetic flux of the anomalous U(1)A. Boundary conditions at the four fixed points break SO (10) to subgroups whose intersection is the Standard Model gauge group. The gauge and Higgs sector consist of "split" SO (10) multiplets. As a consequence of the U(1)A flux, squarks and sleptons are much heavier than gauge bosons, Higgs bosons, gauginos and higgsinos. We thus obtain a picture similar to "split supersymmetry". The flavor structure of the quark and lepton mass matrices is determined by the symmetry breaking at the orbifold fixed points.
Sharma, H. R. Smerdon, J. A.; Nugent, P. J.; Ribeiro, A.; McGrath, R.; McLeod, I.; Dhanak, V. R.; Shimoda, M.; Tsai, A. P.; Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577
2014-05-07
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C{sub 60} on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C{sub 60} molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C{sub 60} molecules atop the Pb islands approaches zero, regardless of the overall C{sub 60} coverage.
Sharma, H R; Smerdon, J A; Nugent, P J; Ribeiro, A; McLeod, I; Dhanak, V R; Shimoda, M; Tsai, A P; McGrath, R
2014-05-01
Crystalline and quasicrystalline allotropes of Pb are formed by evaporation on the fivefold surface of the icosahedral (i) Ag-In-Yb quasicrystal under ultra-high vacuum. Lead grows in three dimensional quasicrystalline order and subsequently forms fivefold-twinned islands with the fcc(111) surface orientation atop of the quasicrystalline Pb. The islands exhibit specific heights (magic heights), possibly due to the confinement of electrons in the islands. We also study the adsorption behavior of C60 on the two allotropes of Pb. Scanning tunneling microcopy reveals that a high corrugation of the quasicrystalline Pb limits the diffusion of the C60 molecules and thus produces a disordered film, similar to adsorption behavior of the same molecules on the clean substrate surface. However, the sticking coefficient of C60 molecules atop the Pb islands approaches zero, regardless of the overall C60 coverage. PMID:24811658
de Boissieu, M; Francoual, S; Kaneko, Y; Ishimasa, T
2005-09-01
We report on the absolute scale measurement of the x-ray diffuse scattering in the ZnMgSc icosahedral quasicrystal and its periodic approximant. Whereas the diffuse scattering in the approximant is purely accounted for by thermal diffuse scattering, an additional signal is observed in the quasicrystal. It is related to phason fluctuations as indicated by its Q(2)(per) dependence. Moreover, when compared to previous measurements carried out on the i-AlPdMn phase, we find that the amount of diffuse scattering is smaller in the i-ZnMgSc phase, in agreement with larger phason elastic constants in this phase. This is confirmed by the observation of a large number of weak Bragg peaks having a high Q(per) reciprocal space component. PMID:16196940
NASA Astrophysics Data System (ADS)
Yamamoto, Akiji; Takakura, Hiroyuki
2003-10-01
A six-dimensional (6D) structure of i-Al-Pd-Mn quasicrystal determined recently [Yamamoto et al., J. Alloys Compd. 342, 159 (2002)] leads to two 1/1 approximant structures of i-Al-Pd-Mn and i-Al-Cu-Ru with the space group Pm3¯ (? Al-Pd-Mn-Si and ? Al-Ru-Cu) by the introduction of appropriate uniform (linear) phason strains. The different clusters in the 1/1 approximants are obtained from the different 3D hyperplane passing through (1,1,1,1,1,1)/4 and (1,0,0,0,0,0)/2 in the 6D icosahedral lattice. It is shown that for all cubic approximant represented by consecutive Fibonacci numbers Fn+1/Fn, two different structures can be obtained in the same manner.
NASA Astrophysics Data System (ADS)
Matveev, Alexei V.; Mayer, Markus; Rösch, Notker
2004-07-01
We describe a general strategy for exploiting spatial symmetry in density functional (DF) calculations of molecules and clusters, following the implementation in the parallel DF program PARAGAUSS. Point group elements are defined via a quaternion parametrization. Symmetrized irreducible bases of vector and projective representations as well as Clebsch-Gordan coefficients are constructed with the help of the eigenfunction method. We discuss the symmetrization of molecular orbitals for nonrelativistic and scalar relativistic DF calculations and molecular two- and four-component spinors for relativistic DF calculations that account for spin-orbit interaction. In addition, we present a strategy to symmetrize spinors simultaneously according to a double group and the corresponding point group. In relativistic DF calculations, this approach allows full exploitation of the symmetry of spin-free operators, e.g., in the numerical integration of the exchange-correlation potential.
Henley, E.M.
1981-09-01
Internal and space-time symmetries are discussed in this group of lectures. The first of the lectures deals with an internal symmetry, or rather two related symmetries called charge independence and charge symmetry. The next two discuss space-time symmetries which also hold approximately, but are broken only by the weak forces; that is, these symmetries hold for both the hadronic and electromagnetic forces. (GHT)
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.
Relativistic Effects and the Unique Low-Symmetry Structures of Gold
Gong, Xingao
structure.1517,19 Indeed, a previous PES and theoretical study on coinage metal clusters has confirmed that Au55 is non- icosahedral, even though Cu55 and Ag55 are icosahedral as evidenced by their simple
Relativistic Pseudospin Symmetry
Ginocchio, Joseph N.
2011-05-06
We show that the pseudospin symmetry that Akito Arima discovered many years ago (with collaborators) is a symmetry of the the Dirac Hamiltonian for which the sum of the scalar and vector potentials are a constant. In this paper we discuss some of the implications of this relativistic symmetry and the experimental data that support these predictions. In his original paper Akito also discussed pseudo-U(3) symmetry. We show that pseudo-U(3) symmetry is a symmetry of the Dirac Hamiltonian for which the sum of harmonic oscillator vector and scalar potentials are equal to a constant, and we give the generators of pseudo-U(3) symmetry. Going beyond the mean field we summarize new results on non relativistic shell model Hamiltonians that have pseudospin symmetry and pseudo-orbital angular momentum symmetry as a dynamical symmetries.
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
Altschul, Brett
2009-12-17
Many important symmetries in physics do not hold exactly. If CPT symmetry were violated, this would have important implications; for example, CPT violation in quantum field theory automatically entails violation of Lorentz symmetry as well. The standard model extension provides a general framework for studying the possible breakdown of these symmetries. Work on this subject has accelerated tremendously in the last fifteen years, and there are many new constraints on Lorentz and CPT symmetry breaking.
Jakse, N; Pasturel, A
2015-08-28
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al80Ni20 alloy upon cooling. Our results evidence a huge increase of local icosahedral ordering (ISRO) in the undercooled regime which is more developed around Ni than Al atoms. We show that ISRO has a strong impact on self-diffusion coefficients of both species and is at the origin of their crossover from Arrhenius to non-Arrhenius behavior around a crossover temperature TX = 1000 K, located in the undercooled region. We also clearly identify that this temperature corresponds to the development of dynamic heterogeneities and to the breakdown of the Stokes-Einstein relation. At temperatures below this crossover, we find that the behavior of the diffusion and relaxation dynamics is mostly incompatible with predictions of the mode-coupling theory. Finally, an analysis of the van Hove function indicates that the crossover temperature TX marks the onset of a change in the diffusion mechanism from a normal flow to an activated process with hopping. From these results, the glass-forming ability of the alloy is discussed. PMID:26328857
NASA Astrophysics Data System (ADS)
Jakse, N.; Pasturel, A.
2015-08-01
We use ab initio molecular dynamics simulations to study the correlation between the local ordering and the dynamic properties of liquid Al80Ni20 alloy upon cooling. Our results evidence a huge increase of local icosahedral ordering (ISRO) in the undercooled regime which is more developed around Ni than Al atoms. We show that ISRO has a strong impact on self-diffusion coefficients of both species and is at the origin of their crossover from Arrhenius to non-Arrhenius behavior around a crossover temperature TX = 1000 K, located in the undercooled region. We also clearly identify that this temperature corresponds to the development of dynamic heterogeneities and to the breakdown of the Stokes-Einstein relation. At temperatures below this crossover, we find that the behavior of the diffusion and relaxation dynamics is mostly incompatible with predictions of the mode-coupling theory. Finally, an analysis of the van Hove function indicates that the crossover temperature TX marks the onset of a change in the diffusion mechanism from a normal flow to an activated process with hopping. From these results, the glass-forming ability of the alloy is discussed.
Maniraj, M; Rai, Abhishek; Barman, S R; Krajci, M; Schlagel, Deborah L; Lograsso, Thomas A; Horn, K
2014-09-01
We study the unoccupied region of the electronic structure of the fivefold symmetric surface of an icosahedral (i) Al-Pd-Mn quasicrystal. A feature that exhibits parabolic dispersion with an effective mass of (1.15±0.1)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)
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.
Rasin, A.
1994-04-01
We discuss the idea of approximate flavor symmetries. Relations between approximate flavor symmetries and natural flavor conservation and democracy models is explored. Implications for neutrino physics are also discussed.
Geometric intrinsic symmetries
Gozdz, A. Szulerecka, A.; Pedrak, A.
2013-08-15
The problem of geometric symmetries in the intrinsic frame of a many-body system (nucleus) is considered. An importance of symmetrization group notion is discussed. Ageneral structure of the intrinsic symmetry group structure is determined.
Polynomial Graphs and Symmetry
ERIC Educational Resources Information Center
Goehle, Geoff; Kobayashi, Mitsuo
2013-01-01
Most quadratic functions are not even, but every parabola has symmetry with respect to some vertical line. Similarly, every cubic has rotational symmetry with respect to some point, though most cubics are not odd. We show that every polynomial has at most one point of symmetry and give conditions under which the polynomial has rotational or…
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.
Heule, Marijn
2010-01-01
We define the concept of an internal symmetry. This is a symmety within a solution of a constraint satisfaction problem. We compare this to solution symmetry, which is a mapping between different solutions of the same problem. We argue that we may be able to exploit both types of symmetry when finding solutions. We illustrate the potential of exploiting internal symmetries on two benchmark domains: Van der Waerden numbers and graceful graphs. By identifying internal symmetries we are able to extend the state of the art in both cases.
Davide Gaiotto; Anton Kapustin; Nathan Seiberg; Brian Willett
2015-01-10
A $q$-form global symmetry is a global symmetry for which the charged operators are of space-time dimension $q$; e.g. Wilson lines, surface defects, etc., and the charged excitations have $q$ spatial dimensions; e.g. strings, membranes, etc. Many of the properties of ordinary global symmetries ($q$=0) apply here. They lead to Ward identities and hence to selection rules on amplitudes. Such global symmetries can be coupled to classical background fields and they can be gauged by summing over these classical fields. These generalized global symmetries can be spontaneously broken (either completely or to a subgroup). They can also have 't Hooft anomalies, which prevent us from gauging them, but lead to 't Hooft anomaly matching conditions. Such anomalies can also lead to anomaly inflow on various defects and exotic Symmetry Protected Topological phases. Our analysis of these symmetries gives a new unified perspective of many known phenomena and uncovers new results.
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
On group Fourier analysis and symmetry preserving discretizations of PDEs
NASA Astrophysics Data System (ADS)
Munthe-Kaas, H. Z.
2006-05-01
In this paper we review some group theoretic techniques applied to discretizations of PDEs. Inspired by the recent years active research in Lie group- and exponential-time integrators for differential equations, we will in the first part of the paper present algorithms for computing matrix exponentials based on Fourier transforms on finite groups. As an example, we consider spherically symmetric PDEs, where the discretization preserves the 120 symmetries of the icosahedral group. This motivates the study of spectral element discretizations based on triangular subdivisions. In the second part of the paper, we introduce novel applications of multivariate non-separable Chebyshev polynomials in the construction of spectral element bases on triangular and simplicial sub-domains. These generalized Chebyshev polynomials are intimately connected to the theory of root systems and Weyl groups (used in the classification of semi-simple Lie algebras), and these polynomials share most of the remarkable properties of the classical Chebyshev polynomials, such as near-optimal Lebesgue constants for the interpolation error, the existence of FFT-based algorithms for computing interpolants and pseudo-spectral differentiation and existence of Gaussian integration rules. The two parts of the paper can be read independently.
Conformal symmetry superalgebras
Paul de Medeiros; Stefan Hollands
2013-06-03
We show how the rigid conformal supersymmetries associated with a certain class of pseudo-Riemannian spin manifolds define a Lie superalgebra. The even part of this superalgebra contains conformal isometries and constant R-symmetries. The odd part is generated by twistor spinors valued in a particular R-symmetry representation. We prove that any manifold which admits a conformal symmetry superalgebra of this type must generically have dimension less than seven. Moreover, in dimensions three, four, five and six, we provide the generic data from which the conformal symmetry superalgebra is prescribed. For conformally flat metrics in these dimensions, and compact R-symmetry, we identify each of the associated conformal symmetry superalgebras with one of the conformal superalgebras classified by Nahm. We also describe several examples for Lorentzian metrics that are not conformally flat.
Baryogenesis from Symmetry Principle
Chee Sheng Fong
2015-08-14
In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario and also to identity the different roles played by the symmetry. This formalism is then applied to the standard model and its supersymmetric extension, which constitute two important foundations for constructing models of baryogenesis.
Baryogenesis from Symmetry Principle
Fong, Chee Sheng
2015-01-01
In this work, a formalism based on symmetry which allows one to express asymmetries of all the particles in terms of conserved charges is developed. The manifestation of symmetry allows one to easily determine the viability of a baryogenesis scenario and also to identity the different roles played by the symmetry. This formalism is then applied to the standard model and its supersymmetric extension, which constitute two important foundations for constructing models of baryogenesis.
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.
Symmetries in atmospheric sciences
Alexander Bihlo
2009-02-24
Selected applications of symmetry methods in the atmospheric sciences are reviewed briefly. In particular, focus is put on the utilisation of the classical Lie symmetry approach to derive classes of exact solutions from atmospheric models. This is illustrated with the barotropic vorticity equation. Moreover, the possibility for construction of partially-invariant solutions is discussed for this model. A further point is a discussion of using symmetries for relating different classes of differential equations. This is illustrated with the spherical and the potential vorticity equation. Finally, discrete symmetries are used to derive the minimal finite-mode version of the vorticity equation first discussed by E. Lorenz (1960) in a sound mathematical fashion.
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.
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
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.
Differential Invariants and Hidden Symmetry
Irina Yehorchenko
2011-02-28
We describe some classes of PDE that display hidden symmetry, with reduced equations having additional symmetry operators compared to the initial equations. Relations between the concepts of hidden and conditional symmetry, and between hidden symmetry and equivalence of classes of equations, is discussed. In particular, we describe equations having hidden and conditional symmetry under rotations and boosts in the Lorentz and Euclid groups.
ERIC Educational Resources Information Center
Marchis, Iuliana
2009-01-01
Symmetry is one of the fundamental concepts in Geometry. It is a Mathematical concept, which can be very well connected with Art and Ethnography. The aim of the article is to show how to link the geometrical concept symmetry with interculturality. For this mosaics from different countries are used.
Symmetries in Lagrangian Dynamics
ERIC Educational Resources Information Center
Ferrario, Carlo; Passerini, Arianna
2007-01-01
In the framework of Noether's theorem, a distinction between Lagrangian and dynamical symmetries is made, in order to clarify some aspects neglected by textbooks. An intuitive setting of the concept of invariance of differential equations is presented. The analysis is completed by deriving the symmetry properties in the motion of a charged…
Lang, C. B.; Schroeck, Mario
2011-10-15
In quantum chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the behavior of meson propagators when removing increasingly more of those modes in the valence sector, thus partially removing effects of chiral symmetry breaking. We find that some of the symmetry aspects are restored (e.g., the masses of {rho} and a{sub 1} approach each other) while confining properties persist.
NASA Astrophysics Data System (ADS)
Castaños, Octavio
2010-09-01
The purpose of this course is to study the evolution of the symmetry concept and establish its influence in the knowledge of the fundamental laws of nature. Physicist have been using the symmetry concept in two ways: to solve problems and to search for new understanding of the world around us. In quantum physics symmetry plays a key role in gaining an understanding of the physical laws governing the behavior of matter and field systems. It provides, generally, a shortcut based on geometry for discovering the secrets of the Universe. Because it is believed that the laws of physics are invariant under discrete and continuous transformation operations of the space and time, there are continuous symmetries, for example, energy and momentum together with discrete ones corresponding to charge, parity and time reversal operations.
Dynamical symmetries for fermions
Guidry, M.
1989-01-01
An introduction is given to the Fermion Dynamical Symmetry Model (FDSM). The analytical symmetry limits of the model are then applied to the calculation of physical quantities such as ground-state masses and B(E{sub 2}) values in heavy nuclei. These comparisons with data provide strong support for a new principle of collective motion, the Dynamical Pauli Effect, and suggest that dynamical symmetries which properly account for the pauli principle are much more persistent in nuclear structure than the corresponding boson symmetries. Finally, we present an assessment of criticisms which have been voiced concerning the FDSM, and a discussion of new phenomena and exotic spectroscopy'' which may be suggested by the model. 14 refs., 8 figs., 4 tabs.
ERIC Educational Resources Information Center
Groetsch, C. W.
2005-01-01
Resistance destroys symmetry. In this note, a graphical exploration serves as a guide to a rigorous elementary proof of a specific asymmetry in the trajectory of a point projectile in a medium offering linear resistance.
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.
Metropolis, N; Rota, G C; Stein, J A
1991-01-01
Although a great deal of work has gone into construction of the irreducible representations of the symmetric group n (and of the general linear group) a simple, intuitive characterization of the symmetry classes is missing. Relying on a systematic distinction between permutations of variables and permutations of places, we provide two such characterizations, showing that elements belonging to any such symmetry class can be described in one of two ways: (i) as the solutions of explicitly given (though not independent) sets of linear equations or (ii) as linear combinations of "simple" elements of a given symmetry class, a simple element being a generalization to an arbitrary symmetry class of the notion of a decomposable skew-symmetric tensor. PMID:11607215
Lovelady, Benjamin C
2015-01-01
According to the Coleman-Mandula theorem, any gauge theory of gravity combined with an internal symmetry based on a Lie group must take the form of a direct product in order to be consistent with basic assumptions of quantum field theory. However, we show that an alternative gauging of a simple group can lead dynamically to a spacetime with compact internal symmetry. The biconformal gauging of the conformal symmetry of n-dim Euclidean space doubles the dimension to give a symplectic manifold. Examining one of the Lagrangian submanifolds in the flat case, we find that in addition to the expected SO(n) connection and curvature, the solder form necessarily becomes Lorentzian. General coordinate invariance gives rise to an SO(n-1,1) connection on the spacetime. The principal fiber bundle character of the original SO(n) guarantees that the two symmetries enter as a direct product, in agreement with the Coleman-Mandula theorem.
NASA Astrophysics Data System (ADS)
Bevan, Adrian John
2014-11-01
Following a brief introduction I report the current status of symmetry violation tests from the BABAR experiment, including recent results on the measurement of T violation, and searches for CP and T violation in mixing.
Symmetries of boundary value problems in mathematical physics
NASA Astrophysics Data System (ADS)
Makai, M.; Orechwa, Y.
1999-10-01
The problem considered here is to find a function satisfying a linear elliptic differential or integral equation inside a finite simply region V and another linear first-order differential or integral equation on the ?V boundary. The symmetries of the above problem form a point group. We show that if the homogeneous problem has only the trivial solution, then the symmetry of the solution inside V inherits the symmetry of the boundary value, given on ?V. The boundary value is decomposed into irreducible components and the physical meaning of the irreducible components is highlighted. We then apply the results to investigate a widely utilized numerical solution technique that is based on a variational principle and utilizes two approximations. The first one approximates, the solution inside V by a polynomial, the second approximation assumes the solution on the boundary to be a low-order polynomial. By means of group representation theory, we show that the mentioned approximations may fail for certain combinations. The predicted problems have been observed in the VARIANT code, which is routinely used to solve the multigroup neutron diffusion equation. Our method is also applicable to the Schrödinger, and to heat conductance and wave equations.
Tarumi, Ryuichi
2013-11-01
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: [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. 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
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
Veesler, David; Ng, Thiam-Seng; Sendamarai, Anoop K.; Eilers, Brian J.; Lawrence, C. Martin; Lok, Shee-Mei; Young, Mark J.; Johnson, John E.; Fu, Chi-yu
2013-01-01
Sulfolobus turreted icosahedral virus (STIV) was isolated in acidic hot springs where it infects the archeon Sulfolobus solfataricus. We determined the STIV structure using near-atomic resolution electron microscopy and X-ray crystallography allowing tracing of structural polypeptide chains and visualization of transmembrane proteins embedded in the viral membrane. We propose that the vertex complexes orchestrate virion assembly by coordinating interactions of the membrane and various protein components involved. STIV shares the same coat subunit and penton base protein folds as some eukaryotic and bacterial viruses, suggesting that they derive from a common ancestor predating the divergence of the three kingdoms of life. One architectural motif (?-jelly roll fold) forms virtually the entire capsid (distributed in three different gene products), indicating that a single ancestral protein module may have been at the origin of its evolution. PMID:23520050
Dai, Tie; Schutgens, Nick A J; Goto, Daisuke; Shi, Guangyu; Nakajima, Teruyuki
2014-12-01
A new global aerosol assimilation system adopting a more complex icosahedral grid configuration is developed. Sensitivity tests for the assimilation system are performed utilizing satellite retrieved aerosol optical depth (AOD) from the Moderate Resolution Imaging Spectroradiometer (MODIS), and the results over Eastern Asia are analyzed. The assimilated results are validated through independent Aerosol Robotic Network (AERONET) observations. Our results reveal that the ensemble and local patch sizes have little effect on the assimilation performance, whereas the ensemble perturbation method has the largest effect. Assimilation leads to significantly positive effect on the simulated AOD field, improving agreement with all of the 12 AERONET sites over the Eastern Asia based on both the correlation coefficient and the root mean square difference (assimilation efficiency). Meanwhile, better agreement of the Ångström Exponent (AE) field is achieved for 8 of the 12 sites due to the assimilation of AOD only. PMID:25017412
Superconductivity and symmetry breaking
NASA Astrophysics Data System (ADS)
Sarasua, L. G.
2012-02-01
In the present work we consider the relation between superconductivity and spontaneous gauge symmetry breaking (SGBS). We show that ODLRO does not require in principle SBGS, even in the presence of particle number fluctuations, by examining exact solutions of a fermionic pairing model. The criteria become equivalent if a symmetry breaking field is allowed, which can be attributed to the interaction with the environment. However, superconducting states without SBGS are not forbidden.
Christian Fleischhack
2015-03-21
The symmetries of paths in a manifold $M$ are classified with respect to a given pointwise proper action of a Lie group $G$ on $M$. Here, paths are embeddings of a compact interval into $M$. There are at least two types of symmetries: Firstly, paths that are parts of an integral curve of a fundamental vector field on $M$ (continuous symmetry). Secondly, paths that can be decomposed into finitely many pieces, each of which is the translate of some free segment, where possibly the translate is cut at the two ends of the paths (discrete symmetry). Here, a free segment is a path $e$ whose $G$-translates either equal $e$ or intersect it in at most finitely many points. Note that all the statements above are understood up to the parametrization of the paths. We will show, for the category of analytic manifolds, that each path is of exactly one of either types. For the proof, we use that the overlap of a path $\\gamma$ with one of its translates is encoded uniquely in a mapping between subsets of $\\dom\\gamma$. Running over all translates, these mappings form the so-called reparametrization set to $\\gamma$. It will turn out that, up to conjugation with a diffeomorphism, any such set is given by the action of a Lie subgroup of $O(2)$ on $S^1$, restricted in domain and range to some compact interval on $S^1$. Now, the infinite subgroups correspond to the continuous symmetry above, finite ones to the discrete symmetry.
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
Kawamura, Yoshiharu
2015-01-01
We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetry is a kind of fermionic symmetry, different from the space-time supersymmetry and the BRST symmetry. Subsidiary conditions on states guarantee the unitarity of systems.
Wallpaper and symmetry Michael Giudici
Giudici, Michael
Wallpaper and symmetry Michael Giudici #12;How many types of wallpaper are there? Will study wallpaper according to the symmetry. If have the same symmetries then say of the same type. #12;What do we will classify types of wallpaper according to their group of symmetries. A different group means different
Yoshiharu Kawamura
2015-05-20
We study the quantization of systems with local particle-ghost symmetries. The systems contain ordinary particles including gauge bosons and their counterparts obeying different statistics. The particle-ghost symmetry is a kind of fermionic symmetry, different from the space-time supersymmetry and the BRST symmetry. Subsidiary conditions on states guarantee the unitarity of systems.
On the symmetry of three identical interacting particles in a one-dimensional box
NASA Astrophysics Data System (ADS)
Amore, Paolo; Fernández, Francisco M.
2015-11-01
We study a quantum-mechanical system of three particles in a one-dimensional box with two-particle harmonic interactions. The symmetry of the system is described by the point group D3d. Group theory greatly facilitates the application of perturbation theory and the Rayleigh-Ritz variational method. A great advantage is that every irreducible representation can be treated separately. Group theory enables us to predict the connection between the states for the small box length and large box length regimes of the system. We discuss the crossings and avoided crossings of the energy levels as well as other interesting features of the spectrum of the system.
Tests of fundamental symmetries
NASA Astrophysics Data System (ADS)
Budker, Dmitry
2015-04-01
``Fundamental symmetry'' refers to invariance of the laws of Nature, including the values of fundamental constants, with respect to a continuous or discrete transformation such as translation in space or time, rotation, spatial (P), time (T), or charge (C) reversal, combinations of these, or permutation of identical quantum particles. All discrete symmetries except for the combined CPT and the permutation symmetry are experimentally known to be violated by the weak interactions; intense searches are conducted for possible small violations of the still-standing discrete as well as the continuous symmetries, which may result from exotic beyond-the-standard-model interactions. In this talk, I will describe some of the recent fundamental-symmetry tests involving our research group (for up-to-date bibliography see http://budker.berkeley.edu/PubList.html), including measuring the effect of the gravitation-field gradient on the value of the fine-structure ``constant,'' and searching for transient and time-dependent effects on atomic magnetometers and clocks.
