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1

NSDL National Science Digital Library

This is a reference web site for group theory and the properties of symmetry point groups. It covers the mathematics and science applications of symmetry relations, including the impact on interactions with specific reference to dipole-transition selection rules. Unit cells, stereograms, and 3D animated molecules are presented as examples of each point group. This web site also provides other symmetry related links and a link to references for symmetry in physics and chemistry.

Goss, Jonathan

2008-12-23

2

A doubly icosahedral complex involves roughly spherical clusters of atoms with icosahedral point-group symmetry, which are themselves, in parallel orientation, icosahedrally packed. These complexes may form cubic crystallites; three structures of this sort have been identified. Analysis of electron diffraction photographs of the decagonal quasicrystal Al6Pd has led to its description as involving pentagonal twinning of an orthorhombic crystal with a = 51.6 Å, b = 37.6 Å, and c = 33.24 Å, with about 4202 atoms in the unit, comprising two 1980-atom doubly icosahedral complexes, each involving icosahedral packing of 45 44-atom icosahedral complexes (at 0 0 0 and 1/2 1/2 1/2) and 242 interstitial atoms. The complexes and clusters are oriented with one of their fivefold axes in the c-axis direction. Images

Pauling, Linus

1989-01-01

3

Simple method to obtain symmetry harmonics of point groups.

We propose a simple, self-consistent method to obtain basis functions of irreducible representations of a finite point group. Our method is based on eigenproblem formulation of a projection operator represented as a nonhomogeneous polynomial of angular momentum L. The method is shown to be more efficient than the usual numerical methods when applied to the analysis of high-order symmetry harmonics in cubic and icosahedral groups. For low-order symmetry harmonics the method provides rational coefficients of expansion in the Y(L,M) basis. PMID:16965069

Boiko, D L; Féron, P; Besnard, P

2006-09-01

4

A 780-atom primitive tetragonal unit with edges 27.3, 27.3, and 12.6 Å is assigned to rapidly solidified Cu5Ni3Si2 and V15Ni10Si by analysis of electron diffraction photographs with the assumption that the crystals contain icosahedral clusters. There are thirty 26-atom clusters at the sigma-phase positions. Apparent 8-fold symmetry results from 45° twinning on the basal plane.

Pauling, Linus

1988-01-01

5

Coronal holes and icosahedral symmetry

NASA Astrophysics Data System (ADS)

In continuation of our study of the application of group theory to the problem of solar wind expansion out of a system of coronal holes, this third paper deals with the formulation and subsequent numerical integration of the basic hydrodynamic equations. After calculating the metric coefficients and the corresponding Christoffel symbols, a description of a numerical procedure exploiting icosahedral symmetry and solutions of the equations are presented for several sets of boundary conditions. The properties of the resulting time-independent three-dimensional fields of number density, velocity and temperature of the solar wind are discussed, and the significance of such solutions, in particular for periods of solar activity maxima, is pointed out.

Kalisch, Herbert; Neutsch, Wolfram; Fichtner, Horst; Sreenivasan, S. Ranga; Shevalier, Maurice

2003-12-01

6

Liquid Crystal Phases Lacking Point Group Symmetry

NASA Astrophysics Data System (ADS)

In his 1974 monographs deGennes describes the smectic CG (SmC_G, G for general), a phase of two-dimensional fluid layers having rod-shaped molecules tilted with respect to the layer normal and ordered such that the principal axes of the optical dielectric tensor generally lie neither along the layer normal nor in the plane of the layer. Such layers are polar, with macroscopic polarization P oriented arbitrarily in the diagonal frame, and thus are not symmetric under any rotation or reflection or nontrivial combination thereof, i.e., belong to the class C1 in the Schoenfliess notation. Furthermore, since they lack mirror symmetry, they are chiral. Although deGennes was not optimistic about the prospect for finding such a phase, it appears once again, if a liquid crystal phase can be described, it can be found. Here we report the observation of C1 layers in a fluid smectic phase of bent core molecules. It is evident from freely suspended films that this molecular layer structure exhibits two spontaneous symmetry-breaking instabilities: polar molecular orientational ordering about the layer normal and molecular tilt. These combine to form a chiral layer structure with a handedness depending on the sign of tilt. This work is supported by NASA Grant NAG3-2457.

Chattham, Nattaporn; Shao, Renfan; Maclennan, Joseph E.; Clark, Noel A.; Korblova, Eva; Walba, David M.

2001-03-01

7

An Online Tutorial for Learning Symmetry and Point Groups

NSDL National Science Digital Library

This free web-based tutorial provides the student with explanations and examples of symmetry elements and makes extensive use of interactive Java applets and flash animation to guide students in seeing the symmetry elements in real molecules. The Java applets provide images generated from crystallographic databases that can be rotated freely in real time. This interactive feature allows students to explore the symmetry of selected molecules and also to test their own understanding. Mouse-over and other flash animations also provide students with a guided means to interpret symmetry elements and how they are depicted. Each symmetry element is discussed in turn with examples and short self-tests that provide immediate feedback to the student.

8

Group Representations and Multinomial Combinatorics of the Icosahedral Symmetry

The icosahedral symmetry is one of the most intriguing symmetries, as it not only presents challenge but it appears in many fullerenes and high energetic materials such as the dodecahedral N{sub 20}. We have considered the combinatorics of all irreducible representations of the icosahedral symmetry for a number of multinomial partitions for vertex, face and edge colorings in this work. We have constructed the combinatorial tables for all irreducible representations for various multinomial partitions of colorings for the vertices, edge and faces of the icosahedron. These techniques should have important applications to enumerations and spectroscopy of fullerenes and high-energy materials such as N{sub 20}.

Balasubramanian, K

2004-02-02

9

The Effect of Instructional Modality and Prior Knowledge on Learning Point Group Symmetry

NASA Astrophysics Data System (ADS)

Many topics in chemistry are difficult for learners to understand, including symmetry. Reasons for this difficulty include its multi-level content, instructional methodologies utilized, and learner variables. This study examined the effect of initial instructional modality and prior knowledge on learning of point group symmetry. Forty-four students in a sophomore-level inorganic chemistry class at a small private university were divided by pre-selected lab groups into two groups, lecture and computer, for introductory information about point group symmetry. Both groups had low prior knowledge of symmetry elements although the lecture group had significantly higher knowledge than the computer group. After initial instruction, the lecture group scored significantly higher than the computer group on a point group assessment, even when prior knowledge was controlled. A second assessment, given after both groups had follow-up information from computer courseware, showed no significant difference between the groups. The computer group significantly improved between the two assessments, the lecture group did not. At the end-of-the semester post-test showed no significant difference between the two groups, although only 50% of the students in each group achieved mastery. Factors affecting the significant improvement of the low prior knowledge, computer group were examined and recommendations for future research provided.

Nottis, Katharyn E. K.; Kastner, Margaret E.

2005-03-01

10

Icosahedral (A5) family symmetry and the golden ratio prediction for solar neutrino mixing

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, varphi=(1+5)\\/2. We

Lisa L. Everett; Alexander J. Stuart

2009-01-01

11

Mechanical Deformation of Spherical Viruses with Icosahedral Symmetry

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.

Vliegenthart, Gerard Adriaan; Gompper, Gerhard

2006-01-01

12

Mechanical deformation of spherical viruses with icosahedral symmetry.

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 gamma (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

Vliegenthart, Gerard Adriaan; Gompper, Gerhard

2006-08-01

13

Application of point-group symmetries in chemistry and physics: A computer-algebraic approach

NASA Astrophysics Data System (ADS)

The present application of computer algebra is reviewed for its use in physical and quantum chemistry. After the rapid development of a great deal of numerical algorithms and codes during the past five decades, it is time that symbolic techniques become available in the chemical sciences. A careful implementation of such symbolic methods will make many tasks more efficient and will facilitate the investigation of many quantum systems. Following a brief account of the advantages and specific requests of applying computer algebra in chemistry and physics, emphasis is placed in this contribution on the BETHE program, a recently developed tool for using point-group symmetries in various fields of chemistry, including molecular spectroscopy, ligand-field theory, and material science, or even for the construction of molecular wave functions. Besides the great promise of symbolic techniques for modern research, their merits for education are pointed out, as computer algebra systems are likely to replace the traditional program languages in the undergraduate programs of chemistry and physics.

Fritzsche, S.

14

The decahedral and icosahedral symmetries often observed in pure metals can be easily explained on the basis of an aperiodic multiple twinning model if defect concentration gradients are present. In this paper, the different behavior of Au and Pt is discussed in detail in terms of defect formation volumes and migration thermodynamics.

Conti, L.G. (Dept. of Chemistry and IMAI-CNR, Univ. of Rome La Sapienza, I-00185 Rome (IT))

1992-05-20

15

Phenomenological theory of icosahedral incommensurate (''quasiperiodic'') order in Mn-Al alloys

The crystal structure with icosahedral point-group symmetry and long-range orientational order observed by Shechtman et al. in Mn-Al alloys can be explained as a multiple-q density-wave structure with only one length scale. Its existence and stability can be understood from a simple Landau theory. The diffraction spots can be indexed by six- (or more-) dimensional space-group symmetries. Icosahedral incommensurate structures constitute natural extensions of smectic, rodlike, and cubic crystal structures.

Bak, P.

1985-04-08

16

Apparent icosahedral symmetry is due to directed multiple twinning of cubic crystals

A proposed structure and successful analysis of a diffraction pattern are offered to settle the question of the nature of the 'icosahedral' MAl6 alloys (where M = Cr, Mn, Fe). How a molten alloy of Mn (or Cr or Fe) and Al might react to sudden cooling is predicted. It is discovered that such an alloy on sudden cooling could

Linus Pauling

1985-01-01

17

Faceting in bond-oriented systems with icosahedral and decagonal symmetry

NASA Astrophysics Data System (ADS)

The recent discoveries of large facets in Al-Li-Cu and other icosahedral quasicrystals, as well as the observation of spatial disorder in these systems, show that disordered systems with long-range bond-orientational order can have growth facets. A fundamental question which naturally arises is whether such systems have equilibrium facets. In this paper, we study the conditions under which a perfect bond-oriented system can facet at T=0. The T=0 equilibrium shapes of bond-oriented systems with icosahedral and decagonal bond-orientational order are discussed. An explicit example is presented to show that disordered systems can have equilibrium facets at T=0. We also give detailed derivation of the surface energy of quasicrystals.

Ho, T. L.; Li, Y. H.; Saam, W. F.; Jaszczak, J. A.

1989-05-01

18

Protruding knob-like proteins violate local symmetries in an icosahedral marine virus

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.

Gipson, Preeti; Baker, Matthew L.; Raytcheva, Desislava; Haase-Pettingell, Cameron; Piret, Jacqueline; King, Jonathan A.; Chiu, Wah

2014-01-01

19

A new Al-Pd-Mn phase, called F2 , and its reversible transformation into an M icosahedral structure at high temperatures were studied by transmission electron microscopy (TEM) and by in-situ X-ray diffraction using synchrotron light sources. The phase F2 appears to be closely related to the F2 super-ordered M icosahedral phase identified by Ishimasa and Mori (1992, Phil. Mag. Lett .,

M. Deboissieu; M. Boudard; T. Ishimasa; E. Elkaim; J. P. Lauriat; A. Letoublon; M. Audierf; M. Duneau; A. Davroski

1998-01-01

20

Dislocations in icosahedral quasicrystals.

Dislocations in quasicrystals, as a direct result of the lack of translational symmetry in these materials, possess various salient features. The Burgers vector of a dislocation in an icosahedral quasicrystal is a 6-dimensional vector, which reflects the fact that the dislocation, besides the phonon-type strain field analogous to dislocations in ordinary crystals, is associated inseparably with a further type of defect, the phasons. Phasons are critically involved in the formation and motion of dislocations in quasicrystals and govern the macroscopic plastic behaviour of these materials. In this article the properties of dislocations in icosahedral quasicrystals are comprehensively reviewed, starting from a continuum-mechanical description, via core-structure simulation, to their full experimental characterization. The experimental results presented address the icosahedral phases in the well explored systems Al-Pd-Mn and Zn-Mg-Dy. PMID:22760204

Feuerbacher, Michael

2012-10-21

21

Amorphization Mechanism of Icosahedral Metal Nanoclusters

The amorphization mechanism of high-symmetry pt nanoclusters is investigated by a combination of Molecular Dynamics simulations and Density Functional calculations. A general mechanism for amorphizaton, involving rosette-like structural transformations at fivefold vertices, is proposed. IN the tosette, a fivefold vertex is transformed into a hexagonal ring. We show that for icosahedral Pt nanoclusters, this transformation is associated with an energy gain, so that their most favorable structures have a low symmetry even at icosahedral magic numbers.

Apra, Edoardo; Baletto, Francesca; Ferrando, Riccardo; Fortunelli, Alessandro

2004-08-06

22

Crystallography of icosahedral crystals

The crystallography of icosahedral crystals is constructed. The actual three-dimensional crystal is represented by a three-dimensional cut in a regular six-dimensional periodic crystal with symmetry described by a six-dimensional space group, and the positions of atoms correspond to an arrangement of hypersurface segments. The resulting crystal cannot in general be viewed as a space-filling arrangemment of a small number of different ''Penrose tiles.'' The intensities of Bragg spots are given directly as the intensities of Bragg spots of the six-dimensional crystal. 16 refs., 2 figs.

Bak, P.

1986-01-01

23

Precipitation of icosahedral Al-Mn during pulsed laser melting

The icosahedral phase has been produced by pulsed laser melting of thin films of Mn-implanted Al. With increasing laser intensity, we observe a mixture of icosahedral and fcc phases followed by a single phase fcc region. Grains as large as 1 ..mu..m in diameter have been observed in 0.1 ..mu..m thick films. Electron diffraction studies of individual icosahedral grains indicate that the rapid growth direction from the melt is along the threefold symmetry axis.

Aziz, M.J.; Budai, J.D.

1986-05-01

24

Quasicrystal with one-dimensional translational symmetry and a tenfold rotation axis

Studies of phase formation in rapidly solidified Al-Mn alloys (composition range 18-22 at. percent Mn) show that an icosahedral phase is replaced by another noncrystallographic phase, a decagonal phase. The decagonal phase is another example of quasicrystal: It has a noncrystallographic point group (10\\/m or 10\\/mmm) together with long-range orientational order and one-dimensional translational symmetry. The decagonal phase is an

L. Bendersky

1985-01-01

25

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

Janner, A

2011-11-01

26

NASA Astrophysics Data System (ADS)

We will present a new theoretical tool, a program called PAM-C2v-2tops, for analysis of the high-resolution torsion-rotation spectra of molecules with two equivalent methyl rotors and C_{2V} symmetry at equilibrium. The new tool belongs to the broad class of effective Hamiltonians, is based on Longuet-Higgins' group theoretical ideas and uses G_{36} permutation-inversion group-theoretical considerations, the principal axis method and a two-step diagonalization procedure. The program was used to carry out a weighted least-squares fit of 1720 microwave, millimeter-wave, and sub-millimeter-wave line frequencies of acetone [(CH_3)_2CO] that are available in the literature. The weighted root-mean-square deviation of 0.93 obtained for a joint fit of the microwave lines belonging to the ground, the lower torsional fundamental, and the higher torsional fundamental states of acetone represents significant progress in comparison with previous fitting attempts, especially for the excited torsional states.

Ilyushin, Vadim V.; Hougen, Jon T.

2013-06-01

27

NASA Astrophysics Data System (ADS)

A program, called PAM_C2v_2tops, for fitting the high-resolution torsion–rotation spectra of molecules with two equivalent methyl rotors and C2v symmetry at equilibrium is described and applied to the spectrum of acetone [(CH3)2CO]. The G36 permutation–inversion group-theoretical considerations used in the design of the program are presented followed by a description of the structure of the program, which uses the principal axis method and a two-step diagonalization procedure. The program was used to carry out a weighted least-squares fit of 1720 microwave, millimeter-wave, and sub-millimeter-wave line frequencies of acetone that are available in the literature. The weighted standard deviation of 0.94 obtained here for a joint fit of rotational lines belonging to the ground, the lower torsional fundamental, and the higher torsional fundamental states of acetone represents significant progress in comparison with previous fitting attempts, especially for the excited torsional states.

Ilyushin, Vadim V.; Hougen, Jon. T.

2013-07-01

28

METHODOLOGICAL NOTES: Elastic properties of icosahedral and decagonal quasicrystals

NASA Astrophysics Data System (ADS)

Problems associated with determining the symmetry properties of the elastic constant tensor of icosahedral and decagonal quasicrystals are reviewed. Notions of elastic isotropy and anisotropy are considered, and their relation to the components of the elastic constant tensor is discussed. The question is addressed of how to determine experimentally whether a system under study is elastically isotropic. Experimental results produced by resonant ultrasound spectroscopy of icosahedral Al-Li-Cu and decagonal Al-Ni-Co single quasicrystals are discussed in detail.

Chernikov, Mikhail A.

2005-04-01

29

NSDL National Science Digital Library

An interactive collection of over 60 unique molecules with interactive display of all symmetry elements and animation of all operations. In addition, an interactive point group symmetry tutorial using the Jmol Java and Chime is available.

Johnson, Dean

30

Icosahedral crystals: Where are the atoms

The positions of atoms in icosahedral crystals are shown to correspond to arrangements of three-dimensional hypersurfaces in six-dimensional periodic lattices. The six-dimensional space-group symmetry allows for crystals which cannot be formed by space-filling decorated tilings (quasicrystals). Structures with continuously varying ''unit cells'' are possible. The connection between tilings, projections, cuts, and density-wave descriptions is pointed out.

Bak, P.

1986-02-24

31

Lasing from dye-doped icosahedral quasicrystals in dichromate gelatin emulsions

We report observation of optically pumped multi-directional lasing at visible wavelengths from dye-doped three-dimensional icosahedral quasicrystals fabricated in dichromate gelatin emulsions using a novel seven-beam optical interference holographic method. The lasing pattern exhibits icosahedral symmetry.

Mang Hin Kok; Weixin Lu; Wing Yim Tam; George K. L. Wong

2009-01-01

32

Hydrodynamics of icosahedral quasicrystals

The equations governing long-wavelength, low-frequency excitations in icosahedral quasicrystals are derived. It is found that while the speeds of the propagating modes are isotropic, the attenuations are not, implying that purely macroscopic experiments can in principle distinguish quasicrystals from crystals, glasses, or conventional incommensurate systems. The coefficient of the anisotropy is, regrettably, quite small. The complete spectrum consists of three

T. C. Lubensky; Sriram Ramaswamy; John Toner

1985-01-01

33

NSDL National Science Digital Library

This website contains interactive activities and explanations of reflective and rotational symmetry. Interactive explorations include identifying letters with reflective symmetry, identifying common symbols and objects with rotational symmetry, creating and guessing tile patterns with rotational and reflective symmetry, and creating a snowflake. Other pages include examples created through using these tools and information for teachers.

Edkins, Jo

2007-01-01

34

An analysis of electron micrographs of Al5Mn quasicrystals obtained by rapidly cooling a molten alloy with composition Al17Mn and removing the Al matrix by electrosolution, revealing aggregates of 20 microcrystals at the corners of a pentagonal dodecahedron, supports the proposal that these microcrystals are cubic crystals twinned about an icosahedral seed, with each cubic microcrystal sharing a threefold axis and three symmetry planes with the seed. Images

Pauling, L

1990-01-01

35

Icosahedral Structure of Aluminum-Lithium Aluminum-Copper and Aluminum-Copper Alloys

NASA Astrophysics Data System (ADS)

Icosahedral alloys are materials whose diffraction patterns display the symmetry of the icosahedron, which is incompatible with the translational symmetry of a crystal. This dissertation describes several diffraction experiments on icosahedral alloys. The incommensurability of icosahedrally symmetric structures leads to extra degrees of freedom in their description; we attempt to understand the unusual disorder of icosahedral phases linked to these extra degrees of freedom. In Chapter I we review the unique properties of icosahedral phases, and then present the results of diffraction experiments in the remaining five chapters. The first (Chapter II) is a crystallographic refinement of a crystalline phase, R Al_{5 cdot 6}Li_{2 cdot 9} Cu, related to icosahedral Al-Li-Cu. We find that this phase is a body centered cubic (BCC) packing of nearly -icosahedral clusters of atoms. Next we present in Chapter III the measurement of over 200 diffraction peaks from a single grain sample of icosahedral Al-Li-Cu. Both integrated intensity of diffraction peaks and their half width at half maximum (HWHM) are modeled as functions of both G _parallel (normal reciprocal space wavevector) and G_bot (the three extra degrees of freedom arising from the icosahedral structure). Chapter IV presents measurements of diffuse scattering in i-(AlLiCu). In Chapter V x-ray diffraction peaks of the icosahedral phase of Al-Cu-Ru are found to have no dependence of HWHM on G_bot , as had been the case of all other alloys previously studied. Finally Chapter VI describes diffraction measurements of icosahedral Al-Cu-Fe, from samples annealed at various temperatures. Annealing at 600^circ C introduces phason disorder into the alloy, while annealing at 700^circC removes it. This result is consistent with random tiling models of the icosahedral phase.

Guryan, Christopher Alan

1990-08-01

36

The possibility of icosahedral order in liquids and its role in glass transition is discussed in a broad context of statistical mechanics of liquid. It is pointed out that the structures of glasses and liquids are described both in terms of the topology of atomic bond networks as well as the local distortion of the atomic bonds. While topology plays a dominant role in covalent glasses, local distortion is likely to be more important for metallic glasses.

Egami, Takeshi [ORNL

2007-01-01

37

Phonons in icosahedral and cubic Al-Li-Cu

NASA Astrophysics Data System (ADS)

We describe the results of inelastic-neutron-scattering measurements on single grains of icosahedral Al-Li-Cu and the related cubic R phase. Measurements along the high-symmetry twofold, threefold, and fivefold axes of the icosahedral phase clearly show the existence of well-defined propagating modes, with isotropic dispersion, near strong Bragg peaks. The spectral weight of the acoustic phonons scale linearly with the integrated intensity of the associated zone centers. In several cases we are able to identify ``quasi''-Brillouin-zones, with stationary points at the ``special'' high-symmetry points of a simple icosahedral lattice. While the phonon dispersion for transverse and longitudinal acoustic modes along the twofold axis of the cubic R phase is quite similar to that found for the icosahedral phase, differences are found in the higher-energy modes; the behavior of the higher-energy modes of the icosahedral phase is consistent with an enhanced degree of spatial localization for these excitations.

Goldman, A. I.; Stassis, C.; de Boissieu, M.; Currat, R.; Janot, C.; Bellissent, R.; Moudden, H.; Gayle, F. W.

1992-05-01

38

NSDL National Science Digital Library

This summary exercise involves crystal system and point group identification and stereo diagram construction. Students are presented with 5 blocks and for each block they must determine it's point group and crystal system, make stereo diagrams showing all symmetry and faces, and draw the blocks by hand or with SHAPE and label the Miller Indices.

Perkins, Dexter

39

NSDL National Science Digital Library

This is an introduction to basic symmetry elements. Students make drawings that show good examples of rotation axes and mirror planes and inversion centers with and without a 2-fold axis. They describe real objects a mirror plane, an inversion center, and 2, 3, 4, and 6-fold axes in 3D. They think about symmetry in atomic structures and indicate which symmetry elements are present in ball and stick models of minerals. Then they count the different kinds of symmetry elements present in wooden blocks and real minerals.

Perkins, Dexter

40

Cubic Icosahedra? A Problem in Assigning Symmetry

ERIC Educational Resources Information Center

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…

Lloyd, D. R.

2010-01-01

41

This book demonstrates the progress in the application of the symmetry concept. Highlights symmetry as a fundamental concept in science and as the best unifying idea crossing various branches of most human activities. In addition to its use in traditional symmetry-oriented fields, the concept has made headway in other areas such as reaction chemistry, musicology, nuclear physics, biology, cosmology, etc. This work, illustrated with over 400 drawings, brings together the most diverse fields from mathematics to psychology, the creative and performing arts and most branches of the sciences.

Hargittai, I.

1986-01-01

42

Disorder in Al-li-cu and Al-mn-si icosahedral alloys.

Faceted dendrites of icosahedral AL(6)Li(3)Cu have been studied by high-resolution x-ray scattering. The samples display long-range icosahedral symmetry both in their diffraction patterns and in their macroscopic morphology. Despite the appearance of well-defined facets, the samples have a high degree of atomic disorder. The Bragg peaks have symmetry-dependent shapes and widths that scale linearly with G perpendicular (phason momentum). The peak widths are surprisingly similar to those found in icosahedral Al-Mn-Si alloys in both their absolute magnitude and their dependence on G perpendicular. The origin of these features in models for the icosahedral phase is discussed. PMID:17816544

Heiney, P A; Bancel, P A; Horn, P M; Jordan, J L; Laplaca, S; Angilello, J; Gayle, F W

1987-10-30

43

So-called icosahedral and decagonal quasicrystals are twins of an 820-atom cubic crystal

It is proposed that a molten alloy may contain a 104-atom cluster with icosahedral symmetry and largely icosahedral packing. The cluster may be described as involving twenty interpenetrating Friauf (1927) polyhedra. On rapid freezing these clusters form cubic crystals related to the beta-W structure. The structure is compatible with X-ray and neutron powder diffraction patterns, the single-crystal precession X-ray patterns

Linus Pauling

1987-01-01

44

In this paper, the geometrical structure and vibrational properties of icosahedral solid boron oxygen B12O2 have been calculated using first principles calculations. The symmetry of crystal vibration modes at the center of Brillouin zone is analyzed based on our numeric results and structure symmetry. The calculated results are compared with available experimental investigations.

Bin Wang; Zhaochuan Fan; Qi Zhou; Xiaoxuan Xu; Min Feng; Xuewei Cao; Yufang Wang

2011-01-01

45

Explanation of peak shapes observed in diffraction from icosahedral quasicrystals

NASA Astrophysics Data System (ADS)

The distinctive peak shapes observed in diffraction studies of the icosahedral phases of Al-Mn, Al-Li-Cu, and related alloys are shown to arise from a specific configuration of quenched phason strains in a grain. This configuration is determined by considerations of symmetry and continuity of the phason field. Al-Mn and Al-Li-Cu peak shapes are explained by minor variations of a single mechanism.

Socolar, Joshua E. S.; Wright, David C.

1987-07-01

46

Mechanical properties of icosahedral virus capsids

NASA Astrophysics Data System (ADS)

Virus capsids are self-assembled protein shells in the size range of 10 to 100 nanometers. The shells of DNA-viruses have to sustain large internal pressures while encapsulating and protecting the viral DNA. We employ computer simulations to study the mechanical properties of crystalline shells with icosahedral symmetry that serve as a model for virus capsids. The shells are positioned on a substrate and deformed by a uni-axial force excerted by a small bead. We predict the elastic response for small deformations, and the buckling transitions at large deformations. Both are found to depend strongly on the number N of elementary building blocks (capsomers), and the Föppl-von Kármán number ? which characterizes the relative importance of shear and bending elasticity.

Vliegenthart, G. A.; Gompper, G.

2007-12-01

47

Molecular dynamics characterization of icosahedral short range order in undercooled copper

NASA Astrophysics Data System (ADS)

The stability of undercooled simple metals is still an intriguing problem for materials science and technology. There is not consensus on the role played by the icosahedral short range order during undercooling. The scenario is even less clear for undercooled metals under external pressure. Extensive molecular dynamics simulations, based on an empirical tight-binding interatomic potential, are performed to explain experimental results recently obtained on liquid and undercooled liquid copper. A common neighbour analysis is used to fully characterize the icosahedral short range order in both undercooled and liquid systems. Moreover, the effect of pressure on icosahedral short range order, is addressed and rationalized. External pressure increases the probability to find atomic bonds with icosahedral symmetry both in the liquid and in the undercooled copper.

Celino, M.

2011-05-01

48

Nanosize icosahedral quasicrystal in Mg90Ca10 glass: An ab initio molecular dynamics study

NASA Astrophysics Data System (ADS)

Rapid solidification of Mg90Ca10 from its liquid state is studied by means of an ab initio molecular dynamics technique, and its local structure is investigated by various analyzing methods. The liquid and amorphous states are found to have slightly different short range order even though the perfect and defective icosahedral bonding environments are major bonding elements of both liquid and amorphous states. Perfect icosahedrons with a small frequency exist in the liquid state, more develop during the cooling process and they become the leading building units in the glass state, indicating an icosahedral short range order in Mg90Ca10 glass. Also the linked icosahedrons lead to an icosahedral medium range order. Furthermore, an ordered arrangement of some icosahedrons in the hexagonal symmetry is observed in the glass model, representing a nanoscale icosahedral quasicrystalline phase in Mg90Ca10 glass.

Durandurdu, Murat

2012-07-01

49

Nanosize icosahedral quasicrystal in Mg90Ca10 glass: an ab initio molecular dynamics study.

Rapid solidification of Mg(90)Ca(10) from its liquid state is studied by means of an ab initio molecular dynamics technique, and its local structure is investigated by various analyzing methods. The liquid and amorphous states are found to have slightly different short range order even though the perfect and defective icosahedral bonding environments are major bonding elements of both liquid and amorphous states. Perfect icosahedrons with a small frequency exist in the liquid state, more develop during the cooling process and they become the leading building units in the glass state, indicating an icosahedral short range order in Mg(90)Ca(10) glass. Also the linked icosahedrons lead to an icosahedral medium range order. Furthermore, an ordered arrangement of some icosahedrons in the hexagonal symmetry is observed in the glass model, representing a nanoscale icosahedral quasicrystalline phase in Mg(90)Ca(10) glass. PMID:22830707

Durandurdu, Murat

2012-07-21

50

Atomic clusters and atomic surfaces in icosahedral quasicrystals.

This paper presents the basic tools commonly used to describe the atomic structures of quasicrystals with a specific focus on the icosahedral phases. After a brief recall of the main properties of quasiperiodic objects, two simple physical rules are discussed that lead one to eventually obtain a surprisingly small number of atomic structures as ideal quasiperiodic models for real quasicrystals. This is due to the fact that the atomic surfaces (ASs) used to describe all known icosahedral phases are located on high-symmetry special points in six-dimensional space. The first rule is maximizing the density using simple polyhedral ASs that leads to two possible sets of ASs according to the value of the six-dimensional lattice parameter A between 0.63 and 0.79 nm. The second rule is maximizing the number of complete orbits of high symmetry to construct as large as possible atomic clusters similar to those observed in complex intermetallic structures and approximant phases. The practical use of these two rules together is demonstrated on two typical examples of icosahedral phases, i-AlMnSi and i-CdRE (RE = Gd, Ho, Tm). PMID:24815972

Quiquandon, Marianne; Portier, Richard; Gratias, Denis

2014-05-01

51

Disorder in Al-Li-Cu and Al-Mn-Si icosahedral alloys

NASA Astrophysics Data System (ADS)

Faceted dendrites of icosahedral Al6Li3Cu have been studied by high-resolution X-ray scattering. The samples display long-range icosahedral symmetry both in their diffraction patterns and in their macroscopic morphology. Despite the appearace of well-defined facets, the samples have a high degree of atomic disorder. The Bragg peaks have symmetry-dependent shapes and widths that scale linearly with G(perpendicular) (phason momentum). The peak widths are surprisingly similar to those found in icosahedral Al-Mn-Si alloys in both their absolute magnitude and their dependence on G(perpendicular). The origin of these features in models for the icoshedral phase is discussed.

Heiney, P. A.; Bancel, P. A.; Horn, P. M.; Jordan, J. L.; Laplaca, S.

1987-10-01

52

Lasing from dye-doped icosahedral quasicrystals in dichromate gelatin emulsions.

Lasing requires an active gain medium and a feedback mechanism. In conventional lasers the feedback is provided externally, e.g. by mirrors. An alternate approach is through Bloch waves in photonic crystals composed of periodic dielectric materials in which propagation of light in certain frequency ranges, known as photonic bandgaps, is forbidden. Compared to periodic crystals, quasicrystals have higher symmetry and are more favorable for the formation of photonic bandgaps. Hence quasicrystals are more efficient in providing the feedback mechanism for lasing. Here we report observation of lasing at visible wavelengths from dye-doped three-dimensional icosahedral quasicrystals fabricated in dichromate gelatin emulsions using a novel seven-beam optical interference holographic method. Multi-directional lasing exhibiting the icosahedral symmetry was observed. The lasing modes and pattern were explained by using the lasing condition expressed in the reciprocal lattice space of the icosahedral quasicrystal. PMID:19399104

Kok, Mang Hin; Lu, Weixin; Tam, Wing Yim; Wong, George K L

2009-04-27

53

Point Groups Based on Methane and Adamantane (Td) Skeletons.

ERIC Educational Resources Information Center

Describes a procedure for constructing point groups based on the symmetric parent molecules of methane and adamantane. Intended for use in teaching concepts such as subgroups and cosets to beginners in group theory. (TW)

Fujita, Shinsaku

1986-01-01

54

X-ray diffraction study of phason strain field in oriented icosahedral Al-Mn

We have produced large area (some square centimeters), crystallographically oriented icosahedral-phase material by implanting Mn ions directly into single-crystal Al substrates. High-resolution x-ray measurements of the positions and line shapes of the quasicrystal diffraction peaks reveal systematic deviations from perfect icosahedral symmetry. A quantitative analysis of the data shows that the samples contain a simple form of phason strain field which depends on the kinetics of grain formation. The results rule out the icosatwin model proposed by Pauling.

Budai, J.D.; Tischler, J.Z.; Habenschuss, A.; Ice, G.E.; Elser, V.

1987-06-01

55

Two-Dimensional Crystals of Icosahedral Viruses at Liquid interfaces

NASA Astrophysics Data System (ADS)

Two-dimensional (2D) assembly of turnip yellow mosaic virus (TYMV) on cationic lipid monolayers is investigated at the air-water interface. TYMV, an icosahedral virus with a diameter of 28 nm, exhibits well-defined roughness, charge distribution, and hydrophilic/hydrophobic patches on its surface. The electrostatic attraction to the lipid-coated aqueous interface provides means to impose a specific virus orientation and hence reduce the number of possible inter-particle interactions. The 2D geometry is particularly advantageous in dissecting the role of anisotropy in aqueous-media assembly, which involves various types of similarly weak interactions. We show that the assembly approach used not only facilitates crystallization but also provides insights on how complex anisotropic interactions can be exploited to generate long-range order. Specifically, we report an in situ x-ray scattering observation of novel 2D crystal forms of TYMV that reflect the virus' icosahedral symmetry. The symmetry, shape, and surface heterogeneities of TYMV suggest a mechanism by which these crystals are stabilized by a combination of hydrophobic, electrostatic, and steric interactions.

Fukuto, Masafumi; Yang, Lin; Checco, Antonio; Kuzmenko, Ivan; Nguyen, Quyen; Mank, Nick; Wang, Qian

2012-02-01

56

Dislocation Study in an Icosahedral Quasicrystal.

National Technical Information Service (NTIS)

A method for determining Burgers vectors of dislocations in icosahedral quasicrystals has been developed. It is based on high resolution electron micrographs and theoretical calculations using the theory behind the cut and projection method. The procedure...

Y. X. Guo S. J. Andersen

1993-01-01

57

Maturation of flaviviruses starts from one or more icosahedrally independent nucleation centres

Flaviviruses assemble as fusion-incompetent immature particles and subsequently undergo conformational change leading to release of infectious virions. Flavivirus infections also produce combined ‘mosaic' particles. Here, using cryo-electron tomography, we report that mosaic particles of dengue virus type 2 had glycoproteins organized into two regions of mature and immature structure. Furthermore, particles of a maturation-deficient mutant had their glycoproteins organized into two regions of immature structure with mismatching icosahedral symmetries. It is therefore apparent that the maturation-related reorganization of the flavivirus glycoproteins is not synchronized across the whole virion, but is initiated from one or more nucleation centres. Similar deviation from icosahedral symmetry might be relevant to the asymmetrical mode of genome packaging and cell entry of other viruses.

Plevka, Pavel; Battisti, Anthony J; Junjhon, Jiraphan; Winkler, Dennis C; Holdaway, Heather A; Keelapang, Poonsook; Sittisombut, Nopporn; Kuhn, Richard J; Steven, Alasdair C; Rossmann, Michael G

2011-01-01

58

Icosahedral quasicrystal decoration models. II. Optimization under realistic Al-Mn potentials

We have constructed and relaxed over 200 different finite structure models for the quasicrystal {ital i}-AlMn based on decorations of the {open_quote}{open_quote}canonical-cell tiling.{close_quote}{close_quote} We adopted {ital ab} {ital initio}-based pair potentials with strong Friedel oscillations, which reproduce the phase diagram of real Al-Mn intermetallic crystal structures fairly well. Our various decoration rules encompass cases with face-centered icosahedral (FCI) symmetry and with simple icosahedral (SI) symmetry, and include additional variations in the occupancy and/or chemistry of certain site types. Each decoration was applied to 11 distinct periodic approximants of the tiling. We found that (i) the relaxed atomic positions of each site type can be closely approximated by fixed positions on each tile type, even though the environments (beyond the first neighbor) are inequivalent. (ii) Models with simple icosahedral (SI) space-group symmetry were better than those with face-centered icosahedral (FCI) space-group symmetry. (iii) {open_quote}{open_quote}Loose{close_quote}{close_quote} decorations, containing voids almost large enough for an atom, were better than the {open_quote}{open_quote}dense{close_quote}{close_quote} decorations which were suggested by packing considerations. (iv) Our results depended on using the realistic potentials; {ital short}-range potentials favor the {open_quote}{open_quote}dense{close_quote}{close_quote} structures, and many details depend on the second or further oscillations in the potentials. (v) For our best model, there is relatively little variation of the energy when tiles are rearranged, i.e., a {ital random}-{ital tiling} {ital model} is a good zero-order description of the system. {copyright} {ital 1996 The American Physical Society.}

Mihalkovic, M. [Department of Physics, Cornell University, Ithaca, New York 14853-2501 (United States)]|[Laboratoire de Thermodynamique et Physique-Chimie Metallurgiques, Ecole Nationale Superieure d`Electronique et d`Electromecanique de Grenoble, Boite Postale 75, 38402 St. Martin d`Heres Cedex (France); Zhu, W.; Henley, C.L. [Department of Physics, Cornell University, Ithaca, New York 14853-2501 (United States); Phillips, R. [Division of Engineering, Brown University, Providence, Rhode Island 02912 (United States)

1996-04-01

59

Icosahedral, decahedral and single faulted particles obtained from carbon soot

NASA Astrophysics Data System (ADS)

In the present work we report the growth of icosahedral, decahedral and single faulted carbon particles by heating carbon soot with 3.4 wt% of C 60-C 70. The heating was carried out at ˜730°C during 45 min in a vacuum of 10 -5 Pa. The carbon particles were identified using high resolution transmission electron microscopy (HREM) and electron energy loss spectroscopy (EELS). It was found that the five-fold structures are similar to those observed in metals but with a larger degree of disorder. High resolution images of the decagonal particles clearly show heptagonal rings of atoms. The existence of five-fold symmetry structures in carbon such as the icosahedron and decahedron adds a new interesting family of carbon structures in addition to the buckyballs and buckytubes.

Miki-Yoshida, M.; Rendón, L.; Tehuacanero, S.; José-Yacamán, M.

60

Icosahedral, decahedral and single faulted particles obtained from carbon soot

NASA Astrophysics Data System (ADS)

In the present work we report the growth of icosahedral, decahedral and single faulted carbon particles by heating carbon soot with 3.4 wt% of C 60-C 70. The heating was carried out at ~730°C during 45 min in a vacuum of 10 -5 Pa. The carbon particles were identified using high resolution transmission electron microscopy (HREM) and electron energy loss spectroscopy (EELS). It was found that the five-fold structures are similar to those observed in metals but with a larger degree of disorder. High resolution images of the decagonal particles clearly show heptagonal rings of atoms. The existence of five-fold symmetry structures in carbon such as the icosahedron and decahedron adds a new interesting family of carbon structures in addition to the buckyballs and buckytubes.