Symmetry of composite crystals
NASA Astrophysics Data System (ADS)
van Smaalen, Sander
1991-05-01
Composite crystals are crystals that consist of two or more subsystems, in first approximation each one having its own three-dimensional periodicity. The symmetry of these subsystems is then characterized by an ordinary space group. Due to their mutual interaction the true structure consists of a collection of incommensurately modulated subsystems. In this paper we derive some general properties for intergrowth structures, using the superspace-group theory as developed by Janner and Janssen [Acta Crystallogr. A36, 408 (1980)]. In particular, the pseudoinverse is defined of the matrices relating the subsystem periodicities to the translation vectors in superspace. This pseudoinverse is then used to reformulate the relations between the structure and symmetry in three-dimensional space and in (3+d)-dimensional superspace. As an extension of the theory, subsystem superspace groups are defined, that characterize the symmetry of the individual, incommen- surately modulated subsystems. The relation between a unified description of the symmetry and an independent description of the subsystems is analyzed in detail, both on the level of the basic structure (translational symmetric subsystems) and on the level of the modulated structure (incommensurately modulated subsystems). The concepts are illustrated by the analysis of the diffraction symmetry of the intergrowth compound Hg3-?AsF6.
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).
Mamone, Salvatore; Johnson, Mark R; Ollivier, Jacques; Rols, Stéphane; Levitt, Malcolm H; Horsewill, Anthony J
2016-01-21
The fine structure of the rotational ground state of molecular ortho-hydrogen confined inside the fullerene cage C60 is investigated by inelastic neutron scattering (INS). The INS line corresponding to transitions between the three sub-levels comprising the ortho ground state to the non-degenerate para ground state was studied as a function of temperature down to 60 mK in neutron energy gain. The experiments show that at ambient pressure the three ortho sub-levels are split into a low energy non-degenerate level and a high energy doubly degenerate level separated by 0.135 ± 0.010 meV. This observation is consistent with hydrogen molecules being located at sites with axial symmetry superseding the icosahedral symmetry of isolated rigid C60 cages in the solid phase. To gain insight into the role of inter-cage interactions in determining the symmetry breaking potential, the effects of hydrostatic pressure on the fine structure of the line was also investigated. The analysis of the INS spectra shows that the potential and the energy levels of H2 are sensitive to the orientation of neighbouring cages, consistent with the low-temperature crystalline phase of C60. PMID:26687060
NASA Astrophysics Data System (ADS)
Ismael, Jenann Tareq
1997-04-01
Structures of many different sorts arise in physics, e.g., the concrete structures of material bodies, the structure exemplified by the spatiotemporal configuration of a set of bodies, the structures of more abstract objects like states, state-spaces, laws, and so on. To each structure of any of these types there corresponds a set of transformations which map it onto itself. These are its symmetries. Increasingly ubiquitous in theoretical discussions in physics, the notion of symmetry is also at the root of some time-worn philosophical debates. This dissertation consists of a set of essays on topics drawn from places where the two fields overlap. The first essay is an informal introduction to the mathematical study of symmetry. The second essay defends a famous principle of Pierre Curie which states that the symmetries of a cause are always symmetries of its effect. The third essay takes up the case of reflection in space in the context of a controversy stemming from one of Kant's early arguments for the substantivality of space. The fourth essay is a discussion of the general conditions under which an asymmetry in a phenomenon suggests an asymmetry in the laws which govern it. The case of reflection in time-specifically, the theoretical strategy used in statistical mechanics to subsume the time-asymmetric phenomena of Thermodynamics under the time-symmetric classical dynamical laws-is used to illustrate the general points. The philosophical heart of the thesis lies in its fifth essay. Here a somewhat novel way of conceiving scientific theorizing is articulated, one suggested by the abstract mathematical perspective of symmetry.
Weakly broken galileon symmetry
NASA Astrophysics Data System (ADS)
Pirtskhalava, David; Santoni, Luca; Trincherini, Enrico; Vernizzi, Filippo
2015-09-01
Effective theories of a scalar phi invariant under the internal galileon symmetry phi?phi+b? x? have been extensively studied due to their special theoretical and phenomenological properties. In this paper, we introduce the notion of weakly broken galileon invariance, which characterizes the unique class of couplings of such theories to gravity that maximally retain their defining symmetry. The curved-space remnant of the galileon's quantum properties allows to construct (quasi) de Sitter backgrounds largely insensitive to loop corrections. We exploit this fact to build novel cosmological models with interesting phenomenology, relevant for both inflation and late-time acceleration of the universe.
I. de Medeiros Varzielas
2015-10-08
CP-odd invariants, independent of basis and valid for any choice of CP transformation are a powerful tool in the study of CP. They are particularly convenient to study the CP properties of models with family symmetries. After interpreting the consequences of adding specific CP symmetries to a Lagrangian invariant under $\\Delta(27)$, I use the invariant approach to systematically study Yukawa-like Lagrangians with an increasing field content in terms of $\\Delta(27)$ representations. Included in the Lagrangians studied are models featuring explicit CP violation with calculable phases (referred to as explicit geometrical CP violation) and models that automatically conserve CP, despite having all the $\\Delta(27)$ representations.
Symmetry in Nature Unit code: MATH35082
Sidorov, Nikita
and stabilizers. 2. Symmetry in geometry: Example classification of triangles 3. Classification: of symmetry, Princeton Science Library (1952) Advanced: M. Golubitsky & I. Stewart, The Symmetry Perspective, Birkhauser
ERIC Educational Resources Information Center
Crumpecker, Cheryl
2003-01-01
Describes an art lesson used with children in the third grade to help them learn about symmetry, as well as encouraging them to draw larger than usual. Explains that students learn about the belief called "Horror Vacui" of the Northwest American Indian tribes and create their interpretation of this belief. (CMK)
Emily Clader; Yongbin Ruan
2015-09-30
These expository notes are based on lectures by Yongbin Ruan during a special semester on the B-model at the University of Michigan in Winter 2014. They outline and compare the mirror symmetry constructions of Batyrev-Borisov, Hori-Vafa, and Berglund-Hubsch-Krawitz.
Killing Tensors and Symmetries
David Garfinkle; E. N. Glass
2010-03-10
A new method is presented for finding Killing tensors in spacetimes with symmetries. The method is used to find all the Killing tensors of Melvin's magnetic universe and the Schwarzschild vacuum. We show that they are all trivial. The method requires less computation than solving the full Killing tensor equations directly, and it can be used even when the spacetime is not algebraically special.
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
NASA Astrophysics Data System (ADS)
Kotov, Alexei; Strobl, Thomas
2016-01-01
The gauge principle is at the heart of a good part of fundamental physics: Starting with a group G of so-called rigid symmetries of a functional defined over space-time ?, the original functional is extended appropriately by additional Lie(G) -valued 1-form gauge fields so as to lift the symmetry to Maps(?, G) . Physically relevant quantities are then to be obtained as the quotient of the solutions to the Euler-Lagrange equations by these gauge symmetries. In this article we show that one can construct a gauge theory for a standard sigma model in arbitrary space-time dimensions where the target metric is not invariant with respect to any rigid symmetry group, but satisfies a much weaker condition: It is sufficient to find a collection of vector fields va on the target M satisfying the extended Killing equationv a(i ; j) = 0 for some connection acting on the index a. For regular foliations this is equivalent to requiring the conormal bundle to the leaves with its induced metric to be invariant under leaf-preserving diffeomorphisms of M, which in turn generalizes Riemannian submersions to which the notion reduces for smooth leaf spaces M / ?. The resulting gauge theory has the usual quotient effect with respect to the original ungauged theory: in this way, much more general orbits can be factored out than usually considered. In some cases these are orbits that do not correspond to an initial symmetry, but still can be generated by a finite-dimensional Lie group G. Then the presented gauging procedure leads to an ordinary gauge theory with Lie algebra valued 1-form gauge fields, but showing an unconventional transformation law. In general, however, one finds that the notion of an ordinary structural Lie group is too restrictive and should be replaced by the much more general notion of a structural Lie groupoid.
Narasimhan, Sri Kamesh; Lu, Xiaoying; Luk, Yan-Yeung
2008-08-01
Ever since point groups of symmetry have been used to describe molecules after Van't Hoff and Le Bel proposed tetrahedral structures for carbon atoms in 1874, it remains difficult to design chiral molecules with polyhedral symmetry T, O, or I. Past theoretical and experimental studies have mainly accomplished molecular structures that have the conformations for satisfying the T symmetry. In this work, we present a general theoretical approach to construct rigid molecular structures that have permanently the symmetry of T, O, and I. This approach involves desymmetrization of the vertices or the edges of Platonic solid-shaped molecules with dissymmetric moieties. Using density functional theory (DFT) and assisted model building and energy refinement (AMBER) computational methods, the structure, the rigidity, and the symmetry of the molecule are confirmed by assessing the lowest energy conformation of the molecule, which is initially presented in a planar graph. This method successfully builds molecular structures that have the symmetry of T, O, and I. Interestingly, desymmetrization of the edges has a more stringent requirement of rigidity than desymmetrization of the vertices for affording the T, O, or I symmetry. PMID:18266212
Guo, Yiming; Stacey, Timothy E; Fredrickson, Daniel C
2014-05-19
The crystal structures of intermetallic phases offer a wealth of geometrical features (helices, multishelled clusters, and host-guest motifs) whose formation has yet to be explained or predicted by chemical theory. A recently developed extension of the acid-base concept to metallic systems, the ?3-acidity model, provides an avenue for developing this understanding for intermetallics formed from transition metals. In this Article, we illustrate how this approach can be used to understand one of the most striking geometrical entities to emerge in intermetallic chemistry, the Mackay cluster of icosahedral quasicrystals. We present ?3-acidity analyses, based on DFT-calibrated Hückel calculations, for a series of Sc-Ir intermetallics: ScIr (CsCl-type), Sc2Ir (Ti2Ni-type), Sc11Ir4, and the Mackay cluster containing phases Sc57Ir13 and Sc44Ir7. We begin by illustrating that a ?3-acidity model correctly predicts that each of these phases is stable relative to disproportionation into their neighboring compounds when a common set of Hückel parameters and d-orbital occupancies is used. Next, we explain these results by developing a relationship between the distance distribution of homoatomic contacts within an atom's coordination sphere and the ?3-neutralization it experiences. For a given average homoatomic distance, the role of heteroatomic contacts is higher when the distribution of homoatomic contacts is narrower. This effect is key to the strength of the acid-base neutralization of the Sc-rich phases, where the Sc atoms find a scarcity of Ir atoms from which to obtain neutralization. Under these circumstances, Sc-Ir contacts should be maximized, whereas the number and distance variations of the Sc-Sc contacts should be minimized. These expectations are borne out by the observed crystal structures. In particular, the Mackay clusters of Sc57Ir13 and Sc44Ir7, in which a central Ir atom is icosahedrally coordinated by a pentagonal dodecahedral array of face-sharing Sc octahedra, represent a natural way of merging the competing needs for enhancing Sc-Ir interactions while diminishing those between the Sc atoms. PMID:24801239
Unal, Baris
2008-12-01
The present work in this dissertation mainly focuses on the clean fivefold surfaces of i-Al-Pd-Mn quasicrystals as well as the nucleation and growth of Ag films on these surfaces. In addition, Ag film growth on NiAl(110) has been explored in the frame of this dissertation. First, we have investigated the equilibration of a fivefold surface of icosahedral Al-Pd-Mn quasicrystal at 900-915 K and 925-950 K, using Omicron variable temperature scanning tunneling microscope (STM). Annealing at low temperatures resulted in many voids on some terraces while the others were almost void-free. After annealing at 925-950K, void-rich terraces became much rarer. Our STM images suggest that through growth and coalescence of the voids, a different termination becomes exposed on host terraces. All of these observations in our study indicate that even after the quasicrystalline terrace-step structure appears, it evolves with time and temperature. More specifically, based on the STM observations, we conclude that during the annealing a wide range of energetically similar layers nucleate as surface terminations, however, with increasing temperature (and time) this distribution gets narrower via elimination of the metastable void-rich terraces. Next, we have examined the bulk structural models of icosahedral Al-Pd-Mn quasicrystal in terms of the densities, compositions and interplanar spacings for the fivefold planes that might represent physical surface terminations. In our analyses, we mainly have focused on four deterministic models which have no partial or mixed occupancy but we have made some comparisons with an undeterministic model. We have compared the models with each other and also with the available experimental data including STM, LEED-IV, XPD and LEIS. In all deterministic models, there are two different families of layers (a pair of planes), and the nondeterministic model contains similar group of planes. These two families differ in terms of the chemical decoration of their top planes. Hence, we name them as Pd+(with Pd) and Pd-(without Pd). Based on their planer structure and the step height, it can be said that these two families can be viable surface terminations. However, besides the Pd content, these two sets differ in terms of relative densities of their top planes as well as the gap separating the layer from the nearest atomic plane. The experimental data and other arguments lead to the conclusion that the Pd- family is favored over the Pd+. This has an important implication on the interpretation of local motifs seen in the high resolution STM images. In other words, the dark stars are not formed by cut-Bergmans rather they are formed by cut-Mackays.
Notation Confusion of Symmetry Species for Molecules with Several Large-Amplitude Internal Motions
NASA Astrophysics Data System (ADS)
Groner, P.
2011-06-01
The Mulliken convention has become the standard notation for symmetry species (irreducible representations) of point groups for quasi-rigid molecules. No such convention exists for symmetry species of symmetry groups for semi-rigid or non-rigid molecules with large amplitude internal motions (LAMs). As a result, we have a situation where we create notations in a do-it-yourself fashion or adopt them from the literature, sometimes even without proper reference to its derivation or to the character table on which it is based. This may be just a nuisance for those who are comfortable enough with group theory and molecular symmetry groups to figure "it" out, but it represents a real problem for everybody else. The notation confusion is illustrated with examples from the literature (both old and new) on molecules with two or more LAMs. Most authors use the notation introduced by Myers and Wilson for molecules such as acetone or propane. No universal notation is in use for molecules with two methyl groups but lower overall symmetry. For example, the notation G_1_8 is used for one of these groups. As it turns out, different people use the same notation for different groups. This presentation is an attempt to bring some light into the dark and to combat confusion with a call for an anti-confusion convention. R. S. Mulliken, Phys. Rev. 43, 279 (1933). R. J. Myers, E. B. Wilson, J. Chem. Phys. 33, 186 (1960).
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
Helical symmetry in linear systems
Bicak, Jiri; Schmidt, Bernd G.
2007-11-15
We investigate properties of solutions of the scalar wave equation and Maxwell's equations on Minkowski space with helical symmetry. Existence of local and global solutions with this symmetry is demonstrated with and without sources. The asymptotic properties of the solutions are analyzed. We show that the Newman-Penrose retarded and advanced scalars exhibit specific symmetries and generalized peeling properties.
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.
Charge Independence and Charge Symmetry
Gerald A. Miller; Willem T. H. van Oers
1994-09-14
Charge independence and charge symmetry are approximate symmetries of nature, violated by the perturbing effects of the mass difference between up and down quarks and by electromagnetic interactions. The observations of the symmetry breaking effects in nuclear and particle physics and the implications of those effects are reviewed.
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…
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…
PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS
P. PAGE; T. GOLDMAN; J. GINOCCHIO
2000-08-01
Ginocchio argued that chiral symmetry breaking in QCD is responsible for the relativistic pseudospin symmetry in the Dirac equation, explaining the observed approximate pseudospin symmetry in sizable nuclei. On a much smaller scale, it is known that spin-orbit splittings in hadrons are small. Specifically, new experimental data from CLEO indicate small splittings in D-mesons. For heavy-light mesons we identify a cousin of pseudospin symmetry that suppresses these splittings in the Dirac equation, known as spin symmetry. We suggest an experimental test of the implications of spin symmetry for wave functions in electron-positron annihilation. We investigate how QCD can give rise to two different dynamical symmetries on nuclear and hadronic scales.
Broken symmetries and signatures
NASA Astrophysics Data System (ADS)
Fitzpatrick, Andrew Liam
We consider three possible extensions of the Standard Model. In the first model, we explore the possibility to solve the strong CP problem and flavor puzzle in a model with fermions in the bulk of a warped extra dimensions, making use of the enhanced spacetime symmetries present in extra dimensions. In the second, we systematically explore the possible low-energy spectrum arising from gauge-mediated supersymmetry breaking when the messenger sector obeys a U(1) R-symmetry and all allowed renormalizable operators in the messenger sector are included. In the third, we study single-field models of inflation using an effective theory for the pions of spontaneously broken time translation invariance and explicitly prove a consistency relation for the three-point function of density perturbations.
A Relativistic Symmetry in Nuclei
Joseph N. Ginocchio
1998-12-14
We review the status of a quasi - degenerate doublets in nuclei, called pseudospin doublets, which were discovered about thirty years ago and the origins of which have remained a mystery, until recently. We show that pseudospin doublets originate from an SU(2) symmetry of the Dirac Hamiltonian which occurs when the scalar and vector potentials are opposite in sign but equal in magnitude. Furthermore, we survey the evidence that pseudospin symmetry is approximately conserved for a Dirac Hamiltonian with realistic scalar and vector potentials. We briefly discuss the relationship of pseudospin symmetry with chiral symmetry and the implications of pseudospin symmetry for the antinucleon spectrum in nuclei.
Symmetries in laminated composite plates
NASA Technical Reports Server (NTRS)
Noor, A. K.
1976-01-01
The different types of symmetry exhibited by laminated anisotropic fibrous composite plates are identified and contrasted with the symmetries of isotropic and homogeneous orthotropic plates. The effects of variations in the fiber orientation and the stacking sequence of the layers on the symmetries exhibited by composite plates are discussed. Both the linear and geometrically nonlinear responses of the plates are considered. A simple procedure is presented for exploiting the symmetries in the finite element analysis. Examples are given of square, skew and polygonal plates where use of symmetry concepts can significantly reduce the scope and cost of analysis.
NASA Technical Reports Server (NTRS)
Lopez, Hiram
1987-01-01
Transmission errors for zeros and ones tabulated separately. Binary-symmetry detector employs psuedo-random data pattern used as test message coming through channel. Message then modulo-2 added to locally generated and synchronized version of test data pattern in same manner found in manufactured test sets of today. Binary symmetrical channel shows nearly 50-percent ones to 50-percent zeroes correspondence. Degree of asymmetry represents imbalances due to either modulation, transmission, or demodulation processes of system when perturbed by noise.
Zheng, Qiang; Wagner, Frank R; Ormeci, Alim; Prots, Yurii; Burkhardt, Ulrich; Schmidt, Marcus; Schnelle, Walter; Grin, Yuri; Leithe-Jasper, Andreas
2015-11-01
Two ternary borides MNi9 B8 (M=Al, Ga) were synthesized by thermal treatment of mixtures of the elements. Single-crystal X-ray diffraction data reveal AlNi9 B8 and GaNi9 B8 crystallizing in a new type of structure within the space group Cmcm and the lattice parameters a=7.0896(3)?Å, b=8.1181(3)?Å, c=10.6497(4)?Å and a=7.0897(5)?Å, b=8.1579(4)?Å, c=10.6648(7)?Å, respectively. The boron atoms build up two-dimensional layers, which consist of puckered [B16 ] rings with two tailing B atoms, whereas the M atoms reside in distorted vertices-condensed [Ni12 ] icosahedra, which form a three-dimensional framework interpenetrated by boron porphyrin-reminiscent layers. An unusual local arrangement resembling a giant metallo-porphyrin entity is formed by the [B16 ] rings, which, due to their large annular size of approximately 8?Å, chelate four of the twelve icosahedral Ni atoms. An analysis of the chemical bonding by means of the electron localizability approach reveals strong covalent B?B interactions and weak Ni?Ni interactions. Multi-center dative B?Ni interaction occurs between the Al-Ni framework and the boron layers. In agreement with the chemical bonding analysis and band structure calculations, AlNi9 B8 is a Pauli-paramagnetic metal. PMID:26418894
Shukla, A. K.; Dhaka, R. S.; Biswas, C.; Banik, S.; Barman, S. R.; Horn, K.; Ebert, Ph.; Urban, K.
2006-02-01
We report x-ray photoelectron spectroscopy (XPS) study of Na and K adlayers on icosahedral Al{sub 70.5}Pd{sub 21}Mn{sub 8.5} (i-Al-Pd-Mn) quasicrystal. The Na 1s core-level exhibits a continuous linear shift of 0.8 eV towards lower binding energies (BE) with increasing coverage up to one monolayer (ML) saturation coverage. In the case of K/i-Al-Pd-Mn, a similar linear shift in the K 2p spectra towards lower BE is observed. In both cases, the plasmon related loss features are observed only above 1 ML. The substrate core-level peaks, such as Al 2p, do not exhibit any shift with the adlayer deposition up to the highest coverage. Based on these experimental observations and previous studies of alkali metal growth on metals, we conclude that below 1 ML, both Na and K form a dispersed phase on i-Al-Pd-Mn and there is hardly any charge transfer to the substrate. The variation of the adlayer and substrate core-level intensities with coverage indicates layer by layer growth.
NASA Astrophysics Data System (ADS)
Goto, D.; Nakajima, T.; Masaki, S.
2014-12-01
Air pollution has a great impact on both climate change and human health. One effective way to tackle with these issues is a use of atmospheric aerosol-chemistry models with high-resolution in a global scale. For this purpose, we have developed an aerosol-chemistry model based on a global cloud-resolving model (GCRM), Nonhydrostatic Icosahedral Atmospheric Model (NICAM; Tomita and Satoh, Fluid. Dyn. Res. 2004; Satoh et al., J. Comput. Phys. 2008, PEPS, 2014) under MEXT/RECCA/SALSA project. In the present study, we have simulated aerosols and tropospheric ozone over Japan by our aerosol-chemistry model "NICAM-Chem" with a stretched-grid system of approximately 10 km resolution, for saving the computer resources. The aerosol and chemistry modules are based on Spectral Radiation-Transport Model for Aerosol Species (SPRINTARS; Takemura et al., J. Geophys. Res., 2005) and Chemical AGCM for Study of Atmospheric Environment and Radiative Forcing (CHASER; Sudo et al., J. Geophys. Res., 2002). We found that our model can generally reproduce both aerosols and ozone, in terms of temporal variations (daily variations of aerosols and diurnal variations of ozone). Under MEXT/RECCA/SALSA project, we also have used these results obtained by NICAM-Chem for the assessment of their impact on human health.
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.
NASA Astrophysics Data System (ADS)
Nakamoto, Kazuo; McKinney, Michael A.
2000-06-01
The C60 molecule (Buckyball/soccer ball) exhibits only 4 IR and 10 Raman bands although it possesses 174 (3 x 60 - 6) normal vibrations. This striking reduction in the number of observed bands is evidently due to the molecule's extremely high symmetry (Ih point group). First, the 120 symmetry elements of its truncated icosahedral structure are identified and the local (site) symmetry of the carbon atoms (Cc) is determined. Use of molecular models greatly facilitates the process in determining the local and molecular symmetries. Then the correlation method is used to derive a table that classifies the 174 normal vibrations into the respective symmetry species of the Ih point group. In this method, symmetry properties of atomic displacements in terms of the local point group (Cc) are correlated with those in terms of the molecular point group (Ih). After the normal vibrations are classified into respective symmetry species, the numbers of IR- and Raman-active vibrations can be determined by the symmetry selection rules for IR and Raman spectra. The vibrational spectra of C60 and C70 (rugby ball) are analyzed by the above procedure, and the results obtained for C28, C32, C50, and dodecahedrane are provided.
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.
Perturbative Symmetries on Noncommutative Spaces
NASA Astrophysics Data System (ADS)
Blohmann, Christian
Perturbative deformations of symmetry structures on noncommutative spaces are studied in view of noncommutative quantum field theories. The rigidity of enveloping algebras of semisimple Lie algebras with respect to formal deformations is reviewed in the context of star products. It is shown that rigidity of symmetry algebras extends to rigidity of the action of the symmetry on the space. This implies that the noncommutative spaces considered can be realized as star products by particular ordering prescriptions which are compatible with the symmetry. These symmetry preserving ordering prescriptions are calculated for the quantum plane and four-dimensional quantum Euclidean space. The result can be used to construct invariant Lagrangians for quantum field theory on noncommutative spaces with a deformed symmetry.
Symmetry properties of conservation laws
Stephen C. Anco
2015-12-06
Symmetry properties of conservation laws of partial differential equations are developed by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law and its associated conserved quantity are invariant (and, more generally, homogeneous) under the action of a symmetry. These results are used to show that a recent conservation law formula (due to Ibragimov) is equivalent to a standard formula for the action of an infinitesimal symmetry on a conservation law multiplier.
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
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.
Classification of Arnold-Beltrami flows and their hidden symmetries
NASA Astrophysics Data System (ADS)
Fré, P.; Sorin, A. S.
2015-07-01
In the context of mathematical hydrodynamics, we consider the group theory structure which underlies the so named ABC flows introduced by Beltrami, Arnold and Childress. Main reference points are Arnold's theorem stating that, for flows taking place on compact three manifolds ?3, the only velocity fields able to produce chaotic streamlines are those satisfying Beltrami equation and the modern topological conception of contact structures, each of which admits a representative contact one-form also satisfying Beltrami equation. We advocate that Beltrami equation is nothing else but the eigenstate equation for the first order Laplace-Beltrami operator ? g d, which can be solved by using time-honored harmonic analysis. Taking for ?3, a torus T 3 constructed as ?3/?, where ? is a crystallographic lattice, we present a general algorithm to construct solutions of the Beltrami equation which utilizes as main ingredient the orbits under the action of the point group B A of three-vectors in the momentum lattice *?. Inspired by the crystallographic construction of space groups, we introduce the new notion of a Universal Classifying Group which contains all space groups as proper subgroups. We show that the ? g d eigenfunctions are naturally arranged into irreducible representations of and by means of a systematic use of the branching rules with respect to various possible subgroups we search and find Beltrami fields with non trivial hidden symmetries. In the case of the cubic lattice the point group is the proper octahedral group O24 and the Universal Classifying Group is a finite group G1536 of order |G1536| = 1536 which we study in full detail deriving all of its 37 irreducible representations and the associated character table. We show that the O24 orbits in the cubic lattice are arranged into 48 equivalence classes, the parameters of the corresponding Beltrami vector fields filling all the 37 irreducible representations of G1536. In this way we obtain an exhaustive classification of all generalized ABC- flows and of their hidden symmetries. We make several conceptual comments about the need of a field-theory yielding Beltrami equation as a field equation and/or an instanton equation and on the possible relation of Arnold-Beltrami flows with (supersymmetric) Chern-Simons gauge theories. We also suggest linear generalizations of Beltrami equation to higher odd-dimensions that are different from the non-linear one proposed by Arnold and possibly make contact with M-theory and the geometry of flux-compactifications.
NASA Astrophysics Data System (ADS)
Dai, Tie; Shi, Guangyu; Nakajima, Teruyuki
2015-06-01
Aerosol optical properties are simulated using the Spectral Radiation Transport Model for Aerosol Species (SPRINTARS) coupled with the Non-hydrostatic ICosahedral Atmospheric Model (NICAM). The 3-year global mean all-sky aerosol optical thickness (AOT) at 550 nm, the Ångström Exponent (AE) based on AOTs at 440 and 870 nm, and the single scattering albedo (SSA) at 550 nm are estimated at 0.123, 0.657 and 0.944, respectively. For each aerosol species, the mean AOT is within the range of the AeroCom models. Both the modeled all-sky and clear-sky results are compared with observations from the Moderate Resolution Imaging Spectroradiometer (MODIS) and the Aerosol Robotic Network (AERONET). The simulated spatiotemporal distributions of all-sky AOTs can generally reproduce the MODIS retrievals, and the correlation and model skill can be slightly improved using the clear-sky results over most land regions. The differences between clear-sky and all-sky AOTs are larger over polluted regions. Compared with observations from AERONET, the modeled and observed all-sky AOTs and AEs are generally in reasonable agreement, whereas the SSA variation is not well captured. Although the spatiotemporal distributions of all-sky and clear-sky results are similar, the clear-sky results are generally better correlated with the observations. The clear-sky AOT and SSA are generally lower than the all-sky results, especially in those regions where the aerosol chemical composition is contributed to mostly by sulfate aerosol. The modeled clear-sky AE is larger than the all-sky AE over those regions dominated by hydrophilic aerosol, while the opposite is found over regions dominated by hydrophobic aerosol.
NASA Astrophysics Data System (ADS)
Lv, Bin-Jiang; Peng, Jian; Chu, Zhong
2015-09-01
The effect of Icosahedral phase (I-phase) on hot deformation behavior, dynamic recrystallization (DRX) evolution, and hot workability of Mg-2.0Zn-0.3Zr-0.2Y alloy has been investigated in the temperature range of 300-500 °C and strain rate range of 0.001-1 s-1 using Gleeble 3500D thermo-mechanical simulator. Based on regression analysis for Arrhenius-type equation of flow behavior, the average activation energy of deformation was determined as Q = 277.8 kJ/mol. The model of DRX evolution is . The DRX model agreed well with the microstructure evolution of the alloy at all deformation conditions. At lower strain rates (0.001-0.01 s-1), continuous DRX (CDRX) is the main DRX mechanism that occurred near the original grain boundaries. Twin-dynamic recrystallization (TDRX) began to occur at lower deformation temperatures and higher strain rates (0.1-1 s-1). At a deformation temperature range of 250 to 350 °C and a strain rate of 1 s-1, the main DRX mechanism is TDRX, and the density of twins decreased, and CDRX began to occur near the original grain boundaries. When the deformation temperature increased to 400 °C, TDRX disappeared and CDRX occurred near original grain boundaries and I-phase particles. According to the flow stress behavior and DRX model, the processing maps have exhibited the optimum deformation conditions to be 450 °C and the strain rate range of 0.01-0.001 s-1.
Symmetry and surface symmetry energies in finite nuclei
Lee, S. J.; Mekjian, A. Z.
2010-12-15
A study of the properties of the symmetry energy of nuclei is presented based on density-functional theory. Calculations for finite nuclei are given so that the study includes isospin-dependent surface symmetry considerations as well as isospin-independent surface effects. Calculations are done at both zero and nonzero temperature. It is shown that the surface symmetry energy term is the most sensitive to the temperature while the bulk energy term is the least sensitive. It is also shown that the temperature-dependence terms are insensitive to the force used and even more insensitive to the existence of neutron skin. Results for a symmetry energy with both volume and surface terms are compared with a symmetry energy with only volume terms along the line of {beta} stability. Differences of several MeV are shown over a good fraction of the total mass range in A. Also given are calculations for the bulk, surface and Coulomb terms.
The force of symmetry revisited: symmetry-to-noise ratios regulate (a)symmetry effects.
Csathó, Arpád; van der Vloed, Gert; van der Helm, Peter A
2004-11-01
Freyd and Tversky's [Am. J. Psychol. 97 (1984) 109] data suggested that human observers tend to overestimate relatively high levels of symmetry (symmetry effect), and tend to underestimate relatively low levels of symmetry (asymmetry effect). However, on the basis of their holographic approach to visual regularity, van der Helm and Leeuwenberg [Psychol. Rev. 103(3) (1996) 429] predicted that, at any level of symmetry, both symmetry and asymmetry effects may occur as a consequence of correct estimates of symmetry-to-noise ratios. This prediction was tested in two experiments, with tasks and stimuli similar to those in Freyd and Tversky's study. First, subjects had to judge whether a noisy symmetry is more similar to a slightly more symmetrical variant or to a slightly less symmetrical variant. Second, for every pair of stimuli in such a triadic comparison, subjects had to judge which stimulus is the more symmetrical one. The results from both experiments show that the occurrence of (a)symmetry effects indeed depends on symmetry-to-noise ratios. PMID:15500805
Symmetry in Nature Unit code: MATH45082
Sidorov, Nikita
. We will discuss the classification of symmetries of repeated patterns, like those in the famous and stabilizers. 2. Symmetry in geometry: Example classification of triangles 3. Classification: of symmetry Symmetry, Princeton Science Library (1952) Advanced: M. Golubitsky & I. Stewart, The Symmetry Perspective
Mednikov, Evgueni G; Jewell, Matthew C; Dahl, Lawrence F
2007-09-19
Presented herein are the preparation and crystallographic/microanalytical/magnetic/spectroscopic characterization of the Pt-centered four-shell 165-atom Pd-Pt cluster, (mu(12)-Pt)Pd(164-x)Pt(x)(CO)(72)(PPh(3))(20) (x approximately 7), 1, that replaces the geometrically related capped three-shell icosahedral Pd(145) cluster, Pd(145)(CO)(x)(PEt(3))(30) (x approximately 60), 2, as the largest crystallographically determined discrete transition metal cluster with direct metal-metal bonding. A detailed comparison of their shell-growth patterns gives rise to important stereochemical implications concerning completely unexpected structural dissimilarities as well as similarities and provides new insight concerning possible synthetic approaches for generation of multi-shell metal clusters. 1 was reproducibly prepared in small yields (<10%) from the reaction of Pd(10)(CO)(12)(PPh(3))(6) with Pt(CO)(2)(PPh(3))(2). Its 165-atom metal-core geometry and 20 PPh(3) and 72 CO ligands were established from a low-temperature (100 K) CCD X-ray diffraction study. The well-determined crystal structure is attributed largely to 1 possessing cubic T(h) (2/m3) site symmetry, which is the highest crystallographic subgroup of the noncrystallographic pseudo-icosahedral I(h) (2/m35) symmetry. The "full" four-shell Pd-Pt anatomy of 1 consists of: (a) shell 1 with the centered (mu(12)-Pt) atom encapsulated by the 12-atom icosahedral Pt(x)Pd(12-x) cage, x = 1.2(3); (b) shell 2 with the 42-atom nu(2) icosahedral Pt(x)Pd(42-x) cage, x = 3.5(5); (c) shell 3 with the anti-Mackay 60-atom semi-regular rhombicosidodecahedral Pt(x)Pd(60-x) cage, x = 2.2(6); (d) shell 4 with the 50-atom nu(2) pentagonal dodecahedral Pd(50) cage. The total number of crystallographically estimated Pt atoms, 8 +/- 3, which was obtained from least-squares (Pt(x)/Pd(1-x))-occupancy analysis of the X-ray data that conclusively revealed the central atom to be pure Pt (occupancy factor, x = 1.00(3)), is fortuitously in agreement with that of 7.6(7) found from an X-ray Pt/Pd microanalysis (WDS spectrometer) on three crystals of 1. Our utilization of this site-occupancy (Pt(x)Pd(1-x))-analysis for shells 1-3 originated from the microanalytical results; otherwise, the presumed metal-core composition would have been (mu(12)-Pt)Pd(164). [Alternatively, the (mu(12)-Pt)M(164) core-geometry of 1 may be viewed as a pseudo-Ih Pt-centered six-shell successive nu(1) polyhedral system, each with radially equivalent vertex atoms: Pt@M(12)(icosahedron)@M(30)(icosidodecahedron)@M(12)(icosahedron)@M(60)(rhombicosidodecahedron)@M(30)(icosidodecahedron)@M(20)(pentagonal dodecahedron)]. Completely surprising structural dissimilarities between 1 and 2 are: (1) to date 1 is only reproducibly isolated as a heterometallic Pd-Pt cluster with a central Pt instead of Pd atom; (2) the 50 atoms comprising the outer fourth nu(2) pentagonal dodecahedral shell in 1 are less than the 60 atoms of the inner third shell in 1, in contradistinction to shell-by-shell growth processes in all other known shell-based structures; (3) the 10 fewer PR3 ligands in 1 necessitate larger bulky PPh(3) ligands to protect the Pd-Pt core-geometry; (4) the 72 CO ligands consist of six bridging COs within each of the 12 pentagons in shell 4 that are coordinated to intershell metal atoms. SQUID magnetometry measurements showed a single-crystal sample of 1 to be diamagnetic over the entire temperature range of 10-300 K. PMID:17722929
Conformal symmetry and unification
Pawlowski, Marek
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.
NASA Astrophysics Data System (ADS)
Weber, S. V.; Casey, D. T.; Pino, J. E.; Rowley, D. P.; Smalyuk, V. A.; Spears, B. K.; Tipton, R. E.
2013-10-01
NIF CH ablator symmetry capsules are filled with hydrogen or helium gas. SymCaps have more moderate convergence ratios ~ 15 as opposed to ~ 35 for ignition capsules with DT ice layers, and better agreement has been achieved between simulations and experimental data. We will present modeling of capsules with CD layers and tritium fill, for which we are able to match the dependence of DT yield on recession distance of the CD layer from the gas. We can also match the performance of CH capsules with D3 He fill. The simulations include surface roughness, drive asymmetry, a mock-up of modulation introduced by the tent holding the capsule, and an empirical prescription for ablator-gas atomic mix. This work performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.
Asymptotic Symmetries and Electromagnetic Memory
Sabrina Pasterski
2015-05-04
Recent investigations into asymptotic symmetries of gauge theory and gravity have illuminated connections between gauge field zero-mode sectors, the corresponding soft factors, and their classically observable counterparts -- so called "memories." Here we complete this triad for the case of large U(1) gauge symmetries at null infinity.
Symmetry in Sign Language Poetry
ERIC Educational Resources Information Center
Sutton-Spence, Rachel; Kaneko, Michiko
2007-01-01
This paper considers the range of ways that sign languages use geometric symmetry temporally and spatially to create poetic effect. Poets use this symmetry in sign language art to highlight duality and thematic contrast, and to create symbolic representations of beauty, order and harmony. (Contains 8 tables, 14 figures and 6 notes.)
ERIC Educational Resources Information Center
Hancock, Karen
2007-01-01
In this article, the author presents a lesson on rotational symmetry which she developed for her students. The aim of the lesson was "to identify objects with rotational symmetry in the staff car park" and the success criteria were "pictures or sketches of at least six objects with different orders of rotation". After finding examples of…
Algebraic aspects of chiral symmetry
Hosaka, Atsushi
2010-12-28
Algebraic realization of chiral symmetry and its implications are studied. Hadrons are classified by linear representations with mixing when chiral symmetry is spontaneously broken. The axial vector coupling constant is then determined by representation mixing. Phenomenological test for measuring g{sub A} of a nucleon resonance is discussed.
Symmetry chains and adaptation coefficients
Fritzer, H.P.; Gruber, B.
1985-06-01
Given a symmetry chain of physical significance it becomes necessary to obtain states which transform properly with respect to the symmetries of the chain. In this article we describe a method which permits us to calculate symmetry-adapted quantum states with relative ease. The coefficients for the symmetry-adapted linear combinations are obtained, in numerical form, in terms of the original states of the system and can thus be represented in the form of numerical tables. In addition, one also obtains automatically the matrix elements for the operators of the symmetry groups which are involved, and thus for any physical operator which can be expressed either as an element of the algebra or of the enveloping algebra. The method is well suited for computers once the physically relevant symmetry chain, or chains, have been defined. While the method to be described is generally applicable to any physical system for which semisimple Lie algebras play a role we choose here a familiar example in order to illustrate the method and to illuminate its simplicity. We choose the nuclear shell model for the case of two nucleons with orbital angular momentum l = 1. While the states of the entire shell transform like the smallest spin representation of SO(25) we restrict our attention to its subgroup SU(6) x SU(2)/sub T/. We determine the symmetry chains which lead to total angular momentum SU(2)/sub J/ and obtain the symmetry-adapted states for these chains.
Baxter operators with deformed symmetry
NASA Astrophysics Data System (ADS)
Chicherin, D.; Derkachov, S.; Karakhanyan, D.; Kirschner, R.
2013-03-01
Baxter operators are constructed for quantum spin chains with deformed s?2 symmetry. The parallel treatment of Yang-Baxter operators for the cases of undeformed, trigonometrically and elliptically deformed symmetries presented earlier and relying on the factorization regarding parameter permutations is extended to the global chain operators following the scheme worked out recently in the undeformed case.
Crystallographic and Spectroscopic Symmetry Notations.
ERIC Educational Resources Information Center
Sharma, B. D.
1982-01-01
Compares Schoenflies and Hermann-Mauguin notations of symmetry. Although the former (used by spectroscopists) and latter (used by crystallographers) both describe the same symmetry, there are distinct differences in the manner of description which may lead to confusion in correlating the two notations. (Author/JN)
Ultraviolet completion without symmetry restoration
NASA Astrophysics Data System (ADS)
Endlich, Solomon; Nicolis, Alberto; Penco, Riccardo
2014-03-01
We show that it is not possible to UV complete certain low-energy effective theories with spontaneously broken spacetime symmetries by embedding them into linear sigma models, that is, by adding "radial" modes and restoring the broken symmetries. When such a UV completion is not possible, one can still raise the cutoff up to arbitrarily higher energies by adding fields that transform nonlinearly under the broken symmetries, that is, new Goldstone bosons. However, this (partial) UV completion does not necessarily restore any of the broken symmetries. We illustrate this point by considering a concrete example in which a combination of spacetime and internal symmetries is broken down to a diagonal subgroup. Along the way, we clarify a recently proposed interpretation of inverse Higgs constraints as gauge-fixing conditions.
Asymptotic symmetries from finite boxes
NASA Astrophysics Data System (ADS)
Andrade, Tomás; Marolf, Donald
2016-01-01
It is natural to regulate an infinite-sized system by imposing a boundary condition at finite distance, placing the system in a 'box.' This breaks symmetries, though the breaking is small when the box is large. One should thus be able to obtain the asymptotic symmetries of the infinite system by studying regulated systems. We provide concrete examples in the context of Einstein-Hilbert gravity (with negative or zero cosmological constant) by showing in 4 or more dimensions how the anti-de Sitter and Poincaré asymptotic symmetries can be extracted from gravity in a spherical box with Dirichlet boundary conditions. In 2 + 1 dimensions we obtain the full double-Virasoro algebra of asymptotic symmetries for AdS3 and, correspondingly, the full Bondi-Metzner-Sachs (BMS) algebra for asymptotically flat space. In higher dimensions, a related approach may continue to be useful for constructing a good asymptotically flat phase space with BMS asymptotic symmetries.
Symmetry inheritance of scalar fields
NASA Astrophysics Data System (ADS)
Smoli?, Ivica
2015-07-01
Matter fields do not necessarily have to share the symmetries with the spacetime they live in. When this happens, we speak of the symmetry inheritance of fields. In this paper we classify the obstructions of symmetry inheritance by the scalar fields, both real and complex, and look more closely at the special cases of stationary and axially symmetric spacetimes. Since the symmetry noninheritance is present in the scalar fields of boson stars and may enable the existence of the black hole scalar hair, our results narrow the possible classes of such solutions. Finally, we define and analyse the symmetry noninheritance contributions to the Komar mass and angular momentum of the black hole scalar hair.
Symmetry theory of the flexomagnetoelectric effect in the Bloch lines
NASA Astrophysics Data System (ADS)
Tanygin, B. M.
2012-05-01
It was shown that there are 48 magnetic point groups of the Bloch lines including 22 (11 time-invariant and 11 time-noninvariant) enantiomorphic and 26 non-enantiomorphic groups. The Bloch lines with the time-noninvariant enantiomorphism have identical types (parities) of the magnetization and polarization dependences. The list of soliton-like Bloch lines is derived from the symmetry classification. The tip electrode method of the creation of these Bloch lines is suggested for the potential applications in the magnetoelectric memory devices. The method of the experimental determination of the flexomagnetoelectric properties of the Bloch lines carried by the Bloch domain wall has been suggested. New type of the flexomagnetoelectric coupling, which is determined by the spatial derivatives of the electric polarization, can be found in the vicinity of the Curie temperature or compensation point of the ferrimagnets. The multi-state Bloch line magnetoelectric/multiferroic memory is proposed. It can be considered as a concept of the magnetoelectric enhancement of existing Bloch line memory invention.
Symmetry invariance of conservation laws
Stephen C. Anco; Abdul H. Kara
2015-10-30
Symmetry invariance of conservation laws of partial differential equations is developed and applied to several examples by using the general method of conservation law multipliers. As main results, simple conditions are given for characterizing when a conservation law and its associated conserved quantity are invariant (and, more generally, homogeneous) under the action of a symmetry. These results are used to show that a recent conservation law formula (due to Ibragimov) is equivalent to a standard formula for the action of an infinitesimal symmetry on a conservation law multiplier.
Entropy from scaling symmetry breaking
NASA Astrophysics Data System (ADS)
Cavalcante, Neymar; Diles, Saulo; Gupta, Kumar S.; de Queiroz, Amilcar R.
2015-05-01
The scaling symmetry in conformal quantum mechanics (CQM) can be broken due to the boundary conditions that follow from the requirement of a unitary time evolution of the Hamiltonian. We show that the scaling symmetry of CQM can be restored by introducing a suitable mixed state, which is associated with a nonvanishing von Neumann entropy. We give an explicit formula for the entropy arising from the mixed state in CQM. Our work provides a direct link between the restoration of a broken symmetry and the von Neumann entropy.
Strangeness and Chiral Symmetry Breaking
Dahiya, Harleen
2010-01-01
The implications of chiral symmetry breaking and SU(3) symmetry breaking have been studied in the chiral constituent quark model ($\\chi$CQM). The role of hidden strangeness component has been investigated for the scalar matrix elements of the nucleon with an emphasis on the meson-nucleon sigma terms. The $\\chi$CQM is able to give a qualitative and quantitative description of the "quark sea" generation through chiral symmetry breaking. The significant contribution of the strangeness is consistent with the recent available experimental observations.
Spectral theorem and partial symmetries
Gozdz, A.; Gozdz, M.
2012-10-15
A novel method of the decompositon of a quantum system's Hamiltonian is presented. In this approach the criterion of the decomposition is determined by the symmetries possessed by the sub-Hamiltonians. This procedure is rather generic and independent of the actual global symmetry, or the lack of it, of the full Hamilton operator. A detailed investigation of the time evolution of the various sub-Hamiltonians, therefore the change in time of the symmetry of the physical object, is presented for the case of a vibrator-plus-rotor model. Analytical results are illustrated by direct numerical calculations.
Symmetry planes of Paleozoic crinoids
Lane, N. G.; Webster, G. D.
1967-11-30
PALEONTOLOGICAL CONTRIBUTIONS November 30, 1967 Paper 25 SYMMETRY PLANES OF PALEOZOIC CRINOIDS N. GARY LANE and G. D. WEBsTER University of California, Los Angeles, and San Diego State College ABSTRACT The homocrinid (E-BC) plane of bilateral symmetry... plane of bilateral sym- metry passes through the E ray and the BC inter- ray (Fig. 2). This symmetry plane attains fullest expression in the bent-crown disparids, the Cal- ceocrinidae, in which the crown is bent to one side over the stem, in the E-BC...
Geometrical spin symmetry and spin
Pestov, I. B.
2011-07-15
Unification of General Theory of Relativity and Quantum Mechanics leads to General Quantum Mechanics which includes into itself spindynamics as a theory of spin phenomena. The key concepts of spindynamics are geometrical spin symmetry and the spin field (space of defining representation of spin symmetry). The essence of spin is the bipolar structure of geometrical spin symmetry induced by the gravitational potential. The bipolar structure provides a natural derivation of the equations of spindynamics. Spindynamics involves all phenomena connected with spin and provides new understanding of the strong interaction.
NASA Astrophysics Data System (ADS)
Tuan, S. F.
2002-06-01
The suggestion by Jaffe that if sigma is a light q2q2 state 0++ then even the fundamental chiral transformation properties of the sigma becomes unclear, has stimulated much interest. Adler pointed out that in fact the seminal work on chiral symmetry via PCAC consistency, is really quite consistent with the sigma being predominantly q2q2. This interpretation was actually backed by subsequent work on effective Lagrangian methods for linear and non linear realizations. More recent work of Achasov suggests that intermediate four-quark states determine amplitudes involving other scalars a0(980) and f0(980) below 1 GeV, and the report by Ning Wu that study on sigma meson in J/psi [right arrow] omega][pi]+[pi- continue to support a non qq sigma with mass as low as 390 MeV. It is also noted that more recent re-analysis of piK scattering by S. Ishida et al. together with the work of the E791 Collaboration, support the existence of the scalar kappa particle with comparatively light mass as well.
Electroweak Symmetry Breaking: With Dynamics
Chivukula, R. Sekhar
2005-03-22
In this note I provide a brief description of models of dynamical electroweak symmetry breaking, including walking technicolor, top-color assisted technicolor, the top-quark seesaw model, and little higgs theories.
PLANE SYMMETRY GROUPS MAXWELL LEVINE
May, J. Peter
known as pla- nar crystallographic groups or wallpaper groups. The seventeen unique plane symmetry, the work of the artist M.C. Escher, and of course wallpaper. We shall discuss the fundamental components
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 ...
Natural quasicrystal with decagonal symmetry
Bindi, Luca
We report the first occurrence of a natural quasicrystal with decagonal symmetry. The quasicrystal, with composition Al[subscript 71]Ni[subscript 24]Fe[subscript 5], was discovered in the Khatyrka meteorite, a recently ...
Symmetries from the solution manifold
NASA Astrophysics Data System (ADS)
Aldaya, Víctor; Guerrero, Julio; Lopez-Ruiz, Francisco F.; Cossío, Francisco
2015-07-01
We face a revision of the role of symmetries of a physical system aiming at characterizing the corresponding Solution Manifold (SM) by means of Noether invariants as a preliminary step towards a proper, non-canonical, quantization. To this end, "point symmetries" of the Lagrangian are generally not enough, and we must resort to the more general concept of contact symmetries. They are defined in terms of the Poincaré-Cartan form, which allows us, in turn, to find the symplectic structure on the SM, through some sort of Hamilton-Jacobi (HJ) transformation. These basic symmetries are realized as Hamiltonian vector fields, associated with (coordinate) functions on the SM, lifted back to the Evolution Manifold through the inverse of this HJ mapping, that constitutes an inverse of the Noether Theorem. The specific examples of a particle moving on S3, at the mechanical level, and nonlinear SU(2)-sigma model in field theory are sketched.
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.
Finiteness, duality, and fermionic symmetry
Yoshiharu Kawamura
2015-03-17
We propose a framework for a new type of finite field theories based on a hidden duality between an ultra-violet and an infra-red region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of the duality transformation, and this feature is compatible with models possessing a specific fermionic symmetry. Theories can be tested indirectly by relations among parameters, reflecting underlying symmetries.
Finiteness, duality, and fermionic symmetry
Kawamura, Yoshiharu
2015-01-01
We propose a framework for a new type of finite field theories based on a hidden duality between an ultra-violet and an infra-red region. Physical quantities do not receive radiative corrections at a fundamental scale or the fixed point of the duality transformation, and this feature is compatible with models possessing a specific fermionic symmetry. Theories can be tested indirectly by relations among parameters, reflecting underlying symmetries.
Symmetry and Visual Hallucinations Martin Golubitsky
Darcy, Isabel K.
, NIH Lie June Shiau Andrew Török Houston Clear Lake Houston Klüver: We wish to stress . . . one point constants. p. 1/3 #12;Planar Symmetry-Breaking Euclidean symmetry: translations, rotations, reflections Symmetry-breaking from translation invariant state in planar systems with Euclidean symmetry leads
Symmetry breaking in the parton distribution functions of the nucleon
NASA Astrophysics Data System (ADS)
Cao, F.-G.
2015-10-01
Parton models predict several symmetries for the parton distribution functions of the nucleon, including flavour symmetry, charge symmetry, and quark-antiquark symmetry. We report calculations using the meson cloud model for the breaking of these symmetries.
O'Hanlon actions by Noether symmetry
F. Darabi
2015-04-14
By using the conformal symmetry between Brans-Dicke action with $\\omega=-\\frac{3}{2}$ and O'Hanlon action, we seek the O'Hanlon actions in Einstein frame respecting the Noether symmetry. Since the Noether symmetry is preserved under conformal transformations, the existence of Noether symmetry in the Brans-Dicke action asserts the Noether symmetry in O'Hanlon action in Einstein frame. Therefore, the potentials respecting Noether symmetry in Brans-Dicke action give the corresponding potentials respecting Noether symmetry in O'Hanlon action in Einstein frame.
Symmetry in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.
1993-01-01
Relationships among polarimetric backscattering coefficients are derived from the viewpoint of symmetry groups. For both reciprocal and non-reciprocal media, symmetry encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered. The derived properties are general and valid to all scattering mechanisms, including volume and surface scatterings and their interactions, in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is also discussed. Orientations of spheroidal scatterers described by spherical, uniform, planophile, plagiothile, erectophile, and extremophile distributions are considered to derive their polarimetric backscattering characteristics. These distributions can be identified from the observed scattering coefficients by comparison with theoretical symmetry calculations. A new parameter is then defined to study scattering structures in geophysical media. Observations from polarimetric data acquired by the Jet Propulsion Laboratory airborne synthetic aperture radar over forests, sea ice, and sea surface are presented. Experimental evidences of the symmetry relationships are shown and their use in polarimetric remote sensing is illustrated. For forests, the coniferous forest in Mt. Shasta area (California) and mixed forest near Presque Isle (Maine) exhibit characteristics of the centrical symmetry at C-band. For sea ice in the Beaufort Sea, multi-year sea ice has a cross-polarized ratio e close to e(sub 0), calculated from symmetry, due to the randomness in the scattering structure. First-year sea ice has e much smaller than e(sub 0) due to the preferential alignment of the columnar structure of the ice. From polarimetric data of a sea surface in the Bering Sea, it is observed that e and e(sub 0) are increasing with incident angle and e is greater than e(sub 0) at L-band because of the directional feature of sea surface waves. Symmetry properties of geophysical media can also be used to calibrate polarimetric radars.