Miki-Yoshida, M.; Rendón, L.; Tehuacanero, S.; José-Yacamán, M.

1993-03-01

61

Radial vibrations of a sodium ion inside icosahedral C60

NASA Technical Reports Server (NTRS)

The very high symmetry of icosahedral C60 suggests that, as a first approximation, an atom trapped inside C60 would be subject to a potential that is radially symmetric about the center. All-electron local-density-functional calculations of the total energy of a sodium ion as a function of radial displacement from the center along the fivefold axis of C60 serve to refine such a radial potential. In particular, the calculations suggest studying potentials that have minima displaced from the center. An analytic functional form for a radial potential having a positive cusp at the origin is proposed, and the s-wave radial solutions of the corresponding Schroedinger equation are examined.

Ballester, J. L.; Dunlap, B. I.

1992-01-01

62

Diffuse scattering from the icosahedral phase alloys

NASA Astrophysics Data System (ADS)

Neutron and X-ray measurements of the diffuse scattering from single-grain samples of the icosahedral phase of Al-Li-Cu are presented. The X-ray measurements were analyzed to determine the integrated intensity of the diffuse scattering relative to the sharp diffraction peaks, as well as the length scale of the correlations which produce the diffuse scattering. The neutron data show that these correlations are static rather than dynamic in nature. A simple model based on the disordered packing of icosahedral clusters of atoms reproduces the unusual ringlike nature of this scattering. Quantitatively, this model overestimates the degree of disorder present in these alloys.

Goldman, A. I.; Guryan, C. A.; Stephens, P. W.; Parsey, J. M., Jr.; Aeppli, G.

1988-10-01

63

Dislocations and mechanical properties of icosahedral quasicrystals

NASA Astrophysics Data System (ADS)

In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals.

Mompiou, Frédéric; Caillard, Daniel

2014-01-01

64

Planar defects in the icosahedral phase in quasicrystal-forming AlCuFe alloys

NASA Astrophysics Data System (ADS)

Electron microscopy has revealed that, upon the formation of a stable icosahedral ( i) AlCuFe phase, there arise a large number of planar defects. The revealed defects are nanometer-sized coherent intergrowths of the P1-pentagonal approximant. It has been found that the formation of these defects is the result of a nonequilibrium intermediate transformation. The intergrowths are located in the planes with the fivefold symmetry axis and give rise to an elastic-strain state of the i-phase. Analysis of the diffraction contrast has revealed the presence of phason and phonon atomic displacements due to the mismatch between the quasiperiodic ( i-phase) and periodic ( P1-phase) lattices. The formed structure exhibits a higher electrical resistance as compared to the i-phase and has been considered as a model state of the imperfect icosahedral phase with preferred phonon displacements.

Shalaeva, E. V.; Prekul, A. F.; Nazarova, S. Z.; Khiller, V. V.

2012-04-01

65

Diffuse Scattering in the Icosahedral AL-Li-Cu Quasicrystal

NASA Astrophysics Data System (ADS)

Electron diffraction patterns of icosahedral quasicrystals frequently exhibit diffuse scattering features. We report a detailed analysis of diffuse scattering in Al{6}Li{3}Cu (T2) quasicrystalline samples. The samples have been specifically heat-treated which allows to observe pronounced diffuse effects. Diffuse streaks are observed along the 5-fold and 2-fold symmetry axes and are elongated perpendicularly to these directions. These streaks are due to discs in the 3-dimensional reciprocal space. The diffuse disc positions are only indexable in the 6-dimensional hyperspace but the disc intensities do not agree with the ones predicted by the Cut-and-Project method. The diffuse discs we observed seem to be related to an original quasicrystalline phenomenon overlapping with the icosahedral phase. Les diagrammes de diffraction électronique des quasicristaux icosaédriques présentent fréquemment des diffusions diffuses. Nous les analysons ici en détails sur des échantillons de phase quasicristalline Al{6}Li{3}Cu (T2) traités thermiquement dans lesquels les diffusions diffuses sont trés prononcées. Les intensités diffuses forment des batônnets centrés sur des positions appartenant aux rangées réciproques d'ordre 5 et d'ordre 2 et allongés perpendiculairement à ces directions. On montre qu'il s'agit en fait de disques diffus. dans le réseau réciproque à 3 dimensions, dont les positions ne peuvent s'indexer que sur le réseau à 6 dimensions. Toutefois, les intensités ne correspondent pas à celle prédites par l'algorithme de Coupe-et-Projection. Les disques de diffusion diffuse semblent relever d'une organisation quasicristalline originale se superposant à la phase icosaédrique.

Proult, A.; Donnadieu, P.; Wang, K.; Garoche, P.

1995-12-01

66

The algebraic theory of quasicrystals with five-fold symmetries

An algebraic binary operation is introduced into quasicrystals admitting five-fold symmetry. In terms of this many quasicrystals displaying full pentagonal or icosahedral symmetry are seen to be finitely generated. Examples are given in dimensions 1, 2, 3 and 4. The operation of left quasicrystal addition is affine-linear. The monoid generated by these operators is discussed and a presentation for it

S. Berman; R. V. Moody

1994-01-01

67

Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal

NASA Astrophysics Data System (ADS)

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.

Cui, C.; Nugent, P. J.; Shimoda, M.; Ledieu, J.; Fournée, V.; Tsai, A. P.; McGrath, R.; Sharma, H. R.

2014-01-01

68

Structure of the twofold surface of the icosahedral Ag-In-Yb quasicrystal.

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

Cui, C; Nugent, P J; Shimoda, M; Ledieu, J; Fournée, V; Tsai, A P; McGrath, R; Sharma, H R

2014-01-01

69

A series of quasi-icosahedral gold fullerene cages: Structures and stability

NASA Astrophysics Data System (ADS)

An icosahedron-based template has been proposed and applied to produce a series of initial icosahedral Aun (n=32, 42, 72, 92, and 122) cages. Relativistic density functional theory calculations have subsequently been performed on these structures. The results show that two new, large cages for Au92 and Au122 have good stability, and that the optimized cages with Ih symmetry are quasi-icosahedron and low-lying in energy. Moreover, the HOMO-LUMO gaps of the Au92 and Au122 cages are very small, suggesting strong metallicity. Analyses of the electronic orbitals show sp-d hybridization in the Au92 and Au122 cages.

Ning, Hua; Wang, Jing; Ma, Qing-Min; Han, Hui-Yun; Liu, Ying

2014-05-01

70

3 nj-symbols and harmonic superposition coefficients: an icosahedral abacus

NASA Astrophysics Data System (ADS)

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.

Aquilanti, Vincenzo; Coletti, Cecilia

2001-08-01

71

Confessions of an icosahedral virus crystallographer

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.

Johnson, John E.

2013-01-01

72

The boron buckyball has an unexpected T h symmetry

The boron buckyball avoids the high symmetry icosahedral cage structure. The previously reported Ih symmetric structure is not an energy minimum in the potential energy surface and exhibits a spontaneous symmetry breaking to yield a puckered cage with a rare Th symmetry. The HOMO–LUMO gap is twice as large as the reported value and amounts to 1.94eV at B3LYP\\/6-31G(d) level.

G. Gopakumar; Minh Tho Nguyen; Arnout Ceulemans

2008-01-01

73

Method of making an icosahedral boride structure

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.

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

74

Twinning of the ordered icosahedral quasicrystals has been studied by transmission electron microscopy in a melt-spun Al{sub 75}Cu{sub 12.5}Fe{sub 12.5} alloy. Dendrites of about 10 {micro}m of the icosahedral phase, formed near the wheel side of the melt spun ribbons, have been observed to twin extensively so that a multiple twinning of the grains is observed. Regions of about 1 {micro}m size are twin related through a common five-fold axis to several neighboring regions. The possibility of different orientations of the twins formed by repeated twinning is infinite. Thus the multiple twinning gives rise to a random symmetry for the whole grain. Depending on the undercooling achieved across the melt-spun ribbons, several related phases like the decagonal quasicrystal and crystalline monoclinic Al{sub 3}Fe phase in ten-fold multiply twinned form were also observed.

Singh, A.; Ranganathan, S. [Indian Institute of Science, Bangalore (India). Centre for Advanced Study] [Indian Institute of Science, Bangalore (India). Centre for Advanced Study

1995-09-01

75

NSDL National Science Digital Library

This unit will teach you how to identify symmetry in everyday objects and mathematical shapes in lines and rotational symmetry. What is line symmetry? Click on the link to find out: Line Symmetry Here is a line activity to see if you understand it: Line Symmetry Class Zone See if you understand the concepts by doing the following quiz: Line Symmetry Work Now for rotational symmetry: Rotational Symmetry See if you understand rotational symmetry by taking this quiz: Rotational Symmetry Work ...

Neubert, Mrs.

2011-03-03

76

NASA Astrophysics Data System (ADS)

Quantum revivals or "super-beats" are predicted to occur when angularly localized symmetric tops states are free to evolve. Similar types of dynamics are expected to involve spherical top superfine and superhyperfine level clusters that are labeled by induced representations of octahedral or tetrahedral symmetries for XY_4, XY_6, and related molecules. A considerably more complicated set of effects are expected for the icosahedral molecule C_ {60} and its related isotopomers. An important difference for icosahedral symmetry is that its superfine splitting ratios are most-irrational (Golden-ratio) fractions that preclude perfect Poincare recurrence of quantum phase while the octahedral splitting ratios are rational. William Harter and Justin Mitchell, International Journal of Molecular Science, 14, 714 (2013).

Harter, William G.; Li, Alvason Zhenhua

2013-06-01

77

Icosahedral gold cage clusters: MatAu12- (M=V, Nb, and Ta)

NASA Astrophysics Data System (ADS)

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, MatAu12- (M=V,Nb,Ta). Electronic and structural properties of these clusters were probed by anion photoelectron spectroscopy and theoretical calculations. Characteristics of the MatAu12- 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 MatAu12- 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 [MatAu12-]X+ salts.

Zhai, Hua-Jin; Li, Jun; Wang, Lai-Sheng

2004-11-01

78

Analysis of phases in the structure determination of an icosahedral virus

The constraints imposed on structure-factor phases by noncrystallographic symmetry (NCS) allow phase improvement, phase extension to higher resolution and hence ab initio phase determination. The more numerous the NCS redundancy and the greater the volume used for solvent flattening, the greater the power for phase determination. In a case analyzed here the icosahedral NCS phasing appeared to have broken down, although later successful phase extension was possible when the envelope around the NCS region was tightened. The phases from the failed phase-determination attempt fell into four classes, all of which satisfied the NCS constraints. These four classes corresponded to the correct solution, opposite enantiomorph, Babinet inversion and opposite enantiomorph with Babinet inversion. These incorrect solutions can be seeded from structure factors belonging to reciprocal-space volumes that lie close to icosahedral NCS axes where the structure amplitudes tend to be large and the phases tend to be 0 or {pi}. Furthermore, the false solutions can spread more easily if there are large errors in defining the envelope designating the region in which NCS averaging is performed.

Plevka, Pavel; Kaufmann, Bärbel; Rossmann, Michael G. (Purdue)

2012-03-15

79

F-type icosahedral phase and a related cubic phase in the Al-Rh-Cu system

An F-type icosahedral phase and a related cubic phase (composition of Al{sub 66.1}Rh{sub 21.5}Cu{sub 12.3}, lattice constant a = l.5380(2) nm, and space group of Fm3) were observed in the Al{sub 63}Rh{sub 18.5}Cu{sub 18.5} alloy by transmission electron microscopy (TEM). The structure of the Al-Rh-Cu cubic phase was determined by single-crystal X-ray analysis. A high-resolution electron microscopic image of the Al-Rh-Cu cubic phase is presented together with a simulated image. The structure of the cubic phase can be described by two types of atom clusters, which have outer shells with icosahedral symmetry. It is suggested that the structure of the Al-Rh-Cu cubic phase is helpful for understanding the structure of the i-Al-Rh-Cu F-type icosahedral quasicrystal.

Li, X.Z. [Univ. of Oslo (Norway); Park, K.T.; Sugiyama, K.; Hiraga, K. [Tohoku Univ., Sendai (Japan). Inst. for Materials Research

1998-06-01

80

Momentum Distribution of Valence Electrons in a Single Al-Li-Cu Icosahedral Quasicrystal

NASA Astrophysics Data System (ADS)

A single Al59.3Li29.3Cu11.4 icosahedral quasicrystalis prepared with the Bridgman method. To study the electronicstructure of this phase, high resolution Compton profiles along theaxes of the five- and two-fold symmetries of the single quasicrystalphase have been measured with 60-keV synchrotron radiation X-rays. TheFermi cutoffs are observed clearly in the profiles. Anisotropy in theelectron momentum distribution is not found. Although the valenceelectron profiles can be fitted with an inverted parabola, thefree-electron model does not explain the shape of profiles and themomentum values of the Fermi cutoffs. Based on a concept of thequasi-Brillouin zone boundary the effects of strong electron-latticeinteraction on the electron momentum distribution have been examined.

Tanaka, Yoshikazu; Sakurai, Yoshiharu; Nanao, Susumu; Shiotani, Nobuhiro; Ito, Masahisa; Sakai, Nobuhiko; Kawata, Hiroshi; Iwazumi, Toshiaki

1994-09-01

81

Structure and reactivity of Bi allotropes on the fivefold icosahedral Al-Pd-Mn quasicrystal surface.

The growth of Bi on a pseudomorphic Bi monolayer on the fivefold surface of the icosahedral Al-Pd-Mn quasicrystal has been investigated using low energy electron diffraction and scanning tunnelling microscopy. Initially randomly oriented pseudocubic islands are formed with a preference for an even number of layers. Subsequently a morphological transformation takes place to hexagonal Bi islands, which align along high symmetry directions of the substrate. The Bi flux is found to have a strong effect on which island structure is preferred. When C(60) is adsorbed on the three different allotropes of Bi present in this system, hexagonal C(60) islands are formed in each case. On the pseudocubic and hexagonal islands, the C(60) islands are aligned with the substrate. We discuss the energetic, kinetic and geometrical factors which influence the morphological transformation referred to above. PMID:21403246

Smerdon, J A; Cross, N; Dhanak, V R; Sharma, H R; Young, K M; Lograsso, T A; Ross, A R; McGrath, R

2010-09-01

82

Structure, Chirality, and Formation of Giant Icosahedral Fullerenes and Spherical Graphitic Onions

We describe the topology, structure, and stability of giant fullerenes exhibiting various symmetries (I, Ih, D2h, T). Our results demonstrate that it is also possible to create two new families of nested-chiral-icosahedral (I) fullerenes namely C260@ C560@ C980@ C1520@..and C140@ C380@ C740@ C1220@..., which exhibit interlayer separations of ca. 3.4. These chiral fullerenes are thought to possess non semiconducting properties. Finally, we study in detail the transformation of polyhedral graphitic particles into quasi-spherical nested giant fullerenes by reorganization of carbon atoms which result in the formation of additional pentagonal and heptagonal carbon rings. These spherical structures are metastable and we believe they could be formed if conditions during formation are extreme such as high energy electron irradiation. There is circumstantial experimental evidence for the presence of heptagonal rings within these spherical fullerenes.

Terrones, Mauricio (IPICYT Potosi Institute of Scientific and Technological Research); Terrones, Guillermo (BATTELLE (PACIFIC NW LAB)); Terrones, Humberto (IPICYT Potosi Institute of Scientific and Technological Research)

2001-12-01

83

The RNA of turnip yellow mosaic virus exhibits icosahedral order

Difference electron density maps, based on structure factor amplitudes and experimental phases from crystals of wild-type turnip yellow mosaic virus and those of empty capsids prepared by freeze-thawing, show a large portion of the encapsidated RNA to have an icosahedral distribution. Four unique segments of base-paired, double-helical RNA, one to two turns in length, lie between 33-A and 101-A radius and are organized about either 2-fold or 5-fold icosahedral axes. In addition, single-stranded loops of RNA invade the pentameric and hexameric capsomeres where they contact the interior capsid surface. The remaining RNA, not seen in electron density maps, must serve as connecting links between these secondary structural elements and is likely icosahedrally disordered. The distribution of RNA observed crystallographically appears to be in agreement with models based on biochemical data and secondary structural analyses.

Larson, Steven B. [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States); Lucas, Robert W. [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States); Greenwood, Aaron [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States); McPherson, Alexander [Department of Molecular Biology and Biochemistry, University of California, Irvine, 560 Steinhaus Hall, Irvine, CA 92697-3900 (United States)]. E-mail: amcphers@uci.edu

2005-04-10

84

NASA Astrophysics Data System (ADS)

Torsion free crystallographic groups, called Bieberbach groups, appear as fundamental groups of compact, connected, flat Riemannian manifolds and have many interesting properties. New properties of the group can be obtained by, not limited to, exploring the groups and by computing their homological functors such as nonabelian tensor squares, the central subgroup of nonabelian tensor squares, the kernel of the mapping of nonabelian tensor squares of a group to the group and many more. In this paper, the homological functor, J(G) of a centerless torsion free crystallographic group of dimension five with a nonabelian point group which is a dihedral point group is computed using commutator calculus.

Ting, Tan Yee; Idrus, Nor'ashiqin Mohd.; Masri, Rohaidah; Sarmin, Nor Haniza; Hassim, Hazzirah Izzati Mat

2014-06-01

85

Dynamical x-ray diffraction from an icosahedral quasicrystal

We present direct evidence of dynamical diffraction of x rays from a quasicrystal. High-resolution x-ray-diffraction measurements of the Al-Pd-Mn face-centered icosahedral quasicrystal were performed, revealing a mosaic full width at half maximum of less than 0.001[degree]. In a second experiment, the anomalous transmission of x rays (the Borrmann effect) was observed. These measurements show that nearly perfect quasicrystals may be grown to centimeter-size dimensions allowing x-ray techniques based upon dynamical diffraction to be brought to bear on the analysis of icosahedral structures.

Kycia, S.W.; Goldman, A.I. (Ames Laboratory and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)); Lograsso, T.A.; Delaney, D.W. (Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)); Black, D. (National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)); Sutton, M.; Dufresne, E.; Bruening, R. (Department of Physics, Centre for the Physics of Materials, McGill University, Montreal, Quebec, H3A 2T8 (Canada)); Rodricks, B. (Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439 (United States))

1993-08-01

86

Lattice Dynamics of Icosahedral {alpha}-Boron under Pressure

The Raman spectrum of icosahedral {alpha}-boron presents a very sharp peak at 525cm{sup -1} that was consistently rejected from the lattice modes but is still unexplained. New Raman scattering experiments under pressure are compared with {bold {ital ab initio}} lattice dynamics calculations. The very good agreement of the mode frequencies and their pressure coefficients yields unambiguous assignment of all observed features, including the 525cm{sup -1} line which is a highly harmonic librational mode of the icosahedron and mainly involves bond bending. This mode is also identified in the Raman spectrum of other icosahedral boron-rich solids. {copyright} {ital 1997} {ital The American Physical Society}

Vast, N.; Zerah, G. [CEA--Commissariat a l`Energie Atomique, CELV, 94195 Villeneuve-Saint-Georges (France)] [CEA--Commissariat a l`Energie Atomique, CELV, 94195 Villeneuve-Saint-Georges (France); Baroni, S. [CECAM--Centre Europeen de Calcul Atomique et Moleculaire, ENS-Lyon, 46 Allee d`Italie, 69007 Lyon (France)] [CECAM--Centre Europeen de Calcul Atomique et Moleculaire, ENS-Lyon, 46 Allee d`Italie, 69007 Lyon (France); Baroni, S. [SISSA--Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014 Trieste (Italy)] [SISSA--Scuola Internazionale Superiore di Studi Avanzati, Via Beirut 2-4, 34014 Trieste (Italy); Besson, J.M.; Polian, A.; Chervin, J.C. [Physique des Milieux Condenses, URA 782, CNRS, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris (France)] [Physique des Milieux Condenses, URA 782, CNRS, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris (France); Grimsditch, M. [Argonne National Laboratories, Argonne, Illinois 60439 (United States)] [Argonne National Laboratories, Argonne, Illinois 60439 (United States)

1997-01-01

87

Core restructuring for magnetic Fe55 icosahedral nanoparticles

NASA Astrophysics Data System (ADS)

We investigate magnetic and structural properties of Fe55 clusters from DFT calculations. Previous calculations indicate the existence of icosahedral clusters with two antiferromagnetic states with magnetic moments smaller than experimentally measured. In the present work, we find a rearrangement of the atoms of the core (the 13 saturated atoms) that tend to form a structure close to a cuboctahedron, preserving the icosahedral structure for the surface shell (the 42 surface atoms). The introduction of a Hubbard correction term leads for the most stable electronic state to a ferromagnetic state and a high magnetic moment in agreement to experiment.

Jedidi, Abdesslem; Markovits, Alexis; Minot, Christian; Abderrabba, Manef

2012-07-01

88

Formation of Surface Layers of Icosahedral Al(Mn).

National Technical Information Service (NTIS)

Surfaces layers of the icosahedral phase of Al(Mn) have been formed from thin, alternating Al/Mn layers deposited on Al or Fe surfaces by rapid electron-beam or laser melting, by ion beam mixing, and by solid-state diffusion. The electron beam and laser t...

J. A. Knapp D. M. Follstaedt

1985-01-01

89

Microindentation of Al-Cu-Fe icosahedral quasicrystal

Many different microindentation experiments have been performed at ambient temperature on icosahedral quasicrystals (QCs). They have shown that icosahedral QCs, such as Al-Cu-Fe, Al-Pd-Mn, Al-Li-Cu, Al-Ru-Cu and Mg-Zn-Y are rather hard and exhibit a low fracture toughness. In other respects, compression experiments have shown that these materials exhibit a brittle-to-ductile transition temperature (BDTT) at about 0.7 T{sub m} where T{sub m} is the melting temperature. Few results have been reported concerning microindentation experiments performed at high temperatures, either in the brittle or in the ductile regime. The hardness behavior of icosahedral QCs as a function of temperature has been presented in two cases, however: Al-Li-Cu and Al-Pd-Mn. This paper is aimed at providing information about microindentation measurements performed on an icosahedral Al-Cu-Fe alloy over an extended temperature range. The results are analyzed within the frame used for previous results obtained in the same alloy by means of compression experiments.

Giacometti, E.; Baluc, N.; Bonneville, J.; Rabier, J.

1999-10-08

90

Icosahedral and Other Quasicrystal Phases in Magnetic Alloy Systems.

National Technical Information Service (NTIS)

The aim of this program was to understand the consequences long-range and short-range icosahedral order on magnetism in quasicrystalline alloys. At the time of its outset, there were no known or suspected magnetic quasicrystals. We set out to make some an...

R. C. O'Handley

1990-01-01

91

Lower energy icosahedral atomic clusters with incomplete core

We propose structures for clusters of 69, 78, 88, 98, 107, 113, and 115 atoms that, although icosahedral in character, do not follow the so-called magic numbers sequence. More important, these structures yield lower Lennard-Jones potential energy than the minimum reported in the literature. Our findings arose by linking a very simple heuristic with a local search algorithm.

D. Romero

1997-01-01

92

Generation of molecular symmetry orbitals for the point and double groups

NASA Astrophysics Data System (ADS)

Symmetry-adapted molecular basis functions are widely applied for the electronic structure computations of molecules and clusters. These functions are obtained by exploiting the symmetry of the system and often help to simplify the computations considerably. In order to facilitate their use in algebraic and numerical computations, here we provide a set of MAPLE procedures which generates these functions by means of projection operators, both within the nonrelativistic and relativistic theory. All commonly applied point and double groups are supported by the program including, in addition, the access to their group-theoretical data such as the symmetry operators, characters, or irreducible representations. Program summaryTitle of program:BETHE Catalogue identifier:ADVU Program summary URL:http://cpc.cs.qub.ac.uk/summaries/ADVU Program obtainable from: CPC Program Library, Queen's University of Belfast, N. Ireland Licensing provisions:none Computer for which the program is designed: All computers with a license of the computer algebra package MAPLE (Maple is a registered trademark of Waterloo Maple Inc.) Installations:University of Kassel (Germany) Operating systems or monitors under which the program has been tested:Linux 8.1+ and Windows2000 Programming language used:MAPLE 7 and 8 Memory required to execute with typical data:10-30 MB No. of lines in distributed program, including test data, etc.:14 190 No. of bytes in distributed program, including test data, etc.:370 795 Distribution format:tar.gz Nature of the physical problem:Molecular and solid-state quantum computations can be simplified considerably if the symmetry of the systems with respect to the rotation and inversion of the coordinates is taken into account. To exploit such symmetries, however, symmetry-adapted basis functions need to be constructed instead of using—as usual—the atomic orbitals as the (one-particle) basis. These so-called symmetry orbitals are invariant with respect to the symmetry operations of the group and are different for the point and double groups, i.e. for nonrelativistic and relativistic computations. Method of solution:Projection operator techniques are applied to generate the symmetry-adapted orbital functions as a linear combinations of atomic orbitals. Restrictions onto the complexity of the problem:The generation of the symmetry orbitals is supported for the cyclic and related groups C, C, C, C, C, the dihedral groups D, D, D, the improper cyclic groups S2n(n?10), the cubic groups O, T, O, T, T as well as the icosahedral groups I and I. In all these cases, the symmetry orbitals can be obtained for either the point or double groups by using a nonrelativistic or, respectively, relativistic framework for the computations. Unusual features of the program:All commands of the BETHE program are available for interactive work. Apart from the symmetry orbitals generation, the program also provides a simple access to the group theoretical data for the presently implemented groups from above. The notation of the symmetry operations and the irreducible representations follows the compilation by Altmann and Herzig [Point-Group Theory Tables, Clarendon Press, Oxford, 1994]. For a quick reference to the program, a description of all user-relevant commands is given in the (user) manual Bethe-commands.ps and is distributed together with the code. Typical running time:Although the program replies 'promptly' on most requests, the running time depends strongly on the particular task.

Rykhlinskaya, K.; Fritzsche, S.

2005-09-01

93

Energy-Momentum Stability of Icosahedral Configurations of Point Vortices on a Sphere

NASA Astrophysics Data System (ADS)

We investigate the nonlinear stability of the icosahedral relative equilibrium configuration of point vortices on a sphere. The relative equilibrium problem is formulated as a problem of finding the nullspace of the configuration matrix that encodes the geometry of the icosahedron, as in Jamaloodeen and Newton (Proc. Royal Soc. A, Math. Phys. Eng. Sci. 462(2075):3277, 2006). The seven-dimensional nullspace of the configuration matrix, A, associated with the icosahedral geometry gives rise to a basis set of vortex strengths for which the icosahedron stays in relative formation, and we use these values to form the augmented Hamiltonian governing the stability. We choose the basis set made up of (i) one element with equal strength vortices on every vertex of the icosahedron (the uniform icosahedron); (ii) six elements made up of equal and opposite antipodal pairs. We start by proving nonlinear stability of the antipodal vortex pair (by direct methods). Following the methods laid out in Simo et al. (Arch. Ration. Mech. Anal. 115(1):15-59, 1991) and Pekarsky and Marsden (J. Math. Phys. 39(11):5894-5907, 1998) and more generally in Marsden and Ratiu (Introduction to Mechanics and Symmetry, 1999), we then combine our knowledge of the nullspace structure of A with the structure of the underlying Hamiltonian, and analyze the stability of the icosahedron using the energy-momentum method. Because the parameter space is large, we focus on the physically motivated and important case obtained by combining the basis elements into (i) the uniform icosahedron; (ii) a von Kármán vortex street configuration of equal and opposite staggered, evenly spaced latitudinal rows equidistant from the equator (Chamoun et al. in Phys. Fluids 21:116603, 2009), and (iii) the North Pole-South Pole equal and opposite vortex pair. Stability boundaries in a three-parameter space are calculated for linear combinations of these grouped basis configurations.

Newton, Paul K.; Ostrovskyi, Vitalii

2012-08-01

94

Chiral symmetry and charge symmetry.

National Technical Information Service (NTIS)

The interconnection of charge symmetry and chiral symmetry breaking are discussed. Some consequences of a partial restoration of chiral symmetry in nuclei is brought out by means of the Nambu-Jona-Lasinio model. 22 refs., 10 figs.

E. M. Henley

1989-01-01

95

Crystalline surface structures induced by ion sputtering of Al-rich icosahedral quasicrystals

Low-energy electron diffraction patterns, produced from quasicrystal surfaces by ion sputtering and annealing to temperatures below {approximately}700 K, can be assigned to various terminations of the cubic CsCl structure. The assignments are based upon ratios of spot spacings, estimates of surface lattice constants, bulk phase diagrams vs surface compositions, and comparisons with previous work. The CsCl overlayers are deeper than about five atomic layers, because they obscure the diffraction spots from the underlying quasicrystalline substrate. These patterns transform irreversibly to quasicrystalline(like) patterns upon annealing to higher temperatures, indicating that the cubic overlayers are metastable. Based upon the data for three chemically identical, but symmetrically inequivalent surfaces, a model is developed for the relation between the cubic overlayers and the quasicrystalline substrate. The model is based upon the related symmetries of cubic close-packed and icosahedral-packed materials. The model explains not only the symmetries of the cubic surface terminations, but also the number and orientation of domains. {copyright} {ital 1998} {ital The American Physical Society}

Shen, Z. [Ames Laboratory of the DOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States); Kramer, M.J. [Ames Laboratory of the DOE and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States); Jenks, C.J. [Ames Laboratory of the DOE, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE, Iowa State University, Ames, Iowa 50011 (United States); Goldman, A.I. [Ames Laboratory of the DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE and Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); Lograsso, T. [Ames Laboratory of the DOE and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE and Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States); Delaney, D. [Ames Laboratory of the DOE, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE, Iowa State University, Ames, Iowa 50011 (United States); Heinzig, M. [Ames Laboratory of the DOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States); Raberg, W. [Institut fuer Physikalische Chemie, Universitaet Bonn, Wegelerstrasse 12, 53115 Bonn (Germany)] [Institut fuer Physikalische Chemie, Universitaet Bonn, Wegelerstrasse 12, 53115 Bonn (Germany); Thiel, P.A. [Ames Laboratory of the DOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)] [Ames Laboratory of the DOE and Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States)

1998-10-01

96

Order parameter symmetry in ferromagnetic superconductors

NASA Astrophysics Data System (ADS)

We analyze the symmetry and nodal structure of the superconducting order parameter in a cubic ferromagnet, such as ZrZn2. We demonstrate how the order parameter symmetry evolves when the electromagnetic interaction of the conduction electrons with the internal magnetic induction and the spin-orbit coupling are taken into account. These interactions break the cubic symmetry and lift the degeneracy of the order parameter. It is shown that the order parameter which appears immediately below the critical temperature has two components, and its symmetry is described by corepresentations of the magnetic point groups. This allows us to make predictions about the location of the gap nodes.

Samokhin, K. V.; Walker, M. B.

2002-11-01

97

NASA Astrophysics Data System (ADS)

The phenomenological and generalized spin-Hamiltonian description for the energy levels of a paramagnetic ion in an arbitrary symmetry crystalline electric field environment are discussed. The transformation properties of both the axial and polar classes of the irreducible tensor operators which may be used in description are investigated. New cosine and sine tesseral tensor operators, which are the real and imaginary linear combinations of these tensor operators for both classes, are defined and their conjugation and transformation properties are determined. The secular equation that results when the spin Hamiltonian is expressed in terms of these new tessera) tensor operators is examined under a rotation about a crystallographic c axis when it coincides with the magnetic z axis. Two distinct cases are found: (1) No angular variation of the EPR spectrum in the c plane is observed when both the cosine and sine tesseral tensors operators are allowed for every term with q ? 0 if these operators are of either the axial and polar class. (2) Some transitions exhibit an angular variation of the EPR spectrum in the c plane when only one of the two tesseral tensor operators is allowed if the tensor operators are of the polar class. This occurs when the point group includes one of the symmetry operations ?v, ?v', ?d or C2'. This angular variation can be used to discriminate between similar point groups which differ by only one of these symmetry operations. It has been oberved by many EPR spectroscopists but its theoretical significance has not been appreciated since it has been believed that the spin Hamiltonian must be consistent with the local site symmetry constrained by the spherical symmetry requirement. This latter requirement arises if the spin Hamiltonian is invariant under parity conjugation which is equivalent to imposing space inversion symmetry. Releasing this constraint means that those ZFS terms for which k is odd are allowed and their matrix elements are not zero for S-state ions if the effect of excited state configurations is included. It is also shown that this c-axis angular variation can be used to determine the values of the off diagonal ZFS parameters.

Tuszynski, J. A.; Buckmaster, H. A.; Chatterjee, R.; Boteler, J. M.

98

Encapsulation of a polymer by an icosahedral virus

The coat proteins of many viruses spontaneously form icosahedral capsids around nucleic acids or other polymers. Elucidating the role of the packaged polymer in capsid formation could promote biomedical efforts to block viral replication and enable use of capsids in nanomaterials applications. To this end, we perform Brownian dynamics on a coarse-grained model that describes the dynamics of icosahedral capsid assembly around a flexible polymer. We identify several mechanisms by which the polymer plays an active role in its encapsulation, including cooperative polymer-protein motions. These mechanisms are related to experimentally controllable parameters such as polymer length, protein concentration, and solution conditions. Furthermore, the simulations demonstrate that assembly mechanisms are correlated to encapsulation efficiency, and we present a phase diagram that predicts assembly outcomes as a function of experimental parameters. We anticipate that our simulation results will provide a framework for designing in vitro assembly experiments on single-stranded RNA virus capsids.

Elrad, Oren M.; Hagan, Michael F.

2011-01-01

99

Unusual properties of icosahedral boron-rich solids

Icosahedral boron-rich solids are materials containing boron-rich units in which atoms reside at an icosahedron's 12 vertices. These materials are known for their exceptional bonding and the unusual structures that result. This article describes how the unusual bonding generates other distinctive and useful effects. In particular, radiation-induced atomic vacancies and interstitials spontaneously recombine to produce the “self-healing” that underlies these

David Emin

2006-01-01

100

A coordination chemistry dichotomy for icosahedral carborane-based ligands

NASA Astrophysics Data System (ADS)

Although the majority of ligands in modern chemistry take advantage of carbon-based substituent effects to tune the sterics and electronics of coordinating moieties, we describe here how icosahedral carboranes—boron-rich clusters—can influence metal-ligand interactions. Using a series of phosphine-thioether chelating ligands featuring meta- or ortho-carboranes grafted on the sulfur atom, we were able to tune the lability of the platinum-sulfur interaction of platinum(II)-thioether complexes. Experimental observations, supported by computational work, show that icosahedral carboranes can act either as strong electron-withdrawing ligands or electron-donating moieties (similar to aryl- or alkyl-based groups, respectively), depending on which atom of the carborane cage is attached to the thioether moiety. These and similar results with carborane-selenol derivatives suggest that, in contrast to carbon-based ligands, icosahedral carboranes exhibit a significant dichotomy in their coordination chemistry, and can be used as a versatile class of electronically tunable building blocks for various ligand platforms.

Spokoyny, Alexander M.; Machan, Charles W.; Clingerman, Daniel J.; Rosen, Mari S.; Wiester, Michael J.; Kennedy, Robert D.; Stern, Charlotte L.; Sarjeant, Amy A.; Mirkin, Chad A.

2011-08-01

101

Monte Carlo simulations of icosahedral quasicrystal growth and melting

NASA Astrophysics Data System (ADS)

Three-dimensional Monte Carlo simulations for atomic growth and melting of icosahedral quasicrystals are presented. It is supposed that the atoms can be locally ordered both icosahedrally and dodecahedrally, and the preferred ordering arises during the growth according to statistical and energetical criteria. All the waiting positions (where an atom could be in principle added) are generated on the cluster surface at every stage of the growth. The binding energies of all atoms and all waiting positions are computed with an oscillating Friedel potential. Then an object, chosen at random from the joined list of surface atoms and waiting positions, is treated according to the Metropolis criterion. The suggested growth process is completely local. It is found that the speed and sign of the process and the resulting structures depend strongly on the growth parameters. Most frequently, the main structural motif of grown clusters is the dodecahedral local ordering (DLO) whereas the icosahedral local ordering (ILO) is usually rare. However, the latter becomes dominant for rather exotic interatomic potentials or for high growth rates. The phenomenon of critical seed size is observed: for those parameters, for which large clusters grow, small enough seeds stop to grow and may even melt. The grown quasicrystals are faceted and their sizes in perpendicular space are rather close to those predicted theoretically and observed experimentally.

Dmitrienko, V. E.; Astaf'ev, S. B.; Kléman, M.

1999-01-01

102

Discrete and continuous symmetries in ?-cluster nuclei

NASA Astrophysics Data System (ADS)

I discuss some properties of the algebraic cluster model which is based on the introduction of a spectrum generating algebra for the relative motion of the clusters. Particular attention is paid to the permutation symmetry of identical clusters. As an example, it is shown how the method can be used to study ?-cluster configurations in 12C and 16O with point group symmetries, D3h and Td, respectively.

Bijker, Roelof

2014-05-01

103

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.

Zwart, P.H.; Grosse-Kunstleve, R.W.; Adams, P.D.

2006-07-31

104

We report methods for the synthesis of vertex-differentiated icosahedral closo-boranes. A single B-OH vertex of the icosahedral borane [closo-B12(OH)12]2? was derivatized to prepare [closo-B12(OR)(OH)11]2? using optimized alkylation conditions and purification procedures. Several representative vertex-differentiated icosahedral closo-boranes were prepared utilizing carbonate ester and azide-alkyne click chemistries on the surface of the closo-B122? core.

Goswami, Lalit N.; Houston, Zachary H.; Sarma, Saurav J.; Li, Hairong; Jalisatgi, Satish S.; Hawthorne, M. Frederick

2012-01-01

105

NASA Astrophysics Data System (ADS)

A Bieberbach group is a torsion free crystallographic group, which is an extension of a free abelian group of finite rank by a finite point group, while homological functors of a group include nonabelian tensor square, exterior square and Schur Multiplier. In this paper, some homological functors of a Bieberbach group of dimension four with dihedral point group of order eight are computed.

Mohammad, Siti Afiqah; Ali, Nor Muhainiah Mohd; Sarmin, Nor Haniza; Idrus, Nor'ashiqin Mohd; Masri, Rohaidah

2014-06-01

106

NASA Astrophysics Data System (ADS)

Hysteresis occurs in a ferromagnet because the magnetization can become unstable and jump to a different state. One of the challenges for micromagnetics is finding all the solution curves for a given variable such as the magnetic field. In this talk I show that the symmetries of magnetic states can be used to analyze existing solutions and obtain new ones. A given particle has a magnetic and a nonmagnetic symmetry group. The nonmagnetic group is determined by the crystallographic point group and the shape of the particle. In response to a given operation in this group, the magnetization and magnetic field transform as pseudovectors. In zero field, every symmetry that leaves the body invariant also maps one equilibrium state onto itself or another state of the same energy. Thus, symmetry operations can quickly generate new solutions. Comparisons between equivalent solutions provide a good estimate of their precision. Magnetic symmetry groups are a combination of spatial operations and time reversal (which changes the sign of the magnetization). They leaves the magnetic field and moment invariant, so the highest symmetry the magnetization can have is determined by the physical symmetry of the particle and the field direction. The single-domain (SD) or ``flower'' state has the highest symmetry. Other states can be traced back to the SD state through bifurcations. The most important such bifurcation, a generalization of curling-mode nucleation, breaks inversion symmetry. The result is that the SD state splits into two states, each of which can be obtained from the other by inversion. For many materials (including magnetite), this bifurcation can occur even when the magnetic field is in an arbitrary direction. An important feature of bifurcations is that the pre-bifurcation state continues as an unstable state. Numerical micromagnetic algorithms can easily be fooled into following the unstable state. Several modelers have obtained a remanent state called the double vortex state. This is the result of a second bifurcation off the unstable state, and is itself unstable. The incorrect choice of continuation at a bifurcation is a major source of error in micromagnetic models, and it is difficult to spot without some understanding of the symmetry.