General-Purpose Icosahedral Structure
NASA Technical Reports Server (NTRS)
Evans, J.
1984-01-01
Scheme based on geodesic sphere approximated by regular icosahedron. Structure rigid and lightweight. Allows access to all subsystems and equipment from outside. Regular icosahedron constructed from triangular panels. Five panels meeting at each corner all rigidly attached to fivesided adapter. Strengthened version useful on Earth for rapidly-erectable temporary shelters, industrial structures, or playground equipment.
Symmetry protected topological orders and the group cohomology of their symmetry group
Chen, Xie
Symmetry protected topological (SPT) phases are gapped short-range-entangled quantum phases with a symmetry G. They can all be smoothly connected to the same trivial product state if we break the symmetry. The Haldane phase ...
Symmetries, Lie Algebras and Representations
NASA Astrophysics Data System (ADS)
Fuchs, Jürgen; Schweigert, Christoph
2003-10-01
Preface; 1. Symmetries and conservation laws; 2. Basic examples; 3. The Lie algebra su(3) and hadron symmetries; 4. Formalization: algebras and Lie algebras; 5. Representations; 6. The Cartan-Weyl basis; 7. Simple and affine Lie algebras; 8. Real Lie algebras and real forms; 9. Lie groups; 10. Symmetries of the root system. The Weyl group; 11. Automorphisms of Lie algebras; 12. Loop algebras and central extensions; 13. Highest weight representations; 14. Verma modules, Casimirs, and the character formula; 15. Tensor products of representations; 16. Clebsch-Gordan coefficients and tensor operators; 17. Invariant tensors; 18. Subalgebras and branching rules; 19. Young tableaux and the symmetric group; 20. Spinors, Clifford algebras, and supersymmetry; 21. Representations on function spaces; 22. Hopf algebras and representation rings; Epilogue; References; Index.
Aspects of Dynamical Symmetry Breaking
NASA Astrophysics Data System (ADS)
Cohler, Lucien Eugene
In order to develop some insight into dynamical symmetry breaking in four dimensional nonabelian theories, a toy model is examined that exhibits some of the features of the more realistic model but remains tractable. The model that is studied is that of QED in three dimensions with N fermion flavors. It will be shown that there are configurations that dynamically break the chiral symmetry of the model. By taking a large number of flavors, a 1/N expansion may be used to simplify the problem which is approached by numerically solving the Schwinger-Dyson equations for the fermion self energy. By comparing the effective potentials of the broken and unbroken solutions it will be shown that the dynamics favors symmetry breaking. In addition, the low energy impact of having a composite Higgs sector will be examined by estimating its contribution to the (rho) parameter.
NASA Astrophysics Data System (ADS)
Jakse, N.; Le Bacq, O.; Pasturel, A.
2005-09-01
Atomic structures of stable liquid and undercooled liquid Al80Mn20 and Al80Ni20 alloys have been calculated by first-principles molecular-dynamics simulations. For both alloys, the local structure as defined by the Faber-Ziman pair-correlation functions is characterized by a strong Al-transition-metal affinity, which leads to a well-pronounced chemical short-range order which is more temperature dependent for Al80Mn20 than for Al80Ni20. In addition, a structural analysis using three-dimensional pair analysis techniques has been performed in details. More particularly, we find that the fivefold local symmetry around Mn atoms is predominant in both stable and undercooled Al80Mn20 alloys and displays no significant variation with temperatures. On the contrary, in Al80Ni20, a strong variation of the topological short-range order is observed since in the undercooled state, the local environment of Ni atoms is characterized by the predominance of the fivefold symmetry over the close-packed local symmetry which is opposed to what occurs in the stable liquid phase.
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.
Symmetry analysis of cellular automata
NASA Astrophysics Data System (ADS)
García-Morales, V.
2013-01-01
By means of B-calculus [V. García-Morales, Phys. Lett. A 376 (2012) 2645] a universal map for deterministic cellular automata (CAs) has been derived. The latter is shown here to be invariant upon certain transformations (global complementation, reflection and shift). When constructing CA rules in terms of rules of lower range a new symmetry, “invariance under construction” is uncovered. Modular arithmetic is also reformulated within B-calculus and a new symmetry of certain totalistic CA rules, which calculate the Pascal simplices modulo an integer number p, is then also uncovered.
Quantum statistics with internal symmetry
NASA Astrophysics Data System (ADS)
Elze, Hans-Thomas; Greiner, Walter
1986-03-01
We formulate a group-theoretical projection technique for the quantum-statistical description of systems with exactly conserved charges corresponding to local non-Abelian gauge symmetries. The formalism is specified for SU(N) internal symmetry and a partition function related to a mixed canonical-grand-canonical ensemble is defined. Its perturbation expansion is derived, and we point out potential applications. We also study single-particle Green's functions for the calculation of mixed ensemble averages with the help of a generalized Wick's theorem and find that a connected-graphs expansion is impossible.
Conformal symmetries of spherical spacetimes
S. Moopanar; S. D. Maharaj
2011-08-20
We investigate the conformal geometry of spherically symmetric spacetimes in general without specifying the form of the matter distribution. The general conformal Killing symmetry is obtained subject to a number of integrability conditions. Previous results relating to static spacetimes are shown to be a special case of our solution. The general inheriting conformal symmetry vector, which maps fluid flow lines conformally onto fluid flow lines, is generated and the integrability conditions are shown to be satisfied. We show that there exists a hypersurface orthogonal conformal Killing vector in an exact solution of Einstein's equations for a relativistic fluid which is expanding, accelerating and shearing.
Skyrmion crystals and their symmetries
Kugler, M. ); Shtrikman, S. )
1989-11-15
We discuss the phase diagram of Skyrmion crystals as a function of both density and pressure. The use of symmetry properties of the various phases and of Fourier expansions tailored to fit these symmetries facilitates our discussion. A simple cubic arrangement of half-Skyrmions is, almost everywhere, the lowest-energy phase. At very high densities the simple cubic phase undergoes a transition to a body-centered-cubic crystal of half-Skyrmions. The transition to a crystal of Skyrmions at low densities, that was previously suggested, is not accessible thermodynamically. A first-order phase transition leading to a phase separation occurs before the previous transition can be reached.
Iterates of maps with symmetry
NASA Technical Reports Server (NTRS)
Chossat, Pascal; Golubitsky, Martin
1988-01-01
Fixed-point bifurcation, period doubling, and Hopf bifurcation (HB) for iterates of equivariant mappings are investigated analytically, with a focus on HB in the presence of symmetry. An algebraic formulation for the hypotheses of the theorem of Ruelle (1973) is derived, and the case of standing waves in a system of ordinary differential equations with O(2) symmetry is considered in detail. In this case, it is shown that HB can lead directly to motion on an invariant 3-torus, with an unexpected third frequency due to drift of standing waves along the torus.
Spontaneous violation of mirror symmetry
Dyatlov, Igor T
2015-01-01
A symmetry violation model is considered for a system that can spontaneously choose between identical states which differ from each other only in weak properties (R-L). Such mirror symmetry allows reproduction of observed qualitative properties of quark and lepton mixing matrices. The lepton mixing matrix evidences in this case in favor of the inverse mass spectrum and the Dirac nature of SM neutrino. Notwithstanding the Dirac properties of neutrino, an exchange of lepton numbers such as $e^{-}+\\mu^{+}\\rightarrow e^{+}+\\mu^{-}$ is possible but with only leptons participating in the process.
Symmetries of coupled harmonic oscillators
NASA Technical Reports Server (NTRS)
Han, D.; Kim, Y. S.
1993-01-01
It is shown that the system of two coupled harmonic oscillators possesses many interesting symmetries. It is noted that the symmetry of a single oscillator is that of the three-parameter group Sp(2). Thus two uncoupled oscillator exhibits a direct product of two Sp(2) groups, with six parameters. The coupling can be achieved through a rotation in the two-dimensional space of two oscillator coordinates. The closure of the commutation relations for the generators leads to the ten-parameter group Sp(4) which is locally isomorphic to the deSitter group O(3,2).
Unparticles and electroweak symmetry breaking
Lee, Jong-Phil
2008-11-23
We investigate a scalar potential inspired by the unparticle sector for the electroweak symmetry breaking. The scalar potential contains the interaction between the standard model fields and unparticle sector. It is described by the non-integral power of fields that originates from the nontrivial scaling dimension of the unparticle operator. It is found that the electroweak symmetry is broken at tree level when the interaction is turned on. The scale invariance of unparticle sector is also broken simultaneously, resulting in a physical Higgs and a new lighter scalar particle.
Spontaneous violation of mirror symmetry
Igor T. Dyatlov
2015-09-24
A symmetry violation model is considered for a system that can spontaneously choose between identical states which differ from each other only in weak properties (R-L). Such mirror symmetry allows reproduction of observed qualitative properties of quark and lepton mixing matrices. The lepton mixing matrix evidences in this case in favor of the inverse mass spectrum and the Dirac nature of SM neutrino. Notwithstanding the Dirac properties of neutrino, an exchange of lepton numbers such as $e^{-}+\\mu^{+}\\rightarrow e^{+}+\\mu^{-}$ is possible but with only leptons participating in the process.
Kastner, Ruth E.
2011-11-29
This paper seeks to clarify features of time asymmetry in terms of symmetry breaking. It is observed that, in general, a contingent situation or event requires the breaking of an underlying symmetry. The distinction between the universal anisotropy of temporal processes and the irreversibility of certain physical processes is clarified. It is also proposed that the Transactional Interpretation of quantum mechanics offers an effective way to explain general thermodynamic asymmetry in terms of the time asymmetry of radiation, where prior such efforts have fallen short.
Symmetry in context: Salience of mirror symmetry in natural Elias H. Cohen # $
Tong, Frank
Symmetry is a biologically relevant, mathematically involving, and aesthetically compelling visual to transformations such as reflection, rotation, and translation (Conway, Burgiel, & Goodman-Strauss, 2008). Symmetry
Charge Symmetry at the Partonic Level
J.T. Londergan, J.-C. Peng, A.W. Thomas
2010-07-01
This review article discusses the experimental and theoretical status of partonic charge symmetry. It is shown how the partonic content of various structure functions gets redefined when the assumption of charge symmetry is relaxed. We review various theoretical and phenomenological models for charge symmetry violation in parton distribution functions. We summarize the current experimental upper limits on charge symmetry violation in parton distributions. A series of experiments are presented, which might reveal partonic charge symmetry violation, or alternatively might lower the current upper limits on parton charge symmetry violation.
Spin symmetry in the antinucleon spectrum.
Zhou, Shan-Gui; Meng, Jie; Ring, P
2003-12-31
We discuss spin and pseudospin symmetry in the spectrum of single nucleons and single antinucleons in a nucleus. As an example we use relativistic mean field theory to investigate single antinucleon spectra. We find a very well developed spin symmetry in single antineutron and single antiproton spectra. The dominant components of the wave functions of the spin doublet are almost identical. This spin symmetry in antiparticle spectra and the pseudospin symmetry in particle spectra have the same origin. However, it turns out that the spin symmetry in antinucleon spectra is much better developed than the pseudospin symmetry in normal nuclear single particle spectra. PMID:14754045
Polarization and Symmetry of Electronic Transitions in Long Fluorescence Lifetime Triangulenium Dyes
Thyrhaug, Erling; Sørensen, Thomas Just; Gryczynski, Ignacy; Gryczynski, Zygmunt; Laursen, Bo W.
2013-01-01
To fully exploit the capabilities of fluorescence probes in modern experiments, where advanced instrumentation is used to probe complex environments, other photophysical properties than emission color and emission intensity are monitored. Each dye property can be addressed individually as well as collectively to provide in-depth information unavailable from the standard intensity measurements. Dyes with long emission lifetimes and strongly polarized transitions enable the monitoring of lifetime changes as well as emission polarization (or anisotropy). Thus experiments can be designed to follow slow dynamics. In this article the UV and visible electronic transitions of a series of red emitting dyes based on the triangulenium motif are investigated. We resolve overlapping features in the spectra and assign transition moment of the molecular axes. The result is the complete Jablonski diagram for the UV and visible spectral region. The symmetries of the studied dyes are shown to have a large influence on the optical response and they are clearly separated into two groups of symmetry by their photophysical properties. The C2v symmetric dyes: azadioxatriangulenium (ADOTA+) and diazaoxatriangulenium (DAOTA+) have high emission anisotropies, fluorescence lifetimes around 20 ns, and fluorescence quantum yields of ~50%. The trioxatriangulenium (TOTA+) and triazatriangulenium (TATA+) dyes—nominally of D3h symmetry—have fluorescence lifetimes around 10 ns lifetimes and fluorescence quantum yields of 10-15%. However, the D3h-symmetry is shown to be lowered to a point group, where the axes transform uniquely such that the degeneracy of the E’-states is lifted. PMID:23391292
A symmetry for vanishing cosmological constant
Recai Erdem
2006-11-21
Two different realizations of a symmetry principle that impose a zero cosmological constant in an extra-dimensional set-up are studied. The symmetry is identified by multiplication of the metric by minus one. In the first realization of the symmetry this is provided by a symmetry transformation that multiplies the coordinates by the imaginary number i. In the second realization this is accomplished by a symmetry transformation that multiplies the metric tensor by minus one. In both realizations of the symmetry the requirement of the invariance of the gravitational action under the symmetry selects out the dimensions given by D = 2(2n+1), n=0,1,2,... and forbids a bulk cosmological constant. Another attractive aspect of the symmetry is that it seems to be more promising for quantization when compared to the usual scale symmetry. The second realization of the symmetry is more attractive in that it is posible to make a possible brane cosmological constant zero in a simple way by using the same symmetry, and the symmetry may be identified by reflection symmetry in extra dimensions.
Symmetry structure and phase transitions
Ashok Goyal; Meenu Dahiya; Deepak Chandra
2002-01-22
We study chiral symmetry structure at finite density and temperature in the presence of external magnetic field and gravity, a situation relevant in the early Universe and in the core of compact stars. We then investigate the dynamical evolution of phase transition in the expanding early Universe and possible formation of quark nuggets and their survival.
Baryon and chiral symmetry breaking
Gorsky, A.; Krikun, A.
2014-07-23
We briefly review the generalized Skyrmion model for the baryon recently suggested by us. It takes into account the tower of vector and axial mesons as well as the chiral symmetry breaking. The generalized Skyrmion model provides the qualitative explanation of the Ioffe’s formula for the baryon mass.
Neutrino Mixing from CP Symmetry
Peng Chen; Chang-Yuan Yao; Gui-Jun Ding
2015-07-13
The neutrino mass matrix has remnant CP symmetry expressed in terms of the lepton mixing matrix, and vice versa the remnant CP transformations allow us to reconstruct the mixing matrix. We study the scenario that all the four remnant CP transformations are preserved by the neutrino mass matrix. The most general parameterization of remnant CP transformations is presented. The lepton mixing matrix is completely fixed by the remnant CP, and its explicit form is derived. The necessary and sufficient condition for conserved Dirac CP violating phase is found. If the Klein four flavor symmetry generated by the postulated remnant CP transformations arises from a finite flavor symmetry group, the phenomenologically viable lepton flavor mixing would be the trimaximal pattern, both Dirac CP phase $\\delta_{CP}$ and Majorana phase $\\alpha_{31}$ are either $0$ or $\\pi$ while another Majorana phase $\\alpha_{21}$ is a rational multiple of $\\pi$. These general results are confirmed to be true in the case that the finite flavor symmetry group is $\\Delta(6n^2)$.
Fundamental Symmetries and Conservation Laws
W. C. Haxton
2009-02-09
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, beta-decay correlation studies, and decays violating separate (family) and total lepton number.
From symmetries to number theory
Tempesta, P.
2009-05-15
It is shown that the finite-operator calculus provides a simple formalism useful for constructing symmetry-preserving discretizations of quantum-mechanical integrable models. A related algebraic approach can also be used to define a class of Appell polynomials and of L series.
Honours Project Symmetry Classifications of
Aslaksen, Helmer
's periodic tilings in Table 1 (see appendix). Firstly, it aims to provide the readers an overview in Table 1 (appendix). Therefore, finally, given an Escher's periodic tiling the reader would be ableHonours Project Symmetry Classifications of Periodic Tilings Escher's drawings Name: Kavitha d
Book Reviews A Fearful Symmetry
Denardo, Dale
Book Reviews A Fearful Symmetry Tiger Bone & Rhino Horn: the Destruction of Wildlife for Tradi markets for medicinal products reputed to contain tiger bone were in the United States, Canada, and West- ern Europe. Several "tiger farmers" in the United States recently have been convicted of raising
Strong coupling electroweak symmetry breaking
Barklow, T.L.; Burdman, G.; Chivukula, R.S.
1997-04-01
The authors review models of electroweak symmetry breaking due to new strong interactions at the TeV energy scale and discuss the prospects for their experimental tests. They emphasize the direct observation of the new interactions through high-energy scattering of vector bosons. They also discuss indirect probes of the new interactions and exotic particles predicted by specific theoretical models.
Platonic Symmetry and Geometric Thinking
ERIC Educational Resources Information Center
Zsombor-Murray, Paul
2007-01-01
Cubic symmetry is used to build the other four Platonic solids and some formalism from classical geometry is introduced. Initially, the approach is via geometric construction, e.g., the "golden ratio" is necessary to construct an icosahedron with pentagonal faces. Then conventional elementary vector algebra is used to extract quantitative…
Superdeformations and fermion dynamical symmetries
Wu, Cheng-Li . Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN . Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN )
1990-01-01
In this talk, I will present a link between nuclear collective motions and their underlying fermion dynamical symmetries. In particular, I will focus on the microscopic understanding of deformations. It is shown that the SU{sub 3} of the one major shell fermion dynamical symmetry model (FDSM) is responsible for the physics of low and high spins in normal deformation. For the recently observed phenomena of superdeformation, the physics of the problem dictates a generalization to a supershell structure (SFDSM), which also has an SU{sub 3} fermion dynamical symmetry. Many recently discovered feature of superdeformation are found to be inherent in such an SU{sub 3} symmetry. In both cases the dynamical Pauli effect plays a vital role. A particularly noteworthy discovery from this model is that the superdeformed ground band is not the usual unaligned band but the D-pair aligned (DPA) band, which sharply crosses the excited bands. The existence of such DPA band is a key point to understand many properties of superdeformation. Our studies also poses new experimental challenge. This is particularly interesting since there are now plans to build new and exciting {gamma}-ray detecting systems, like the GAMMASPHERE, which could provide answers to some of these challenges. 34 refs., 11 figs., 5 tabs.
Concomitant Ordering and Symmetry Lowering
ERIC Educational Resources Information Center
Boo, William O. J.; Mattern, Daniell L.
2008-01-01
Examples of concomitant ordering include magnetic ordering, Jahn-Teller cooperative ordering, electronic ordering, ionic ordering, and ordering of partially-filled sites. Concomitant ordering sets in when a crystal is cooled and always lowers the degree of symmetry of the crystal. Concomitant ordering concepts can also be productively applied to…
Turning Students into Symmetry Detectives
ERIC Educational Resources Information Center
Wilders, Richard; VanOyen, Lawrence
2011-01-01
Exploring mathematical symmetry is one way of increasing students' understanding of art. By asking students to search designs and become pattern detectives, teachers can potentially increase their appreciation of art while reinforcing their perception of the use of math in their day-to-day lives. This article shows teachers how they can interest…
Sullivan, John M.
Math 303 Planar Wallpaper Symmetry Groups A finite figure with mirror symmetry has dihedral Dn symmetry for some n, meaning that there are n mirror lines meeting at equal angles of /n. In a wallpaper possibilities we have listed are the only wallpaper groups in the plane. One proof of this fact is based
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.
An Elementary Course in Mathematical Symmetry.
ERIC Educational Resources Information Center
Rose, Bruce I.; Stafford, Robert D.
1981-01-01
A college course designed to teach students about the mathematics of symmetry using pieces of wallpaper and cloth designs is presented. Mathematical structures and the symmetry of graphic designs provide the starting point for instruction. (MP)
Universal Formulation For Symmetries In Computed Flows
NASA Technical Reports Server (NTRS)
Pao, S. Paul; Abdol-Hamid, Khaled S.
1995-01-01
Universal formulation for high-order symmetries in boundary conditions on flows devised. Eliminates need for special procedures to incorporate symmetries and corresponding boundary conditions into computer codes solving Navier-Stokes and Euler equations of flow.
Inflation, symmetry, and B-modes
Hertzberg, Mark Peter
We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing ...
Symmetry aspects of nonholonomic field theories
Vankerschaver, J
2007-01-01
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with the underlying geometric philosophy, a small modification of the derivation of the momentum lemma allows us to treat also generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover...
What symmetries can do for you
NASA Astrophysics Data System (ADS)
Nucci, M. C.
2015-04-01
Several applications of Lie symmetries and its generalisation are presented: from turning butterflies into tornados, to its applications in epidemics, population dynamics, and ultimately converting classical problems into the quantum realm. Applications of nonclassical symmetries are also illustrated.
Noncovariant Local Symmetry in Abelian Gauge Theories
Hyun Seok Yang; Bum-Hoon Lee
1995-10-21
We find non-covariant local symmetries in the Abelian gauge theories. The N\\"other charges generating these symmetries are nilpotent as BRST charges, and they impose constraints on the physical states.
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.
Symmetry in Chinese Arts Yip Lixia, Sabrina
Aslaksen, Helmer
Symmetry in Chinese Arts Done by: Group 3 Lim Li Yan Yip Lixia, Sabrina Lee Weitian, Ivan Zhong Shengmin Goh Yoon Keong 1 #12;2 CONTENTS · Introduction · Symmetry in Chinese Literature · Chinese Paper Cuttings · Symmetry in Chinese buildings · Chinese Music · Conclusion · Bibliography #12;3 Introduction
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
Multilinear Algebra and Tensor Symmetries Roe Goodman
Goodman, Roe
Multilinear Algebra and Tensor Symmetries Roe Goodman Introduction to Math at Rutgers August 28, 2011 Roe Goodman Multilinear Algebra and Tensor Symmetries #12;Vector Spaces and Duality F = field: R) Ã? (column vector) Roe Goodman Multilinear Algebra and Tensor Symmetries #12;Change of Basis vs. Moving
The transmission of symmetry in liquid crystals
Jie Xu; Pingwen Zhang
2015-09-22
The existing experiments and simulations suggest that the molecular symmetry is always transmitted to homogeneous phases in liquid crystals. It has been proved for rod-like molecules. We conjecture that it holds for three other symmetries, and prove it for some molecules of these symmetries.
Superalgebra and fermion-boson symmetry
Miyazawa, Hironari
2010-01-01
Fermions and bosons are quite different kinds of particles, but it is possible to unify them in a supermultiplet, by introducing a new mathematical scheme called superalgebra. In this article we discuss the development of the concept of symmetry, starting from the rotational symmetry and finally arriving at this fermion-boson (FB) symmetry. PMID:20228617
Quantum ergodicity and symmetry reduction
Benjamin Küster; Pablo Ramacher
2015-09-03
We study the ergodic properties of eigenfunctions of Schr\\"odinger operators on a closed connected Riemannian manifold $M$ in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an isometric effective action of a compact connected Lie group $G$. We prove an equivariant quantum ergodicity theorem assuming that the symmetry-reduced Hamiltonian flow on the principal stratum of the singular symplectic reduction of $M$ is ergodic. We deduce the theorem by proving an equivariant version of the semiclassical Weyl law, relying on recent results on singular equivariant asymptotics. It implies an equivariant version of the Shnirelman-Zelditch-Colin-de-Verdi\\`{e}re theorem, as well as a representation theoretic equidistribution theorem. In case that $G$ is trivial, one recovers the classical results.
Adding CP to flavour symmetries
NASA Astrophysics Data System (ADS)
de Medeiros Varzielas, I.
2015-07-01
I propose the use of CP-odd invariants, which are independent of basis and valid for any choice of CP transformation, as a powerful approach to study CP in the presence of flavour symmetries. As examples of the approach I focus on Lagrangians invariant under ?(27). I comment on the consequences of adding a specific CP symmetry to a Lagrangian and distinguish cases where several ?(27) singlets are present depending on how they couple to the triplets. One of the examples included is a very simple toy model with explicit CP violation with calculable phases, which is referred to as explicit geometrical CP violation by comparison with previously known cases of (spontaneous) geometrical CP violation.
Dark Matter and Global Symmetries
Yann Mambrini; Stefano Profumo; Farinaldo S. Queiroz
2015-08-26
General considerations in general relativity and quantum mechanics rule out global symmetries in the context of any consistent theory of quantum gravity. Motivated by this, we derive stringent and robust bounds from gamma-ray, X-ray, cosmic ray, neutrino and CMB data on models that invoke global symmetries to stabilize the dark matter particle. Under realistic assumptions we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime. We then specialize our analysis and apply our bounds to specific models such as the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. In the supplemental material we derive robust, updated model-independent limits on the dark matter lifetime.
Dark Matter and Global Symmetries
Mambrini, Yann; Queiroz, Farinaldo S
2015-01-01
General considerations in general relativity and quantum mechanics rule out global symmetries in the context of any consistent theory of quantum gravity. Motivated by this, we derive stringent and robust bounds from gamma-ray, X-ray, cosmic ray, neutrino and CMB data on models that invoke global symmetries to stabilize the dark matter particle. Under realistic assumptions we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad mass range (keV-TeV), including the WIMP regime. We then specialize our analysis and apply our bounds to specific models such as the Two-Higgs-Doublet, Left-Right, Singlet Fermionic, Zee-Babu, 3-3-1 and Radiative See-Saw models. In the supplemental material we derive robust, updated model-independent limits on the dark matter lifetime.
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.