Newell, A. J.

2002-12-01

107

Coherent coexistence of nanodiamonds and carbon onions in icosahedral core-shell particles

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.

Shevchenko, Vladimir Ya.; Madison, Alexey E.; Mackay, Alan L.

2007-01-01

108

Formation of icosahedral Al-Mn by ion implantation into oriented crystalline films

The icosahedral quasicrystal phase has been produced by precipitation from the solid phase during ion implantation of Mn into oriented films of fcc Al on NaCl. Implantations at substrate temperatures of 20/sup 0/C, 150/sup 0/C, and 275/sup 0/C resulted in amorphous, icosahedral, and crystalline phases, respectively. Microdiffraction patterns were obtained from individual icosahedral grains which had precipitated within the bulk of the Al grains. They are oriented with three mutually perpendicular twofold axes of the icosahedral structure parallel to the (001), (110), and (110) directions of the fcc Al matrix.

Budai, J.D.; Aziz, M.J.

1986-02-15

109

On the construction of Kramers paired double group symmetry functions

NASA Astrophysics Data System (ADS)

Relativistic quantum chemical calculations on molecular systems can greatly be expedited by making use of the full molecular symmetry, including both double point group and time-reversal symmetry. A simple yet general scheme is proposed here to make double point group symmetry functions also form Kramers pairs such that the resulting operator matrices have the desired structure (i.e., quaternion, complex, or real). The key idea is to insert appropriate phase factors into the symmetry functions or make a suitable unitary transformation of them. Arbitrary finite double point groups can be handled in the same way. As for a product basis, the same symmetrization can be achieved by simple modifications of the vector coupling (Clebsch-Gordan) coefficients. This is especially of interest to, e.g., time-dependent relativistic density functional linear response theory or relativistic two-electron repulsion integral evaluations in general. Several examples are provided to illustrate the algorithm and its efficiency.

Peng, Daoling; Ma, Jianyi; Liu, Wenjian

110

Non-centro-symmetric characteristics are observed in the experimental electron diffraction patterns (EDPs) from the icosahedral quasicrystalline precipitates in ZrAlNiCuNb alloys. Different from the well-known breaking of the Friedel's law, where a strong dynamical effect will reveal in EDPs the concealed non-centro-symmetry originated from the crystal structures themselves, the current results can be interpreted in terms of changes in deviation parameters due to a delicate combination of the linear phason strain characteristic of quasicrystals and the curvature of Ewald sphere. After taking this effect into consideration, the corresponding simulated EDPs fit quite well to the experimental data. PMID:24041584

Xiong, Dongxia; Lu, Lu; Wang, Jianbo; Zhao, Dongshan; Sun, Yufeng

2013-01-01

111

A thermodynamically stable face-centred icosahedral phase with a pentagonal dodecahedral solidification morphology has been found in Zn?Mg?RE (RE ? Y, Tb, Dy, Ho or Er) alloys. We report here the structure, stability and morphology in this new group of icosahedral alloys on the basis of results for the Zn?Mg?Y system.

A. Niikura; A. P. Tsai; A. Inoue; T. Masumoto

1994-01-01

112

ERIC Educational Resources Information Center

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…

Jittam, Piyachat; Ruenwongsa, Pintip; Panijpan, Bhinyo

2008-01-01

113

The atomic structure of the threefold surface of the icosahedral Ag-In-Yb quasicrystal

NASA Astrophysics Data System (ADS)

We report a study of the atomic structure of the threefold icosahedral (i-)Ag-In-Yb quasicrystal surface using scanning tunneling microscopy (STM) and low energy electron diffraction (LEED). The LEED confirms that the surface exhibits quasicrystalline long-range order with the threefold symmetry expected from the bulk. The STM reveals large atomically flat terraces separated by steps of different heights. A comparison of atomically resolved STM images for the terraces and the step-height distribution with the bulk structure of isostructural i-Cd-Yb shows that the terraces are formed at bulk planes intersecting the centers of the rhombic triacontahedral clusters that make up the bulk structure of the system. However, the stability of particular terraces may be influenced by the density of atoms in the interstices (glue atoms that bind the clusters) in the terraces and also by the chemical environment in the underlying atomic plane. The surface exhibits screw dislocations, which is explained in terms of a continuous atomic density along the threefold axis.

Cui, C.; Nugent, P. J.; Shimoda, M.; Ledieu, J.; Fournée, V.; Tsai, A. P.; McGrath, R.; Sharma, H. R.

2012-11-01

114

The atomic structure of the threefold surface of the icosahedral Ag-In-Yb quasicrystal.

We report a study of the atomic structure of the threefold icosahedral (i-)Ag-In-Yb quasicrystal surface using scanning tunneling microscopy (STM) and low energy electron diffraction (LEED). The LEED confirms that the surface exhibits quasicrystalline long-range order with the threefold symmetry expected from the bulk. The STM reveals large atomically flat terraces separated by steps of different heights. A comparison of atomically resolved STM images for the terraces and the step-height distribution with the bulk structure of isostructural i-Cd-Yb shows that the terraces are formed at bulk planes intersecting the centers of the rhombic triacontahedral clusters that make up the bulk structure of the system. However, the stability of particular terraces may be influenced by the density of atoms in the interstices (glue atoms that bind the clusters) in the terraces and also by the chemical environment in the underlying atomic plane. The surface exhibits screw dislocations, which is explained in terms of a continuous atomic density along the threefold axis. PMID:23044476

Cui, C; Nugent, P J; Shimoda, M; Ledieu, J; Fournée, V; Tsai, A P; McGrath, R; Sharma, H R

2012-11-01

115

The twofold-axis electron-diffraction photographs of icosahedral quasicrystals are of three kinds, reflecting three different structures of the cubic crystals that by icosahedral twinning form the quasicrystals. The first kind, represented by Al13Cu4Fe3, contains two very large icosahedral complexes, each of about 4680 atoms, in the body-centered arrangement, with six smaller icosahedral complexes (104 atoms each) in the principal interstices. The second kind, represented by Al5Mn, contains four of the very large complexes in the face-centered arrangement (cubic close packing), with four of the smaller clusters in the interstices. The third kind, represented by Al6CuLi3, contains eight icosahedral complexes, each of about 1350 atoms, in the ?-W arrangement. The supporting evidence for these cubic structures is discussed as well as other evidence showing that the simple quasicrystal theory, which states that quasicrystals do not involve any translational identity operations, has to be modified. Images

Pauling, Linus

1989-01-01

116

Nonhydrostatic icosahedral atmospheric model (NICAM) for global cloud resolving simulations

NASA Astrophysics Data System (ADS)

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.

Satoh, M.; Matsuno, T.; Tomita, H.; Miura, H.; Nasuno, T.; Iga, S.

2008-03-01

117

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

Marzec, C J; Day, L A

1993-01-01

118

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...

119

Symmetry, Landau theory and polytope models of glass

NASA Astrophysics Data System (ADS)

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.

Nelson, David R.; Widom, Michael

1984-08-01

120

We prove mirror symmetry for supersymmetric sigma models on Kahler manifolds in 1+1 dimensions. The proof involves establishing the equivalence of the gauged linear sigma model, embedded in a theory with an enlarged gauge symmetry, with a Landau-Ginzburg theory of Toda type. Standard R -> 1\\/R duality and dynamical generation of superpotential by vortices are crucial in the derivation. This

Kentaro Hori; Cumrun Vafa

2000-01-01

121

NASA Astrophysics Data System (ADS)

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”.

Dewar, R. L.; Hudson, S. R.

1998-01-01

122

Difference in Icosahedral Short-Range Order in Early and Late Transition Metal Liquids

NASA Technical Reports Server (NTRS)

New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in-situ synchrotron x-ray diffraction measurements of electrostatically-levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid. although this has been predicted by theoretical studies on atomic clusters.

Lee, G. W.; Gangopadbyay, A. K.; Kelton, K. F.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.

2004-01-01

123

Difference in Icosahedral Short-Range Order in Early and Late Transition Metals Liquids

NASA Technical Reports Server (NTRS)

New short-range order data are presented for equilibrium and undercooled liquids of Ti and Ni. These were obtained from in-situ synchrotron x-ray diffraction measurements of electrostatically-levitated droplets. While the short-range order of liquid Ni is icosahedral, consistent with Frank's hypothesis, significantly distorted icosahedral order is observed in liquid Ti. This is the first experimental observation of distorted icosahedral short-range order in any liquid, although this has been predicted by theoretical studies on atomic clusters.

Lee, G. W.; Gangopadhyay, A. K.; Kelton, K. F.; Hyers, R. W.; Rathz, T. J.; Rogers, J. R.

2003-01-01

124

New Stable Icosahedral Quasicrystal in Mg-Pd-Al System

NASA Astrophysics Data System (ADS)

A thermodynamically stable icosahedral phase (I-phase) has been found to form in Mg-Pd-Al alloys in the compositional range 13 to 15 at%Pd and 42 to 44 at%Al. The X-ray diffraction measurements have shown that the I-phase is of the Frank-Kasper type (FK-type), as in Al-Li-Cu and Mg-Ga-Zn alloys. The stability of the I-phase has been confirmed by the result that it shows no transformation by annealing for 40 h at temperatures just below the melting point. The electrons per atom ratio (e/a) for the Mg-Pd-Al I-phase is ˜2.15, which is nearly equal to those for other stable FK-type I-phases. This result suggests that the energy-band structure plays a dominant role in the formation of I-phases.

Koshikawa, Naokiyo; Sakamoto, Shinya; Edagawa, Keiichi; Takeuchi, Shin

1992-07-01

125

Intermediate-valence icosahedral Au-Al-Yb quasicrystal

NASA Astrophysics Data System (ADS)

A quasiperiodic intermediate-valence (IV) system is realized in an icosahedral Au-Al-Yb quasicrystal. X-ray absorption spectroscopy near the Yb L3 edge indicates that quasiperiodically arranged Yb ions assume a mean valence of 2.61, between a divalent state (4f14, J=0) and a trivalent one (4f13, J=7/2). Magnetization measurements demonstrate that the 4f holes in this quasicrystal have a localized character. The magnetic susceptibility shows a Curie-Weiss behavior above ˜100 K with an effective magnetic moment of 3.81?B per Yb. Moreover, a crystalline approximant to this quasicrystal is an IV compound. We propose a heterogeneous IV model for the quasicrystal, whereas the crystalline approximant is most likely a homogeneous IV system. At temperatures below ˜10 K, specific heat and magnetization measurements reveal non-Fermi-liquid behavior in both the quasicrystal and its crystalline approximant without either doping, pressure, or field tuning.

Watanuki, Tetsu; Kashimoto, Shiro; Kawana, Daichi; Yamazaki, Teruo; Machida, Akihiko; Tanaka, Yukinori; Sato, Taku J.

2012-09-01

126

NASA Astrophysics Data System (ADS)

By investigating the magnetism of spins on a quasiperiodic lattice, we present an experimental study of static and dynamic magnetic properties, specific heat, and magnetic entropy of the Gd3Au13Sn4 quasicrystalline approximant. The magnetic sublattice of Gd3Au13Sn4 is a periodic arrangement of nonoverlapping spin clusters of almost perfect icosahedral symmetry, where gadolinium localized f magnetic moments are distributed on equilateral triangles. The absence of disorder on the magnetic sublattice and the antiferromagnetic (AFM) interactions between the nearest-neighbor spins distributed on triangles result in geometrical frustration of spin-spin interactions. Thus, the Gd3Au13Sn4 phase can be viewed as a prototype site-ordered, geometrically frustrated spin system on icosahedral clusters. The zero-field-cooled and field-cooled magnetic susceptibilities, the alternating current susceptibility, the thermoremanent magnetization, the memory effect, the magnetic specific heat, and the magnetic entropy all show that the spin system undergoes at low temperatures a transition to a nonergodic state at the spin freezing temperature Tf ? 2.8 K. Below this, the ergodicity is broken on the experimental timescale, because the thermally activated correlation times for the spin reorientations become macroscopically long. The magnetic state achieved at low temperatures by continuous cooling in low magnetic fields is likely a superposition of (1) metastable states with randomly frozen spins that have no long-range order yet undergo gradual spin-freezing dynamics and (2) an AFM-like magnetically ordered state with critical slowing dynamics. The magnetic properties of the site-ordered, geometrically frustrated Gd3Au13Sn4 system are discussed in comparison to site-disordered spin glasses that contain both randomness and frustration.

Koželj, P.; Jazbec, S.; Vrtnik, S.; Jelen, A.; Dolinšek, J.; Jagodi?, M.; Jagli?i?, Z.; Boulet, P.; de Weerd, M. C.; Ledieu, J.; Dubois, J. M.; Fournée, V.

2013-12-01

127

Fish Viruses: A Double-Stranded RNA Icosahedral Virus from a North American Cyprinid.

National Technical Information Service (NTIS)

A previously unreported virus disease of cultured golden shiners (Notemigonus crysoleucas) is described. The condition is called golden shiner virus (GSV) disease. The virus is icosahedral, measures approximately 70 nm, is ether and heat resistant, stable...

J. A. Plumb P. R. Bowser J. M. Grizzle A. J. Mitchell

1978-01-01

128

Structure of Al-Li-Cu Icosahedral Crystals and Penrose Tiling,

National Technical Information Service (NTIS)

We report synchrotron x ray powder diffraction measurements of the Aluminum Lithium Copper 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 a...

Y. Shen S. J. Poon W. Dmowski T. Egami G. J. Shiflet

1987-01-01

129

Evolution of icosahedral clusters during the rapid solidification of liquid TiAl alloy

NASA Astrophysics Data System (ADS)

The evolution characteristics of icosahedral clusters during the rapid solidification of TiAl alloy under different cooling rates are investigated based on molecular dynamics simulations. The short-range order structural properties of liquid and amorphous TiAl alloy are analyzed by several structural characterization methods. It is found that the cooling rate plays a key role during the evolution of icosahedral clusters and has significant effect on the glass transition temperature. Simultaneously, the medium-range order structural evolutions are described in detail by quantitative method and visualization technology during the rapid solidification. The results reveal that the medium-range order icosahedral clusters have good structural stability and configural continuity during the rapid cooling process. Furthermore, the icosahedral structures have significant improvements with decreasing cooling rate. The structures block the crystal nucleation and improve the glass forming ability of supercooled liquid.

Xie, Zhuo-Cheng; Gao, Ting-Hong; Guo, Xiao-Tian; Qin, Xin-Mao; Xie, Quan

2014-05-01

130

NASA Astrophysics Data System (ADS)

This study performs dc conductivity and static magnetic-susceptibility measurements on Li- and Cu-doped ?-rhombohedral boron (?-rhombohedral B), which is a unique polymorphic semiconducting (group III) material composed of B12 icosahedral clusters. dc conductivity results show a variable-range-hopping (VRH)-type temperature dependence with a typical localization length of about ~1 Å. In addition, the density of states (DOS) at the Fermi energy, which is calculated from fitted parameters of VRH conduction, was found to have a peak with respect to metal concentration, such that at the highest concentration (Li7.9B105 and Cu4.2B105), metal-doped ?-rhombohedral B appears to revert back to an insulator, instead of showing insulator-to-metal transition. Corresponding static magnetic-susceptibility results, however, show a contribution from Pauli paramagnetism in the temperature-independent component ?0, where a similar concentration dependence is shows to that in the DOS of VRH conduction. Based on these properties, we discuss the possibility of filling the intrinsic acceptor band, which originates from the uppermost molecular bonding orbital of the B12 icosahedral cluster that is split by the Jahn-Teller effect. ?-rhombohedral B's crystalline structure can also be viewed as a slightly distorted face-centered cubic (fcc) packing of B84 soccer-ball-shaped clusters covalently bound to each other and containing a relatively large number of large-size interstitial doping sites. This structure is considered to be topologically similar to that of fcc C60, although the bonding mechanisms of their clusters are different, and therefore we also describe the similarities and differences between them.

Matsuda, H.; Nakayama, T.; Kimura, K.; Murakami, Y.; Suematsu, H.; Kobayashi, M.; Higashi, I.

1995-08-01

131

Some proofs are presented of Goldstone's conjecture, that if there is continuous symmetry transformation under which the Lagrangian is invariant, then either the vacuum state is also invariant under the transformation, or there must exist spinless particles of zero mass.

Jeffrey Goldstone; Abdus Salam; Steven Weinberg

1962-01-01

132

Speckle in the diffraction patterns of Hendricks-Teller and icosahedral glass models

NASA Technical Reports Server (NTRS)

It is shown that the X-ray diffraction patterns from the Hendricks-Teller model for layered systems and the icosahedral glass models for the icosahedral phases show large fluctuations between nearby scattering wave vectors and from sample to sample, that are quite analogous to laser speckle. The statistics of these fluctuations are studied analytically for the first model and via computer simulations for the second. The observability of these effects is discussed briefly.

Garg, Anupam; Levine, Dov

1988-01-01

133

Structure of Al-Li-Cu icosahedral crystals and Penrose tiling

NASA Astrophysics Data System (ADS)

Synchrotron X-ray powder-diffraction measurements of the Al-Li-Cu icosahedral phase are reported. The 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.

Shen, Y.; Poon, S. J.; Shiflet, G. J.; Dmowski, W.; Egami, T.

1987-04-01

134

Highly ordered structure of icosahedral quasicrystals in Zn-Mg-RE (RE ? rare earth metals) systems

A new group of stable icosahedral phases (i-phases) in the Zn-Mg-RE system were found to have an ideal composition close to Zn50 Mg42RE8 (RE ? Y, Gd, Tb, Dy, Ho or Er). The new i-phases exhibit a highly ordered and nearly perfect face-centred icosahedral lattice as revealed by electron and X-ray diffraction and high-resolution electron microscopy. Powder X-ray diffraction indicates

A. P. Tsai; A. Niikura; A. Inoue; T. Masumoto; Y. Nishida; K. Tsuda; M. Tanaka

1994-01-01

135

Experimental Observation and Confirmation of Icosahedral W@Au12 and Mo@Au12 Molecules

The recently predicted W@Au12 cluster has been observed and probed experimentally using anion photoelectron spectroscopy. It is shown that this unique molecule and its Mo congener indeed possess an icosahedral structure and a large HOMO-LUMO gap. Relativistic density functional theory is used to calculate their geometries, energetics, and energy spectra. The simulated density-of-states spectra are in good agreement with the photoelectron spectra, confirming the icosahedral structure of these complexes.

Li, Xi; Boggavarapu, Kiran; Li, Jun; Zhai, Hua Jin; Wang, Lai-Sheng

2002-12-16

136

NSDL National Science Digital Library

This unit from Illuminations provides students with the opportunity to learn about the mathematical properties of rotations. These lessons investigate rotational symmetry by fixing the center of an object and then turning it. The relationship between rotations and symmetry is also examined. The unit consists of 4 lessons, each of which should require 1 class period to complete. The material is appropriate for grades 9-12.

2010-12-07

137

NASA Astrophysics Data System (ADS)

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.

Cai, Tanhong

2001-07-01

138

Symmetry breaking and hole localization in multiple core electron ionization.

Motivated by recent opportunitites to study hollow molecules with multiple core holes offered by X-ray free electron lasers, we revisit the core-hole localization and symmetry breaking problem, now studying ionization of more than one core electron. It is shown, using a N2 molecule with one, two, three, and four core holes, for example, that in a multiconfigurational determination of the core ionization potentials employing a molecular point group with broken inversion symmetry, one particular configuration is sufficient to account for the symmetry breaking relaxation energy in an independent particle approximation in the case of one or three holes, whereas the choice of point group symmetry is unessential for two and four holes. The relaxation energy follows a quadratic dependence on the number of holes in both representations. PMID:23859627

Carravetta, V; Ågren, H

2013-08-01

139

Icosahedral quasicrystal structure determination: Al-Cu-Li

This dissertation reports the theoretical study of the determination of quasicrystal atomic structures. A new method is developed for phasing the quasicrystal diffraction data (neutron, X-ray diffraction). A mathematical model is built which explicitly relates quasicrystals to their related periodic crystals. A test of the method is made on a simple theoretical system, the icosahedral quasiperiodic Ammann tiling decorated with point scatterers (Dirac [sigma] scattering potential) on vertices. A success is achieved in reconstructing the phases of the quasicrystal. The method is applied to a real quasicrystal system, the icosahedral quasicrystal i(Al[sub .570]Cu[sub .108]Li[sub .322]), where single-grain X-ray as well as neutron diffraction data are available, and the structure of the related large-unit-cell crystal of R(Al[sub .564]Cu[sub .116]Li[sub .320]), is well known. The reconstructed phases give the density of scatterers, which can then be used in the analysis of the atomic structure, and provide a guide to the final structure modeling. The validity of the method is evaluated with respect to the non-negativity of the resulting electron densities. In order to identify the negativity due to the intensity cut-off, the negativity is evaluated as a function of the cut-off and compared with the exact and reconstructed quasiperiodic Ammann tilings as well as with the experimental and model crystal data of R(Al[sub .564]Cu[sub .116]Li[sub .320]). It is concluded that the negativity of the reconstructed quasiperiodic electron density of i(Al[sub .570]Cu[sub .108]Li[sub .322]) is consistent with a cut-off effect. Modeling of the i(Al[sub .570]Cu[sub .108]Li[sub .322]) atomic structure in six-dimensional hyperspace is discussed. It is assumed that atomic surfaces can be modeled by polyhedra which can be described by a finite number of parameters. The authors successfully generated a model which agrees with the experimental data.

Qiu, S.Y.

1992-01-01

140

Symmetry and equivalence restrictions in electronic structure calculations

NASA Technical Reports Server (NTRS)

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.

Bauschlicher, Charles W., Jr.; Taylor, Peter R.

1988-01-01

141

Magnetic properties of icosahedral Al-Cr-Mn-Ge alloys

NASA Astrophysics Data System (ADS)

Alloys in the series Al65Cr20-xMnxGe15 (0<=x<=20) have been produced by melt spinning. These rapidly solidified alloys have been found to be single phase and of the icosahedral structure. Magnetic-susceptibility measurements reveal a moment of 0.45?B for Cr in the Al65Cr20Ge15 alloy. This is the first observation of a local moment on Cr in a quasicrystal. In the Al65Mn20Ge15 alloy a moment of 2.10?B for Mn is observed, which is the largest moment observed in Al-Mn-metalloid quasicrystal alloys. The compositional dependence of the magnetic moment is consistent with at least two classes of magnetic sites. Spin-glass behavior is observed below 8 K in the Al65Mn20Ge15 alloy. Measurements of the time dependence of the magnetization, in a field of 1 T, and from the zero-field-cooled state have been made for the Al65Mn20Ge15 alloy, revealing logarithmic relaxation. Analysis of this data using a first-order rate equation and a distribution of energy barriers reveals an average energy barrier of 6.8 meV.

McHenry, M. E.; Dunlap, R. A.; Srinivas, V.; Bahadur, D.; O'handley, R. C.

1990-04-01

142

Mechanical properties of icosahedral boron carbide explained from first principles

NASA Astrophysics Data System (ADS)

An exhaustive DFT study of the structural defects of icosahedral B4C and of their behavior under high pressure has been performed. Among the possible atomic structures, the lowest value of the formation energy has been found for the polar model B4C^P, which consists of one distorted icosahedron and of one CBC chain. This result, together with the inspection of the vibrational and NMR spectra, has proved that B4C^P is the proper structural model for B4C.[1,2] Consequently, B4C^P has been used as a matrix to isolate the defects. The native defects have been identified and shown to be energetically stable at high pressure. Most vacancy locations in B4C^P are found to be energetically unstable and only a boron vacancy in the CBC chain is stable. A cluster of this vacancy is shown to induce a dynamical instability of the icosahedra when the pressure is increased. The dynamical failure of shocked B4C [3] is attributed to the increase in the concentration of these unstable vacancies under plastic deformation. 1. R. Lazzari, N.Vast, J.M. Besson, S. Baroni and A. Dal Corso, Phys. Rev. Lett. 83 (1999) 3230. 2. F. Mauri, N. Vast and C.J. Pickard, Phys. Rev. Lett. 87 (2001) 085506. 3. T. Vogler, W. Reinhart and L. Chhabildas, J. Appl. Phys. 95 (2004) 4173.

Raucoules, Roman; Vast, Nathalie; Betranhandy, Emmanuel; Sjakste, Jelena

2011-03-01

143

Dynamic Paper Constructions for Easier Visualization of Molecular Symmetry

ERIC Educational Resources Information Center

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…

Sein, Lawrence T., Jr.

2010-01-01

144

Web-Supported Chemistry Education: Design of an Online Tutorial for Learning Molecular Symmetry

This paper describes our use of the ADDIE protocol to design and develop an interactive tutorial for students learning molecular symmetry operations and point groups. The tutorial provides a 3-D environment where students can examine molecules, structures, and symmetry elements. Most such tutorials are connected to courses or instructors in ways that make them difficult for others to use. Our

Ali Korkmaz; William S. Harwood

2004-01-01

145

ERIC Educational Resources Information Center

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…

Attanucci, Frank J.; Losse, John

2008-01-01

146

Disorder in Al-Mn-Fe icosahedral alloys introduced by iron

Considerable effort is directed nowadays towards obtaining large and perfect icosahedral phases (IP), in order to study their specific properties related to the lack of translational periodicity. However, real IP in the most Al-TM systems (TM = transition metal) contain structural defects, which clearly differentiate them from the ideal ones. In local models for describing quasicrystals the IP is assumed to be a 3D network of complex Mackay icosahedra connected through faces and vertices. Here the quasiperiodical order becomes apparent by the parallelism of the interatomic bonds in the neighboring icosahedra. Local models introduce also an element of randomness by assuming a statistic occupancy of the icosahedral faces and vertices. Thus different but equivalent ways to built an assembly of icosahedra appeared to be the cause of an intrinsic topological disorder and the spatial correlation of icosahedra in a real IP would be limited to regions of pseudocoherence. In the limit of the highest disorder a real quasicrystal approaches a dense random packing of icosahedra or fragments of them. The specific icosahedral order would be disrupted by localized defects (local violation of the matching rules), broadly classified as phonon and phason strains. In the IP phason strains are definitely more significant as they measure the degradation of the icosahedral order with respect the ideal one, i.e. the ability to stabilize an icosahedral phase for a certain composition. It is the purpose of this paper to demonstrate some of these concepts.

Nistor, L.C.; Teodorescu, V.; Manaila, R. (Inst. of Atomic Physics, Bucharest (Romania))

1993-06-01

147

NASA Astrophysics Data System (ADS)

We will consider the role played by electron-vibration and electron-electron interactions, through Jahn-Teller (JT) and Coulomb interactions, respectively, in icosahedral systems in which triplet electronic states are coupled to hg-type vibrations. Starting from the electronic terms that arise from consideration of Coulomb interactions, we introduce JT couplings both within the terms and between nondegenerate terms. We show how the symmetry of the JT distortion can change when extra electrons are added, and give the conditions under which JT distortions can be suppressed entirely when the Coulomb interactions are sufficiently large. The relevance of our results to anions of the fullerene molecule C60 are briefly discussed, and existing experimental measurements are used to estimate values for the quadratic JT coupling constants for these anions.

Alqannas, Haifa S.; Lakin, Andrew J.; Farrow, Joseph A.; Dunn, Janette L.

2013-10-01

148

NASA Astrophysics Data System (ADS)

We investigated the phason-strain-field influences on electronic and vibrational properties of two icosahedral quasicrystals, Al-Li-Cu and Al-Fe-Cu. For that purpose we performed low-temperature specific-heat measurements on samples before and after annealing treatments that allowed strong phason-strain elimination. The electronic specific heat for the two systems is found to be scarcely sensitive to the annealing treatments, while the vibrational specific heat displays a different behavior: it remains unchanged in Al-Li-Cu, but is strongly reduced in Al-Fe-Cu after annealing. We interpret this to arise from the correlation between the symmetry of the phason-strain field and the electronic and vibrational properties.

Wang, K.; Garoche, P.

1997-01-01

149

Magnetic properties of icosahedral Al-Cr-Mn-Ge alloys

Alloys in the series Al{sub 65}Cr{sub 20{minus}{ital x}}Mn{sub {ital x}}Ge{sub 15} (0{le}{ital x}{le}20) have been produced by melt spinning. These rapidly solidified alloys have been found to be single phase and of the icosahedral structure. Magnetic-susceptibility measurements reveal a moment of 0.45{mu}{sub {ital B}} for Cr in the Al{sub 65}Cr{sub 20}Ge{sub 15} alloy. This is the first observation of a local moment on Cr in a quasicrystal. In the Al{sub 65}Mn{sub 20}Ge{sub 15} alloy a moment of 2.10{mu}{sub {ital B}} for Mn is observed, which is the largest moment observed in Al-Mn-metalloid quasicrystal alloys. The compositional dependence of the magnetic moment is consistent with at least two classes of magnetic sites. Spin-glass behavior is observed below 8 K in the Al{sub 65}Mn{sub 20}Ge{sub 15} alloy. Measurements of the time dependence of the magnetization, in a field of 1 T, and from the zero-field-cooled state have been made for the Al{sub 65}Mn{sub 20}Ge{sub 15} alloy, revealing logarithmic relaxation. Analysis of this data using a first-order rate equation and a distribution of energy barriers reveals an average energy barrier of 6.8 meV.

McHenry, M.E. (Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (USA) Department of Metallurgical Engineering Materials Science, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213 (USA)); Dunlap, R.A.; Srinivas, V. (Department of Physics, Dalhousie University, Halifax, Nova Scotia, Canada B3H3J5 (CA)); Bahadur, D. (Advanced Centre for Materials Science, Indian Institute of Technology, Kanpur, India 208016 (IN)); O'Handley, R.C. (Department of Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA) Department of Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (USA))

1990-04-01

150

- 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

None

2011-10-06

151

- Physics, as we know it, attempts to interpret the diverse natural phenomena as particular manifestations of general laws. This vision of a world ruled by general testable laws is relatively recent in the history of mankind. Basically it was initiated by the Galilean inertial principle. The subsequent rapid development of large-scale physics is certainly tributary to the fact that gravitational and electromagnetic forces are long-range and hence can be perceived directly without the mediation of highly sophisticated technical devices. - The discovery of subatomic structures and of the concomitant weak and strong short-range forces raised the question of how to cope with short-range forces in relativistic quantum field theory. The Fermi theory of weak interactions, formulated in terms of point-like current-current interaction, was well-defined in lowest order perturbation theory and accounted for existing experimental data.However, it was inconsistent in higher orders because of uncontrollable divergent quantum fluctuations. In technical terms, in contradistinction to quantum electrodynamics, the Fermi theorywas not “renormalizable”. This difficulty could not be solved by smoothing the point-like interaction by a massive, and therefore short-range, charged “vector” particle exchange: theories with massive charged vector bosons were not renormalizable either. In the early nineteen sixties, there seemed to be insuperable obstacles to formulating a consistent theory with short-range forces mediated by massive vectors. - The breakthrough came from the notion of spontaneous symmetry breaking which arose in the study of phase transitions and was introduced in field theory by Nambu in 1960. - Ferromagnets illustrate the notion in phase transitions. Although no direction is dynamically preferred, the magnetization selects a global orientation. This is a spontaneous broken symmetry(SBS)of rotational invariance. Such continuous SBS imply the existence of “massless” modes (here spin-waves), which are the ancestors of the NG bosons discussed below. Fluctuations of the order parameter (the magnetization) are described by a “massive” SBS mode. - In field theory, Nambu showed that broken chiral symmetry from a spontaneous generation of hadron masses induces massless pseudoscalar modes (identified with a massless limit of pion fields). This illustrates a general phenomenon made explicit by Goldstone: massless Nambu-Goldstone (NG) bosons are a necessary concomitant of spontaneously broken continuous symmetries. Massive SBS scalars bosons describe, as in phase transitions, the fluctuations of the SBS order parameters. - In 1964, with Robert Brout, we discovered a mechanism based on SBS by which short range interactions are generated from long range ones. A similar proposal was then made independently by Higgs in a different approach. Qualitatively, our mechanism works as follows. The long range fundamental electromagnetic and gravitational interactions are governed by extended symmetries,called gauge symmetries, which were supposed to guarantee that the elementary field constituents which transmit the forces, photons or gravitons, be massless. We considered a generalization of the electromagnetic “vector” field, known as Yang-Mills fields, and coupled them to fields which acquire from SBS constant values in the vacuum. These fields pervade space, as did magnetization, but they have no spatial orientation: they are “scalar’’ fields. The vector Yang-Mills fields which interact with the scalar fields become massive and hence the forces they mediate become short ranged. We also showed that the mechanism can survive in absence of elementary scalar fields. - Because of the extended symmetries, the nature of SBS is profoundly altered: the NG fields are absorbed into the massive vector Yang-Mills fields and restore the gauge symmetry. This has a dramatic consequence. To confront precision experiments, the mechanism should be consistent at the quantum mechanical level, or in technical terms, should yield a “renormalizab

None

2011-02-24

152

Positron annihilation studies of an icosahedral quasicrystal and the cubic R phase of Al-Li-Cu

NASA Astrophysics Data System (ADS)

Positron annihilation lifetime and Doppler-broadening measurements have been performed for Bridgman-grown single-grained icosahedral quasicrystal and cubic R phase of Al-Li-Cu. The results are consistent with the existence of triacontahedral clusters with the vacant center in the icosahedral phase as well as in the R phase.

Ohata, T.; Kanazawa, I.; Iwashita, T.; Kishi, K.; Takeuchi, S.

1990-10-01

153

The stress potential function theory for plane elasticity of icosahedral quasicrystals is developed. By introducing stress functions, huge numbers of basic equations involving elasticity of icosahedral quasicrystals are reduced to a single partial differential equation of the 12th order. The general solution of the equation is expressed by 6 analytic functions of complex variable z = x+iy.

Lian-He Li; Tian-You Fan

2006-01-01

154

Partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals

The atomic dynamics of an Al-Ni-Fe decagonal quasicrystal and an Al-Cu-Fe icosahedral quasicrystal are investigated experimentally using the isotopic contrast method in inelastic neutron scattering. The partial spectra of thermal vibrations of copper, nickel, iron, and aluminum atoms in the decagonal and icosahedral quasicrystals are reconstructed directly from the experimental data without recourse to model concepts. The limiting energies and positions of the main features in the partial spectra of atomic thermal vibrations in decagonal and icosahedral quasicrystals are determined. It is established that, in the quasicrystals under investigation, the copper and nickel atoms are bound more weakly than the iron atoms and that the partial vibrational spectrum of aluminum atoms in the quasicrystals is considerably harder than the spectrum of pure metallic aluminum.

Parshin, P. P.; Zemlyanov, M. G. [Russian Research Centre 'Kurchatov Institute' (Russian Federation)], E-mail: zeml@isssph.kiae.ru; Brand, R. A. [Gerhard-Mercator Universitaet Duisburg (Germany)

2007-05-15

155

Does an icosahedral short-range order prevail in glass-forming Zr-Cu melts?

NASA Astrophysics Data System (ADS)

We report on investigations of the static structure factors of glass-forming Zr-Cu alloy melts by combination of the containerless processing technique of electrostatic levitation with diffraction of neutron and synchrotron radiation. The partial Bhatia-Thornton structure factors SNN and SNC were determined from the two total structure factors. While it is widely assumed in literature that the good glass-forming ability of Zr-Cu is related to an icosahedral short-range order prevailing in the melt, our partial structure factors demonstrate that the liquid Zr-Cu is not characterized by a dominant icosahedral short-range order.

Holland-Moritz, Dirk; Yang, Fan; Kordel, Tobias; Klein, Stefan; Kargl, Florian; Gegner, Jan; Hansen, Thomas; Bednarcik, Jozef; Kaban, Ivan; Shuleshova, Olga; Mattern, Norbert; Meyer, Andreas

2012-12-01

156

Inelastic-neutron-scattering measurements of phonons in icosahedral Al-Li-Cu

NASA Astrophysics Data System (ADS)

Inelastic-neutron-scattering measurements on a single grain of icosahedral Al-Li-Cu are presented. Within experimental error the acoustic-phonon dispersion at small, but finite, q is independent of direction, confirming the isotropic elasticity expected for icosahedral crystals. By following the longitudinal-phonon dispersion curve along a fivefold axis we can identify the location of ``quasi-Brillouin-zone boundary.'' The measurements also suggest the presence of an optical or localized mode along the twofold axis at approximately 10-11 meV. We compare these results to theoretical calculations for one- and two-dimensional quasiperiodic systems.

Goldman, A. I.; Stassis, C.; Bellissent, R.; Moudden, H.; Pyka, N.; Gayle, F. W.

1991-04-01

157

NMR study of Li in Al-Li-Cu icosahedral alloys

NASA Astrophysics Data System (ADS)

Nuclear magnetic resonance (NMR) results are presented for lithium in several powder samples with a composition near Al6Li3Cu which suggest a strong relationship between the cubic R phase and the icosahedral phase. All NMR spectra show a broad component which arises from a site in R-phase samples as well as what appears to be a similar site in the icosahedral phase. The pure R phase and samples with an appreciable amount of R-phase material exhibit a second very narrow peak attributable to Li atoms undergoing rapid motion at a different and perhaps interstitial site.

Lee, Cheol; White, David; Suits, B. H.; Bancel, P. A.; Heiney, P. A.

1988-05-01

158

Growth-induced phason strains in icosahedral quasicrystals of Al-Li-Cu

NASA Astrophysics Data System (ADS)

Growth-induced phason strains have been examined by x-ray diffraction in icosahedral quasicrystals of Al-Li-Cu produced by various growth techniques. We find that the amplitudes of peak position shifts indicative of phason strains are about 7 times larger in the melt-spun ribbons as compared with the Bridgman-grown icosahedral crystals and increase logarithmically with growth velocity. The line shapes vary systematically reflecting the growth-induced microstructures. In contrast, the intrinsic peak broadening is very similar for all samples regardless of the growth condition.

Chen, H. S.; Kortan, A. R.; Parsey, J. M., Jr.

1988-07-01

159

Surface preparation and characterization of the icosahedral Al-Pd-Mn-Ga quasicrystal

Auger electron spectroscopy and low-energy electron diffraction (LEED) provide basic information about the structure and composition of the fivefold surface of the quaternary quasicrystal, icosahedral Al67Pd4Mn21Ga8. Surface preparation techniques established previously for two of the icosahedral ternary alloys, Al-Pd-Mn and Al-Cu-Fe, appear to be similarly effective for Al-Pd-Mn-Ga. After annealing in the range 600-950 K, the surface concentration of Ga is constant and low. After annealing in the range 900-950 K, a good LEED pattern is obtained. LEED indicates that Ga changes the surface structure significantly.

Heinzig, Mark; Jenks, Cynthia J.; Van Hove, Michel; Fisher, Ian; Canfield, Paul; Thiel, Patricia A.

2002-01-08

160

Symmetry is usually viewed as a discrete feature: an object is either symmetric or non-symmetric. Following the view that symmetry is a continuous feature, a continuous symmetry measure (CSM) has been developed to evaluate symmetries of shapes and objects. In this paper the authors extend the symmetry measure to evaluate the imperfect symmetry of fuzzy shapes, i.e. shapes with uncertain

Hagit Zabrodsky Hel-or; Shmuel Peleg; David Avnir

1994-01-01

161

Icosahedral B12-containing core-shell structures of B80.