Gauge Symmetry and Neural Networks
Tetsuo Matsui
2001-12-26
We propose a new model of neural network. It consists of spin variables to describe the state of neurons as in the Hopfield model and new gauge variables to describe the state of synapses. The model possesses local gauge symmetry and resembles lattice gauge theory of high-energy physics. Time dependence of synapses describes the process of learning. The mean field theory predicts a new phase corresponding to confinement phase, in which brain loses ablility of learning and memory.
Chiral symmetry in rotating systems
NASA Astrophysics Data System (ADS)
Malik, Sham S.
2015-08-01
The triaxial rotating system at critical angular momentum I ?Iband exhibits two enatiomeric (the left- and right-handed) forms. These enatiomers are related to each other through dynamical chiral symmetry. The chiral symmetry in rotating system is defined by an operator ? ˆ =Rˆy (?) T ˆ, which involves the product of two distinct symmetries, namely, continuous and discrete. Therefore, new guidelines are required for testing its commutation with the system Hamiltonian. One of the primary objectives of this study is to lay down these guidelines. Further, the possible impact of chiral symmetry on the geometrical arrangement of angular momentum vectors and investigation of observables unique to nuclear chiral-twins is carried out. In our model, the angular momentum components (J1, J2, J3) occupy three mutually perpendicular axes of triaxial shape and represent a non-planar configuration. At certain threshold energy, the equation of motion in angular momentum develops a second order phase transition and as a result two distinct frames (i.e., the left- and right-handed) are formed. These left- and right-handed states correspond to a double well system and are related to each other through chiral operator. At this critical angular momentum, the centrifugal and Coriolis interactions lower the barrier in the double well system. The tunneling through the double well starts, which subsequently lifts the degeneracy among the rotational states. A detailed analysis of the behavior of rotational energies, spin-staggering, and the electromagnetic transition probabilities of the resulting twin-rotational bands is presented. The ensuing model results exhibit similarities with many observed features of the chiral-twins. An advantage of our formalism is that it is quite simple and it allows us to pinpoint the understanding of physical phenomenon which lead to chiral-twins in rotating systems.
Geometric Endoscopy and Mirror Symmetry
Edward Frenkel; Edward Witten
2008-04-05
The geometric Langlands correspondence has been interpreted as the mirror symmetry of the Hitchin fibrations for two dual reductive groups. This mirror symmetry, in turn, reduces to T-duality on the generic Hitchin fibers, which are smooth tori. In this paper we study what happens when the Hitchin fibers on the B-model side develop orbifold singularities. These singularities correspond to local systems with finite groups of automorphisms. In the classical Langlands Program local systems of this type are called endoscopic. They play an important role in the theory of automorphic representations, in particular, in the stabilization of the trace formula. Our goal is to use the mirror symmetry of the Hitchin fibrations to expose the special role played by these local systems in the geometric theory. The study of the categories of A-branes on the dual Hitchin fibers allows us to uncover some interesting phenomena associated with the endoscopy in the geometric Langlands correspondence. We then follow our predictions back to the classical theory of automorphic functions. This enables us to test and confirm them. The geometry we use is similar to that which is exploited in recent work by B.-C. Ngo, a fact which could be significant for understanding the trace formula.
Generalization of Friedberg-Lee symmetry
Huang Chaoshang; Li Tianjun; Liao Wei; Zhu Shouhua
2008-07-01
We study the possible origin of Friedberg-Lee symmetry. First, we propose the generalized Friedberg-Lee symmetry in the potential by including the scalar fields in the field transformations, which can be broken down to the Friedberg-Lee symmetry spontaneously. We show that the generalized Friedberg-Lee symmetry allows a typical form of Yukawa couplings, and the realistic neutrino masses and mixings can be generated via the seesaw mechanism. If the right-handed neutrinos transform nontrivially under the generalized Friedberg-Lee symmetry, we can have the testable TeV scale seesaw mechanism. Second, we present two models with the SO(3)xU(1) global flavor symmetry in the lepton sector. After the flavor symmetry breaking, we can obtain the charged lepton masses, and explain the neutrino masses and mixings via the seesaw mechanism. Interestingly, the complete neutrino mass matrices are similar to those of the above models with generalized Friedberg-Lee symmetry. So the Friedberg-Lee symmetry is the residual symmetry in the neutrino mass matrix after the SO(3)xU(1) flavor symmetry breaking.
Relativity symmetries and Lie algebra contractions
Cho, Dai-Ning; Kong, Otto C.W.
2014-12-15
We revisit the notion of possible relativity or kinematic symmetries mutually connected through Lie algebra contractions under a new perspective on what constitutes a relativity symmetry. Contractions of an SO(m,n) symmetry as an isometry on an m+n dimensional geometric arena which generalizes the notion of spacetime are discussed systematically. One of the key results is five different contractions of a Galilean-type symmetry G(m,n) preserving a symmetry of the same type at dimension m+n?1, e.g. a G(m,n?1), together with the coset space representations that correspond to the usual physical picture. Most of the results are explicitly illustrated through the example of symmetries obtained from the contraction of SO(2,4), which is the particular case for our interest on the physics side as the proposed relativity symmetry for “quantum spacetime”. The contractions from G(1,3) may be relevant to real physics.
Unified framework of topological phases with symmetry
NASA Astrophysics Data System (ADS)
Gu, Yuxiang; Hung, Ling-Yan; Wan, Yidun
2014-12-01
In topological phases in 2 +1 dimensions, anyons fall into representations of quantum group symmetries. As proposed in our work [Hung and Wan, Int. J. Mod. Phys. B 28, 1450172 (2014), 10.1142/S0217979214501720], the physics of a symmetry enriched phase can be extracted by the mathematics of (hidden) quantum group symmetry breaking of a "parent phase." This offers a unified framework and classification of the symmetry enriched (topological) phases, including symmetry protected trivial phases as well. In this paper, we extend our investigation to the case where the "parent" phases are non-Abelian topological phases. We show explicitly how one can obtain the topological data and symmetry transformations of the symmetry enriched phases from that of the "parent" non-Abelian phase. Two examples are computed: (1) the Ising×Ising¯ phase breaks into the Z2 toric code with Z2 global symmetry; (2) the SU (2) 8 phase breaks into the chiral Fibonacci × Fibonacci phase with a Z2 symmetry, a first non-Abelian example of symmetry enriched topological phase beyond the gauge-theory construction.
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
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.
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.
Skyrmion and chiral symmetry breaking
Braghin, F.L.
2004-12-02
A chiral coupling is considered for the Skyrme model to a light scalar meson which develops a classical component, eventually representing the scalar quark-anti-quark condensate of the spontaneous breakdown of chiral symmetry. This scalar field leads to a modification in the chiral radius which becomes a dynamical variable and tends to acquire values close to zero inside the topological soliton. A chiral rotation of the scalar and pseudoscalar fields can lead to the linear sigma model favoring the identification of the scalar field to the scalar sigma. The role of the scalar field mass is discussed.
Relativistic RPA in axial symmetry
D. Pena Arteaga; P. Ring
2009-09-12
Covariant density functional theory, in the framework of self-consistent Relativistic Mean Field (RMF) and Relativistic Random Phase approximation (RPA), is for the first time applied to axially deformed nuclei. The fully self-consistent RMF+RRPA equations are posed for the case of axial symmetry and non-linear energy functionals, and solved with the help of a new parallel code. Formal properties of RPA theory are studied and special care is taken in order to validate the proper decoupling of spurious modes and their influence on the physical response. Sample applications to the magnetic and electric dipole transitions in $^{20}$Ne are presented and analyzed.
History of electroweak symmetry breaking
NASA Astrophysics Data System (ADS)
Kibble, T. W. B.
2015-07-01
In this talk, I recall the history of the development of the unified electroweak theory, incorporating the symmetry-breaking Higgs mechanism, as I saw it from my standpoint as a member of Abdus Salam's group at Imperial College. I start by describing the state of physics in the years after the Second World War, explain how the goal of a unified gauge theory of weak and electromagnetic interactions emerged, the obstacles encountered, in particular the Goldstone theorem, and how they were overcome, followed by a brief account of more recent history, culminating in the historic discovery of the Higgs boson in 2012.
Killing Symmetries as Hamiltonian Constraints
Lusanna, Luca
2015-01-01
The existence of a Killing symmetry in a gauge theory is equivalent to the addition of extra Hamiltonian constraints in its phase space formulation, which imply restrictions both on the Dirac observables (the gauge invariant physical degrees of freedom) and on the gauge freedom. When there is a time-like Killing vector field only pure gauge electromagnetic fields survive in Maxwell theory in Minkowski space-time , while in ADM canonical gravity in asymptotically Minkowskian space-times only inertial effects without gravitational waves survive.
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.
Symmetry properties in polarimetric remote sensing
NASA Technical Reports Server (NTRS)
Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.
1992-01-01
This paper presents the relations among polarimetric backscattering coefficients from the viewpoint of symmetry groups. Symmetry of geophysical media encountered in remote sensing due to reflection, rotation, azimuthal, and centrical symmetry groups is considered for both reciprocal and nonreciprocal cases. On the basis of the invariance under symmetry transformations in the linear polarization basis, the scattering coefficients are related by a set of equations which restrict the number of independent parameters in the polarimetric covariance matrix. The properties derived under these transformations are general and apply to all scattering mechanisms in a given symmetrical configuration. The scattering coefficients calculated from theoretical models for layer random media and rough surfaces are shown to obey the derived symmetry relations. Use of symmetry properties in remote sensing of structural and environmental responses of scattering media is discussed. As a practical application, the results from this paper provide new methods for the external calibration of polarimetric radars without the deployment of man-made calibration targets.
Symmetry and Dirac points in graphene spectrum
Gregory Berkolaiko; Andrew Comech
2015-04-23
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.
Discrete symmetries and mixing of Dirac neutrinos
NASA Astrophysics Data System (ADS)
Esmaili, Arman; Smirnov, Alexei Yu.
2015-11-01
We study the mixing of the Dirac neutrinos in the residual symmetries approach. The key difference from the Majorana case is that the Dirac mass matrix may have larger symmetries: G?=Zn with n ?3 . The symmetry group relations have been generalized to the case of Dirac neutrinos. Using them, we have found all new relations between mixing parameters and corresponding symmetry assignments, which are in agreement with the present data. The viable relations exist only for the charged lepton residual symmetry G?=Z2. The relations involve elements of the rows of the Pontecorvo-Maki-Nakagawa-Sakata matrix and lead to precise predictions of the 2-3 mixing angle and certain ranges of the C P violation phase. For larger symmetries G?, an agreement with the data can be achieved if ˜10 % corrections related to breaking of G? and G? are included.
Interface gapless states from interfacial symmetries
NASA Astrophysics Data System (ADS)
Takahashi, Ryuji; Murakami, Shuichi
2015-03-01
Previously we have shown that at an interface between two topological insulators with opposite Dirac velocities, gapless interface states protected by mirror symmetry appear. We can calculate the interface dispersion using the Fu-Kane-Mele (FKM) tight-binding model, and it typically consists of Dirac cones. In this presentation, we report another kind of interface metallic states; the Fermi surface forms loops (``Fermi loop''), rather than isolated Dirac points, sometimes seen in the interface of the FKM models. Such a degeneracy along a loop is unexpected. This Fermi loop appears when the whole junction system preserves particle-hole symmetry, while each system breaks particle-hole symmetry. We call this symmetry ``interfacial particle-hole symmetry'' (IPHS). We discuss the IPHS in general systems and show that the Fermi loop results from a sign change of a Pfaffian of some matrix, defined only in junctions with IPHS symmetry.
Beyond bilateral symmetry: geometric morphometric methods for any type of symmetry
2011-01-01
Background Studies of symmetric structures have made important contributions to evolutionary biology, for example, by using fluctuating asymmetry as a measure of developmental instability or for investigating the mechanisms of morphological integration. Most analyses of symmetry and asymmetry have focused on organisms or parts with bilateral symmetry. This is not the only type of symmetry in biological shapes, however, because a multitude of other types of symmetry exists in plants and animals. For instance, some organisms have two axes of reflection symmetry (biradial symmetry; e.g. many algae, corals and flowers) or rotational symmetry (e.g. sea urchins and many flowers). So far, there is no general method for the shape analysis of these types of symmetry. Results We generalize the morphometric methods currently used for the shape analysis of bilaterally symmetric objects so that they can be used for analyzing any type of symmetry. Our framework uses a mathematical definition of symmetry based on the theory of symmetry groups. This approach can be used to divide shape variation into a component of symmetric variation among individuals and one or more components of asymmetry. We illustrate this approach with data from a colonial coral that has ambiguous symmetry and thus can be analyzed in multiple ways. Our results demonstrate that asymmetric variation predominates in this dataset and that its amount depends on the type of symmetry considered in the analysis. Conclusions The framework for analyzing symmetry and asymmetry is suitable for studying structures with any type of symmetry in two or three dimensions. Studies of complex symmetries are promising for many contexts in evolutionary biology, such as fluctuating asymmetry, because these structures can potentially provide more information than structures with bilateral symmetry. PMID:21958045
Inflation, Symmetry, and B-Modes
Mark P. Hertzberg
2015-07-27
We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over the inflationary potential. We find that this leads to models in good agreement with recent data. On the other hand, there are attempts in the literature to deviate from this paradigm by invoking other symmetries and corrections. In particular: in a suite of recent papers, several authors have made the claim that standard Einstein gravity with a cosmological constant and a massless scalar carries conformal symmetry. They further claim that such a theory carries another hidden symmetry; a global SO(1,1) symmetry. By deforming around the global SO(1,1) symmetry, they are able to produce a range of inflationary models with asymptotically flat potentials, whose flatness is claimed to be protected by these symmetries. These models tend to give rise to B-modes with small amplitude. Here we explain that these authors are merely introducing a redundancy into the description, not an actual conformal symmetry. Furthermore, we explain that the only real (global) symmetry in these models is not at all hidden, but is completely manifest when expressed in the Einstein frame; it is in fact the shift symmetry of a scalar field. When analyzed systematically as an effective field theory, deformations do not generally produce asymptotically flat potentials and small B-modes, but other types of potentials with B-modes of appreciable amplitude. Such simple models typically also produce the observed red spectral index, Gaussian fluctuations, etc. In short: simple models of inflation, organized by expanding around a shift symmetry, are in excellent agreement with recent data.
$f(T)$ cosmology via Noether symmetry
K. Atazadeh; F. Darabi
2012-05-10
We consider Noether symmetry approach to find out exact cosmological solutions in $f(T)$-gravity. Instead of taking into account phenomenological models, we apply the Noether symmetry to the $f(T)$ gravity. As a result, the presence of such symmetries selects viable models and allow to solve the equations of motion. We show that the generated $f(T)$ leads to a power law expansion for the cosmological scale factor.
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.
The near-symmetry of proteins.
Bonjack-Shterengartz, Maayan; Avnir, David
2015-04-01
The majority of protein oligomers form clusters which are nearly symmetric. Understanding of that imperfection, its origins, and perhaps also its advantages requires the conversion of the currently used vague qualitative descriptive language of the near-symmetry into an accurate quantitative measure that will allow to answer questions such as: "What is the degree of symmetry deviation of the protein?," "how do these deviations compare within a family of proteins?," and so on. We developed quantitative methods to answer this type of questions, which are capable of analyzing the whole protein, its backbone or selected portions of it, down to comparison of symmetry-related specific amino-acids, and which are capable of visualizing the various levels of symmetry deviations in the form of symmetry maps. We have applied these methods on an extensive list of homomers and heteromers and found that apparently all proteins never reach perfect symmetry. Strikingly, even homomeric protein clusters are never ideally symmetric. We also found that the main burden of symmetry distortion is on the amino-acids near the symmetry axis; that it is mainly the more hydrophilic amino-acids that take place in symmetry-distortive interactions; and more. The remarkable ability of heteromers to preserve near-symmetry, despite the different sequences, was also shown and analyzed. The comprehensive literature on the suggested advantages symmetric oligomerizations raises a yet-unsolved key question: If symmetry is so advantageous, why do proteins stop shy of perfect symmetry? Some tentative answers to be tested in further studies are suggested in a concluding outlook. PMID:25354765
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.
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.
Spinor Structure and Internal Symmetries
NASA Astrophysics Data System (ADS)
Varlamov, V. V.
2015-10-01
Spinor structure and internal symmetries are considered within one theoretical framework based on the generalized spin and abstract Hilbert space. Complex momentum is understood as a generating kernel of the underlying spinor structure. It is shown that tensor products of biquaternion algebras are associated with the each irreducible representation of the Lorentz group. Space-time discrete symmetries P, T and their combination PT are generated by the fundamental automorphisms of this algebraic background (Clifford algebras). Charge conjugation C is presented by a pseudoautomorphism of the complex Clifford algebra. This description of the operation C allows one to distinguish charged and neutral particles including particle-antiparticle interchange and truly neutral particles. Spin and charge multiplets, based on the interlocking representations of the Lorentz group, are introduced. A central point of the work is a correspondence between Wigner definition of elementary particle as an irreducible representation of the Poincaré group and SU(3)-description (quark scheme) of the particle as a vector of the supermultiplet (irreducible representation of SU(3)). This correspondence is realized on the ground of a spin-charge Hilbert space. Basic hadron supermultiplets of SU(3)-theory (baryon octet and two meson octets) are studied in this framework. It is shown that quark phenomenologies are naturally incorporated into presented scheme. The relationship between mass and spin is established. The introduced spin-mass formula and its combination with Gell-Mann-Okubo mass formula allows one to take a new look at the problem of mass spectrum of elementary particles.
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.
Symmetry and Symmetry Breaking in Planetary Magnetic Fields
NASA Astrophysics Data System (ADS)
Cao, H.; Russell, C. T.; Aurnou, J. M.; Soderlund, K. M.; Dougherty, M. K.
2014-12-01
Six out of eight solar system planets currently possess global-scale intrinsic magnetic fields. Different symmetry and symmetry breaking with respect to the spin-axis and the equatorial plane of the host planet can be found for different planetary magnetic fields. With respect to the spin-axis, the magnetic fields of Mercury, Earth, Jupiter, and Saturn are dominated by the axisymmetric part while the magnetic fields of Uranus and Neptune show no such alignment. Moreover, non-axisymmetric components have not been determined unambiguously for the magnetic fields of Mercury and Saturn. With respect to the equatorial plane, the magnetic fields of Earth, Jupiter, and Saturn show small but non-negligible asymmetry while the magnetic field of Mercury shows a significant asymmetry. The magnetic fields of Uranus and Neptune likely possess similar strength in the two hemispheres divided by the equatorial plane, but this needs to be confirmed with future measurements. Here we present our interpretation of the magnetic fields of Mercury and Saturn, both of which are often referred to as anomalous dipolar dynamos. For Mercury, we will show that volumetrically distributed buoyancy sources in its liquid iron core can naturally lead to equatorial symmetry breaking in the dynamo generated magnetic field as observed by MESSENGER. We will also show that the size of the solid inner core inside Mercury is likely smaller than 1000 km and could be detected indirectly with high-spatial-resolution magnetic field measurements near Mercury's north pole. In addition, we will show that degree-2 longitudinal variations observed in the magnetic equator positions of Mercury could have an internal origin. For Saturn's magnetic field, although its extreme axisymmetry could in principle be explained by a stably-stratified electrically-conducting layer on top of the dynamo region, more features such as equator-to-pole field contrasts cannot be explained by this same mechanism simultaneously. Towards this end, we will show the possible link between the features in Saturn's magnetic field and dynamics in the semi-conducting region of Saturn.
Interpretation of symmetry experiments on Omega
NASA Astrophysics Data System (ADS)
Lours, Laurence; Bastian, Josiane; Monteil, Marie-Christine; Philippe, Franck; Jadaud, Jean-Paul
2006-10-01
The interpretation of the symmetry experiments performed on Omega in 2005 with 3 cone LMJ-like irradiation is presented here. The goal of this campaign was the characterization of the irradiation symmetry by X-ray imaging of the D2Ar capsule. Images of backlit implosion (as done in earlier campaigns with foam balls) and core emission were obtained on the same shot, and can be compared to FCI2 simulations. This set of shots comfirms former results with foam balls of a good symmetry control with 3 cones in empty hohlraums. The influence of the hohlraum shape on symmetry is also studied by comparison of cylindrical hohlraums vs rugby ones.
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.
Noether gauge symmetry approach in quintom cosmology
NASA Astrophysics Data System (ADS)
Aslam, Adnan; Jamil, Mubasher; Momeni, Davood; Myrzakulov, Ratbay; Rashid, Muneer Ahmad; Raza, Muhammad
2013-12-01
In literature usual point like symmetries of the Lagrangian have been introduced to study the symmetries and the structure of the fields. This kind of Noether symmetry is a subclass of a more general family of symmetries, called Noether gauge symmetries (NGS). Motivated by this mathematical tool, in this paper, we study the generalized Noether symmetry of quintom model of dark energy, which is a two component fluid model with quintessence and phantom scalar fields. Our model is a generalization of the Noether symmetries of a single and multiple components which have been investigated in detail before. We found the general form of the quintom potential in which the whole dynamical system has a point like symmetry. We investigated different possible solutions of the system for diverse family of gauge function. Specially, we discovered two family of potentials, one corresponds to a free quintessence (phantom) and the second is in the form of quadratic interaction between two components. These two families of potential functions are proposed from the symmetry point of view, but in the quintom models they are used as phenomenological models without clear mathematical justification. From integrability point of view, we found two forms of the scale factor: one is power law and second is de-Sitter. Some cosmological implications of the solutions have been investigated.
Symmetry Principles of the Unified Field Theory
John A. Gowan
2009-07-03
The principles of energy, symmetry, entropy, and causality conservation are discussed in a "Tetrahedron Model" of a conceptually complete "T.O.E.:" "The charges of matter are the symmetry debts of light" (Noether's Theorem). Symmetry debts for each force as well as gravitation's conservation roles are considered. Special attention is given to the weak force. Charge invariance (including "Lorentz Invariance") and "Noether's Theorem" are seen as keys to understanding the local action of the forces. A synthesis between the "Tetrahedron Model" and global vs local gauge symmetry concepts as found in the "Standard Model" of physics is presented.
Chiral symmetry on the edge of two-dimensional symmetry protected topological phases
Chen, Xie
Symmetry protected topological (SPT) states are short-range entangled states with symmetry. The boundary of a SPT phases has either gapless excitations or degenerate ground states, around a gapped bulk. Recently, we proposed ...
Karlsson, K. F.; Dupertuis, M. A.; Oberli, D. Y.; Pelucchi, E.; Rudra, A.; Kapon, E.; Holtz, P. O.
2011-12-23
The results of a group theoretical analysis of the excitonic fine structure are presented and compared with spectroscopic data on single quantum dots. The spectral features reveal the signatures of a symmetry higher than the crystal symmetry (C{sub 3v}). A consistent picture of the fine structure patterns for various exciton complexes is obtained with group theory and the concepts of symmetry elevation and symmetry breaking.
Vishnevskiy, Yury V; Tikhonov, Denis S; Reuter, Christian G; Mitzel, Norbert W; Hnyk, Drahomír; Holub, Josef; Wann, Derek A; Lane, Paul D; Berger, Raphael J F; Hayes, Stuart A
2015-12-21
Because of the comparable electron scattering abilities of carbon and boron, the electron diffraction structure of the C2v-symmetric molecule closo-1,2-C2B10H12 (1), one of the building blocks of boron cluster chemistry, is not as accurate as it could be. On that basis, we have prepared the known diiodo derivative of 1, 9,12-I2-closo-1,2-C2B10H10 (2), which has the same point-group symmetry as 1 but in which the presence of iodine atoms, with their much stronger ability to scatter electrons, ensures much better structural characterization of the C2B10 icosahedral core. Furthermore, the influence on the C2B10 geometry in 2 of the antipodally positioned iodine substituents with respect to both carbon atoms has been examined using the concerted application of gas electron diffraction and quantum chemical calculations at the MP2 and density functional theory (DFT) levels. The experimental and computed molecular geometries are in good overall agreement. Molecular dynamics simulations used to obtain vibrational parameters, which are needed for analyzing the electron diffraction data, have been performed for the first time for this class of compound. According to DFT calculations at the ZORA-SO/BP86 level, the (11)B chemical shifts of the boron atoms to which the iodine substituents are bonded are dominated by spin-orbit coupling. Magnetically induced currents within 2 have been calculated and compared to those for [B12H12](2-), the latter adopting a regular icosahedral structure with Ih point-group symmetry. Similar total current strengths are found but with a certain anisotropy, suggesting that spherical aromaticity is present; electron delocalization in the plane of the hetero atoms in 2 is slightly hindered compared to that for [B12H12](2-), presumably because of the departure from ideal icosahedral symmetry. PMID:26625008
Inflation, symmetry, and B-modes
NASA Astrophysics Data System (ADS)
Hertzberg, Mark P.
2015-05-01
We examine the role of using symmetry and effective field theory in inflationary model building. We describe the standard formulation of starting with an approximate shift symmetry for a scalar field, and then introducing corrections systematically in order to maintain control over the inflationary potential. We find that this leads to models in good agreement with recent data. On the other hand, there are attempts in the literature to deviate from this paradigm by envoking other symmetries and corrections. In particular: in a suite of recent papers, several authors have made the claim that standard Einstein gravity with a cosmological constant and a massless scalar carries conformal symmetry. They claim this conformal symmetry is hidden when the action is written in the Einstein frame, and so has not been fully appreciated in the literature. They further claim that such a theory carries another hidden symmetry; a global SO (1 , 1) symmetry. By deforming around the global SO (1 , 1) symmetry, they are able to produce a range of inflationary models with asymptotically flat potentials, whose flatness is claimed to be protected by these symmetries. These models tend to give rise to B-modes with small amplitude. Here we explain that standard Einstein gravity does not in fact possess conformal symmetry. Instead these authors are merely introducing a redundancy into the description, not an actual conformal symmetry. Furthermore, we explain that the only real (global) symmetry in these models is not at all hidden, but is completely manifest when expressed in the Einstein frame; it is in fact the shift symmetry of a scalar field. When analyzed systematically as an effective field theory, deformations do not generally produce asymptotically flat potentials and small B-modes as suggested in these recent papers. Instead, deforming around the shift symmetry systematically, tends to produce models of inflation with B-modes of appreciable amplitude. Such simple models typically also produce the observed red spectral index, Gaussian fluctuations, etc. In short: simple models of inflation, organized by expanding around a shift symmetry, are in excellent agreement with recent data.
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
Electroweak symmetry breaking via QCD.
Kubo, Jisuke; Lim, Kher Sham; Lindner, Manfred
2014-08-29
We propose a new mechanism to generate the electroweak scale within the framework of QCD, which is extended to include conformally invariant scalar degrees of freedom belonging to a larger irreducible representation of SU(3)c. The electroweak symmetry breaking is triggered dynamically via the Higgs portal by the condensation of the colored scalar field around 1 TeV. The mass of the colored boson is restricted to be 350??GeV?mS?3??TeV, with the upper bound obtained from perturbative renormalization group evolution. This implies that the colored boson can be produced at the LHC. If the colored boson is electrically charged, the branching fraction of the Higgs boson decaying into two photons can slightly increase, and moreover, it can be produced at future linear colliders. Our idea of nonperturbative electroweak scale generation can serve as a new starting point for more realistic model building in solving the hierarchy problem. PMID:25215976
Wormhole dynamics in spherical symmetry
Hayward, Sean A.
2009-06-15
A dynamical theory of traversable wormholes is detailed in spherical symmetry. Generically a wormhole consists of a tunnel of trapped surfaces between two mouths, defined as temporal outer trapping horizons with opposite senses, in mutual causal contact. In static cases, the mouths coincide as the throat of a Morris-Thorne wormhole, with surface gravity providing an invariant measure of the radial curvature or ''flaring-out''. The null energy condition must be violated at a wormhole mouth. Zeroth, first, and second laws are derived for the mouths, as for black holes. Dynamic processes involving wormholes are reviewed, including enlargement or reduction, and interconversion with black holes. A new area of wormhole thermodynamics is suggested.
PREFACE: Symmetries in Science XVI
NASA Astrophysics Data System (ADS)
2014-10-01
This volume of the proceedings ''Symmetries in Science XVI'' is dedicated to the memory of Miguel Lorente and Allan Solomon who both participated several times in these Symposia. We lost not only two great scientists and colleagues, but also two wonderful persons of high esteem whom we will always remember. Dieter Schuch, Michael Ramek There is a German saying ''all good things come in threes'' and ''Symmetries in Science XVI'', convened July 20-26, 2013 at the Mehrerau Monastery, was our third in the sequel of these symposia since taking it over from founder Bruno Gruber who instigated it in 1988 (then in Lochau). Not only the time seemed to have been perfect (one week of beautiful sunshine), but also the medley of participants could hardly have been better. This time, 34 scientists from 16 countries (more than half outside the European Union) came together to report and discuss their latest results in various fields of science, all related to symmetries. The now customary grouping of renowned experts and talented newcomers was very rewarding and stimulating for all. The informal, yet intense, discussions at ''Gasthof Lamm'' occurred (progressively later) each evening till well after midnight and finally till almost daybreak! However, prior to the opening ceremony and during the conference, respectively, we were informed that Miguel Lorente and Allan Solomon had recently passed away. Both attended the SIS Symposia several times and had many friends among present and former participants. Professor Peter Kramer, himself a long-standing participant and whose 80th birthday commemoration prevented him from attending SIS XVI, kindly agreed to write the obituary for Miguel Lorente. Professors Richard Kerner and Carol Penson (both also former attendees) penned, at very short notice, the tribute to Allan Solomon. The obituaries are included in these Proceedings and further tributes have been posted to our conference website. In 28 lectures and an evening poster-session, topics ranging from theoretical chemistry and molecular physics via fundamental problems in quantum theory to thermodynamics, nonlinear dynamics, soliton theory and finally cosmology, were examined and lively discussed. Nearly all the talks can also be viewed on the conference website. The majority of participants contributed to these Proceedings but some were unable to do so as their results were either previously submitted or published elsewhere. We refer to: · Quesne C 2013, J. Math. Phys. 54, 102102. · Spera M 2013, (Nankai Series in Pure, Applied Mathematics and Theoretical Physics): 11 Symmetries and Groups in Contemporary Physics: pp. 593-598 Proceedings of the XXIX International Colloquium on Group-Theoretical Methods in Physics Tianjin, China, 20 - 26 August 2012 (World Scientific, Singapore) · Snobl L and Winternitz P 2014, Classification and Identification of Lie Algebras, CRM Monograph Series 33 (Montreal) ISBN-10: 0-8218-4355-9, ISBN-13: 978-0-8218-4355-0 (http://www.ams.org/bookstore?fn=20&arg1=crmmseries&ikey=CRMM-33). Our personal thanks to Daniel and family! Endless support from the Schenk Family who, among other things, sponsored (yet again) the entire conference dinner (including wines and banquet hall) meant that some costs could be alleviated. We could therefore assist various colleagues from economically-weak countries, despite the lack of external funding. A financial deficit meant we would have had to forego the Conference Proceedings, published in previous years by IOP. After long deliberations, and with donations from Gerhard Berssenbrügge, Dr. Dr. Stephan Hauk and Dr. Volker Weisswange, this could be facilitated. We are very grateful to these private donors for their generous and wholehearted support. The staff of Collegium Mehrerau is also to be thanked for their hospitality. Finally, our sincere thanks to Yvette not only for her preparatory work and support during the conference, but also for her persistent interest and help in producing the Proceedings within a reasonable time. Dieter Schuch, Frankfurt am Main, Germany Mi
Symmetry breaking in tensor models
NASA Astrophysics Data System (ADS)
Benedetti, Dario; Gurau, Razvan
2015-11-01
In this paper we analyze a quartic tensor model with one interaction for a tensor of arbitrary rank. This model has a critical point where a continuous limit of infinitely refined random geometries is reached. We show that the critical point corresponds to a phase transition in the tensor model associated to a breaking of the unitary symmetry. We analyze the model in the two phases and prove that, in a double scaling limit, the symmetric phase corresponds to a theory of infinitely refined random surfaces, while the broken phase corresponds to a theory of infinitely refined random nodal surfaces. At leading order in the double scaling limit planar surfaces dominate in the symmetric phase, and planar nodal surfaces dominate in the broken phase.
Mirror Symmetry in Emergent Gravity
Hyun Seok Yang
2015-11-19
Given a six-dimensional symplectic manifold $(M, B)$, a nondegenerate, co-closed four-form $C$ introduces a dual symplectic structure $\\widetilde{B} = *C $ independent of $B$ via the Hodge duality $*$. We show that the doubling of symplectic structures due to the Hodge duality results in two independent classes of noncommutative U(1) gauge fields by considering the Seiberg-Witten map for each symplectic structure. As a result, emergent gravity suggests a beautiful picture that the variety of six-dimensional manifolds emergent from noncommutative U(1) gauge fields is doubled. In particular, the doubling for the variety of emergent Calabi-Yau manifolds allows us to arrange a pair of Calabi-Yau manifolds such that they are mirror to each other. Therefore, we argue that the mirror symmetry of Calabi-Yau manifolds is the Hodge theory for the deformation of symplectic and dual symplectic structures.
Teaching symmetry in the introductory physics curriculum
Hill, C. T.; Lederman, L. M.
2000-01-01
Modern physics is largely defined by fundamental symmetry principles and Noether's Theorem. Yet these are not taught, or rarely mentioned, to beginning students, thus missing an opportunity to reveal that the subject of physics is as lively and contemporary as molecular biology, and as beautiful as the arts. We prescribe a symmetry module to insert into the curriculum, of a week's length.
On systems having Poincaré and Galileo symmetry
Holland, Peter
2014-12-15
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.
The Absolute Normal Scores Test for Symmetry.
ERIC Educational Resources Information Center
Penfield, Douglas A.; Sachdeva, Darshan
Behavioral scientists often wish to determine if a sample has been taken from a symmetric population. Similarly, classroom teachers are interested in symmetry if they wish to grade on a "curve." Previously, the sign test, the Wilcoxon test and the t-test have been used to test a hypothesis concerning the symmetry of a distribution of scores about…
Residual symmetries in the lepton mass matrices
Walter Grimus
2013-10-23
It has been suggested that residual symmetries in the charged-lepton and neutrino mass matrices can possibly reveal the flavour symmetry group of the lepton sector. We review the basic ideas of this purely group-theoretical approach and discuss some of its results. Finally, we also list its shortcomings.
Frieze and Wallpaper Symmetry Groups Classification under
Frieze and Wallpaper Symmetry Groups Classification under Affine and Perspective Distortion Yanxi wallpaper groups. Computer algorithms for Frieze and wallpaper symmetry group classification are developed repeated along one dimension, and the seventeen wallpaper groups [26] for patterns extended by two linearly
Frieze and Wallpaper Symmetry Groups Classification under
Collins, Robert T.
Frieze and Wallpaper Symmetry Groups Classification under Affine and Perspective Distortion Yanxi groups and 17 wallpaper groups. Computer algorithms for Frieze and wallpaper symmetry group. These are the seven Frieze groups [14, 29] for 2D patterns repeated along one dimension, and the seventeen wallpaper
Symmetry violation in nuclei Vladimir Gudkov1
and on a search for the possible manifestation of new physics in low energy nuclear interactions. The importance of the fundamental symmetries tests and a search for new physics is underlined in the third recommendation-unseen violations of time-reversal symmetry, and other key ingredients of the New Standard Model of fundamental
PT-symmetry in honeycomb photonic lattices
Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri; Segev, Mordechai
2011-08-15
We apply gain and loss to honeycomb photonic lattices and show that the dispersion relation is identical to tachyons--particles with imaginary mass that travel faster than the speed of light. This is accompanied by -symmetry breaking in this structure. We further show that the -symmetry can be restored by deforming the lattice.
Broken chiral symmetry on a null plane
Beane, Silas R.
2013-10-15
On a null-plane (light-front), all effects of spontaneous chiral symmetry breaking are contained in the three Hamiltonians (dynamical Poincaré generators), while the vacuum state is a chiral invariant. This property is used to give a general proof of Goldstone’s theorem on a null-plane. Focusing on null-plane QCD with N degenerate flavors of light quarks, the chiral-symmetry breaking Hamiltonians are obtained, and the role of vacuum condensates is clarified. In particular, the null-plane Gell-Mann–Oakes–Renner formula is derived, and a general prescription is given for mapping all chiral-symmetry breaking QCD condensates to chiral-symmetry conserving null-plane QCD condensates. The utility of the null-plane description lies in the operator algebra that mixes the null-plane Hamiltonians and the chiral symmetry charges. It is demonstrated that in a certain non-trivial limit, the null-plane operator algebra reduces to the symmetry group SU(2N) of the constituent quark model. -- Highlights: •A proof (the first) of Goldstone’s theorem on a null-plane is given. •The puzzle of chiral-symmetry breaking condensates on a null-plane is solved. •The emergence of spin-flavor symmetries in null-plane QCD is demonstrated.
Seitz symbols for crystallographic symmetry operations.
Glazer, A Michael; Aroyo, Mois I; Authier, André
2014-05-01
The aim of this report is to describe the Seitz notation for symmetry operations adopted by the Commission on Crystallographic Nomenclature as the standard convention for Seitz symbolism of the International Union of Crystallography. The established notation follows the existing crystallographic conventions in the descriptions of symmetry operations. PMID:24815978
CP Symmetry in Particle Introduction Results
?umer, Slobodan
CP Symmetry in Particle Physics Introduction Results B-Factory Interpretation Exp. method Future/19Physics in Ljubljana, FMF, July 2011 j j y y #12;Introduction Why CP (A)Symmetry? Introduction Results B anti-baryons annihilated, while 1/109 baryons did not? p y anti-particles #12;Introduction Why CP (A
Symmetry aspects of nonholonomic field theories
J. Vankerschaver; D. Martin de Diego
2007-12-14
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with the underlying geometric philosophy, a small modification of the derivation of the momentum lemma allows us to treat also generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover both energy conservation (a previously known result), as well as a modified conservation law associated with spatial translations.
Symmetry aspects of nonholonomic field theories
NASA Astrophysics Data System (ADS)
Vankerschaver, Joris; Martín de Diego, David
2008-01-01
The developments in this paper are concerned with nonholonomic field theories in the presence of symmetries. Having previously treated the case of vertical symmetries, we now deal with the case where the symmetry action can also have a horizontal component. As a first step in this direction, we derive a new and convenient form of the field equations of a nonholonomic field theory. Nonholonomic symmetries are then introduced as symmetry generators whose virtual work is zero along the constraint submanifold, and we show that for every such symmetry, there exists a so-called momentum equation, describing the evolution of the associated component of the momentum map. Keeping up with the underlying geometric philosophy, a small modification of the derivation of the momentum lemma allows us to also treat generalized nonholonomic symmetries, which are vector fields along a projection. Such symmetries arise for example in practical examples of nonholonomic field theories such as the Cosserat rod, for which we recover both energy conservation (a previously known result) and a modified conservation law associated with spatial translations.
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.
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
Quantum Mechanical Observers and Time Reparametrization Symmetry
Eiji Konishi
2012-12-20
We propose that the degree of freedom of measurement by quantum mechanical observers originates in the Goldstone mode of the spontaneously broken time reparametrization symmetry. Based on the classification of quantum states by their non-unitary temporal behavior as seen in the measurement processes, we describe the concepts of the quantum mechanical observers via the time reparametrization symmetry.
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.
Topological symmetry breaking by quantum wormholes
Mignemi, S.; Moss, I. )
1993-10-15
In multiply connected spacetimes which contain quantum wormholes it may be possible to break gauge symmetries without the usual Higgs fields. In a simple model, symmetry breaking is favored by the quantum effects of Dirac Fermions and leads to vector boson masses related to the wormhole separation.
Electroweak Symmetry Breaking and the Higgs Boson
Antonio Pich
2015-12-29
The first LHC run has confirmed the Standard Model as the correct theory at the electroweak scale, and the existence of a Higgs-like particle associated with the spontaneous breaking of the electroweak gauge symmetry. These lectures overview the present knowledge on the Higgs boson and discuss alternative scenarios of electroweak symmetry breaking which are already being constrained by the experimental data.
Mathematical models of spontaneous symmetry breaking
G. Sardanashvily
2008-02-17
The Higgs mechanism of mass generation is the main ingredient in the contemporary Standard Model and its various generalizations. However, there is no comprehensive theory of spontaneous symmetry breaking. We summarize the relevant mathematical results characterizing spontaneous symmetry breaking phenomena in algebraic quantum theory, axiomatic quantum field theory, group theory, and classical gauge theory.
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.
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.
cover image Symmetry-breaking transitions
Loss, Daniel
Symmetry-breaking transitions: Dynamics of broken symmetry Richard D. Averitt 640 Quantum information Johnpierre Paglione and Richard L. Greene letters 659 The uncertainty principle in the presence of quantumcapacitance circuit Christophe Mora and Karyn Le Hur 702 interplay of quantum criticality and geometric frustration
Dynamic Symmetry Breaking by Simulating Zykov Contraction
Mitchell, David G.
Dynamic Symmetry Breaking by Simulating Zykov Contraction Bas Schaafsma, Marijn J.H. Heule@ch.tudelft.nl, marijn@heule.nl, h.vanmaaren@tudelft.nl Abstract. We present a new method to break symmetry in graph. Schaafsma, M.J.H. Heule, and H. van Maaren clique [19]. Although effective and cheap (a large clique is easy
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.
Heavy-Quark Symmetry and Skyrmions
Dong-Pil Min; Yongseok Oh; Byung-Yoon Park; Mannque Rho
1994-12-15
We review recent development on combining heavy-quark symmetry and chiral symmetry in the skyrmion structure of the baryons containing one or more heavy quarks, c (charmed) and b (bottom). We describe two approaches: One going from the chiral symmetry regime of light quarks to the heavy-quark symmetry regime which will be referred to as ``bottom-up" approach and the other going down from the heavy-quark limit to the realistic finite-mass regime which will be referred to as ``top-down." A possible hidden connection between the two symmetry limits is suggested. This review is based largely on the work done -- some unpublished -- by the authors since several years.
Hojman symmetry in f(T) theory
NASA Astrophysics Data System (ADS)
Wei, Hao; Zhou, Ya-Nan; Li, Hong-Yu; Zou, Xiao-Bo
2015-11-01
Today, f(T) theory has been one of the popular modified gravity theories to explain the accelerated expansion of the universe without invoking dark energy. In this work, we consider the so-called Hojman symmetry in f(T) theory. Unlike Noether conservation theorem, the symmetry vectors and the corresponding conserved quantities in Hojman conservation theorem can be obtained by using directly the equations of motion, rather than Lagrangian or Hamiltonian. We find that Hojman symmetry can exist in f(T) theory, and the corresponding exact cosmological solutions are obtained. We find that the functional form of f(T) is restricted to be the power-law or hypergeometric type, while the universe experiences a power-law or hyperbolic expansion. These results are different from the ones obtained by using Noether symmetry in f(T) theory. Therefore, it is reasonable to find exact cosmological solutions via Hojman symmetry.
Chiral symmetries associated with angular momentum
NASA Astrophysics Data System (ADS)
Bhattacharya, M.; Kleinert, M.
2014-03-01
In quantum mechanics courses, symmetries of a physical system are usually introduced as operators which commute with the Hamiltonian. In this paper we will consider chiral symmetries which anticommute with the Hamiltonian. Typically, introductory courses at the (under)graduate level do not discuss these simple, useful and beautiful symmetries at all. The first time a student encounters them is when the Dirac equation is discussed in a course on relativistic quantum mechanics, or when particle-hole symmetry is studied in the context of superconductivity. In this paper, we will show how chiral symmetries can be simply elucidated using the theory of angular momentum, which is taught in virtually all introductory quantum mechanics courses.
Symmetry-protected adiabatic quantum transistors
Dominic J. Williamson; Stephen D. Bartlett
2015-05-15
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.
Anomalous Symmetry Fractionalization and Surface Topological Order
NASA Astrophysics Data System (ADS)
Chen, Xie; Burnell, F. J.; Vishwanath, Ashvin; Fidkowski, Lukasz
2015-10-01
In addition to possessing fractional statistics, anyon excitations of a 2D topologically ordered state can realize symmetry in distinct ways, leading to a variety of symmetry-enriched topological (SET) phases. While the symmetry fractionalization must be consistent with the fusion and braiding rules of the anyons, not all ostensibly consistent symmetry fractionalizations can be realized in 2D systems. Instead, certain "anomalous" SETs can only occur on the surface of a 3D symmetry-protected topological (SPT) phase. In this paper, we describe a procedure for determining whether a SET of a discrete, on-site, unitary symmetry group G is anomalous or not. The basic idea is to gauge the symmetry and expose the anomaly as an obstruction to a consistent topological theory combining both the original anyons and the gauge fluxes. Utilizing a result of Etingof, Nikshych, and Ostrik, we point out that a class of obstructions is captured by the fourth cohomology group H4(G ,U (1 )) , which also precisely labels the set of 3D SPT phases, with symmetry group G . An explicit procedure for calculating the cohomology data from a SET is given, with the corresponding physical intuition explained. We thus establish a general bulk-boundary correspondence between the anomalous SET and the 3D bulk SPT whose surface termination realizes it. We illustrate this idea using the chiral spin liquid [U (1 )2 ] topological order with a reduced symmetry Z2×Z2?SO (3 ) , which can act on the semion quasiparticle in an anomalous way. We construct exactly solved 3D SPT models realizing the anomalous surface terminations and demonstrate that they are nontrivial by computing three-loop braiding statistics. Possible extensions to antiunitary symmetries are also discussed.
Symmetry-Protected Quantum Spin Hall Phases in Two Dimensions
Liu, Zheng-Xin
Symmetry-protected topological (SPT) states are short-range entangled states with symmetry. Nontrivial SPT states have symmetry-protected gapless edge excitations. In 2 dimension (2D), there are an infinite number of ...
Symmetry-protected topological phases in noninteracting fermion systems
Wen, Xiao-Gang
Symmetry-protected topological (SPT) phases are gapped quantum phases with a certain symmetry, which can all be smoothly connected to the same trivial product state if we break the symmetry. For noninteracting fermion ...
Infinite-dimensional symmetry for wave equation with additional condition
Irina Yehorchenko; Alla Vorobyova
2009-10-13
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
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
Symmetries in fluctuations far from equilibrium.
Hurtado, Pablo I; Pérez-Espigares, Carlos; del Pozo, Jesús J; Garrido, Pedro L
2011-05-10
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Symmetries in fluctuations far from equilibrium
Hurtado, Pablo I.; Pérez-Espigares, Carlos; del Pozo, Jesús J.; Garrido, Pedro L.
2011-01-01
Fluctuations arise universally in nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. To sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation that links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti–Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager’s reciprocity relations and Green–Kubo formulas. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields. PMID:21493865
Sufficient symmetry conditions for Topological Quantum Order
Nussinov, Zohar; Ortiz, Gerardo
2009-01-01
We prove sufficient conditions for Topological Quantum Order at zero and finite temperatures. The crux of the proof hinges on the existence of low-dimensional Gauge-Like Symmetries, thus providing a unifying framework based on a symmetry principle. These symmetries may be actual invariances of the system, or may emerge in the low-energy sector. Prominent examples of Topological Quantum Order display Gauge-Like Symmetries. New systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin exchange and Jahn–Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. We analyze the physical consequences of Gauge-Like Symmetries (including topological terms and charges) and show the insufficiency of the energy spectrum, topological entanglement entropy, maximal string correlators, and fractionalization in establishing Topological Quantum Order. General symmetry considerations illustrate that not withstanding spectral gaps, thermal fluctuations may impose restrictions on suggested quantum computing schemes. Our results allow us to go beyond standard topological field theories and engineer systems with Topological Quantum Order. PMID:19805113
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.
Dynamical flavor origin of ZN symmetries
NASA Astrophysics Data System (ADS)
Sierra, D. Aristizabal; Dhen, Mikaël; Fong, Chee Sheng; Vicente, Avelino
2015-05-01
Discrete Abelian symmetries (ZN ) are a common "artifact" of beyond the standard model physics models. They provide different avenues for constructing consistent scenarios for lepton and quark mixing patterns, radiative neutrino mass generation as well as dark matter stabilization. We argue that these symmetries can arise from the spontaneous breaking of the Abelian U (1 ) factors contained in the global flavor symmetry transformations of the gauge-invariant kinetic Lagrangian. This will be the case provided the ultraviolet completion responsible for the Yukawa structure involves scalar fields carrying nontrivial U (1 ) charges. Guided by minimality criteria, we demonstrate the viability of this approach with two examples: first, we derive the "scotogenic" model Lagrangian, and second, we construct a setup where the spontaneous symmetry-breaking pattern leads to a Z3 symmetry which enables dark matter stability as well as neutrino mass generation at the two-loop order. This generic approach can be used to derive many other models, with residual ZN or ZN1×⋯×ZNk symmetries, establishing an intriguing link between flavor symmetries, neutrino masses and dark matter.
Wang, Xuelei; Zuo, Tianming; Olmstead, Marilyn M; Duchamp, James C; Glass, Thomas E; Cromer, Frank; Balch, Alan L; Dorn, Harry C
2006-07-12
Herein, we report the preparation, purification, and characterization of a mixed trimetallic nitride endohedral metallofullerene, CeSc(2)N@C(80). Single-crystal X-ray diffraction shows that CeSc(2)N@C(80) consists of a four-atom asymmetric top (CeSc(2)N) inside a C(80) (I(h)()) carbon cage. Unlike the situation in most endohedrals of the M(3)N@C(2)(n)() type, the nitride ion is not located at the center of the carbon cage but is offset by 0.36 A in order to accommodate the large Ce(III) ion. The cage carbon atoms near the endohedral Ce and Sc atoms exhibit significantly larger pyramidal angles than the other carbon atoms on the C(80) cage. Surprisingly, at ambient temperature, the (13)C NMR spectrum exhibits isotropic motional averaging yielding only two signals (3 to 1 intensity ratio) for the icosahedral C(80) cage carbons. At the same temperature, the (45)Sc NMR exhibits a relatively narrow, symmetric signal (2700 Hz) with a small temperature-dependent Curie shift. A rotation energy barrier (E(a) = 79 meV) was derived from the (45)Sc NMR line-width analysis. Finally, the XPS spectrum for CeSc(2)N@C(80) confirms a +3 oxidation state for cerium, Ce(3+)(4f(1)5d(0)). This oxidation state and the Curie shift are consistent with a weakly paramagnetic system with a single buried f electron spin. PMID:16819883
NASA Astrophysics Data System (ADS)
Takeuchi, Tsunehiro; Mizutani, Uichiro; Yamaguchi, Shinji; Fukunaga, Toshiharu; Mizuno, Takayuki; Tanaka, Nobuo
1998-11-01
The rhombic-triacontahedral-type quasicrystal (RT-QC), its (1/1, 1/1, 1/1) approximant (RT-1/1) and the Mackay-icosahedral-type quasicrystal (MI-QC) can be formed in the Al-Mg-Pd system. The radial distribution function RDF(r) spectra of the three compounds is derived from neutron diffraction experiments. Powdered x-ray diffraction Rietveld refinement is also carried out to determine the atomic structure of the RT-1/1, and the refined data are converted to the RDF(r). The interatomic distance of the Al-Pd pair in the RT-1/1 and RT-QC is found to be remarkably shortened relative to that calculated from the hard sphere model with Goldschmidt radii. In the MI-QC, the interatomic distance of the Al-Pd pair is further shortened. In addition, the shortening of the interatomic distance is also observed in the Mg-Pd pair. The valence band spectra studied by the x-ray photoemission spectroscopy and soft x-ray spectroscopy clearly show the formation of the bonding and antibonding states associated with the Al-Pd and Mg-Pd atomic pairs in the MI-QC. The results are consistent with the shortening of the interatomic distances derived from the structure analysis. The reason for the possession of the highest resistivity in the MI-QC among the three compounds is attributed to the formation of the covalent bonding between Al-Pd and Mg-Pd atomic pairs.
Lattices of Graphical Gaussian Models with Symmetries
Gehrmann, Helene
2011-01-01
We study the structure of graphical Gaussian models which place symmetry restrictions on concentrations or partial correlations. The models can be represented by vertex and edge coloured graphs, in which parameters which are associated with equally coloured vertices or edges are restricted to being identical. We are particularly interested in two symmetry model classes within the model types with desirable model properties which express themselves in regularity of graph colouring. We demonstrate that each model class forms a complete lattice with respect to model inclusion and therefore qualifies for the Edwards-Havr\\'anek model selection procedure, giving a first model selection algorithm for graphical Gaussian models with symmetries.