Low-lying icosahedral (I(h)) B(12)-containing structures of B(80) are explored, and a number of core-shell isomers are found to have lower energy than the previous predicted B(80) fullerene. The structural transformation of boron clusters from tubular structure to core-shell structure may occur at a critical size less than B(80). PMID:20448877

Li, Hui; Shao, Nan; Shang, Bo; Yuan, Lan-Feng; Yang, Jinlong; Zeng, Xiao Cheng

2010-06-14

162

Structural Relationship between Icosahedral and Frank-Kasper Phases of Al-Li-Cu,

National Technical Information Service (NTIS)

We report on an X-ray diffraction study of the structure of the icosahedral and Frank-Kasper phases of Al5-5Li3-3Cu. It is shown that the two phases have very similar local structure up to about 20 angstroms, while the long-range structure is quite distin...

W. Dmowski T. Egami Y. Shen S. J. Poon G. J. Shiflet

1987-01-01

163

Calculation of vibrational spectra of an icosahedral quasicrystal AlCuFe

Vibrational spectra of an icosahedral quasicrystal AlCuFe have been calculated on the basis of a crystalline 1/1 approximant by the recurrence method. To describe the interaction of atoms in a quasicrystal, the semiempirical EAM model was used. It is shown that the calculated spectra are in satisfactory agreement with the experimental neutron inelastic scattering data.

Rudenko, A. N., E-mail: ran@infoteck.ru; Mazurenko, V. G. [Ural State University (Russian Federation)

2007-11-15

164

Capping-agent-free synthesis of substrate-supported porous icosahedral gold nanoparticles

NASA Astrophysics Data System (ADS)

We report a new capping-agent-free strategy for the synthesis of substrate-supported porous icosahedral Au nanoparticles (NPs) with rough naked surfaces, based on the crystallization from substrate-supported thin solution layers followed by solid-phase thermolysis. The plasmonic properties of icosahedral Au NPs have been studied using single particle dark-field scattering microscopy and spectroscopy. The two distinct localized surface plasmon resonance (LSPR) bands observed in the single particle dark-field spectra can be ascribed to the quadrupole resonance at ca. 425 nm and the size-dependent dipole resonance in the red region (645-708 nm). The unique rough naked surface, the facile synthesis, together with the ability to control the nanoparticle size and to vary the LSPR frequency in the red region, would make the substrate-supported porous icosahedral Au NPs promising on multiple levels in the applications of catalysis, ultrasensitive biosensors, and in surface-enhanced Raman scattering (SERS).We report a new capping-agent-free strategy for the synthesis of substrate-supported porous icosahedral Au nanoparticles (NPs) with rough naked surfaces, based on the crystallization from substrate-supported thin solution layers followed by solid-phase thermolysis. The plasmonic properties of icosahedral Au NPs have been studied using single particle dark-field scattering microscopy and spectroscopy. The two distinct localized surface plasmon resonance (LSPR) bands observed in the single particle dark-field spectra can be ascribed to the quadrupole resonance at ca. 425 nm and the size-dependent dipole resonance in the red region (645-708 nm). The unique rough naked surface, the facile synthesis, together with the ability to control the nanoparticle size and to vary the LSPR frequency in the red region, would make the substrate-supported porous icosahedral Au NPs promising on multiple levels in the applications of catalysis, ultrasensitive biosensors, and in surface-enhanced Raman scattering (SERS). Electronic supplementary information (ESI) available: SEM images of icosahedral Au(iii) NPs before being subjected to solid-phase thermolysis. See DOI: 10.1039/c3nr34000g

Wu, Ji Hong; Guan, Zhenping; Yang, Su Ke; Yuan, Peiyan; Xu, Qing-Hua; Xu, Guo Qin

2013-03-01

165

NASA Astrophysics Data System (ADS)

We show by molecular dynamics simulations that symmetrical quasi-icosahedral structures can be formed in fivefold twinned metallic nanowires (Cu, Au, and Ag) under dynamic tensile loading. The quasi-icosahedral structure, different from the icosahedral nanoclusters found in the past, consists of a twisted original fivefold twinned axis and ten secondary fivefold deformation twins, with five preexisting prismatic and fifteen tetrahedral subunits joined adjacently. Formation of these structures is observed in the necking region during the plastic deformation with successive twinning processes and is found to be independent on the cross-sectional shape as well as the tensile strain rate of the nanowires.

Jiang, Shan; Shen, Yonggang; Zheng, Yonggang; Chen, Zhen

2013-07-01

166

Chiral Symmetry and Chiral-Symmetry Breaking.

National Technical Information Service (NTIS)

These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the real...

M. E. Peskin

1982-01-01

167

Overview of Molecular Symmetry Operations and Symmetry

NSDL National Science Digital Library

This site provides an overview of symmetry operations from a chemistry perspective. The site includes animated and interactive activities designed for students learning about symmetry operations. Tutorial exercises are provided.

168

NASA Astrophysics Data System (ADS)

This article presents a statistical study based on molecular dynamics simulations of the formation of icosahedral nanowires from the breakage of Al, Ni and Cu nanowires. These icosahedral nanowires, which show large stability, are created by the emergence of new units of 5 + 1 atoms (atomic pentagonal rings plus one atom at the top) due to the anisotropic growing mechanism induced by nanowire stretching. The appearance of each new 5 + 1 atomic set (an inelastic atomic rearrangement) during the stretching is matched with a sudden decrease of the force exerted on nanowire extremes. We have also demonstrated that the icosahedral formation is favoured when stretching takes place along the [1?0?0] and [1?1?0] crystallographic directions. We demonstrate that, as result of a balance between two competitive mechanisms, there exists an optimal temperature that provides the larger icosahedral nanowires production for each metallic species.

García-Mochales, P.; Peláez, S.; Serena, P. A.; Guerrero, C.; Paredes, R.

2013-06-01

169

NASA Astrophysics Data System (ADS)

Room temperature57Fe Mössbauer effect spectra of several Al-TM-Fe icosahedral quasicrystals are reported. Results of fits to discrete sites and to various distributions of quadrupole splittings are presented. Mean isomer shifts,overline ? , and quadrupole splittings, ?, are shown to be insensitive to the fitting procedure used. Trends inoverline ? andoverline ? for the icosahedral phase may be indicative of a Hume-Rothery stabilization mechanism.

Lawther, D. W.; Dunlap, R. A.; Srinivas, V.; Lloyd, D. J.; Jha, S.

1990-08-01

170

Magnetic field dependence of the rare earth B 12 icosahedral cluster compound GdB 18Si 5

Magnetic field dependence of the rare earth B12 icosahedral cluster compound GdB18Si5 was investigated. GdB18Si5 is the only system in the rare earth boron icosahedral cluster compounds in which 3 dimensional long range order has been observed. GdB18Si5 exhibits an antiferromagnetic transition at TN=3.2K, with the spins antiferromagnetically aligned in-plane, perpendicular to [001]. The magnetic phase diagram was determined for

Takao Mori

2005-01-01

171

NASA Astrophysics Data System (ADS)

Computational calculations of Becke's three-parameter hybrid method using the LYP correlation functional (B3LYP) have been performed on (B 12H 12) 2- dodecaborane anions with different boron isotopic compositions. This was done in order to investigate isotopic dependence of vibrational spectral properties of B 12 icosahedra, and for comparison of the optical vibrational properties of the icosahedral molecule with the characteristics of inter- or intra-icosahedral optical phonon vibrational modes in boron-rich crystals.

Nogi, Naoyuki; Tanaka, Satoru

2006-09-01

172

An icosahedral algal virus has a complex unique vertex decorated by a spike

Paramecium bursaria Chlorella virus-1 is an icosahedrally shaped, 1,900-?-diameter virus that infects unicellular eukaryotic green algae. A 5-fold symmetric, 3D reconstruction using cryoelectron microscopy images has now shown that the quasiicosahedral virus has a unique vertex, with a pocket on the inside and a spike structure on the outside of the capsid. The pocket might contain enzymes for use in the initial stages of infection. The unique vertex consists of virally coded proteins, some of which have been identified. Comparison of shape, size, and location of the spike with similar features in bacteriophages T4 and P22 suggests that the spike might be a cell-puncturing device. Similar asymmetric features may have been missed in previous analyses of many other viruses that had been assumed to be perfectly icosahedral.

Cherrier, Mickael V.; Kostyuchenko, Victor A.; Xiao, Chuan; Bowman, Valorie D.; Battisti, Anthony J.; Yan, Xiaodong; Chipman, Paul R.; Baker, Timothy S.; Van Etten, James L.; Rossmann, Michael G.

2009-01-01

173

This project set out to use these multilingual programming techniques to parallelize an existing Fortran program. This program is an implementation of the shallow water equations using the icosahedral hexagonal grid system to integrate over a sphere. Our objective was to test the usefulness of multilingual techniques, to evaluate the new language PCN (Program Composition Notation), and to investigate the parallel execution characteristics of the icosahedral-hexagonal algorithm. Two features of PCN make it a useful language for parallelization. The first of these is single assignment variables. Communication and synchronization between processes is represented by reading and writing to these variables. This feature simplifies the specification of complex protocols, reducing them to variable creation and assignment. Second, PCN decouples process mapping from concurrent execution. Mapping is specified annotations to procedure calls, which indicate the processor on which execution of the procedure is to take place. Variables passed into the procedure then become message streams to that processor. 8 refs., 2 figs.

Hammond, S.J. (Maine Univ., Orono, ME (USA). Dept. of Computer Science)

1991-01-01

174

Formation of a well ordered ultrathin aluminum oxide film on icosahedral AlPdMn quasicrystal

We have exposed the pentagonal surface of icosahedral AlPdMn quasicrystal kept at 700 K to several hundred langmuirs of O{sub 2}, which results in the formation of a 5 A thick, well ordered aluminum oxide film. The local structure of the film resembles that of the oxide layers formed on ordered binary alloys of Al except that the quasicrystalline substrate makes the film consist of five pairs of nanometer-size aluminum oxide domains exposing their nominal (111) faces parallel to the substrate surface and rotated by 72 deg. with respect to each other. The orientational relationship between these domains and the substrate is a consequence of the affinity of the icosahedral structure of AlPdMn to the CsCl structure.

Longchamp, J.-N.; Burkardt, S.; Weisskopf, Y. [Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich (Switzerland); Erbudak, M. [Laboratory for Solid State Physics, ETH Zurich, 8093 Zurich (Switzerland); Department of Physics, Faculty of Arts and Sciences, Bogazici University, 34342 Bebek, Istanbul (Turkey)

2007-09-01

175

Adsorption sites on icosahedral quasicrystal surfaces: dark stars and white flowers.

From other work, two preferred sites have been suggested for metals and semimetals adsorbed on the fivefold surfaces of icosahedral, Al-based quasicrystals. Because of their appearance in scanning tunneling microscopy (STM) images, these sites are known as dark stars and white flowers. In this paper, we analyze four bulk structural models in physical space to determine the types, chemical decorations, and densities of the dark star-and, to a lesser extent, the white flower-adsorption sites for the fivefold planes of icosahedral Al-Pd-Mn. We find that the chemical decorations of these sites are heterogeneous, even within a single model. Both features are also structurally heterogeneous, according to STM measurements, and the structural variation is consistent with the bulk structure models. Finally, from the models, the density of dark stars in the planes correlates with the step height. This may explain previous experimental observations of different properties for different terraces. PMID:21817296

Unal, Bari?; Jenks, C J; Thiel, P A

2009-02-01

176

The Capsid Proteins of a Large, Icosahedral dsDNA Virus

Summary Chilo iridescent virus (CIV) is a large (~1850 Å diameter) insect virus with an icosahedral, T=147 capsid, a dsDNA genome, and an internal lipid membrane. The structure of CIV was determined to 13 Å resolution by means of cryo-electron microscopy (cryoEM) and three-dimensional image reconstruction. A homology model of P50, the CIV major capsid protein (MCP), was built based on its amino acid sequence and the structure of the homologous Paramecium bursaria chlorella virus 1 (PBCV-1) Vp54 MCP. This model was fitted into the cryoEM density for each of the 25 trimeric CIV capsomers per icosahedral asymmetric unit. A difference map, in which the fitted CIV MCP capsomers were subtracted from the CIV cryoEM reconstruction, showed that there are at least three different types of minor capsid proteins associated with the capsomers outside the lipid membrane. “Finger” proteins are situated at many, but not all, of the spaces between three adjacent capsomers within each trisymmetron, and “zip” proteins are situated between sets of three adjacent capsomers at the boundary between neighboring trisymmetrons and pentasymmetrons. Based on the results of segmentation and density correlations, there are at least eight finger proteins, and three dimeric and two monomeric zip proteins in one asymmetric unit of the CIV capsid. These minor proteins appear to stabilize the virus by acting as intercapsomer cross-links. One transmembrane “anchor” protein per icosahedral asymmetric unit, which extends from beneath one of the capsomers in the pentasymmetron to the internal leaflet of the lipid membrane, may provide additional stabilization for the capsid. These results are consistent with the observations for other large, icosahedral dsDNA viruses that also utilize minor capsid proteins for stabilization and determining their assembly.

Yan, Xiaodong; Yu, Zeyun; Zhang, Ping; Battisti, Anthony J.; Chipman, Paul R.; Bajaj, Chandrajit; Bergoin, Max; Rossmann, Michael G.; Baker, Timothy S.

2010-01-01

177

The dynamical characteristics of the tropical tropopause layer (TTL) are investigated using the Nonhydrostatic Icosahedral Atmospheric Model (NICAM) run on the Earth Simulator under an aqua planet condition. Two experiments are performed: one with a 3.5 km horizontal spacing and a three-dimensional snapshot output and another with a 7 km horizontal spacing and 3-hourly averages for 1 month. The number

H. Kubokawa; M. Fujiwara; T. Nasuno; M. Satoh

2010-01-01

178

Regulation of Icosahedral Virion Capsid Size by the in vivo Activity of a Cloned Gene Product

Determination of icosahedral virion capsid size can be directly studied during helper-dependent lytic development of satellite P4 because the assembly pathway specified by the P2 helper virus is altered to yield smaller-sized capsids. Size determination (sid) mutations identify a P4-encoded function regulating this process. To determine whether the sid gene product is necessary and sufficient to redirect the assembly pathway,

Manju Agarwal; Michel Arthur; Robert D. Arbeit; Richard Goldstein

1990-01-01

179

Near-atomic resolution reconstructions of icosahedral viruses from electron cryo-microscopy

Nine different near-atomic resolution structures of icosahedral viruses, determined by electron cryo-microscopy and published between early 2008 and late 2010, fulfill predictions made 15 years ago that single-particle cryo-EM techniques could visualize molecular detail at 3 – 4 Å resolution. This review summarizes technical developments, both in instrumentation and in computation, that have led to the new structures, which advance our understanding of virus assembly and cell entry.

Grigorieff, Nikolaus; Harrison, Stephen C.

2011-01-01

180

High temperature vacancy studies of icosahedral Zn65Mg25Er10 quasicrystal

Formation of thermal vacancies in icosahedral Zn65Mg25Er10 quasicrystals has been specifically studied from room temperature to about 720 K by positron annihilation spectroscopy employing two-detector coincident Doppler broadening techniques. Significant vacancy formation was observed for temperatures higher than 0.6Tm. An apparent vacancy formation enthalpy of 1.2 eV was determined. The results are discussed in comparison with high temperature vacancy processes

F. Ye; W. Sprengel; X. Y. Zhang; E. Uhrig; W. Assmus; H.-E. Schaefer

2004-01-01

181

Capping-agent-free synthesis of substrate-supported porous icosahedral gold nanoparticles.

We report a new capping-agent-free strategy for the synthesis of substrate-supported porous icosahedral Au nanoparticles (NPs) with rough naked surfaces, based on the crystallization from substrate-supported thin solution layers followed by solid-phase thermolysis. The plasmonic properties of icosahedral Au NPs have been studied using single particle dark-field scattering microscopy and spectroscopy. The two distinct localized surface plasmon resonance (LSPR) bands observed in the single particle dark-field spectra can be ascribed to the quadrupole resonance at ca. 425 nm and the size-dependent dipole resonance in the red region (645-708 nm). The unique rough naked surface, the facile synthesis, together with the ability to control the nanoparticle size and to vary the LSPR frequency in the red region, would make the substrate-supported porous icosahedral Au NPs promising on multiple levels in the applications of catalysis, ultrasensitive biosensors, and in surface-enhanced Raman scattering (SERS). PMID:23455229

Wu, Ji Hong; Guan, Zhenping; Yang, Su Ke; Yuan, Peiyan; Xu, Qing-Hua; Xu, Guo Qin

2013-04-01

182

Relaxation of icosahedral-cage silicon clusters via tight-binding molecular dynamics

We have used a tight-binding total-energy expression for silicon to study the stability and structure of relatively large silicon clusters. Relaxation is performed using a fictitious Lagrangian and molecular dynamics. Specifically, we have looked at the relaxation of 50-, 60-, and 70-atom spheroidal hollow (icosahedral-cage-structure) clusters. We find that these clusters are not stable and relax into structures which look like puckered balls. Our results show that the unrelaxed clusters are metallic and the relaxed clusters are insulating with the Fermi level passing between localized states. We have also examined the relaxation of large clusters (size of about 100 atoms) extracted from pure diamond, fcc, and sc bulk silicon. We find that the cohesive energies of the relaxed icosahedral-cage clusters are greater than the relaxed diamond clusters and less than the relaxed fcc clusters. We also find that a single layer of flat silicon graphite is not stable and relaxes into a nonplanar layer with properties very similar to those of the relaxed icosahedral clusters.

Khan, F.S. (Department of Electrical Engineering, The Ohio State University, Columbus, Ohio 43210 (USA) Department of Physics, Brookhaven National Laboratory, Upton, New York 11973 (USA)); Broughton, J.Q. (Complex Systems Theory Group, Naval Research Laboratory, Washington, D.C. 20375 (USA))

1991-05-15

183

NASA Astrophysics Data System (ADS)

It is well-known that vibronic interactions can be modelled in terms of an effective Hamiltonian incorporating first and second-order reduction factors (RFs), particularly when analysing the spectroscopic properties. Measurements and calculations of the RFs as a function of the strength of vibronic coupling are therefore of much interest. In this paper, we develop a new general method for determining second-order RFs (soRFs) from the strength of the Jahn-Teller (JT) coupling for systems in which electron orbital degeneracy or pseudo-degeneracy exists. These include in particular the fullerene molecule C60, pseudo-Jahn-Teller molecules and impurity centres in crystals. In order to calculate the important soRFs for intermediate to strong coupling, it is necessary to determine non-Condon corrections to the strong coupling values obtained using the Franck-Condon (FC) approximation. This gives an additional contribution to the nuclear polarizability of the system, thus enabling the electrons to follow the nuclear vibrations. These non-Condon corrections are derived using perturbation theory and are found to be inversely proportional to the square of the JT energy. The validity of the approximation is first tested in the cubic T\\otimes t_2 JT system due to its relative simplicity. It is found that the results are closer to those obtained earlier by numerical methods than the analytical FC values alone. Results are then presented that are applicable to C60- anions.

Bates, Colin A.; Abou-Ghantous, Michel; Dunn, Janette L.; Al-Hazmi, Faten; Polinger, Victor Z.; Moujaes, Elie A.

2004-07-01

184

Symmetry-adapted spherical harmonics method for high-resolution 3D single-particle reconstructions.

Three-dimensional (3D) reconstruction is the last and an essential step toward high-resolution structural determination in single-particle cryo-electron microscopy (cryoEM). We have implemented a new algorithm for reconstructing 3D structures of macromolecular complexes with icosahedral symmetry from cryoEM images. Icosahedral symmetry-adapted functions (ISAFs) are used to interpolate structural factors in the reciprocal space to generate a 3D reconstruction in spherical coordinates. In our implementation, we introduced a recursive method for deriving higher order ISAFs from three lower order seed functions. We demonstrate improvements of our new method in both the noise suppression and the effective resolution in 3D reconstruction over the commonly used Fourier-Bessel synthesis method introduced by Crowther et al. three decades ago. Our 3D reconstruction method can be extended to macromolecular complexes with other symmetry types and is thus likely to impact future high-resolution cryoEM single-particle reconstruction efforts in general. PMID:17977017

Liu, Hongrong; Cheng, Lingpeng; Zeng, Songjun; Cai, Canying; Zhou, Z Hong; Yang, Qibin

2008-01-01

185

Geometric intrinsic symmetries

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.

Gozdz, A., E-mail: Andrzej.Gozdz@umcs.lublin.pl; Szulerecka, A.; Pedrak, A. [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)] [University of Maria Curie-Sklodowska, Institute of Physics, Department of Mathematical Physics (Poland)

2013-08-15

186

NSDL National Science Digital Library

This engaging lesson simultaneously involves animals, flowers, mathematical patterns, and art. Students will learn to discern between radial symmetry, bilateral symmetry, and asymmetry by observing and classifying objects, shapes, and photos and by determ

Eichinger, John

2009-05-30

187

Symmetry can simplify the control of dynamic legged sys tems. In this paper, the symmetries studied describe motion of the body and legs in terms of even and odd functions of time. A single set of equations describes symmetric running for systems with any number of legs and for a wide range of gaits. Techniques based on symmetry have been

Marc H. Raibert

1986-01-01

188

Flowers can be classified into two basic types according to their symmetry: regular flowers have more than one plane of symmetry and irregular flowers have only a single plane of symmetry. The irregular condition is thought to have evolved many times independently from the regular one: most commonly through the appearance of asymmetry along the dorso-ventral axis of the flower.

Enrico S. Coen; Jacqueline M. Nugent; Da Luo; Desmond Bradley; Pilar Cubas; Mark Chadwick; Lucy Copsey; Rosemary Carpenter

1995-01-01

189

Chiral symmetry and chiral-symmetry breaking

These lectures concern the dynamics of fermions in strong interaction with gauge fields. Systems of fermions coupled by gauge forces have a very rich structure of global symmetries, which are called chiral symmetries. These lectures will focus on the realization of chiral symmetries and the causes and consequences of thier spontaneous breaking. A brief introduction to the basic formalism and concepts of chiral symmetry breaking is given, then some explicit calculations of chiral symmetry breaking in gauge theories are given, treating first parity-invariant and then chiral models. These calculations are meant to be illustrative rather than accurate; they make use of unjustified mathematical approximations which serve to make the physics more clear. Some formal constraints on chiral symmetry breaking are discussed which illuminate and extend the results of our more explicit analysis. Finally, a brief review of the phenomenological theory of chiral symmetry breaking is presented, and some applications of this theory to problems in weak-interaction physics are discussed. (WHK)

Peskin, M.E.

1982-12-01

190

A 3-D Finite-Volume Non-hydrostatic Icosahedral Model (NIM)

NASA Astrophysics Data System (ADS)

The Nonhydrostatic Icosahedral Model (NIM) formulates the latest numerical innovation of the three-dimensional finite-volume control volume on the quasi-uniform icosahedral grid suitable for ultra-high resolution simulations. NIM's modeling goal is to improve numerical accuracy for weather and climate simulations as well as to utilize the state-of-art computing architecture such as massive parallel CPUs and GPUs to deliver routine high-resolution forecasts in timely manner. NIM dynamic corel innovations include: * A local coordinate system remapped spherical surface to plane for numerical accuracy (Lee and MacDonald, 2009), * Grid points in a table-driven horizontal loop that allow any horizontal point sequence (A.E. MacDonald, et al., 2010), * Flux-Corrected Transport formulated on finite-volume operators to maintain conservative positive definite transport (J.-L, Lee, ET. Al., 2010), *Icosahedral grid optimization (Wang and Lee, 2011), * All differentials evaluated as three-dimensional finite-volume integrals around the control volume. The three-dimensional finite-volume solver in NIM is designed to improve pressure gradient calculation and orographic precipitation over complex terrain. NIM dynamical core has been successfully verified with various non-hydrostatic benchmark test cases such as internal gravity wave, and mountain waves in Dynamical Cores Model Inter-comparisons Projects (DCMIP). Physical parameterizations suitable for NWP are incorporated into NIM dynamical core and successfully tested with multimonth aqua-planet simulations. Recently, NIM has started real data simulations using GFS initial conditions. Results from the idealized tests as well as real-data simulations will be shown in the conference.

Lee, Jin

2014-05-01

191

Mg32(Zn,Al)49-type icosahedral quasicrystals formed by solid-state reaction and rapid solidification

NASA Astrophysics Data System (ADS)

Icosahedral quasicrystals of Al-Mg-Zn, Al-Mg-Cu, Al-Li-Zn, and Al-Li-Cu are formed by low-temperature annealing of solid-solution alloys. Comparison is made with icosahedral Al-Mg-Cu, Al-Mg-Zn, and Al-Li-Cu prepared by rapid solidification. The compositions of the icosahedral compounds formed by solid-state reaction are similar to those observed in the rapidly solidified samples. The stability of these new phases is discussed. X-ray line intensities are found to agree well with the computed intensities for a quasicrystalline model based on the (Mg-Zn-Al)-type decoration of the three-dimensional Penrose tiles.

Cassada, W. A.; Shen, Y.; Poon, S. J.; Shiflet, G. J.

1986-11-01

192

NASA Astrophysics Data System (ADS)

The correlation between structural relaxation and the medium-range structures formed by icosahedral cluster packing in CuZr supercooled metallic glass-forming liquids was studied via molecular dynamics simulations. We find that compared to the amount of icosahedral clusters, the medium-range structures formed by icosahedral cluster packing play more important and controlling roles in the structural relaxation process of the supercooled liquids. The relaxation times of local structures depend exponentially on the connectivity of local structures. Despite the argument whether there is a specific connection between the static structure and dynamic property of glass formers in particle level, it does exist on larger length scale. Our results demonstrate that dynamical heterogeneity is indeed correlated with the medium-range static atomic structures in the supercooled glass-forming liquids.

Wu, Z. W.; Li, M. Z.; Wang, W. H.; Liu, K. X.

2013-08-01

193

Short-range order and singularities of the electronic structure of icosahedral quasicrystals

NASA Astrophysics Data System (ADS)

For icosahedral phases of the Al-Cu-Fe system, components of the electrical conductivity, magnetic susceptibility, Hall effect, and heat capacity associated with thermally induced charge carriers for the first time have been considered jointly over a wide temperature range. It has been shown that the full range of thermal effects can be understood in the framework of the unified concept, which is based on an inhomogeneous system of two-level electronic excitations. A model of the inhomogeneous electronic state and the mechanism of its formation with the dominant role of short-range order have been proposed.

Prekul, A. F.; Shchegolikhina, N. I.

2013-11-01

194

Formation of an Icosahedral Quasicrystal in the Mg-Al-Pt System

A Frank-Kasper-type (FK-type) icosahedral phase (i-phase) has been found to form in the Mg-Al-Pt system of Mg45Al42Pt13 composition. The i-phase is formed by heating an amorphous phase produced by a melt-spinning technique up to 673 K@. We have also investigated the formation of the FK-type i-phase in the ternary Mg-Al-X (X=Co, Ni, Rh and Au) systems and find no trace

Naokiyo Koshikawa; Shinichi Yoda; Keiichi Edagawa; Shin Takeuchi

2001-01-01

195

Solution growth of a binary icosahedral quasicrystal of Sc[subscript 12]Zn[subscript 88

We report the discovery of a binary icosahedral phase in a Sc-Zn alloy obtained through solution-growth, producing millimeter-sized, facetted, single grain quasicrystals that exhibit different growth morphologies, pentagonal dodecahedra, and rhombic triacontahedra, under only marginally different growth conditions. These two morphologies manifest different degrees of quasicrystalline order. The discovery of i-Sc{sub 12}Zn{sub 88} suggests that a re-examination of binary phase diagrams at compositions close to crystalline approximant structures may reveal other binary quasicrystalline phases.

Canfield, P.C.; Caudle, M.L.; Ho, C.-S.; Kreyssig, A.; Nandi, S.; Kim, M.G.; Lin, X.; Kracher, A.; Dennis, K.W.; McCallum, R.W.; Goldman, A.I. (Iowa State)

2010-07-23

196

Dynamical x-ray diffraction from an icosahedral Al-Pd-Mn quasicrystal

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.

Kycia, S.

1996-04-23

197

The properties of the (n,n) icosahedral family of carbon fullerenes up to n = 10 (6000 atoms) have been investigated through ab initio quantum-mechanical simulation by using a Gaussian type basis set of double zeta quality with polarization functions (84?000 atomic orbitals for the largest case), the hybrid B3LYP functional and the CRYSTAL14 code featuring generalization of symmetry treatment. The geometry of giant fullerenes shows hybrid features, between a polyhedron and a sphere; as n increases, it approaches the former. Hexagon rings at face centres take a planar, graphene-like configuration; the 12 pentagon rings at vertices impose, however, a severe structural constraint to which hexagon rings at the edges must adapt smoothly, adopting a bent (rather than sharp) transversal profile and an inward longitudinal curvature. The HOMO and LUMO electronic levels, as well as the band gap, are well described using power laws. The gap is predicted to become zero for n ? 34 (69?360 atoms). The atomic excess energy with respect to the ideal graphene sheet goes to zero following the log(Nat)/Nat law, which is well described through the continuum elastic theory applied to graphene; the limits for the adopted model are briefly outlined. Compared to larger fullerenes of the series, C60 shows unique features with respect to all the considered properties; C240 presents minor structural and energetic peculiarities, too. PMID:24879509

Noël, Yves; De La Pierre, Marco; Zicovich-Wilson, Claudio M; Orlando, Roberto; Dovesi, Roberto

2014-06-11

198

Mode characteristics for two-dimensional equilateral-polygonal microresonators are investigated based on symmetry analysis and finite-difference time-domain numerical simulation. The symmetries of the resonators can be described by the point group C{sub Nv}, accordingly, the confined modes in these resonators can be classified into irreducible representations of the point group C{sub Nv}. Compared with circular resonators, the modes in equilateral-polygonal resonators have different characteristics due to the break of symmetries, such as the split of double-degenerate modes, high field intensity in the center region, and anomalous traveling-wave modes, which should be considered in the designs of the polygonal resonator microlasers or optical add-drop filters.

Yang Yuede; Huang Yongzhen [State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, Chinese Academy of Sciences, P.O. Box 912, Beijing 100083 (China)

2007-08-15

199

Medium-range icosahedral order in quasicrystal-forming Zr{sub 2}Pd binary metallic glass

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.

Huang Li [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Fang, X. W. [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Department of Physics and Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China); Wang, C. Z.; Ho, K. M. [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Department of Physics, Iowa State University, Ames, Iowa 50011 (United States); Kramer, M. J. [Ames Laboratory, U.S. Department of Energy, Ames, Iowa 50011 (United States); Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States); Ding, Z. J. [Department of Physics and Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)

2011-06-06

200

Ion beam induced destabilization of icosahedral structures in gas phase prepared FePt nanoparticles

Multiply twinned FePt nanoparticles with icosahedral structures were prepared by dc magnetron sputtering in argon. The icosahedral structure of these particles is known to be very stable against structural transformations into both the face-centered cubic phase (fcc, A1) and the chemically ordered tetragonal L1{sub 0} phase upon in-flight or post-deposition thermal annealing. Irradiation of these multiply twinned FePt particles with 5 keV He ions, however, resulted in a transformation into predominantly single crystalline fcc particles at high ion fluences of f>10{sup 17} ions/cm{sup 2}. Adjacent particles were observed to coalesce under the effect of He irradiation, and the size of individual particles was found to be slightly reduced, which indicates a high atomic mobility owing to temporarily enhanced defect concentrations caused by the ion bombardment. Strikingly, there was no indication for the occurrence of L1{sub 0} ordered FePt nanoparticles upon ion irradiation in these samples.

Dmitrieva, Olga; Rellinghaus, Bernd; Kaestner, Jochen; Liedke, Maciej Oskar; Fassbender, Juergen [Experimentalphysik, AG Farle, Universitaet Duisburg - Essen, D-47048 Duisburg (Germany); IFW Dresden, Institut fuer Metallische Werkstoffe, D-01171 Dresden (Germany); Experimentalphysik, AG Farle, Universitaet Duisburg - Essen, D-47048 Duisburg (Germany); Fachbereich Physik, Technische Universitaet Kaiserslautern, D-67663 Kaiserslautern, Germany and Forschungszentrum Rossendorf, Institut fuer Ionenstrahlphysik und Materialforschung, D-01314 Dresden (Germany); Forschungszentrum Rossendorf, Institut fuer Ionenstrahlphysik und Materialforschung, D-01314 Dresden (Germany)

2005-05-15

201

Crystal-symmetry preserving Wannier states for fractional Chern insulators

NASA Astrophysics Data System (ADS)

Recently, many numerical evidences of fractional Chern insulator, i.e., the fractional quantum Hall states on lattices, are proposed when a Chern band is partially filled. Some trial wave functions of fractional Chern insulators can be obtained by mapping the fractional quantum Hall wave functions defined in the continuum onto the lattice through the Wannier state representation [Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.126803 107, 126803 (2011)] in which the single particle Landau orbits in the Landau levels are identified with the one-dimensional Wannier states of the Chern bands with Chern number C=1. However, this mapping generically breaks the lattice point group symmetry. In this paper we discuss a general approach of modifying the mapping to accommodate the lattice rotational symmetry. The wave functions constructed through this modified mapping should serve as better trial wave functions in the thermodynamical limit and on the rotationally invariant finite lattice. Also these wave functions will form a good basis for the construction of lattice symmetry preserving pseudopotential formalism for fractional Chern insulators. The focus of this paper shall be mainly on the C4 rotational symmetry of square lattices. Similar analysis can be straightforwardly generalized to triangular or hexagonal lattices with C6 symmetry. We also generalize the discussion to the lattice symmetry of fractional Chern insulators with high Chern number bands.

Jian, Chao-Ming; Qi, Xiao-Liang

2013-10-01

202

The mechanism of the dominance (preponderance) of the 0+ ground state for random interactions is proposed to be the chaotic realization of the highest rotational symmetry. This is a consequence of a general principle on the chaos and symmetry that the highest symmetry is given to the ground state if sufficient mixing occurs in a chaotic way by a random interaction. Under this symmetry-realization mechanism, the ground-state parity and isospin can be predicted so that the positive parity is favored over the negative parity and the isospin T = 0 state is favored over higher isospin. It is further suggested how one can enhance the realization of highest symmetries within random interactions. Thus, chaos and symmetry are shown to be linked deeply.

Otsuka, Takaharu [Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); Center for Nuclear Study, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); RIKEN, Hirosawa, Wako-shi, Saitama, 351-0198 (Japan); Shimizu, Noritaka [Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); RIKEN, Hirosawa, Wako-shi, Saitama, 351-0198 (Japan)

2004-09-13

203

NASA Technical Reports Server (NTRS)

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.

Dyall, Kenneth G.; Arnold, James O. (Technical Monitor)

1994-01-01

204

NSDL National Science Digital Library

In this problem set, students are given space group symmetry diagrams for primitive (P) orthorhombic space groups. For each diagram they must write down the symmetry axis (either 2 or 21) that is parallel to each major axis, and give the symmetry plane (a, b, c, n, or m) that is normal (perpendicular)to each. They must also give the simplified Hermann-Mauguin symbol for the space group.

205

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.

Sekhar Chivukula

2010-01-08

206

Performance Analysis of high-order remap-type advection scheme on icosahedral-hexagonal grid

NASA Astrophysics Data System (ADS)

A comparative performance analysis on computational cost of second order advection schemes FF-CSLAM (Flux form conservative semi-Lagrangian multi-tracer transport scheme) and it's two simplifications on Icosahedral grid has been presented. Tracer transport is one of the main building blocks in atmospheric models and hence their performance greatly determines the overall performance of the model. FF-CSLAM falls in the category of arbitrary Lagrangian Eulerian (ALE) scheme. It exploits the finite volume formulation and therefore it is inherently conservative. Flux-area through edges are approximated with great circle arcs in an upwind fashion. Bi-quadratic sub-grid scale reconstructions using weighted least-squares method is employed to approximate trace field. Area integrals on the overlapped region of flux-area and static Eulerian meshes are evaluated via line-integrals. A brief description of implementation of FF-CSLAM on icosahedral -hexagonal meshes along with and its numerical accuracy in terms of standard test cases will be presented. A comparative analysis of the computational overhead is necessary to assess the suitability of FF-CSLAM for massively parallel and multi-threading computer architectures in comparison to other advection schemes implemented on icosahedral grids. The main focus of this work is to present the implementation of the shared memory parallelization and to describe the memory access pattern of the numerical scheme. FF-CSLAM is a remap-type advection scheme, thus extra calculation are done in comparison to the other advection schemes. The additional computations are associated with the search required to find the overlap area between the area swept through the edge and the underlining grid. But the experiments shows that the associated computational overhead is minimal for multi-tracer transport. It will be shown that for the Courant Number less than one, FF-CSLAM, the computations are not expensive. Since the grid cells are arranged in rectangular array just like cubed-sphere or lat-lon grids, the schemes computational performance is similar to that of the similar schemes on geodesic grids.

Mittal, Rashmi; Dubey, Sarvesh; Saxena, Vaibhav; Meurdesoif, Yann

2014-05-01

207

NSDL National Science Digital Library

In this simulation, you will learn about axial symmetry and the difference between the axes. Just drag and drop the shapes onto the grid and choose between the different axes of symmetry to see the effect it has on the various shapes.

2007-01-01

208

Symmetries in Lagrangian Dynamics

ERIC Educational Resources Information Center

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…

Ferrario, Carlo; Passerini, Arianna

2007-01-01

209

Symmetry in Mathematics Learning.

ERIC Educational Resources Information Center

Discusses the creed in symmetry and the omnipresence of symmetrical relationships in mathematics and nature, discusses mathematicians' attraction toward looking for symmetrical relationships as an unstated problem-solving heuristic, and shows how symmetry can be used as a didactical tool. (Author/MKR)

Dreyfus, Tommy; Eisenberg, Theodore

1989-01-01

210

Better Verification Through Symmetry

We address the state explosion problem in automatic verification of finite-state systemsby exploiting symmetries in the system description.We make symmetries easy to detect by introducing a new data type scalarset, a finiteand unordered set, to our description language. The set of operations on scalarsets arerestricted so that states are guaranteed to have the same future behavior, up to permutationof the

C. Norris Ip; David L. Dill

1996-01-01

211

NSDL National Science Digital Library

In this hands-on activity, learners make New Year's Eve party hats out of wrapping paper. Learners use symmetry and measurement to cut out shapes they need to assemble the hats. In a related video, Mr. O and his assistants explain how to make the party hats using rotational symmetry. Learners can watch this video before creating their hats.

Houston, Children'S M.

2011-01-01

212

Defining criteria for oligomannose immunogens for HIV using icosahedral virus capsid scaffolds.

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

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

213

Terrace-dependent nucleation of small Ag clusters on a five-fold icosahedral quasicrystal surface

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.

Unal, B.; Evans, J.W.; Lograsso, T.A.; Ross, A.R.; Jenks, C.J.; Thiel, P.A.

2007-07-21

214

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

Legendre, Matthieu; Bartoli, Julia; Shmakova, Lyubov; Jeudy, Sandra; Labadie, Karine; Adrait, Annie; Lescot, Magali; Poirot, Olivier; Bertaux, Lionel; Bruley, Christophe; Couté, Yohann; Rivkina, Elizaveta; Abergel, Chantal; Claverie, Jean-Michel

2014-03-18

215

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

Yan, Xiaodong; Cardone, Giovanni; Zhang, Xing; Zhou, Z Hong; Baker, Timothy S

2014-04-01

216

Family hierarchy from symmetry breaking

We investigate symmetry breaking patterns from replicated gauge groups which generate anomaly-free and family-dependent U(1) symmetries. We discuss the extent to which these symmetries can explain the observed hierarchies of fermion masses and mixings.