Symmetries and Dynamics of Discrete Systems
Vladimir V. Kornyak
2007-10-08
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program constructs and investigates phase portraits of discrete dynamical systems modulo groups of their symmetries, searches dynamical systems possessing specific properties, e.g., reversibility, computes microcanonical partition functions and searches phase transitions in mesoscopic systems. Some computational results and observations are presented. In particular, we explain formation of moving soliton-like structures similar to ``spaceships'' in cellular automata.
Symmetries and Dynamics of Discrete Systems
Kornyak, Vladimir V
2007-01-01
We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program constructs and investigates phase portraits of discrete dynamical systems modulo groups of their symmetries, searches dynamical systems possessing specific properties, e.g., reversibility, computes microcanonical partition functions and searches phase transitions in mesoscopic systems. Some computational results and observations are presented. In particular, we explain formation of moving soliton-like structures similar to ``spaceships'' in cellular automata.
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.
A symmetry-breaking electromechanical detector
NASA Astrophysics Data System (ADS)
Mahboob, I.; Froitier, C.; Yamaguchi, H.
2010-05-01
The dynamical double well potential underpinning the stable oscillation phases in an electromechanical parametric resonator is manipulated via a secondary field excitation applied at the natural frequency of the oscillator. This enables symmetry to be lifted in the dynamical potential well and results in the parametric resonator oscillating with a preferred phase. The ability to break symmetry in the dynamical double well potential permits the realization of a symmetry-breaking detector which can resolve resonance frequency (f0) shifts of ?f0/f0˜10-7 in a single-shot measurement.
Nonanomalous discrete R symmetry decrees three generations.
Evans, Jason L; Ibe, Masahiro; Kehayias, John; Yanagida, Tsutomu T
2012-11-01
We show that more than two generations of quarks and leptons are required to have an anomaly free discrete R symmetry larger than R parity, provided that the supersymmetric standard model can be minimally embedded into a grand unified theory. This connects an explanation for the number of generations with seemingly unrelated problems such as supersymmetry breaking, proton decay, the ? problem, and the cosmological constant through a discrete R symmetry. We also show that three generations is uniquely required by a nonanomalous discrete R symmetry in classes of grand unified theories such as the ones based on (semi)simple gauge groups. PMID:23215270
Electromagnetic radiation under explicit symmetry breaking.
Sinha, Dhiraj; Amaratunga, Gehan A J
2015-04-10
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna. PMID:25910163
Neutrino Mixing and Leptogenesis in $?-?$ Symmetry
E. I. Lashin; N. Chamoun; C. Hamzaoui; S. Nasri
2015-05-21
We study the consequences of the $Z_2$-symmetry behind the $\\mu$--$\\tau$ universality in neutrino mass matrix. We then implement this symmetry in the type-I seesaw mechanism and show how it can accommodate all sorts of lepton mass hierarchies and generate enough lepton asymmetry to interpret the observed baryon asymmetry in the universe. We also show how a specific form of a high-scale perturbation is kept when translated via the seesaw into the low scale domain, where it can accommodate the neutrino mixing data. We finally present a realization of the high scale perturbed texture through addition of matter and extra exact symmetries.
Neutrino mixing and leptogenesis in ? -? symmetry
NASA Astrophysics Data System (ADS)
Lashin, E. I.; Chamoun, N.; Hamzaoui, C.; Nasri, S.
2015-06-01
We study the consequences of the Z2 symmetry behind the ? -? universality in the neutrino mass matrix. We then implement this symmetry in the type-I seesaw mechanism and show how it can accommodate all sorts of lepton mass hierarchies and generate enough lepton asymmetry to interpret the observed baryon asymmetry in the universe. We also show how a specific form of a high-scale perturbation is kept when translated via the seesaw into the low scale domain, where it can accommodate the neutrino mixing data. We finally present a realization of the high scale perturbed texture through the addition of matter and extra exact symmetries.
Electromagnetic Radiation under Explicit Symmetry Breaking
NASA Astrophysics Data System (ADS)
Sinha, Dhiraj; Amaratunga, Gehan A. J.
2015-04-01
We report our observation that radiation from a system of accelerating charges is possible only when there is explicit breaking of symmetry in the electric field in space within the spatial configuration of the radiating system. Under symmetry breaking, current within an enclosed area around the radiating structure is not conserved at a certain instant of time resulting in radiation in free space. Electromagnetic radiation from dielectric and piezoelectric material based resonators are discussed in this context. Finally, it is argued that symmetry of a resonator of any form can be explicitly broken to create a radiating antenna.
Constraints on leptogenesis from a symmetry viewpoint
Gonzalez Felipe, R.; Serodio, H.
2010-03-01
It is shown that type I seesaw models based on the standard model Lagrangian extended with three heavy Majorana right-handed fields do not have leptogenesis in leading order, if the symmetries of mass matrices are also the residual symmetry of the Lagrangian. In particular, flavor models that lead to a mass-independent leptonic mixing have a vanishing leptogenesis CP asymmetry. Based on symmetry arguments, we prove that in these models the Dirac-neutrino Yukawa coupling combinations relevant for leptogenesis are diagonal in the physical basis where the charged leptons and heavy Majorana neutrinos are diagonal.
Discrete symmetries and de Sitter spacetime
Cot?escu, Ion I. Pascu, Gabriel
2014-11-24
Aspects of the ambiguity in defining quantum modes on de Sitter spacetime using a commuting system composed only of differential operators are discussed. Discrete symmetries and their actions on the wavefunction in commonly used coordinate charts are reviewed. It is argued that the system of commuting operators can be supplemented by requiring the invariance of the wavefunction to combined discrete symmetries- a criterion which selects a single state out of the ?-vacuum family. Two such members of this family are singled out by particular combined discrete symmetries- states between which exists a well-known thermality relation.
Charge Independence and Symmetry of Nuclear Forces
G. A. Miller
1994-06-20
Charge independence and symmetry are approximate symmetries of nature. The observations of the small symmetry breaking effects and the consequences of those effects are reviewed. The effects of the mass difference between up and down quarks and the off shell dependence $q^2$ of $\\rho^0$-$\\omega$ mixing are stressed. In particular, I argue that models which predict a strong $q^2$ dependence of $\\rho^0$-$\\omega$ mixing seem also to predict a strong $q^2$ variation for the $\\rho^0$-$\\gamma^*$ matrix element, in contradiction with experiment.
Soliton quantization and internal symmetry
NASA Astrophysics Data System (ADS)
Dorey, Nicholas; Hughes, James; Mattis, Michael P.
1994-04-01
We apply the method of collective coordinate quantization to a model of solitons in two spacetime dimensions with a global U(1) symmetry. In particular we consider the dynamics of the charged states associated with rotational excitations of the soliton in the internal space and their interactions with the quanta of the background field (mesons). By solving a system of coupled saddle-point equations we effectively sum all tree graphs contributing to the one-point Green's function of the meson field in the background of a rotating soliton. We find that the resulting one-point function evaluated between soliton states of definite U(1) charge exhibits a pole on the meson mass shell and we extract the corresponding S-matrix element for the decay of an excited state via the emission of a single meson using the standard Lehmann-Symanzik-Zimmermann reduction formula. This S-matrix element has a natural interpretation in terms of an effective Lagrangian for the charged soliton states with an explicit Yukawa coupling to the meson field. We calculate the leading-order semiclassical decay width of the excited soliton states and discuss the consequences of these results for the hadronic decay of the ? resonance in the Skyrme model.
Supertwistors, massive superparticles and ?-symmetry
NASA Astrophysics Data System (ADS)
de Azcárraga, J. A.; Izquierdo, J. M.; Lukierski, J.
2009-01-01
We consider a D = 4 two-twistor lagrangian for a massive particle that incorporates the mass-shell condition in an algebraic way, and extend it to a two-supertwistor model with N = 2 supersymmetry and central charge identified with the mass. In the purely supertwistorial picture the two D = 4 super twistors are coupled through a Wess-Zumino term in their fermionic sector. We demonstrate how the ?-gauge symmetry appears in the purely supertwistorial formulation and reduces by half the fermionic degrees of freedom of the two supertwistors; a formulation of the model in terms of ?-invariant degrees of freedom is also obtained. We show that the ?-invariant supertwistor coordinates can be obtained by dimensional (D = 6 ? D = 4) reduction from a D = 6 supertwistor. We derive as well by 6 ? 4 reduction the N = 2 D = 4 massive superparticle model with Wess-Zumino term introduced in 1982. Finally, we comment on general superparticle models constructed with more than two supertwistors.
Structural symmetry in evolutionary games.
McAvoy, Alex; Hauert, Christoph
2015-10-01
In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time, for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be 'evolutionarily equivalent' in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term 'homogeneous' should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry. PMID:26423436
Bilateral symmetry across Aphrodite Terra
NASA Technical Reports Server (NTRS)
Crumpler, L. S.; Head, J. W.; Campbell, D. B.
1987-01-01
There are three main highland areas on Venus: Beta Regio, Ishtar Terra and Aphrodite Terra. The latter is least known and the least mapped, yet existing analyses of Aphrodite Terra based on available Pioneer-Venus orbiter data suggest that it may be the site of extensive rifting. Some of the highest resolution (30 km) PV data (SAR) included most of the western half of Aphrodite Terra. Recent analysis of the SAR data together with Arecibo range-doppler topographic profiling (10 X 100 km horizontal and 10 m vertical resolution) across parts of Aphrodite, further characterized the nature of possible tectonic processes in the equatorial highlands. The existence of distinct topographic and radar morphologic linear discontinuities across the nearly east-west strike of Aphrodite Terra is indicated. Another prominent set of linear features is distinctly parallel to and orthogonal to the ground tracks of the PV spacecraft and are not included because of the possibility that they are artifacts. Study of the northwest trending cross-strike discontinuities (CSD's) and the nature of topographic and morphologic features along their strike suggest the presence of bilateral topographic and morphologic symmetry about the long axis of Aphrodite Terra.
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
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
Neutrino mass textures and partial ? -? symmetry
NASA Astrophysics Data System (ADS)
Lashin, E. I.; Chamoun, N.; Hamzaoui, C.; Nasri, S.
2014-05-01
We discuss the viability of the ? -? interchange symmetry imposed on the neutrino mass matrix in the flavor space. Whereas the exact symmetry is shown to lead to textures of a completely degenerate spectrum, which is incompatible with the neutrino oscillation data, introducing small perturbations into the preceding textures, inserted in a minimal way, leads, however, to four deformed textures representing an approximate ?-? symmetry. We motivate the form of these "minimal" textures, which disentangle the effects of the perturbations, and present some concrete realizations assuming exact ? -? at the Lagrangian level but at the expense of adding new symmetries and matter fields. We find that all of these deformed textures are capable of accommodating the experimental data, and in all types of neutrino mass hierarchies, particularly the nonvanishing value for the smallest mixing angle.
Twist liquids and gauging anyonic symmetries
NASA Astrophysics Data System (ADS)
Teo, Jeffrey; Hughes, Taylor; Fradkin, Eduardo
2015-03-01
Topological phases of matter in (2 + 1) D are frequently equipped with global symmetries that relabel anyons without changing the fusion and braiding structures. Twist defects are static symmetry fluxes that permute the labels of orbiting anyons. Gauging or melting these symmetries by quantizing defects into dynamical excitations leads to a wide class of more exotic topological phases known as twist liquids. We formulate a general gauging framework, characterize the anyon structure of twist liquids and provide solvable lattice models that capture the gauging phase transitions. Generalizing a discrete gauge theory, we represent the anyons in a twist liquid by compositions of not only fluxes and charges but also quasiparticle supersectors. We show the gauging transition amplifies the total quantum dimension by | G | , the order of the symmetry group, and thus modifies the topological entanglement entropy.
Entangling symmetry and topology in correlated electrons
Wang, Chong, Ph. D. Massachusetts Institute of Technology
2015-01-01
In this thesis, I study a class of exotic quantum matter named Symmetry-Protected Topological (SPT) phases. These are short-range-entangled quantum phases hosting non-trivial states on their boundaries. In the free-fermion ...
Space and time from translation symmetry
Schwarz, A.
2010-01-15
We show that the notions of space and time in algebraic quantum field theory arise from translation symmetry if we assume asymptotic commutativity. We argue that this construction can be applied to string theory.
Vector models of gravitational Lorentz symmetry breaking
Michael D. Seifert
2009-06-08
Spontaneous Lorentz symmetry breaking can occur when the dynamics of a tensor field cause it to take on a non-zero expectation value in vacuo, thereby providing one or more "preferred directions" in spacetime. Couplings between such fields and spacetime curvature will then affect the dynamics of the metric, leading to interesting gravitational effects. Bailey & Kostelecky developed a post-Newtonian formalism that, under certain conditions concerning the field's couplings and stress-energy, allows for the analysis of gravitational effects in the presence of Lorentz symmetry breaking. We perform a systematic survey of vector models of spontaneous Lorentz symmetry breaking. We find that a two-parameter class of vector models, those with kinetic terms we call "pseudo-Maxwell," can be successfully analyzed under the Bailey-Kostelecky formalism, and that one of these two "dimensions" in parameter space has not yet been explored as a possible mechanism of spontaneous Lorentz symmetry breaking.
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.
Symmetry energy coefficients for asymmetric nuclear matter
Fábio L. Braghin
2003-12-16
Symmetry energy coefficients of asymmetric nuclear matter are investigated as the inverse of nuclear matter polarizabilities with two different approaches. Firstly a general calculation shows they may depend on the neutron-proton asymmetry itself. The choice of particular prescriptions for the density fluctuations lead to certain isospin (n-p asymmetry) dependences of the polarizabilities. Secondly, with Skyrme type interactions, the static limit of the dynamical polarizability is investigated corresponding to the inverse symmetry energy coefficient which assumes different values at different asymmetries (and densities and temperatures). The symmetry energy coefficient (in the isovector channel) is found to increase as n-p asymmetries increase. The spin symmetry energy coefficient is also briefly investigated.
CHAOTIC ATTRACTORS AND EVOLVING PLANAR SYMMETRY
Reiter, Clifford A.
.S.A e-mail: reiterc@lafcol.lafayette.edu LISA M. VISLOCKY Lafayette College, Box 9486, Easton PA 18042 chaotic attractors with cyclic, dihedral and some of the planar crystallographic symmetries. Carter et al
$?(27)$ family symmetry and neutrino mixing
Ivo de Medeiros Varzielas
2015-08-03
The observed neutrino mixing, having a near maximal atmospheric neutrino mixing angle and a large solar mixing angle, is close to tri-bi-maximal. This structure may be related to the existence of a discrete non-Abelian family symmetry. In this paper the family symmetry is the non-Abelian discrete group $\\Delta(27)$, a subgroup of $SU(3)$ with triplet and anti-triplet representations. Different frameworks are constructed in which the mixing follows from combining fermion mass terms with the vacuum structure enforced by the discrete symmetry. Mass terms for the fermions originate from familon triplets, anti-triplets or both. Vacuum alignment for the family symmetry breaking familons follows from simple invariants.
From Symmetries to Quarks and Beyond
NASA Astrophysics Data System (ADS)
Meshkov, Sydney
2015-03-01
Attempts to understand the plethora of meson baryon and meson resonances by the introduction of symmetries, which led to the invention of quarks and the quark model, and finally to the formulation of QCD, are described.
Matrix Models, Emergent Spacetime and Symmetry Breaking
Grosse, Harald; Steinacker, Harold; Lizzi, Fedele
2009-12-15
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum numbers of fermions.
Dynamic Symmetry Breaking by Simulating Zykov Contraction
Kuzmanov, Georgi
Dynamic Symmetry Breaking by Simulating Zykov Contraction Bas Schaafsma, Marijn Heule and Hans van Maaren Department of Software Technology, Delft University of Technology schaafsma@ch.tudelft.nl, marijn@heule
Modelling Symmetry Classes 233 and 432.
ERIC Educational Resources Information Center
Dutch, Steven I.
1986-01-01
Offers instructions and geometrical data for constructing solids of the enantiomorphous symmetry classes 233 and 432. Provides background information for each class and highlights symmetrical relationships and construction patterns. (ML)
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). ...
COVER IMAGE Time-reversal symmetry makes
Loss, Daniel
COVER IMAGE Time-reversal symmetry makes massless Dirac fermions in topological insulators `gapless COMMENTARY 828 A complex legacy Cristopher Moore THESIS 831 Age of reason Mark Buchanan BOOKS & ARTS 832
Hidden gauge symmetry in holomorphic models
NASA Astrophysics Data System (ADS)
Margalli, Carlos A.; Vergara, J. David
2015-10-01
We study the effect of a hidden gauge symmetry on complex holomorphic systems. For this purpose, we show that intrinsically any holomorphic system has this gauge symmetry. We establish that this symmetry is related to the Cauchy-Riemann equations, in the sense that the associated constraint is a first class constraint only in the case that the potential be holomorphic. As a consequence of this gauge symmetry on the complex space, we can fix the gauge condition in several ways and project from the complex phase-space to real phase space. Different projections are gauge related on the complex phase-space but are not directly related on the real physical phase-space.
Noether's second theorem for BRST symmetries
Bashkirov, D.; Giachetta, G.; Mangiarotti, L.; Sardanashvily, G.
2005-05-01
We present Noether's second theorem for graded Lagrangian systems of even and odd variables on an arbitrary body manifold X in a general case of BRST symmetries depending on derivatives of dynamic variables and ghosts of any finite order. As a preliminary step, Noether's second theorem for Lagrangian systems on fiber bundles Y{yields}X possessing gauge symmetries depending on derivatives of dynamic variables and parameters of arbitrary order is proved.
Partial dynamical symmetries in quantum systems
A. Leviatan
2011-12-22
We discuss the the notion of a partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by only a subset of solvable eigenstates, while other eigenstates are strongly mixed. We present an explicit construction of Hamiltonians with this property, including higher-order terms, and portray their significance for spectroscopy and shape-phase transitions in nuclei. The occurrence of both a single PDS, relevant to stable structures, and of several PDSs, relevant to coexistence phenomena, are considered.
A Hidden Symmetry of the Galileon
Kurt Hinterbichler; Austin Joyce
2015-07-04
We show that there is a special choice of parameters for which the galileon theory is invariant under an enhanced shift symmetry whose non-linear part is quadratic in the coordinates. This symmetry fixes the theory to be equivalent to one with only even powers of the field, with no free coefficients, and accounts for the improved soft limit behavior observed in the quartic galileon S-matrix.
Nanostructure symmetry: Relevance for physics and computing
Dupertuis, Marc-André; Oberli, D. Y.; Karlsson, K. F.; Dalessi, S.; Gallinet, B.; Svendsen, G.
2014-03-31
We review the research done in recent years in our group on the effects of nanostructure symmetry, and outline its relevance both for nanostructure physics and for computations of their electronic and optical properties. The exemples of C3v and C2v quantum dots are used. A number of surprises and non-trivial aspects are outlined, and a few symmetry-based tools for computing and analysis are shortly presented.
Conservation Laws and Non-Lie Symmetries
Anthony C. L Ashton
2008-10-05
We introduce a method to construct conservation laws for a large class of linear partial differential equations. In contrast to the classical result of Noether, the conserved currents are generated by any symmetry of the operator, including those of the non-Lie type. An explicit example is made of the Dirac equation were we use our construction to find a class of conservation laws associated with a 64 dimensional Lie algebra of discrete symmetries that includes CPT.
Projective representations from quantum enhanced graph symmetries
NASA Astrophysics Data System (ADS)
Kaufmann, R. M.; Khlebnikov, S.; Wehefritz—Kaufmann, B.
2015-04-01
We define re-gaugings and enhanced symmetries for graphs with group labels on their edges. These give rise to interesting projective representations of subgroups of the automorphism groups of the graphs. We furthermore embed this construction into several higher levels of generalization using category theory and show that they are natural in that language. These include projective representations of the re-gauging groupoid and a novel generalization to all symmetries of the graph.
Enhanced Coset Symmetries and Higher Derivative Corrections
Neil Lambert; Peter West
2006-08-17
After dimensional reduction to three dimensions, the lowest order effective actions for pure gravity, M-theory and the Bosonic string admit an enhanced symmetry group. In this paper we initiate study of how this enhancement is affected by the inclusion of higher derivative terms. In particular we show that the coefficients of the scalar fields associated to the Cartan subalgebra are given by weights of the enhanced symmetry group.
Black Hole Thermodynamics and Lorentz Symmetry
Jacobson, Ted
2008-01-01
Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe the arguments leading to that conclusion. We suggest the implication that Lorentz symmetry should be viewed as an emergent property of the macroscopic world, required by the second law of black hole thermodynamics.
Symmetry energy in cold dense matter
Kie Sang Jeong; Su Houng Lee
2015-09-18
We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction to the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.
SUGRA new inflation with Heisenberg symmetry
Antusch, Stefan; Cefalà, Francesco E-mail: stefan.antusch@unibas.ch
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
A new paradigm for animal symmetry.
Holló, Gábor
2015-12-01
My aim in this article is to soften certain rigid concepts concerning the radial and bilateral symmetry of the animal body plan, and to offer a more flexible framework of thinking for them, based on recent understandings of how morphogenesis is regulated by the mosaically acting gene regulatory networks. Based on general principles of the genetic regulation of morphogenesis, it can be seen that the difference between the symmetry of the whole body and that of minor anatomical structures is only a question of a diverse timing during development. I propose that the animal genome, as such, is capable of expressing both radial and bilateral symmetries, and deploys them according to the functional requirements which must be satisfied by both the anatomical structure and body as a whole. Although it may seem paradoxical, this flexible view of symmetry, together with the idea that symmetry is strongly determined by function, bolsters the concept that the presence of the two main symmetries in the animal world is not due to chance: they are necessary biological patterns emerging in evolution. PMID:26640644
Symmetry energy in cold dense matter
NASA Astrophysics Data System (ADS)
Jeong, Kie Sang; Lee, Su Houng
2016-01-01
We calculate the symmetry energy in cold dense matter both in the normal quark phase and in the 2-color superconductor (2SC) phase. For the normal phase, the thermodynamic potential is calculated by using hard dense loop (HDL) resummation to leading order, where the dominant contribution comes from the longitudinal gluon rest mass. The effect of gluonic interaction on the symmetry energy, obtained from the thermodynamic potential, was found to be small. In the 2SC phase, the non-perturbative BCS paring gives enhanced symmetry energy as the gapped states are forced to be in the common Fermi sea reducing the number of available quarks that can contribute to the asymmetry. We used high density effective field theory to estimate the contribution of gluon interaction to the symmetry energy. Among the gluon rest masses in 2SC phase, only the Meissner mass has iso-spin dependence although the magnitude is much smaller than the Debye mass. As the iso-spin dependence of gluon rest masses is even smaller than the case in the normal phase, we expect that the contribution of gluonic interaction to the symmetry energy in the 2SC phase will be minimal. The different value of symmetry energy in each phase will lead to different prediction for the particle yields in heavy ion collision experiment.
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…
Symmetry analysis of crystalline spin textures in dipolar spinor condensates
Cherng, R. W.; Demler, E.
2011-05-15
We study periodic crystalline spin textures in spinor condensates with dipolar interactions via a systematic symmetry analysis of the low-energy effective theory. By considering symmetry operations which combine real- and spin-space operations, we classify symmetry groups consistent with nontrivial experimental and theoretical constraints. Minimizing the energy within each symmetry class allows us to explore possible ground states.
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.
Scalar Field Theories with Polynomial Shift Symmetries
Tom Griffin; Kevin T. Grosvenor; Petr Horava; Ziqi Yan
2015-08-04
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.
Symmetry Energy I: Semi-Infinite Matter
Pawel Danielewicz; Jenny Lee
2008-10-29
Energy for a nucleus is considered in macroscopic limit, in terms of nucleon numbers. Further considered for a nuclear system is the Hohenberg-Kohn energy functional, in terms of proton and neutron densities. Finally, Skyrme-Hartree-Fock calculations are carried out for a half-infinite particle-stable nuclear-matter. In each case, the attention is focused on the role of neutron-proton asymmetry and on the nuclear symmetry energy. We extend the considerations on the symmetry term from an energy formula to the respective term in the Hohenberg-Kohn functional. We show, in particular, that in the limit of an analytic functional, and subject to possible Coulomb corrections, it is possible to construct isoscalar and isovector densities out of the proton and neutron densities, that retain a universal relation to each other, approximately independent of asymmetry. In the so-called local approximation, the isovector density is inversely proportional to the symmetry energy in uniform matter at the local isoscalar density. Generalized symmetry coefficient of a nuclear system is related, in the analytic limit of a functional, to an integral of the isovector density. We test the relations, inferred from the Hohenberg-Kohn functional, in the Skyrme-Hartree-Fock calculations of half-infinite matter. Within the calculations, we obtain surface symmetry coefficients and parameters characterizing the densities, for the majority of Skyrme parameterizations proposed in the literature. The volume-to-surface symmetry-coefficient ratio and the displacement of nuclear isovector relative to isoscalar surfaces both strongly increase as the slope of symmetry energy in the vicinity of normal density increases.
Energy bands: Chern numbers and symmetry
Iwai, T.; Zhilinskii, B.
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.
Scalar Field Theories with Polynomial Shift Symmetries
NASA Astrophysics Data System (ADS)
Griffin, Tom; Grosvenor, Kevin T.; Ho?ava, Petr; Yan, Ziqi
2015-12-01
We continue our study of naturalness in nonrelativistic QFTs of the Lifshitz type, focusing on scalar fields that can play the role of Nambu-Goldstone (NG) modes associated with spontaneous symmetry breaking. Such systems allow for an extension of the constant shift symmetry to a shift by a polynomial of degree P in spatial coordinates. These "polynomial shift symmetries" in turn protect the technical naturalness of modes with a higher-order dispersion relation, and lead to a refinement of the proposed classification of infrared Gaussian fixed points available to describe NG modes in nonrelativistic theories. Generic interactions in such theories break the polynomial shift symmetry explicitly to the constant shift. It is thus natural to ask: Given a Gaussian fixed point with polynomial shift symmetry of degree P, what are the lowest-dimension operators that preserve this symmetry, and deform the theory into a self-interacting scalar field theory with the shift symmetry of degree P? To answer this (essentially cohomological) question, we develop a new graph-theoretical technique, and use it to prove several classification theorems. First, in the special case of P = 1 (essentially equivalent to Galileons), we reproduce the known Galileon N-point invariants, and find their novel interpretation in terms of graph theory, as an equal-weight sum over all labeled trees with N vertices. Then we extend the classification to P > 1 and find a whole host of new invariants, including those that represent the most relevant (or least irrelevant) deformations of the corresponding Gaussian fixed points, and we study their uniqueness.