Fu-Sin Ling; Pierre Ramond

2003-01-01

217

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.

Pauling, L. (Linus Pauling Institute of Science and Medicine, Palo Alto, CA (USA))

1988-07-01

218

NASA Astrophysics Data System (ADS)

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.

Castaños, Octavio

2010-09-01

219

Polymer quantization and symmetries

NASA Astrophysics Data System (ADS)

Polymer quantization was rediscoveredPlease see acknowledgements. 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 realized 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 and the polymer-quantized scalar field.

Date, Ghanashyam; Kajuri, Nirmalya

2013-04-01

220

NASA Astrophysics Data System (ADS)

The importance of symmetries in 5D orbifold theories is discussed, in particular their role played in UV sensitivity of physical observables; as an example, the Higgs mass in the Barbieri-Hall-Nomura model is considered.

Pilo, L.

2003-03-01

221

ERIC Educational Resources Information Center

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.

Groetsch, C. W.

2005-01-01

222

NSDL National Science Digital Library

This online text is an exhaustive description of the role of symmetry in the degeneracy of a single-particle bound state system in quantum mechanics. Both non-relativistic and relativistic examples are studied.

Mcintosh, Harold

2006-07-22

223

Dynamical symmetries for fermions

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.

Guidry, M.

1989-01-01

224

Crystal point group symmetry is shown to protect Majorana fermions (MFs) in spinfull superconductors (SCs). We elucidate the condition necessary to obtain MFs protected by the point group symmetry. We argue that superconductivity in Sr2RuO4 hosts a topological phase transition to a topological crystalline SC, which accompanies a d-vector rotation under a magnetic field along the c axis. Taking all three bands and spin-orbit interactions into account, symmetry-protected MFs in the topological crystalline SC are identified. Detection of such MFs provides evidence of the d-vector rotation in Sr2RuO4 expected from Knight shift measurements but not yet verified. PMID:24010466

Ueno, Yuji; Yamakage, Ai; Tanaka, Yukio; Sato, Masatoshi

2013-08-23

225

Second order symmetry operators

NASA Astrophysics Data System (ADS)

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac–Weyl equation and the Maxwell equation on a curved four-dimensional Lorentzian manifold. The conditions for existence of symmetry operators for the different equations are seen to be related. Computer algebra tools have been developed and used to systematically reduce the equations to a form which allows geometrical interpretation.

Andersson, Lars; Bäckdahl, Thomas; Blue, Pieter

2014-07-01

226

NSDL National Science Digital Library

Educational consultant and textbook author Jill Britton is the author of these metasites listing Web resources for grade 5-8 mathematics. Each metasite revolves around a certain topic. The second metasite, Investigating Patterns: Symmetry and Tessellations, contains subtopics such as soapbubbles and honeycombs, Islamic tessellations, M.C. Escher, symmetry by paper folding, and more. Other types of links given on these pages are to merchants selling educational materials, sites on the history of mathematics, and activities with holiday themes.

Britton, Jill.

2001-01-01

227

We review the current status of heavy-quark symmetry and its applications to weak decays of hadrons containing a single heavy quark. After an introduction to the underlying physical ideas, we discuss in detail the formalism of the heavy-quark effective theory, including a comprehensive treatment of symmetry breaking corrections. We then illustrate some nonperturbative approaches, which aim at a dynamical, QCD-based

Matthias Neubert

1994-01-01

228

Universal behavior in an irreversible model with C3v symmetry

NASA Astrophysics Data System (ADS)

We analyze the critical behavior of a two-dimensional irreversible cellular automaton whose dynamic rules are invariant under the symmetry operations of the point group C3v. We study the dynamical phase transition that takes place in the model and obtain the static and short-time critical exponents by the use of Monte Carlo simulations. Our results indicate that the present model is in the same universality class as the three-state Potts model.

Brunstein, Adriana; Tomé, Tânia

1999-10-01

229

The multitude of archaea and bacteria inhabiting extreme environments has only become evident during the last decades. As viruses apply a significant evolutionary force to their hosts, there is an inherent value in learning about viruses infecting these extremophiles. In this study, we have focused on one such unique virus-host pair isolated from a hypersaline environment: an icosahedral, membrane-containing double-stranded DNA virus--Salisaeta icosahedral phage 1 (SSIP-1) and its halophilic host bacterium Salisaeta sp. SP9-1 closely related to Salisaeta longa. The architectural principles, virion composition, and the proposed functions associated with some of the ORFs of the virus are surprisingly similar to those found in viruses belonging to the PRD1-adenovirus lineage. The virion structure, determined by electron cryomicroscopy, reveals that the bulk of the outer protein capsid is composed of upright standing pseudohexameric capsomers organized on a T = 49 icosahedral lattice. Our results give a comprehensive description of a halophilic virus-host system and shed light on the relatedness of viruses based on their virion architecture. PMID:22509017

Aalto, Antti P; Bitto, David; Ravantti, Janne J; Bamford, Dennis H; Huiskonen, Juha T; Oksanen, Hanna M

2012-05-01

230

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

Stagno, Vincenzo; Bindi, Luca; Shibazaki, Yuki; Tange, Yoshinori; Higo, Yuji; Mao, H-K; Steinhardt, Paul J; Fei, Yingwei

2014-01-01

231

The multitude of archaea and bacteria inhabiting extreme environments has only become evident during the last decades. As viruses apply a significant evolutionary force to their hosts, there is an inherent value in learning about viruses infecting these extremophiles. In this study, we have focused on one such unique virus–host pair isolated from a hypersaline environment: an icosahedral, membrane-containing double-stranded DNA virus—Salisaeta icosahedral phage 1 (SSIP-1) and its halophilic host bacterium Salisaeta sp. SP9-1 closely related to Salisaeta longa. The architectural principles, virion composition, and the proposed functions associated with some of the ORFs of the virus are surprisingly similar to those found in viruses belonging to the PRD1–adenovirus lineage. The virion structure, determined by electron cryomicroscopy, reveals that the bulk of the outer protein capsid is composed of upright standing pseudohexameric capsomers organized on a T = 49 icosahedral lattice. Our results give a comprehensive description of a halophilic virus–host system and shed light on the relatedness of viruses based on their virion architecture.

Aalto, Antti P.; Bitto, David; Ravantti, Janne J.; Bamford, Dennis H.; Huiskonen, Juha T.; Oksanen, Hanna M.

2012-01-01

232

NASA Astrophysics Data System (ADS)

Symmetries govern Nature ubiquitously from the beauty of human faces to the local gauge invariance of quantum field theory. Magnetic order in frustrated magnets can occur without space inversion symmetry. When it relaxes to the magnetically-ordered configuration through exchange-striction, lattice can also loose inversion symmetry, leading to the presence of ferroelectric polarization. In these magnetically-driven ferroelectrics, dielectric properties turn out to be highly susceptible to applied magnetic fields. Both symmetric and antisymmetric exchange coupling can be involved in the exchange-striction. One form of symmetry often broken in Nature is the symmetry between left- and right-handedness. For example, the manner in which light propagates naturally selects one handedness, and is customarily described by a right-handed rule, depicting the relationship among the oscillating electric field, magnetic field and propagation vector of light. Chiral molecules also have a definite handedness, and given the preponderance of chiral molecules, it is not surprising that most complex proteins as well as their constituent amino acids are chiral. What is remarkable however, is that most of naturally occurring amino acids share the same chirality; only left-handedness. Such handedness, or chirality, appears to be a characteristic signature of life. In the multiferroic spinel CoCr2O4, conical magnetic order accompanies ferroelectric polarization as well as ferromagnetic moment. The relevant handedness and chirality in the multiferroic state will be also discussed.

Cheong, Sang-Wook

2008-03-01

233

NASA Astrophysics Data System (ADS)

The definition of an aperiodic crystal (quasicrystal) as a solid that is characterized by the forbidden symmetry suggests the existence of an unsolved problem, because, in a mutually exclusive manner, it appeals to the fundamental theorem of classical crystallography. Using the Penrose tiling as an example, we have investigated the symmetry properties of aperiodic tilings for the purpose to establish the allowed symmetry groups of quasicrystals. The filling of the Euclidean space according to an aperiodic law is considered as the action of an infinite number of group elements on a fundamental domain in the non-Euclidean space. It is concluded that all locally equivalent tilings have a common "parent" structure and, consequently, the same symmetry group. An idealized object, namely, an infinitely refined tiling, is introduced. It is shown that the symmetry operations of this object are operations of the similarity (rotational homothety). A positive answer is given to the question about a possible composition of operations of the similarity with different singular points. It is demonstrated that the transformations of orientation-preserving aperiodic crystals are isomorphic to a discrete subgroup of the Möbius group PSL(2, ?); i.e., they can be realized as discrete subgroups of the full group of motions in the Lobachevsky space. The problem of classification of the allowed types of aperiodic tilings is reduced to the procedure of enumeration of the aforementioned discrete subgroups.

Madison, A. E.

2013-04-01

234

High-T{sub C} superconductivity is possible upon metallic-element doping into {beta}-rhombohedral boron ({beta}-B{sub 105}), which is one of the boron icosahedral cluster solids. We attempted magnesium (Mg) doping into {beta}-B{sub 105} and discussed the possibility of metal transition and superconductivity. We achieved Mg doping into {beta}-B{sub 105} at a high Mg concentration of up to MgB{sub 11.5} (8.6 Mg/cell), i.e., electron doping sufficient for the Fermi energy (E{sub F}) to reach the conduction band over the intrinsic acceptor level (IAL) and trapping levels. However, neither metal transition nor superconductivity was observed. The changes in the structure and electronic properties are discussed on the basis of the results of x-ray powder diffraction using the Rietveld method and electrical conductivity and magnetic susceptibility measurements, respectively. We estimated the density of states near E{sub F} and discussed the electronic states of {beta}-B{sub 105}. From the result, it is suggested that a localized state exists above the IAL probably originating from the B{sub 28} cluster with structural defects.

Hyodo, H.; Araake, S.; Hosoi, S.; Kimura, K. [Department of Advanced Materials Science, The University of Tokyo, 277-8561 Chiba (Japan); Soga, K. [Department of Materials Science and Technology, Tokyo University of Science, 278-8510 Chiba (Japan); Sato, Y.; Terauchi, M. [Institute for Multidisciplinary Research for Advanced Materials, Tohoku University, 980-8577 Miyagi (Japan)

2008-01-01

235

Moving of fullerene between potential wells in the external icosahedral shell.

The results of the theoretical investigation of the behavior of fullerenes C20 and C60 inside the icosahedral external shell on example of carbon nanoclusters, C20 @?240 and C60 @?540 , are presented in this article. The multiwell potential of interaction between fullerenes in investigated nanoclusters is calculated to reveal the regularities of moving for internal fullerene in the field of holding potential of the external shell. The possible variants of fullerenes C20 and C60 moving between the potential wells are predicted on base of topology data of the fullerenes relative positioning in nanoparticle and analysis of relief of the energy surface of interaction between fullerenes. The formulated prediction is confirmed by the data of the numerical experiment. The investigation of two-shell fullerenes allows to conclude that the light fullerene ?20 will probably jump between the potential wells already at small temperatures (139-400 K) if the external shell is slightly bigger. © 2014 Wiley Periodicals, Inc. PMID:24771272

Glukhova, Olga E; Kolesnikova, Anna S; Slepchenkov, Michael M; Shunaev, Vladislav V

2014-06-30

236

Structural model and electronic structure of the icosahedral Al-Ga-Pd-Mn quasicrystal

NASA Astrophysics Data System (ADS)

The structural model and the electronic structure of a newly discovered i-Al-Ga-Pd-Mn icosahedral quasicrystal with composition Al67Ga4Pd21Mn8 were studied by density functional methods. Calculations are based on the Quandt-Elser periodic approximant model of i-Al-Pd-Mn , which was fully relaxed. To determine which Al sites in the i-Al-Ga-Pd-Mn are occupied by Ga, total energies were compared, showing that Ga substitutes two of the aluminum glue atoms, Al5 and Al6 , but no Al atoms that are part of a Bergman cluster. Since only specific Al sites are substituted by Ga, i-Al-Ga-Pd-Mn is predicted to be a true quaternary quasicrystal, structurally isomorphous with i-Al-Pd-Mn . Calculation of the electronic density of states of i-Al-Ga-Pd-Mn and its comparison to i-Al-Pd-Mn predicts that 4% Al?Ga substitution in the i-Al-Pd-Mn lattice should have negligible influence on the electronic properties of this quasicrystal.

Zijlstra, E. S.; Bose, S. K.; Dolinšek, J.

2005-09-01

237

The ability of ortho-, meta- and para-carboranes to enhance the emission intensity has been compared. For this purpose a series of carborane-appended 1,3,5-triphenylbenzene (TB) and 1,3,5- tris(biphenyl-4-yl)benzene (TBB) containing three ortho-, meta- and para-carborane clusters directly attached to the conjugated cores have been synthesized employing Suzuki, Heck, and trimerization reactions. The incorporation of the icosahedral carboranes was associated with a red shift in the UV absorption spectrum of up to 13 nm as well as enhancements of the emission intensities of up to 154%. The presence of ortho-carboranes showed the maximum red shift in the UV spectrum whereas the maximum enhancement of the emission intensity was observed in the presence of meta-carborane clusters. The order of ?-conjugation extension is found to be ortho > meta ? para. A comparative thermal analysis indicated o-carborane-appended trimers to be the most thermally stable in the series. Proton NMR spectra of reported carborane-appended trimers indicated that ortho- and meta-carborane cages have benzenelike characteristics. PMID:21612206

Dash, Barada Prasanna; Satapathy, Rashmirekha; Gaillard, Elizabeth R; Norton, Kathleen M; Maguire, John A; Chug, Neha; Hosmane, Narayan S

2011-06-20

238

Valence band structure of the icosahedral Ag-In-Yb quasicrystal

The valence band structure of the icosahedral (i) Ag-In-Yb quasicrystal, which is isostructural to the binary i-Cd-Yb system, is investigated by ultraviolet photoemission spectroscopy (UPS). Experimental results are compared with electronic-structure calculations of a cubic approximant of the same phase. UPS spectra from the fivefold, threefold, and twofold i-Ag-In-Yb surfaces reveal that the valence band near to the Fermi level is dominated by Yb 4f-derived states, in agreement with calculations. The spectra also exhibit peaks which are surface core level shifted, caused by changes in the electronic structure in surface layers. Calculations yield a pseudogap in the density of states due to a hybridization of the Yb 5d band with the Ag 5p and In 5p bands. Both experimental and calculated band features are very similar to those of Cd-Yb. The modification of the band structure after surface treatment by sputtering and by oxidation is also studied. Additionally, the work function of i-Ag-In-Yb measured from the width of UPS spectrum is found to be almost unaffected by surface orientation, but increases after sputtering or oxidation.

Sharma, H. R.; Simutis, G.; Dhanak, V. R.; Nugent, P. J.; McGrath, R. [Surface Science Research Centre and Department of Physics, University of Liverpool, Liverpool L69 3BX (United Kingdom); Cui, C. [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577 (Japan); Shimoda, M. [National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Tsai, A. P. [Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai 980-8577 (Japan); National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047 (Japan); Ishii, Y. [Department of Physics, Chuo University, Kasuga, Tokyo 112-8551 (Japan)

2010-03-01

239

NASA Astrophysics Data System (ADS)

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.

Dykeman, Eric C.; Sankey, Otto F.

2010-02-01

240

There exists a widely held notion that gravitational effects can strongly violate global symmetries. If this is correct, it may lead to many important consequences. We argue, in particular, that nonperturbative gravitational effects in the axion theory lead to a strong violation of {ital CP} invariance unless they are suppressed by an extremely small factor {ital g}{approx_lt}10{sup {minus}82}. One could hope that this problem disappears if one represents the global symmetry of a pseudoscalar axion field as a gauge symmetry of the Ogievetsky-Polubarinov-Kalb-Ramond antisymmetric tensor field. We show, however, that this gauge symmetry does not protect the axion mass from quantum corrections. The amplitude of gravitational effects violating global symmetries could be strongly suppressed by {ital e}{sup {minus}{ital S}}, where {ital S} is the action of a wormhole which may absorb the global charge. Unfortunately, in a wide variety of theories based on the Einstein theory of gravity the action appears to be fairly small, {ital S}{similar_to}10. However, we find that the existence of wormholes and the value of their action are extremely sensitive to the structure of space on the nearly Planckian scale. We consider several examples (Kaluza-Klein theory, conformal anomaly, {ital R}{sup 2} terms) which show that modifications of the Einstein theory on the length scale {ital l}{approx_lt}10{ital M}{sub {ital P}}{sup {minus}1} may strongly suppress violation of global symmetries. We find also that in string theory there exists an additional suppression of topology change by the factor {ital e}{sup {minus}8{pi}2}/{ital g}{sup 2}. This effect is strong enough to save the axion theory for the natural values of the stringy gauge coupling constant.

Kallosh, R.; Linde, A.; Linde, D.; Susskind, L. [Department of Physics, Stanford University, Stanford, California 94305-4060 (United States)] [Department of Physics, Stanford University, Stanford, California 94305-4060 (United States); [California Institute of Technology, Pasadena, California 91125 (United States)

1995-07-15

241

Single-grain precession x-ray diffraction photographs of Al6CuLi3 have been successfully indexed on the basis of icosahedral twinning of cubic crystals with a 1012-atom primitive cubic unit with edge 25.70 Å, giving support to the proposal that the so-called icosahedral quasicrystals are twins of crystals containing eight large icosahedral clusters in the ?-W arrangement. In this compound two of the clusters consist of 104 atoms and six consist of 136 atoms, with 24 atoms shared. The same structure is assigned to the C-phase, Al37Cu3Li21Mg3, and to GaMg2Zn3. A theory of icosahedral quasicrystals and amorphous metals is described.

Pauling, Linus

1988-01-01

242

A unified structure theory of icosahedral quasicrystals, combining the twinned-cubic-crystal theory and the Penrose-tilling-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.

Linus Pauling

1988-01-01

243

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.

Pauling, Linus

1988-01-01

244

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.

Pauling, L. (Linus Pauling Institute of Science and Medicine, Palo Alto, CA (USA))

1988-11-01

245

Dynamical (super) symmetry breaking

Dynamical Symmetry Breaking (DSB) is a concept theoristsrely on very often in the discussions of strong dynamics, model building,and hierarchy problems. In this talk, I will discuss why this is such apermeating concept among theorists and how they are used in understandingphysics. I also briefly review recent progress in using dynamicalsymmetry breaking to construct models of supersymmetry breaking andfermion masses.

Murayama, Hitoshi

2000-10-03

246

Symmetry in Constraint Programming

Symmetry in constraints has always been important but in recent years has become a ma- jor research area in its own right. A key problem in constraint programming has long been recognised: search can revisit equivalent states over and over again. In principle this prob- lem has been solved, with a number of different techniques. As we write, research remains

Ian P. Gent; Karen E. Petrie; Jean-Francois Puget

247

We show how to exploit symmetry in model checking for concurrent systems containing many identical or isomorphic components. We focus in particular on those composed of many isomorphic processes. In many cases we are able to obtain significant, even exponential, savings in the complexity of model checking.

E. Allen Emerson; A. Prasad Sistla

1993-01-01

248

NSDL National Science Digital Library

In this math activity, learners experiment with the concept of symmetry. Learners use mirrors to identify which pictures, letters, and shapes are symmetrical and then complete the missing halves for images. This activity guide contains a material list, sample questions to ask, literary connections, extensions, and alignment to local and national standards.

Houston, Children'S M.

2014-04-08

249

Tessellations: Geometry and Symmetry

NSDL National Science Digital Library

This lesson is designed to develop students' understanding of polygons and symmetry by exploring tessellations and their geometric properties. This lesson provides links to discussions and activities related to tessellations as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

2010-01-01

250

Symmetry and structure of SrTiO3 nanotubes

NASA Astrophysics Data System (ADS)

The full study of perovskite type nanotubes with square morphology is given for the first time. The line symmetry group L = ZP (a product of one axial point group P and one infinite cyclic group Z of generalized translations) of single-walled (SW) and double-walled (DW) SrTiO3 nanotubes (NT) is considered. The nanotube is defined by the square lattice translation vector L = l1a + l2b and chiral vector R = n1a + n2b, (l1, l2, n1 and n2 are integers). The nanotube of the chirality (n1,n2) is obtained by folding the (001) slabs of two- layers (with the layer group P4mm) and of three layers (with the layer group P4/mmm) in a way that the chiral vector R becomes circumference of the nanotube. Due to the orthogonality relation (RL) = 0, l1/l2 = -n2/n1 i.e. SW nanotubes with square morphology are commensurate for any rolling vector R(n1,n2). For SW (n,0) NTs the line symmetry groups belong to family 11 (T^Dnh) and are n/mmm or for even and odd n, respectively. For SW (n,n) NTs the line symmetry groups (2n)n/mcm belong to family 13 (T2n1 Dnh). The line symmetry group of a double-wall nanotube is found as intersection L2 = Z2P2 = (L ? L') of the symmetry groups L and L' of its single-wall constituents as earlier considered for DW CNTs. The symmetry group of DWNT (n,0)@M(n,0) belongs to the same family 11 (T^Dnh) as its SW constituents. The symmetry group of DWNT (n,n)@M(n,n) depends on the parity of M. For DW NTs with odd M, the line symmetry groups are the same as for their SW constituents and belong to family 13 (T2n1 Dnh). For even M, the rotations about screw axis of order 2n are changed by rotations around pure rotation axis of order n so that DW NT line symmetry groups belong to family 11 (T^Dnh). Commensurate STO DWNTs (n1,0)@(n2,0) and (n1, n1)@(n2, n2) belong to family 11 (T^Dnh) with n equal to the greatest common divisor of n1 and n2.

Evarestov, Robert

2011-06-01

251

A highly symmetric four-dimensional quasicrystal

A quasiperiodic pattern (or quasicrystal) is constructed in real four-dimensional Euclidean space, having the noncrystallographic reflection group (3,3,5) of order 14400 as its point group. It is obtained as a projection of the eight-dimensional lattice E 8, and has as a cross-section a three-dimensional quasicrystal with icosahedral symmetry.

Veit Elser; N. J. A. Sloane

1987-01-01

252

Improved Statistics for Determining the Patterson Symmetry fromUnmerged Diffraction Intensities

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.

Sauter, Nicholas K.; Grosse-Kunstleve, Ralf W.; Adams, Paul D.

2006-01-09

253

From the quaternary Ti-Zr-Hf-Ni phase diagram, the cross-section at 20 at.% Ni was selected for investigation. The icosahedral quasicrystalline, crystalline and amorphous phases were observed to form in nine kinds of rapidly solidified (Ti{sub x}Zr{sub y}Hf{sub z}){sub 80}Ni{sub 20} (x + y + z = 1) alloys at different compositions. The quasilattice constants of 0.519 and 0.531 nm were obtained for the icosahedral phase formed in the melt-spun Ti{sub 40}Zr{sub 20}Hf{sub 20}Ni{sub 20} and Ti{sub 20}Zr{sub 40}Hf{sub 20}Ni{sub 20} alloys, respectively. The icosahedral phase formed in the melt-spun Ti{sub 40}Zr{sub 20}Hf{sub 20}Ni{sub 20} alloy especially is thermodynamically stable. The supercooled liquid region of the Ti{sub 20}Zr{sub 20}Hf{sub 40}Ni{sub 20} glassy alloy reached 64 K. From these results a comparison of quasicrystal-forming and glass-forming abilities was carried out. The quasicrystal-forming ability was reduced and glass-forming ability was improved with an increase in Hf and Zr contents in the (Ti{sub x}Zr{sub y}Hf{sub z}){sub 80}Ni{sub 20} alloys. On the other hand, an increase in Ti content caused an improvement in quasicrystal-forming ability.

Chen, N. [Department of Materials Science, Graduate School, Tohoku University, Sendai 980-8577 (Japan) and Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai 980-8577 (Japan)]. E-mail: asyzxy@imr.edu; Louzguine, D.V. [Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai 980-8577 (Japan); Ranganathan, S. [Department of Metallurgy, Indian Institute of Science, Bangalore 560 012 (India); Inoue, A. [Institute for Materials Research, Tohoku University, Katahira 2-1-1, Aoba-Ku, Sendai 980-8577 (Japan)

2005-02-01

254

Dynamical Symmetries in Classical Mechanics

ERIC Educational Resources Information Center

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…

Boozer, A. D.

2012-01-01

255

Reflections on Symmetry and Proof

ERIC Educational Resources Information Center

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…

Merrotsy, Peter

2008-01-01

256

Powerful symmetry principles have guided physicists in their quest for nature's fundamental laws. The successful gauge theory of electroweak interactions postulates a more extensive symmetry for its equations than are manifest in the world. The discrepancy is ascribed to a pervasive symmetry-breaking field, which fills all space uniformly, rendering the Universe a sort of exotic superconductor. So far, the evidence

Frank Wilczek

2005-01-01

257

A cyclic heat-treatment process was used to prepare single grains of the quasicrystalline icosahedral phase, {psi}{endash}Al{sub 65}Cu{sub 23}Fe{sub 12}. Alloys of appropriate composition are melted and chill cast into copper molds. Multiple cyclic heat treatments at successively higher temperatures below 860{degree}C, the peritectic decomposition temperature of the quasicrystal phase, are used to enhance the growth of the {psi} phase. Single grains up to 10 mm{times}5 mm{times}5 mm have been prepared. {copyright} {ital 1996 Materials Research Society.}

Lograsso, T.A.; Delaney, D.W. [Metallurgy and Ceramics Program, Ames Laboratory, U.S. Department of Energy, Iowa State University, Ames, Iowa 50011 (United States)

1996-09-01

258

Simulation of ion-beam channeling in icosahedral Al[sub 63]Cu[sub 25]Fe[sub 12

Monte Carlo simulations of channeling on the icosahedral quasicrystal Al[sub 63]Cu[sub 25]Fe[sub 12] were made, using an experimentally determined structure model for this phase. The channeling effect was found to be nearly as good as for a normal, periodic crystal. Dip widths are in agreement with experimental values, but minimum yields are not. The minimum yield is inversely proportional to the beam energy at low energy. Future experiments to be done are proton-induced-x-ray-channeling experiments and Rutherford-backscattering-channeling experiments at low energy.

du Marchie van Voorthuysen, E.H.; Smulders, P.J.M.; van Smaalen, S. (Materials Science Centre, University of Groningen, Nijenborgh 4, NL 9747 AG Groningen (Netherlands))

1993-10-01

259

Icosahedral short-range order in amorphous Cu80Si20 by ab initio molecular dynamics simulation study

Short-range order in liquid and amorphous structures of Cu80Si20 is studied by ab initio molecular dynamics simulations. We performed the simulations at 1140 and 300 K respectively to investigate the local structure change from liquid to amorphous. The result of structure factor in comparison with experimental data indicates that our simulation of amorphous Cu80Si20 is reliable. By using the bond-angle distribution function, Honeycutt–Andersen index, Voronoi tessellation method, and the atomistic cluster alignment method, the icosahedral short-range order in the system is revealed. Strong Cu–Si interaction was also observed.

Wu, S.; Kramer, Matthew J.; Fang, Xiaowei; Wang, Shy-Guey; Wang, Cai-Zhuang; Ho, Kai-Ming; Ding, Z.J.; Chen, L.Y.

2012-04-26

260

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.

Tai, K. P.; Gao, N.; Dai, X. D.; Li, J. H.; Lai, W. S.; Liu, B. X. [Advanced Materials Laboratory, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084 (China)

2006-08-28

261

Dark discrete gauge symmetries

NASA Astrophysics Data System (ADS)

We investigate scenarios in which dark matter is stabilized by an Abelian ZN discrete gauge symmetry. Models are surveyed according to symmetries and matter content. Multicomponent dark matter arises when N is not prime and ZN contains one or more subgroups. The dark sector interacts with the visible sector through the renormalizable kinetic mixing and Higgs portal operators, and we highlight the basic phenomenology in these scenarios. In particular, multiple species of dark matter can lead to an unconventional nuclear recoil spectrum in direct detection experiments, while the presence of new light states in the dark sector can dramatically affect the decays of the Higgs at the Tevatron and LHC, thus providing a window into the gauge origin of the stability of dark matter.

Batell, Brian

2011-02-01

262

A broken symmetry ontology: Quantum mechanics as a broken symmetry

The author proposes a new broken symmetry ontology to be used to analyze the quantum domain. This ontology is motivated and grounded in a critical epistemological analysis, and an analysis of the basic role of symmetry in physics. Concurrently, he is led to consider nonheterogeneous systems, whose logical state space contains equivalence relations not associated with the causal relation. This allows him to find a generalized principle of symmetry and a generalized symmetry-conservation formalisms. In particular, he clarifies the role of Noether's theorem in field theory. He shows how a broken symmetry ontology already operates in a description of the weak interactions. Finally, by showing how a broken symmetry ontology operates in the quantum domain, he accounts for the interpretational problem and the essential incompleteness of quantum mechanics. He proposes that the broken symmetry underlying this ontological domain is broken dilation invariance.

Buschmann, J.E.

1988-01-01

263

PSEUDOSPIN SYMMETRY IN NUCLEI, SPIN SYMMETRY IN HADRONS

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.

P. PAGE; T. GOLDMAN; J. GINOCCHIO

2000-08-01

264

NASA Technical Reports Server (NTRS)

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.

Lopez, Hiram

1987-01-01

265

NASA Astrophysics Data System (ADS)

Music and Physics are very close because of the symmetry that appears in music. A periodic wave is what music really is, and there is a field of Physics devoted to waves researching. The different musical scales are the base of all kind of music. This article tries to show how this musical scales are made, how the consonance is the base of many of them and how symmetric they are.

Herrero, O. F.

2010-06-01

266

Symmetries in laminated composite plates

NASA Technical Reports Server (NTRS)

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.

Noor, A. K.

1976-01-01

267

NASA Astrophysics Data System (ADS)

Projective symmetry groups are the mathematical tools which make it possible to list and classify mean-field spin liquids (SLs) based on a parton construction. The seminal work of Wen [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.65.165113 65, 165113 (2002)] and its subsequent extension to bosons by Wang and Vishwanath [Phys. Rev. BPRBMDO1098-012110.1103/PhysRevB.74.174423 74, 174423 (2006)] concerned the so-called symmetric SLs; i.e., states that break neither lattice symmetries nor time reversal invariance. Here we generalize this tool to chiral (time reversal symmetry breaking) SLs described in a Schwinger boson mean-field approach and illustrate it on the triangular lattice, which can harbor nine different weakly symmetric SLs (two symmetric SLs and seven chiral SLs) with nearest neighbor bond operators only. Results for other lattices (square and kagome) are given in the Appendixes. Application of this new approach has recently led to the discovery of two chiral ground states on the kagome lattice [Messio , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.108.207204 108, 207204 (2012); Fåk , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.109.037208 109, 037208 (2012)]. The signature of a time reversal symmetry breaking SL is the presence in the ground state of nontrivial fluxes of loop operators that break some lattice point group symmetries. The physical significance of these gauge invariant quantities is discussed both in the classical limit and in the quantum SL and their expressions in terms of spin observables are given.

Messio, Laura; Lhuillier, Claire; Misguich, Grégoire

2013-03-01

268

NASA Astrophysics Data System (ADS)

For the example of nonrigid nitromethane and toluene molecules CH3NO2 and CH3C6H5 in the ground electronic states, the possibility of using the observed symmetry properties of internal dynamics of a nonrigid molecule for the correct choice of its equilibrium configurations is considered in the case where different possible geometries of such configurations correspond to the same point group.

Burenin, A. V.

2013-12-01

269

An analysis of the crystallographically determined structures of the icosahedral protein coats of Tomato Bushy Stunt Virus, Southern Bean Mosaic Virus, Satellite Tobacco Necrosis Virus, Human Rhinovirus 14 and Mengovirus around their fivefold axes is presented. Accessibilities surfaces, electrostatic energy profile calculations, ion-protein interaction energy calculations, free energy perturbation methods and comparisons with structures of chelating agents are used in this study. It is concluded that the structures built around the viral fivefold axes would be adequate for ion binding and transport. Relative ion preferences are derived for the binding sites, using free energy perturbation methods, which are consistent with the experimental data when available. In the cases where crystallographic studies determined the existence of ions on the fivefold axes, our results indicate that they would correspond to ions in crystallization or purification buffers. The environment of the fivefold axes are rich in polar residues in all icosahedral viral structures whose atomic coordinates are available, including some that are not being analyzed in detail in this work. The fivefold channel-like structures have most of the basic properties expected for real ion channels including a funnel at the entrance, a polar internal environment with frequent alternation of acidic and basic residues, ion binding sites, the capability to induce ion dehydration and ion transit from the external viral surface to the binding sites. Images FIGURE 2 FIGURE 3 FIGURE 4 FIGURE 5 FIGURE 6 FIGURE 7

Kalko, S G; Cachau, R E; Silva, A M

1992-01-01

270

The N2 bond cleavage is the rate-limiting step in the synthesis of ammonia, and ruthenium is a catalyst well known for this reaction. The double-icosahedral (D5h) Ru19 cluster is famous as an active catalyst, and has a remarkable stability towards the adsorption of H2, N2 and CO. Using first-principles calculations, we have investigated the adsorption and dissociation of dinitrogen on a double-icosahedral Ru19 cluster. Our results show that the hollow site in the rhombus region (BHB site) of the Ru19 cluster possesses the greatest catalytic activity to dissociate N2, with the reaction barrier of 0.89 eV and an exothermicity of -1.45 eV. Multiple coadsorption of N2 on the cluster (i.e. coadsorption of 2N2 and 3N2 on a single Ru19 cluster) causes the barrier to dissociate N2 to be less on a BHB site than for adsorption of a single N2. To understand the catalytic properties of a Ru19 cluster towards N2 bond cleavage, we calculated the electron population, vibrational wavenumbers and local densities of states; the results are explicable. PMID:24622677

Yeh, Chen-Hao; Lin, Yu-Chieh; Ho, Jia-Jen

2014-04-28

271

Symmetry and perturbation theory

NASA Astrophysics Data System (ADS)

A co-chain map for the G invariant De Rham complex -- New examples of trihamiltonian structures linking different Lenard chains -- Wave propagation in an elastic medium: GDS equations -- Parametric excitation in nonlinear dynamics -- Collisionless action-minimizing trajectories for the equivariant 3-body problem in R2 -- The Lagrangian and Hamiltonian formulations for a special class of non-conservative systems -- Shadowing chains of collision orbits for the elliptic 3-body problem -- Similarity reductions of an optical model -- Fold, transcritical and pitchfork singularities for time-reversible systems -- Homographic three-body motions with positive and negative masses -- Remarks on conformal Killing tensors and separation of variables -- A regularity theory for optimal partition problems -- Lambda and mu-symmetries -- Potential symmetries and linearization of some evolution equations -- Periodic solutions for zero mass nonlinear wave equations -- Fundamental covariants in the invariant theory of Killing tensors -- Global geometry of 3-body trajectories with vanishing angular momentum -- The relation between the topological structure of the set of controllable affine systems and topological structures of the set of controllable homogenuous systems in low dimension -- On preservation of action variables for satellite librations in elliptic orbits with account of solar light pressure -- An explicit solution of the (quantum) elliptic Calogero-Sutherland model -- An application of the Melnikov integral to a restricted three body problem -- Reductions of integrable equations and automorphic Lie algebras -- Geometric reduction of Poisson operators -- Closed manifolds admitting metrics with the same geodesics -- A transcritical-flip bifurcation in a model for a robot-arm -- Alignment and the classification of Lorentz-signature tensors -- Renormalization group symmetry and gas dynamics -- Refined computation of hypernormal forms -- New order reductions for Euler-Lagrange equations -- Regularity of pseudogroup orbits -- Relaxation times to equilibrium in Fermi-Pasta-Ulam system -- Energy cascade in Fermi-Pasta-Ulam models -- On Birkhoff method for integrable lagrangian systems -- Symmetry of singularities and orbit spaces of compact linear groups -- Symmetric solutions in molecular potentials -- Variational approach to soliton generation and stability analysis of multidimensional nonlinear Schrodinger equation -- Differential invariants for infinite-dimensional algebras.

Gaeta, Giuseppe

272

This paper is an expository account of the development of soliton\\u000amathematics, from its inception in famous numerical experiments of\\u000aFermi-Pasta-Ulam and Zabusky-Kruskal to the recent synthesis of Terng-Uhlenbeck\\u000a(dg-ga\\/9707004) that explains hidden symmetries of soliton equations in terms\\u000aof loop-groups acting by dressing transformations. The inverse scattering\\u000amethod is explained in detail, first using inverse scattering for the\\u000aSchroedinger

Richard S. Palais

1997-01-01

273

Mirror symmetry without corrections

We give geometric explanations and proofs of various mirror symmetry\\u000aconjectures for $T^{n}$-invariant Calabi-Yau manifolds when instanton\\u000acorrections are absent. This uses fiberwise Fourier transformation together\\u000awith base Legendre transformation.\\u000a We discuss mirror transformations of\\u000a (i) moduli spaces of complex structures and complexified symplectic\\u000astructures, $H^{p,q}$'s, Yukawa couplings;\\u000a (ii) sl(2)xsl(2)-actions;\\u000a (iii) holomorphic and symplectic automorphisms and\\u000a (iv) A- and B-connections,

Naichung Conan Leung

2000-01-01

274

Crystal Symmetry Algorithms in a High-Throughput Framework for Materials

NASA Astrophysics Data System (ADS)

The high-throughput framework AFLOW that has been developed and used successfully over the last decade is improved to include fully-integrated software for crystallographic symmetry characterization. The standards used in the symmetry algorithms conform with the conventions and prescriptions given in the International Tables of Crystallography (ITC). A standard cell choice with standard origin is selected, and the space group, point group, Bravais lattice, crystal system, lattice system, and representative symmetry operations are determined. Following the conventions of the ITC, the Wyckoff sites are also determined and their labels and site symmetry are provided. The symmetry code makes no assumptions on the input cell orientation, origin, or reduction and has been integrated in the AFLOW high-throughput framework for materials discovery by adding to the existing code base and making use of existing classes and functions. The software is written in object-oriented C++ for flexibility and reuse. A performance analysis and examination of the algorithms scaling with cell size and symmetry is also reported.

Taylor, Richard

275

NASA Astrophysics Data System (ADS)

This article begins with a simple proof of the existence of squash operators compatible with the Bennett-Brassard 1984 (BB84) protocol that suits single-mode as well as multimode threshold detectors. The proof shows that, when a given detector is symmetric under cyclic group C4, and a certain observable associated with it has rank two as a matrix, then there always exists a corresponding squash operator. Next, we go on to investigate whether the above restriction of “rank two” can be eliminated; i.e., is cyclic symmetry alone sufficient to guarantee the existence of a squash operator? The motivation behind this question is that, if this were true, it would imply that one could realize a device-independent and unconditionally secure quantum key distribution protocol. However, the answer turns out to be negative, and moreover, one can instead prove a no-go theorem that any symmetry is, by itself, insufficient to guarantee the existence of a squash operator.

Tsurumaru, Toyohiro

2010-01-01

276

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.

Tsurumaru, Toyohiro [Mitsubishi Electric Corporation, Information Technology R and D Center, 5-1-1 Ofuna, Kamakura-shi, Kanagawa, 247-8501 Japan (Japan)

2010-01-15

277

NASA Technical Reports Server (NTRS)

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.

Rosensteel, George

1995-01-01

278

Symmetry perception in the blind.

Bilateral mirror symmetry, especially vertical symmetry, is a powerful phenomenon in spatial organization of visual shapes. However, the causes of vertical symmetry salience in visual perception are not completely clear. Here we investigated whether the perceptual salience of vertical symmetry depends on visual experience by testing a group of congenitally blind individuals in a memory task in which either horizontal or vertical symmetry was used as an incidental feature. Both blind and sighted subjects remembered more accurately configurations that were symmetrical compared to those that were not. Critically, whereas sighted subjects displayed a higher level of facilitation by vertical than horizontal symmetry, no such difference was found in the blind. This suggests that the perceptual salience of the vertical dimension is visually based. PMID:20444438

Cattaneo, Zaira; Fantino, Micaela; Silvanto, Juha; Tinti, Carla; Pascual-Leone, Alvaro; Vecchi, Tomaso

2010-07-01

279

We have observed dynamical diffraction in the

Jach, T. [National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)] [National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States); Zhang, Y.; Colella, R. [Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States)] [Department of Physics, Purdue University, West Lafayette, Indiana 47907 (United States); de Boissieu, M.; Boudard, M. [LTPCM-ENSEEG, BP 75, 38402 St. Martin d`Heres Cedex (France)] [LTPCM-ENSEEG, BP 75, 38402 St. Martin d`Heres Cedex (France); Goldman, A.I.; Lograsso, T.A.; Delaney, D.W. [Department of Physics and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States)] [Department of Physics and Ames Laboratory, Iowa State University, Ames, Iowa 50011 (United States); Kycia, S. [CHESS, Cornell University, Ithaca, New York 14853 (United States)] [CHESS, Cornell University, Ithaca, New York 14853 (United States)

1999-04-01

280

Pairing symmetry in cuprate superconductors

Pairing symmetry in the cuprate superconductors is an important and controversial topic. The recent development of phase-sensitive tests, combined with the refinement of several other symmetry-sensitive techniques, has for the most part settled this controversy in favor of predominantly d-wave symmetry for a number of optimally hole- and electron-doped cuprates. This paper begins by reviewing the concepts of the order

C. C. Tsuei; J. R. Kirtley

2000-01-01

281

Optical Möbius Symmetry in Metamaterials

NASA Astrophysics Data System (ADS)

We experimentally observed a new topological symmetry in optical composites, namely, metamaterials. While it is not found yet in nature materials, the electromagnetic Möbius symmetry discovered in metamaterials is equivalent to the structural symmetry of a Möbius strip, with the number of twists controlled by the sign change of the electromagnetic coupling between the meta-atoms. We further demonstrate that metamaterials with different coupling signs exhibit resonance frequencies that depend only on the number but not the locations of the “twists,” thus confirming its topological nature. The new topological symmetry found in metamaterials may enable unique functionalities in optical materials.

Chang, Chih-Wei; Liu, Ming; Nam, Sunghyun; Zhang, Shuang; Liu, Yongmin; Bartal, Guy; Zhang, Xiang

2010-12-01

282

Nuclear experiments which probe the parity and time-reversal symmetries are reviewed. The P-violating NN interaction, studied in the NN system and in light nuclei, provides a unique window on the neutral current quark-quark interaction. Results at low energy are in accord with expectations. However, surprises may occur when higher energies are studied in more detail. Sensitive probes of T-violation via detailed balance, T-odd correlations in ..gamma.. and ..beta..-decay, T-odd effects in low-energy neutron scattering, and searches for nuclear electric dipole moments (EDM) are discussed. No T-violation is observed, but in several cases substantial improvements in the experimental sensitivity are imminent. Existing EDM limits are almost good enough to eliminate one of the leading theoretical explanations for CP violation.

Adelberger, E.G.

1984-11-15

283

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

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

284

We report on the absolute scale measurement of the x-ray diffuse scattering in the ZnMgSc icosahedral quasicrystal and its periodic approximant. Whereas the diffuse scattering in the approximant is purely accounted for by thermal diffuse scattering, an additional signal is observed in the quasicrystal. It is related to phason fluctuations as indicated by its Q{sub per}{sup 2} dependence. Moreover, when compared to previous measurements carried out on the i-AlPdMn phase, we find that the amount of diffuse scattering is smaller in the i-ZnMgSc phase, in agreement with larger phason elastic constants in this phase. This is confirmed by the observation of a large number of weak Bragg peaks having a high Q{sub per} reciprocal space component.

Boissieu, M. de [Laboratoire de Thermodynamique et de Physico-Chimie Metallurgique, UMR CNRS 5614, ENSEEG-INPG, BP 75, 38402 Saint Martin d'Heres (France); Francoual, S. [Laboratoire de Thermodynamique et de Physico-Chimie Metallurgique, UMR CNRS 5614, ENSEEG-INPG, BP 75, 38402 Saint Martin d'Heres (France); Institut Laue Langevin, BP 156, 38042 Grenoble Cedex 9 (France); Kaneko, Y.; Ishimasa, T. [Research Group of Material Physics, Graduate School of Engineering, Hokkaido University, Kita-ku, Sapporo, 060-8628 (Japan)

2005-09-02

285

NASA Astrophysics Data System (ADS)

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.

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

286

Symmetry behavior at finite temperature

Spontaneous symmetry breaking at finite temperature is studied. We show that for the class of theories discussed, symmetry is restored above a critical temperature betac-1. We determine betac by a functional-diagrammatic evaluation of the effective potential and the effective mass. A formula for betac is obtained in terms of the renormalized parameters of the theory. By examining a large subset

L. Dolan; R. Jackiw

1974-01-01

287

Unique horizontal symmetry of leptons

There is a group-theoretical connection between fermion mixing matrices and minimal horizontal symmetry groups. Applying this connection to the tribimaximal neutrino mixing matrix, we show that the minimal horizontal symmetry group for leptons is uniquely S{sub 4}, the permutation group of four objects.

Lam, C. S. [Department of Physics, McGill University, Montreal, Q.C., H3A 2T8 (Canada) and Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1 (Canada)

2008-10-01

288

Superflavor symmetry for heavy particles

NASA Astrophysics Data System (ADS)

We extend the heavy quark spin and flavor symmetry discussed by Voloshin and Shifman and by Isgur and Wise to systems in which the heavy colored particles have different spins. We discuss in detail the superflavor symmetry between a heavy quark and a heavy color triplet scalar.

Georgi, Howard; Wise, Mark B.

1990-06-01

289

ERIC Educational Resources Information Center

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…

Hancock, Karen

2007-01-01

290

Symmetry in Sign Language Poetry

ERIC Educational Resources Information Center

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.)

Sutton-Spence, Rachel; Kaneko, Michiko

2007-01-01

291

Symmetry and Tilings: An Exploration

NSDL National Science Digital Library

Students are directed to read through a Web-based tutorial on Symmetry and Tilings in the form of an short and colorful article entitled Tilings and Tesselations; afterwards, they answer several questions on tilings (tessellations), tiling terminology, types of symmetry (isometries), periodic tilings and Penrose tilings.

Rutledge, James

292

DGBV Algebras and Mirror Symmetry

We describe some recent development on the theory of formal Frobenius manifolds via a construction from differential Gerstenhaber-Batalin-Vilkovisk (DGBV) algebras and formulate a version of mirror symmetry conjecture: the extended deformation problems of the complex structure and the Poisson structure are described by two DGBV algebras; mirror symmetry is interpreted in term of the invariance of the formal Frobenius manifold

Huai-Dong Cao; Jian Zhou

2000-01-01

293

Geometric Endoscopy and Mirror Symmetry

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

Edward Frenkel; Edward Witten

2007-01-01

294

Crystallographic characterization and molecular symmetry of edestin, a legumin from hemp.

Edestin, a legumin class reserve protein from hemp seeds having six identical subunits was crystallized from ammonium phosphate at pH 5 and subsequently characterized by X-ray diffraction. The crystals are of space group R32 with a = 127 A and gamma = 116 degrees having an equivalent triply centered hexagonal cell of a = b = 215 A, c = 80 A. There is one hexameric protein in the rhombohedral unit cell, hence the subunits of the Edestin molecule must be arranged with 32 point group symmetry. PMID:8289257

Patel, S; Cudney, R; McPherson, A

1994-01-01

295

Symmetries in geology and geophysics.

Symmetries have played an important role in a variety of problems in geology and geophysics. A large fraction of studies in mineralogy are devoted to the symmetry properties of crystals. In this paper, however, the emphasis will be on scale-invariant (fractal) symmetries. The earth's topography is an example of both statistically self-similar and self-affine fractals. Landforms are also associated with drainage networks, which are statistical fractal trees. A universal feature of drainage networks and other growth networks is side branching. Deterministic space-filling networks with side-branching symmetries are illustrated. It is shown that naturally occurring drainage networks have symmetries similar to diffusion-limited aggregation clusters. PMID:11607719

Turcotte, D L; Newman, W I

1996-12-10

296

Algorithms for computer detection of symmetry elements in molecular systems.

Simple procedures for the location of proper and improper rotations and reflexion planes are presented. The search is performed with a molecule divided into subsets of symmetrically equivalent atoms (SEA) which are analyzed separately as if they were a single molecule. This approach is advantageous in many aspects. For instance, in those molecules that are symmetric rotors, the number of atoms and the inertia tensor of the SEA provide one straight way to find proper rotations of any order. The algorithms are invariant to the molecular orientation and their computational cost is low, because the main information required to find symmetry elements is interatomic distances and the principal moments of the SEA. For example, our Fortran implementation, running on a single processor, took only a few seconds to locate all 120 symmetry operations of the large and highly symmetrical fullerene C720, belonging to the Ih point group. Finally, we show how the interatomic distances matrix of a slightly unsymmetrical molecule is used to symmetrize its geometry. PMID:24403016

Beruski, Otávio; Vidal, Luciano N

2014-02-01

297

Symmetry in distributed systems

A distributed computing system can be considered to be symmetric because of its topology or because of its behavior. Unfortunately, these different definitions can categorize the same system differently. The choice of definition becomes important when one is trying to prove that certain problems, such as the Dining Philosophers problem, cannot be solved on symmetric distributed computing systems. Since the behavioral definitions are based on the possible patterns of computation, it is much easier to use them for these proofs. However, behavioral definitions frequently are undecidable; topological definitions admit straightforward decision procedures. This thesis presents a new definition for symmetry, called similarity, that, while based on behavior of processes, is decidable given the initial configuration of the system. The decision procedure for similarity depends partly on the model of computation being used, but a way to discover these decision procedures is given and is used to find decision procedures for a wide range of models of distributed computation. Distributed versions of these decision procedures form the basis of solutions to the problem of selecting a process as the leader. The thesis also shows how to use similarity to compare the relative power of different models of computation.

Johnson, R.E.

1987-01-01

298

Spectral theorem and partial symmetries

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.

Gozdz, A. [University of Maria Curie-Sklodowska, Department of Mathematical Physics, Institute of Physics (Poland); Gozdz, M. [University of Maria Curie-Sklodowska, Department of Complex Systems and Neurodynamics, Institute of Informatics (Poland)

2012-10-15

299

Unification of gauge symmetries in theories with dynamical symmetry breaking

We analyze approaches to the partial or complete unification of gauge symmetries in theories with dynamical symmetry breaking. Several types of models are considered, including those that (i) involve sufficient unification to quantize electric charge, (ii) attempt to unify the three standard-model gauge interactions in a simple Lie group that forms a direct product with an extended technicolor group, and, most ambitiously, (iii) attempt to unify the standard-model gauge interactions with (extended) technicolor in a simple Lie group.

Christensen, Neil D.; Shrock, Robert [C.N. Yang Institute for Theoretical Physics, State University of New York, Stony Brook, New York 11794 (United States)

2005-08-01

300

Peccei-Quinn symmetry from a gauged discrete R symmetry

NASA Astrophysics Data System (ADS)

The axion solution to the strong CP problem calls for an explanation as to why the Lagrangian should be invariant under the global Peccei-Quinn (PQ) symmetry, U(1)PQ, to such a high degree of accuracy. In this paper, we point out that the U(1)PQ can indeed survive as an accidental symmetry in the low-energy effective theory, if the standard model gauge group is supplemented by a gauged and discrete R symmetry, ZNR, forbidding all dangerous operators that explicitly break the Peccei-Quinn symmetry. In contrast to similar approaches, the requirement that the ZNR symmetry be anomaly-free forces us, in general, to extend the supersymmetric standard model by new matter multiplets. Surprisingly, we find a large landscape of viable scenarios that all individually fulfill the current experimental constraints on the QCD vacuum angle as well as on the axion decay constant. In particular, choosing the number of additional multiplets appropriately, the order N of the ZNR symmetry can take any integer value larger than 2. This has interesting consequences with respect to possible solutions of the ? problem, collider searches for vectorlike quarks and axion dark matter.

Harigaya, Keisuke; Ibe, Masahiro; Schmitz, Kai; Yanagida, Tsutomu T.

2013-10-01

301

Calculated phase diagram of doped BaFe2As2 superconductor in a C4-symmetry breaking model

NASA Astrophysics Data System (ADS)

We develop a minimal multiorbital tight-binding model with realistic hopping parameters. The model breaks the symmetry of the tetragonal point group by lowering it from C4 to D2d, which accurately describes the Fermi surface evolution of the electron-doped BaFe2-xCoxAs2 and hole-doped Ba1-yKyFe2As2 compounds. An investigation of the phase diagram with a mean-field t\\text{-}U\\text{-}V Bogoliubov-de Gennes Hamiltonian results in agreement with the experimentally observed electron- and hole-doped phase diagram with only one set of t, U and V parameters. Additionally, the self-consistently calculated superconducting order parameter exhibits s^+/- -wave pairing symmetry with a small d-wave pairing admixture in the entire doping range, which is the subtle result of the weakly broken symmetry and competing interactions in the multiorbital mean-field Hamiltonian.

Tai, Yuan-Yen; Zhu, Jian-Xin; Graf, Matthias J.; Ting, C. S.

2013-09-01

302

The Limits of Custodial Symmetry

NASA Astrophysics Data System (ADS)

We introduce a toy model implementing the proposal of using a custodial symmetry to protect the ZbL bar {b}L coupling from large corrections. This "doublet-extended standard model" adds a weak doublet of fermions (including a heavy partner of the top quark) to the particle content of the standard model in order to implement an O(4) × U(1)X SU(2)L × SU(2)R × PLR × U(1)X symmetry in the top-quark mass generating sector. This symmetry is softly broken to the gauged SU(2)L × U(1)Y electroweak symmetry by a Dirac mass M for the new doublet; adjusting the value of M allows us to explore the range of possibilities between the O(4)-symmetric (M ? 0) and standard-model-like (M ? ?) limits.

Chivukula, R. Sekhar; Foadi, Roshan; Simmons, Elizabeth H.; di Chiara, Stefano

303

Combining Flavour and CP Symmetries

NASA Astrophysics Data System (ADS)

I shortly review the impact of the most recent neutrino oscillation data on our attempts to construct a realistic model for neutrino masses and mixing angles. Models based on anarchy and its variants remain an open possibility, reinforced by the latest experimental findings. Many models based on discrete symmetries no longer work in their simplest realizations. I illustrate several proposals that can rescue discrete symmetries. In particular I discuss the possibility of combining discrete flavour symmetries and CP, and I describe a recently proposed symmetry breaking pattern that allows to predict all mixing parameters, angles and phases, in terms of a single real unknown. I analyze several explicit examples of this construction, providing new realistic mixing patterns.

Feruglio, Ferruccio

2013-07-01

304

Electroweak Symmetry Breaking: With Dynamics

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.

Chivukula, R. Sekhar [Department of Physics and Astronomy, Michigan State University, East Lansing, MI 48824 (United States)

2005-03-22

305

Nucleon- nucleon interaction and symmetries.

National Technical Information Service (NTIS)

With the advent of the possibility to study nucleon-nucleon scattering at medium energies, its extension to investigate fundamental symmetries was recognized early on. It was precisely the introduction of rotational invariance, parity conservation, time r...

W. T. H. Van Oers

1992-01-01

306

Daughters, Conspiracies, and Lorentz Symmetry.

National Technical Information Service (NTIS)

The Freedman-Wang prescription for the introduction of daughter trajectories is generalized to the arbitrary-spin case. The daughter problem is then investigated, within the framework of Lorentz symmetry, and a Regge-type representation for the asymptotic...

K. M. Bitar G. L. Tindle

1968-01-01

307

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.

Larson, E.T.; Eilers, B.; Menon, S.; Reiter, D.; Ortmann, A.; Young, M.J.; Lawrence, C.M.

2009-06-03

308

Anomalies and Discrete Chiral Symmetries

The quantum anomaly that breaks the U(1) axial symmetry of massless multi-flavored QCD leaves behind a discrete flavor-singlet chiral invariance. With massive quarks, this residual symmetry has a close connection with the strong CP-violating parameter theta. One result is that if the lightest quarks are degenerate, then a first order transition will occur when theta passes through pi. The resulting framework helps clarify when the rooting prescription for extrapolating in the number of flavors is valid.

Creutz, M.

2009-09-07

309

Conformal symmetry in quantum finance

NASA Astrophysics Data System (ADS)

The quantum finance symmetries are studied. In order to do this, the one dimensional free non-relativistic particle and its symmetries are revisited and the particle mass is identified as the inverse of square of the volatility. Furthermore, using financial variables, a Schrödinger algebra representation is constructed. In addition, it is shown that the operators of this last representation are not hermitian and not conserved.

Romero, Juan M.; Martínez Miranda, Elio; Lavana, Ulises

2014-05-01

310

Broken Symmetries and Magnetic Dynamos

NASA Technical Reports Server (NTRS)

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.

Shebalin, John V.

2007-01-01

311

Family Symmetry and Neutrino Mixing

The observed quark hierarchies suggest a simple family symmetry. Generalized to leptons through grand-unified quantum numbers, it produces a neutrino mixing matrix with order-1 numu-nutau mixing, and order- lambda3 nue-numu and nue-nutau mixings. The intrafamily hierarchy and observed neutrino mass differences together require this symmetry to be anomalous, suggesting through the Green-Schwarz mechanism a string or M-theory origin for the

John K. Elwood; Nikolaos Irges; Pierre Ramond

1998-01-01

312

Superflavor symmetry for heavy particles

We extend the heavy quark spin and flavor symmetry discussed by Voloshin and Shifman and by Isgur and Wise to systems in which the heavy colored particles have different spins. We discuss in detail the superflavor symmetry between a heavy quark and a heavy color triplet scalar. Research supported in part by the Department of Energy under contract No. DE-ACO381-ER40050.

Howard Georgi; Mark B. Wise

1990-01-01

313

The bending potential energy surfaces of several electronic states of Si3 and its anion have been investigated within C2v point-group symmetry, by using the complete active space SCF method. The investigation is confined to the C2v ? D?h path to elucidate the correlations between linear and bent electronic states. The majority of the singlet and triplet states of Si3 exhibit

Josef Kalcher; Alexander F. Sax

1998-01-01

314

NASA Astrophysics Data System (ADS)

In situ high-pressure x-ray diffraction experiments have been performed on quasicrystalline Ti-Zr-Ni in energy-dispersive mode using synchrotron radiation. Pressures up to 30 GPa were generated using a diamond anvil cell. The bulk modulus of Ti-Zr-Ni was determined to be B0 = 166 GPa+/-13 GPa. Some of the experiments were performed under slightly non-hydrostatic conditions. In these runs, deviations from a standard equation of state could be observed and these are due to additional strains. According to the model of Singh and Kennedy for elastically isotropic solids, these strains are proportional to the non-hydrostatic stress component and indirectly proportional to the shear modulus of the sample. From our measurements, the shear modulus of icosahedral Ti-Zr-Ni was estimated to be µ?7 GPa with a relative error of about 50%. This value is low compared to the shear moduli of icosahedral Al-Cu-Fe, Al-Pd-Mn (for both, µ?65 GPa) and Al-Li-Cu (µ = 38 GPa). The Poisson's ratio of Ti-Zr-Ni was determined to be ? = 0.48+/-0.015. This value is close to the maximum value which is allowed by the laws of thermodynamics, namely ? = 0.5. The Poisson's ratios of common metals (??1/3) and other icosahedral alloys like Al-Cu-Fe (? = 0.19), Al-Pd-Mn (? = 0.28) and Al-Li-Cu (? = 0.25) are much lower.

Ponkratz, U.; Nicula, R.; Jianu, A.; Burkel, E.

2000-09-01

315

Symmetry in polarimetric remote sensing

NASA Technical Reports Server (NTRS)

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.

Nghiem, S. V.; Yueh, S. H.; Kwok, R.

1993-01-01

316

Na9K16TI~25: A New Phase Containing Naked Icosahedral Cluster Fragments Ti99-

The phase Na{sub 9}K{sub 16}Tl{sub 25.25(2)} was synthesized by fusion of the elements in sealed Ta containers followed by quenching and annealing at 250 C. The structure established by single crystal X-ray diffraction means (P6{sub 3}/m, Z = 2, a = 19.376(3) {angstrom}, c = 11.480(2) {angstrom}) features Tl{sub 9}{sup 9-} clusters. These are well separated by cations that bridge between, faces, edges, and vertices of the clusters; sodium appears to be essential in this role. This is the third compound known to contain Tl{sub 9} clusters, but here two of nine sites are partially occupied, which can be interpreted as a 70:30 mixture of Tl{sub 9} and Tl{sub 7} units in the same cavity. This Tl{sub 9} example also displays lower symmetry (C{sub s}) but requires the same 2n skeletal electrons. EHTB electronic structure calculations indicate that the Fermi level intersects a finite densities-of-states (DOS), and only some bonds are optimized at E{sub F}, giving some insight regarding the site of Tl deficiency. Direct geometric relationships are found among Tl{sub 13}, Tl{sub 9}, Tl{sub 7} and Tl{sub 5} clusters through systematic removal of vertices.

Li, Bin; Corbett, John D.

2007-12-05

317

Motor-driven packaging of a dsDNA genome into a preformed protein capsid through a unique portal vertex is essential in the life cycle of a large number of dsDNA viruses. We have used single-particle electron cryomicroscopy to study the multilayer structure of the portal vertex of the bacteriophage T7 procapsid, the recipient of T7 DNA in packaging. A focused asymmetric reconstruction method was developed and applied to selectively resolve neighboring pairs of symmetry-mismatched layers of the portal vertex. However, structural features in all layers of the multilayer portal vertex could not be resolved simultaneously. Our results imply that layers with mismatched symmetries can join together in several different relative orientations, and that orientations at different interfaces assort independently to produce structural isomers, a process that we call combinatorial assembly isomerism. This isomerism explains rotational smearing in previously reported asymmetric reconstructions of the portal vertex of T7 and other bacteriophages. Combinatorial assembly isomerism may represent a new regime of structural biology in which globally varying structures assemble from a common set of components. Our reconstructions collectively validate previously proposed symmetries, compositions, and sequential order of T7 portal vertex layers, resolving in tandem the 5-fold gene product 10 (gp10) shell, 12-fold gp8 portal ring, and an internal core stack consisting of 12-fold gp14 adaptor ring, 8-fold bowl-shaped gp15, and 4-fold gp16 tip. We also found a small tilt of the core stack relative to the icosahedral fivefold axis and propose that this tilt assists DNA spooling without tangling during packaging.

Guo, Fei; Liu, Zheng; Vago, Frank; Ren, Yue; Wu, Weimin; Wright, Elena T.; Serwer, Philip; Jiang, Wen

2013-01-01

318

Exploiting Symmetry In Temporal Logic Model Checking

In practice, finite state concurrent systems often exhibit considerable symmetry. We investigate techniques for reducing the complexity of temporal logic model checking in the presence of symmetry. In particular, we show that symmetry can frequently be used to reduce the size of the state space that must be explored during model checking. In the past, symmetry has been exploited in

Edmund M. Clarke; Thomas Filkorn; Somesh Jha

1993-01-01

319

Exploiting Symmetry in Temporal Logic Model Checking

In practice, finite state concurrent systems often exhibit considerable symmetry. We investigate techniques for reducing the complexity of temporal logic model checking in the presence of symmetry. In particular, we show that symmetry can frequently be used to reduce the size of the state space that must be explored during model checking. In the past, symmetry has been exploited in

Edmund M. Clarke; Somesh Jha; Reinhard Enders; Thomas Filkorn

1996-01-01

320

NASA Astrophysics Data System (ADS)

In this paper the partial symmetry method in the intrinsic nuclear frame is analyzed to obtain physical partial symmetries from the so-called formal symmetries of intrinsic sub-Hamiltonians. Derivation of the physical symmetries is illustrated by an example that shows in a detailed way the symmetry structure of the corresponding energy spectra of the total Hamiltonian.

P?drak, A.; Gó?d?, A.

2014-05-01

321

Exploiting matrix symmetries and physical symmetries in matrix product states and tensor trains

We focus on symmetries related to matrices and vectors appearing in the simulation of quantum many-body systems. Spin Hamiltonians have special matrix-symmetry properties such as persymmetry. Furthermore, the systems may exhibit physical symmetries translating into symmetry properties of the eigenvectors of interest. Both types of symmetry can be exploited in sparse representation formats such as Matrix Product States (MPS) for

Thomas K. Huckle; Konrad Waldherr; Thomas Schulte-Herbrüggen

2012-01-01

322

New building blocks in the 2/1 crystalline approximant of a Bergman-type icosahedral quasicrystal

The refined x-ray crystal structure of the phase Mg27Al10.7(2)Zn47.3(2) (Pa3) establishes it as the new 2/1 Bergman-type approximant of the icosahedral quasicrystal. The primitive cubic lattice consists of condensed triacontahedral and novel prolate rhombohedral (PR) clusters. Each triacontahedron encapsulates the traditional, multiply endohedral Bergman-type clusters, and each PR encapsulates an Al2 dimer. This phase exhibits the same long-range order as recently established for the Tsai-type Sc–Mg–Zn 2/1 approximant crystal, with substantial geometric and atomic distribution differences between the two only in the short range orders. This common feature suggests that Bergman- and Tsai-type quasicrystals may be more similar than earlier conceived. Factors germane to the formation of, and the differences between, Bergman- vs. Tsai-type 1/1 and 2/1 approximate structures are considered, including notably different distributions of the more electropositive elements.

Lin, Qisheng; Corbett, John D.

2006-01-01

323

Background Carboxysomes are polyhedral protein microcompartments found in many autotrophic bacteria; they encapsulate the CO2 fixing enzyme, ribulose-1,5-bisphosphate carboxylase/oxygenase (RubisCO) within a thin protein shell and provide an environment that enhances the catalytic capabilities of the enzyme. Two types of shell protein constituents are common to carboxysomes and related microcompartments of heterotrophic bacteria, and the genes for these proteins are found in a large variety of bacteria. Methodology/Principal Findings We have created a Halothiobacillus neapolitanus knockout mutant that does not produce the two paralogous CsoS4 proteins thought to occupy the vertices of the icosahedral carboxysomes and related microcompartments. Biochemical and ultrastructural analyses indicated that the mutant predominantly forms carboxysomes of normal appearance, in addition to some elongated microcompartments. Despite their normal shape, purified mutant carboxysomes are functionally impaired, although the activities of the encapsulated enzymes are not negatively affected. Conclusions/Significance In the absence of the CsoS4 proteins the carboxysome shell loses its limited permeability to CO2 and is no longer able to provide the catalytic advantage RubisCO derives from microcompartmentalization. This study presents direct evidence that the diffusion barrier property of the carboxysome shell contributes significantly to the biological function of the carboxysome.

Cai, Fei; Menon, Balaraj B.; Cannon, Gordon C.; Curry, Kenneth J.; Shively, Jessup M.; Heinhorst, Sabine

2009-01-01

324

The first morphological evidence of African swine fever virus (ASFV) assembly is the appearance of precursor viral membranes, thought to derive from the endoplasmic reticulum, within the assembly sites. We have shown previously that protein p54, a viral structural integral membrane protein, is essential for the generation of the viral precursor membranes. In this report, we study the role of protein p17, an abundant transmembrane protein localized at the viral internal envelope, in these processes. Using an inducible virus for this protein, we show that p17 is essential for virus viability and that its repression blocks the proteolytic processing of polyproteins pp220 and pp62. Electron microscopy analyses demonstrate that when the infection occurs under restrictive conditions, viral morphogenesis is blocked at an early stage, immediately posterior to the formation of the viral precursor membranes, indicating that protein p17 is required to allow their progression toward icosahedral particles. Thus, the absence of this protein leads to an accumulation of these precursors and to the delocalization of the major components of the capsid and core shell domains. The study of ultrathin serial sections from cells infected with BA71V or the inducible virus under permissive conditions revealed the presence of large helicoidal structures from which immature particles are produced, suggesting that these helicoidal structures represent a previously undetected viral intermediate.

Suarez, Cristina; Gutierrez-Berzal, Javier; Andres, German; Salas, Maria L.; Rodriguez, Javier M.

2010-01-01

325

NASA Astrophysics Data System (ADS)

A novel accurate numerical model for shallow water equations on sphere have been developed by implementing the high order multi-moment constrained finite volume (MCV) method on the icosahedral geodesic grid. High order reconstructions are conducted cell-wisely by making use of the point values as the unknowns distributed within each triangular cell element. The time evolution equations to update the unknowns are derived from a set of constrained conditions for two types of moments, i.e. the point values on the cell boundary edges and the cell-integrated average. The numerical conservation is rigorously guaranteed. In the present model, all unknowns or computational variables are point values and no numerical quadrature is involved, which particularly benefits the computational accuracy and efficiency in handling the spherical geometry, such as coordinate transformation and curved surface. Numerical formulations of third and fourth order accuracy are presented in detail. The proposed numerical model has been validated by widely used benchmark tests and competitive results are obtained. The present numerical framework provides a promising and practical base for further development of atmospheric and oceanic general circulation models.

Ii, Satoshi; Xiao, Feng

2010-03-01

326

Polarization and Symmetry of Electronic Transitions in Long Fluorescence Lifetime Triangulenium Dyes

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.

Thyrhaug, Erling; S?rensen, Thomas Just; Gryczynski, Ignacy; Gryczynski, Zygmunt; Laursen, Bo W.

2013-01-01

327

Aspects of Dynamical Symmetry Breaking

NASA Astrophysics Data System (ADS)

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.

Cohler, Lucien Eugene

328

Symmetries in geometrical optics: theory

NASA Astrophysics Data System (ADS)

A study of light and charged-particle optical systems with inversion, reflection, rotation, translation, and/or glide symmetries is presented. The constraints imposed by the various symmetries on the first-order properties of a lens are investigated. In particular, the mathematical structures of the deflection vectors and the transfer matrices are described for various symmetrical systems. In the course of studying the translation and the glide symmetries, a simple technique for characterizing a general system of N identical components in series (or cascade) is also developed, based on the linear algebra theory of factoring matrices into Jordan canonical forms. Applications of these results are presented in a follow-up paper [J. Opt. Soc. Am. 12, XXXX (1995)]. Copyright (c) 1995 Optical Society of America

Szilagyi, M.; Mui, P. H.

1995-12-01

329

Symmetry analysis of cellular automata

NASA Astrophysics Data System (ADS)

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.

García-Morales, V.

2013-01-01

330

Symmetries of coupled harmonic oscillators

NASA Technical Reports Server (NTRS)

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).

Han, D.; Kim, Y. S.

1993-01-01

331

Symmetry perception for target screening

NASA Astrophysics Data System (ADS)

A shape-based algorithm, designated SPOT, is applied to the output of ARL"s, contrast-like feature based, FLIR anomaly target detector in an effort to improve clutter rejection. The shape-based algorithm uses a spatial symmetry operator that discriminates man-made structures in imagery. The method uses no predetermined templates or filters, which would be range and/or aspect dependent, but rather generates templates on-the-fly from the input data. Results explore the application of one such symmetry operator, and present a comparative analysis of target detection performance, based on ROC curves and detection histograms.

Weber, Bruce A.

2005-05-01

332

Iterates of maps with symmetry

NASA Technical Reports Server (NTRS)

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.

Chossat, Pascal; Golubitsky, Martin

1988-01-01

333

NASA Astrophysics Data System (ADS)

By means of space-group symmetry arguments, we argue that the electronic pairing in iron-based high-temperature superconductors shows a structure which is a linear combination of planar s-wave and d-wave symmetry channels, both preserving the three-dimensional A1g irreducible representation of the corresponding crystal point group. We demonstrate that the s- and d-wave channels are determined by the parity under reflection of the electronic orbitals through the iron planes and by improper rotations around the iron sites. We provide evidence of these general properties by performing accurate quantum Monte Carlo (QMC) ab initio calculations of the pairing function, for a FeSe lattice with tetragonal experimental geometry at ambient pressure. We find that this picture survives even in the FeSe under pressure and at low temperatures, when the tetragonal point-group symmetry is slightly broken. In order to achieve a higher resolution in momentum space we introduce a BCS model that faithfully describes our QMC variational pairing function on the simulated 4x4 FeSe unit cell. This allows us to provide a k-resolved image of the pairing function and show that nonisotropic contributions in the BCS gap function are related to the improper s-wave symmetry. Our theory can rationalize and explain a series of contradictory experimental findings, such as the observation of twofold symmetry in the FeSe superconducting phase, the anomalous drop of Tc with Co impurity in LaFeAsO(1-x)Fx, the s- to d-wave gap transition in BaFe2As2 under K doping, and the nodes appearing in the LiFeAs superconducting gap upon P isovalent substitution.

Casula, M.; Sorella, S.

2013-10-01

334

Concomitant Ordering and Symmetry Lowering

ERIC Educational Resources Information Center

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…

Boo, William O. J.; Mattern, Daniell L.

2008-01-01

335

Superdeformations and fermion dynamical symmetries

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.

Wu, Cheng-Li (Drexel Univ., Philadelphia, PA (USA). Dept. of Physics and Atmospheric Science Tennessee Univ., Knoxville, TN (USA). Dept. of Physics and Astronomy Joint Inst. for Heavy Ion Research, Oak Ridge, TN (USA))

1990-01-01

336

From symmetries to number theory

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.

Tempesta, P., E-mail: p.tempesta@fis.ucm.e [Universidad Complutense, Departamento de Fisica Teorica II, Facultad de Fisicas (Spain)

2009-05-15

337

Entanglement renormalization and gauge symmetry

A lattice gauge theory is described by a redundantly large vector space that is subject to local constraints and can be regarded as the low-energy limit of an extended lattice model with a local symmetry. We propose a numerical coarse-graining scheme to produce low-energy, effective descriptions of lattice models with a local symmetry such that the local symmetry is exactly preserved during coarse-graining. Our approach results in a variational ansatz for the ground state(s) and low-energy excitations of such models and, by extension, of lattice gauge theories. This ansatz incorporates the local symmetry in its structure and exploits it to obtain a significant reduction of computational costs. We test the approach in the context of a Z{sub 2} lattice gauge theory formulated as the low-energy theory of a specific regime of the toric code with a magnetic field, for lattices with up to 16x16 sites (16{sup 2}x2=512 spins) on a torus. We reproduce the well-known ground-state phase diagram of the model, consisting of a deconfined and spin-polarized phases separated by a continuous quantum phase transition, and obtain accurate estimates of energy gaps, ground-state fidelities, Wilson loops, and several other quantities.

Tagliacozzo, L.; Vidal, G. [School of Mathematics and Physics, University of Queensland, QLD 4072 (Australia)

2011-03-15

338

Kohn's theorem and Galilean symmetry

NASA Astrophysics Data System (ADS)

The relation between the separability of a system of charged particles in a uniform magnetic field and Galilean symmetry is revisited using Duval's “Bargmann framework”. If the charge-to-mass ratios of the particles are identical, e/m=? for all particles, then the Bargmann space of the magnetic system is isometric to that of an anisotropic harmonic oscillator. Assuming that the particles interact through a potential which only depends on their relative distances, the system splits into one representing the center of mass plus a decoupled internal part, and can be mapped further into an isolated system using Niederer's transformation. Conversely, the manifest Galilean boost symmetry of the isolated system can be “imported” to the oscillator and to the magnetic systems, respectively, to yield the symmetry used by Gibbons and Pope to prove the separability. For vanishing interaction potential the isolated system is free and our procedure endows all our systems with a hidden Schrödinger symmetry, augmented with independent internal rotations. All these properties follow from the cohomological structure of the Galilei group, as explained by Souriau's “décomposition barycentrique”.

Zhang, P.-M.; Horvathy, P. A.

2011-08-01

339

Platonic Symmetry and Geometric Thinking

ERIC Educational Resources Information Center

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…

Zsombor-Murray, Paul

2007-01-01

340

Turning Students into Symmetry Detectives

ERIC Educational Resources Information Center

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…

Wilders, Richard; VanOyen, Lawrence

2011-01-01

341

CPT symmetry and neutral kaons

We discuss the accuracy of CPT invariance tests in the neutral kaon decays. The possible CPT non-invariance is parametrized by amplitudes of two types: (i) CP violating, but T conserving, and (ii) T violating, but CP conserving. It is shown that the experimental data are consistent with CPT symmetry essentially within two standard deviations. The source of this not quite

V. V. Barmin; V. G. Barylov; I. V. Chuvilo; G. V. Davidenko; V. S. Demidov; A. G. Dolgolenko; A. G. Meshkovsky; L. B. Okun; V. A. Shebanov; M. Baldo-Ceolin; E. Calimani; S. Ciampolillo; F. Mattioli; G. Miari; A. Sconza

1984-01-01

342

Spacetime symmetries and neutral kaons

NASA Astrophysics Data System (ADS)

In this work, CP and CPT violation in the neutral-meson systems is discussed. Emphasis is placed on the neutral kaons. Studies are performed demonstrating the symmetry-violating behavior of neutral mesons in classical analogue systems. Phenomena relevant to spacetime-symmetry breaking as seen in neutral mesons are considered. To demonstrate key features of spacetime-symmetry violations, classical oscillating systems are sought as analogue models for the neutral meson systems, Coupled oscillators with two degrees of freedom are considered. It is shown that some classical systems are insufficient to model spacetime-symmetry breaking in a natural way, No-go results are presented for undamped systems and for systems using two one-dimensional oscillators. A model of a two-dimensional oscillator with rheonomic constraints is given to parallel spontaneous T and CPT violation. Studies are presented of the physical phenomena involving CPT breaking in neutral mesons. CPT violation is investigated within the framework of a standard-model extension. This theoretical model assumes small CPT and Lorentz violation via spontaneous symmetry breaking in an underlying more fundamental theory. This standard-model extension contains a term testable only in neutral-meson systems. Some experimental methods are discussed using decays of unboosted correlated kaons to test the relevant parameter of the CPT-violating model. In the context of the standard-model extension, the CPT-violating phenomenological parameter depends on the momentum of the mesons as well as on sidereal time. Decay-rate asymmetries incorporating these features could test the parameters of the standard-model extension.

Roberts, Agnes

343

Irreducible structure, symmetry and average of Eshelby's tensor fields in isotropic elasticity

NASA Astrophysics Data System (ADS)

The strain field ?(x) in an infinitely large, homogenous, and isotropic elastic medium induced by a uniform eigenstrain ?0 in a domain ? depends linearly upon ?0 : ?ij(x)=Sijkl?(x)?kl0. It has been a long-standing conjecture that the Eshelby's tensor field S?(x) is uniform inside ? if and only if ? is ellipsoidally shaped. Because of the minor index symmetry Sijkl?=Sjikl?=Sijlk?, S? might have a maximum of 36 or nine independent components in three or two dimensions, respectively. In this paper, using the irreducible decomposition of S?, we show that the isotropic part S of S? vanishes outside ? and is uniform inside ? with the same value as the Eshelby's tensor S0 for 3D spherical or 2D circular domains. We further show that the anisotropic part A?=S?-S of S? is characterized by a second- and a fourth-order deviatoric tensors and therefore have at maximum 14 or four independent components as characteristics of ?'s geometry. Remarkably, the above irreducible structure of S? is independent of ?'s geometry (e.g., shape, orientation, connectedness, convexity, boundary smoothness, etc.). Interesting consequences have implication for a number of recently findings that, for example, both the values of S? at the center of a 2D Cn(n?3,n?4)-symmetric or 3D icosahedral ? and the average value of S? over such a ? are equal to S0.