Universal symmetry-protected topological invariants for symmetry-protected topological states
Hung, Ling-Yan
Symmetry-protected topological (SPT) states are short-range entangled states with a symmetry G. They belong to a new class of quantum states of matter which are classified by the group cohomology H[superscript d+1](G,R/Z) ...
Group Parametrized Tunneling and Local Symmetry Conditions
NASA Astrophysics Data System (ADS)
Harter, William; Mitchell, Justin
2010-06-01
Recently, Hougen showed an ad hoc symmetry-based parameterization scheme for analyzing tunneling dynamics and high resolution spectra of fluxional molecular structure similar to S-parameter analysis of superfine structure in SF_6 or NH_3 maser inversion dynamics by Feynman et.al. The problem is that ad hoc parametrization, like path integration in general, can lead to logjams of parameters or ``paths'' with no way to pick out the relevant ones. We show a way to identify and use relevant parameters for a tunneling Hamiltonian H having global G-symmetry-defined bases by first expressing H as a linear combination bar ? ^i {bar g}_i of operators in dual symmetry group bar G. The coefficients bar ? ^i are parameters that define a complete set of allowed paths for any H with G-symmetry and are related thru spectral decomposition of G to eigensolutions of H. Quantum G vs.bar G duality generalizes lab -vs. -body and state -vs. -particle. The number of relevant bar ? ^i-parameters is reduced if a system tends to stick in states of a local symmetry subgroup LsubsetG so the H spectrum forms level clusters labeled by induced representations d(?)(L)\\uparrowG. A cluster-(?) has one E(epsilon)-level labeled by G species (epsilon) for each L species (?) in Depsilon(G)downarrowL by Frobenius reciprocity. Then we apply local symmetry conditions to each irrep Depsilon(bar ? ^i {bar g}_i) that has already been reduced with respect to local symmetry L. This amounts to setting each off-diagonal component Dj,kepsilon(H) to zero. Local symmetry conditions may tell which bar ? ^i-parameters are redundant or zero and directly determine d(?)\\uparrowG tunneling matrix eigenvalues that give E(epsilon)-levels as well as eigenvectors. Otherwise one may need to choose a particular localizing subgroup chain LsubsetL_1subsetL_2...G and further reduce the number of path parameters to facilitate spectral fitting. J.T. Hougen, 2009 MSS RJ01, {J Mol Spect 123, 197 (1987) W.G. Harter and J. C. Mitchell, 2009 MSS RJ05 (See also following talk.) R.P. Feynman, R. B. Leighton, M. Sands, Lectures on Physics Vol.3 (Addison Wesley 1964) p.9-1 W.G. Harter, Principles of Symmetry, Dynamics, and Spectroscopy, (Wiley Interscience, 1993) p.265
Yukawa Textures from Family Symmetry and Unification
Allanach, Benjamin C; Leontaris, George K; Lola, S
1997-01-01
In this letter, we show how the combination of both a gauged U(1)_X family symmetry and an extended vertical gauge symmetry in a single model, allows for the presence of additional Clebsch texture zeroes in the fermion mass matrices. This leads to new structures for the textures, with increased predictivity, as compared to schemes with enhanced family symmetries only. We illustrate these ideas in the context of the Pati-Salam gauge group SU(4)xSU(2)_LxSU(2)_R$ supplemented by a U(1)_X gauged family symmetry. In the case of symmetric mass matrices, two of the solutions of Ramond, Roberts and Ross that may not be obtained by family symmetries only, are accurately reproduced. For non-symmetric textures, new structures arise in models of this type. To distinguish between the solutions in this latter case, we performed a numerical fit to the charged fermion mass and mixing data. The best solution we found allows a fit with a total chi^2 of 0.39, for three degrees of freedom.
Symmetry in social exchange and health
NASA Astrophysics Data System (ADS)
Siegrist, Johannes
2005-10-01
Symmetry is a relevant concept in sociological theories of exchange. It is rooted in the evolutionary old norm of social reciprocity and is particularly important in social contracts. Symmetry breaking through violation of the norm of reciprocity generates strain in micro-social systems and, above all, in victims of non-symmetric exchange. In this contribution, adverse healthconsequences of symmetry breaking in contractual social exchange are analysed, with a main focus on the employment contract. Scientific evidence is derived from prospective epidemiological studies testing the model of effort-reward imbalance at work. Overall, a twofold elevated risk of incident disease is observed in employed men and women who are exposed to non-symmetric exchange. Health risks include coronary heart disease, depression and alcohol dependence, among others. Preliminary results suggest similar effects on health produced by symmetry breaking in other types of social relationships (e.g. partnership, parental roles). These findings underline the importance of symmetry in contractual social exchange for health and well-being.
Spontaneous symmetry breaking in interdependent networked game.
Jin, Qing; Wang, Lin; Xia, Cheng-Yi; Wang, Zhen
2014-01-01
Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor ? is smaller than a threshold value ?(C), the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds ?(C), spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method. PMID:24526076
Detection of symmetry-enriched topological phases
NASA Astrophysics Data System (ADS)
Huang, Ching-Yu; Chen, Xie; Pollmann, Frank
2014-07-01
Topologically ordered systems in the presence of symmetries can exhibit new structures which are referred to as symmetry-enriched topological (SET) phases. We introduce simple methods to detect certain SET orders directly from a complete set of topologically degenerate ground-state wave functions. In particular, we first show how to directly determine the characteristic symmetry fractionalization of the quasiparticles from the reduced density matrix of the minimally entangled states. Second, we show how a simple generalization of a nonlocal order parameter can be measured to detect SET phases. The usefulness of the proposed approach is demonstrated by examining two concrete model states which exhibit SET phases: (i) a spin-1 model on the honeycomb lattice and (ii) the resonating valence bond (RVB) state on a kagome lattice. We conclude that the spin-1 model and the RVB state are in the same SET phases.
Geometric symmetries in superfluid vortex dynamics
Kozik, Evgeny; Svistunov, Boris
2010-10-01
Dynamics of quantized vortex lines in a superfluid feature symmetries associated with the geometric character of the complex-valued field, w(z)=x(z)+iy(z), describing the instant shape of the line. Along with a natural set of Noether's constants of motion, which - apart from their rather specific expressions in terms of w(z) - are nothing but components of the total linear and angular momenta of the fluid, the geometric symmetry brings about crucial consequences for kinetics of distortion waves on the vortex lines, the Kelvin waves. It is the geometric symmetry that renders Kelvin-wave cascade local in the wave-number space. Similar considerations apply to other systems with purely geometric degrees of freedom.
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.
Preserving Symmetry in Preconditioned Krylov Subspace Methods
NASA Technical Reports Server (NTRS)
Chan, Tony F.; Chow, E.; Saad, Y.; Yeung, M. C.
1996-01-01
We consider the problem of solving a linear system Ax = b when A is nearly symmetric and when the system is preconditioned by a symmetric positive definite matrix M. In the symmetric case, one can recover symmetry by using M-inner products in the conjugate gradient (CG) algorithm. This idea can also be used in the nonsymmetric case, and near symmetry can be preserved similarly. Like CG, the new algorithms are mathematically equivalent to split preconditioning, but do not require M to be factored. Better robustness in a specific sense can also be observed. When combined with truncated versions of iterative methods, tests show that this is more effective than the common practice of forfeiting near-symmetry altogether.
Symmetry issues in Directly Irradiated Targets
NASA Astrophysics Data System (ADS)
Ramis, R.; Temporal, M.; Canaud, B.; Brandon, V.
2013-11-01
In direct drive Inertial Confinement Fusion (ICF), the typical laser beam to laser beam angle is around 30°. This fact makes the study of the irradiation symmetry a genuine 3D problem. In this paper we use the three dimensional version of the MULTI hydrocode to assess the symmetry of such ICF implosions. More specifically, we study a shock-ignition proposal for the Laser-Mégajoule facility (LMJ) in which two of the equatorial beam cones are used to implode and precompress a spherical capsule (the "reference" capsule of HiPER project) made of 0.59 mg of pure Deuterium-Tritium mixture. The symmetry of this scheme is analysed and optimized to get a design inside the operating limits of LMJ. The studied configuration has been found essentially axial-symmetric, so that the use of 2D hydrocodes would be appropriate for this specific situation.
Topological phases with generalized global symmetries
Beni Yoshida
2015-08-14
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported on a $(d+1)$-colorable graph by using a family of unitary phase gates, known as multi-qubit control-$Z$ gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Non-triviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Topological phases with generalized global symmetries
Yoshida, Beni
2015-01-01
We present simple lattice realizations of symmetry-protected topological (SPT) phases with $q$-form global symmetries where charged excitations have $q$ spatial dimensions. Specifically, we construct $d$ space-dimensional models supported on a $(d+1)$-colorable graph by using a family of unitary phase gates, known as multi-qubit control-$Z$ gates in quantum information community. In our construction, charged excitations of different dimensionality may coexist and form a short-range entangled state which is protected by symmetry operators of different dimensionality. Non-triviality of proposed models, in a sense of quantum circuit complexity, is confirmed by studying protected boundary modes, gauged models and corresponding gapped domain walls. We also comment on applications of our construction to quantum error-correcting codes, and discuss corresponding fault-tolerant logical gates.
Dark Matter Stability without New Symmetries
Oscar Cata; Alejandro Ibarra
2014-08-28
The stability of dark matter is normally achieved by imposing extra symmetries beyond those of the Standard Model of Particle Physics. In this paper we present a framework where the dark matter stability emerges as a consequence of the Standard Model symmetries. The dark matter particle is an antisymmetric tensor field (analogous to the one used for spin-1 mesons in QCD), singlet under the Standard Model gauge group. The Lagrangian possesses an accidental $Z_2$ symmetry which makes the dark matter stable on cosmological time scales. Interactions with the Standard Model fields proceed through the Higgs portal, which allows the observed dark matter abundance to be generated via thermal freeze-out. We also discuss the prospects for observing this dark matter particle in direct detection experiments.
New Algorithms For Automated Symmetry Recognition
NASA Astrophysics Data System (ADS)
Paul, Jody; Kilgore, Tammy Elaine; Klinger, Allen
1988-02-01
In this paper we present new methods for computer-based symmetry identification that combine elements of group theory and pattern recognition. Detection of symmetry has diverse applications including: the reduction of image data to a manageable subset with minimal information loss, the interpretation of sensor data,1 such as the x-ray diffraction patterns which sparked the recent discovery of a new "quasicrystal" phase of solid matter,2 and music analysis and composition.3,4,5 Our algorithms are expressed as parallel operations on the data using the matrix representation and manipulation features of the APL programming language. We demonstrate the operation of programs that characterize symmetric and nearly-symmetric patterns by determining the degree of invariance with respect to candidate symmetry transformations. The results are completely general; they may be applied to pattern data of arbitrary dimension and from any source.
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.
PT-Symmetry-Breaking Chaos in Optomechanics.
Lü, Xin-You; Jing, Hui; Ma, Jin-Yong; Wu, Ying
2015-06-26
We demonstrate PT-symmetry-breaking chaos in an optomechanical system, which features an ultralow driving threshold. In principle, this chaos will emerge once a driving laser is applied to the cavity mode and lasts for a period of time. The driving strength is inversely proportional to the starting time of chaos. This originally comes from the dynamical enhancement of nonlinearity by field localization in the PT-symmetry-breaking phase. Moreover, this chaos is switchable by tuning the system parameters so that a PT-symmetry phase transition occurs. This work may fundamentally broaden the regimes of cavity optomechanics and nonlinear optics. It offers the prospect of exploring ultralow-power-laser-triggered chaos and its potential applications in secret communication. PMID:26197125
Workshop on electroweak symmetry breaking: proceedings
Hinchliffe, I.
1984-10-01
A theoretical workshop on electroweak symmetry breaking at the Superconducting Supercollider was held at Lawrence Berkeley Laboratory, June 4-22, 1984. The purpose of the workshop was to focus theoretical attention on the ways in which experimentation at the SSC could reveal manifestations of the phenomenon responsible for electroweak symmetry breaking. This issue represents, at present, the most compelling scientific argument for the need to explore the energy region to be made accessible by the SSC, and a major aim of the workshop was to involve a broad cross section of particle theorists in the ongoing process of sharpening the requirements for both accelerator and detector design that will ensure detection and identification of meaningful signals, whatever form the electroweak symmetry breaking phenomenon should actually take. Separate entries were prepared for the data base for the papers presented.
Discrete Abelian gauge symmetries and axions
NASA Astrophysics Data System (ADS)
Honecker, Gabriele; Staessens, Wieland
2015-07-01
We combine two popular extensions of beyond the Standard Model physics within the framework of intersecting D6-brane models: discrete ?n symmetries and Peccei-Quinn axions. The underlying natural connection between both extensions is formed by the presence of massive U(1) gauge symmetries in D-brane model building. Global intersecting D6-brane models on toroidal orbifolds of the type T6/?2N and T6/?2 × ?2M with discrete torsion offer excellent playgrounds for realizing these extensions. A generation-dependent ?2 symmetry is identified in a global Pati-Salam model, while global left-right symmetric models give rise to supersymmetric realizations of the DFSZ axion model. In one class of the latter models, the axion as well as Standard Model particles carry a non-trivial ?3 charge.
Arbitrary lattice symmetries via block copolymer nanomeshes
Majewski, Pawel W.; Rahman, Atikur; Black, Charles T.; Yager, Kevin G.
2015-01-01
Self-assembly of block copolymers is a powerful motif for spontaneously forming well-defined nanostructures over macroscopic areas. Yet, the inherent energy minimization criteria of self-assembly give rise to a limited library of structures; diblock copolymers naturally form spheres on a cubic lattice, hexagonally packed cylinders and alternating lamellae. Here, we demonstrate multicomponent nanomeshes with any desired lattice symmetry. We exploit photothermal annealing to rapidly order and align block copolymer phases over macroscopic areas, combined with conversion of the self-assembled organic phase into inorganic replicas. Repeated photothermal processing independently aligns successive layers, providing full control of the size, symmetry and composition of the nanoscale unit cell. We construct a variety of symmetries, most of which are not natively formed by block copolymers, including squares, rhombuses, rectangles and triangles. In fact, we demonstrate all possible two-dimensional Bravais lattices. Finally, we elucidate the influence of nanostructure on the electrical and optical properties of nanomeshes. PMID:26100566
Collective neutrino oscillations and spontaneous symmetry breaking
NASA Astrophysics Data System (ADS)
Duan, Huaiyu
2015-08-01
Neutrino oscillations in a hot and dense astrophysical environment such as a core-collapse supernova pose a challenging, seven-dimensional flavor transport problem. To make the problem even more difficult (and interesting), neutrinos can experience collective oscillations through nonlinear refraction in the dense neutrino medium in this environment. Significant progress has been made in the last decade towards the understanding of collective neutrino oscillations in various simplified neutrino gas models with imposed symmetries and reduced dimensions. However, a series of recent studies seem to have "reset" this progress by showing that these models may not be compatible with collective neutrino oscillations because the latter can break the symmetries spontaneously if they are not imposed. We review some of the key concepts of collective neutrino oscillations by using a few simple toy models. We also elucidate the breaking of spatial and directional symmetries in these models because of collective oscillations.
Block type symmetry of bigraded Toda Hierarchy
Chuanzhong Li; Jingsong He; Yucai Su
2012-01-21
In this paper, we define Orlov-Schulman's operators $M_L$, $M_R$, and then use them to construct the additional symmetries of the bigraded Toda hierarchy (BTH). 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 literature. By acting on two different spaces under the weak W-constraints we find in particular two representations of this Block type Lie algebra.
Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking.
Griffin, Tom; Grosvenor, Kevin T; Ho?ava, Petr; Yan, Ziqi
2015-12-11
Without Lorentz invariance, spontaneous global symmetry breaking can lead to multicritical Nambu-Goldstone modes with a higher-order low-energy dispersion ??k^{n} (n=2,3,…), whose naturalness is protected by polynomial shift symmetries. Here, we investigate the role of infrared divergences and the nonrelativistic generalization of the Coleman-Hohenberg-Mermin-Wagner (CHMW) theorem. We find novel cascading phenomena with large hierarchies between the scales at which the value of n changes, leading to an evasion of the "no-go" consequences of the relativistic CHMW theorem. PMID:26705623
Broken symmetry in ideal magnetohydrodynamic turbulence
NASA Technical Reports Server (NTRS)
Shebalin, John V.
1993-01-01
A numerical study of the long-time evolution of a number of cases of inviscid, isotropic, incompressible, three-dimensional fluid, and magneto-fluid turbulence has been completed. The results confirm that ideal magnetohydrodynamic turbulence is non-ergodic if there is no external magnetic field present. This is due essentially to a canonical symmetry being broken in an arbitrary dynamical representation. The broken symmetry manifests itself as a coherent structure, i.e., a non-zero time-averaged part of the turbulent magnetic field. The coherent structure is observed, in one case, to contain about eighteen percent of the total energy.
Symmetry and Integrability of Classical Field Equations
C. J. Papachristou
2008-05-14
A number of characteristics of integrable nonlinear partial differential equations (PDE's) for classical fields are reviewed, such as Backlund transformations, Lax pairs, and infinite sequences of conservation laws. An algebraic approach to the symmetry problem of PDE's is described, suitable for PDE's the solutions of which are non-scalar fields (e.g., are in the form of matrices). A method is proposed which, in certain cases, may "unify" the symmetry and integrability properties of a nonlinear PDE. Application is made to the self-dual Yang-Mills equation and the Ernst equation of General Relativity.
Chiral symmetry restoration in strange hadronic matter
P. Wang; V. E. Lyubovitskij; Th. Gutsche; Amand Faessler
2004-07-16
The phase transition of chiral symmetry restoration in strange hadronic matter is studied in the chiral SU(3) quark mean field model. When the baryon density is larger than a critical density $\\rho_c$, the minimal energy density of the system occurs at the point where the effective masses of nucleon, $\\Lambda$ or $\\Xi$ drop to zero. The physical quantities change discontinuously at this density and the system will be in the phase of chiral symmetry restoration. A rich phase structure of strange hadronic matter with different strangeness fraction $f_s$ is obtained.
A new symmetry in collective motion
Ginocchio, J.N.
1991-01-01
The purity of intrinsic states of nuclei with respect to a proton-neutron boson symmetry (F-spin) is shown to be largely determined by the difference between proton and neutron deformations and not by whether the Hamiltonian is an F-spin scalar. F-spin mixing in the ground state band of {sup 165}Ho is estimated using recent pion single-charge-exchange data. A B(M1) sum rule is derived using F-spin symmetry. 27 refs., 1 fig.
A symmetry principle for topological quantum order
Nussinov, Zohar Ortiz, Gerardo
2009-05-15
We present a unifying framework to study physical systems which exhibit topological quantum order (TQO). The major guiding principle behind our approach is that of symmetries and entanglement. These symmetries may be actual symmetries of the Hamiltonian characterizing the system, or emergent symmetries. To this end, we introduce the concept of low-dimensional Gauge-like symmetries (GLSs), and the physical conservation laws (including topological terms, fractionalization, and the absence of quasi-particle excitations) which emerge from them. We prove then sufficient conditions for TQO at both zero and finite temperatures. The physical engine for TQO are topological defects associated with the restoration of GLSs. These defects propagate freely through the system and enforce TQO. Our results are strongest for gapped systems with continuous GLSs. At zero temperature, selection rules associated with the GLSs enable us to systematically construct general states with TQO; these selection rules do not rely on the existence of a finite gap between the ground states to all other excited states. Indices associated with these symmetries correspond to different topological sectors. All currently known examples of TQO display GLSs. Other systems exhibiting such symmetries include Hamiltonians depicting orbital-dependent spin-exchange and Jahn-Teller effects in transition metal orbital compounds, short-range frustrated Klein spin models, and p+ip superconducting arrays. The symmetry based framework discussed herein allows us to go beyond standard topological field theories and systematically engineer new physical models with finite temperature TQO (both Abelian and non-Abelian). Furthermore, we analyze the insufficiency of entanglement entropy (we introduce SU(N) Klein models on small world networks to make the argument even sharper), spectral structures, maximal string correlators, and fractionalization in establishing TQO. We show that Kitaev's Toric code model and Wen's plaquette model are equivalent and reduce, by a duality mapping, to an Ising chain, demonstrating that despite the spectral gap in these systems the toric operator expectation values may vanish once thermal fluctuations are present. This illustrates the fact that the quantum states themselves in a particular (operator language) representation encode TQO and that the duality mappings, being non-local in the original representation, disentangle the order. We present a general algorithm for the construction of long-range string and brane orders in general systems with entangled ground states; this algorithm relies on general ground states selection rules and becomes of the broadest applicability in gapped systems in arbitrary dimensions. We exactly recast some known non-local string correlators in terms of local correlation functions. We discuss relations to problems in graph theory.
Hopf bifurcation in the presence of symmetry
NASA Technical Reports Server (NTRS)
Golubitsky, M.; Stewart, I.
1985-01-01
Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.
Singularities, horizons, firewalls, and local conformal symmetry
Hooft, Gerard 't
2015-01-01
The Einstein-Hilbert theory of gravity can be rephrased by focusing on local conformal symmetry as an exact, but spontaneously broken symmetry of nature. The conformal component of the metric field is then treated as a dilaton field with only renormalizable interactions. This imposes constraints on the theory, which can also be viewed as demanding regularity of the action as the dilaton field variable tends to 0. In other words, we have constraints on the small distance behaviour. Our procedure appears to turn a black hole into a regular, topologically trivial soliton without singularities, horizons of firewalls, but many questions remain.
Discrete flavor symmetry and minimal seesaw mechanism
Park, N. W.; Nam, K. H.; Siyeon, Kim
2011-03-01
This work proposes a neutrino mass model that is derived using the minimal seesaw mechanism, which contains only two right-handed neutrinos, under the non-Abelian discrete flavor symmetry S{sub 4} x Z{sub 2}. Two standard model doublets, L{sub {mu}} and L{sub {tau}}, are assigned simultaneously to a 2 representation of S{sub 4}. When the scalar fields introduced in this model, in addition to the standard model Higgs, and the leptons are coupled within the symmetry, the seesaw mechanism results in the tribimaximal neutrino mixing. This study examined the possible deviations from tribimaximal mixing related to the experimental data.
Discrete flavor symmetry and minimal seesaw mechanism
K. H. Nam; N. W. Park; Kim Siyeon
2011-01-21
This work proposes a neutrino mass model that is derived using the minimal seesaw mechanism which contains only two right-handed neutrinos, under the non-abelian discrete flavor symmetry $\\mathbb{S}_4\\otimes\\mathbb{Z}_2$. Two standard model doublets, $L_\\mu$ and $L_\\tau$, are assigned simultaneously to a $\\mathbf{2}$ representation of $\\mathbb{S}_4$. When the scalar fields introduced in this model, addition to the Standard Model Higgs, and the leptons are coupled within the symmetry, the seesaw mechanism results in the tri-bi-maximal neutrino mixing. This study examined the possible deviations from TBM mixing related to the experimental data.
Spontaneous symmetry breaking and macroscopic entanglement
A. Hamma; S. M. Giampaolo; F. Illuminati
2015-01-28
In the presence of interactions with the environment, decoherence selects stable classical states, the pointer states, while suppressing arbitrary macroscopic coherent superpositions. In close analogy, the metastable symmetry-breaking ground states of many-body Hamiltonians should be the ones with the least macroscopic entanglement and thus the most classical ones among all possible quantum ground states. By considering the mutual information based on the 2-Renyi entanglement entropy and using a locality result, we show that symmetry-breaking states have the least macroscopic entanglement and, consequently, that they are the ones selected in real world by environmental decoherence.
Mechanical PT symmetry in coupled optomechanical systems
NASA Astrophysics Data System (ADS)
Xu, Xun-Wei; Liu, Yu-xi; Sun, Chang-Pu; Li, Yong
2015-07-01
We propose to realize mechanical parity-time (PT ) symmetry in two coupled optomechanical systems. To provide gain to one mechanical resonator and the same amount of damping to the other, the two optical cavities should be driven by blue- and red-detuned laser fields, respectively. After adiabatically eliminating the degrees of freedom of the cavity modes, we derive a formula to describe the PT symmetry of two coupled mechanical resonators. Mechanical PT -symmetric phase transition is demonstrated by the dynamical behavior of the mechanical resonators. Moreover, we study the effect of the quantum noises on the dynamical behavior of the mechanical resonators when the system is in the quantum regime.
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.
Non-standard symmetries and quantum anomalies
Visinescu, Anca; Visinescu, Mihai
2008-08-31
Quantum anomalies are investigated on curved spacetimes. The intimate relation between Killing-Yano tensors and non-standard symmetries is pointed out. The gravitational anomalies are absent if the hidden symmetry is associated to a Killing-Yano tensor. The axial anomaly in a background gravitational field is directly related with the index of the Dirac operator. In the Dirac theory on curved spaces, Killing-Yano tensors generate Dirac-type operators involved in interesting algebraic structures. The general results are applied to the 4-dimensional Euclidean Taub-NUT space.
Wormholes and Peccei-Quinn symmetries
Choi, K.; Holman, R. )
1990-01-08
We show how wormholes and Peccei-Quinn symmetries are in fact complementary in solving the strong {ital CP} problem. On the one hand, Peccei-Quinn symmetries are shown to provide us with a wormhole parameter that couples only to the QCD anomaly. This then allows us to implement the wormhole solution to the strong {ital CP} problem constructed previously by the present authors as well as by Preskill, Trivedi, and Wise. On the other hand, wormholes are shown to drive the axion mass to zero or to the wormhole scale, thus avoiding the axion-energy-density crisis in either case.
Black Hole Thermodynamics and Lorentz Symmetry
Ted Jacobson; Aron C. Wall
2010-02-04
Recent developments point to a breakdown in the generalized second law of thermodynamics for theories with Lorentz symmetry violation. It appears possible to construct a perpetual motion machine of the second kind in such theories, using a black hole to catalyze the conversion of heat to work. Here we describe and extend the arguments leading to that conclusion. We suggest the inference that local Lorentz symmetry may be an emergent property of the macroscopic world with origins in a microscopic second law of causal horizon thermodynamics.