Zheng, Q.-S.; Zhao, Z.-H.; Du, D.-X.

2006-02-01

344

Studies on noble-metal-decorated carbon nanostructures are reported almost on a daily basis, but detailed studies on the nanoscale interactions for well-defined systems are very rare. Here we report a study of reduced graphene oxide (rGOx) homogeneously decorated with palladium (Pd) nanoclusters with well-defined shape and size (2.3 ± 0.3 nm). The rGOx was modified with benzyl mercaptan (BnSH) to improve the interaction with Pd clusters, and N,N-dimethylformamide was used as solvent and capping agent during the decoration process. The resulting Pd nanoparticles anchored to the rGOx-surface exhibit high crystallinity and are fully consistent with six-shell cuboctahedral and icosahedral clusters containing ?600 Pd atoms, where 45% of these are located at the surface. According to X-ray photoelectron spectroscopy analysis, the Pd clusters exhibit an oxidized surface forming a PdOx shell. Given the well-defined experimental system, as verified by electron microscopy data and theoretical simulations, we performed ab initio simulations using 10 functionalized graphenes (with vacancies or pyridine, amine, hydroxyl, carboxyl, or epoxy groups) to understand the adsorption process of BnSH, their further role in the Pd cluster formation, and the electronic properties of the graphene-nanoparticle hybrid system. Both the experimental and theoretical results suggest that Pd clusters interact with functionalized graphene by a sulfur bridge while the remaining Pd surface is oxidized. Our study is of significant importance for all work related to anchoring of nanoparticles on nanocarbon-based supports, which are used in a variety of applications. PMID:24758410

Gracia-Espino, Eduardo; Hu, Guangzhi; Shchukarev, Andrey; Wågberg, Thomas

2014-05-01

345

NASA Astrophysics Data System (ADS)

Fine-grained Al-Cu-Fe-(B) icosahedral poly-quasicrystals (IQCs) as the main materials and fine-grained Al-Pd-Mn IQCs as the supplements, both prepared by powder metallurgy, are uniaxially deformed at various temperatures and strain rates. The systematic study shows the dependences of curves of the true stress versus true strain on several parameters, such as temperature, strain rate and grain size. For Al-Cu-Fe IQCs with grain sizes of about 10-30 ?m, QC-specific intra-granular softening drop appears in the deformation curves at lower temperatures and/or faster strain rates, but disappears in those curves at higher temperatures and/or slower strain rates, which suggests that the inter-granular effects such as grain-boundary sliding should be taken into account to interpret the continuous hardening, similarly to conventional poly-crystals. For Al-Cu-Fe-B IQCs with smaller grain sizes of about 1 ?m and fine-grained Al-Pd-Mn IQCs with grain sizes of about 10 ?m, QC-specific intra-granular softening drop is absent for all the deformation curves at the possible lowest temperature and fastest strain rate. This implies that the smaller the grain size, the more the inter-granular contribution. At the same time, due to the rapid recovery caused by intense diffusion in small-sized grains, the intra-granular quasicrystal lattice reorders rapidly from disordering, which also inhibits the intra-granular softening drop to some extent.

Wang, Jian-Bo; Ma, Jia-Yan; Lu, Lu; Xiong, Dong-Xia; Zhao, Dong-Shan; Wang, Ren-Hui

2007-08-01

346

The realm of Tsai-type (YCd(6)-type) quasicrystals (QCs) and their approximants (ACs) continues to expand to the east in the periodic table. The heavy tetrel Sn is now one of the major components in the new Ca(15.0(5))Au(60.0(4))Sn(25.0(2)) (atom %) icosahedral QC and in the corresponding 1/1 and 2/1 ACs. (The 2/1 AC with Yb is also established.) Single-crystal X-ray diffraction on a 1/1 AC gives the refined formula of Ca(3)Au(14.36(3))Sn(4.38(5)) in space group Im3, a = 15.131(1) Å, whereas a representative 2/1 AC gives Ca(13)Au(47.2(1))Sn(28.1(1)), Pa3 and a = 24.444(1) Å. Both ACs contain five-shell multiply endohedral triacontahedral clusters as the common building blocks, as in the parent structure of YCd(6). The 2/1 AC also contains four Ca(2)-dimer-centered prolate rhombohedra (PRs) in the unit cell. The long-range order between triacontahedra and PRs in the 2/1 AC is the same as those in Bergman-type 2/1 ACs. A TB-LMTO-ASA calculation on an ideal 1/1 AC model reveals a shallow pseudogap in the total densities-of-states data around the Fermi energy, as expected. The depth of the pseudogap is considerably enhanced through interactions between the Ca 3d states and s and p states of Au and Sn. PMID:20939550

Lin, Qisheng; Corbett, John D

2010-11-15

347

Algorithm that Exploits Symmetries in Bifurcation Problems,

National Technical Information Service (NTIS)

Frequently bifurcations in nonlinear eigenvalue problems are due to symmetries in the problem. At bifurcation points the symmetries in the solution are typically reduced on the bifurcating branches. We present an algorithm that by making explicit use of t...

W. Hackbusch K. Witsch

1987-01-01

348

Universal Formulation For Symmetries In Computed Flows

NASA Technical Reports Server (NTRS)

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.

Pao, S. Paul; Abdol-Hamid, Khaled S.

1995-01-01

349

Symmetry theory of the flexomagnetoelectric effect in the Bloch lines

NASA Astrophysics Data System (ADS)

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.

Tanygin, B. M.

2012-05-01

350

Symmetry, broken symmetry, and handedness in bimanual coordination dynamics

The symmetrical dynamics of 1:1 rhythmic bimanual coordination may be specified by an order parameter equation involving the relative phase between rhythmic components, and an interlimb coupling which determines the relative attractiveness of in-phase and anti-phase patterns. Symmetry breaking of these dynamics can occur via the difference in the natural frequencies, ??, of the left and right rhythmic components, or

P. J. Treffner; M. T. Turvey

1996-01-01

351

Structures and relative stabilities of carbon clusters belonging to different families have been investigated for diameters d < or = 5 nm based on an efficient semiempirical molecular dynamics (MD) scheme as well as a density functional theory based simulation. Carbon clusters studied include fullerenes and fullerene-derived structures (e.g., cages and onions), icosahedral structures, bucky-diamond structures, and clusters cut from the bulk diamond with spherical and facetted truncations. The reason for using a semiempirical MD is partly due to the large number of different cases (or carbon allotropes) investigated and partly due to the size of the clusters investigated in this work. The particular flavor of the semiempirical MD scheme is based on a self-consistent and environment-dependent Hamiltonian developed in the framework of linear combination of atomic orbitals. We find that (i) among the families of carbon clusters investigated, fullerene structures have the lowest energy with the relative energy ordering being E(fullerene) < E(onion) < E(icosahedral) < E(bucky-diamond) < E(bulk-truncated), (ii) a crossover between bucky-diamond and icosahedral structures is likely at d approximately 8 nm, (iii) the highest occupied molecular orbital-lowest unoccupied molecular orbital gap as a function of the diameter for the case of fullerenes shows an oscillatory behavior with the gap ranging from 2 eV to 6 meV, and the gap approaching that of gapless graphite for d > 3.5 nm, and (iv) there can be three types of phase transformations depending on the manner of heating and cooling in our simulated annealing studies: (a) a bucky-diamond structure --> an onionlike structure, (b) an onionlike --> a cage structure, and (c) a bucky-diamond --> a cage structure. PMID:19449944

Yu, M; Chaudhuri, I; Leahy, C; Wu, S Y; Jayanthi, C S

2009-05-14

352

Emergent symmetry on black hole horizons

NASA Astrophysics Data System (ADS)

For a stationary and axisymmetric black hole, there is a natural way to split the fields into a probe sector and a background sector. The equations of motion for the probe sector enjoy a significantly enhanced symmetry on the black hole horizon. The extended symmetry is conformal in four dimensions, while in higher dimensions it is much bigger. This puts conformal symmetry at the bottom of the ladder of symmetries that can arise on black hole horizons in generic dimensions.

Mei, Jianwei

2014-03-01

353

Electrical and magnetic property of Al62Cu25.5Fe12.5 icosahedral quasicrystal: Spin-orbit scattering

NASA Astrophysics Data System (ADS)

We report here electrical and magnetic properties of Al62Cu25.5Fe12.5 icosahedral quasicrystal. We have measured the electrical resistivity from 2K to 300K and observed negative temperature coefficient of resistivity above 15K. Below 15K we see a decrease in resistivity showing maxima around 15K. Upon application of a high magnetic field of 5 Tesla the maxima disappears and below 15 K the resistivity rises sharply. Magnetoresistance was measured at various temperatures as a function of applied field and we observe positive magnetoresistance for all temperatures. We have attributed these effects arising due to spin-orbit scattering.

Ray, M. K.; Bagani, K.; Ghosh, B.; Sardar, M.; Banerjee, S.; Srivastava, V. C.; Mukhopadhyay, N. K.

2013-02-01

354

NASA Astrophysics Data System (ADS)

We construct a local structural model for Ni-Zr-Nb glassy alloys, Ni48Zr40Nb24, which contains eight icosahedra of Ni5Zr5Nb3 as the structural units. We fully optimize the 112-atom structures by first principles calculation, and find two characteristic phases in the structures depending on the alignment of the icosahedra: an amorphous phase where the icosahedral structure well remains and a periodic phase corresponding to crystallization where the icosahedra change to fcc-like cuboctahedra. Nb atom-clustering may play a key role in anti-crystallization.

Fujima, Nobuhisa; Hoshino, Toshiharu; Fukuhara, Mikio

2013-08-01

355

Global Bifurcation of Periodic Solutions with Symmetry,

National Technical Information Service (NTIS)

If we are given a dynamic system with some built-in symmetry, should we except periodic motions which somehow reflect this symmetry. And how would periodicity harmonize with symmetry. We are lead from dynamics to topology algebra, singularity theory, nume...

B. Fiedler

1987-01-01

356

Symmetry Breaking for Black-Scholes Equations

NASA Astrophysics Data System (ADS)

Black-Scholes equation is used to model stock option pricing. In this paper, optimal systems with one to four parameters of Lie point symmetries for Black-Scholes equation and its extension are obtained. Their symmetry breaking interaction associated with the optimal systems is also studied. As a result, symmetry reductions and corresponding solutions for the resulting equations are obtained.

Yang, Xuan-Liu; Zhang, Shun-Li; Qu, Chang-Zheng

2007-06-01

357

Superalgebra and fermion-boson symmetry

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.

Miyazawa, Hironari

2010-01-01

358

Determination of approximate symmetries of differential equations

There has been considerable progress in the theory and computer implementation of symbolic computation algorithms to automatically deter- mine and exploit exact symmetries of exact differential equations. Such pro- grams usually apply a finite number of exact differentiations and eliminations to the overdetermined linearized equations for the unknown symmetries (the symmetry defining equations), to complete them to certain involutive or

Joe Bonasia; Francois Lemaire; Greg Reid; Lihong Zhi

359

Lorentz Symmetry Effects Connected with Cosmological Expansion

The possible extension of the laws of physics beyond the Standard Model and into deviations from Lorentz and Poincar'e symmetries leads to a search for observable tests, both local and cosmological. I discuss the consequences for Lorentz symmetry of a hyperbolic cosmological geometry expanding in cosmic time. The high symmetry of the cosmic background radiation suggests that the expanding geometry

Felix T. Smith

2010-01-01

360

General Formalism for the BRST Symmetry

NASA Astrophysics Data System (ADS)

Abstract In this paper we will discuss Faddeev—Popov method for gauge theories with a general form of gauge symmetry in an abstract way. We will then develope a general formalism for dealing with the BRST symmetry. This formalism will make it possible to analyse the BRST symmetry for any theory.

Suhail, Ahmad

2013-04-01

361

Symmetry and TLM method in nonlinear magnetostatics

Exploitation of geometrical symmetry in magnetostatic problems with asymmetry in excitation is generally solved by using a symmetric decomposition technique derived from group theory. However, the nonlinearity makes this method invalid since the material property no longer shares this symmetry. A method that makes the exploitation of symmetry feasible is proposed. It consists of replacing the nonlinear material by a

Jacques Lobry; J. Trecat; C. Broche

1996-01-01

362

Higher-level mechanisms detect facial symmetry

The role of symmetry detection in early visual processing and the sensitivity of biological visual systems to symmetry across a wide range of organisms suggest that symmetry can be detected by low-level visual mechanisms. However, computational and functional considerations suggest that higher-level mechanisms may also play a role in facial symmetry detection. We tested this hypothesis by examining whether symmetry detection is better for faces than comparable patterns, which share low-level properties with faces. Symmetry detection was better for upright faces than for inverted faces (experiment 1) and contrast-reversed faces (experiment 2), implicating high-level mechanisms in facial symmetry detection. In addition, facial symmetry detection was sensitive to spatial scale, unlike low-level symmetry detection mechanisms (experiment 3), and showed greater sensitivity to a 45° deviation from vertical than is found for other aspects of face perception (experiment 4). These results implicate specialized, higher-level mechanisms in the detection of facial symmetry. This specialization may reflect perceptual learning resulting from extensive experience detecting symmetry in faces or evolutionary selection pressures associated with the important role of facial symmetry in mate choice and ‘mind-reading’ or both.

Rhodes, Gillian; Peters, Marianne; Lee, Kieran; Morrone, M. Concetta; Burr, David

2005-01-01

363

Higher-level mechanisms detect facial symmetry.

The role of symmetry detection in early visual processing and the sensitivity of biological visual systems to symmetry across a wide range of organisms suggest that symmetry can be detected by low-level visual mechanisms. However, computational and functional considerations suggest that higher-level mechanisms may also play a role in facial symmetry detection. We tested this hypothesis by examining whether symmetry detection is better for faces than comparable patterns, which share low-level properties with faces. Symmetry detection was better for upright faces than for inverted faces (experiment 1) and contrast-reversed faces (experiment 2), implicating high-level mechanisms in facial symmetry detection. In addition, facial symmetry detection was sensitive to spatial scale, unlike low-level symmetry detection mechanisms (experiment 3), and showed greater sensitivity to a 45 degrees deviation from vertical than is found for other aspects of face perception (experiment 4). These results implicate specialized, higher-level mechanisms in the detection of facial symmetry. This specialization may reflect perceptual learning resulting from extensive experience detecting symmetry in faces or evolutionary selection pressures associated with the important role of facial symmetry in mate choice and 'mind-reading' or both. PMID:16006321

Rhodes, Gillian; Peters, Marianne; Lee, Kieran; Morrone, M Concetta; Burr, David

2005-07-01

364

An Animated Interactive Overview of Molecular Symmetry

NSDL National Science Digital Library

An Animated Interactive Overview of Molecular Symmetry is a series of Web pages designed to help instructors teach molecular symmetry. These pages combine interactive Jmol images and instructional text that allow students to examine and explore the operations and elements that give rise to molecular symmetry.

365

Symmetry Breaking in Neuroevolution: A Technical Report

Artificial Neural Networks (ANN) comprise important symmetry properties, which can influence the performance of Monte Carlo methods in Neuroevolution. The problem of the symmetries is also known as the competing conventions problem or simply as the permutation problem. In the literature, symmetries are mainly addressed in Genetic Algoritm based approaches. However, investigations in this direction based on other Evolutionary Algorithms

Onay Urfalioglu; Orhan Arikan

2011-01-01

366

The title compound is synthesized by direct reaction of the elements at 500 C followed by slow cooling. Na{sub 12}K{sub 38}Tl{sub 48}Au{sub 2} crystallizes hexagonal and is constituted (in terms of oxidation states) as (Na{sup +}){sub 12}(K{sup +}){sub 38}(Tl{sub 7}{sup 7{minus}}){sub 3}(Tl{sub 9}{sup 9{minus}}){sub 3}(Au{sup {minus}}){sub 2}. Both clusters have C{sub 2{nu}} symmetry and can be viewed as fragments of a centered icosahedral Tl{sub 13}. The Tl{sub 7}{sup 7{minus}} cluster is an oblate pentagonal bipyramid with an apex-apex bond distance of 3.39 {angstrom}, and Tl{sub 9}{sup 9{minus}} can be best derived from the centered icosahedron by removal of four adjoining vertexes (or as two fused pentagonal bipyramids). The isolated Au{sup {minus}} is bound in a trigonal antiprism of potassium. The compound is structurally electron-precise (Zintl phase), but it shows characteristics of a very poor metal ({rho}{sub 298} {approximately} 760 {mu}{Omega}(cm)) with a Pauli-like susceptibility of {approximately}1.4 {times} 10{sup {minus}3} emu/mol over 50--300 K after correction for Larmor precession of cluster orbitals. EHMO results for the bonding in Tl{sub 7}{sup 7{minus}} and factors that stabilize this compound are presented and discussed.

Huang, D.P.; Dong, Z.D.; Corbett, J.D. [Ames Lab., IA (United States)] [Ames Lab., IA (United States); [Iowa State Univ., IA (United States). Dept. of Chemistry

1998-11-02

367

Efficient asynchronous distributed symmetry breaking

This paper considers symmetry-breaking in an asynchronousdistributed network. We present and analyzea randomized protocol that constructs a maximalindependent set in O(logn) expected time, and alsoa protocol for the dining philosophers problem thatschedules a job that competes with ffi other jobs in expected O(ffi) time, which is optimal. The best previousalgorithms for dining philosophers achieved onlyO(ffi2). In addition, the new protocols

Baruch Awerbuch; Lenore J. Cowen; Mark A. Smith

1994-01-01

368

Time Dependent Hohlraum Symmetry Control

NASA Astrophysics Data System (ADS)

NIF indirect-drive ICF simulations suggest that excessive time-dependent flux asymmetry excursions can impose irreversible distortions on imploding capsules, leading to reduced compression and loss of ignition. (J.D. Lindl, Phys. Plasmas), (1995)., (S.W. Haan et al.), Phys. Plasmas (1995). Flux asymmetries for the baseline NIF cylindrical hohlraum illuminated by rings of laser beams vary in time principally due to motion of the hot laser illuminated rings of plasma as the hohlraum wall blows inward. NIF ignition hohlraums are designed to provide adequate continuous control for these asymmetries by varying the power ratio between at least two sets of beam rings, a technique demonstrated recently at the Nova facility. A simpler, rudimentary demonstration of time-dependent control of the lowest order flux asymmetry in hohlraums has also been performed at the Omega laser facility, by staggering appropriately pointed beams in time. In this fashion, the asymmetry excursion due to wall motion could be either enhanced or reduced while maintaining time-integrated symmetry. Time-resolved hohlraum asymmetries are inferred in all cases from micron-accuracy measurements of contour distortions in imploding witness capsules and foam balls. The results that distinguish between attempts at enhancing and reducing symmetry swing are in agreement with simulations, and hence demonstrate understanding of time-dependent symmetry control. The results are also well matched by a simple, semi-empirical, time-dependent view factor model incorporating both wall motion and changing hohlraum albedo. The model has also proved useful in gaining insight into time-dependent flux asymmetry behavior in other recent Omega symmetry experiments investigating NIF-like multiple ring illumination schemes.

Landen, O. L.

1998-11-01

369

Chiral symmetry and nucleon structure

Recently it has been realized that significant tests of the validity of QCD are available in low energy experiments (E < 500 MeV) by exploiting the property of (broken) chiral symmetry. This technique has been highly developed in The Goldstone boson sector by the work of Gasser and Leutwyler. Application to the nucleon system is much more difficult and is now being carefully developed.

Holstein, B.R. (Massachusetts Univ., Amherst, MA (United States). Dept. of Physics and Astromony Washington Univ., Seattle, WA (United States). Inst. for Nuclear Theory)

1992-01-01

370

Transformation optics and hidden symmetries

NASA Astrophysics Data System (ADS)

Symmetry plays an important role in physics providing a means of classification and a route to understanding. Here we show that an apparently unsymmetrical structure, in our example an ellipse/spheroid, has a more symmetrical partner with an identical spectrum and through which its electromagnetic properties can be classified and calculated analytically. We use the powerful tool of transformation optics to establish this relationship which has wide application beyond the simple example we give in this paper.

Kraft, Matthias; Pendry, J. B.; Maier, S. A.; Luo, Yu

2014-06-01

371

Geometric Aspects of Mirror Symmetry

The geometric aspects of mirror symmetry are reviewed, with an eye towards\\u000afuture developments. Given a mirror pair (X,Y) of Calabi-Yau threefolds, the\\u000abest-understood mirror statements relate certain small corners of the moduli\\u000aspaces of X and of Y. We will indicate how one might go beyond such statements,\\u000aand relate the moduli spaces more globally. In fact, in the

David R. Morrison

2000-01-01

372

Mirror Symmetry And Quantum Geometry

Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ D-branes wrapped on torus fibers to reproduce the mirror duality itself, realizing the program of Strominger-Yau-Zaslow in a slightly different context. Floer theory

Kentaro Hori

2002-01-01

373

Symmetry analysis of talus bone

Objective The main object of this study was to use a geometric morphometric approach to quantify the left-right symmetry of talus bones. Methods Analysis was carried out using CT scan images of 11 pairs of intact tali. Two important geometric parameters, volume and surface area, were quantified for left and right talus bones. The geometric shape variations between the right and left talus bones were also measured using deviation analysis. Furthermore, location of asymmetry in the geometric shapes were identified. Results Numerical results showed that talus bones are bilaterally symmetrical in nature, and the difference between the surface area of the left and right talus bones was less than 7.5%. Similarly, the difference in the volume of both bones was less than 7.5%. Results of the three-dimensional (3D) deviation analyses demonstrated the mean deviation between left and right talus bones were in the range of -0.74 mm to 0.62 mm. It was observed that in eight of 11 subjects, the deviation in symmetry occurred in regions that are clinically less important during talus surgery. Conclusions We conclude that left and right talus bones of intact human ankle joints show a strong degree of symmetry. The results of this study may have significance with respect to talus surgery, and in investigating traumatic talus injury where the geometric shape of the contralateral talus can be used as control. Cite this article: Bone Joint Res 2014;3:139–45.

Islam, K.; Dobbe, A.; Komeili, A.; Duke, K.; El-Rich, M.; Dhillon, S.; Adeeb, S.; Jomha, N. M.

2014-01-01

374

Symmetries and constant mean curvature surfaces

NASA Astrophysics Data System (ADS)

In this paper, we discuss the Lie symmetries, symmetry algebra and symmetry reductions of the equation which describes constant mean curvature surfaces via the generalized Weierstrass-Enneper formulae. First we point out that the equation admits an infinite-dimensional symmetry Lie algebra. Then using symmetry reductions, we obtain two integrable Hamiltonian systems (one autonomous, the other nonautonomous) with two degrees of freedom. The autonomous one was obtained by Konopelchenko and Taimanov by other means. Our method provides a new approach for construction of constant mean curvature surfaces.

Cao, Xi-Fang; Tian, Chou

2001-04-01

375

Novel symmetries in vector Schwinger model

NASA Astrophysics Data System (ADS)

We derive nilpotent and absolutely anticommuting (anti-)co-BRST symmetry transformations for the bosonized version of (1+1)-dimensional (2D) vector Schwinger model. These symmetry transformations turn out to be the analog of co-exterior derivative of differential geometry as the total gauge-fixing term remains invariant under it. The exterior derivative is realized in terms of the (anti-)BRST symmetry transformations of the theory whereas the bosonic symmetries find their analog in the Laplacian operator. The algebra obeyed by these symmetry transformations turns out to be exactly same as the algebra obeyed by the de Rham cohomological operators of differential geometry.

Gupta, Saurabh

2014-05-01

376

Lie group symmetries and Riemann function of Klein-Gordon-Fock equation with central symmetry

NASA Astrophysics Data System (ADS)

In the present paper Lie symmetry group method is applied to find new exact invariant solutions for Klein-Gordon-Fock equation with central symmetry. The found invariant solutions are important for testing finite-difference computational schemes of various boundary value problems of Klein-Gordon-Fock equation with central symmetry. The classical admitted symmetries of the equation are found. The infinitesimal symmetries of the equation are used to find the Riemann function constructively.

Kochetov, Bogdan A.

2014-06-01

377

Phase diagram of doped BaFe2As2 superconductor under broken C4 symmetry

NASA Astrophysics Data System (ADS)

We developed a minimal multi-orbital tight-binding model with realistic hopping parameters that breaks the symmetry of the point group by lowering it from C4 to D2d. The model accurately describes the Fermi surface evolution of the electron, BaFe2-xCoxAs2, and hole, Ba1-yKyFe2As2, doped compounds. Since in this class of materials the competing superconductivity and co-linear antiferromagnetism rely on the evolution of the Fermi surface with doping, we investigated the phase diagram with a mean-field t-U-V Bogoliubov-de Gennes equation. Our results match the experimental electron-doped phase diagram. Furthermore, the model is in reasonable agreement with the experimental hole-doped part with only one set of t, U and V parameters. The self-consistently calculated superconducting order parameter exhibits s+/-d pairing symmetry in the entire doping range. It is the subtle result of competing interactions in the multi-orbital mean-field Hamiltonian based on the broken C4 symmetry and might be observable in STM and ARPES experiments.

Tai, Yuan-Yen; Zhu, Jian-Xin; Graf, Matthias J.; Ting, C. S.

2013-03-01

378

Generalized CP and ?(96) family symmetry

NASA Astrophysics Data System (ADS)

We perform a comprehensive study of the ?(96) family symmetry combined with the generalized CP symmetry HCP. We investigate the lepton mixing parameters which can be obtained from the original symmetry ?(96)?HCP breaking to different remnant symmetries in the neutrino and charged lepton sectors, namely G? and Gl subgroups in the neutrino and the charged lepton sector, respectively, and the remnant CP symmetries from the breaking of HCP are HCP? and HCPl, respectively, where all cases correspond to a preserved symmetry smaller than the full Klein symmetry, as in the semidirect approach, leading to predictions which depend on a single undetermined real parameter, which may be fitted to the reactor angle for example. We discuss 26 possible cases, including a global ?2 determination of the best fit parameters and the correlations between mixing parameters, in each case.

Ding, Gui-Jun; King, Stephen F.

2014-05-01

379

Symmetry measures of the electron density.

In this communication we define electronic symmetry operation and symmetry group measures, eSOM and eSGM, respectively, develop the basic algorithms to obtain them, and give some examples of the possible applications of these new computational tools. These new symmetry measures based on the electron density have been tested in an analysis of (a) the inversion symmetry for heteronuclear diatomic molecules, for the eclipsed and staggered conformations of ethane and tetrafluoroethane, and for a series of octahedral sulfur halides; (b) the reflection symmetry of three different conformers of tetrafluoroethene; and (c) the loss of C(6) symmetry along the B(2u) distortion mode of benzene and an analysis of rotational symmetry for different six-member ring heterocycles. PMID:20652983

Casanova, David; Alemany, Pere; Alvarez, Santiago

2010-10-01

380

Non-Abelian discrete R symmetries

NASA Astrophysics Data System (ADS)

We discuss non-Abelian discrete R symmetries which might have some conceivable relevance for model building. The focus is on settings with supersymmetry, where the superspace coordinate transforms in a one-dimensional representation of the non-Abelian discrete symmetry group. We derive anomaly constraints for such symmetries and find that novel patterns of Green-Schwarz anomaly cancellation emerge. In addition we show that perfect groups, also in the non- R case, are always anomaly-free. An important property of models with non-Abelian discrete R symmetries is that superpartners come in different representations of the group. We present an example model, based on a symmetry, to discuss generic features of models which unify discrete R symmetries, entailing solutions to the ? and proton decay problems of the MSSM, with non-Abelian discrete flavor symmetries.

Chen, Mu-Chun; Ratz, Michael; Trautner, Andreas

2013-09-01

381

Acidities of closo-1-COOH-1,7-C2B10H11 and Amino Acids Based on Icosahedral Carbaboranes.

Carborane clusters are not found in Nature and are exclusively man-made. In this work we study, both experimentally and computationally, the gas-phase acidity (measured GA = 1325 kJ·mol(-1), computed GA = 1321 kJ·mol(-1)) and liquid-phase acidity (measured pKa = 2.00, computed pKa = 1.88) of the carborane acid closo-1-COOH-1,7-C2B10H11. The experimental gas-phase acidity was determined with electrospray tandem mass spectrometry (ESI/MS), by using the extended Cooks kinetic method (EKM). Given the similar spatial requirements of the title icosahedral cage and benzene and the known importance of aminoacids as a whole, such a study is extended, within an acid-base context, to corresponding ortho, meta, and para amino acids derived from icosahedral carborane cages, 1-COOH-n-NH2-1, n-R with {R = C2B10H10, n = 2, 7, 12}, and from benzene {R = C6H4, n = 2, 3, 4}. A remarkable difference is found between the proportion of neutral versus zwitterion structures in water for glycine and the carborane derived amino acids. PMID:24661082

Dávalos, Juan Z; González, Javier; Ramos, Rocío; Hnyk, Drahomír; Holub, Josef; Santaballa, J Arturo; Canle-L, Moisés; Oliva, Josep M

2014-04-17

382

NASA Astrophysics Data System (ADS)

Problem of the origin of the enhanced paramagnetism of icosahedral phases below room temperature is studied experimentally. Temperature dependences of the magnetic susceptibility (?( T)), Hall constant ( R H( T)), and conductivity (?( T)) of the i phase of a nominal composition of Al63Cu25Fe12 are studied at temperatures of 4.2 400 K in magnetic fields of to 5 T. Temperature-dependent components of these quantities, namely, ? t , ? t , and R t were separated. The temperature-dependent component of the magnetic susceptibility ? t is approximately proportional to T 2. The number of thermally-induced charge carries n t and the ratio ? t / n t are approximately proportional to T 3 and T -1, respectively. Thus, we found two distinctive criteria indicating that temperature-induced changes in the conduction-electron paramagnetism play a substantial role in the magnetic properties of icosahedral phases at low temperatures. Earlier, these changes were considered to be substantial only at temperatures above the Debye temperature.

Prekul, A. F.; Shchegolikhina, N. I.; Shalaeva, E. V.

2008-08-01

383

Orf virus, the prototype parapoxvirus, is responsible for contagious ecthyma in sheep and goats. The central region of the viral genome codes for proteins highly conserved among vertebrate poxviruses and which are frequently essential for viral proliferation. Analysis of the recently published genome sequence of orf virus revealed that among such essential proteins, the protein orfv075 is an orthologue of D13, the rifampin resistance gene product critical for vaccinia virus morphogenesis. Previous studies showed that D13, arranged as “spicules,” is necessary for the formation of vaccinia virus immature virions, a mandatory intermediate in viral maturation. We have determined the three-dimensional structure of recombinant orfv075 at ?25-Å resolution by electron microscopy of two-dimensional crystals. orfv075 organizes as trimers with a tripod-like main body and a propeller-like smaller domain. The molecular envelope of orfv075 shows unexpectedly good agreement to that of a distant homologue, VP54, the major capsid protein of Paramecium bursaria Chlorella virus type 1. Our structural analysis suggests that orfv075 belongs in the double-barreled capsid protein family found in many double-stranded DNA icosahedral viruses and supports the hypothesis that the nonicosahedral poxviruses and the large icosahedral DNA viruses are evolutionarily related.

Hyun, Jae-Kyung; Coulibaly, Fasseli; Turner, Adrian P.; Baker, Edward N.; Mercer, Andrew A.; Mitra, Alok K.

2007-01-01

384

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

Keunen, R; Cathcart, N; Kitaev, V

2014-06-26

385

NASA Astrophysics Data System (ADS)

The roles of deep convection and generated waves in the Tropical Tropopause Layer (TTL) are investigated using a global nonhydrostatic model, the Nonhydrostatic ICosahedral Atmospheric Model (NICAM), which runs on the Earth Simulator with a horizontal spacing of 7 km. The model data, which successfully simulated a Madden-Julian Oscillation (MJO) event for the period between 15 December 2006 and 15 January 2007, are analyzed. The frequency of deep convective clouds that reach the TTL is one of the key diagnostics for dehydration and transport. The present results revealed that the proportion of cumulus clouds that penetrate the lapse-rate tropopause and the bottom boundary of the TTL (defined as the lapse rate minimum) is 0.5% and 20%, respectively, in the region between 5S and 5N. This result is reasonably consistent with atmospheric observations. Deep convective activity that reaches the TTL was observed over southern Africa, the Indian Ocean, the Indonesian maritime continent, the western Pacific, and southern America. Deep convection over the continents was most active during the local evening period. Over the oceans, high clouds reaching the tropopause were seen over the Indian Ocean and the seas around Java, where two tropical cyclones were generated. Prominent diurnal variations in tropopause temperature associated with deep convection occurred over the Indonesian maritime continent. These diurnal variations were superimposed on large, low frequency temperature variations associated with equatorial Kelvin waves generated by the MJO convection. Because of coarse vertical resolution, temperature variation simulated by NICAM are larger than those in the real atmosphere. The two tropical cyclones caused relatively large tropopause temperature variations with a cyclone scale (500 km horizontally). The gravity waves generated by tropical cyclones cause small tropopause temperature variations that extend for 1000 km from the cyclone. We conclude that the Kelvin waves associated with the MJO convection cause the largest amplitude of temperature variations in the TTL and that tropical cyclones and diurnal variations of convective activity have large local impacts on temperature variations in the TTL.

Fujiwara, M.; Kubokawa, H.; Nasuno, T.; Yamamoto, M.; Miura, H.; Satoh, M.

2012-12-01

386

Effective second-order nonlinearity in acentric optical crystals with low symmetry.

We derive explicit expressions in the frame of the optical indicatrix for the second-order effective nonlinearity in biaxial crystals with point groups 2, m, and 1, governing the conversion efficiency in three-wave nonlinear optical interactions. The tabulated expressions for the monoclinic symmetry classes 2 and m are valid for all possible orientations of the optical indicatrix relative to the crystallographic frame and for propagation along an arbitrary direction outside the principal planes. They can be used for direct estimation of the effective nonlinearity in the same frame where the phase-matching loci are calculated. The relevant properties and conventions used for the newly emerging acentric monoclinic crystals belonging to the borate family are summarized and tabulated. The derivations are expected to help establish adherence to uniform nomenclature and conventions for these novel inorganic nonlinear crystals, and to eliminate ambiguity and increasing confusion in the literature and in the industrial specifications. The general expressions for the effective nonlinearity are reduced for triclinic crystals of point group 1 to simplified forms in the principal planes. PMID:16294974

Tzankov, Pancho; Petrov, Valentin

2005-11-10

387

Type II hidden symmetries through weak symmetries for some wave equations

NASA Astrophysics Data System (ADS)

The Type II hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a Lie-point symmetry. In [Gandarias RML. Type-II hidden symmetries through weak symmetries for nonlinear partial differential equations. J Math Anal Appl 2008;348:752-9] it was shown that the provenance of the Type II Lie point hidden symmetries found for differential equations can be explained by considering weak symmetries or conditional symmetries of the original PDE. In this paper we analyze the connection between one of the methods analyzed in [Abraham-Shrauner B, Govinder KS. Provenance of Type II hidden symmetries from nonlinear partial differential equations. J Nonlin Math Phys 2006;13:612-22] and the weak symmetries of some partial differential equations in order to determine the source of these hidden symmetries. We have considered some of the models presented in [Abraham-Shrauner B, Govinder KS. Provenance of Type II hidden symmetries from nonlinear partial differential equations. J Nonlin Math Phys 2006;13:612-22], as well as the linear two-dimensional and three-dimensional wave equations [Abraham-Shrauner B, Govinder KS, Arrigo JA. Type II hidden symmetries of the linear 2D and 3D wave equations. J h Phys A Math Theor 2006;39:5739-47].

Gandarias, M. L.; Bruzón, M. S.

2010-02-01

388

Using the molecular strong-field approximation we consider the effects of molecular symmetry on the ionization of molecules by a strong, linearly polarized laser pulse. Electron angular distributions and total ionization yields are calculated as a function of the relative orientation between the molecule and the laser polarization. Our studies focus on ethylene (C{sub 2}H{sub 4}), benzene (C{sub 6}H{sub 6}), fluorobenzene (C{sub 6}H{sub 5}F), and ortho chlorofluorobenzene (1,2 C{sub 6}H{sub 4}ClF), the molecules representing four different point groups. The results are compared with experiments, when available, and with the molecular tunneling theory appropriately extended to nonlinear polyatomic molecules. Our investigations show that the orientational dependence of ionization yields is primarily determined by the nodal surface structure of the molecular orbitals.

Kjeldsen, Thomas K.; Bisgaard, Christer Z.; Madsen, Lars Bojer; Stapelfeldt, Henrik [Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C (Denmark); Department of Chemistry, University of Aarhus, 8000 Aarhus C (Denmark)

2005-01-01

389

Symmetry of the Adèlic Grassmannian

We give a geometric construction of the $${\\\\mathcal{W}_{1+\\\\infty}}$$ vertex algebra as the infinitesimal form of a factorization structure on an adèlic Grassmannian. This gives a concise interpretation\\u000a of the higher symmetries and Bäcklund-Darboux transformations for the KP hierarchy and its multicomponent extensions in terms\\u000a of a version of “$${\\\\mathcal{W}_{1+\\\\infty}}$$-geometry”: the geometry of $${\\\\mathcal{D}}$$-bundles on smooth curves, or equivalently torsion-free sheaves

David Ben-Zvi; Thomas Nevins

2010-01-01

390

Dynamical symmetries in noncommutative theories

In the present work we study dynamical space-time symmetries in noncommutative relativistic theories by using the minimal canonical extension of the Doplicher, Fredenhagen, and Roberts algebra. Our formalism is constructed in an extended space-time with independent degrees of freedom associated with the object of noncommutativity {theta}{sup {mu}}{sup {nu}}. In this framework we consider theories that are invariant under the Poincare group P or under its extension P{sup '}, when translations in the extra dimensions are permitted. The Noether's formalism adapted to such extended x+{theta} space-time is employed.

Amorim, Ricardo [Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, 21945-970 Rio de Janeiro (Brazil)

2008-11-15

391

We point out that a light scalar field fluctuating around a symmetry-enhanced point can generate large non-Gaussianity in density fluctuations. We name such a particle an 'ungaussiton', a scalar field dominantly produced by the quantum fluctuations, generating sizable non-Gaussianity in the density fluctuations. We derive a consistency relation between the bispectrum and the trispectrum, {tau}{sub NL}{approx}10{sup 3}{center_dot}f{sub NL}{sup 4/3}, which can be extended to arbitrarily high order correlation functions. If such a relation is confirmed by future observations, it will strongly support this mechanism.

Suyama, Teruaki [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277 8582 (Japan)] [Institute for Cosmic Ray Research, University of Tokyo, Kashiwa 277 8582 (Japan); Takahashi, Fuminobu, E-mail: suyama@icrr.u-tokyo.ac.jp, E-mail: fuminobu.takahashi@ipmu.jp [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Chiba 277-8568 (Japan)] [Institute for the Physics and Mathematics of the Universe, University of Tokyo, Chiba 277-8568 (Japan)

2008-09-15

392

NASA Astrophysics Data System (ADS)

An algorithm is proposed to perform the reduction of direct product representations of finite groups and, in particular, to perform the complete symmetry adaption of power representations, which may be used to obtain compact analytical representations of potential energy surfaces following an idea described in Marquardt and Quack [J. Chem. Phys. 109, 10628 (1998)]. The algorithm is general in the sense that it can be applied to any finite group being characterized by its set of irreducible representations. It is automatic in the sense that, in case the reduction yields multiple degenerate irreducible subspaces of the same species, all degenerate irreducible subspaces are obtained with a coherent phase relation. The algorithm is based on the standard reduction rule of traditional representation theory. A symbolic algebra computer program based on MAPLE is presented and applied here to obtain the complete list of symmetry adapted expressions of bond angle coordinates up to the fourth power in all irreducible representations of the C3v and Td point groups.

Marquardt, Roberto; Sagui, Kenneth

393

Superconformal symmetry, NMSSM, and inflation

We identify a particularly simple class of supergravity models describing superconformal coupling of matter to supergravity. In these models, which we call the canonical superconformal supergravity models, the kinetic terms in the Jordan frame are canonical, and the scalar potential is the same as in the global theory. The pure supergravity part of the total action has a local Poincare supersymmetry, whereas the chiral and vector multiplets coupled to supergravity have a larger local superconformal symmetry. The scale-free globally supersymmetric theories, such as the NMSSM with a scale-invariant superpotential, can be naturally embedded into this class of theories. After the supergravity embedding, the Jordan frame scalar potential of such theories remains scale free; it is quartic, it contains no mass terms, no nonrenormalizable terms, no cosmological constant. The local superconformal symmetry can be broken by additional terms, which, in the small field limit, are suppressed by the gravitational coupling. This can be achieved by introducing the nonminimal scalar-curvature coupling, and by taking into account interactions with a hidden sector. In this approach, the smallness of the mass parameters in the NMSSM may be traced back to the original superconformal invariance. This allows one to address the {mu} problem and the cosmological domain wall problem in this model, and to implement chaotic inflation in the NMSSM. We discuss the gravitino problem in the NMSSM inflation, as well as the possibility to obtain a broad class of new versions of chaotic inflation in supergravity.

Ferrara, Sergio [Physics Department, Theory Unit, CERN, CH 1211, Geneva 23 (Switzerland); INFN - Laboratori Nazionali di Frascati, Via Enrico Fermi 40, 00044 Frascati (Italy); Kallosh, Renata; Linde, Andrei; Marrani, Alessio [Department of Physics, Stanford University, Stanford, California 94305 (United States); Van Proeyen, Antoine [Instituut voor Theoretische Fysica, Katholieke Universiteit Leuven, Celestijnenlaan 200D, B-3001 Leuven (Belgium)

2011-01-15

394

Symmetry properties in polarimetric remote sensing

NASA Technical Reports Server (NTRS)

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.

Nghiem, S. V.; Yueh, S. H.; Kwok, R.; Li, F. K.

1992-01-01

395

Icosahedral galloxane clusters.

Hydrolysis of 'tris(aryl or alkyl)gallium(III)' species results in the formation of spheroidal dodecameric galloxane mixed oxide-hydroxide clusters, and shows that the gallium centres and associated residual alkyl/aryl groups are arranged at the polyhedral vertices of pseudo-icosahedra. PMID:17844757

McKinlay, Robert M; Dalgarno, Scott J; Nichols, Peter J; Papadopoulos, Stavroula; Atwood, Jerry L; Raston, Colin L

2007-06-21

396

Restoration of chiral symmetry in excited hadrons

Physics of the low-lying and high-lying hadrons in the light flavor sector is\\u000areviewed. While the low-lying hadrons are strongly affected by the spontaneous\\u000abreaking of chiral symmetry, in the high-lying hadrons the chiral symmetry is\\u000arestored. A manifestation of the chiral symmetry restoration in excited hadrons\\u000ais a persistence of the chiral multiplet structure in both baryon and meson

L. Ya. Glozman

2004-01-01

397

Teaching Space Group Symmetry through Problems

Symmetry in the solid state is often neglected in chemical education. Worked examples of high symmetry structures including NaCl, CaF2, K2SiF6, hexamethylenetetramine, and cubane help the student visualize space group symmetry. The student first determines the number of molecules or formula units per cell from the density and unit-cell dimensions. The numbers of atoms of each element are then compared

George L. Hardgrove Jr.

1997-01-01

398

Tractable Symmetry Breaking Using Restricted Search Trees

We present a new conceptual abstraction in symmetry breaking - the GE-tree. The construction and traversal of a GE-tree breaks all symmetries in any constraint satisfaction or similar prob- lem. We give a polynomial-time algorithm for this construction in the case of CSPs with arbitrary value symmetries. We have implemented this technique, and supply experimental evidence of its practical ef-

Colva M. Roney-dougal; Ian P. Gent; Tom Kelsey; Steve Linton

2004-01-01

399

Symmetry breaking in monoatomic 2-lattices

In this paper we describe all the possibilities for symmetry-breaking transformations in monoatomic 2-lattices (crystal structures with two identical points in their unit translational cell). This is done by establishing the symmetry hierarchies (partial ordering) for the arithmetic classes of symmetry groups of these crystals, shown in Fig. 1. We also study the ‘Ericksen–Pitteri neighbourhoods’ for monoatomic 2-lattices, thus making

Giuseppe Fadda; Giovanni Zanzotto

2001-01-01

400

Discrete gauge symmetry in continuum theories

We point out that local symmetries can masquerade as discrete global symmetries to an observer equipped with only low-energy probes. The existence of the underlying local gauge invariance can, however, result in observable Aharonov-Bohm-type effects. Black holes can therefore carry discrete gauge charges: a form of nonclassical ''hair.'' Neither black-hole evaporation, wormholes, nor anything else can violate discrete gauge symmetries. In supersymmetric unified theories such discrete symmetries can forbid proton-decay amplitudes that might otherwise be catastrophic.

Krauss, L.M.; Wilczek, F.

1989-03-13

401

Functional ferroic heterostructures with tunable integral symmetry.

The relation between symmetry and functionality was pinpointed by Pierre Curie who stated that it is the symmetry breaking that creates physical properties. This fundamental principle is nowadays used for engineering heterostructures whose integral symmetry leads to exotic phenomena such as one-way transparency. For switching devices, however, such symmetry-related functionalities cannot be used because the symmetry in conventional heterostructures is immutable once the material has been synthesized. Here we demonstrate a concept for post-growth symmetry control in PbZr0.2Ti0.8O3 and BiFeO3-based heterostructures. A conducting oxide is sandwiched between two ferroelectric layers, and inversion symmetry is reversibly switched on or off by layer-selective electric-field poling. The generalization of our approach to other materials and symmetries is discussed. We thus establish ferroic trilayer structures as device components with reversibly tunable symmetry and demonstrate their use as light emitters that can be activated and deactivated by applying moderate electric voltages. PMID:24985711

Becher, C; Trassin, M; Lilienblum, M; Nelson, C T; Suresha, S J; Yi, D; Yu, P; Ramesh, R; Fiebig, M; Meier, D

2014-01-01

402

Issues in standard model symmetry breaking

This work discusses the symmetry breaking sector of the SU(2) x U(1) electroweak model. The first two chapters discuss Higgs masses in two simple Higgs models. The author proves low-enery theorems for the symmetry breaking sector: The threshold behavior of gauge-boson scattering is completely determined, whenever the symmetry breaking sector meets certain simple conditions. The author uses these theorems to derive event rates for the superconducting super collider (SSC). The author shows that the SSC may be able to determine whether the interactions of the symmetry breaking sector are strong or weak. 54 refs.

Golden, M.

1988-04-01

403

Evidence for Tetrahedral Symmetry in O16

NASA Astrophysics Data System (ADS)

We derive the rotation-vibration spectrum of a 4? configuration with tetrahedral symmetry Td and show evidence for the occurrence of this symmetry in the low-lying spectrum of O16. All vibrational states with A, E, and F symmetry appear to have been observed as well as the rotational bands with LP=0+, 3-, 4+, 6+ on the A states and part of the rotational bands built on the E, F states. We derive analytic expressions for the form factors and B(EL) values of the ground-state rotational band and show that the measured values support the tetrahedral symmetry of this band.

Bijker, R.; Iachello, F.

2014-04-01

404

To fully exploit the capabilities of fluorescence probes in modern experiments, where advanced instrumentation is used to probe complex environments, other photophysical properties than emission color and emission intensity are monitored. Each dye property can be addressed individually as well as collectively to provide in-depth information unavailable from the standard intensity measurements. Dyes with long emission lifetimes and strongly polarized transitions enable the monitoring of lifetime changes as well as emission polarization (anisotropy). Thus experiments can be designed to follow slow dynamics. The UV and visible electronic transitions of a series of red-emitting dyes based on the triangulenium motif are investigated. We resolve overlapping features in the spectra and assign the orientation of the transition moments to the molecular axes. The result is the complete Jablonski diagram for the UV and visible spectral region. The symmetries of the studied dyes are shown to have a large influence on the optical response, and they are clearly separated into two groups of symmetry by their photophysical properties. The C(2v) symmetric dyes, azadioxatriangulenium (ADOTA(+)) and diazaoxatriangulenium (DAOTA(+)), have high emission anisotropies, fluorescence lifetimes around 20 ns, and fluorescence quantum yields of ?50%. The trioxatriangulenium (TOTA(+)) and triazatriangulenium (TATA(+)) dyes-nominally of D(3h) symmetry-have fluorescence lifetimes around 10 ns lifetimes and fluorescence quantum yields of 10-15%. However, the D(3h) symmetry is shown to be lowered to a point group, where the axes transform uniquely such that the degeneracy of the E' states is lifted. PMID:23391292

Thyrhaug, Erling; Sørensen, Thomas Just; Gryczynski, Ignacy; Gryczynski, Zygmunt; Laursen, Bo W

2013-03-14

405

PREFACE: Symmetries in Science XV

NASA Astrophysics Data System (ADS)

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

Schuch, Dieter; Ramek, Michael

2012-08-01

406

NASA Astrophysics Data System (ADS)

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 (C3v). 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.

Karlsson, K. F.; Dupertuis, M. A.; Oberli, D. Y.; Pelucchi, E.; Rudra, A.; Holtz, P. O.; Kapon, E.

2011-12-01

407

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.

Karlsson, K. F. [Ecole Polytechnique Federale de Lausanne (EPFL), Laboratory of Physics of Nanostructures, CH-1015 Lausanne (Switzerland); Linkoeping University, Department of Physics, Chemistry, and Biology (IFM), Semiconductor Materials, S-58183 Linkoeping (Sweden); Dupertuis, M. A.; Oberli, D. Y.; Pelucchi, E.; Rudra, A.; Kapon, E. [Ecole Polytechnique Federale de Lausanne (EPFL), Laboratory of Physics of Nanostructures, CH-1015 Lausanne (Switzerland); Holtz, P. O. [Linkoeping University, Department of Physics, Chemistry, and Biology (IFM), Semiconductor Materials, S-58183 Linkoeping (Sweden)

2011-12-23

408

Permutation symmetry for theta functions

This paper does for combinations of theta functions most of what Carlson (2004) [1] did for Jacobian elliptic functions. In each case the starting point is the symmetric elliptic integral R{sub F} of the first kind. Its three arguments (formerly squared Jacobian elliptic functions but now squared combinations of theta functions) differ by constants. Symbols designating the constants can often be used to replace 12 equations by three with permutation symmetry (formerly in the letters c, d, n for the Jacobian case but now in the subscripts 2, 3, 4 for theta functions). Such equations include derivatives and differential equations, bisection and duplication relations, addition formulas (apparently new for theta functions), and an example of pseudoaddition formulas.

Carlson, B.C.

2011-01-21

409

Wormhole dynamics in spherical symmetry

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.

Hayward, Sean A. [Center for Astrophysics, Shanghai Normal University, 100 Guilin Road, Shanghai 200234 (China)

2009-06-15

410

Rare Isotopes and Fundamental Symmetries

NASA Astrophysics Data System (ADS)

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.

Brown, B. Alex; Engel, Jonathan; Haxton, Wick; Ramsey-Musolf, Michael; Romalis, Michael; Savard, Guy

2009-01-01

411

We report the results of a {sup 27}Al nuclear magnetic resonance study of icosahedral quasicrystalline Al{sub 70}Re {sub 8.6}Pd{sub 21.4} at temperatures between 0.04 and 300K and in magnetic fields between 1.5 and 7T. At very low temperatures we have found that the temperature dependence of the spin-lattice relaxation rate T{sup {minus}1}{sub 1}(T) shows new and unexpected features which we associate with a gradual real-space localization of the itinerant charge carriers. Above 20K, T{sup {minus}1}{sub 1}(T) contains both a linear- and a cubic-in-{ital T} term, previously observed for other quasicrystals. {copyright} {ital 1997} {ital The American Physical Society}

Gavilano, J.L.; Ambrosini, B.; Vonlanthen, P.; Chernikov, M.A.; Ott, H.R. [Laboratorium fuer Festkoerperphysik, Eidgenoessische Technische Hochschule-Hoenggerberg, CH-8093 Zuerich (Switzerland)] [Laboratorium fuer Festkoerperphysik, Eidgenoessische Technische Hochschule-Hoenggerberg, CH-8093 Zuerich (Switzerland)

1997-10-01

412

A comparison of periodic approximants and their quasicrystalline counterparts offers the opportunity to better understand the structure, physical properties and stabilizing mechanisms of these complex phases. We present a combined experimental and computational study of the lattice dynamics of the icosahedral quasicrystals i-ZnMgSc and i-ZnAgSc and compare these to the lattice dynamics of the cubic 1/1-approximant Zn6Sc. The two phases, quasicrystal and approximant, are built up from the same atomic clusters, which are packed either quasiperiodically or on a body centered cubic lattice, respectively. Using inelastic neutron scattering and atomic scale simulations, we show that the vibrational spectra of these three systems are very similar, however, they contain a clear signature of the increasing structural complexity from approximant to quasicrystal. PMID:24445750

Euchner, H; Yamada, T; Rols, S; Ishimasa, T; Ollivier, J; Schober, H; Mihalkovic, M; de Boissieu, M

2014-02-01

413

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.

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

414

Lumazine synthase catalyzes the penultimate step in the synthesis of riboflavin in plants, fungi, and microorganisms. The enzyme displays two quaternary structures, the pentameric forms in yeast and fungi and the 60-meric icosahedral capsids in plants and bacteria. To elucidate the structural features that might be responsible for differences in assembly, we have determined the crystal structures of lumazine synthase, complexed with the inhibitor 5-nitroso-6-ribitylamino-2,4-pyrimidinedione, from spinach and the fungus Magnaporthe grisea to 3.3 and 3.1 A resolution, respectively. The overall structure of the subunit and the mode of inhibitor binding are very similar in these enzyme species. The core of the subunit consists of a four-stranded parallel beta-sheet sandwiched between two helices on one side and three helices on the other. The packing of the five subunits in the pentameric M. grisea lumazine synthase is very similar to the packing in the pentameric substructures in the icosahedral capsid of the plant enzyme. Two structural features can be correlated to the differences in assembly. In the plant enzyme, the N-terminal beta-strand interacts with the beta-sheet of the adjacent subunit, thus extending the sheet from four to five strands. In fungal lumazine synthase, an insertion of two residues after strand beta1 results in a completely different orientation of this part of the polypeptide chain and this conformational difference prevents proper packing of the subunits at the trimer interface in the icosahedron. In the spinach enzyme, the beta-hairpin connecting helices alpha4 and alpha5 participates in the packing at the trimer interface of the icosahedron. Another insertion of two residues at this position of the polypeptide chain in the fungal enzyme disrupts the hydrogen bonding in the hairpin, and the resulting change in conformation of this loop also interferes with proper intrasubunit contacts at the trimer interface.

Persson, K.; Schneider, G.; Jordan, D. B.; Viitanen, P. V.; Sandalova, T.

1999-01-01

415

Reducing Symmetry in a Combinatorial Design Problem

Abstract: A combinatorial design problem is considered which can be modelled as a constraint satisfactionproblem in several dierent ways. The models all have a large number of symmetries which causediculties when searching for solutions. Dierent approaches to reducing the symmetry are discussed:remodelling the problem; adding constraints to the model at the outset; and adding constraints duringsearch to prevent symmetric assignments

Barbara M. Smith; Hd Dh Huddersfield

2001-01-01

416

Reflections on symmetries at SPIN '94

NASA Astrophysics Data System (ADS)

In my view, the parallel sessions on ``Symmetries'' were amongst the most stimulating sessions of this conference. Speakers reported on experimental tests of Charge Symmetry, Parity, and Time Reversal violation and their theoretical interpretation, spanning a wide range of energy scales and experimental techniques. I hope that this brief summary will whet the reader's appetite to explore the many contributed papers which follow.

Page, S. A.

1995-07-01

417

PREFACE: Symmetries and Integrability of Difference Equations

The notion of integrability was first introduced in the 19th century in the context of classical mechanics with the definition of Liouville integrability for Hamiltonian flows. Since then, several notions of integrability have been introduced for partial and ordinary differential equations. Closely related to integrability theory is the symmetry analysis of nonlinear evolution equations. Symmetry analysis takes advantage of the

Adam Doliwa; Risto Korhonen; Stéphane Lafortune

2007-01-01

418

Symmetry and stability of the geomagnetic field

Computer simulations of the geodynamo reveal a strong inverse correlation between stability and equatorial symmetry of the simulated field. This result is consistent with the paleomagnetically inferred degree of symmetry of Earth's magnetic field during the past 150 Ma, which reversed polarity more frequently when it was more symmetrical. A geodynamo simulation with solid inner core much smaller than it

R. S. Coe; G. A. Glatzmaier

2006-01-01

419

Seitz symbols for crystallographic symmetry operations.

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

Glazer, A Michael; Aroyo, Mois I; Authier, André

2014-05-01

420

Topological symmetry breaking by quantum wormholes

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.

Mignemi, S.; Moss, I. (Department of Physics, University of Newcastle upon Tyne, NE1 7RU (United Kingdom))

1993-10-15

421

NOTE: Circular symmetry in topologically massive gravity

NASA Astrophysics Data System (ADS)

We re-derive, compactly, a topologically massive gravity (TMG) decoupling theorem: source-free TMG separates into its Einstein and Cotton sectors for spaces with a hypersurface-orthogonal Killing vector, here concretely for circular symmetry. We then generalize the theorem to include matter; surprisingly, the single Killing symmetry also forces conformal invariance, requiring the sources to be null.

Deser, S.; Franklin, J.

2010-05-01

422

Large lepton mixings from continuous symmetries

Within the broad context of quark-lepton unification, we investigate the implications of broken continuous family symmetries which result from requiring that in the limit of exact symmetry, the Dirac mass matrices yield hierarchical masses for the quarks and charged leptons, but lead to degenerate light neutrino masses as a consequence of the seesaw mechanism, without requiring hierarchical right-handed neutrino mass

Lisa Everett; Pierre Ramond

2007-01-01

423

Order in the Universe: The Symmetry Principle.

ERIC Educational Resources Information Center

The first two papers in this booklet provide a review of the pervasiveness of symmetry in nature and art, discussing how symmetry can be traced through every domain open to our understanding, from all aspects of nature to the special provinces of man; the checks and balances of government, the concept of equal justice, and the aesthetic ordering…

Foundation for Integrative Education, Inc., New York, NY.

424

Teaching symmetry in the introductory physics curriculum

NASA Astrophysics Data System (ADS)

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, of a week's length, to insert into the curriculum.

Hill, Christopher T.; Lederman, Leon M.

2000-09-01

425

Broken symmetry in the boundary element method

The boundary element method is applied to structures with broken symmetry. A matrix reduction technique allows one to treat separately the symmetric and nonsymmetric parts. The full symmetry of the former is taken into account thanks to group representation theory. Numerical results are given

Jacques Lobry; J. Trecat; C. Broche

1995-01-01

426

Symmetry in critical random Boolean network dynamics

NASA Astrophysics Data System (ADS)

Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be used both to greatly simplify analysis and to characterize different types of dynamics. Symmetry in Boolean networks is found by determining the frequency at which the various Boolean output functions occur. There are classes of functions that consist of Boolean functions that behave similarly. These classes are orbits of the controlling symmetry group. We find that the symmetry that controls the critical random Boolean networks is expressed through the frequency by which output functions are utilized by nodes that remain active on dynamical attractors. This symmetry preserves canalization, a form of network robustness. We compare it to a different symmetry known to control the dynamics of an evolutionary process that allows Boolean networks to organize into a critical state. Our results demonstrate the usefulness and power of using the symmetry of the behavior of the nodes to characterize complex network dynamics, and introduce an alternative approach to the analysis of heterogeneous complex systems.

Hossein, Shabnam; Reichl, Matthew D.; Bassler, Kevin E.

2014-04-01

427

PT-symmetry in honeycomb photonic lattices

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.

Szameit, Alexander; Rechtsman, Mikael C.; Bahat-Treidel, Omri; Segev, Mordechai [Physics Department and Solid State Institute, Technion, 32000 Haifa (Israel)

2011-08-15

428

Gauging hidden symmetries in two dimensions

We initiate the systematic construction of gauged matter-coupled supergravity theories in two dimensions. Subgroups of the affine global symmetry group of toroidally compactified supergravity can be gauged by coupling vector fields with minimal couplings and a particular topological term. The gauge groups typically include hidden symmetries that are not among the target-space isometries of the ungauged theory. The gaugings constructed

Henning Samtleben; Martin Weidner

2007-01-01

429

Broken chiral symmetry on a null plane

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.

Beane, Silas R., E-mail: silas@physics.unh.edu

2013-10-15

430

Symmetry and electron transfer in biomolecules

We present the theory of finite temperature electron transfer between biomolecules with mirror symmetry, such as DNA base pairs. The symmetry requirement alters the coupling between the nuclear coordinates and the electronic degrees of freedom. We show that for this new coupling the classical theory of Garg, Onuchic and Ambegaokar [1] of electron transfer breaks down. We present a modified

Maria R. D'Orsogna; Robijn Bruinsma

2002-01-01

431

Symmetry and Controllability for Quantum Spin Networks

NASA Astrophysics Data System (ADS)

Symmetry is found to be an important tool to study the controllability problems in quantum control. Based on quantum spin networks subject to control of a single node by a local potential (Z-control), we have considered the relation of symmetriy and subspace controllability. Focusing on the single excitation subspace it is shown that for single-node Z-controls external symmetries are characterized by eigenstates of the system Hamiltonian that have zero overlap with the control node, and there are no internal symmetries. For uniformly coupled XXZ chains a characterization of all possible symmetries is derived from Bethe ansatz. Moreover, for uniform Heisenberg and XX chains, basic number theory can be used to prove that the lack of symmetry is equivalent to subspace controllability. On the other hand, symmetries in the Hamiltonian can be classified into two types: the internal and the external symmetries. Based on the external symmetries, we can rigorously prove the subspace controllability in each of the invariant subspaces for both XXZ and XYZ chains, but not for XX or Ising chains. All these results are useful to design the appropriate control strategy when implementing QIP in real physical systems.

Wang, Xiaoting; Schirmer, Sophie; Burgarth, Daniel; Pemberton-Ross, Peter; Jacobs, Kurt

2013-03-01

432

Type-II hidden symmetries through weak symmetries for nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

The Type-II hidden symmetries are extra symmetries in addition to the inherited symmetries of the differential equations when the number of independent and dependent variables is reduced by a Lie point symmetry. In [B. Abraham-Shrauner, K.S. Govinder, Provenance of Type II hidden symmetries from nonlinear partial differential equations, J. Nonlinear Math. Phys. 13 (2006) 612-622] Abraham-Shrauner and Govinder have analyzed the provenance of this kind of symmetries and they developed two methods for determining the source of these hidden symmetries. The Lie point symmetries of a model equation and the two-dimensional Burgers' equation and their descendants were used to identify the hidden symmetries. In this paper we analyze the connection between one of their methods and the weak symmetries of the partial differential equation in order to determine the source of these hidden symmetries. We have considered the same models presented in [B. Abraham-Shrauner, K.S. Govinder, Provenance of Type II hidden symmetries from nonlinear partial differential equations, J. Nonlinear Math. Phys. 13 (2006) 612-622], as well as the W=VV equations of associativity in two-dimensional topological field theory which reduces, in the case of three fields, to a single third order equation of Monge-Ampère type. We have also studied a second order linear partial differential equation in which the number of independent variables cannot be reduced by using Lie symmetries, however when is reduced by using nonclassical symmetries the reduced partial differential equation gains Lie symmetries.

Gandarias, M. L.

2008-12-01

433

Discrete symmetries and models of flavor mixing

NASA Astrophysics Data System (ADS)

Evidences of a discrete symmetry behind the pattern of lepton mixing are analyzed. The program of "symmetry building" is outlined. Generic features and problems of realization of this program in consistent gauge models are formulated. The key issues include the flavor symmetry breaking, connection of mixing and masses, ad hoc prescription of flavor charges, "missing" representations, existence of new particles, possible accidental character of the TBM mixing. Various ways are considered to extend the leptonic symmetries to the quark sector and to reconcile them with Grand Unification. In this connection the quark-lepton complementarity could be a viable alternative to TBM. Observational consequences of the symmetries and future experimental tests of their existence are discussed.

Smirnov, Alexei Yu

2011-12-01

434

Heavy Diquark Symmetry Constraints for Strong Decays

NASA Astrophysics Data System (ADS)

The heavy diquark symmetry (HDS) of doubly heavy baryons (DHBs) provides new insights into the spectroscopy of these hadrons. We derive the consequences of this symmetry for the mass spectra and the decay widths of DHBs. We compare these symmetry constraints to results from a nonrelativistic quark model for the mass spectra and results from the 3P0 model for strong decays. The quark model we implement was not constructed with these symmetries and contains interactions which explicitly break HDS. Nevertheless these symmetries emerge. We argue that the 3P0 model and any other model for strong transitions which employs a spectator assumption explicitly respects HDS. We also explore the possibility of treating the strange quark as a heavy quark and apply these ideas to ?, ?c and ?b baryons.

Eakins, B.; Roberts, W.

2012-10-01

435

NASA Astrophysics Data System (ADS)

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.

Nakamoto, Kazuo; McKinney, Michael A.

2000-06-01

436

Hidden symmetry-breaking picture of symmetry-protected topological order

NASA Astrophysics Data System (ADS)

We generalize the hidden symmetry-breaking picture of symmetry-protected topological (SPT) order developed by Kennedy and Tasaki in the context of the Haldane phase. Our generalization applies to a wide class of SPT phases in one-dimensional spin chains, protected by an on-site representation of a finite Abelian group. This generalization takes the form of a nonlocal unitary map that relates local symmetry-respecting Hamiltonians in an SPT phase to local Hamiltonians in a symmetry-broken phase. Using this unitary, we establish a relation between the two-point correlation functions that characterize fully symmetry-broken phases with the string-order correlation functions that characterize the SPT phases, therefore establishing the perspective in these systems that SPT phases are characterized by hidden symmetry breaking. Our generalization is also applied to systems with continuous symmetries, including SO(2k+1) and SU(k).

Else, Dominic V.; Bartlett, Stephen D.; Doherty, Andrew C.

2013-08-01

437

Symmetries of doubly heavy baryons

NASA Astrophysics Data System (ADS)

For very heavy quarks, the two heavy quarks in a doubly heavy baryon are expected to form a pointlike, heavy diquark in an antitriplet color configuration. In this limit the dynamics of the light degrees of freedom 'factorize' from the dynamics of the heavy diquark system, and a superflavor symmetry emerges which relates the properties of doubly heavy baryons to heavy mesons. The charm quark may not be heavy enough for the cc diquark in a ?cc to be regarded as pointlike. However, there are indications from the results of a nonrelativistic constituent quark model that many of the consequences of factorization emerge even though the model does not assume a quark-diquark structure and the mean separation of the two heavy quarks in the model is not small. We discuss the consequences of factorization for the spectroscopy of doubly heavy baryons and compare these consequences to results from a quark model. We also discuss the possibility of treating the strange quark as a heavy quark and applying these ideas to the ?.

Eakins, Benjamin; Roberts, Winston

2013-10-01

438

Bilateral symmetry across Aphrodite Terra

NASA Technical Reports Server (NTRS)

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.

Crumpler, L. S.; Head, J. W.; Campbell, D. B.

1987-01-01

439

Symmetry and twinning in boltwoodite

The authors give the results of an x-ray diffraction and chemical analysis of boltwoodite from Namibia. Chemical analysis revealed that as well as potassium there was a considerable amount of sodium; thus one may speak of sodium boltwoodite with the molecular ratio K/sub 2/O:Na/sub 2/O = 2 : 1. The potassium and sodium are partly replaced by H/sub 3/O. The idealized formula is (K,Na)/sub 2-x/(H/sub 2/O)/sub x/ x (UO/sub 2/SiO/sub 4/) x H/sub 2/O; the symmetry is monoclinic, the space group being C/sup 2//sub 2h/ = P2/sub 1//m, with a = 6.65 A, b = 7.07 A, c = 7.11 A, ..beta.. = 105/sup 0/30', Z = 2. The acicular crystals are elongated along (010) with a very pronounced cleavage in 001. The cleavage plane is (101). The mineral bears a very marked resemblance to kasolite.

Strunz, H.; Tennyson, C.

1981-11-01

440

Symmetries in fluctuations far from equilibrium

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.

Hurtado, Pablo I.; Perez-Espigares, Carlos; del Pozo, Jesus J.; Garrido, Pedro L.

2011-01-01

441

Dark Matter from Binary Tetrahedral Flavor Symmetry

NASA Astrophysics Data System (ADS)

Binary Tetrahedral Flavor Symmetry, originally developed as a quark family symmetry and later adapted to leptons, has proved both resilient and versatile over the past decade. In 2008 a minimal T' model was developed to accommodate quark and lepton masses and mixings using a family symmetry of (T'xZ2). We examine an expansion of this earlier model using an additional Z2 group that facilitates predictions of WIMP dark matter, the Cabibbo angle, and deviations from Tribimaximal Mixing, while giving hints at the nature of leptogenesis.

Eby, David; Frampton, Paul

2012-03-01

442

Indirect Drive ICF Symmetry Experiments on Omega

NASA Astrophysics Data System (ADS)

We report results of measurements of the symmetry of the soft x-ray drive from cylindrical hohlraum experiments on the OMEGA laser. Techniques used included measuring the symmetry of x-ray self-emission from implosions; x-ray backlighting of implosion targets; and following the shock-compressed boundary in foam-ball surrogate targets. The pointing and timing of 10 (out of 30 used) of Omega's beams was varied, to demonstrate time-dependent control of drive symmetry. We will present experimental details of these experiments.

Turner, R. E.; Landen, O. L.; Amendt, P. A.; Decker, C. D.; Glendinning, S. G.; Hammel, B. A.; Kalantar, D. H.; Seka, W.; Morse, S.; Pien, G.; Murphy, T.; Delamater, N.

1997-11-01

443

Exploring Symmetry to Assist Alzheimer's Disease Diagnosis

NASA Astrophysics Data System (ADS)

Alzheimer's disease (AD) is a progressive neurodegenerative disorder first affecting memory functions and then gradually affecting all cognitive functions with behavioral impairments and eventually causing death. Functional brain imaging as Single-Photon Emission Computed Tomography (SPECT) is commonly used to guide the clinician's diagnosis. The essential left-right symmetry of human brains is shown to play a key role in coding and recognition. In the present work we explore the implications of this symmetry in AD diagnosis, showing that recognition may be enhanced when considering this latent symmetry.

Illán, I. A.; Górriz, J. M.; Ramírez, J.; Salas-Gonzalez, D.; López, M.; Padilla, P.; Chaves, R.; Segovia, F.; Puntonet, C. G.

444

Noether symmetry in f(R) cosmology

NASA Astrophysics Data System (ADS)

The Noether symmetry of a generic f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the resulting form of f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effective equation of state parameter for the corresponding cosmology and show that our model can provide a gravitational alternative to the quintessence.

Vakili, Babak

2008-06-01

445

NSDL National Science Digital Library

This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: Each shape below has a line of symmetry. Draw a line of symmetry for each shape. Not every shape has an line of symmetry. Which of the four shapes belo...

446

Lepton Symmetry and Self-Mass.

National Technical Information Service (NTIS)

The paper considers the symmetry of leptonic weak and electromagnetic interactions unified in a model free of quadratic divergences. Explicit values for intermediate boson masses and coupling constants are obtained from the requirement of finite self-mass...

J. Pestieau P. Roy

1969-01-01

447

Symmetry and the Cosmic Microwave Background

NASA Technical Reports Server (NTRS)

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.

Wollock, Edward J.

2012-01-01

448

Space and time from translation symmetry

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.

Schwarz, A. [Department of Mathematics, University of California-Davis, California 95616-8633 (United States)

2010-01-15

449

Chiral Symmetry Breaking in Finite Quantum Electrodynamics.

National Technical Information Service (NTIS)

The dynamical breakdown of chiral symmetry in a finite Abelian gauge theory using a variational approach for the effective potential for composite operators is discussed. It is shown that, at least in a variational approach, the fermion either remains mas...

J. C. Montero V. Pleitez

1987-01-01

450

First Order Ratio for Mid Symmetry Scale

NASA Astrophysics Data System (ADS)

To see a way it is in far greater symmetry overall we key a toy Omega =1 universe to the maximum integral submultiple least integer ratio where onehalf the maximum (delta rho )/(rho ) wavelength has the value slantfrac {1}{8} asymmetry at onehalf R_s system radius. A tacit transpose scaling basis: X(3) _{1- SCALE 1 to 0} = Y_{1- SYMMETRY 1 to 0} wherein symmetry degenerates exponentially proportional and asymptotic to linear lower scale rectifies the above and another point. It is where the value of symmetry crosses onehalf : 1-(3) surd onehalf R_s. A harmonic expansion is tuned to allow the state to occur and refer on in forming a (Doroshkevich 1970) collapse redshift probability distribution function. The function, in a sense, may act as an age ordinal field where the ratio above can trace through the dimension of trans relativistic perspective in phase-space, discrete time series.

von Gronefeld, P.

1996-12-01

451

Spontaneous chiral symmetry breaking in metamaterials.

Spontaneous chiral symmetry breaking underpins a variety of areas such as subatomic physics and biochemistry, and leads to an impressive range of fundamental phenomena. Here we show that this prominent effect is now available in artificial electromagnetic systems, enabled by the advent of magnetoelastic metamaterials where a mechanical degree of freedom leads to a rich variety of strong nonlinear effects such as bistability and self-oscillations. We report spontaneous symmetry breaking in torsional chiral magnetoelastic structures where two or more meta-molecules with opposite handedness are electromagnetically coupled, modifying the system stability. Importantly, we show that chiral symmetry breaking can be found in the stationary response of the system, and the effect is successfully demonstrated in a microwave pump-probe experiment. Such symmetry breaking can lead to a giant nonlinear polarization change, energy localization and mode splitting, which provides a new possibility for creating an artificial phase transition in metamaterials, analogous to that in ferrimagnetic domains. PMID:25033837

Liu, Mingkai; Powell, David A; Shadrivov, Ilya V; Lapine, Mikhail; Kivshar, Yuri S

2014-01-01

452

Symmetry reduction of quasi-free states

NASA Astrophysics Data System (ADS)

Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is noncompact, the group averaging prescription relies on technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein-Gordon field on Minkowski spacetime by a noncompact subgroup of the Poincaré group consisting of a 1-parameter family of boosts, a 1-parameter family of spatial translations and a set of discrete translations. We show that the symmetry-reduced CCR algebra and vacuum state correspond to that used by each of Berger, Husain, and Pierri for the polarized Gowdy T3 quantum gravity model.

Torre, C. G.

2009-06-01

453

Symmetries and Systematics of Doubly Heavy Hadrons

NASA Astrophysics Data System (ADS)

We discuss the extension of the superflavor symmetry of doubly heavy baryons to states which contain an excited heavy diquark and we examine some of the consequences of this symmetry for the spectra of doubly heavy baryons and heavy mesons. We explore the ramifications of a proposed symmetry that relates heavy diquarks to doubly heavy mesons. We present a method for determining how the excitation energy of a system containing two heavy quarks will scale as one changes the strength of the interactions and the reduced mass of the system. We use this to derive consequences of the heavy diquark-doubly heavy meson symmetry. We compare these consequences to the results of a quark model as well as the experimental data for doubly and singly heavy mesons. We also discuss the possibility of treating the strange quark as a heavy quark and apply the ideas developed here to strange hadrons.

Eakins, B.; Roberts, W.

454

NSDL National Science Digital Library

These 4 activities, part of the Mathematics Developmental Continuum of the State of Victoria, Australia, are intended to introduce young learners to line and rotational symmetry. Supporting documents, materials, and progress indicators are included.

2009-09-24

455

Symmetry reduction by lifting for maps

NASA Astrophysics Data System (ADS)

We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, the existence of a symmetry no longer implies the existence of an invariant. Conversely, a map with an invariant need not have a symmetry. We show that when a symmetry flow has a global Poincaré section there are coordinates in which the map takes a reduced, skew-product form, and hence allows for reduction of dimensionality. We show that the reduction of a volume-preserving map again is volume preserving. Finally we sharpen the Noether theorem for symplectic maps. A number of illustrative examples are discussed and the method is compared with traditional reduction techniques.

Dullin, H. R.; Lomelí, H. E.; Meiss, J. D.

2012-06-01

456

Neutrino mass textures and partial ? -? symmetry

NASA Astrophysics Data System (ADS)

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.

Lashin, E. I.; Chamoun, N.; Hamzaoui, C.; Nasri, S.

2014-05-01

457

Analysis of Symmetry in Chemical Reactions.

National Technical Information Service (NTIS)

The authors investigated the effect of the symmetry of the electronic and nuclear motion in chemical reactions. The analysis focuses on concerted reactions which are defined to be describable by a single transition matrix. The transition matrix for rearra...

T. F. George J. Ross

1971-01-01

458

Compact stars and the symmetry energy

NASA Astrophysics Data System (ADS)

The effect of the symmetry energy on some properties of compact stars which contain strange degrees of freedom is discussed. Both the onset of hyperons or kaon condensation will be considered. The hyperon-meson couplings are chosen according to experimental values of the hyperon nuclear matter potentials and possible uncertainties are considered. It is shown that a softer symmetry energy affects the onset of strangeness, namely neutral (negatively charged) strange particles set on at larger (smaller) densities, and gives rise to a smaller strangeness fraction as a function of density. A softer symmetry energy will possibily give rise to maximum mass configurations with larger masses. Hyperon-meson couplings have a strong effect on the mass of the star. It is shown that, for stars with masses above 1 Msolar, the radius of the star varies linearly with the symmetry energy slope L.

Providência, Constana; Cavagnoli, Rafael; Menezes, Debora P.; Panda, Prafulla K.; Rabhi, Aziz

2013-02-01

459

Dynamical symmetry approach to periodic Hamiltonians

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1,1) and so(2,2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and find that the complementary series plays a central role as well as nonunitary representations. (c) 2000 American Institute of Physics.

Li, Hui [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120 (United States)] [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120 (United States); Kusnezov, Dimitri [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120 (United States)] [Center for Theoretical Physics, Sloane Physics Laboratory, Yale University, New Haven, Connecticut 06520-8120 (United States)

2000-05-01

460

Symmetry breaking of quasihelical stellarator equilibria

A mean-field Ohm's law is used to determine the effects of the bootstrap current on quasihelically symmetric stellarator equilibria. The Ohm's law leads to the conclusion that the effects of the bootstrap current break the quasihelical stellarator symmetry at second order in an inverse aspect ratio expansion of the magnetic field strength. The level of symmetry breaking suggests that good approximations to quasihelical stellarator fusion reactors may not be attainable.

Weening, R.H. (Department of Physics, College of William and Mary, Williamsburg, Virginia 23185 (United States))

1993-04-01